Materials_2018_11_235_doi103390ma11020235_

Materials 2018, 11, 235; doi:10.3390/ma11020235 www.mdpi.com/journal/materials

Article

Influence of Temperature on Corrosion Behavior of 2A02 Al Alloy in Marine Atmospheric Environments Min Cao 1,2, Li Liu 1,2,*, Lei Fan 2, Zhongfen Yu 1,2, Ying Li 2, Emeka E. Oguzie 3 and Fuhui Wang 1,2

1 Corrosion and Protection Division, Shenyang National Laboratory for Material Science, Northeastern University, NO. 3-11, Wenhua Road, Heping District, Shenyang 110819, China; [email protected] (M.C.); [email protected] (Z.Y.); [email protected] (F.W.)

2 Institute of Metal Research, Chinese Academy of Sciences, Wencui Road 62, Shenyang 110016, China; [email protected] (L.F.); [email protected] (Y.L.);

3 Electrochemistry and Materials Science Research Laboratory, Department of Chemistry, Federal University of Technology Owerri, PMB 1526 Owerri, Nigeria; [email protected]

* Correspondence: [email protected]; Tel. /Fax: +86-24-2392-5323

Received: date 25 December 2017; Accepted: 31 January 2018; Published: 3 February 2018

Abstract: The corrosion behavior of 2A02 Al alloy under 4 mg/cm2 NaCl deposition at different temperatures (from 30 to 80 °C) has been studied. This corrosion behavior was researched using mass-gain, scanning electron microscopy-SEM, laser scanning confocal microscopy-LSCM, X-ray photoelectron spectroscopy-XPS and other techniques. The results showed and revealed that the corrosion was maximal at 60 °C after 200 h of exposure. The increase of temperature not only affected the solubility of oxygen gas in the thin film, but also promoted the transport of ions (such as Cl−), and the formation of protective AlO(OH), which further affects the corrosion speed.

Keywords: 2A02 Al alloy; NaCl deposit; marine atmospheric corrosion; temperature

1. Introduction

Atmospheric corrosion results from chemical or physical reactions between a material and the surrounding atmosphere, and is one of the most widely studied topics in the field of corrosion. The corrosion of the Al alloy has been investigated in several studies. However, most of these studies were conducted in a laboratory environment [1–13] due to the rapid results and economic efficiency provided by accelerated tests. It was found that serious marine atmospheric corrosion was caused by the combined action of multifactor conditions (such as sunshine, temperature, and rain) on the metal surface [14]. The marine atmospheric environment is characterized by permanently high temperatures (from sunshine) and relatively high humidity with considerable NaCl precipitation. The corrosion of materials, therefore, is accelerated by the high levels of humidity, temperature, and salinity in the marine atmospheric environment.

Al alloys are extensively employed as structural materials in the fields of transportation, electrical engineering, and aerospace applications [15–17]. For example, 2A02 Al alloy is commonly used as an engine fan blade material for marine serving aircraft and becomes exposed to harsh corrosive conditions in the marine environment when the aircraft is in service. Therefore, it is necessary to determine the corrosion mechanism of the alloy in such environments, and to develop effective corrosion control strategies. One of the unique features that will influence corrosion mechanisms during long-term service is the formation of a deposited salt layer on the surface of the alloy, which aggravates corrosion. This salt layer must, therefore, be taken into consideration in simulating corrosion in marine atmospheric environments.

The atmospheric corrosion behavior of Al alloys in various environments has mainly been investigated through field studies [18–22]. Compared with pure Al, Al alloys with second-phase

Materials 2018, 11, 235 2 of 22

particles exhibit improved mechanical properties but reduced corrosion resistance [23]. Al alloys can undergo different forms of corrosion, such as pitting corrosion [24], intergranular corrosion [25,26], and even exfoliation corrosion [27]. It has been accepted that the corrosion resistance of Al alloys is related to the formation of a passive oxide film, which naturally develops on the alloy surface under normal atmospheric conditions. However, halide ions, especially chloride ions (Cl−) in the marine atmospheric environmental attack and compromise this passive film, resulting in accelerated corrosion [28–30]. Abiola et al. [31] studied the effects of environmental factors on the atmospheric corrosion of metallic materials such as mild steel, and showed that Cl− is the most significant factor to accelerate the corrosion rate. That is, chloride plays a critical role in localized corrosion such as pitting corrosion, intergranular corrosion, and stress corrosion cracking [32,33].

Al alloy corrosion in the marine atmospheric environment is not only affected by the high salt content in the environment, but also by a combination of meteorological and pollution factors [14]. Nishimura et al. [34] found that in such environments, the relative humidity and high salinity are complementary; the higher the humidity, the greater the availability of Cl− to cause corrosion of the Al alloy. It is well recognized that atmospheric corrosion takes place only when the metal is wetted [35]. Wetting time is thus regarded as an important determinant of atmospheric corrosion. Wetting condition is usually generated by vapor condensation. The extent of condensation depends on the water content of the air and the temperature of the metal substrate surface. When the water content reaches the saturation level, water condenses in the form of dew. The critical role played by dew formation in the atmospheric corrosion of metals has been well documented [36].

Of the key determinants of marine atmospheric corrosion (high humidity, high temperature, and high salinity), the effects of different temperatures have been the least systematically investigated. This is despite the fact that the temperature influences the formation of water films on metal surfaces as well as the subsequent electrochemical reactions. High temperatures hinder the formation of water films [34,36], in which case the electrochemical reaction is unlikely to initiate and progress. At the same time, temperature also influences the rates and mechanisms of electrochemical reactions [37–39]. Han and Li [35] observed that the weight gain and maximum pitting depth of LY12 Al in 1 mg/100 cm2 Cl− increased with rising temperature. Sharifi-Asla et al. [37] found that increasing the temperature from 25 to 85 °C led to a decrease in the resistance against localized corrosion of carbon steel in saturated Ca(OH)2 solution containing Cl−. Blucher et al. [40] reported a very strong positive correlation between temperature and the rate of NaCl-induced corrosion in humid air. Additionally, Esmaily et al. [41] reported that the temperature dependence of the atmospheric corrosion of AM50 alloy is attributed to the Al content in the alloy. Several crystalline magnesium hydroxy carbonates formed at 4 and 22 °C, but were absent at −4 °C. This indicates that temperature can remarkably influence the corrosion behavior of Al alloys. It is thus surprising that only a few studies have focused on the effects of different temperatures on corrosion, especially for specialized alloys such as 2A02 Al. This study is, therefore, focused on the influence of different temperatures on the corrosion behavior of 2A02 alloy in marine atmospheric environments.

Some recent studies have investigated long-term atmospheric corrosion of Al alloys. Sun et al. [42–46] investigated the mass loss and degradation of mechanical properties, including pit depth evolution, for AA2024-T4 after 20 years of atmospheric exposure. Such real-time, long-term exposure studies are surely immensely beneficial for our understanding of the mechanisms of corrosion in atmospheric environments. Nonetheless, systematic investigations in accelerated modified marine atmospheric environments significantly shorten the time interval for obtaining useful information to enable the design and implementation of effective corrosion control measures.

Accordingly, in the present study, laboratory-accelerated modified marine atmospheric corrosion experiments were designed. A special device was built to simulate a marine atmospheric environment identical to the actual service environment of an aircraft engine fan blade. The corrosion behavior of the 2A02 Al alloy was studied at different temperatures in this accelerated modified marine atmospheric environment using mass-gain, scanning electron microscopy (SEM), X-ray diffraction (XRD), energy-dispersive X-ray spectroscopy (EDS), laser scanning confocal

Materials 2018, 11, 235 3 of 22

microscopy (LSCM), electron probe X-ray microanalysis (EPMA), and X-ray photoelectron spectroscopy (XPS) techniques. The effect of temperature on the initial corrosion behavior of 2A02 Al alloy in this marine atmospheric environment is discussed based on these experimental results.

2. Experimental Procedures

2.1. Materials Preparation

The test alloy samples were produced from bare 2A02 Al alloy plates (without Al cladding), with the following chemical composition (in wt %): Si: 0.30, Fe: 0.30, Cu: 2.6, Mg: 2.0, Zn: 0.10, Mn: 0.45, Ti: 0.15, Al: 94.1.

The material was cut into coupons with the dimensions 10 mm × 15 mm × 2 mm. Before the experiments, the samples were ground with 800 grit SiC paper, degreased and cleaned with acetone and ethanol in an ultrasonic bath, and then dried in flowing cool air. All the samples (original samples) were weighed and the surface area (S) was measured before the experiments.

2.2. Corrosion Testing

The accelerated modified testing involved deposition of a solid NaCl layer on the surface of 2A02 Al alloy samples (not NaCl spray). The deposited NaCl layer was applied to preheat the sample surfaces by repeatedly brushing with a saturated solution of NaCl in water. The surface density of the deposited NaCl was approximately 4 ± 0.2 mg/cm2 [47,48]. The experimental simulation device, as illustrated in Figure 1, is divided into three parts: a water bath, a glass test container, and a perforated intermediate bulkhead. Temperature control (±0.5 °C) is achieved using the water bath, whereas the temperature in the test glass container is further calibrated by a thermometer. In order to mimic the service temperature of the aircraft engine fan blade, the selected exposure temperatures were 30, 40, 50, 60, 70, and 80 °C.

Figure 1. Schematic of a specially designed experimental device to simulate a modified marine atmospheric environment. It includes a water bath device to control the experimental temperature, a large glass bottle filled with deionized water, a samples holder above the deionized water in the large glass bottle. The bottleneck is small enough to prevent the evaporation of water. The most important feature is that both the sample holder and deionized water are in the temperature-controlled part of the glass bottle, which can maintain the temperature of the samples, and the deionized water is the same, and therefore, the humidity in the glass bottle can be exactly controlled.

Materials 2018, 11, 235 4 of 22

The relative humidity was maintained at 98 ± 2%, which represents an extreme humidity for atmospheric corrosion. The metal surface under this condition can form a stable NaCl solution film of thickness closely related to the environmental humidity and the surface state of the sample, and independent of temperature. The NaCl solution film thickness can be calculated using the mass of NaCl solution (m), surface area (S) and NaCl solution density ( ): ℎ = ∙ (1)

According to our measurements, the thickness of the thin liquid film was 0.21 mm. The mass gain measurements were carried out using an analytical balance with an accuracy of

0.01 mg, and the weighing at each temperature included six parallel samples. Taking the weight gain of the exposed samples and uncorroded samples into account, the actual weight gain was obtained. The corrosion products were chemically removed by pickling in the solution (50 mL H3PO4 + 20 g CrO3 + 1 L H2O) for 5–10 min at 80 °C, after which the samples were rinsed with deionized water [44]. The corrosion morphologies of the exposed samples with and without corrosion products were observed by SEM with EDS (INSPECT F50, FEI, Hillsboro, America) and LSCM (OLS4000, Olympus, Tokyo, Japan). The corrosion products were scraped off from the metallic substrate using a blade and characterized by XRD (X’Pert Pro, Pananlytital, Netherlands). A step-scanning X-ray diffractometer was used, with Cu Kα radiation, in the scanning range 10–90°. Furthermore, the elemental distribution and chemical composition of corrosion products were analyzed by EPMA (EPMA 1610, Shimadzu, Kyoto, Japan) and XPS (ESCALAB250, Thermo Fisher Scientific, Shanghai, China). EPMA equipment was a Shimadzu Model EPMA-1610 electron probe microanalyzer at an accelerated voltage of 15 kV. XPS tested powder samples that were scraped off from the metallic substrate. We chose the Al Kα radiation (1486.6 eV) as a monochromatic X-ray source. The light beam was 500 μm in diameter, with a pass energy of 50 eV. The binding energy of the carbon adsorption energy calibration was 284.6 eV.

3. Results

Longitudinal (L-section), long transverse (T-section), and short transverse (S-section) are the terms conventionally used to label the three directions along the microstructure of 2A02 Al alloy. Figure 2a shows the typical microstructure of 2A02 Al alloy viewed with SEM (in backscattered electron mode), and the three-dimensional stereogram indicates the existence and distribution of constituent particles. The L-Section direction corresponds to the Al plate rolling direction, and the S-Section was the experimental side in this work. Figure 2b shows the S-Section microstructure of 2A02 Al alloy. The additional EDS results of the second phases evidenced: (i) the presence of Al, Mg and Cu elements in most of the particles; (ii) the presence of Al and Cu in the other small pellets and (iii) the presence of Al, Fe, Cu, Mn, and Si elements in some narrow strip particles. The composition of the second phases in 2XXX series Al alloys has been investigated by many researchers [49,50]. The S phase, which consists of Al, Mg, and Cu, is commonly Al2CuMg in 2XXX series Al alloys. The θ (CuAl2) phase consists of Al and Cu, and the AlFeCuMnSi phase consists of Al, Fe, Cu, Mn, and Si. In general, the second phases observed include: the Al-Cu-Mg phase identified as Al2CuMg (S phase), the Al-Cu phase identified as CuAl2 (θ phase), and the AlFeCuMnSi phase, as illustrated in Figure 1b.

Materials 2018, 11, 235 5 of 22

Figure 2. SEM morphologies of a typical microstructure of 2A02 Al alloy. (a) three-dimensional whole stereogram microstructure with S-section, T-section, and L-section; (b) detailed surface morphology of 2A02 Al alloy on S-Section microstructure.

3.1. Corrosion Kinetics

Figure 3A shows the mass gain as a function of exposure time for the corrosion of 2A02 Al alloy exposed under solid NaCl deposit in 98 ± 2% relative humidity at different temperatures. It is found that mass gain continuously increased, with no pronounced restraint in the later stages at 30, 40, 50, and 60 °C. However, for 70 and 80 °C, the mass gain increases with time at the initial stage before 72 h, but exhibits a significant drop after 144 h for 70 °C and 120 h for 80 °C. Furthermore, by comparing the mass gain at different temperatures under the same exposure time, it can be seen that higher temperature can accelerate corrosion rates at the initial stages of corrosion, especially before 72 h. With prolonged exposure, this trend was only sustained at temperatures ≤60 °C, whereas the mass gain at 70 and 80 °C decreased after 72 h. Interestingly, after 200 h, the maximum mass gain was observed at 60 °C. Therefore, the corrosion behavior of this Al alloy under the test conditions manifests two distinguishing time intervals: the early stages of corrosion (1–72 h) and the later stages of corrosion (72–200 h), both of which are indicated by the dash-dot line in Figure 3A. The early stage of all the curves at different temperatures shows a trend of sustained increase in the corrosion rate; however, in the later stage, the curves present a descending trend for 70 and 80 °C.

Figure 3B shows the oxidation weight gain per unit time, that is, the corrosion rate of 2A02 Al alloy at different temperatures and different times. It is found that the corrosion rate of 2A02 Al alloy at other temperatures decreases with time, except for 30 °C. Compared with the corrosion rate at different temperatures under the same time, it is found that the corrosion rate is similar to that in Figure 3A. Corrosion rates of 2A02 Al alloy at 30, 40, 50 and 60 °C increased with the increase of temperature at the same time. For 70 and 80 °C, the corrosion rate is also divided into two stages: in the initial stage (before 72 h), the corrosion rate increases with the increase of temperature, while in the latter stage (after 72 h), the corrosion rate at 80 °C rapidly decreased. In conjunction with the above analysis of Figure 3A,B, we chose the temperatures of 30, 60, and 80 °C to perform further detailed measurements according to the characteristics of the mass gain curves.

Materials 2018, 11, 235 6 of 22

Figure 3. (A) Mass gain versus exposure time for 2A02 Al alloy exposed under 4 ± 0.2 mg/cm2 solid NaCl deposit in 98 ± 2% humidity at (a) 30,(b) 40, (c) 50, (d) 60, (e) 70, and (f) 80 °C; (B) Corrosion rate versus exposure time for 2A02 Al alloy exposed under 4 ± 0.2 mg/cm2 solid NaCl deposit in 98 ± 2% humidity at (a) 30,(b) 40, (c) 50, (d) 60, (e) 70, and (f) 80 °C.

3.2. Morphology and Composition

Figure 4 shows SEM images of the surface morphology of the samples at 30, 60, and 80 °C after corrosion for 72 h. Figure 4a shows that the corrosion products formed at 30 °C covered the entire surface of the sample, which have a clear and wood-shaving shape, as shown in Figure 4b. The EDS results show the corrosion product in region A to be rich in the elements O and Al. Figure 4c shows that the corrosion products formed at 60 °C contain a dark compact inner layer and a loose white outer layer. This white loose outer layer also has shaving-shaped particles, though significantly smaller and more fine-grained than those formed at 30 °C. The EDS results show that there are Al oxides in the outer layer, whereas the inner layer comprised a mixture of Al, Cu, Mg, and O. The morphology of the corrosion products at 80 °C, as shown in Figure 4e, is characterized by a compact layer with tiny particles scattered on its surface. However, the larger magnification image in Figure 4f gives information that the dense layer contains a lot of corrosion defects with high Cl content.

0 24 48 72 96 120 144 168 192 216

0.0

0.5

1.0

1.5

2.0

2.5

(A)

(a) 30oC

(b) 40oC

(d) 60oC

(e) 70oC

(f) 80oC

M as

s g

ai n (

m g

/c m

2 )

Time (h)

(d)

(e)

(c)

(b)

(f)

(a)

0 24 48 72 96 120 144 168 192 216

0.02

0.04

0.06

0.08

0.10

0.12

0.14

0.16

0.18

0.20 (a) 30 oC

(b) 40oC

(d) 60oC

(e) 70oC

(f) 80oC

(d)

(e)

(f)

(a)

C o rr

o si

o n r

at e

(g /(

m 2 *

h ))

Time (h)

(B)

Materials 2018, 11, 235 7 of 22

Figure 4. SEM images of microscopic surface morphology of the samples after corrosion 72 h under 4 ± 0.2 mg/cm2 solid NaCl deposit in 98 ± 2% humidity: (a,b) at 30 °C; (c,d) at 60 °C; and (e,f) at 80 °C. EDS results for A-E locations were also presented.

The surface morphologies of the corrosion scales formed on samples after corrosion at several temperatures for 200 h are shown in Figure 5. Figure 5a shows that the corrosion product formed at 30 °C comprised a dark compact inner corrosion layer and a loose white outer layer. From the enlarged photograph of the loose white outer layer in Figure 5b, wood-shaving shaped Al oxides (region C) with similar morphology to those in Figure 4b can also be found. The EDS result of region A in Figure 5a indicates that the inner layer is rich in the elements O, Al and a little Cu, whereas region B appears as flakey Al oxide containing the residual original salt. For the tests conducted at 60 °C, it can be seen from Figure 6c that the Al oxide film was more complete than that formed at 30 °C, but exhibited obvious crack detachment. The inner products contain O, Al, Mg, and Cu. The areas free of cracks are packed by lump-like-shaped particles, mainly comprising Al and O. For the corrosion scale formed at 80 °C, as shown in Figure 5e, the tiny white particles in the outer layer of Al oxide are evenly dispersed on the surface, whereas the inner compact layer contains Al, O, and Cu.

Materials 2018, 11, 235 8 of 22

Figure 5. SEM images of microscopic surface morphology of the samples after corrosion 200 h under 4 ± 0.2 mg/cm2 solid NaCl deposit in 98 ± 2% humidity: (a,b) at 30 °C; (c,d) at 60 °C; and (e,f) at 80 °C. EDS results for A-G locations were also presented.

In order to get a better understanding of the corrosion behavior of the 2A02 Al alloy, LSCM was used to characterize the substrate surface after removal of the corrosion products. Figure 6 shows the morphologies of 2A02 Al alloy substrates devoid of corrosion products after 72 h of corrosion at 30, 60, and 80 °C. LSCM can provide insights regarding the inner structure and the stereoscopic structure of the 2A02 Al alloy substrate. All the results are obtained under the same test conditions and displayed at the same magnification (the size is 128 μm × 128 μm) for a clear comparison. From the results, it is clear that the 2A02 Al alloy underwent localized corrosion, especially pitting corrosion. The change of color in the LSCM images indicates the pit depths. With the increase in temperature from 30, through 60, to 80 °C, it can be seen that the number of pits increased correspondingly. The pit depth was measured using the software OLS4000, all of which are shown

Materials 2018, 11, 235 9 of 22

in Figure 7. The corrosion pit depths at 30 and 60 °C were rather similar, but became more pronounced at elevated temperatures. Apparently, corrosion pits would develop at all temperatures in the range of 3–80 °C, but pit sizes and depths varied with increasing temperature.

Figure 6. LSCM morphologies of 2A02 Al alloy substrate on removal of corrosion products after corrosion 72 h (a) at 30 °C; (b) at 60 °C; and (c) at 80 °C.

Figure 7. Measured results of corrosion pitting depths of 2A02 Al alloy substrate on removal of corrosion products after corrosion 72 h at 30 °C, 60 °C and 80 °C. This result corresponds to Figure 6 and was obtained from measured results by LSCM using our own software OLS4000.

Figure 8 shows the LSCM morphologies of 2A02 Al alloy substrates without the corrosion product after 200 h at different temperatures. The results show striking deviations from those obtained after 72 h of corrosion. As shown in the results, the number of pits changed in the order: 60 °C < 30 °C < 80 °C. However, the corrosion pit depths in Figure 8 as well as the measured depth data in Figure 9 show that the deepest pits appeared at 60 °C, whereas the average value of pit depth at 30 °C is greater than that at 80 °C. In other words, the value of pit depth changed in the order: 60 °C > 30 °C > 80 °C. Indeed, the change trend of results in Figures 7 and 9 are consistent with those in the mass gain curves shown in Figure 3A.

30 40 50 60 70 80 1

C o

rr o

si o

n p

it ti

ng d

ep th

( μm

)

Temperature (oC)

Materials 2018, 11, 235 10 of 22

Figure 8. LSCM morphologies of 2A02 Al alloy substrate on removal of corrosion products after corrosion for 200 h (a) at 30 °C; (b) at 60 °C; and (c) at 80 °C.

Figure 9. Measured results of corrosion pitting depths of 2A02 Al alloy substrate on removal of corrosion products after corrosion for 200 h at 30 °C, 60 °C and 80 °C. This result corresponds to Figure 8 and was obtained from measured results by LSCM using our own software OLS4000.

Figure 10a shows the XRD patterns of the corrosion products formed on the surface of 2A02 Al alloy after 72 h corrosion at 30, 60, and 80 °C. The thickness of the corrosion scales after exposure at different temperatures, deduced from the mass gain obtained by the analysis in Figure 3, is much larger than the XRD detection depth. Therefore, corrosion products were scratched from the samples and the resulting powders were tested by XRD. According to the ICDD cards, Al(OH)3, AlCl3, and Al2O3 were present on all samples. For the results at 80 °C, two diffraction peaks around 2θ = 14° and 2θ = 49° were detected, which are ascribed to AlO(OH). It is noteworthy that AlO(OH) is only detected on the sample at 80 °C.

Figure 10b shows the XRD patterns of the corrosion products formed on the surface of 2A02 Al alloy after 200 h of corrosion. The corrosion products Al(OH)3, AlCl3, and Al2O3 can be detected on all samples corroded at different temperatures, whereas AlO(OH) was again only detected on samples corroded at 80 °C.

30 40 50 60 70 80

C o

rr o si

o n

p it

ti n g

d ep

th (

μm )

Temperature (oC)

Materials 2018, 11, 235 11 of 22

Figure 10. XRD patterns of the corrosion products formed on the surface of 2A02 Al alloy under 4 ± 0.2 mg/cm2 solid NaCl deposit in 98 ± 2% humidity, at 30 °C, 60 °C, and 80 °C: (a) corrosion for 72 h and (b) corrosion for 200 h.

By comparing the XRD results for samples obtained after 72 and 200 h at 30, 60, and 80 °C, it is clear that Al2O3, Al(OH)3, and AlCl3 formed during both time intervals and at all the temperatures, but AlO(OH) was only detected at 80 °C.

4. Discussion

4.1. Pitting Corrosion of 2A02 Al Alloy in the Accelerated Modified Marine Atmospheric Tests

The corrosion process of 2A02 Al alloy under the thin electrolyte film is subject to the general rule of electrochemical corrosion and also has the characteristics of atmospheric corrosion. The relative humidity was 98 ± 2% in this experiment, and thus a thin water film visible to the naked eye formed on the surface of all samples. The thickness of the thin electrolyte film was very thin, approximately 0.21 mm, which was calculated using Equation (1). In this case, oxygen in the air can diffuse at a high speed through the liquid film to the surface of the metal. Therefore, the overall corrosion process is a couple of reactions: the electrochemical dissolution of the Al alloy and the cathodic reduction of molecular oxygen.

Figure 11a shows the morphology of the 2A02 Al alloy substrate without the corrosion product layer after 200 h of corrosion at 60 °C. From Figure 11, it is clear that the pits formed around the second-phase particles included the Al-Cu-Mg and Al-Cu phases in 2A02 Al alloy, as indicated by the red line. Corrosion mainly takes place on Al substrates around these second phase particles. The differences in chemical potentials between the Al-Cu-Mg and Al-Cu phases and the Al substrate lead to electrochemical reactions on the thin electrolyte film: these second phases function as

10 20 30 40 50 60 70 80 90

80 o C

60 o C

30 o C

In te

n si

ty (

a. u

)

2θ( o )

E D

E C

Α Α

Α Al(OH)3 Β Al C AlO(OH) D Al2O3 E AlCl3

(a)

10 20 30 40 50 60 70 80 90

2θ( o )

E D

C ΑΑ

Α Α

Α Al(OH)3 Β Al C AlO(OH) D Al2O3 E AlCl3

30 o C

60 o C

80 o C

In te

n si

ty (

a. u)

(b)

Materials 2018, 11, 235 12 of 22

cathodes and the Al substrate metal as the anode [46]. The electrochemical reaction accelerates the dissolution of the Al substrate around the Al-Cu-Mg and Al-Cu phases, and pitting corrosion occurs. The areas around the second phases have been found to be common sites for pit nucleation [51]. Figure 11b shows the EPMA maps of the elemental distribution of the cross-section of 2A02 Al alloy under 4 ± 0.2 mg/cm2 solid NaCl deposit in 70% humidity at 60 °C within 200 h. The corrosion occurs along the interface of the second-phase particle, which could be the intergranular corrosion. In this experiment, Mg is exhausted after 200 h of corrosion, as shown by the red circle in Figure 11b, where Mg in the second phase was consumed, leaving only Cu. This implies that the initial corrosion on 2A02 Al alloy should occur at the Al-Cu-Mg phase. Mg initially dissolves in the second phase, and after it is exhausted, the remaining second phase functions as a cathode phase around the dissolving Al. Some studies report that Mg is first corroded in the second phase and in some areas, local dissolution is on the threshold of pit initiation [51]. This is evidence that localized dissolution of the Al substrate initiates around the second-phase particles.

Figure 11. (a) Detailed information of pits on the 2A02 Al alloy substrate by removing of corrosion products after corrosion for 200 h under 4 ± 0.2 mg/cm2 solid NaCl deposit in 98 ± 2% humidity at 60 °C. This picture shows the surface morphology obtained by SEM. It shows that pits formed around the second phases on 2A02 Al alloy include Al-Cu-Mg/Al-Cu phases; (b) EPMA maps of the elemental distribution of the cross-section of 2A02 Al alloy under 4 ± 0.2 mg/cm2 solid NaCl deposit in 70% humidity at 60 °C within 200 h, the detailed information of the area of corrosion around Al-Cu-Mg/Al-Cu phases.

Materials 2018, 11, 235 13 of 22

Therefore, Al-Cu-Mg and Al-Cu act as the cathode in the electrochemical reaction and the following reaction takes place:

O2 + 2H2O + 4e− = 4OH− (2)

The partial anodic reaction occurring at anodic sites (the place around the second phase) during the localized corrosion of Al alloys under the thin electrolyte film is:

Al = Al3+ + 3e− (3)

Thus, as a result of the electrochemical reaction, the concentration of hydroxide ions increases in the localized corrosion sites; therefore, the local pH becomes more alkaline, and the following chemical reaction occurs [50]:

Al3+ + 3OH− = Al(OH)3 (4)

Meanwhile, it has been generally acknowledged that the presence of chloride ions in an environment leads to pitting corrosion of Al alloys. Several mechanisms have been proposed to illustrate the role of chloride ions in the pitting corrosion of passivating metallic materials such as Al alloys [52–54].

The AlCl3 identified in this work provides proof that chloride ions react with cations, such as Al3+, to form chloride-containing compounds. Some mechanisms have been proposed to describe the formation of AlCl3 [55]:

Al(OH)3 + 3Cl− = AlCl3 + 3OH− (5)

Furthermore, according to Equations (1) and (5), the pH at the corrosion sites will become more alkaline. Therefore, we washed the sample and measured the pH of the cleaning solution by an acidometer. The measured pH was approximately 9.21, which is consistent with the expected alkaline value. NaCl is very corrosive in this environment, because Na+ supports the development of high pH in the cathodic areas, resulting in alkaline dissolution of the alumina passive film and rapid general corrosion.

Under some conditions, Al(OH)3 would further transform into Al2O3 and AlO(OH) [56]:

2Al(OH)3 = Al2O3 + 3H2O or Al(OH)3 = AlO(OH) + H2O (6)

AlO(OH) was only found at 80 °C, not 30 °C or 60 °C.

4.2. Effect of Temperature on the Corrosion Behavior of 2A02 Al Alloy in Accelerated Modified Marine Atmospheric Tests

It is well known that high humidity can cause liquid films to form on the surface of samples, and that the higher the humidity, the thicker the thin electrolyte film. The thickness of the thin electrolyte film, in turn, affects the diffusion of oxygen and the concentration of salt in the thin electrolyte film. However, in this 98 ± 2% relative humidity environment, salt can be fully dissolved in the liquid film; this is to ensure the samples have the same film thickness and same NaCl salinity under different temperatures. Then, the temperature is the only variable environmental factor. To get a better understanding of the influence of temperature, we discuss the effects of temperature on 2A02 Al alloy corrosion from the following perspectives.

First, the temperature can influence the diffusion of ions in the thin electrolyte film, and especially the oxygen molecules, which directly react via the cathode reaction in local corrosion. Because of the temperature changes, the oxygen solubility and oxygen diffusivity in the liquid film will change, which directly affect the electrochemical reaction of the cathode, and then affect the corrosion. The solubility coefficient β is affected not only by temperature but also the composition of the solution. The experimental changeable factor is temperature in the test, and others are stable. Therefore, other factors have not been discussed. According to Henry’s Law, the solubility of oxygen in the thin electrolyte film is related to oxygen partial pressure and the thin electrolyte film temperature at the gas-water interface. The higher the temperature, the higher the partial pressure of water vapor, so that the lower the partial pressure of oxygen results in a lower the content of

Materials 2018, 11, 235 14 of 22

dissolved oxygen in water. The oxygen diffusivity C in the thin electrolyte film can be estimated by the Arrhenius law. According to the Arrhenius law, the relationship between the oxygen diffusion coefficient and temperature T is C = K Po2 exp(−β/T). When the oxygen diffusion coefficient is calculated, the oxygen diffusivity C can be obtained. It can be seen that the diffusion coefficient increases with increasing temperature.

The cathodic reaction in Equation (2) is the rate-limiting step of this electrochemical experiment. Therefore, the dissolved oxygen solubility and oxygen diffusivity in the thin electrolyte film can significantly affect the rate of 2A02 Al corrosion. The increase in temperature causes the oxygen diffusion coefficient to increase, and the dissolved oxygen solubility decreases in the thin electrolyte film. Therefore, there is an optimal temperature (in this test it is 60 °C), at which the dissolved oxygen solubility and oxygen diffusivity are moderate, and in turn maximize the corrosion speed of 2A02 Al alloy. The mass-gain changes with temperature are well associated with the trade-off between decreasing dissolved oxygen solubility and the increasing oxygen diffusivity in the thin electrolyte film.

In addition to affecting the diffusion of oxygen in the thin film, the temperature can also affect the diffusion behavior of the metal ions, Cl−, or other electric-charged species in the oxide film, which further affects the corrosion speed. Therefore, this is discussed below.

According to the corrosion kinetics curve of 2A02 Al alloy at different temperatures in Figure 3A, the parabolic law was used to fit the corrosion kinetics curve and then obtain the rate coefficient. The rate coefficient is equal to the diffusion coefficient under this test. Figure 12 shows the trend chart of the relationship between the diffusion coefficient and temperature. The diffusion coefficient increases with increasing temperature. Therefore, a high temperature can promote the diffusion of the metal ions, Cl−, and other electric-charged species. High temperatures can also promote the diffusion of the corrosive Cl− in the thin liquid film to the substrate through the corrosion products, which accelerates the rate of pitting corrosion of Al alloy during the whole corrosion process. Figure 13 shows the EPMA maps of the elemental distribution in the cross-section of 2A02 Al alloy corrosion products after 200 h corrosion at 30, 60, and 80 °C. At 30 °C, there is no obvious aggregation of Cl−. Rather, Cl− dispersed throughout the entire corrosion layer. However, an aggregation of Cl− is then obvious in the inner corrosion layer near the interface between the substrate and corrosion product at 60 and 80 °C. This aggregation is more significant at 80 °C than that at 60 °C. This, once again, proves that Cl− diffuses faster to the substrate with increasing temperature. Another feature of temperature in the electrochemical corrosion is that the number of the surface reactivity points increases with the increase in temperature for the electrochemical reaction on the surface of 2A02 Al alloy. More active spots thus speed up the reactions (2)–(3) and accelerate the corrosion process. Therefore, the number of pits at 80 °C is highest in Figure 8. However, the corrosion rate exhibits a decreasing trend when the temperature is higher than 60 °C (see Figure 4). This phenomenon is unexpected and inconsistent with the above temperature acceleration theory. Possible reasons to explain this slowdown are discussed below.

Materials 2018, 11, 235 15 of 22

Figure 12. Trend chart of the relationship between the diffusion coefficient and temperature.

Figure 13. EPMA maps of the elemental distribution of the cross-section of 2A02 Al alloy after corrosion for 200 h at (a) 30; (b) 60; (c) 80 °C.

Figure 14 shows the cross-sectional morphology of the corrosion product layers formed on 2A02 Al alloy after 200 h of corrosion at several temperatures. It shows that corrosion products have two layers: a loose outer layer and a compact inner layer at all three temperatures. It is interesting that the interface between both layers looks like the original base metal surface. The second phase remained in the compact inner layer of corrosion products, which seemed no longer involved in the corrosion process. The enlarged morphology images of the inner oxide layers formed at the three temperatures showed obvious cracks appearing in the inner layer at 30 °C, and a small number of cracks were found in the inner layer of the corrosion products formed at 60 °C. However, the cracks are almost unseen in the inner layer of the corrosion products formed at 80 °C. This possibly

30 40 50 60 70 80

0.00

0.02

0.04

0.06

0.08

0.10

D if

fu si

o n

co ef

fi ci

en t

(m g

/( cm

3 •h

))

Temperature ( o C)

Materials 2018, 11, 235 16 of 22

suggests that the inner layer of the corrosion products became more and more compact with increasing temperature.

Figure 14. Cross-sectional morphology of the corrosion product layers formed on 2A02 Al alloy after corrosion for 200 h at (a) 30; (b) 60; (c) 80 °C.

Figure 15 shows XRD patterns of the inner oxide layer of the corrosion products formed after 200 h corrosion at the three temperatures (polished samples with SiC paper to remove the outer corrosion layer, and verify it by SEM to observe the sample polished cross-section). It shows that AlO(OH) was only detected at 80 °C. AlO(OH) is thought to be produced by reaction (6), and the Gibbs free energy (ΔG°) vs. temperature of reaction (6) can be calculated from the relative thermodynamic data [57]. Figure 16 shows the calculated ΔG° values for reaction (6) of 2A02 Al alloy at different temperatures. This Gibbs free energy is calculated using the software HSC Chemistry 6.0, which is designed for various kinds of chemical reactions and equilibria calculations. The temperature, molar mass, and reaction (6) are written into the software and the software automatically gives the value of the Gibbs free energy and reaction constant for the reaction (6) at different temperatures. It can be seen from Figure 16 that ∆G° in reaction (6) is negative, and the higher the temperature; the more negative its value. Moreover, according to Kc values at each temperature, the higher the reaction temperature, the larger Kc, and the easier the reaction to form AlO (OH). Clearly, the more negative values of ΔG° and more positive values of Kc at 80 °C can make the reaction (6) more easily achievable. From the calculated ΔG° values of reaction (6), it is clear that the reaction will occur when the temperature is more than 30 °C. The higher ΔG° at 30 and 60 °C means there will be lower amounts of AlO(OH) at these temperatures, thus accounting for the inability to detect AlO(OH) by XRD at 30 and 60 °C. At 80 °C, AlO(OH) is more easily formed, with higher amounts in the inner layer. We have determined that AlO(OH) can penetrate into the pores and cracks in the oxide film on the surface of 2A02 Al alloy through the thin liquid film, and then the colloidal particles close up the pores and cracks, thus slowing down the corrosion rate [58–60]. It is, therefore, clear that the formation of AlO(OH) can close up the inner cracks in the oxide film, thereby preventing further corrosion as observed at 80 °C.

Materials 2018, 11, 235 17 of 22

Figure 15. XRD patterns of the inner corrosion products formed on the surface of 2A02 Al alloy after exposure at different temperatures for 200 h.

Figure 16. The values of reaction Gibbs free energy and formation constants for reaction (6) at different temperatures.

Reactions (1)–(5) describe in detail the corrosion mechanism of 2A02 Al alloy in the simulated marine atmospheric environment. The relative compositions of the corrosion products directly reflect the reaction conditions during the test. Through the analysis of the corrosion products composition and the electrochemical reactions, we know that a protective product AlO(OH) was produced as well as the destructive product AlCl3. It is well known that Cl− plays a key role in the chloride-induced pitting model, and that AlCl3 may be formed according to reaction (5). Therefore, the content of AlCl3 contained in corrosion products in this test reflects the degree of the pitting corrosion. Hence, by comparing the relative content of AlCl3 and AlO(OH) in the corrosion products

10 20 30 40 50 60 70 80 90

In te

n si

ty (

a. u

)

2θ ( o )

CC ΑΑ Α

Α Al(OH)3 Β Al C AlO(OH) D Al2O3 E AlCl3

D C

Α Α

80 o C

60 o C

30 o C

30 40 50 60 70 80 -10

-8

-6

-4

-2

G ib

b s

fr ee

e n er

g y c

h an

g es

( K

J• m

o l-1

)

Temperature (oC)

Al(OH) 3 =AlO(OH)+H

2 O

F o

rm at

io n

c o

n st

an t

(K C )

Materials 2018, 11, 235 18 of 22

of 2A02 Al alloy formed at different temperatures, we can evaluate the relative rates of the corrosion processes.

Figure 17 shows the XPS results of the powder corrosion product of 2A02 Al alloy formed after 200 h of corrosion in the simulated marine atmospheric environment at different temperatures. The corrosion scales were scraped off from the corroded samples of 2A02 Al alloy. The powder samples could subsequently be comprehensively characterized to provide information about the composition of the corrosion layer. Through the XPS-peak-differentiation of Al at different temperatures, we detected the presence of Al2O3, Al(OH)3, and AlCl3 formed at all the temperatures, but AlO(OH) only appeared at 70 and 80 °C. This result is consistent with the XRD analysis. In XPS analysis, all the possible compounds containing Al were deduced from the XPS-peak-differentiation, and the peak area of the possible compound represents its relative content in the corrosion products. However, it should be noted that the relative content of different compounds containing the same element can only be compared in the same sample. In order to give a clearer description about the content of the corrosion products, the intensity curves in the XPS results were processed to be displayed numerically. The compound atomic percentage, which is represented by the XPS-peak-differentiation area percentage, was used to express the content of the corrosion products. The ratio of the AlCl3 peak area to that of the total Al is regarded as the content percentage of AlCl3 in the sample, as shown in Figure 17. The content percentages for other compounds containing Al were similarly obtained. The calculated contents of each compound produced at different temperatures are shown in Table 1.

Figure 17. XPS result of 2A02 Al alloy prepared in the simulated marine atmospheric corrosion environment within 200 h at (a) 30; (b) 40; (c) 50; (d) 60; (e) 70; and (f) 80 °C.

Table 1 The contents of each compound produced at different temperatures (at %).

Contents 30 °C 40 °C 50 °C 60 °C 70 °C 80 °C

0.06 0.09 0.12 0.16 0.14 0.11

0.75 0.56 0.39 0.22 0.35 0.53 0 0 0 0 0.15 0.13 ( ) 0.19 0.35 0.49 0.62 0.36 0.23

80 78 76 74 72 70 68 66 82 80 78 76 74 72 70 68 82 80 78 76 74 72 70 68 66

82 80 78 76 74 72 70 68 66 82 80 78 76 74 72 70 68 6682 80 78 76 74 72 70 68 66

(f)(e)

(c)

(d)

(b)30 o C

AlCl 3

In te

n s it y (

a .u

)

Binding Energy (eV)

(a)

Al(OH) 3

Al 2 O

40 o C

In te

n s it y (

a .u

)

Binding Energy (eV)

Al(OH) 3

Al 2 O

AlCl 3

50 o C

In te

n s it y (

a .u

)

Binding Energy (eV)

Al(OH) 3

Al 2 O

AlCl 3

60 o C

In te

n s it y (

a .u

)

Binding Energy (eV)

Al(OH) 3

Al 2 O

AlCl 3

80 o C

In te

n s it y (

a .u

)

Binding Energy (eV)

Al(OH) 3

Al 2 O

AlCl 3

AlO(OH)

70 o C

In te

n s it y (

a .u

)

Binding Energy (eV)

Al(OH) 3

Al 2 O

AlCl 3

AlO(OH)

Materials 2018, 11, 235 19 of 22

The relative content of AlCl3 in the corrosion products increased with temperature up to 60 °C. As we know that AlCl3 was produced in the process of electrochemical corrosion (Equation (5)), the involvement of Cl− as a reactant in Equation (5) is the precondition for pitting corrosion, so the amount of AlCl3 can be used to evaluate the degree of corrosion. The higher the amount of AlCl3, the more reaction (5) may occur, and the more serious the pitting corrosion. Meanwhile, we know the relatively high corrosivity of AlCl3 is explained by the formation of an acidic surface electrolyte and by the high solubility of aluminum hydroxy chloride [61,9]. Therefore, the presence of AlCl3 can accelerate the corrosion of 2A02 Al alloy. The relative content of Al2O3 in corrosion products decreased at first and then increased with increasing temperature, reaching a minimum at 60 °C. Al2O3 has stable chemical performance, excellent dielectric properties as well as resistance to chemical corrosion. The dense Al2O3 layer thus possesses good corrosion protection properties. The relative content of Al(OH)3 in corrosion products increased at first and then decreased with increasing temperature. The combined XPS results of AlCl3 and Al2O3 clearly show that the corrosion susceptibility of 2A02 Al was highest at 60 °C. AlO(OH) was mainly detected at 70 and 80 °C, and has been shown to penetrate and seal up the pit pores, to form a corrosion-resistant layer [58]. According to cross-sectional morphologies of the corrosion products in Figure 14, we can also see that the corrosion products have a more compact structure at the interface between the corrosion products and base metal.

5. Conclusions

In this study, effect of temperature on corrosion behavior of 2A02 Al alloy in a simulated marine atmospheric environment has been systematically investigated. It is found that high temperatures not only decrease the dissolved oxygen solubility and increase the oxygen diffusivity in the liquid film, but also promote the transport of ions (such as Cl−) and accelerate the formation of Al corrosion products. The formation of AlO(OH) can make the inner layer of the passive film more compact and ultimately hinders further corrosion.

Effect of temperature on the corrosion mechanism is elucidated as follows. At low temperature (<60 °C), the slower Cl− diffusion, low content of AlCl3 and AlO(OH) and high content of Al2O3, make the corrosion rate very low. At high temperature (>60 °C), while the diffusion of Cl is fast, the higher AlO(OH) content causes the inner corrosion layer to be significantly protected, and thus reduces corrosion rate. Therefore, there is a middle temperature, 60 °C, which has quick Cl diffusion and less AlO(OH) content; hence, the corrosion rate of 2A02 Al alloy at this temperature is maximal.

Acknowledgments: This investigation was supported by the National Natural Science Fund of China under the contract No. 51622106, the National Key Basic Research and Development Plan of China under the Contract No. 2014CB643303, and The National Key Research and Development Program of China (2017YFB0702303).

Author Contributions: The tests were carried out by Min Cao, characterization was performed by Li Liu, and the experimental scheme was framed by Fuhui Wang. The manuscript was composed by Min Cao and revised by Li Liu, Zhongfen Yu and Emeka E. Oguzie.

Conflicts of Interest: The authors declare no conflict of interest.

References

1. Wang, Z.Y.; Ma, T.; Han, W.; Yu, G.C. Corrosion behavior on aluminum alloy LY12 in simulated atmospheric corrosion process. Trans. Nonferrous Metal. Soc. 2007, 17, 326–334.

2. Cai, J.P.; Liu, M.; Luo, Z.H.; Tang, Z.H.; Li, B.; Zhang, X.Y.; Lu, F.; Tao, C.H. Study on accelerated tests for aluminum alloy atmospheric corrosion. J. Chin. Soc. Corros. Prot. 2005, 25, 262–266.

3. Wang, B.B.; Wang, Z.Y.; Han, W.; Wang, C.; Ke, W. Effects of magnesium chloride-based multicomponent salts on atmospheric corrosion of aluminum alloy 2024. Trans. Nonferrous Metal. Soc. 2013, 23, 1199–1208.

4. Shi, Y.Y.; Zhang, Z.; Su, J.X.; Cao, F.H.; Zhang, J.Q. Electrochemical noise study on 2024-T3 aluminum alloy corrosion in simulated acid rain under cyclic wet-dry condition. Electrochim. Acta 2006, 51, 4977– 4986.

Materials 2018, 11, 235 20 of 22

5. Astarita, A.; Bitondo, C.; Squillace, A.; Armentani, E.; Bellucci, F. Stress corrosion cracking behaviour of conventional and innovative aluminium alloys for aeronautic applications. Surf. Interface Anal. 2013, 45, 1610–1618.

6. Zheng, Q.F.; Sun, S.Q.; Wen, J.G.; Li, D.F. Effects of the soluble salts in desert dust on atmospheric corrosion of aluminium. J. Chin. Soc. Corros. Prot. 2010, 30, 72–77.

7. Liu, M.; Cai, J.P.; Zhang, X.Y.; Lu, F. Study on simulative and accelerated tests of 2A12 aluminum alloy marine corrosion. J. Mater. Eng. 2010, z1, 348–351, 376.

8. Cheng, Y.L.; Zhang, Z.; Cao, F.H.; Li, J.F.; Zhang, J.Q.; Wang, J.M.; Cao, C.N. A study of the corrosion of aluminum alloy 2024-T3 under thin electrolyte layers. Corros. Sci. 2004, 46, 1649–1667.

9. Blucher, D.B.; Svensson, J.E.; Johansson, L.G. The influence of CO2, AlCl3·6H2O, MgCl2·6H2O, Na2SO4 and NaCl on the atmospheric corrosion of aluminium. Corros. Sci. 2006, 48, 1848–1866.

10. Cheng, Y.L.; Cao, F.H.; Zhang, Z.; Zhang, J.Q.; Wang, J.M.; Cao, C.N. Electrochemical noises of LC4, LY12 and pure Al in NaCl solution. Acta Metall. Sin. 2002, 38, 74–78.

11. Moutarlier, V.; Gigandet, M.P.; Normand, B.; Pagetti, J. EIS characterisation of anodic films formed on 2024 aluminium alloy, in sulphuric acid containing molybdate or permanganate species. Corros. Sci. 2005, 47, 937–951.

12. Dan, Z.; Muto, I.; Hara, N. Effects of environmental factors on atmospheric corrosion of aluminium and its alloy under constant dew point conditions. Corros. Sci. 2012, 57, 22–29.

13. Wang, B.B.; Wang, Z.Y.; Wang, C.; Han, W.; Ke, W. Corrosion behaviour of Al alloy LC4 in simulated salt lake atmospheric environment. In Proceedings of the 7th Cross-Strait Conference on Materials, Kunming, China, 25–31 July 2010; Volume 79.

14. Natesan, M.; Venkatachari, G.; Palaniswamy, N. Kinetics of atmospheric corrosion of mild steel, zinc, galvanized iron and aluminium at 10 exposure stations in India. Corros. Sci. 2006, 48, 3584–3608.

15. Rafi, H.K.; Ram, G.D.J.; Phanikumar, G.; Rao, K.P. Microstructure and tensile properties of friction welded aluminum alloy AA7075-T6. Mater. Des. 2010, 31, 2375–2380.

16. Liu, Y.; Meng, G.Z.; Cheng, Y.F. Electronic structure and pitting behavior of 3003 aluminum alloy passivated under various conditions. Electrochim. Acta 2009, 54, 4155–4163.

17. Dursun, T.; Soutis, C. Recent Developments in Advanced Aircraft Aluminium Alloys. Mater. Des. 2014, 56, 862–871.

18. Ferrer, K.S.; Kelly, R.G. Comparison of methods for removal of corrosion product from AA2024-T3. Corrosion 2001, 57, 110–117.

19. Graedel, T.E.; Leygraf, C. Corrosion mechanisms for nickel exposed to the atmosphere. J. Electrochem. Soc. 2000, 147, 1010–1014.

20. Vera, R.; Delgado, D.; Rosales, B.M. Effect of atmospheric pollutants on the corrosion of high power electrical conductors: Part 1. aluminium and AA6201 alloy. Corros. Sci. 2006, 48, 2882–2900.

21. Wranglen, G. An Introduction to Corrosion and Protection of Metals; Chapman and Hall: London, UK, 1985. 22. Liu, Y.; Wang, Z.; Ke, W. Study on influence of native oxide and corrosion products on atmospheric

corrosion of pure Al. Corros. Sci. 2014, 80, 169–176. 23. Nakazato, R.Z.; Codaro, E.N.; Horovistiz, A.; Hein, R. A metallurgical study of aluminium alloys used as

aircraft components. Prakt. Metallogr. 2001, 38, 74–87. 24. Oguzie, E.E. Corrosion inhibition of aluminum in acidic and alkaline media by sansevieria trifasciata

extract. Corros. Sci. 2007, 49, 1527–1539. 25. Sun, S.; Zheng, Q.; Li, D.; Wen, J. Long-term atmospheric corrosion behaviour of aluminium alloys 2024

and 7075 in urban, coastal and industrial environments. Corros. Sci. 2009, 51, 719–727. 26. Knight, S.; Salagaras, M.; Trueman, A. The study of intergranular corrosion in aircraft aluminium alloys

using X-ray tomography. Corros. Sci. 2011, 53, 727–734. 27. Sun, S.Q.; Zheng, Q.F.; Li, D.F.; Hu, S.Q.; Wen, J.G. Exfoliation corrosion of extruded 2024-T4 in the coastal

environments in china. Corros. Sci. 2011, 53, 2527–2538. 28. Ezuber, H.; El-Houd, A.; El-Shawesh, F. A study on the corrosion behavior of aluminum alloys in

seawater. Mater. Des. 2008, 29, 801–805. 29. Gudic, S.; Smoljko, I.; Kliskic, M. Electrochemical behavior of aluminum alloys containing indium and tin

in NaCl solution. Mater. Chem. Phys. 2010, 121, 561–566. 30. Lin, F.; Cai, J.; Qi, Z. Corrosion behavior of LY12 aluminum alloy with cyclic immersion corrosion test. J.

Chin. Soc. Corros. Prot. 2009, 29, 215–219.

Materials 2018, 11, 235 21 of 22

31. Abiola, O.K. Adsorption of 3-(4-amino-2-methyl-5-pyrimidyl methyl)-4-methyl thiazolium chloride on mild steel. Corros. Sci. 2006, 48, 3078–3090.

32. Prosek, T.; Lversen, A.; Taxén, C.; Thierry, D. Low-temperature stress corrosion cracking of stainless steels on the atmosphere in the presence of chloride deposits. Corrosion 2009, 65, 105–117.

33. Hastuty, S.; Nishikata, A.; Tsuru, T. Pitting corrosion of type 430 stainless steel under chloride solution droplet. Corros. Sci. 2010, 52, 2035–2043.

34. Nishimura, T.; Katayama, H.; Noda, K.; Kodama, T. Electrochemical behavior of rust formed on carbon steel in a wet/dry environment containing chloride ions. Corrosion 2000, 56, 935–941.

35. Han D.; Li D. Influence of temperature on initial corrosion of LY12 in marine atmosphere. Mater. Prot. 2007, 40, 7–19.

36. Xu N.X.; Zhao L.Y.; Ding C.H.; Zhang C.D; Li R.S.; Zhong Q.D. Laboratory observation of dew formation at an early stage of atmospheric corrosion of metals. Corros. Sci. 2002, 44, 163–170.

37. Sharifi-Asla S.; Mao F.; Lu P.; Kursten B.; Macdonald D.D. Exploration of the effect of chloride ion concentration and temperature on pitting corrosion of carbon steel in saturated Ca(OH)2 solution. Corros. Sci. 2015, 98, 708–715.

38. Anwar M.S.; Prifiharni S.; Mabruri E. The effect of tempering temperature on pitting corrosion resistance of 420 stainless steels, AIP Conference Proc. 2016, 1725, 020005; 10.1063/1.4945459.

39. Liu J.; Alfantazi A.; Asselin E. Effects of Temperature and sulfate on the pitting corrosion of titanium in high-temperature chloride solutions. J. Electrochem. Soc. 2015, 162, 189–196.

40. Blücher, D.B.; Svensson, J.E.; Johansson, L.G. The NaCl-induced atmospheric corrosion of aluminum: The influence of carbon dioxide and temperature. J. Electrochem. Soc. 2003, 150, B93–B98.

41. Esmaily, M.; Shahabi-Navid, M.; Svensson, J.-E.; Halvarsson, M.; Nyborg, L.; Cao, Y.; Johansson, L.-G. Influence of temperature on the atmospheric corrosion of the Mg–Al alloy AM50. Corros. Sci. 2015, 90, 420– 433.

42. Zheng, Q.F.; Sun, S.Q.; Wen, J.G.; Li, D.F. Atmospheric corrosion behaviours of aluminum and aluminum alloys in desert atmosphere of southern xinjiang province, china. Chin. J. Nonferrous Met. 2009, 19, 353–359.

43. Sun, S.Q.; Zheng, Q.F.; Li, D.F.; Chen, J.; Wen, J.G. Long-term atmospheric corrosion behavior of LY12 aluminum alloy. J. Chin. Soc. Corros. Prot. 2009, 29, 442–446.

44. Wang, B.B.; Wang, Z.Y.; Han, W.; Ke, W. Atmospheric corrosion of aluminium alloy 2024-T3 exposed to salt lake environment in western china. Corros. Sci. 2012, 59, 63–70.

45. Fuente, D.D.L.; Otero-Huerta, E.; Morcillo, M. Studies of long-term weathering of aluminium in the atmosphere. Corros. Sci. 2007, 49, 3134–3148.

46. He, Y.; Cui, R.; An, T. Long-Term atmospheric corrosion of aluminum alloy 2024-T4 in a coastal environment. J. Mater. Eng. Perform. 2015, 24, 2764–2773.

47. Shu, Y.; Wang, F.; Wu, W. Synergestic effect of NaCl and water vapor on the corrosion of 1Cr11Ni2W2MoV steel at 500–700 °C. Oxid. Met. 1999, 51, 97–110.

48. Shu, Y.; Wang, F.; Wu, W. Corrosion behavior of Ti60 alloy coated with a solid NaCl deposit in O2 plus water vapor at 500–700 °C. Oxid. Met. 1999, 52, 463–473.

49. Zhu D.Q.; Van Ooij W.J. Corrosion protection of AA 2024-T3 by bis-[3-(triethoxysilyl)propyl] tetrasulfide in neutral sodium chloride solution. Part 1: corrosion of AA 2024-T3. Corros. Sci. 2003, 45, 2163–2175.

50. Shao M.H.; Fu Y.; Hu R.G; Lin C. A study on pitting corrosion of aluminum alloy 2024-T3 by scanning microreference electrode technique. Mater. Sci. Eng. A 2003, 344, 323–327.

51. Mol, J.M.C. A filiform corrosion and potentiodynamic polarisation study of some aluminium alloys. J. Mater. Sci. 2000, 35, 1629–1639.

52. Lunt, T.T.; Scully, J.R.; Brusamarello, V.; Mikhailov, A.S.; Hudson, J.L. Spatial Interactions among Localized Corrosion Sites: Experiments and Modeling. J. Electrochem. Soc. 2002, 149, B163–B173.

53. Lucente, A.M.; Scully, J.R. Pitting and Alkaline Dissolution of anAmorphous–Nanocrystalline Alloy with Solute-Lean Nanocrystals. Corros. Sci. 2007, 49, 2351–2361.

54. Strehblow H.H. Mechanisms of Pitting Corrosion in Corrosion Mechanisms in Theory and Practice; Marcel Dekker: New York, NY, USA, 2002.

55. Li, T.; Li, X.G.; Dong, C.F.; Cheng, Y.F. Characterization of atmospheric corrosion of 2A12 aluminum alloy in tropical marine environment. J. Mater. Eng. Perform. 2010, 19, 591–598.

56. Macdonald, D.D. The point defect model for the passive state. J. Electrochem. Soc. 1992, 139, 3434–3449.

Materials 2018, 11, 235 22 of 22

57. Liang, Y.J.; Che, Y.C. Thermodynamic Data of Inorganic Compounds; Northeastern University Press: Shenyang, China, 1993.

58. Zhou, Q.; He, C.; Cai, Q.K.; Shao, Z. Research progress in sol-gel technology applied in the surface treatment for aluminum alloy. Mater. Rev. 2007, 21, 83–86.

59. Zhu, Z. Anodized and Surface Treatment Technology on Al Alloy; Chemical Industry Press: Beijing, China, 2004; pp. 100–110.

60. Xie, W.; Liu, Y.; Zhang, F.; Li, Y.; Guo, Y. Preparation of bochmite sol by sol-gel method. Membr. Sci. Technol. 2005, 25, 71–73.

61. Seinfeld, J.H.; Pandis, S.N. Amospheric Chemistry and Physics: From Air Pollution to Climate Change; John Wiley & Sons, Inc.; New York, NY, USA, 1998.

© 2018 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

Research Article Protection against Corrosion of Aluminum Alloy in Marine Environment by Lawsonia inermis

H. M. Hajar,1 F. Zulkifli,1 M. G. Mohd Sabri,2 and W. B. Wan Nik1

1School of Ocean Engineering, Universiti Malaysia Terengganu, 21030 Kuala Terengganu, Terengganu, Malaysia 2School of Fundamental Science, Universiti Malaysia Terengganu, 21030 Kuala Terengganu, Terengganu, Malaysia

Correspondence should be addressed to W. B. Wan Nik; [email protected]

Received 6 June 2016; Revised 14 September 2016; Accepted 21 September 2016

Academic Editor: Michael J. Schütze

Copyright © 2016 H. M. Hajar et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

The corrosion performance of aluminum alloy 5083 (AA5083) was investigated in the splash zone area simulated in salt spray cabinet at ambient temperature. Three paint formulations were prepared in accordance with different percentages of henna extract. FTIR method was used to determine the constituent of henna while weight loss and electrochemical method were applied to investigate the inhibition behaviour. The findings show that corrosion rate of aluminum alloy decreased with the increases of henna extract in the coating formulation. The rise of charge transfer resistance (𝑅ct) value has contributed to the greater protection of the coated aluminum. The decrease in double layer capacitance value (𝐶dl) is another indicator that a better protective barrier has been formed in the presence of henna in the coating matrix.

1. Introduction

Aluminum was used widely in many sectors such as chem- ical plant, manufacturing lines, and marine industries. The advantage of using aluminum is due to their excellent corrosion resistance property and thus it becomes a priority in materials selections in most industries [1]. Aluminum alloy with 5000 series is excellent for the construction of small leisure boats, workboats, and the large high-speed passenger ship. The advantages of 5000 series aluminum are improved stability, reduced draft, minimized maintenance, and increased speed of the boats or ships. Unfortunately, aluminum suffers corrosion in the harsh environment such as seawater [2]. To overcome the problem, a few corrosion controls and prevention methods have been proposed. The method proposed includes material selection, coatings, cor- rosion inhibitors, cathodic protection, and also change in design [3]. Other than that, the mechanism of the corrosion protection consists of two mechanisms which are physical barrier effect and anodic protection. For physical barrier effect, the polymer coating acts as a barrier to the direct exposure of oxidants and aggressive anions. Meanwhile, the anodic protection system works when the conducting

polymer with strong oxidative property acts as an oxidant to the test metals [4].

Interests in finding an effective corrosion inhibitor have become a major concern among researchers. Substance con- taining heteroatoms such as O, N, or S and multiple bonds was proven to be an excellent inhibitor. However, there are several factors contributing to a better inhibition efficiency such as the number and types of adsorbing groups as well as their molecular size, molecular structure, and mode of interaction with the corroding metal surface [5]. Henna, a herb which is widely used for dyeing purposes, has been studied because of its excellent inhibitive property and being relatively cheap and eco-friendly substance.

2. Methods

Henna extracts were obtained through rotary evaporation process and then used as corrosion inhibitor. Aluminum alloy 5083 was used as a substrate and the preparations of specimens (coupons) were referred to the American Society for Testing and Materials (ASTM) specifications. The coupons were coated with the paint incorporated with henna

Hindawi Publishing Corporation International Journal of Corrosion Volume 2016, Article ID 4891803, 5 pages http://dx.doi.org/10.1155/2016/4891803

2 International Journal of Corrosion

Preparation of specimens (ASTM D4258)

Preparation of henna extraction (ASTM)

FTIR (ASTM E168)

Salt spray test (ASTM B117)

EIS (ASTM G106)Weight loss Tensile test (ASTM D638-14)

Result analysis

Figure 1: Methodological flow chart.

extract. The sample undergoes corrosion process in salt spray chamber where seawater was used as a corrosive medium. Figure 1 shows the flow of methodology in this study.

2.1. Sample Preparation. AA5083 was cut into square shape with the dimension of 25 mm × 25 mm × 3 mm. It was polished by using 600, 800, and 1200 grit emery paper. The coupons were cleaned by using acetone and distilled water. The initial weights of specimens were recorded for each coupon and it was classified according to the characterization and period of exposure to seawater in salt spray chamber. This study investigated three different concentrations of henna extract which consist of 0%, 5% and 10% in coating matrix.

2.2. Extraction Preparation. Henna extraction has been used as corrosion inhibitor for aluminum alloy protection in this study. Dried henna leaves were crushed into powder. The henna powder was immersed in the ethanol solution and left for a week. After one week, the solutions were filtered. The remaining filtrates were collected and put into rotary evaporator (Rotavap) for extraction process.

2.3. Coating Preparation. The paint used in this experiment is alkyd paint. The paint was incorporated with henna extract until the mixture has become homogenous. A magnetic stirrer was used to mix the alkyd paint and henna extract. The percentage of henna extract in alkyd paint is tabulated in Table 1.

2.4. Salt Spray Test. Based on the industrial practices, salt spray cabinet is widely used to test components and coated panels for corrosion resistance [6]. In this research, salt spray cabinet Model DF/MP/450 had been used and was conducted according to ASTM B117.

The seawater used in salt spray test was obtained from Universiti Malaysia Terengganu hatchery. Seawater is an aggressive and complex electrolyte that affect nearly all

Table 1: Types of coating produced.

Paint Henna extract (%) Paint 1 (P1) 0 Paint 2 (P2) 5 Paint 3 (P3) 10

structural material to some extent and also seawater is the best media to be applied as a real environment to speed up the process of material corrosion.

2.5. Fourier Transform Infrared. The purpose of conducting Fourier Transform Infrared (FTIR) test is to expand the infor- mation of surface analysis and it is also used to characterize the coatings. Initially, Attenuated Total Reflectance (ATR) was used to examine the materials but abandoned after it only gave weak spectrum.

2.6. Weight Loss Measurement. In weight loss measurement, the coupons were cleaned using acetone and rinsed with distilled water. The coupons were weighed before they were left exposed in the salt spray chamber (𝑊𝑖).

Analytical balance was used as the weighing device with the sensitivity up to 4 decimal places in gram. The weight obtained after exposure is known as final weight (𝑊𝑓). Weight loss determination was carried out using the following equation.

Weight loss formula is as follows:

𝑊𝐿 =𝑊𝑖−𝑊𝑓, (1) where𝑊𝐿 is weight loss (mg),𝑊𝑖 is initial weight (mg), and𝑊𝑓 is final weight (mg).

Weight loss (%) formula is as follows:

𝑊𝐿 (%) = 100−(1− 𝑊𝑖𝑊𝑓), (2)

where𝑊𝐿 is weight loss (%),𝑊𝑖 is initial weight (mg), and𝑊𝑓 is final weight (mg).

Corrosion rate formula is as follows:

CR= 87.6× 𝑊𝐿𝐷𝐴𝑇, (3) where CR is corrosion rate (mm/year),𝑊𝐿 is weight loss (mg),𝐷 is density of material (g/cm3),𝐴 is area of material (cm2), and𝑇 is time (hour). 2.7. Tensile Test. Tensile test was carried out by hydraulically operated tensile testing machine with the maximum capacity of 50 kN under static load condition. The load is uniaxially applied on the specimen at a crosshead speed of 5 mm/min. The data was collected using a computer control software package.

International Journal of Corrosion 3

Figure 2: Lawsone molecular structure.

3. Results and Discussion

The data were collected through several methods including FTIR spectroscopy, weight loss measurement, Electrochemi- cal Impedance Spectroscopy (EIS), and tensile test. All data were analyzed and represented in the form of graph and tables.

3.1. Fourier Transform Infrared. Figure 2 shows the molecular structure of lawsone which is the main component in henna. Three major functional groups which can be derived from the structure are phenols O-H and C=O and alkenes C=C [7]. They are also known as flavanoids which consists of carbonyl group (C=O, Ketone), O-H group, and aromatic group [8].

Figure 3 shows the IR spectrum of henna. The phenolic group (O-H) stretch appeared at 3299 cm−1. The aromatic C=C stretching frequency appeared at 1735.2 cm−1 while the C=O stretching frequency appeared at 1625.1 cm−1. The IUPAC name of henna is 2-hydroxy-1,4-naphthoquinone [9]. The phenol group of lawsone would donate electron to the metal to achieve its noble state or orbit, whereas the metal would receive the electron to become more stable. This occurrence causes the indirect retardation of further redox reaction and could resist corrosion from acting [10].

3.2. Weight Loss Measurement. Figure 4 shows the weight losses of the coated samples in the absence and presence of henna as inhibitor. The formulation of 10% of henna extract (P3) coating shows the most stable performance followed by 5% of henna extract (P2) coating. The presence of phenol group in lawsone structure helps the metal become more stable via the electron donation of phenol group [11] and also it was able to give more protection to the surface of aluminum alloy AA5083 which is exposed to oxygen [12].

Figure 4 also shows that 10% of henna extract coating has the lowest amount of weight loss. This is because the henna extract contained in the coating used is in the highest percentage. Not only do the coatings ensure the adhesion between metal substrate and organic coatings, but also they are providing a thin barrier with the efficient effect against oxygen diffusion on metal interface. The highest percentage of henna extract had caused the decrease in weight loss due to the inhibitive effect of lawsone by the formation of insoluble complex compounds combined with the metal cations [13].

Figure 5 shows the result of corrosion rates calculated from the weight losses data. The graph shows that the value of corrosion rate for coating incorporated with henna extract is lower than bare metal. As the concentration of henna in

Table 2: Electrochemical parameters of coated sample in the presence and absence of henna extract.

Henna extract (%) 𝑅ct (kΩcm−2) 𝐶dl (𝜇F cm−2) 0 0.567820 0.018342 5 1.346021 0.001354 10 1.890300 0.000034

the coating matrix increases, the corrosion rate was found to decrease. The coated samples without any inhibitor coating show a slight increase of corrosion rate. Upon incorporation of henna, the inhibitive action of Lawsonia extract could be due to the adsorption of its molecules on the substrate surface making a barrier in order to protect its surface [9].

3.3. Electrochemical Impedance Spectroscopy (EIS). Table 2 shows the values of charge transfer resistance and double layer capacitance of AA5083. The data shows that coated samples incorporated with henna have produced higher charge transfer resistance (𝑅ct) compared to bare metal. The highest resistance obtained in this research is the coated sample with 10% of henna extract coating.

Figure 6 shows the Nyquist plot of AA5083 with and without coating. It can be seen that the coated coupon with 0% henna extract exhibits the smallest semicircle, followed by a coated coupon incorporated with 5% of henna extract. The largest semicircle is represented by 10% henna extract. The size of the semicircle contributes to the degree of corrosion resistance. The larger semicircle indicates a better degree of resistance. Increasing value of 𝑅ct with the addition of henna extract percentage gave a better performance to retard corrosion due to the formation of oxide layer [8].

A high antioxidant property of henna has contributed to the increment of electrical resistance on the aluminum surface [14]. It indicates that when a percentage of henna extracts increase, the corrosion resistance also increases and the corrosion rate decreases. Furthermore, the high impedance value of the coating is related to the formation of the deposited layer and consequently slows down the rate of electrolyte penetration into the coating [15].

3.4. Tensile Strength. Figure 7 shows the plot of stress and strain curve. The coupons show a linearity at the beginning until reaching the ultimate stress around 175 MPa. Then, the stress value decreases until it goes into necking phase and rupture.

Ultimate strength or tensile strength is obtained by dividing maximum load by original area of cross section of coupon.

The tensile stress is achieved where the decrease in the cross-sectional area is greater than the increase in defor- mation load which is caused by strain hardening. In this region, plastic deformation was concerned. The stress begin to decrease. Coupon begins to neck down rapidly when the cross-sectional area decreases far more rapidly than the load increasing by strain hardening [16]. The actual load required

4 International Journal of Corrosion

Henna commercial

63 3.

876 8.

2 81

9. 6

87 9.

10 47

.212 63

13 76

.1 14

51 .7

15 08

.7 15

40 .1

16 31

.1 16

56 .1

16 96

.7 17

11 .9

28 55

.3 29

27 .2

33 53

Molecular mass: 174.153 2-Hydroxy-1,4-naphthoquinone

−10

100 %

3500 3000 2500 2000 1500 1000 500 4000 Wavenumbers (cm−1)

Alkenes (C-H)

1735.2 cm−1 Carbonyl

(C=O) 1625.1 cm−1

Phenol (O-H)

3299 cm−1

∗∗∗∗∗ Henna commercial

Formula: C10H6 O3

Figure 3: IR spectra for henna extraction using FTIR.

5 10 15 20 25 30 Immersion days (days)

0.05

0.1

0.15

0.2

0.25

0.3

W ei

gh t l

os s (

% )

Bare 0%

5% 10%

Figure 4: Result of weight loss of coupons.

to deform the coupon falls off and stress continues to decrease until fracture occurs.

4. Conclusions

The henna extract acts as an excellent inhibitor in way of protective coating method. The highest percentage of henna extract provides the highest resistant layer and makes the

5 10 15 20 25 30 Immersion days (days)

C or

ro si

on ra

te (m

m /y

0.05

0.1

0.15

0.2

0.25

Bare 0%

5% 10%

Figure 5: Corrosion rate of coupons until day 30.

coupon less corroded. Paint 3 with 10% of henna extract gives the lowest value of corrosion rate which is 0.0296 mm/year compared to bare metal, paint 1, and paint 2.

The stress-strain curve shows a linearity in the beginning until stress exceeds about 175 MPa. The stress keeps decreas- ing until, at a certain point, it goes into necking phase and rupture.

Competing Interests

The authors declare that they have no competing interests.

International Journal of Corrosion 5

0 500

1000 1500 2000 2500 3000 3500 4000 4500 5000

0 5000 10000 15000 20000 25000

− Z

im ag

in e

(Ω ·c

m 2 )

Zreal (Ω·cm 2)

Bare 0% henna 5% henna 10% henna

Figure 6: Nyquist plot of bare and coated samples.

100

150

200

250

St re

ss (M

pa )

0.2 0.4 0.6 0.8 10 Strain

Day 30 Day 5

Figure 7: Stress and strain curve of a coated aluminum alloy.

Acknowledgments

The authors greatly acknowledge the Research Fund Look East Policy 2.0, Vot. no. 53168 and also Miss. Nadia Zahamudin and Mr. Tan Wu Huei for their direct contribu- tion in this study.

References

[1] S.-J. Kim and S.-K. Jang, “Effects of solution heat treatment on corrosion resistance of 5083F Al alloy,” Transactions of Nonferrous Metals Society of China, vol. 19, no. 4, pp. 887–891, 2009.

[2] Z. Ahmad and B. J. Abdul Aleem, “Degradation of aluminum metal matrix composites in salt water and its control,” Materials and Design, vol. 23, no. 2, pp. 173–180, 2002.

[3] ASM International, “The effects and economic impact of cor- rosion,” in Corrosion: Understanding the Basics, pp. 1–20, ASM International, 2000.

[4] T. Ohtsuka, “Corrosion protection of steels by conducting polymer coating,” International Journal of Corrosion, vol. 2012, Article ID 915090, 7 pages, 2012.

[5] A. Nahlé, I. Abu-Abdoun, I. Abdel-Rahman, and M. Al-Khayat, “UAE neem extract as a corrosion inhibitor for carbon steel in HCl solution,” International Journal of Corrosion, vol. 2010, Article ID 460154, 9 pages, 2010.

[6] M. Belkhaouda, L. Bazzi, R. Salghi et al., “Effect of the heat treatment on the behaviour of the corrosion and passivation of 3003 aluminium alloy in synthetic solution,” Journal of Materials and Environmental Science, vol. 1, no. 1, pp. 25–33, 2010.

[7] K. S. Singh, Y. V. Singh, and M. Singh, “Agro-history, uses and distribution of henna (Lawsoniainermis L. Syn. Alba Lam),” in Henna: Cultivation, Improvement and Trade Jodhpur, Central Arid Zone Research Institute, 2005.

[8] F. Gapsari, R. Soenoko, A. Suprapto, and W. Suprapto, “Bee wax propolis extract as eco-friendly corrosion inhibitors for 304SS in sulfuric acid,” International Journal of Corrosion, vol. 2015, Article ID 567202, 10 pages, 2015.

[9] A. Y. El-Etre, M. Abdallah, and Z. E. El-Tantawy, “Corrosion inhibition of some metals using lawsonia extract,” Corrosion Science, vol. 47, no. 2, pp. 385–395, 2005.

[10] W. B. Wan Nik, F. Zulkifli, R. Rosliza, and M. M. Rahman, “Lawsonia Inermis as green inhibitor for corrosion protection of aluminium alloy,” International Journal of Modern Engineer- ing and Research Technology, vol. 1, pp. 723–728, 2011.

[11] A. Hamdy and N. S. El-Gendy, “Thermodynamic, adsorption and electrochemical studies for corrosion inhibition of carbon steel by henna extract in acid medium,” Egyptian Journal of Petroleum, vol. 22, no. 1, pp. 17–25, 2013.

[12] A. Yağan, N. Ö. Pekmez, and A. Yildiz, “Corrosion inhibition by poly(N-ethylaniline) coatings of mild steel in aqueous acidic solutions,” Progress in Organic Coatings, vol. 57, no. 4, pp. 314– 318, 2006.

[13] A. Motalebi, M. Nasr-Esfahani, R. Ali, and M. Pourriahi, “Improvement of corrosion performance of 316L stainless steel via PVTMS/henna thin film,” Progress in Natural Science: Materials International, vol. 22, no. 5, pp. 392–400, 2012.

[14] E. Akbarinezhad, F. Rezaei, and J. Neshati, “Evaluation of a high resistance paint coating with EIS measurements: effect of high AC perturbations,” Progress in Organic Coatings, vol. 61, no. 1, pp. 45–52, 2008.

[15] A. Al-Borno, X. Chen, and S. K. Dhoke, “Effect of high temperature sodium hydroxide immersion on fusion bond epoxy coating,” International Journal of Corrosion, vol. 2015, Article ID 903478, 7 pages, 2015.

[16] S. J. Kim and J. Y. Ko, “Investigation on optimum protection potential of high-strength Al alloy (5456-H116) for application in ships,” Journal of the Korean Society of Marine Engineering, vol. 30, no. 1, pp. 157–168, 2006.

Submit your manuscripts at http://www.hindawi.com

Scientifica Hindawi Publishing Corporation http://www.hindawi.com Volume 2014

Corrosion International Journal of

Hindawi Publishing Corporation http://www.hindawi.com Volume 2014

Polymer Science International Journal of

Hindawi Publishing Corporation http://www.hindawi.com Volume 2014

Ceramics Journal of

Hindawi Publishing Corporation http://www.hindawi.com Volume 2014

Composites Journal of

Nanoparticles Journal of

Hindawi Publishing Corporation http://www.hindawi.com Volume 2014

International Journal of

Biomaterials

Hindawi Publishing Corporation http://www.hindawi.com Volume 2014

Nanoscience Journal of

Textiles Hindawi Publishing Corporation http://www.hindawi.com Volume 2014

Journal of

Nanotechnology Hindawi Publishing Corporation http://www.hindawi.com Volume 2014

Journal of

Crystallography Journal of

Hindawi Publishing Corporation http://www.hindawi.com Volume 2014

The Scientific World Journal Hindawi Publishing Corporation http://www.hindawi.com Volume 2014

Hindawi Publishing Corporation http://www.hindawi.com Volume 2014

Coatings Journal of

Advances in

Materials Science and Engineering Hindawi Publishing Corporation http://www.hindawi.com Volume 2014

Smart Materials Research

Hindawi Publishing Corporation http://www.hindawi.com Volume 2014

Metallurgy Journal of

Hindawi Publishing Corporation http://www.hindawi.com Volume 2014

BioMed Research International

Materials Journal of

Hindawi Publishing Corporation http://www.hindawi.com Volume 2014

N a n o m a te ri a ls

Hindawi Publishing Corporation http://www.hindawi.com Volume 2014

Journal of

Nanomaterials

Research Article Protection against Corrosion of Aluminum Alloy in Marine Environment by Lawsonia inermis

H. M. Hajar,1 F. Zulkifli,1 M. G. Mohd Sabri,2 and W. B. Wan Nik1

Correspondence should be addressed to W. B. Wan Nik; [email protected]

Received 6 June 2016; Revised 14 September 2016; Accepted 21 September 2016

Academic Editor: Michael J. Schütze

1. Introduction

polymer with strong oxidative property acts as an oxidant to the test metals [4].

2. Methods

Hindawi Publishing Corporation International Journal of Corrosion Volume 2016, Article ID 4891803, 5 pages http://dx.doi.org/10.1155/2016/4891803

2 International Journal of Corrosion

Preparation of specimens (ASTM D4258)

Preparation of henna extraction (ASTM)

FTIR (ASTM E168)

Salt spray test (ASTM B117)

EIS (ASTM G106)Weight loss Tensile test (ASTM D638-14)

Result analysis

Figure 1: Methodological flow chart.

extract. The sample undergoes corrosion process in salt spray chamber where seawater was used as a corrosive medium. Figure 1 shows the flow of methodology in this study.

The seawater used in salt spray test was obtained from Universiti Malaysia Terengganu hatchery. Seawater is an aggressive and complex electrolyte that affect nearly all

Table 1: Types of coating produced.

Paint Henna extract (%) Paint 1 (P1) 0 Paint 2 (P2) 5 Paint 3 (P3) 10

structural material to some extent and also seawater is the best media to be applied as a real environment to speed up the process of material corrosion.

Weight loss formula is as follows:

𝑊𝐿 =𝑊𝑖−𝑊𝑓, (1) where𝑊𝐿 is weight loss (mg),𝑊𝑖 is initial weight (mg), and𝑊𝑓 is final weight (mg).

Weight loss (%) formula is as follows:

𝑊𝐿 (%) = 100−(1− 𝑊𝑖𝑊𝑓), (2)

where𝑊𝐿 is weight loss (%),𝑊𝑖 is initial weight (mg), and𝑊𝑓 is final weight (mg).

Corrosion rate formula is as follows:

International Journal of Corrosion 3

Figure 2: Lawsone molecular structure.

3. Results and Discussion

Table 2: Electrochemical parameters of coated sample in the presence and absence of henna extract.

Henna extract (%) 𝑅ct (kΩcm−2) 𝐶dl (𝜇F cm−2) 0 0.567820 0.018342 5 1.346021 0.001354 10 1.890300 0.000034

Ultimate strength or tensile strength is obtained by dividing maximum load by original area of cross section of coupon.

4 International Journal of Corrosion

Henna commercial

63 3.

876 8.

2 81

9. 6

87 9.

10 47

.212 63

13 76

.1 14

51 .7

15 08

.7 15

40 .1

16 31

.1 16

56 .1

16 96

.7 17

11 .9

28 55

.3 29

27 .2

33 53

Molecular mass: 174.153 2-Hydroxy-1,4-naphthoquinone

−10

100 %

3500 3000 2500 2000 1500 1000 500 4000 Wavenumbers (cm−1)

Alkenes (C-H)

1735.2 cm−1 Carbonyl

(C=O) 1625.1 cm−1

Phenol (O-H)

3299 cm−1

∗∗∗∗∗ Henna commercial

Formula: C10H6 O3

Figure 3: IR spectra for henna extraction using FTIR.

5 10 15 20 25 30 Immersion days (days)

0.05

0.1

0.15

0.2

0.25

0.3

W ei

gh t l

os s (

% )

Bare 0%

5% 10%

Figure 4: Result of weight loss of coupons.

to deform the coupon falls off and stress continues to decrease until fracture occurs.

4. Conclusions

The henna extract acts as an excellent inhibitor in way of protective coating method. The highest percentage of henna extract provides the highest resistant layer and makes the

5 10 15 20 25 30 Immersion days (days)

C or

ro si

on ra

te (m

m /y

0.05

0.1

0.15

0.2

0.25

Bare 0%

5% 10%

Figure 5: Corrosion rate of coupons until day 30.

coupon less corroded. Paint 3 with 10% of henna extract gives the lowest value of corrosion rate which is 0.0296 mm/year compared to bare metal, paint 1, and paint 2.

The stress-strain curve shows a linearity in the beginning until stress exceeds about 175 MPa. The stress keeps decreas- ing until, at a certain point, it goes into necking phase and rupture.

Competing Interests

The authors declare that they have no competing interests.

International Journal of Corrosion 5

0 500

1000 1500 2000 2500 3000 3500 4000 4500 5000

0 5000 10000 15000 20000 25000

− Z

im ag

in e

(Ω ·c

m 2 )

Zreal (Ω·cm 2)

Bare 0% henna 5% henna 10% henna

Figure 6: Nyquist plot of bare and coated samples.

100

150

200

250

St re

ss (M

pa )

0.2 0.4 0.6 0.8 10 Strain

Day 30 Day 5

Figure 7: Stress and strain curve of a coated aluminum alloy.

Acknowledgments

The authors greatly acknowledge the Research Fund Look East Policy 2.0, Vot. no. 53168 and also Miss. Nadia Zahamudin and Mr. Tan Wu Huei for their direct contribu- tion in this study.

References

[2] Z. Ahmad and B. J. Abdul Aleem, “Degradation of aluminum metal matrix composites in salt water and its control,” Materials and Design, vol. 23, no. 2, pp. 173–180, 2002.

[3] ASM International, “The effects and economic impact of cor- rosion,” in Corrosion: Understanding the Basics, pp. 1–20, ASM International, 2000.

[4] T. Ohtsuka, “Corrosion protection of steels by conducting polymer coating,” International Journal of Corrosion, vol. 2012, Article ID 915090, 7 pages, 2012.

[9] A. Y. El-Etre, M. Abdallah, and Z. E. El-Tantawy, “Corrosion inhibition of some metals using lawsonia extract,” Corrosion Science, vol. 47, no. 2, pp. 385–395, 2005.

Submit your manuscripts at http://www.hindawi.com

Scientifica Hindawi Publishing Corporation http://www.hindawi.com Volume 2014

Corrosion International Journal of

Hindawi Publishing Corporation http://www.hindawi.com Volume 2014

Polymer Science International Journal of

Hindawi Publishing Corporation http://www.hindawi.com Volume 2014

Ceramics Journal of

Hindawi Publishing Corporation http://www.hindawi.com Volume 2014

Composites Journal of

Nanoparticles Journal of

Hindawi Publishing Corporation http://www.hindawi.com Volume 2014

International Journal of

Biomaterials

Hindawi Publishing Corporation http://www.hindawi.com Volume 2014

Nanoscience Journal of

Textiles Hindawi Publishing Corporation http://www.hindawi.com Volume 2014

Journal of

Nanotechnology Hindawi Publishing Corporation http://www.hindawi.com Volume 2014

Journal of

Crystallography Journal of

Hindawi Publishing Corporation http://www.hindawi.com Volume 2014

The Scientific World Journal Hindawi Publishing Corporation http://www.hindawi.com Volume 2014

Hindawi Publishing Corporation http://www.hindawi.com Volume 2014

Coatings Journal of

Advances in

Materials Science and Engineering Hindawi Publishing Corporation http://www.hindawi.com Volume 2014

Smart Materials Research

Hindawi Publishing Corporation http://www.hindawi.com Volume 2014

Metallurgy Journal of

Hindawi Publishing Corporation http://www.hindawi.com Volume 2014

BioMed Research International

Materials Journal of

Hindawi Publishing Corporation http://www.hindawi.com Volume 2014

N a n o m a te ri a ls

Hindawi Publishing Corporation http://www.hindawi.com Volume 2014

Journal of

Nanomaterials

International Journal of Academic Scientific Research

ISSN: 2272-6446 Volume 3, Issue 4 (November-December 2015), PP 37-45 www.ijasrjournal.org

www.ijasrjournal.org 37 | Page

Effect of Surface Roughness on Corrosion behavior of Aluminum

Alloy 6061 in Salt Solution (3.5%NaCl)

Ahmad Almansour 1 , Mazen Azizi

2 , Abdul Munem Jesri

3 , Sami Entakly

1,2 (Department of Material Engineering, Aleppo University, Syria)

3 (Department of Production Engineering Aleppo University, Syria)

4 (PhD Candidate, Department of Production Engineering Aleppo University, Syria)

Abstract: The corrosion of AA6061 after changing the roughness at different degrees was investigated. The aim of

this work was to determine the effect of roughness on corrosion behavior of AA6061.

The roughness of samples were (Ra= 0.64, 1.83, 3.48, 7.04 μm). The mechanical properties were investigated by

hardness tests and tension tests. The corrosion behavior was investigated by immersion tests in 3.5% NaCl salt

solutions. The microstructure was investigated by optical microscope.

The results showed that the corrosion rate deceased gradually in alkaline salt solution with decreasing the

roughness. However in acidic and neutral salt solutions, with decreasing roughness the corrosion rates decreased

gradually with the existence of a sharp steps in decreasing.

Keywords: Aluminum Alloys, AA6061, Corrosion of Aluminum, Surface Roughness.

1. Introduction

Corrosion is the transformation of a metal through a chemical or electrochemical reactions,

starting at its surface. Although all metals have a tendency to be oxidized, some will oxidize more easily than others.

That will be done as a result of contact with an electrolyte like water or moist air. Aluminum is one of these metals,

aluminum surface will react spontaneously to form aluminum oxide. This oxide layer is tightly bonded with surface

of metal and doesn’t have defects.This natural, stable oxide layer is an integral part of the aluminum surface, thus

protecting it from further oxidation [1].

There are two factors affecting the corrosion resistance of wrought aluminum alloys, related with

surface, the first is the near surface that will be full of dislocation and deformations, and this will induce the

corrosion. In addition the boundaries of grains will be active, and any pre-heating will cause precipitate of secondary

phases that affect corrosion, so a subsequent high shear finishing processes like grinding are applied to remove

these layers.

This is can be noted in automotive applications, where alloys of the Al-Mg-Si-(Cu) family (AA6xxx)

are used for external closure panels. Materials of these sheet are generally supplied in a cleaned state, and therefore

resist corrosion. However, mechanical grinding is frequently applied as process prior to final cleaning, pre-treatment

International Journal of Academic Scientific Research

ISSN: 2272-6446 Volume 3, Issue 4 (November-December 2015), PP 37-45

www.ijasrjournal.org 38 | Page

and painting at the automotive manufacturer and this process typically produces fine surface layers of several

micrometers thickness. The relatively thick layers were not removed by cleaning and pre-treatment [2].

Studies had been achieved in Innoval Technology about shear processing of aluminum alloy surfaces

and its influence on corrosion. The mechanical processes were hot or cold rolling, grinding, machining or cutting

and these process will change the surface structure. The surface microstructure is locally transformed and if the

surface shear is high enough, a fine grain size layer will result. This layer has very different optical, mechanical and

electrochemical properties differ of bulk microstructure. These properties can be used to understand why and how

aluminum alloys corrode either as a result of mechanical abrasion, or during preparing samples for electrochemical

testing, or in service [3].

In 2006, a research about precipitation and corrosion behavior of Nano-Structured Near-Surface

Layers on an AA6111 Aluminium Alloy was performed. This alloy 6061-T6 with magnesium and silicon has high

strength, excellent formability, good weldability and good corrosion resistance. The most application of this alloy

application is in the ship building and transport industries where welding often forms part of the manufacturing

process. Al6061-T651 is, however, prone to corrosion in chloride-containing environments. A nano-structured,

near-surface layer has been generated by mechanically grinding an AA6111 alloy. After heat treatment at 180°C for

30 minutes, Q phase particles, ~20 nm diameter, were precipitated preferentially at grain boundaries within the

nano-structured near surface layer. Other precipitates were not observed in the bulk alloy after this heat treatment.

This preferential precipitation results in the near-surface layers having increased corrosion susceptibility than the

whole microstructure, due to the micro-galvanic coupling between the precipitates at grain boundary and the grain

matrix. It is expected that localized attack is intergranular [4].

The second factor is the shape of this layer that will be the same of shape base metal, curvatures,

meanders…etc. and this presents important role in corrosion resistance, where some sites will be weak and may

deteriorate and initiate local corrosion attacks. Especially for aluminum used in exterior architectural applications,

aggressive elements such as chloride ions (Cl - ), sulphates (SO4

-- ) or others, may be potential causes of corrosion

depending on the local environment. For this reason, an effective lifetime protective surface treatment is essential

for architectural applications [1].

Fig.1. Shape of oxide film that will form on surface of Aluminum Alloy [1].

By grinding and polishing process it is possible to remove the deformed layer and get finer surface,

and this will reflect on corrosion behavior, so in this research we will study the effect of surface roughness on

corrosion behavior of wrought aluminum alloy 6061.

It is obvious that research on the relationship between surface roughness and corrosion rate is not

taking much concern from scientists. The present work is a contribution to this field to shed the light on the

importance of surface roughness and its influence on corrosion rate.

International Journal of Academic Scientific Research

ISSN: 2272-6446 Volume 3, Issue 4 (November-December 2015), PP 37-45

www.ijasrjournal.org 39 | Page

2. Experimental procedure

2.1. Sample Preparation

AA6061 with base composition by weight % is 1Mg, 0.56Si, 0.28Fe, 0.08Cu, 0.23Mn, 0.61Mg,

0.05Zi, 0.02Cr, and 0.04Ti was used in this study. The composition was measured by spectrometer XMF 104 that

manufactured by Unsisantis Europe company in Germany. The condition of alloy was as received from

manufacturing operation “hot rolled” and thus the specimens was full of dislocations.

Specimens with dimensions 19×15×7 mm were used. The emery papers and Al2O3 powder and diamond

powder were used to obtain specimens with different surface roughness. The degree of roughness was measured by

roughness machine tester TR110, produced by TIME HOLLND Company, China. Table 1 shows the different

samples related with roughness.

Table 1. Samples of Specimens related with Roughness

Samples Ra (μm) 1 0.64

2 1.83

3 2.06

4 3.48

5 7.04

2.2. Mechanical tests

2.2.1. Hardness test

Brinell test was applied to determine the hardness with ERNSL apparatus provided from ERNST

Company, Italy. The ball steel diameter was 5 mm, the applied force was 125 kg.

2.3. Optical Microscopy Observation

The samples of alloy AA6061 were examined using an optical microscope B-353 provided by

Optica Company, Germany.

2.4. Corrosion test

The corrosion tests were carried out in salt solutions 3.5wt% NaCl with different values of

PH(2,7,12) which was prepared using standard procedures, by adding highly pure NaCl to reagent water (3.5% NaCl

with 96.5% H2O), and the salt was dissolved in the water by using the magnetic mixer GD503, manufactured by

Sartorius company, Germany. This concentration is approximate to salts concentrations in sea water and this

percentage causes the higher corrosion of aluminum because of the quantity of dissolute Oxygen and ion

conductivity at higher values. This solution was divided into three groups. HCl was added to the first group to obtain

acidic solution, NaOH was added to the second group to obtain alkaline solution, and the third group was left

without additions to keep neutral solution. The value of PH for three groups were controlled by PH Meter P11,

manufactured by Sartorius Company, Germany.

The samples were degreased with acetone and then rinsed in distilled water before immersion in test

solutions. The electro-chemical experiment was monitored for 8 days. The corrosion test results were evaluated

using weight loss. The weight loss (mg) for each sample was evaluated by finding the difference in weight “final

weight initial weight” considering the total surface area of the specimen in accordance with ASTM G311 standard

International Journal of Academic Scientific Research

ISSN: 2272-6446 Volume 3, Issue 4 (November-December 2015), PP 37-45

www.ijasrjournal.org 40 | Page

recommended practice ASTM, 1994. For this purpose weighting apparatus, M-power, produced by Satorius

company, Germany was used.

Corrosion rate for each specimen was evaluated from the weight loss measurement following standard

procedures as relation down.

CR: corrosion rate (mm/year).

W: reduction in weight (gr).

A: area (mm 2 ).

T: time of immersion (hours).

D: density of AA6061 (gr/cm 3 )

3. Results

3.1. Mechanical Properties:

3.1.1. Hardness Test:

The average value of hardness was 275 BHN. This high value was a result of dislocations and defects

during manufacturing process.

3.1.2. Tension Test:

Table.2 shows the average values that results from tension test, the strength of specimen in addition to

elongation. The value of elongation was low because of defects in specimen.

Table.2 Results of tension test

Strength (Mpa) Yield Strength (Mpa) Elongation ΔL/L% 242 195 9

3.2. Optical Microscopy observation:

Figure.2 shows the microstructure of the Specimens, the microstructure is consist of aluminum matrix and

precipitates of Mg2Si dispread on it.

Fig.2. Microstructure of Aluminum Alloy 6061

International Journal of Academic Scientific Research

ISSN: 2272-6446 Volume 3, Issue 4 (November-December 2015), PP 37-45

www.ijasrjournal.org 41 | Page

3.3. Corrosion Test:

3.3.1. Corrosion Rate:

Table 2 shows results of immersion test in acidic salt solution, the corrosion rate of as received sample

of AA6061 is gradually decreasing with decreasing of Ra and the sharp decreasing get when the Ra has the value

(0.64μm).

Table 2: Corrosion rates of samples of AA6061 in acidic salt solutions, immersion time was eight days

Sample Ra (μm) Corrosion rate (mm/y)

1 0.64 0.002223639 2 1.83 0.007792235 3 2.06 0.00845617 4 3.48 0.008821884 5 7.04 0.008911285

The results showed in table 2 was represented in Fig 3.

Fig 3. Corrosion rates of AA6061 samples in acidic salt solution.

Table 3 shows results of immersion test in neutral salt solution, the corrosion rate of as received sample of

AA6061 is sharply decreasing with decreasing of Ra between values (2.06-7.04 μm), then decreasing gradually up to value (0.64μm).

Table 3: Corrosion rates of samples of AA6061 in neutral salt solutions, immersion time was eight days

Sample Ra (μm) Corrosion rate (mm/y)

1 0.64 0.001067847 2 1.83 0.00115001 3 2.06 0.001337646 4 3.48 0.001749653 5 7.04 0.002265203

The results showed in table 3 was represented in Fig 4.

0,001

0,002

0,003

0,004

0,005

0,006

0,007

0,008

0,009

0,01

0,64 1,83 2,06 3,48 7,04

C o

rr o

si o

n r

a te

( m

m /y

)

Roughness Ra (μm)

International Journal of Academic Scientific Research

ISSN: 2272-6446 Volume 3, Issue 4 (November-December 2015), PP 37-45

www.ijasrjournal.org 42 | Page

Fig 4. Corrosion rates of AA6061 samples in neutral salt solution.

Table 4 shows results of immersion test in alkaline salt solution, the corrosion rate of as received sample of

AA6061 is gradually decreasing with decreasing of Ra between values.

Table 4: Corrosion rates of samples of AA6061 in alkaline salt solutions, immersion time was eight days

Sample Ra (μm) Corrosion rate (mm/y)

1 0.64 0.016949 2 1.83 0.019374 3 2.06 0.020567 4 3.48 0.021979 5 7.04 0.022121

The results showed in table 4 was represented in Fig 5.

Fig 5. Corrosion rates of AA6061 samples in alkaline salt solution.

0,0005

0,001

0,0015

0,002

0,0025

0,64 1,83 2,06 3,48 7,04

o rr

o si

o n

r a

te (

m m

/y )

Roughness Ra (μm)

0,005

0,01

0,015

0,02

0,025

0,64 1,83 2,06 3,48 7,04

C o

rr o

si o

n r

a te

( m

m /y

)

Roughness Ra (μm)

International Journal of Academic Scientific Research

ISSN: 2272-6446 Volume 3, Issue 4 (November-December 2015), PP 37-45

www.ijasrjournal.org 43 | Page

In case of alkaline solutions PH=12, the values of Corrosion rates were observed to be more than acidic and

neutral solution.

One of the main corrosive reactions is:

NaOH+Al+H2O→NaAlO3+H2O ………(1) [5].

With decreasing the roughness, the contact surface with solution is reducing, and as a result the quantity of reaction

is reduced, consequently the corrosion rate is reduced.

However, the mechanism of corrosion of the Al matrix in neutral media is related with the formation o f protective

layer of aluminum hydroxides Al(OH)3.

Al → Al+3 + 3e - ……. (2)

Al+3 + 3H2O → Al(OH)3 + 3H+ ……….. (3) [6] The Al(OH)3 layer becomes more protector with decreasing the roughness, because the defects is lowered.

In acidic solution, the solubility of Al 3+

facilitates the dissolution of the Al matrix and further accelerates

the chloride attack.

The cl - ions will initiate at weak sites in the oxide film by chloride attack, The resulting HCl formation

inside the pit causes accelerated pit propagation, This product was considered to be AlCl3 or Al(OH)2Cl [7].The

decreasing of roughness reduce the weak sites on surface and consequently reduce the corrosion rate.

3.3.2. Shape of Corrosion:

Fig.6 shows the optical micrograph of AA6061 surfaces after removing from immersion solutions. In the

alkaline solutions, the surfaces of specimens for different roughness are covered with Al(OH)3 and the general

corrosion is controlled. In acidic and neutral solutions, pits were observed on surfaces and with increasing in

roughness the pits increased.

4. Conclusions

This paper studied effect of degree of roughness on corrosion behavior of aluminum alloy AA6061. The

roughness was achieved on specimens by grinding in different emery paper in addition to use Al2O3 powder, and

diamond powder, to obtain on five surfaces.

The immersion corrosion tests in 3.5% salt solutions with different values of PH were applied. With the

decrease in the roughness, the corrosion rate decrease, because of, in alkaline solution, the contact surface between

solution and specimen was reduced and by this the corrosion reactions became less.

In neutral solution, the corrosion depend on Al(OH)3 layer that formed, and with decreasing the roughness

this layer became more protecting.

In acidic solution, with decreasing the roughness, the sites of collection the HCl were reduced, and by this

the chloride aggressive became less.

International Journal of Academic Scientific Research

ISSN: 2272-6446 Volume 3, Issue 4 (November-December 2015), PP 37-45

www.ijasrjournal.org 44 | Page

Roughness

Ra (μm) PH =2 PH =7 PH=12

0.64

1.83

2.06

3.48

7.04

Scale

Fig.6. Shape of corroded specimens

REFERENCES

[1] Christian Vargel, Corrosion of Aluminum, (Elsevier Journal, Paris, France, 2004).

[2] Scamans G M, Afseth A, Thompson G E and Zhou X 2000 Proceeding of 2nd International Conference on Aluminium Surface

Science and Technology (Manchester) p9.

[3] Geoff Scamans, Shear processing of aluminium alloy surfaces and its influence on corrosion, (Innoval Technology Limited).

[4] X Zhou, Precipitation and Corrosion Behaviour of Nano-Structured Near-Surface Layers on an AA6111 Aluminium Alloy, Journal of

Physics: Conference Series 26 (2006) 103–106.

International Journal of Academic Scientific Research

ISSN: 2272-6446 Volume 3, Issue 4 (November-December 2015), PP 37-45

www.ijasrjournal.org 45 | Page

[5] Marcos D. Navarro, Stress Assisted Corrosion of Aluminum 6061 in Base Chemical Solution, California State University, Sacramento

-Ronald E. McNair Scholar.

[6] Hani Aziz Ameen, Evaluation of the pitting corrosion for aluminum alloys 7020 in 3.5% NaCl solution with range of temperature

(100-500)°C, AMERICAN JOURNAL OF SCIENTIFIC AND INDUSTRIAL STRIAL RESEARCH,2011.

[7] B. Zaid, D. Saidi, A. Benzaid, S. Hadji, Effects of PH and chloride concentration on pitting corrosion of AA6061 aluminum alloy

,(Corrosion Science 50 (2008) 1841–1847).

See discussions, stats, and author profiles for this publication at: https://www.researchgate.net/publication/267596825

The Relationship Between Surface Roughness and Corrosion

Conference Paper · November 2013

DOI: 10.1115/IMECE2013-65498

CITATIONS

6 READS

2,678

3 authors:

Some of the authors of this publication are also working on these related projects:

surface engineering View project

Low Temperature Degradation of Tetragonal Zirconia View project

A. S. Toloei

15 PUBLICATIONS 54 CITATIONS

SEE PROFILE

Vesselin Stoilov

University of Windsor

46 PUBLICATIONS 176 CITATIONS

SEE PROFILE

Derek Northwood

University of Windsor

403 PUBLICATIONS 6,558 CITATIONS

SEE PROFILE

All content following this page was uploaded by Vesselin Stoilov on 13 October 2015.

The user has requested enhancement of the downloaded file.

https://www.researchgate.net/publication/267596825_The_Relationship_Between_Surface_Roughness_and_Corrosion?enrichId=rgreq-33c06e6a4a1b252d560ad0fd839a4b62-XXX&enrichSource=Y292ZXJQYWdlOzI2NzU5NjgyNTtBUzoyODQxNTkzMjM5ODM4NzJAMTQ0NDc2MDI3MDAzNA%3D%3D&el=1_x_2&_esc=publicationCoverPdf

https://www.researchgate.net/project/surface-engineering-3?enrichId=rgreq-33c06e6a4a1b252d560ad0fd839a4b62-XXX&enrichSource=Y292ZXJQYWdlOzI2NzU5NjgyNTtBUzoyODQxNTkzMjM5ODM4NzJAMTQ0NDc2MDI3MDAzNA%3D%3D&el=1_x_9&_esc=publicationCoverPdf

https://www.researchgate.net/project/Low-Temperature-Degradation-of-Tetragonal-Zirconia?enrichId=rgreq-33c06e6a4a1b252d560ad0fd839a4b62-XXX&enrichSource=Y292ZXJQYWdlOzI2NzU5NjgyNTtBUzoyODQxNTkzMjM5ODM4NzJAMTQ0NDc2MDI3MDAzNA%3D%3D&el=1_x_9&_esc=publicationCoverPdf

https://www.researchgate.net/?enrichId=rgreq-33c06e6a4a1b252d560ad0fd839a4b62-XXX&enrichSource=Y292ZXJQYWdlOzI2NzU5NjgyNTtBUzoyODQxNTkzMjM5ODM4NzJAMTQ0NDc2MDI3MDAzNA%3D%3D&el=1_x_1&_esc=publicationCoverPdf

https://www.researchgate.net/profile/A_Toloei?enrichId=rgreq-33c06e6a4a1b252d560ad0fd839a4b62-XXX&enrichSource=Y292ZXJQYWdlOzI2NzU5NjgyNTtBUzoyODQxNTkzMjM5ODM4NzJAMTQ0NDc2MDI3MDAzNA%3D%3D&el=1_x_4&_esc=publicationCoverPdf

https://www.researchgate.net/profile/Vesselin_Stoilov?enrichId=rgreq-33c06e6a4a1b252d560ad0fd839a4b62-XXX&enrichSource=Y292ZXJQYWdlOzI2NzU5NjgyNTtBUzoyODQxNTkzMjM5ODM4NzJAMTQ0NDc2MDI3MDAzNA%3D%3D&el=1_x_4&_esc=publicationCoverPdf

https://www.researchgate.net/institution/University_of_Windsor?enrichId=rgreq-33c06e6a4a1b252d560ad0fd839a4b62-XXX&enrichSource=Y292ZXJQYWdlOzI2NzU5NjgyNTtBUzoyODQxNTkzMjM5ODM4NzJAMTQ0NDc2MDI3MDAzNA%3D%3D&el=1_x_6&_esc=publicationCoverPdf

https://www.researchgate.net/profile/Derek_Northwood?enrichId=rgreq-33c06e6a4a1b252d560ad0fd839a4b62-XXX&enrichSource=Y292ZXJQYWdlOzI2NzU5NjgyNTtBUzoyODQxNTkzMjM5ODM4NzJAMTQ0NDc2MDI3MDAzNA%3D%3D&el=1_x_4&_esc=publicationCoverPdf

Proceedings of the ASME 2013 International Mechanical Engineering Congress & Exposition IMECE2013

November 13-21, 2013, San Diego, California, USA

IMECE2013-65498

THE RELATIONSHIP BETWEEN SURFACE ROUGHNESS AND CORROSION

Alisina Toloei University of Windsor, Dept. of Mechanical,

Automotive and Materials Engineering Windsor, Ontario, N9B 3P4, Canada Tel: +1 (519) 253 -3000 Ext.(5980)

Email: [email protected]

Vesselin Stoilov University of Windsor, Dept. of Mechanical,

Automotive and Materials Engineering Windsor, Ontario, N9B 3P4, Canada

Tel: +1 (519) 253-3000 Ext.(4149) Email: [email protected]

Derek Northwood University of Windsor, Dept. of Mechanical,

Automotive and Materials Engineering Windsor, Ontario, N9B 3P4, Canada Tel: +1 (519) 253-3000 Ext.(4785)

Email: [email protected]

ABSTRACT

There are different parameters which can

affect electrochemical reactions such as type of

electrolyte, velocity, temperature, oxidizing

agents, impurities, anode material type and

surface treatment. It has been shown that pre-

treatment of working electrode (anode) through

abrasion techniques is one of the most important

parameters affecting on Tafel slopes and

consequently corrosion rate. Surface roughness of

the metal surface is a major influence on general

corrosion, nucleation of metastable pitting and

pitting potential as well.

In this study different surface roughnesses

were created on nickel surface by SiC papers and

corrosion properties were compared.

Electrochemical impedance spectroscopy (EIS)

and profilometry tests were carried out on all the

samples and the results were compared with

another sample prepared through laser ablation

method. Corrosion rate values were calculated and

were compared with EIS results for all the

samples and a trend in the effect of roughness on

corrosion protection of nickel was introduced. SEM

and 3D roughness images were taken and

compared for all of the samples before and after

corrosion tests. Different mechanisms were

distinguished for samples created through

different methods. The lower the roughness

values, the more the corrosion resistance. Sample

with patterns created through laser ablation

method showed the best protection properties

compared to other samples.

INTRODUCTION

Nickel is an important metal and it is used in a

large number of industrial applications such as

rechargeable batteries, coinage, filters and is

widely used as an alloying element in ferrous and

nonferrous alloys due to its strength, toughness

and corrosion resistance [1-3]. The corrosion

resistance of nickel is due to the formation of a

passive film on its surface upon exposure to the

corrosive media. Nevertheless, nickel could be

attacked by acidic media at a considerable rate.

mailto:[email protected]

This is why nickel has been the subject of

significant number of studies related to dissolution

and passivation mechanisms in acid medium [4-

6].

Material composition, manufacturing geometry

and roughness have been considered as important

parameters in determining corrosion properties of

the materials [7, 8]. Surface roughness plays a

significant role on the corrosion behaviour of

metals. It has been reported that an increase in

the surface roughness of magnesium alloy AZ91

[9], stainless steels [10, 11], copper [12],

aluminum and titanium-based alloys [13]

increases the pitting susceptibility and general

corrosion rate. Typically, the general and localized

corrosion behaviour of alloys would depend on

their passivation properties. Hence, it is important

to know the passivation behavior of alloys with

different surface finish to correlate the surface

roughness to their general corrosion and pitting

tendency [7, 9]. For metals with the ability to

form a passive layer, a decrease in surface

roughness increases the corrosion resistance but

for the ones with no passive film a reverse trend

has been observed e.g. mild steel [14] and AE44

magnesium alloy [7].

Surfaces with different roughness finishes showed

that increase in the roughness lowers the pitting

potential in 304L stainless steel in chloride

solution [15]. Burstein et.al [16] showed that the

smoother surface in stainless steel is less capable

of propagating metastable pits than the rougher

one, mainly because the sites of pitting on the

smoother surface are on average more open.

Sharland [17] suggested that the local

concentration of a solution was influenced by the

geometry of surface’s peaks and valleys. This in

turn, affected the diffusion of active ions during

corrosion process He also suggests that the

corrosion resistance is closely related to the

distribution of the valleys on the surface. The

significant influence of the valleys on corrosion

resistance is related to the depth of the valleys

which affects the diffusion of active ions during

corrosion [17-20].

There are different methods to evaluate the effect

of surface roughness on corrosion behavior of

metals such as potantiodynamic polarization

method [21] and electrochemical impedance

spectroscopy (EIS). EIS is the most suitable

method for a detailed analysis of electrochemical

reactions mechanisms and kinetics. Impedance

diagrams provide data on the elementary steps

occurring in an electrochemical reaction and on

their kinetics. They also allow a thorough study of

the role of intermediate species adsorbed on the

surface and of reaction mechanisms, as well as a

study of the properties of passive films [22]. The

impedance characteristics of an electrode in acid

solutions depend largely on the type of the surface

pretreatment and surface roughness of the

electrode [10, 23]. In this study the corrosion

behavior of aligned roughness and patterned

surfaces of nickel created through laser ablation

were investigated in dilute sulphuric acid and EIS

was used to study the effect of the formation of

passive layer in both cases.

MATERIALS AND METHODS

Figure 1: 3D topography image for samples G180 (a) before and (b)

after corrosion tests

Sample Preparation

15 × 15 × 1 mm high purity (99.7%) nickel

sheets were used as the test material. For

obtaining different surface roughness, the samples

were unidirectionally grinded with different grits of

silicon carbide (SiC) (i.e., 60, 180, 320 and 800)

and the samples were named with letter “G”.

Before use, they were embedded in mounting

materials and mechanically polished. Their active

test area is 1 cm 2 . An additional sample with

predetermined surface pattern was created by

laser ablation method. Patterns were labeled using

DxLy format where D is the hole diameter and L is

the inter-hole spacing (D10L20). To create the

holes, a copper bromide laser was used and single

pulse was applied. Nitrogen gas was blown in

order to protect the surface from oxidation.

All electrochemical experiments were conducted at

room temperature. A classical three-electrode cell

was used with a saturated calomel electrode as

reference and platinum wire as counter electrode.

Prior to testing, the samples were allowed for 30

minutes to reach a stable open circuit potential.

Electrochemical measurements (open circuit

potential, potentiodynamic polarization, and

electrochemical impedance spectroscopy) were

carried out in a 0.5 M H2SO4 solution using a

CHI660D, Electrochemical Workstation Beta,

(version 11.17). A potentiodynamic polarization

technique was used to evaluate the parameters

related to corrosion and EIS measurements were

made in order to investigate the effect of surface

modification on the general corrosion resistance of

the surface. EIS diagrams were then recorded at

the open circuit potential for nickel samples. To

ensure a complete characterization of the

electrode/electrolyte interface and corresponding

processes, EIS measurements were made over six

Figure 2: SEM of the sample G320 (a) before and (b) after corrosion and patterned sample (c) before and (d) after corrosion.

frequency decades from 10 mHz to 10 kHz at

open circuit (i.e., corrosion) potential and the best

equivalent circuit model was selected. The main

focus of this study is to compare samples with

roughnesses prepared by using SiC papers and

the patterned sample from corrosion point of view,

formation of passive layer and evaluate corrosion

properties of different samples using EIS method.

Equivalent circuit is determined, EIS curves are

fitted and corresponding values of the equivalent

elements are calculated.

In order to measure surface roughness

parameters and obtain 3-dimensional images of

the samples a Wyko Surface Profiling System NT-

1100 was used. Average surface roughness (Ra)

has been used as a roughness parameter in order

to describe the unique features of the surfaces.

Finally to compare the surface structure and

composition before and after potentiodynamic

testing, scanning electron microscopy (SEM) was

performed.

All testing procedures were validated by using a

reference system of pure Ni(99.7%) with surface

roughness <50nm. A detailed description of the

validation procedures can be found in [21]. RESULTS AND DISCUSSION

Roughness measurements:

It is seen in Table 1 that by increasing the grit number, the average roughness value decreased

both before and after corrosion testing but higher

roughness values have seen for all samples after

corrosion testing. The patterned sample however

had higher roughness values and significantly

lower roughness change after corrosion testing

compared to the samples with the unidirectional

grinding roughness.

Table 1: Roughness values for samples before and after corrosion.

Sample

Roughness values

Ra (Before Corrosion

Testing)

(nm)

Ra (After

Corrosion Testing)

(nm)

G60 704.00 1680.00

G180 276.00 802.28

G320 193.80 552.10

G800 41.10 289.58

D10L20 526.10 778.23

For sake of brevity a sample 3D topography image

for samples G180 has been shown as an example

before and after corrosion tests in Fig.1(a) and

(b). As a result of corrosion the uniform area has

changed to a surface with deeper grooves with

higher roughness value. Rougher surfaces with

deeper groves have lower openness (ratio of width

to depth at opening of the grooves) which limit

the diffusion of the corrosive ions out of the

formed grooves, hence have a higher possibility to

grow larger [11]. On smooth surfaces however the

formation of stable passive film is more possible

to occur which will result in less corrosion [20]. In

the patterned sample also there was an increase

in surface roughness after corrosion testing and in

the 3D roughness image there was no significant

change in the surface appearance which will be in

agreement with the results of the corrosion rate,

EIS and SEM analysis. Scanning electron microscopy

Figures 2(a, b). illustrate SEM images of

sample G320 before and after corrosion as one of

the examples of samples with unidirectional

roughness. It is obvious that the corrosion is more

significant along the grooves. Lee, et.al, also

reported that the deep valleys on the ground

surface are favorable sites for pit nucleation [18].

For rougher surfaces more surface degradation

was observed after corrosion testing. The results

are in agreement with the corrosion rate, EIS and

roughness observations. Figures 2(c) and 2(d)

show the microstructure of patterned sample

before and after the corrosion tests. No severe

corrosion on the surface is observed in the SEM

images. This is also in a good agreement with the

measured electrochemical values. The reason for

this phenomenon is due to the formation of

passive oxide layer and existence of air pockets

inside the holes [24] Electrochemical measurements:

Corrosion rate (CR) values were calculated

using the Tafel extrapolation method and are

summarized in Table 2. As it is seen, by

decreasing the roughness value from sample G60

to G800 the CR values decreased. It has been

suggested that this variation in CR were primarily

due to the anodic behavior of the alloy [9, 21].

Table 2: Corrosion parameters for samples with different

roughness

Sample Ecorr

(mV)

βa

(mV)

βc

(mV)

Corrosion

Rate

(mil/year)

G60 -319 104.7 114.6 9.53

G180 -325.5 111.2 113.8 8.35

G320 -300.8 100.0 112.1 7.96

G800 -272.9 82.3 107.9 5.48

D10L20 -327.4 153.4 128.5 2.61

The patterned sample created by laser ablation

method had the lowest value of the corrosion rate

compared to the samples with unidirectional

grinding roughness (Blue point in Fig.3). The

authors have shown that in patterned sample

alternating solid/liquid zones, stable air/vapour

pockets and a passive oxide layer has been

formed and the existence of air/vapor pockets

prevented the dissolution of this layer. Therefore,

the contact area between the corrosive solution

and the substrate has decreased which

consequently results in decrease in the corrosion

rate [24, 25].

Nyquist and Bode plots are the two common

methods for displaying EIS data. The Nyquist

representation has the real part of the complex

impedance plotted on the X-axis and the

imaginary part on the Y-axis. Figure 4 shows the

Nyquist impedance plots of nickel with different

surface roughness in 0.5M sulphuric acid. The

plots of nickel shown in this figure consist of

distorted semicircles. A similar behavior is

observed for all samples. As seen, the size of the

semicircle, increases with decreasing roughness.

The Nyquist plots were analyzed by fitting the

experimental data to the equivalent circuit model

shown in Fig.5. In this circuit Rs represents the

solution resistance; Rct is the charge transfer

resistance and CPE is constant phase element

related to the double-layer capacitance (Cdl).

Figure 5: Schematic for the equivalent circuit of nickel [26-28].

Rs is in a series with a parallel combination of a

constant phase element CPE (Q) and Rct. Q is used

instead of Cdl to account for the depression of the

capacitive loop [29]. The CPE is a generalized

frequency dependent element which impedance is

given by:

Figure 4: Nyquist plots of nickel for different surface roughness

Figure 3: Change of corrosion rate for samples with different

roughness values

ZCPE=1/(Q(iω) n

)

(1)

Where, i = (-1) 1/2

, ω is the angular frequency, ω =

2πf and f is the frequency. n=0 corresponds to a

pure resistor, n=1 to a pure capacitor and n=0.5

to a Warburg type impedance [30]. Changes in n

values have been related to diffusion process,

porosity and roughness [31].

By plotting the Nyquist diagrams, it is seen that all

diagrams are characterized by depressed

capacitive loop with the theoretical center located

below the real axis. This feature reflects surface

inhomogeneity which results from surface

roughness of structural or interfacial region. These

results are consistent with literature [23, 27]. This

shape of the Nyquist plots suggests that charge

transfer controls the corrosion of Ni in acid

solutions [28]. The capacitance loops in Figure 4

enlarge by the decrease of roughness which

indicates that the corrosion is mainly a charge

transfer process [32]. It means that the resistance

is proportional to the decrease of roughness.

Namely, the lower the roughness, the higher the

resistance. It is worth noting that the decrease of

roughness in H2SO4 solution does not change

substantially the shape of the plots but increases

the impedance. This observation confirms the

suggestion that roughness does not alter the

mechanism of corrosion reaction but decrease the

corrosion by retarding the charge transfer. [28]

The same can be seen in the Bode plots which

represents a log/log plot of the magnitude of

impedance plotted on the Y-axis and the angular

frequency plotted on the horizontal axis. As it is

seen in Fig.6, the total impedance of smooth

nickel samples in solutions is relatively high

compared with rough samples. The patterned

sample again shows highest impedance value.

Bode plots show only one phase maximum at

intermediate frequencies. This result indicates that

the corrosion process occurs via one step

corresponds to one time constant [28]. The Bode

plot show that by decreasing the roughness value

maximum phase angle shifts to lower frequencies

and the polarization resistance increases resulting

in less corrosion [27]. According to Fig.7, for

lower roughness values the phase angle is around

80° suggesting that the electrochemical process

occurring at high frequency decreases the

corrosion rate [27]. It is also said that the

maximum phase angle θmax is less than 80° as a

result of the roughness of the electrode surface

[28]. Corrosion of Ni in H2SO4 solution also

enhances the roughness of the electrode surface

and therefore reduces the value of θmax.

Therefore, higher corrosion rate is related to

Figure 6: Bode plots for nickel for different surface roughness

higher roughness value. Thus, the lowest value of

θmax is related to more corroded sample which is

the one with the highest roughness [28].

The EIS parameters of Ni in 0.5 M H2SO4 with

different roughnesses are given in Table 3.

Increasing Rct values with decrease of the

roughness, for nickel, suggests a decrease of the

corrosion rate since the Rct value, is a measure of

electron transfer across the surface, and it is

inversely proportional to the corrosion rate [26].

Similar trend has been reported by Hong et.al. in

their potantiodynamic tests and EIS analysis that

says the total number of the surface sites

available for metastable pits on the electrode at a

given potential decreases with increasing the grit

number of the silicon carbide paper for final

surface grinding and it implies that metastable pit

or pits starting to grow on the smoother surfaces

is more difficult than that on the rougher surfaces

[10]. The smooth surfaces also have fewer places

for pit nucleation and can quickly form a passive

film [7]. Rough surfaces also limiting diffusion out

of the grooves or forming pits and also are able to

trap the corrosive ions and the corrosion products,

allowing for more pitting to occur on the semi-

polished samples [10, 11, 20]. In the fitting

method, a combination of randomize followed by

Levenberg-Marquardt fitting, was used [33].

Based on equivalent circuit model in Figure 5, the

plots are best fitted and the fitting results are

shown in Fig.8. as solid lines passing through the

testing results.

There is a good agreement between experimental

and fitted impedance spectra as well as a good

correlation between the corrosion rate and 𝑅ct values.

In the case of the patterned sample, according to

the author’s work, the retention of the passive

oxide layer inside the holes doesn’t let the fluid

reach the bottom of the patterned hole. It has

been resulted in less contact area between

solution and the substrate and consequently will

result in smaller corrosion rate of the patterned

sample [24].

Table 3: values of the equivalent elements

Sample Rs

(Ω)

Rct

(Ω)

CPE

(Ω -1

cm -2

S n )

G60 7.99 1664.2 5.58E-05 0.898

G180 9.21 3514.7 3.76E-05 0.922

G320 8.56 3764 4.51E-05 0.920

G800 8.68 4463.1 4.57E-05 0.920

D10L20 8.98 4733.5 4.52E-05 0.922

Figure 7: Bode phase plots for nickel for different surface roughness

Figure 8: Fitted curve for the selected equivalent circuit

CONCLUSIONS:

The effect of different roughness created on

nickel surface was investigated through EIS, Tafel

extrapolation method, roughness measurement

and SEM. A smoother surface in the case of the

unidirectional rough surfaces will result in lower

corrosion rate of nickel samples. So, samples with

lower roughness act as better barrier to

penetration of the aggressive electrolyte to the

metal substrate. This is mainly due to the fact that

nickel forms a stable passive layer/film which

significantly reduces further mass loss(corrosion).

The introduction of the unidirectional roughness

effectively increased the area of the contact

surface between the electrolyte and the metal

surface, which in turn led to increase of the

corrosion rate. In contrast, in the patterned

surface has the highest roughness but showed the

smallest corrosion rate compared to the

unidirectional roughness samples. This result was

consistently repeated in the roughness

measurements, EIS analysis, potentiodynamic

polarization tests and SEM images. The clear

conclusion based on these results is that the

corrosion mechanism governing the

electrochemical process in the patterned surface

and the unidirectional surface roughness are

different. The most likely explanation of the

superior performance of the patterned surface is

the formation of heterogeneous wetting interface

(trapped air pockets within the surface holes),

which significantly reduced the electrolyte/metal

surface area and the corresponding corrosion rate

[25]. REFERENCES

[1] Kear, G., Barker, B. D., Stokes, K., and Walsh, F. C.,

2004, "Flow influenced electrochemical corrosion of nickel

aluminium bronze - Part II. Anodic polarisation and

derivation of the mixed potential," Journal of Applied

Electrochemistry, 34(12), pp. 1241-1248.

[2] Sato, N., and Okamoto, G., 1981, Comprehensive

Treatise of Electrochemistry, Plenum Publishers, New

York.

[3] Singh, R. N., and Singh, V. B., 1993, "Corrosion

behavior and inhibitive effects of organotin compounds on

nickel in formic acid," Corrosion, 49(7), pp. 569-575.

[4] Barbosa, M. R., Real, S. G., Vilche, J. R., and Arvia, A.

J., 1988, "Comparative Potentiodynamic Study of Nickel

in Still and Stirred Sulfuric Acid‐ Potassium Sulfate

Solutions in the 0.4–5.7 pH Range," Journal of the

Electrochemical Society, 135(5), pp. 1077-1085.

[5] Keddam, M., Takenouti, H., and Yu, N., 1985,

"Transpassive Dissolution of Ni in Acidic Sulfate Media: A

Kinetic Model," Journal of The Electrochemical Society,

132(11), pp. 2561-2566.

[6] Macdougall, B., 1979, "Effect of Chloride Ion on the

Localized Breakdown of Nickel Oxide Films," Journal of

The Electrochemical Society, 126(6), pp. 919-925.

[7] Alvarez, R. B., Martin, H. J., Horstemeyer, M. F.,

Chandler, M. Q., Williams, N., Wang, P. T., and Ruiz, A.,

2010, "Corrosion relationships as a function of time and

surface roughness on a structural AE44 magnesium

alloy," Corrosion Science, 52(5), pp. 1635-1648.

[8] Hilbert, L. R., Bagge-Ravn, D., Kold, J., and Gram, L.,

2003, "Influence of surface roughness of stainless steel

on microbial adhesion and corrosion resistance,"

International Biodeterioration & Biodegradation, 52(3), pp.

175-185.

[9] Walter, R., and Kannan, M. B., 2011, "Influence of

surface roughness on the corrosion behaviour of

magnesium alloy," Materials & Design, 32(4), pp. 2350-

2354.

[10] Hong, T., and Nagumo, M., 1997, "Effect of surface

roughness on early stages of pitting corrosion of Type

301 stainless steel," Corrosion Science, 39(9), pp. 1665-

1672.

[11] Zuo, Y., Wang, H., and Xiong, J., 2002, "The aspect

ratio of surface grooves and metastable pitting of

stainless steel," Corrosion Science, 44(1), pp. 25-35.

[12] Li, W., and Li, D. Y., 2006, "Influence of surface

morphology on corrosion and electronic behavior," Acta

Materialia, 54(2), pp. 445-452.

[13] Cabrini, M., Cigada, A., Rondell, G., and Vicentini, B.,

1997, "Effect of different surface finishing and of

hydroxyapatite coatings on passive and corrosion current

of Ti6Al4V alloy in simulated physiological solution,"

Biomaterials, 18(11), pp. 783-787.

[14] Abosrra, L., Ashour, A. F., Mitchell, S. C., and

Youseffi, M., "Corrosion of Mild Steel and 316L Austenitic

Stainless Steel with Different Surface Roughness in

Sodium Chloride Saline Solutions," WIT Transactions on

Engineering Sciences, pp. 161-172.

[15] Burstein, G., and Pistorius, P., 1995, "Surface

Roughness and the Metastable Pitting of Stainless Steel

in Chloride Solutions," Corrosion, 15(5), pp. 380-385.

[16] Burstein, G., and Vines, S., 2001, "Repetitive

Nucleation of Corrosion Pits on Stainless Steel and the

Effects of Surface Roughness," Journal of The

Electrochemical Society, 148(12), pp. 504-516.

[17] Sharland, S. M., 1987, "A review of the theoretical

modelling of crevice and pitting corrosion," Corrosion

Science, 27(3), pp. 289-323.

[18] Lee, S. M., Lee, W. G., Kim, Y. H., and Jang, H.,

2012, "Surface roughness and the corrosion resistance of

21Cr ferritic stainless steel," Corrosion Science, 63(0), pp.

404-409.

[19] Sasaki, K., and Burstein, G. T., 1996, "The

generation of surface roughness during slurry erosion-

corrosion and its effect on the pitting potential," Corrosion

Science, 38(12), pp. 2111-2120.

[20] Suter, T., Müller, Y., Schmutz, P., and von

Trzebiatowski, O., 2005, "Microelectrochemical Studies of

Pit Initiation on High Purity and Ultra High Purity

Aluminum," Advanced Engineering Materials, 7(5), pp.

339–348.

[21] Toloei, A. S., Stoilov, V., and Northwood, D. O., 2013,

"The Effect of Different Surface Topographies on the

Corrosion Behaviour of Nickel," WIT Transactions on

Engineering Science, 77, pp. 193-204.

[22] Ponthiaux, P., Wenger, F., Drees, D., and Celis, J. P.,

2004, "Electrochemical techniques for studying

tribocorrosion processes," Wear, 256(5), pp. 459-468.

[23] Rammelt, U., and Reinhard, G., 1990, "On the

applicability of a constant phase element (CPE) to the

estimation of roughness of solid metal electrodes,"

Electrochimica Acta, 35(6), pp. 1045-1049.

[24] Toloei, A., Stoilov, V., and Northwood, D. O., 2012,

"The Effect of Creating Different Size Surface Patterns on

Corrosion Properties of Nickel," ASME International

Mechanical Engineering Congress & Exposition

(IMECE2012)Houston, USA, IMECE2012-89407.

[25] Bigdeli Karimi, M., Stoilov, V., and Northwood, D. O.

2011, "Improving Corrosion Performance by Surface

Patterning," WIT Transactions on Engineering Sciences,

72, pp. 85-93.

[26] Abd-El-Nabey, B. A., Abdel-Gaber, A. M., Said Ali, M.

E., Khamis, E., and El-Housseiny, S., 2012, "Cannabis

Plant Extract as Inhibitor for the Corrosion of Nickel in 0.5

M H2SO4," International Journal of Electrochemical

Science, 7, pp. 11811 - 11826.

[27] Gonçalves, R. S., Azambuja, D. S., and Serpa Lucho,

A. M., 2002, "Electrochemical studies of propargyl alcohol

as corrosion inhibitor for nickel, copper, and copper/nickel

(55/45) alloy," Corrosion Science, 44(3), pp. 467-479.

[28] Hamed, E., Abd El-Rehim, S. S., El-Shahat, M. F.,

and Shaltot, A. M., 2012, "Corrosion inhibition of nickel in

H2SO4 solution by alanine," Materials Science and

Engineering: B, 177(5), pp. 441-448.

[29] Hermas, A. A., and Morad, M. S., 2008, "A

comparative study on the corrosion behaviour of 304

austenitic stainless steel in sulfamic and sulfuric acid

solutions," Corrosion Science, 50(9), pp. 2710-2717.

[30] Morad, M. S., 2000, "An electrochemical study on the

inhibiting action of some organic phosphonium

compounds on the corrosion of mild steel in aerated acid

solutions," Corrosion Science, 42(8), pp. 1307-1326.

[31] Chen, Y., and Jepson, W. P., 1999, "EIS

measurement for corrosion monitoring under multiphase

flow conditions," Electrochimica Acta, 44(24), pp. 4453-

4464.

[32] Bentiss, F., Lagrenee, M., Traisnel, M., and Hornez,

J. C., 1999, "The corrosion inhibition of mild steel in acidic

media by a new triazole derivative," Corrosion Science,

41(4), pp. 789-803.

[33] Nocedal, J., and Wright, S. J., 1999, Numerical

Optimization, Springer, USA.

View publication statsView publication stats

https://www.researchgate.net/publication/267596825

Int. J. Electrochem. Sci., 10 (2015) 5222 - 5237

International Journal of

ELECTROCHEMICAL SCIENCE

www.electrochemsci.org

Corrosion Prevention by Applied Coatings on Aluminum Alloys

in Corrosive Environments

Jingyi Yue, Yan Cao *

Institute for Combustion Science and Environmental Technology, Department of Chemistry, Western

Kentucky University, Bowling Green, KY 42101, USA

Phone number: (270) 779-0202 * E-mail: [email protected]

Received: 25 February 2015 / Accepted: 28 March 2015 / Published: 27 May 2015

In this study, the corrosion resistance of selected aluminum alloys with various combinations of

commercial coatings was investigated using the Tafel electrochemical method in water and simulated

salt water environments. The microtopography of the surfaces of the metals and applied coatings was

tested using atomic force microscopy (AFM) and optical microscopy (OM) analysis. The combination

of an environmentally friendly electrodeposited ceramic coating with a primer and topcoat, which

results in a chromium-free coating, exhibited a higher polarization resistance and a lower corrosion

rate than the traditional chromate conversion coating combination. Coating defects and pores, which

were revealed by the AFM images, were demonstrated to contribute to higher corrosion rates.

Keywords: Corrosion; Aluminum alloy; Coating; Tafel; AFM.

1. INTRODUCTION

Aluminum alloys are widely used in the chemical, aerospace, food, electronics and marine

industries due to their low price, low density and great strength. However, the application of aluminum

alloys is restricted by their high chemical activity and potentially poor corrosion resistance. Although

the formation of an oxide layer increases the corrosion resistance of the alloy, this layer is easily

eroded. This erosion can be attributed to defects in the oxide layers. Defects are more likely to be

exposed to the atmosphere and suffer attacks from chloride ions, leading to more serious corrosion

cracks [1]. Corrosion prevention for aluminum alloys has long been an important research area for

maintaining the use of this very abundant and easily machined element. Sea water is considered one of

the most corrosive natural environments, as it contains the highly corrosive chloride ion. The majority

http://www.electrochemsci.org/

mailto:[email protected]

Int. J. Electrochem. Sci., Vol. 10, 2015

5223

of corrosion protection studies focused on useful and economical coating methods [2-4]. Organic or

inorganic barrier layers are generally applied to effectively control the corrosion rates of applied

aluminum alloys, thus avoiding the occurrence of the cathode reaction [5]. Traditionally, corrosion

prevention coatings have been classified into three types, including chromium conversion coatings,

primers, and topcoats. The chromates are regarded as highly effective and widely used corrosion

inhibitors, especially for aluminum and its alloys in aerospace applications. The chromate conversion

coating is reported to contain primarily Cr 6+

, which is capable of repairing imperfections and defects in

the coating [6-9]. Therefore, the chromate conversion coating is considered to be a more effective

coating for corrosion protection. However, these traditional coatings may consist of metals, such as

chromium and zinc, which are harmful for health during the ablation process in corrosive

environments and which also increase the manufacturing costs [10]. Taking environmental and

economic issues into consideration, a large number of studies concentrated on new coatings to avoid

the use of chromates [11-14]. This work aimed to investigate and compare the corrosion performance

of environmental electrodeposited ceramic coatings, which are chromium-free, and traditional toxic

conversion coatings. The corrosion rates of the coated aluminum alloys were determined using an

accurate electrochemical method based on the ASTM standard method under different simulated

corrosive environments.

2. EXPERIMENTAL

2.1 Coating materials

Materials:

The coated samples were made of aluminum alloys (AA5086), of which the composition is

listed in Table 1.

Table 1. Composition of aluminum alloys (wt%)

Element Si Fe Cu Mn Mg Cr Zn

Wt% 0.4 0.5 0.1 0.2 3.5 0.05 0.25

Table 2. Detailed description of commercial coating samples

Coating Description Thickness

(Min)

Thickness

(Max)

Comment

None Aluminum Alloy N/A N/A AA5086

Chromate Lyfanite (ALODINE® 713) 30 mg/ft² 90 mg/ft² Conversion coating

E-coating Electrodeposition Coating 0.0005 inch 0.0009 inch Cationic Epoxy Electrocoat

Primer Primer 0.0015 inch 0.003 inch Strontium Chromate Epoxy Primer

Topcoat Topcoat 0.0012 inch 0.0014 inch High Solids Acrylic Bake Enamel

EC² Alodine® EC 0.0002 inch 0.0003 inch Micron ceramic coating

(chromium-free)

Int. J. Electrochem. Sci., Vol. 10, 2015

5224

The protection system consists of two categories of coatings, including a chromate conversion

coating (trade name Alodine 713) and a micron ceramic coating (Alodine ECC 9000), as well as a

cationic epoxy coating, a strontium chromate epoxy primer and a high solids acrylic bake enamel, as

listed in Table 2. Specifically, the aluminum alloys (AA5086) were coated with chromate, epoxy

coating, primers, and topcoat for the Category 1 samples and with ceramic coating, primer and topcoat

for the Category 2 samples. The specific coatings applied in this study are shown in Table 3.

Table 3. Coatings applied to the tested samples

Sample

code

Testing in water Sample Testing in simulated sea water

A Aluminum only I Aluminum only

B Chromate J Chromate

C Chromate + Epoxy K Chromate + Epoxy

D Chromate + Epoxy + Primer L Chromate + Epoxy + Primer

E Chromate + Epoxy + Primer + Topcoat M Chromate + Epoxy + Primer + Topcoat

F Ceramic N Ceramic

G Ceramic + Primer O Ceramic + Primer

H Ceramic + Primer + Topcoat P Ceramic + Primer + Topcoat

The pre-treatment of the specimens included two processes. First, the specimens were

mechanically polished with 200 mm SiC paper. Second, the specimens were treated with a chemical

cleaning and degreasing process to keep the specimens free from grease, oil and contamination. The

specimens were continuously treated using a phosphoric acid-based detergent acid at 46 o C for 10

minutes and then treated with 50 g/l of NaOH at 52 o C for 5 minutes. Finally, the specimens were

treated with Alodine 713 (chromate) or Alodine ECC 9000 (ceramic). The chromate coating was

applied using the immersion process at 65 o C for 5 minutes, and the samples were then dried in an

oven at 90 o C for 3 minutes. The ceramic coating was applied via an immersion process at 49

o C for 3

minutes, and the samples were then dried in an oven at 60 o C for 3 minutes. The chromate-coated

specimen then received an epoxy coating via the cationic electrodeposition method (Powercorn 590-

534), with a baking temperature of 190 o C for 20 minutes. The epoxy coating was applied using the

spraying method for 15 minutes and baked at 65 o C for 30 minutes, and full curing required up to 7

days without heating. The topcoat (i.e., the acrylic-based polyurethane coating) was also applied using

the spray method for 15 minutes and was cured by baking at 80 o C for 30 minutes.

The coated aluminum alloy plates (AA5086) were cut into a round shape with a section area of

2 cm 2 using a diamond saw. Both categories of samples were tested in deionized (DI) water and

simulated salt water. Samples A to H were tested in DI water electrolyte, and samples I-P were tested

in salt water electrolyte.

Int. J. Electrochem. Sci., Vol. 10, 2015

5225

2.2 Corrosion Testing (Potentiodynamic Polarization)

The corrosion resistance of the coatings was tested using a three-electrode system connected to

the electrochemical workstation Model CHI660 E, as shown in Figure 1 on the right. The samples

were loaded onto a U-tube corrosion chamber setup, which is shown in Figure 1 on the left.

Potentiodynamic polarization resistance measurement was based on ASTM Standard G59. Corrosion

resistance was estimated from the polarization curve that was generated using the Tafel technique.

Figure 1. U-tube chamber (left) and electrochemical workstation (right)

Table 4. Composition of simulated salt water

Components Wt % Solution Concentration (g/l)

NaCl 58.490 24.530

MgCl2·6H2O 26.460 5.200

Na2SO4 9.750 4.090

CaCl2 2.765 1.160

KCl 1.645 0.695

NaHCO3 0.477 0.201

KBr 0.238 0.101

H3BO3 0.071 0.027

SrCl2·6H2O 0.095 0.025

NaF 0.007 0.003

The sample was located in the center of the U-tube chamber, with the coated bottom side of the

loaded sample in contact with the selected electrolyte (i.e., either DI water or salt water in this study)

and the uncoated upper side of the sample connected to the working electrode. Prior to being loaded

onto the U-tube chamber, the sample was sequentially wet polished on the uncoated side using 240 grit

and 600 grit SiC paper. The sample was then degreased using acetone and rinsed using distilled water.

The counter electrode and reference electrode and the delivery of the purging gas are installed through

Int. J. Electrochem. Sci., Vol. 10, 2015

5226

another opening of the U-tube chamber. The counter and reference electrodes were a platinum strip

with a diameter of 0.3 mm and a saturated calomel electrode, respectively. The working area of the

working electrode was 2 cm 2 . The testing temperature was maintained at ambient temperature (25

o C).

The composition of the simulated salt water is listed in Table 4. The test cell was purged using

nitrogen, with a flow rate of 150 cm 3 /min. The purging started at least 30 minutes prior to sample

loading and was maintained throughout the test. The polarization measurements were carried out at a

scan rate of 1 mV/s, with a potential range from -300 mV to -900 mV.

2.3 Corrosion rate calculation

The corrosion potentials (Ecorr), anodic and cathodic Tafel slopes (ba and bc), and corrosion

current density (Icorr) could be determined using polarization curves obtained from the CHI 660E

software. The polarization resistance (Rp) of the corrosion process can be calculated according to Eq 1,

as follows:

Eq 1

The corrosion rate can be further determined according to Eq 2:

Eq 2

Where K=3.27×10 -3

mm g/μA cm yr, the equivalent weight Ew = 9.09 for the specific

aluminum alloy, and ρ = 2.66 g/cm 3 for the specific aluminum alloy.

2.4. Atomic Force Microscopy and Optical Microscopy Images

The microtopography of specific samples was identified using an Olympus BX60M confocal

optical microscope (OM). A Multimode Atomic Force Microscope (AFM) 5500 from Agilent was

used in contact mode under ambient conditions to characterize the coated samples. Silicon AFM

probes with an aluminum reflex coating were used in contact mode and purchased from TED PELLA,

INC. The radius of the probes was 30 nm, with a constant force of 0.2 N/m and a resonant frequency of

13 kHz.

3. RESULTS

3.1 Corrosion test

The polarization curves of the two categories of coated aluminum alloy samples and untreated

aluminum alloy samples are shown in Figure 2 and Figure 3. A summary of the results of the

polarization tests is shown in Table 5.

Int. J. Electrochem. Sci., Vol. 10, 2015

5227

Table 5. Parameters of the potentiodynamic polarization curves for samples with different coatings

Sample A C E F G H

Ecorr vs SCE/V -0.67 -0.61 -0.60 -0.65 -0.59 -0.58

ba (mV/dec) 489.6 485.5 427.8 497.6 485.5 474.9

bc (mV/dec) 542.5 506.3 588.9 514.8 505.8 546.8

icorr (μA cm -2

) 0.069 0.015 0.014 0.048 0.009 0.0056

Rp (kΩ) 1616.275 7207.5 7905.5 2284.4 11874.7 19631.6

Figure 2 shows the corrosion resistance of the samples coated with the Category 1 chromate

and epoxy coating series. Sample C, which was coated with chromate and an epoxy coating, possessed

a lower corrosion current density (0.015 μA cm -2

) than the uncoated sample A (0.069 μA cm -2

). In

addition, the corrosion potential of sample C revealed a shift towards a more positive value, which was

approximately 0.06 V higher than that of sample A. This result can be attributed to the chromate and

epoxy coating on sample C, which can effectively prevent the corrosion of aluminum alloys and thus

increase corrosion resistance. Sample E, which was coated with a primer and topcoat in addition to the

coating described for sample C, exhibited a slightly lower corrosion current density (0.014 μA cm -2

)

and a more positive shift in the corrosion potential in comparison to sample C (-0.6 V). The corrosion

resistance of sample E was further increased due to the application of two more coatings in comparison

to sample C. Furthermore, the polarization resistance of sample E was increased to 7905.5 kΩ, which

was much higher than the values obtained for samples A and C, which were 1616.3 kΩ and 7207.5 kΩ,

respectively.

Figure 2. Potentiodynamic polarization curves of samples A, C and E in DI water

Figure 3 plots the polarization curves of the Category 2 samples, which possessed a ceramic

coating, primer and topcoat. Sample F was coated with ceramic, which is chromium-free and

considered to be an environmental coating. This sample exhibited a corrosion current density and a

Int. J. Electrochem. Sci., Vol. 10, 2015

5228

corrosion potential of 0.048 μA cm -2

and -0.65 V, respectively. Both of these values proved that the

corrosion resistance of sample F with the ceramic coating was slightly but not significantly better than

that of the uncoated sample A (0.069 μA cm -2

and -0.67 V, respectively). Sample G, which had an

additional primer coating on top of the ceramic coating described for sample F, exhibited significantly

improved corrosion resistance performance based on a significantly reduced corrosion current density

of 0.009 μA cm -2

and a large positive shift in corrosion potential to -0.59 V, as well as a significantly

increased polarization resistance of 11874.7 kΩ. This significant change in corrosion resistance (i.e.,

increased corrosion potential and decreased corrosion current density) may have occurred because the

effective combination of the ceramic coating and primer provided coverage that can significantly

reduce defects and limit corrosion attack. The corrosion resistance performance of sample H was only

slightly enhanced by the addition of one more topcoat onto sample G. The corrosion current density,

the corrosion potential and the polarization resistance of sample H were 0.0056 μA cm -2

, -0.58V and

19631.6 kΩ, respectively. These values were similar to those of sample G.

Figure 3. Potentiodynamic polarization curves of samples A, F, G and H in DI water

Figure 4 shows that the corrosion rates of commercial coatings on aluminum alloys in different

electrolytes varied, with an order of magnitude from 10 -6

to 10 -4

mpy. The corrosion rates of samples

A-E were tested in pure water. Sample E, which was coated with four layers, including chromate,

epoxy coating, primer, and topcoat, exhibited the lowest corrosion rate, with an order of magnitude of

10 -6

mpy. The bare aluminum alloy (sample A) had the highest corrosion rate, on the order of 10 -4

mpy. The reduction of the corrosion rate was largest between samples A (bare aluminum) and B

(coated with chromate oxide film), indicating that the chromate oxide film was very effective for

corrosion resistance. This resistance could be attributed to the fact that the rough surface of the bare

aluminum had many imperfections, rubs and scratches, which were healed when the chromate oxide

Int. J. Electrochem. Sci., Vol. 10, 2015

5229

film was applied. This finding is in accordance with the unique self-healing ability and electrochemical

protection of chromate oxide [15, 16]. Sample C had an additional epoxy coating in comparison to

sample B and exhibited a corrosion rate one order of magnitude lower than that of sample B. This

difference occurred because the coating on sample C provided better coverage for a continuous

reduction in the surface roughness, leading to improved corrosion resistance. However, no appreciable

difference in corrosion rates was observed between sample D (with one more primer coating than

Sample C) and sample E (with one more top coating than sample D). The corrosion rates of these

samples were 3.04E -5

and 3.01E -5

mm/y, respectively. Corrosion tests of samples I-M were conducted

in simulated salt water. For all of the samples, the corrosion rates in salt water were significantly

different than those obtained in DI water. The corrosion resistance of the samples was significantly

weaker in the salt water condition. This difference may be attributed to the high concentration of

chloride ions in the salt water, which increased the electric conductivity and resulted in a high

corrosion rate [17]. Sample I, which had no coatings, exhibited the highest corrosion rate of 0.01

mm/y.

Figure 4. Corrosion rates of Category 1 samples tested in salt water and DI water

From Figure 5, it was noted that sample N, which was coated with the ceramic coating,

exhibited a corrosion rate of 0.0016 mm/y in salt water; this value was ten times lower than that of the

original sample I (bare aluminum alloy). Correspondingly, the corrosion rate of sample F (9.69E -05

mm/y), which had the same ceramic coating, in DI water was three times lower than that of sample A.

Samples O and G have the same coatings (i.e., the ceramic coating plus primer), but these two samples

exhibited a large difference in corrosion resistance between salt water and DI water due to the

existence of chloride ions. The corrosion rates of samples O and G were 2.85E -04

and 2.16E -05

mm/y,

respectively. The primer coating was more effective for protecting against corrosion, especially in salt

Int. J. Electrochem. Sci., Vol. 10, 2015

5230

water. Both samples P and H were coated with one more layer of top coating than samples O and G;

the corrosion rates of these two samples were 1.39E -04

and 1.12E -05

mm/y, respectively, which were

nearly one times lower than those of samples O and G. This result revealed that the application of top

coatings could further reduce corrosion rates.

Figure 5. Corrosion rates of Category 2 samples in salt water and DI water

Based on Figure 6, the coating combination of the ceramic coating, primer and topcoat

significantly reduced the corrosion rate in comparison to the coating combination of chromate coating,

epoxy coating, primer and topcoat. Specifically, the corrosion rates of samples P and H, which had the

same coating combination in the ceramic series, in simulated salt water and pure water were 1.39E -04

and 1.12E -05

mm/y, respectively. These two corrosion rates were nearly two times lower than those of

the coating combination of chromate and epoxy (i.e., samples M and E), which had corrosion rates of

2.7E -04

and 3.02E -05

mm/y, respectively. Therefore, the chromium-free environmental ceramic coating

appeared to have better corrosion resistance than the chromate and epoxy coating. The excellent

corrosion resistance of the ceramic coating series can be attributed to the superior adhesion of ceramic

and to the effective combination of the ceramic with the strontium chromate primer. The primer has a

strong anti-corrosion capability when the aluminum is coated with another material that is porous or

can provide excellent adhesion [18]. Ceramic served as a better base for the primer than the chromate

and epoxy coating. The unique porous surface of the ceramic coating on aluminum was revealed by the

AFM images, as shown in Figure 11a.

Int. J. Electrochem. Sci., Vol. 10, 2015

5231

Figure 6. Comparison of the corrosion rates of specific samples in salt water and DI water

4. DISCUSSION

The cathodic reaction for aluminum alloys in pure water or saline electrolyte solution has been

proved to be the reduction of oxygen, as follows [19]:

2H2O + O2 + 4e - → 4OH

- Eq. 3

The anodic reaction for aluminum alloys occurs as the following reaction:

Al → Al 3+

+ 3e -

Eq. 4

Al 3+

+ 3OH - → Al(OH)3 Eq. 5

2Al + 6OH

- → Al2O3 + 3H2O + 6e

- Eq. 6

The corrosion of uncoated bare aluminum alloys, especially in the saline electrolyte solution, is

much more severe than that of the coated metal. The existence of chloride ions increases the corrosion

process by dissolving the Al and forming aluminum oxide on the surface [20]. For coated samples, the

anodic reactions (shown in Eq.4, Eq.5 and Eq.6) were significantly restricted due to the mass-transfer

barrier effect of the coatings. Therefore, the corrosion rate of the coated samples was significantly

reduced in comparison to the bare metal. The coating layers function as barrier films to slow the

transport of ions from the outer environment toward the bare metal. Increasing the coating layers

improves the corrosion resistance of the bare metal, although the corrosion cannot be fully eliminated.

Further studies that used AFM revealed the formation or the existence of pores during the coating

process; the pores could be eliminated by increasing the coating layers. This result is presented and

discussed in detail later.

Sketches and corrosion resistance schematics of the Category 2 coatings that were applied to

the aluminum alloys are shown in Figure 7. The first coating was applied via micron ceramic coating.

The formation of the porous structure of this layer during the coating process is of interest. The second

Int. J. Electrochem. Sci., Vol. 10, 2015

5232

coating was an epoxy primer, which significantly reduced the porous surface. Because the distribution

of pores is irregular, the positions of the pores in each of the two layers are not exactly matched [21].

The top layer is generally less porous to restrict the mass transfer of ions. The application of multiple

coats forms a special structure that improves the anti-corrosion capabilities of the underlying bare

metal. However, this process cannot completely avoid electrolyte ion transport through the coating.

Figure 7. Sketches of the pore distributions of coatings on the aluminum alloys in the context of

polarization resistance

The polarization resistance, which was obtained from polarization curves, can be used to

investigate the influence of functional coatings on corrosion and to determine the resistance

capabilities of anti-corrosion coatings. The incremental percentage of polarization resistance achieved

with various coatings can be expressed by the following equation:

where θ indicates the increment of polarization resistance. Rp’ and Rp represent the

polarization resistance of the coated sample and uncoated sample, respectively.

Figure 8. The increment of polarization resistance values for the Category 1 coating that was applied

to aluminum in salt and pure water.

Int. J. Electrochem. Sci., Vol. 10, 2015

5233

The polarization resistance values of the Category 1 coated samples in water are shown in

Figure 8. The polarization resistance of the chromate-coated sample was only increased by 30%,

although the chromate coating exhibits a good adhesion capability and is thus always used as the first

and required base for the next coat. However, this coating is less likely to have good coverage on the

bare aluminum alloy. The second epoxy coating was applied over the chromate coating and exhibited a

77% increment of Rp. The defects and roughness of the chromate coating were significantly improved

by this second layer. The high increment of Rp also indicates that the less porous epoxy coating tends

to be a more effective barrier for preventing electrolyte ion transport. However, in terms of commercial

application, the epoxy coating is typically coated with one more topcoat because the epoxy coating is

vulnerable and degradable under ultraviolet light [19, 22]. Thus, the specimen with the primer and

topcoat exhibited no significant differences in Rp in this study.

The Category 1 coated samples tested in salt water are shown in Figure 8. Notably, the

chromate-coated sample exhibits a large percentage increase in Rp. The chromate conversion coating

was much more efficient as a resistant barrier in the salt water environment than in water. The

chromate, which is retained in the conversion coating, is the king of soluble, oxidizing, and high-

valence ions (in CrO4 2-

or Cr2O7 2-

) [9]. The protective layer is formed when the ion is converted to an

insoluble and low-valence form (Cr2O3 or Cr(OH)3) [23]. The reduction reaction of this process is as

follows:

Cr2O7 2-

+ 8H + + 6e

- → 2Cr(OH)3 + H2O Eq. 7

The existence of Cl - would accelerate the chromate reduction, in which the reduction products

serve as inhibitors [15]. This effect was observed in previous studies, as the Cr(VI) content of the

coating decreased and the content of Cr(III) increased when the coating was exposed to NaCl or salt

water [9, 24]. The serious localized pin corrosion of bare aluminum can be significantly reduced by the

reduction of chromate. Similarly, this study demonstrated that the chromate coating significantly

reduced the corrosion rate in salt water in comparison to the bare metal.

Figure 9. The increment of polarization resistance values of the Category 2 coating that was applied to

aluminum in salt and pure water.

The polarization resistance values of the Category 2 coatings in water are shown in Figure 9.

The ceramic coating only increased the Rp value by 29.24%. The principal property of the ceramic

Int. J. Electrochem. Sci., Vol. 10, 2015

5234

coating is its excellent adhesion capability, despite its porous surface. The porous surface generates a

weaker barrier for restricting the transportation of electrolyte ions, leading to a lower Rp. However, the

good adhesion properties of this layer enable the primer coating to be applied tightly. As expected, the

Rp value of the primer coating increased by 86.38% in comparison to the bare metal specimen. The

outermost coating (i.e., the topcoat) serves as a seal and decoration and contributes a small increment

of Rp. Figure 9 shows the same coating system tested in salt water. Similar to the results obtained for

the Category 1 coating, the Rp values of the ceramic coating were increased by 88.81% in salt water.

This result demonstrated the necessity and importance of the ceramic coating, in addition to the primer

and topcoat, in the salt water environment. The environmental benefits of using the ceramic coating

were apparent in comparison to the chromate-based coating. As expected, the combined primer and

topcoat only resulted in a limited improvement in Rp (99.55%) in the salty water environment.

However, the effectiveness of these coats for improving the Rp was still desired to nearly stop the

transportation of electrolyte ions and subsequent corrosion.

The microtopography of different samples has a significant impact on the corrosion

performance of the samples. Typical samples, which were tested using AFM and OM analysis, are

shown in Figure 10 and Figure 11. The same scale was applied to the images of two different samples

using the same magnification method. The maximum resolution of the images using OM is

approximately 500 um based on the confocal optical technology; in comparison, AFM can achieve a

much higher resolution of below 1 um (10-100 nm), depending on the scan time and the diameter of

the AFM tips. Images (a) and (b) were obtained using OM for samples A and C, respectively, and

images (c) and (d) were obtained using AFM for samples A and C, respectively.

Figure 10. OM and AFM images of sample A (bare aluminum alloy) and sample C (coated with

chromate and epoxy coating)

Int. J. Electrochem. Sci., Vol. 10, 2015

5235

A comparison of the AFM images and the OM images provides a good example of how more

detailed local information can be obtained by using AFM to explore the microtopography,

homogeneity and defects of applied coatings. The images of sample A that were obtained using both

AFM (Figure 10c) and OM (Figure 10a) clearly revealed the existence of rougher surfaces on sample

A than on sample C (Figure 10b and Figure 10d), which had the applied coatings. For rougher

surfaces, the specific surface area was larger, leading to the acceleration of the corrosion reaction

kinetics. This effect partially contributed to the higher corrosion rates that were observed for sample A

than for sample C, consistent with the aforementioned corrosion rates of sample A and sample C.

Further investigations of the obtained sample images indicated that the coating on sample C had a

good coverage over the whole surface in the investigated area, indicating an acceptable homogeneity

of the coating application. Furthermore, no defects were detected on the surface of sample C on a

nanometer scale, although a few spots were identified that were more or less thick than other parts of

the surface.

Figure 11. OM images of (a, b) samples F (coated with ceramic) and G (coated with ceramic and

primer), and AFM images (c, d) of samples H (coated with ceramic, primer and topcoat) and M

(coated with chromate, epoxy, primer and topcoat).

Figure 11 shows OM images typical of samples F and G and AFM images typical of samples H

and M. Sample F, which had a ceramic coating, exhibited porous surfaces with a pore diameter near 20

um (shown in Figure 11a). This porous topography was beneficial and appropriate for the adherence of

new coatings [25]. That finding was consistent with the former result concerning the good corrosion

resistance of sample G, which has an additional primer coating on this primary porous surface. The

Int. J. Electrochem. Sci., Vol. 10, 2015

5236

porous surface promoted good deposition of the primer. The newly formed coverage eliminated

surface roughness and covered surface defects, leading to a significant reduction in the corrosion rate

in comparison to the initial coating, even though some size-reduced submicron pores can still be seen

on the surface pores (shown in Figure 11b). Figure 11c depicts sample H, which has one more topcoat

than sample G. The topography of this sample was much smoother and flatter than that of sample G,

and the corrosion rate of sample H was reduced further. This result again provided evidence that low

surface roughness provides less surface area for attack by the corrosive environment. Sample M, which

is shown in Figure 11d, possessed numerous holes on its surface, which might be caused by the coating

process. Defects in the surface provided more chances for electrolyte ions to attack the surface; thus,

the corrosion rate of sample M was slightly higher than those discussed above.

4. CONCLUSIONS

An investigation of the corrosion resistance of different combinations of coatings on aluminum

alloys was conducted. The major conclusions of this study were:

1. The corrosion resistance experiment that was conducted in simulated salt water resulted

in more serious corrosion for all of the tested samples than the experiment conducted in distilled water.

Especially for rare aluminum alloy samples, the difference in the corrosion rate between these two

electrolyte environments was significant; the corrosion rate values obtained in salt water were two

orders of magnitude higher than those obtained in distilled water.

2. The environmentally friendly coating combination (i.e., the ceramic coating, primer and

topcoat (samples P and H)) exhibited excellent corrosion resistance in comparison to the coating

combination of chromate, epoxy coating, primer and topcoat (samples M and E). The corrosion rates

of these coatings were as low as 1.39E -4

and 1.12E -5

mm/y in salt water and distilled water,

respectively. The overall polarization resistance exhibited high increments of 91.76% in the water

environment and 99.55% in the salty water environment.

3. The unique properties of the ceramic coating, which exhibited a porous surface in the

OM investigations, can provide excellent adherence for subsequent coatings. By adding new primer

coatings on the ceramic layer (sample G), the size of the pores on the surface was significantly

reduced, thus further decreasing the corrosion rate.

ACKNOWLEDGEMENTS

This work was supported by the Kentucky Energy And Environment Cabinet (KEEC) Research Funds,

under contracts of the term 2014-2015, PON2 127 1300002875, and the U.S. Department of

Agriculture (6445-12 630-003-00D).

References

1. S.-I. Pyun and W.-J. Lee, Corros. Sci., 43 (2001) 353-363

2. J. Prakash, B. Tripathi and S. K. Ghosh, Intelligent Coatings for Corrosion Control, (2014) 93

Int. J. Electrochem. Sci., Vol. 10, 2015

5237

3. D. oriso a, H. hwald and D. G. Shchukin, Acs. Appl. Mater. Inter., 4 (2012) 2931-2939

4. E. A. Esfahani, H. Salimijazi, M. A. Golozar, J. Mostaghimi and L. Pershin, J. Therm. Spray Techn.,

21 (2012) 1195-1202

5. C. Vargel, Corrosion of Aluminium, Elsevier (2004)

6. W. G. Fahrenholtz, M. J. O'Keefe, H. Zhou and J. Grant, Surf. Coat. Tech., 155 (2002) 208-213

7. H. Isaacs, K. Sasaki, C. Jeffcoate, V. Laget and R. Buchheit, J. Electrochem. Soc., 152 (2005) B441-

B447

8. M. Kendig, A. J. Davenport and H. Isaacs, Corros. Sci., 34 (1993) 41-49

9. J. Zhao, L. Xia, A. Sehgal, D. Lu, R. McCreery and G.S., Surf. Coat. Tech., 140 (2001) 51-57

10. S. Bertling, Identification of thin surface films on aluminium with FTIR spectroscopy, Report

NTIS 96(4), 1996.

11. M. E. Nanna and G. P. Bierwagen, JCT. Res., 1 (2004) 69-80

12. I. Aziz, Q. Zhang and M. Xiang, J. Rare Earth, 28 (2010) 109-116

13. R. G. Buchheit, M. Bode and G. Stoner, Corrosion, 50 (1994) 205-214

14. M. Bethencourt, F. Botana, J. Calvino, M. Marcos and M. Rodriguez-Chacon, Corros. Sci., 40

(1998) 1803-1819

15. M. Kendig and R. Buchheit, Corrosion, 59 (2003) 379-400

16. L. Xia and R. L. McCreery, J. Electrochem. Soc., 145 (1998) 3083-3089

17. H. Altun and S. Sen, Mater. Design., 25 (2004) 637-643

18. J. D. Minford, Handbook of aluminum bonding technology and data, CRC Press (1993)

19. C. Dong, H. Sheng, Y. An, X. Li, K. Xiao and Y. Cheng, Prog. Org. Coat., 67 (2010) 269-273

20. E. McCafferty, Uptake of Chloride Ions and the Pitting of Aluminum, Surface Chemistry of

Aqueous Corrosion Processes, Springer (2015) pp. 71-75

21. B. Fernandez-Perez, J. Gonzalez-Guzman, S. Gonzalez and R. Souto, Int. J. Electrochem. Sci., 9

(2014) 2067-2079

22. A. Rezig, T. Nguyen, D. Martin, L. Sung, X. Gu, J. Jasmin and J. W. Martin, J. Coat. Technol.

Res., 3 (2006) 173-184

23. S. Pommiers-Belin, J. Frayret, A. Uhart, J. Ledeuil, J.-C. Dupin, A. Castetbon and M. Potin-

Gautier, Appl. Surf. Sci., 298 (2014) 199-207

24. G. S. Frankel, DTIC Document, (2001)

25. M. Popa, C. Vasilescu, S. I. Drob, P. Osiceanu, M. Anastasescu and J. M. Calderon-Moreno, J.

Brazil. Chem. Soc., 24 (2013) 1123-1134

article distributed under the terms and conditions of the Creative Commons Attribution license

(http://creativecommons.org/licenses/by/4.0/).

http://www.electrochemsci.org/

ISSN:1369 7021 © Elsevier Ltd 2008OCTOBER 2008 | VOLUME 11 | NUMBER 1014

Corrosion-resistant metallic coatings

The epidermis–dermis–subcutaneous system is able both to resist

and repair damage and also regrow over a defect that exposes

underlying tissue. These are admirable qualities in biological

systems because these processes are repetitive, autonomous,

and can be triggered by damage without external intervention1.

In corrosion of metallic materials, dip, spray, chemically or

electrodeposited organic-based, metallic, and ceramic coatings are

often used to protect a substrate from corrosive damage2.

Natural passive films, artificially grown oxide layers (i.e. anodized

and sealed), and conversion coatings3–5 can also protect underlying

metals and alloys. Successful native passive films can form a protective

layer over many metals if the ingredients for passivation (i.e. alloying

elements) are present in high enough concentration in the underlying

alloy. The oxide quickly and automatically reforms to repair defects

in many environments. Conversion coatings and anodized layers rely

on the formation of a chemically engineered layer based both on

We describe recent computational and experimental studies on the corrosion properties of metallic coatings that can be tailored (tuned) to deliver up to three corrosion-inhibiting functions to an underlying substrate. Attributes are tuned by a selection of alloy compositions and nanostructures, ideally in alloy systems that offer flexibility of choice to optimize the corrosion-resisting properties. An amorphous Al-based coating is tuned for corrosion protection by on-demand release of ionic inhibitors to protect defects in the coating, by formation of an optimized barrier to local corrosion in Cl– containing environments, as well as by sacrificial cathodic prevention. Further progress in this field could lead to the design of the next generation of adaptive or tunable coatings that inhibit corrosion of underlying substrates.

F. Presuel-Moreno1, M. A. Jakab2, N. Tailleart3, M. Goldman4, and J. R. Scully3*

1 Florida Atlantic University, Boca Raton, FL 33431, USA,†

2 Southwest Research Institute, San Antonio, TX 78238-5166, USA†

3 Department of Materials Science and Engineering, University of Virginia, Charlottesville, VA 22904–2442, USA

4Constellation Power Company, Calvert Cliffs, MD 20657, USA†

*E-mail : [email protected]

†Formerly at MSE, University of Virginia, VA, 22904-4246, USA

MT1110p14_23.indd 14MT1110p14_23.indd 14 18/09/2008 15:32:1418/09/2008 15:32:14

mailto:[email protected]

Corrosion-resistant metallic coatings REVIEW

OCTOBER 2008 | VOLUME 11 | NUMBER 10 15

the oxidation of elements in the metal as well as on incorporation of

selected species in a pretreatment bath to reinforce the natural oxide.

Controlled additions of specific molecules to the conversion coating

bath are required and these can seldom be applied in the field.

Corrosion protection by passive films and coatings Passive films, conversion coatings, and metallic and organic coatings

confer corrosion protection via a variety of mechanisms, including

formation of barriers to the penetration of corrodants; high ionic

resistivity in surface layers to minimize electrochemical reactions

under the coating at the metal–coating interface; active corrosion

inhibition where an inhibitor is stored, released, and delivered to a

defect; and sacrificial cathodic protection. Chromate systems possess

this active corrosion inhibition property6 but are being phased out due

to their high toxicity and carcinogenicity7. Oxides may also exhibit

ion-selective permeability, as well as a desirable potential and/or pH

of zero charge to limit detrimental anion (Cl–) adsorption and ingress8.

Enhanced adhesion, control of the liquid chemistry at the metal–

coating interface and superhydrophobic properties9,10 may also operate

in many exciting new systems.

Active corrosion inhibition Traditionally, metallic coatings serve only one or two functions.

For example, Zn has excellent corrosion resistance and functions

as a sacrificial anode11. Zn galvanizing provides sacrificial cathodic

protection and acts as a barrier12 but does not usually supply inhibitor

ions. The release of Zn ions during the sacrificial protection of

galvanized steels11,13 only provides a small additional benefit compared

to galvanic protection provided by the potential driving force. Metallic

coatings used to protect Al alloys14,15 consist of a thin layer of nearly

pure Al mechanically bonded to standard precipitation age-hardened

Al alloys. The coating sacrificially cathodically protects the Al alloy

substrate (a beneficial form of galvanic corrosion) but does not provide

active corrosion inhibition. Galvanic throwing power is limited because

the roll-bonded cladding16 has a limited electrochemical driving force

for protection. The open circuit potential (OCP) of AlcladTM alloys

is only ~80–100 mV below that of the structural substrate, such as

AA 2024-T317, and their pitting potentials (Epit) are actually below

that of underlying structural Al alloys. The consequential virtual

non-polarizability enables cathodic protection of the aerospace alloy

but also ensures a high self-corrosion rate and considerable anodic

inefficiency.

Long-range corrosion protection of coating defects In the case of a coating containing active corrosion inhibitors or

passivators that are stored, released, and transported, defects such

as a scratch in the coating may be protected over long distances

(i.e. possess a chemical throwing power) due to concentration

(e.g. chemical potential) gradient-driven random transport from

inhibitor-rich regions to unprotected sites. Sacrificial cathodic

protection (i.e. galvanic throwing power) may also operate over long

distances. The distance over which protection can be afforded is

a function of the electrochemical properties of both the sacrificial

anode and the unprotected site as well as the geometry and ionic

conductivity of the ionic phase (often a thin electrolyte exposed to the

atmosphere) over the coating. The electric field in the ionic solution

established by the potential driving force difference between the

anodic and cathodic half cell potentials facilitates long-range cathodic

polarization. Such long-range functionality is superior to that of

biological systems where an internal circulatory system is required to

repair damaged sites1,18. Similarly, self-healing of mechanical damage

in man-made materials requires locally distributed microcapsules,

or encased composites containing gels or monomeric polymers and

catalysts spaced at a short distance from defects1,19–22. The monomer

cannot be easily supplied over long distances to repair damage sites.

One vision for new coatings with multiple, tunable functions Unfortunately, existing corrosion protecting metallic coatings cannot

provide active corrosion inhibitors to protect defects via transport of

the inhibitor through the liquid corrosive phase. Moreover, corrosion

properties are rarely tunable. For instance, the behavior of metallic

claddings is often fixed by rather inflexible limits on compositions and

microstructures. Therefore, there are few user-adjustable parameters

available to tune cathodic protection to mitigate certain localized

corrosion processes triggered above certain potential thresholds

(e.g. pitting, stress corrosion, exfoliation at high potentials, or H

embrittlement at very negative potentials). In addition, cathodic

protection, active chemical inhibition, as well as the presence of a local

corrosion barrier, are desired simultaneously. The addition of inhibitors

is a particular challenge for metallic materials. While sacrificial and

barrier attributes can be adjusted somewhat by changing composition

or structure, inhibitors can rarely be added to a solid. Moreover,

inhibitors, stored in the solid state, must be released as a liquid-soluble

molecular or ionic species to enable transport through the liquid

corrosive phase to a defect. In contrast, sparingly soluble inhibiting

pigments can readily be added to organic coatings and released by

chemical dissolution. An added challenge for both organic and metallic

coatings is the desire to trigger inhibitor release on-demand so that the

stored inhibitor is used only when it is needed.

We will now discuss some recent computational and experimental

studies where several corrosion-protecting functions are achieved

simultaneously in a single metallic coating. The desired properties

include active corrosion inhibitor supplied on demand to enable

corrosion inhibition and/or autonomous repair. Sacrificial anode-based

cathodic protection and barrier properties can also be tailored to

MT1110p14_23.indd 15MT1110p14_23.indd 15 18/09/2008 15:32:5018/09/2008 15:32:50

REVIEW Corrosion-resistant metallic coatings

OCTOBER 2008 | VOLUME 11 | NUMBER 1016

protect various substrates in a range of environments. Moreover, the

electric field created by the galvanic couple between the coating and

the substrate can be manipulated to augment transport of inhibitors

over large distances. To demonstrate this possibility we discuss a

specific nanoengineered, spray-applied, amorphous metallic alloy

(Fig. 1) that illustrates some of the mitigation strategies and functions

desired and achievable using a nanoengineered metallic coating such

as a corrosion-inhibiting system. The challenges and issues involved in

achieving these functions are highlighted.

Materials and fabrication of tunable amorphous metallic coatings The challenges of tailoring the properties of metallic coatings compared

to polymer-based coatings are numerous. In the case of polymers,

a micrometer- or nanometer-scale composite can be created by

mixing in the liquid state, and thus with great flexibility, a monomer,

resin, filler, solvent, etc., and a phase encapsulating the inhibitor

(e.g. strontium chromate pigment) in a slurry that is then reacted in

various ways and solidified in a rigid state below the polymer glass

transition temperature, Tg. In contrast, metallic coatings are often

applied at high temperatures and involve delivering a liquid metal via

either a hot dip or spray process. Such heating may adversely alter

the microstructure of the underlying alloy. Physical and chemical

vapor deposition, pulsed thermal spray (PTS), cold spray (CS), and

mechanical cladding are alternative methods to avoid excessive

temperatures. Numerous nonequilibrium alloying techniques may also

be employed to add beneficial alloying elements in significant enough

concentrations to have a major impact on properties. Corrosion barrier

properties can be improved by several routes. Minimizing structural

defects such as intermetallic and metalloid phases and optimization

of certain compositions in solid solution both usually significantly

improve corrosion ‘barrier’ properties. Therefore, methods to produce

supersaturated solid solutions which lack intermetallic and metalloid

phases are highly desired. By using metallic glasses, metallic elements

may be added or mixed in a soluble liquid solution with improved,

although not unlimited, flexibility, and then solidified and trapped

below Tg to achieve chemically homogeneous solid solutions. Moreover,

active corrosion inhibitors might be supplied if some of the added

alloying elements can function in this capacity. Amongst the possible

replacements for Cr(VI)23–27, transition metal (TM) and rare-earth (RE)

metal ions (Co2+, MoO4 2– and Ce3+) are possible choices to inhibit

localized corrosion of Al alloys23–25 and steels26–27. These elements

also can be alloyed to form Al-based metallic glasses. RE metal ions

may serve as inhibitors if they can be incorporated and released by

a chemical or electrochemical process. Alloying a crystalline metal

with these elements is traditionally difficult because of their limited

Fig. 1 Schematic of a structural high-strength precipitation age-hardened alloy (in this case AA 2024-T351, a Al–Cu–Mg alloy) protected against corrosion by a

system comprising a Al–Co–Ce metallic coating, an organic primer, and an organic topcoat. The corrosive environment is the layer of aqueous electrolyte on top

of the coating. The structural alloy is a polycrystalline alloy with Cu-rich coarse constituent particles labeled ‘IMC’ (for intermetallic compounds), grain boundaries

and fine nanoscale, precipitates. Several macroscopic defects are shown. They include a coating with a scratch through to this substrate alloy, and a scratch through

the organic coating. Ideally the metallic coating (a) functions as a barrier to corrosion, (b) delivers corrosion inhibitors indicated as released Ce3+ in the case of the

Al–Co–Ce coating, and (c) serves as a sacrificial anode to deliver cathodic protection (indicated by electrons, e–). Other enhancements include a graded coating

composition and mixed metallic phases potentially optimized to enhance bonding and ductility on the inner layer to serve as a barrier to corrosion on the outer

layers as well as to place the interface in compression to suppress fatigue of the substrate. Inhibitors released from the coating system can inhibit both anodic pits

(local corrosion attack) as well as strong cathodic reactions at Cu-rich IMC. Inhibitors and cathodic protection (electrons, e–) can inhibit pitting as well as more

advanced forms of attack such as intergranular corrosion. (Courtesy of King A. University of Virginia)

MT1110p14_23.indd 16MT1110p14_23.indd 16 18/09/2008 15:32:5118/09/2008 15:32:51

Corrosion-resistant metallic coatings REVIEW

OCTOBER 2008 | VOLUME 11 | NUMBER 10 17

solubility in the solid state28. This problem can be overcome by using

a glassy alloy that dissolves these alloying elements in solid solution.

Indeed, certain Al–TM and Al–refractory metal alloys29,30 can exhibit

enhanced local corrosion barrier24 and sacrificial anode-based cathodic

protection qualities31,32. The Al–RE–TM alloy series is of particular

interest because of its good glass-forming abilities33,34, high strength,

low density, and superior corrosion properties35–37.

In fact, a new amorphous Al–Co–Ce alloy system was recently

synthesized38–40 as an environmentally compliant metal coating with

multiple corrosion protection functionalities41–43. The notion of a

multifunctional metallic coating need not be restricted to Al–TM–RE

and there are likely to be many alloys that can be designed following

these general strategies. The goal was to simultaneously provide a

corrosion barrier, sacrificial anode-based cathodic protection42,44, or

prevention44 as well as active corrosion protection (e.g. contain and

deliver a supply of inhibiting cations that can be released to suppress

corrosion) to minimize corrosion at coating defects that expose the

underlying structural alloy45–47. Fig. 1 highlights this overall strategy.

Cathodic protection abilities may also be optimized by lowering the

OCP of the coating relative to the underlying substrate. For instance,

the OCP of the Al–Co–Ce alloy can be lowered as much as 750 mV

below that of AA 2024-T3 depending on the alloy composition and

solution pH41,48–50. Amorphous Al alloys also have the ability to store

beneficial alloying elements in solid solution. For instance, the selected

transition and RE metals (e.g. Ni, Fe, Co, Ce, Y, Gd) added as alloying

elements improve amorphicity in concentrations up to about 15 at.%.

Co, Ni, or Fe improve the resistance of Al to local corrosion, while

Ce3+, Y3+, and Gd3+ are good corrosion inhibitors when added as salt

in aqueous solutions40,51. The amorphous alloy can be formed over a

wide range of Co and Ce compositions, as seen in Fig. 238. The alloy’s

amorphous state is very stable.

High-velocity oxygen-fuel spray (HVOF), CS and PTS methods

are possible deposition methods to apply such coatings. PTS utilizes

high heating and large quenching rates, which allows for either

amorphous or crystalline powder feedstock material (Fig. 3) to develop

an amorphous or nanocrystalline coating on a substrate material.

The structure of the feedstock material tends to dictate the resulting

structure of the coating. The coating powder and deposited layer

are shown in Fig. 4a–d. The feedstock powder is often supplied as a

controlled particle size distribution ranging from 0.5 to 20 µm, although

larger powder sizes can be attempted (Fig. 4a). PTS is distinguished

by rapid particle acceleration and heating, a minimal residence time

within a high enthalpy environment, and rapid particle quenching

upon interaction with the target substrate52,53. The quenching rate

for particles less than 20 µm in size can be as high as 106 K/s54. Also

notable is that naturally aging precipitation age-hardened aerospace

alloys, such as the AA 2024-T3 substrates, do not exceed 60 ºC during

the coating process54. Reduced substrate thermal loading enables short

stand-off coating capability that, from an application standpoint, is

desirable because it allows for localized repairs of the coating where

a physical defect exists exposing the underlying structural alloy and

gives the capability for coating complex geometries55. The pulsed spray

stream rasters over the surface of the substrate in such a way that the

resulting spray-applied coating is actually a built-up series of layers.

PTS and HVOF coatings have the advantage of accepting the feedstock

powder for these alloys in either crystalline or amorphous forms, as the

feedstock particles can melt mid-process as long as powders are small.

The HVOF process has a large quench rate, similar to that of the PTS

Fig. 3 X-ray diffration patterns for the Al88Co10Ce2 feedstock powder, an as-

deposited PTS coating, and an amorphous Al84Co7.5Ce8.5 melt-spun ribbon

(MSR) indicating an amorphous structure in the MSR but the presence of Al

face-centered cubic nanocrystals in both the sprayed coating and powder

Fig. 2 Map of Al–Co–Ce alloy compositions that yield amorphous, amorphous/

crystalline, and crystalline nanostructures in the Al–Co–Ce alloy system

based on the at.% Co and Ce present in solid solution Al. The map shown was

produced at a high cooling rate and results may differ at different cooling

rates. The crystal structures were determined by both X-ray diffraction and

transmission electron microscopy analysis.(Reproduced with permission from.

MT1110p14_23.indd 17MT1110p14_23.indd 17 18/09/2008 15:32:5318/09/2008 15:32:53

REVIEW Corrosion-resistant metallic coatings

OCTOBER 2008 | VOLUME 11 | NUMBER 1018

process56. High-density samples with favorable corrosion properties

can be achieved57–63. The CS process utilizes the plastic deformation of

the sprayed, solid, feedstock particles on impact with the substrate to

achieve a uniform coating55. The spray event occurs below the melting

point of the spray materials, so less microstructural change and less

oxidation should occur55. Numerous metallic coatings have also been

deposited by these methods64–70.

Al–Co–Ce alloy coatings have been produced by both HVOF and

PTS with thicknesses ranging from 75 to 600 µm often with good

adhesion and low porosity. In some studies these have been compared

to melt-spun ribbon (MSR) alloys produced by the traditional method

of streaming the molten alloy on to a spinning copper wheel to enable

rapid quench rates.

Tunable barrier properties in multifunctional amorphous Al–TM–RE coatings Coatings which act as barriers to corrosion are commonly used and

date back to the use of noble decorative and corrosion-resistant

metallic coatings71. However, as in the case of sacrificial cathodic

protection, barrier properties are often fixed by rather inflexible alloy

compositions and structures. Porosity in coatings is often minimized by

increasing coating thickness.

The advanced processing methods discussed above enable new

coating compositions which break out of old constraints on alloy

Fig. 5 Comparison of E–log(i) curves for an as-deposited PTS Al–Co–Ce coating

to the same coating with a hole drilled which exposes the AA 2024-T351

substrate. Data for AA 2024-T351 and a Al87Co7Ce6 MSR are also presented.

Tests were performed in deaerated 0.006 M NaCl solution at a neutral pH and

enable determination of pitting potential, Epit, repassivation potential, Erp, and

open circuit potential, OCP. The higher pitting potential indicates a greater

resistance to pitting. A more negative OCP than AA 2024-T3 indicates that the

sprayed coating can cathodically protect the AA 2024-T3 alloy at scratches.

The total area tested was 0.238 cm2, the area of the exposed substrate/drilled

hole was 2 × 10–3 cm2. These results show that a PTS Al–Co–Ce alloy coating

exhibits a much great pitting potential than the AA 2024-T3 substrate in the

Electrochem. Soc.)

Fig. 4 (a) Conventional secondary electron imaging (LEI) scanning electron microscopy (SEM) image of the Al88Co10Ce2 feedstock powder used for spray-applied

coatings. (b) LEI cross-sectional SEM image of an as-deposited PTS coating showing good adhesion with AA 2024-T351 (Al–Cu–Mg alloy). (c) LEI SEM image of

cross-sectioned and polished PTS coating showing pulse-deposited layers and level of porosity. (d) Confocal scanning laser microscropy (CSLM) image of an-

(b)(a)

MT1110p14_23.indd 18MT1110p14_23.indd 18 18/09/2008 15:32:5518/09/2008 15:32:55

Corrosion-resistant metallic coatings REVIEW

OCTOBER 2008 | VOLUME 11 | NUMBER 10 19

composition. In one study of an Al–Co–Ce alloy, three parameters

were obtained from E–I plots (tests performed in NaCl) (Fig. 5) to

characterize corrosion properties over a flexible range of compositions.

These were the OCP, the pitting potential, Epit, and the repassivation

potential, Erp. Epit and Erp are indicators of the pitting resistance,

while OCP helps forecast the galvanic corrosion behavior of an alloy

(e.g. potential driving force for sacrificial cathodic protection when

coupled to a substrate). Various regression models suitable for use with

alloys where the composition is constrained to 100% were explored

and two examples are shown in Figs. 6 and 744. Plots include possible

substrate structural materials (AA 2024-T3, Aermet 100® steel, etc.). The influence of Co on the OCP is based on Co’s effect on the cathodic

kinetics of Al–Co–Ce alloys. By increasing the reaction rate for both

the O reduction reaction (ORR) and the H evolution reaction (HER),

additions of Co in solid solution results in a higher OCP. The decrease

in OCP associated with the addition of Ce is most likely due to the

suppression of the ORR by Ce. The positive influence of Co on Erp is

due to the decreased hydrolysis product of this cation72, probably

resulting in a less aggressive pit environment and reduced anodic

dissolution rates of a Al–Co solid solution. A complex trend with Co

was seen. A parabolic shape also described the effect of Al and Ce

on Erp. These three elemental behaviors, when considered together,

describe a complex balance where Co and Ce reduce the aggressiveness

of the pit solution: Co lowers the dissolution rate while Al aids oxide

formation in an aggressive acidic solution. Therefore, optimization

of alloying elements produces the highest Erp values, with a complex

dependency of Erp on alloy content. To optimize the composition so as

to provide a barrier with the highest resistance to localized corrosion,

Co amounts should be relatively high (6-8 at.%), and Ce contents

moderately low (3-5 at.%) in this particular alloy.

Tunable sacrificial anode-based cathodic protection in Al–TM–RE coatings Sacrificial anode-based cathodic protection when two or more metals

are galvanically coupled is a potent electrochemical protection

method12. A coating that can polarize an exposed substrate material

just a few hundred millivolts below its OCP can lower its corrosion

rate by a factor of 100 or more. It is often more useful to polarize

many structural materials that corrode by local corrosion mechanisms

such as pitting or intergranular corrosion above some critical threshold

potential (i.e. Epit) to levels below this threshold potential. This is

accomplished by engineering a galvanic couple potential below Epit or

Erp. This is called cathodic prevention. Unfortunately, the governing

properties needed to optimize cathodic protection or prevention

(material-dependent OCP, and electrochemical current–potential

characteristics) have previously only been optimized through trial and

error. Moreover, parameters such as OCP are often rather inflexible

due to the limited choices of alloy composition and structure available.

Fig. 6 Relationship between the repassivation potential, ERP, and alloy content

in solid solution (Co at.% and Ce at.%). The relationship shown is plotted

from polynomial expressions developed from Scheffé polynomials based

on tests conducted on amorphous MSR of various Al–Co–Ce alloys in 0.6 M

NaCl solution at neutral pH. The ERP of the Al–Co–Ce alloy is compared to

AA 2024-T3 and high-purity Al. These results show that the repassivation

potential and thus barrier resistance to pitting can be controlled by controlling

the alloying content in solid solution.

Fig. 7 Predicted values of the open circuit potential (OCP) for the solid solution

Al–Co–Ce alloy system over a range of solid solution Co at.% and Ce at.%

contents, utilizing a Scheffé model with two inverse terms, demonstrating the

range of OCP possible within the Al–Co–Ce alloy system. These OCP values are

compared to AA2024-T3 and Aermet 100® OCP values. These are alloys the

Al–Co–Ce alloy might be designed to protect. The more negative OCP of the

Al–Co–Ce alloy compared to AA 2024-T3 and Aermet 100 confirms not only

the feasibility of this material to serve as a sacrificial anode but shows that the

driving force for cathodic protection can be tuned. The calculated values were

based on tests conducted on amorphous MSR of various Al–Co–Ce alloys in 0.6

M NaCl solution deaerated, at neutral pH.

MT1110p14_23.indd 19MT1110p14_23.indd 19 18/09/2008 15:33:0318/09/2008 15:33:03

REVIEW Corrosion-resistant metallic coatings

OCTOBER 2008 | VOLUME 11 | NUMBER 1020

Extreme cathodic potentials are not desired because ‘overprotection’

can lead to adverse side effects such as H embrittlement, alkaline

attack, and paint blistering. Therefore, tunable cathodic protection is a

highly desired capability.

The flexibility in OCP achieved by selecting particular compositions

of the Al–Co–Ce alloy system (Fig. 7) is extremely beneficial, as it

enables application of varying degrees of cathodic protection. By

choosing an Al–Co–Ce composition with relatively low Co (3-5

at.%) and low Ce levels (3–5 at.%) a sacrificial anode material can

be produced with a moderately low OCP value, to avoid cathodic

overprotection. An example is Al90Co5Ce5. The unique combination

of OCP values more negative than pure Aermet 100 ® or AA 2024-T3

along with an enhancement of barrier properties in the coating makes

this amorphous Al–Co–Ce alloy particularly well suited to serve as

a protective coating material. The enhanced resistance to localized

corrosion offered by this alloy results in greater Faradiac efficiency for

the sacrificial material, extending the theoretical lifetime of protection

compared to the Al–Zn and Al–Mg alloys used as Al alloy cladding

materials.

The sacrificial anode-based cathodic protection attributes sought

have been recently investigated by computational methods42,45,73–75

focusing on galvanic couples between a metallic coating and

exposed substrate under atmospheric conditions73. Fig. 8a shows

how atmospheric exposure (a thin electrolyte layer) of a structural

Al alloy covered by a metallic coating with a scratch at the center of

the sample Fig. 1) was modeled. A metric of the cathodic throwing

power of the sacrificially anodic Al–Co–Ce alloy was taken as the

galvanic couple potential distribution along the horizontal axis

of Fig. 8a and its proximity relative to the OCP of the Al–Co–Ce

coating and the AA 2024-T3 Epit. A figure of merit used is ∆E, given as (Epit 2024 – Ecouple), where Ecouple is the interfacial galvanic couple

potential at the centerline of the scratch, CL (Fig. 8b). Effective cathodic

prevention design maximizes ∆E. The maximum ∆E that can be achieved during galvanic coupling is termed ∆Emax and is defined by Epit2024 – Eocp of the Al–Co–Ce alloy.

Fig. 9 shows the extent of polarization given by the parameter ∆E obtained for a variety of situations as a function of scratch width at

a fixed sample length. The parameter ∆E is shown as the ordinate for each case, with the value of ∆E at S = 0 being the theoretical ∆Emax (i.e. Epit-2024 – EOCP, AlCoCe). The theoretical limit is approached for

small scratches. A greater extent of protection can be achieved when

the Cl– concentration is low. The potential distribution model predicts

that substantial sacrificial cathodic prevention of an AA 2024-T3

scratch could be achieved with a nanoengineered alloy coating.

The extent of the sacrificial cathodic protection provided by the

Al–Co–Ce alloys is a function of pH, Cl– concentration, the cathodic

kinetics on the AA 2024-T3, and the Co content of the metallic

coating. The metallic coating provides the best protection (i.e. largest

cathodic polarization of the scratch) when it is tailored to contain a

low Co content, and is exposed to either high or low pH solutions

of low Cl– concentration. Finally, the combination of chemical and

electrochemical protection predicted by computational modeling

has been verified via experiments involving defects machined into

PTS Al–Co–Ce alloys over AA 2024-T3. Corrosion protection is indeed

Fig. 8 (a) Schematic of the geometry associated with the galvanic coupling modeled between an Al–Co–Ce alloy coating (left) and AA 2024-T3 substrate (right)

exposed as a scratch in a thin electrolyte (e.g. corrosive solution) of thickness δ. Symmetry considerations allow solution of half of the scratch (S) exposing AA 2024-T3 by applying a zero flux boundary at CL. The half-scratch length, S, was varied from 500 to 5000 µm in width while the total length of the coating–scratch

system was held constant at 1 cm. The JO = 0 boundary condition reflects the physical situation at the right end of a specimen. This system was used to conduct

finite element modeling of the galvanic protection provided by the Al–Co–Ce coating to the AA 2024-T3 scratch. (b) In this plot the galvanic couple potential

based on material properties, electrolyte characteristics, and physical geometry is plotted as a function of horizontal position along the coating/scratch surface of

Fig. 8a, showing the effect of scratch length (indicated at far right) on the galvanic couple potential achieved. The scratch is located on the right-hand side. Model

parameters: variable S, Co ~ 3–5 at %, idl on AA 2024-T3 of 1.6 A/m 2, in solution of pH 3 and 0.05 M Cl–. The vertical line indicates the position of the interface

between metallic coating and substrate for the 5000 µm scratch. The dotted horizontal line indicates Epit of AA 2024-T3. Any galvanic couple potential below this

line indicates successful cathodic prevention. Thus, for this situation scratches 500–2500 µm in halfwidth are protected, while half-scratch widths of 5000 and 3500

µm are not protected against pitting near the centerline of the scratch at the far right. This is because the throwing power of the coating is inadequate to drive the

(b)(a)

MT1110p14_23.indd 20MT1110p14_23.indd 20 18/09/2008 15:33:0518/09/2008 15:33:05

Corrosion-resistant metallic coatings REVIEW

OCTOBER 2008 | VOLUME 11 | NUMBER 10 21

provided in experiments when the PTS coating is electrically coupled to

the AA 2024-T3 substrate.

On-demand active-corrosion inhibition based on tunable Al–TM–RE alloy coatings Controlled-release technologies are often used to supply chemicals

at given rates76,77. Release often occurs upon contact with solution.

However, slow release only when needed is often desired. Conducting

electroactive polymers are one means to provide controlled drug

delivery77. In corrosion protection, triggered or on-demand release

of inhibitor ions is also very important. Conductive polymers have

recently been utilized as reservoirs for corrosion inhibitors whose

triggered release occurs by galvanic reduction or ion exchange78–82.

Amorphous Al–Co–Ce alloys enable pH-controlled release of corrosion-

inhibiting ions from a metallic coating. The pH change that triggers

release is a consequence of the chemistry changes brought about by

corrosion itself43. Therefore, on-demand release occurs as a result of

exposure to corrosive species when corrosion initiates, for instance,

pH. ‘Turning off’ inhibitor release also occurs when the pH returns

to near-neutral and changes the local pH of the solution over the

coating. For a metal coating to behave like a pigmented paint that

can supply active corrosion inhibitors, several attributes are desired83.

The coating must store enough inhibitor to supply the critical inhibitor

concentration once released. The aqueous solution formed over the

metal surface must accumulate enough inhibitor to achieve the critical

inhibitor concentration, Ccrit, needed to stop corrosion in reasonable

time periods. This necessitates a high inhibitor capacity in the alloy

and a finite release rate. The Ccrit must be lower than the saturation

concentration of the inhibitor ion in the solution. The Ccrit in a given

electrolyte volume must be low enough so that the alloy can readily

release enough ions to achieve it without completely depleting the

inhibitor capacity83.

Al–Co–Ce alloys releasing Ce3+ meet these requirements. The

inhibitor is stored in the alloy and in its air-formed oxide layer in

valence states that are useful for corrosion inhibition. Inhibitors are

released by pH-dependent chemical dissolution of the oxide or direct

oxidation of the metal23–25 (Fig. 10). Ce and Co oxides are highly

soluble at low pH, insoluble under neutral, and partially soluble under

alkaline conditions (Fig. 11) 13,84. Thus, a pH change can be exploited

to trigger Co2+ and Ce3+ release. A pH change occurs during corrosion

Fig. 9 Cathodic polarization obtained with AlcladTM compared to the

Al–Co–Ce metallic coating expressed as the potential difference, ∆E, between Epit and the galvanic couple potential at the center of the scratch (x = 1 cm;

at C-line of Fig. 8a) attained for different scratch widths at a fixed half sample

length of 1 cm. The theoretical ∆Emax for AlcladTM and the other coatings are shown on the ordinate at S = 0. The potential difference between the Epit

of AA2024-T3 and the galvanic couple potential at x = 1 cm are shown in

the plot for each half-scratch width. Boundary conditions for the AlcladTM

used: ipass=0.002 A/m2, EpitAlclad 45 mV below Epit2024. The conditions

include 0.05 M Cl– and a pH of 3, with idl = 0.4 A/m2 for the various alloys

compositions. The results indicate that the Al–Co–Ce coating protects better

than AlcladTM as indicated by the larger ∆E. This suggests that the Al–Co–Ce coating can protect bigger scratches by cathodic prevention. Moreover, a low

Co content (i.e. 0–1 > 3–5% Co > 7–9% Co ) in the Al–Co–Ce alloy helps to

2007 J. Electrochem. Soc.)

Fig. 10 Schematic illustration of Al–Co–Ce coating (dark grey) on AA2024-T3 with a defect exposing the AA2024-T3 substrate. The less noble coating has been

tuned to possess an OCP more negative (–) than the underlying structural alloy. Consequently, cationic inhibitors released from the dissolving coating can be

transported to the defect by both migration as well as diffusion, while anionic species are transported in the opposite direction. A coating could also be engineered

to enable anionic transport by migration to the scratch as long as the polarity was reversed. This could be accomplished by tailoring the coating composition and

structure to create a coating with a potential greater than that of the scratch. The behavior shown has been confirmed for both MSR and spray-applied coatings.

MT1110p14_23.indd 21MT1110p14_23.indd 21 18/09/2008 15:33:0718/09/2008 15:33:07

REVIEW Corrosion-resistant metallic coatings

OCTOBER 2008 | VOLUME 11 | NUMBER 1022

which releases metal cations that hydrolyze to produce H+ at anodic

sites. High cathodic reactions at cathodic sites often increase the pH.

Therefore, when a metal is scratched and a galvanic couple forms

between the coating and newly exposed substrate, the pH will drop

over the anodic coating and rise at the cathodic scratch site. pH-

dependent release rates were found for Al–Co–Ce–(Mo) alloys41

(Fig. 11). The inhibitor ions released diffuse and then migrate towards

the damage site, reach Ccrit and suppress corrosion (Fig. 10). When

corrosion of the structural alloy stops, the pH of the environment

returns to neutral and Ce3+ is subsequently released at much lower

rate.

Computational studies42,45,73–75, have also been used to study

inhibitor release from such metallic substrates. Studies of inhibitor

release, transport, and achievement of Ccrit were conducted with and

without migration through the electrolyte phase. Migration-based

transport of Ce3+ to the scratch occurs due to the potential difference

established between the OCPs of AA 2024-T3 and the Al–Co–Ce

metallic coating. The time needed to reach Ccrit over the scratch was

determined, accounting for both transport processes as well as the

effect of temporal and position varying local release rates. Fig. 12

shows how the released Ce3+ profile develops with time and position in

one example. Migration aids Ce transport (for OCPAlCoCe < OCPAA2024),

explaining the uphill transport of Ce3+. The Ccrit,Ce is reached at the

coating–scratch interface at various times for different scratch lengths.

Accumulation was limited by ionic transport.

In summary, corrosion inhibition of a AA 2024-T351 scratch can

be achieved with ions released from a metallic coating. Experimental

exposure of AA 2024-T3 in a corrosive solution near an electrically

isolated Al87Co7Ce6 alloy confirmed computational modeling. The

Ce3+ supplied significantly decreased the maximum corrosion pit sizes

on the AA 2024-T3 surface below a critical size43. This is important in

aerospace structural materials, such as fuselage and wing skins, because

large corrosion pits above approximately 110 µm greatly reduce fatigue

life85,86.

Summary A multifunctional amorphous alloy has been described that possesses

three corrosion protection abilities when deployed as a coating over

structural alloys. The coating (i) functions as a local corrosion barrier,

(ii) serves as a sacrificial anode, and (iii) supplies soluble ions used as

corrosion inhibitors by engineering metallurgical and electrochemical

properties. The alloy system described is just one example of many

exciting new possibilities in metallic coatings enabled by the progress

in amorphous and nanocrystalline alloy development, as well as novel

synthesis and coating deposition methods. In the case presented,

excellent inherent resistance to corrosion is achieved through

structural amorphicity and choice of composition to optimize corrosion

functions. For instance, tunable electrochemical and chemical throwing

powers to achieve long-range protection of substrate defects can be

achieved. These concepts are generic and other alloys can in principle

be developed to optimize these functions. Such alloys can also be

manipulated to enable transport of inhibiting cations by both migration

and diffusion. Inhibitor release can be triggered on-demand.

Acknowledgments A Multi-University Research Initiative (Grant No. F49602–01–1–0352)

entitled ‘The Development of an Environmentally Compliant Multifunctional

Fig. 11 Effect of pH of a NaCl solution on the release rate of Al3+, Co2+, and

Ce3+ ions from an amorphous Al87Co8.7Ce4.3 MSR alloy in comparison to

high-purity Al. This plot illustrates that a shift in the electrolyte pH from the

near-neutral range typical of a benign solution to either the acidic or alkaline

range of a corrosive solution would help trigger the release of Ce cations (as

well as Al). This plot illustrates a mechanism for triggered release where the

environmental stimulus is the pH change.

Fig. 12 Computational model calculations of Ce3+ profiles in the electrolyte

phases (see Fig. 8a) with time and position over an Al–Co–Ce coating (left)

with exposed AA 2024-T3 substrate alloy (right). The plot indicates that Ce3+

can build up over the AA 2024-T3 on the right and even continues to build up

against the concentration gradient. This is due to the migration of Ce3+ in the

electric field formed in the electrolyte. The greater Ce3+ concentration near

the interface is due to slightly elevated release at high pH as indicated in Fig.

11. Computational results shown are for the selected case of initial solution

pH 6, 0.05 M Cl–, S = 1500 µm and slow ORR kinetics on the metallic coating

and AA2024-T3 (right). The vertical line indicates the position of the scratch

with the coating at the left and exposed AA 2024-T3 on the right as depicted

MT1110p14_23.indd 22MT1110p14_23.indd 22 18/09/2008 15:33:0918/09/2008 15:33:09

Corrosion-resistant metallic coatings REVIEW

OCTOBER 2008 | VOLUME 11 | NUMBER 10 23

Coating for Aerospace Applications using Molecular and NanoEngineering

Methods’ initially supported this work under the direction of Jennifer Gresham,

at air force office of scientific research (AFOSR). Coating development was

supported by AFOSR under Robert Manz and Jennifer Gresham in collaboration

with Enigmatics, Inc. and SAIC. In particular, the support and insight of Ben

Gauthier and Schmuel Eidelman is greatly appreciated. Additional financial

support was provided by the National Science Foundation DMR-NSF-0504983

under the direction of Harsh D. Chopra.

REFERENCES

1. Balazs, A. C., Mater. Today (2007) 10, 18

2. Davis, J. R., et al., ASM Metals Handbook, vol. 9, ASM International, Metals Park,

OH, (1987), 13 Corrosion

3. Newhard, N. J., Metal Finish. (1972) 7, 49

4. Korinek, K., Chromate conversion coatings. In ASM Metals Handbook, vol. 9,

Davis, J. R., et al., ASM International, Metals Park, OH, (1987), 13 Corrosion, 389

5. Cape, T. W., Phosphate conversion coatings. In ASM Metals Handbook, vol. 9,

Davis, J. R., et al., ASM International, Metals Park, OH, (1987), 13 Corrosion, 383

6. Ilevbare, G. O., et al., Corrosion (2000) 56, 227

8. Natishan, P. M., et al., J. Electrochem. Soc. (1986) 133, 1061

9. Prakash, S. S., et al., Nature (1995) 375, 431

10. Prakash, S. S., et al., Nature (1995) 374, 439

11. Tsuru, T., et al., Corrosion Prevention Mechanism for New Galvanized Steels,

Beijing, (2005) 12. Jones, D. A., Principles and Prevention of Corrosion, Prentice-Hall, (1996)

13. Pourbaix, M., Atlas of Electrochemical Equilibria in Aqueous Solutions, National

Association of Corrosion Engineers, (1974)

14. Reddy, C. M., et al., Corrosion (2000) 56, 819

15. Walton, C. J., et al., Corrosion (1953) 9, 345

16. Brown, R. H., et al., Engineering laminates. In Alclad and Clad Aluminum Alloy

Products, Dietz, A. G. H., (ed.), MIT Press, (1969), 227

17. Davis, J. R., Corrosion of Aluminum and Aluminum Alloys, ASM International,

Materials , (1999)

18. Pang, J. W. C., and Bond, I. P., Compos. A Appl. Sci. Manuf. (2005) 36, 183

19. Peyratout, C. S., and Dahne, L., Angew. Chem., Int. Ed. Engl. (2004) 43, 3762

20. Toohey, K. S., et al., Nat. Mater. (2007) 6, 581

21. Fery, A., et al., New J. Phys. (2004) 6, 18, doi:10.1088/1367-2630/6/1/018 22. Gupta, S., et al., Nat. Mater. (2006) 5, 229

23. Kabasakaloglu, M., et al., Mater. Corros. (1997) 48, 744

24. Shaw, B. A., et al., J. Electrochem. Soc. (1990) 137, 359

25. Hinton, B. R. W., et al., Metals Forum (1984) 7, 211

26. Virtanen, S., et al., Corros. Sci. (1997) 39, 1879

27. Ilevbare, G. O., and Burstein, G. T., Corros. Sci. (2003) 45, 1545

28. Hatch, J. E., Aluminum: Properties and Physical Metallurgy, American Society of

Metals, Metals, (1984)

29. Moshier, W. C., et al., J. Electrochem. Soc. (1986) 133, 1063

30. Moshier, W. C., et al., J. Electrochem. Soc. (1987) 134, 2677

31. Sanchette, F., et al., Surf. Coat. Technol. (1998) 98, 1162

32. Sanchette, F., and Billard, A., Surf. Coat. Technol. (2001) 142, 218

33. Sweitzer, J. E., et al., Electrochem. Solid-State Lett. (1999) 2, 267

34. Sweitzer, J. E., et al., Electrochim. Acta (2003) 48, 1223

35. Lucente, A. M., and Scully, J. R., Electrochem. Solid-State Lett. (2007) 10, C39

36. Lucente, A. M., and Scully, J. R., Corros. Sci. (2007) 49, 2351

37. Lucente, A. M., and Scully, J. R., J. Electrochem. Soc. (2008) 155, C234

38. Gao, M. C., et al., Metall. Mater. Trans. A (2007) 38A, 2540

39. Inoue, A., et al., Jpn. J. Appl. Phys. (1988) 27, L1796

40. Kabacoff, L. T., et al., Mater. Sci. Eng. A (1991) 134, 1288

41. Goldman, M. E., et al., Electrochem. Solid-State Lett. (2005) 8, B1

42. Presuel-Moreno, F. J., et al., J. Electrochem. Soc. (2005) 152, B302

43. Jakab, M. A., and Scully, J. R., Nat. Mater. (2005) 4, 667

44. Scully, J. R., et al., Corrosion (2008) 64, 210

45. Presuel-Moreno, F. J., et al., J. Electrochem Soc. (2006) 153, B486

46. Jakab, M. A., et al., Corrosion (2005) 61, 246

47. Jakab, M. A., and Scully, J. R., Corrosion (2008) 64, 198

48. Goldman, M., Demonstration of Tunable Corrosion Properties of the Al–Co–Ce

Alloy System, MS thesis, University of Virginia, (2005)

49. Goldman, M. E., et al., Amorphous Metallic Coatings with Tunable Corrosion

Properties Based on Al–Co–Ce-(Mo) Alloy Compositions. NACE, (2004), Paper

No. 4276

50. Goldman, M. E., et al., Selected Corrosion Properties of a New Amorphous

Al–Co–Ce Alloy System. (2003)

51. Davis, G. D., et al., Surf. Interface Anal. (1987) 10, 168

52. Gauthier, B., et al., Spray Applied Amorphous/Nanocrystalline Aluminum Alloy

Coatings as a Replacement for Aluminum Cladding, Tri Service corrosion

conference Denver (2007) 53. Gauthier, B., et al., ECS Transactions (2008) 11, 59

54. Gauthier, B., et al., Unpublished PTS data, 2007

55. Li, C. J., et al., Thin Solid Films (2005) 489, 79

56. Meng, Q., et al., Characterization and Mechanical/Corrosion Properties of

Amorphous Al–Co–Ce Coatings, Orlando, FL, (2005) 57. Kawakita, J., et al., Surf. Coat. Technol. (2003) 166, 17

58. Kawakita, J., et al., Sci. Technol. Adv. Mater. (2003) 4, 281

59. Ishikawa, Y., et al., J. Thermal Spray Technol. (2005) 14, 384

60. Kawakita, J., et al., Surf. Coat. Technol. (2006) 200, 4414

61. Kuroda, S., et al., Corrosion (2006) 62, 635

62. Wang, A. P., et al., Mater. Sci. Eng. A (2007) 449, 277

63. Connolly, B. J., et al., Corros. Eng. Sci. Technol. (2004) 39, 137

64. Agarwal, A., et al., JOM (2002) 54, 42

65. Burkle, G., et al., Metastable, Mechanically Alloyed and Nanocrystalline Materials

(2002) 386–3, 571

66. Dent, A. H., et al., Surf. Coat. Technol. (2001) 139, 244

67. Edris, H., et al., J. Mater. Sci. (1997) 32, 863

68. Guilemany, J. M., et al., Scr. Metall. Mater. (1995) 33, 55

69. He, J. H., et al., Metall. Mater. Trans. A (2000) 31, 541

70. Lau, M. L., et al., Nanostruct. Mater. (1999) 12, 319

71. Cramer, S. D., et al., Corrosion of clad metals. In ASM Metals Handbook, Baboian,

R., ASM International, (2005), 13B Corrosion Materials, 442

72. Baes, C. F., and Mesmer, R. E., The Hydrolysis of Cations, Robert E. Krieger,

Malabar, FL, (1986)

73. Wang, H., et al., Electrochim. Acta (2004) 49, 239

74. Lee, J. S., et al., J. Electrochem Soc. (2004) 151, B423

75. Stewart, K. C., Intermediate Attack in Crevice Corrosion by Cathodic Focusing, PhD

thesis, University of Virginia, Charlottesville, VA, 1999

76. Cussler, E. L., Diffusion – Mass Transfer in Fluid Systems, Cambridge University

Press, (1997)

77. Pernaut, J.-M., and Reynolds, J. R., J. Phys. Chem. B (2000) 104, 4080

78. Kendig, M., et al., Progr. Org. Coat. (2003) 47, 183

79. Kinlen, P. J., et al., Corrosion (2002) 58, 490

80. Kinlen, P. J., et al., J. Electrochem. Soc.(1999) 146, 3690

81. Kendig, M., and Hon, M., Corrosion (2004) 60, 1024

82. Cook, A., et al., Curr. Appl. Phys. (2004) 4, 133

83. Sinko, J., Progr. Org. Coat. (2001) 42, 267

84. Hayes, S. A., et al., J. Electrochem. Soc. (2002) 149, C623

85. Chen, G., et al., Pitting corrosion and fatigue crack nucleation. In Effects of the

Environment on the Initiation of Crack Growth, Van der Sluys, W. A., Piascik, R. S.,

and Zawierucha, R., (eds.) ASTM, (1997), 18 86. Rokhlin, S. I., et al., Eng. Fract. Mech. (1999) 62, 425

MT1110p14_23.indd 23MT1110p14_23.indd 23 18/09/2008 15:33:1018/09/2008 15:33:10

Corrosion-resistant metallic coatings

Corrosion protection by passive films and coatings
Active corrosion inhibition
Long-range corrosion protection of coating defects
One vision for new coatings with multiple, tunable functions
Materials and fabrication of tunable amorphous metallic coatings
Tunable barrier properties in multifunctional amorphous Al–TM–RE coatings
Tunable sacrificial anode-based cathodic protection in Al–TM–RE coatings
On-demand active-corrosion inhibition based on tunable Al–TM–RE alloy coatings
Summary
Acknowledgments
REFERENCES

CORROSION IN MARINE

ENVIRONMENT

-Mandar Kulkarni

2011A1PS417G

Marine Corrosion is the deterioration of metal in Marine environment due to various

processes like electrochemical reaction. The structures which are damaged by in marine

environment are as follows:

Marine structures damaged by Corrosion:

1. Boats and vessels. 2. Harbor and oil exploration facilities. 3. Ports. 4. Monuments erected in sea.

The corrosion of these structures can result in premature failures, reduced service life, increased maintenance costs and safety hazards. So it is very important to study the types of corrosion observed, materials used and protection methods used for these types of corrosion.

The Types of Corrosion in Marine Environment:

1. Galvanic Corrosion:

The most widespread corrosion in marine environments is Galvanic Corrosion .General

corrosion appears as a continuous layer of corrosion over an entire surface area. It occurs more

often for objects exposed to air such as pipings and plates on exposed structures such as offshore

platforms and ship. These are not found when objects are totally submerged in water.

Galvanic corrosion occurs when two different types of metals are put into contact with

each other while they are immersed in an electrolyte, such as seawater. The reason corrosion

takes place between two different, coupled metals is that a voltage difference (potential) exists

between them. The result is that one metal corrodes faster and other noble metal corrodes slower

or ceases to corrode. The galvanic series is used to determine the potential for corrosion.

The first sign of galvanic corrosion is paint blistering (starting on sharp edges) below the

water line—a white powdery substance forms on the exposed metal areas. As the corrosion

continues, the exposed metal areas will become deeply pitted, as the metal is actually eaten

away.

Galvanic corrosion of aluminum drive units—or any underwater aluminum on a boat—is

accelerated by attaching stainless steel components like propellers, trim planes (if connected to

engine ground), and aftermarket steering aids. In doing this, we introduce a dissimilar metal to

which electrons from the drive unit will follow. Another condition that will increase the speed or

intensity of galvanic corrosion is the removal or reduction in surface area of sacrificial anodes.

Galvanic corrosion continually affects all underwater aluminum, but at a reduced rate when no

dissimilar metals are connected to the aluminum parts. When in contact with an electrolyte, most

metals form small anodes and cathodes on their surfaces due to such things as alloy segregation,

impurities, or cold working. Galvanic corrosion is used to protect ship hulls by bolting zinc anodes to steel hulls.

2. Intergranular Corrosion Intergranular corrosion is a microscopic form of corrosion that is caused by the potential difference between the grain boundaries of the metal and the grain bodies. When the grain bodies

are anodic to grain boundaries corrosion occurs along the grain boundaries. The result is porous

and a weakened structure. This type of corrosion is common for cast iron placed in sea water,

and it occurs in brass having more than 15% zinc.

3. Stress Corrosion Cracking Stress corrosion cracking (SCC) is an insidious type of corrosion that can occur when

stainless steel develops very minute cracks from being under tensile stress. Most sailors know

that a sailboat’s rigging is one of the areas on the vessel that bears considerable load. The

components on the rigging that are stressed while the vessel is under sail include the chainplates,

stempiece, and their bolting systems; backstay connections to the stern; toggles and clevis pins;

rolled swages; tangs (shroud connections to the mast); the actual stays and shrouds, etc.

4. Crevice Corrosion This occurs due to limited availability of oxygen. A crevice may be formed under any of the following: deposits (such as silt or sand), plastic washers, fibrous gaskets, or tightly wrapped

fishing line. It can also form where moisture can get in and not back out, forming a stagnant

zone.

5. Erosion Corrosion This occurs when sea water is flowing and it is often found in bends and elbows of pipes. Corrosion due to cavitation is also caused due to sea water but the mechanism is different.

6. Marine Growth A lot of hard growth occurs on all submerged metal. Marine organisms are attracted to the high electrical current generated by Zinc. Anodes with a lower mV potential will not attract

the same level of growth.

Selecting Right Material Selecting right material for a particular application can avoid or minimize corrosion. Some typical requirements and procedures to select the best possible material are shown below:

Protection Methods

It is always said that “Prevention is always better than cure.” The optimum time to

prevent this is the design stage; the worst time is after the existence of corrosion has been

discovered. Some of the protection methods used are given below:

1. Cathodic Protection: Cathodic Protection is the most common form of corrosion protection for a submerged

material; and it is best used in conjugation with paints and coatings. Two types of Cathodic

protection are used:

 Galvanic cathode protection

 Impressed current system

The impressed current system is a more permanent system and requires the use of

external electrical power. Galvanic protection uses aluminum, magnesium or zinc anodes that are

attached to the steel material in sea water. The principle is that when a metal receives electrons it

becomes cathode, and can no longer corrode. The metals providing electrons are sacrificial

anodes and they corrode. Cathodic Protection is extensively used to protect ship hulls by bolting

zinc anodes to steel hulls. Zinc acts as sacrificial anode and protects the steel hull.

2. Design Good design incorporates corrosion protection methods during the design stage itself.

Geometric configurations that are known to cause or accelerate corrosion can be eliminated.

Examples are elimination of crevices, stagnant areas, stress risers.

3. Antifouling Paint on Drives Fouling is a major concern in many situations. Marine animals (barnacles, Mussels, etc.) and vegetation can make life miserable for boaters. Antifouling paints are available, but some

can affect corrosion protection or even accelerate corrosion. Tributyltin-(sometimes referred to

as TBT or organotin) based antifouling paints are used to control fouling and do not cause

corrosion problems for aluminum drives.

4. Galvanic Isolators Galvanic isolators are solid-state devices that are part of a series connected in line to the

boat's green safety ground lead ahead of all grounding connections on the boat. This device

functions as a filter, blocking the flow of destructive low voltage galvanic (DC) currents but still

maintaining the integrity of the safety grounding circuit.

Corrosion Protection Testing For diagnostic tests, a simple digital volt/ohm meter (multimeter) is necessary. An analog

version may be used, but it must be a high-impedance model. Even the most inexpensive digital

volt/ohm meter has high impedance. One of the most helpful methods for determining if

corrosion below the waterline is occurring is through the measurement of the hull potential.

The parameters for Corrosion testing in Marine Environment are as follows:

1. Temperature 2. Depth 3. Salinity 4. Water Current 5. Meteorological 6. Waves and Tides 7. Water Samples 8. Sediment Samples

Some of the devices used to measure these parameters are Current Meters, Anemometers, Tide

and Wave Gauges, Multi parallel Systems, Water Samplers, Laser Systems, etc. Tests can be

designed for these parameters using the above mentioned instruments. The results of these tests

can be used to prevent corrosion in the marine environment.

Int. J. Electrochem. Sci., 7 (2012) 2846 - 2859

International Journal of

ELECTROCHEMICAL SCIENCE

www.electrochemsci.org

Corrosion Passivation in Natural Seawater of Aluminum Alloy

1050 Processed by Equal-Channel-Angular-Press

El-Sayed M. Sherif 1,3,*

, Ehab A. El-Danaf 2 , Mahmoud S. Soliman

2 , Abdulhakim A. Almajid

1,2

1 Center of Excellence for Research in Engineering Materials (CEREM), College of Engineering, King

Saud University, P. O. Box 800, Al-Riyadh 11421, Saudi Arabia 2 Department of Mechanical Engineering, College of Engineering, King Saud University, P.O. Box

800, Al-Riyadh 11421, Saudi Arabia 3 Electrochemistry and Corrosion Laboratory, Department of Physical Chemistry, National Research

Centre (NRC), Dokki, 12622 Cairo, Egypt * E-mail: [email protected]

Received: 7 February 2012 / Accepted: 11 March 2012 / Published: 1 April 2012

The corrosion and corrosion passivation of aluminum alloy 1050 (AA 1050) that was fabricated by

equal-channel angular press (ECAP) after different pass time numbers, namely, 0, 1, 2, and 4, in

Arabian Gulf water (AGW) have been reported. The study was carried out using cyclic

potentiodynamic polarization (CPP), chronoamperometric current-time (CT), and electrochemical

impedance spectroscopy (EIS) measurements after 20 min and 10 days immersion in the AGW

solutions. CPP experiments showed lower corrosion rate and higher corrosion resistance for the

ECAPed alloy than annealed one; this effect increases with increasing the number of pass time. CT

curves at ‒630 mV vs. Ag/AgCl and EIS spectra indicated that the increase of pass time highly

decreases both uniform and pitting corrosion. Results collectively proved that the corrosion rate

decreases and resistance for uniform and pitting attacks increases with increasing the number of pass

time and the best performance was obtained for ECAPed AA 1050 alloy after 4 passes. For that the

behavior of the cast alloy was compared to the ECAPed one after 4 passes was also reported after 10

days immersion before measurements.

Keywords: Aluminum alloy 1050; natural seawater; corrosion measurements; ECAP; electrochemical

measurements

1. INTRODUCTION

The microstructure of metals can be significantly changed by subjecting the material to severe

plastic deformation through procedures such as equal channel angle pressing (ECAP) and high

http://www.electrochemsci.org/

mailto:[email protected]

Int. J. Electrochem. Sci., Vol. 7, 2012

2847

pressure torsion. These procedures lead to substantial grain refinement so that the grains are reduced to

the submicrometer or even the nanometer range [1,2]. ECAP is a processing procedure whereby an

intense plastic strain is imposed by pressing a sample in a special die. The die consists of two channels

equal in cross section, intersecting at an angle ɸ, which is a subject of research in ECAP usually

ranging from 90 o to 157

o [3]

. There is also an additional angle, which defines the arc of curvature at

the outer point of intersection of the two channels, and also it has been a subject of research. A

schematic of the die can be seen in Fig. 1.

Of the various procedures that impose severe deformation, ECAP is especially the most

attractive processing technique. ECAP have been utilized not only to obtain ultrafine-grained (UFG)

materials but also to produce extraordinary mechanical and physical properties without remarkably

changing the geometry of a bulk material. Materials processed with ECAP become superior to that of

conventional coarse-grained materials [4-9]. The significant feature of ECAP is that because the billet

retains the same cross-sectional area so that repetitive pressings are feasible, materials processed by

ECAP may be deformed to very high strains wherein the subgrain boundaries evolve into high-angle

boundaries through the absorption of dislocations, thereby producing arrays of ultrafine grains

separated by high-angle grain boundaries. By contrast, this evolution cannot be achieved in more

conventional metal-working processes because of the natural limit imposed on the total strain

introduced during deformation [10].

Protecting aluminum from being corroded has been investigated either by adding other alloying

elements and/or by decreasing the aggressiveness of its surrounding corrosive environments.

Decreasing the corrosivity of the environments can be done mostly by using corrosion inhibitors [11-

17] or protective coatings [18, 19]. The inhibition of the alloy surface is usually obtained by inorganic

oxidants such as chromate, molybdate, and tungstate [20-23] or organic compounds having polar

groups, such as oxygen, sulfur and nitrogen as well as heterocyclic compounds containing functional

groups and conjugated double bonds [11-17]. ECAP is considered as one of the very useful methods

for producing ultra-fine microstructures of Al-based alloys with significantly improved mechanical

properties and higher corrosion resistance [24-26]. In addition, some ultra-fine grained Al-based alloys

produced by ECAP showed a superplastic forming capability [27, 28].

The objective of this work was to study the effect of ECAP pass time number that varied from

1 to 4 on the corrosion of the annealed aluminum alloy 1050 (AA 1050) in Arabian Gulf water. A

particular attention was paid to the effect of pass time number on the pitting corrosion of the AA 1050.

The study was achieved by using different electrochemical techniques such as cyclic potentiodynamic

polarization, chronoamperometric current-time variations, and electrochemical impedance

spectroscopy.

2. EXPERIMENTAL PROCEDURE

2.1. Fabrication of the ECAPed AA 1050

The die, Fig. 1, was manufactured from hot work tool steel. The die angles were designed and

manufactured to have: =0 and ɸ=90 o . Route BC, where the sample was rotated by 90

o between

Int. J. Electrochem. Sci., Vol. 7, 2012

2848

subsequent pressings was adopted in the present study. Commercial purity aluminum (AA 1050)

containing the following impurities, Fe–0.40% min, Si–0.25%, Cu–0.05%, Mn–0.05%, Mg–0.05%,

Cr–0.05%, Zn–0.05%, V–0.05%, Ti–0.03%, others 0.03% and Al–balance) with purity of 99.5% was

used in this study. The material was supplied as cold rolled plates of 15 mm thickness. Cylindrical

samples were machined parallel to the rolling direction, and then annealed at a temperature of 600 o C

for 8 hours, to give an average grain size of about 600µm. The annealed samples were lubricated using

graphite based lubricant and pressed in the ECAP die. The Vickers microhardness (kg/mm 2 ) was

measured using a Buehler micromet hardness tester at a load of 300 g and the reported value is the

average of 20 readings. Samples of about 6 mm in length were cut from the ECAP processed samples

and pressed in a direction parallel to the extrusion direction to document the yield strength.

Figure 1. Schematic representation of the ECAP process showing the billet axes system xyz and the

reference shear axis system x’y’z’.

2.2. Corrosion tests

2.2.1. Chemicals and electrochemical cell

The natural sea water was brought from the Arabian Gulf at the eastern region (Jubail,

Dammam, Saudi Arabia) and was used as received. An electrochemical cell with a three-electrode

configuration was used for electrochemical measurements. Annealed and ECAPed AA 1050 rods were

used in this study. The AA 1050 rod, a platinum foil, and a Metrohm Ag/AgCl electrode (in 3 M KCl)

were used as working, counter, and reference electrodes, respectively.

The AA 1050 rods for electrochemical measurements were prepared by welding a copper wire

to a drilled hole was made on one face of the rod; the rod with the attached wire were then cold

mounted in resin and left to dry in air for 24 h at room temperature. Before measurements, the other

face of the Al electrode, which was not drilled, was grinded successively with metallographic emery

paper of increasing fineness of up to 800 grits. The electrodes were then washed with doubly distilled

water, degreased with acetone, washed using doubly distilled water again and finally dried with tissue

paper. In order to prevent the possibility of crevice corrosion during measurement, the interface

x

y

z

Int. J. Electrochem. Sci., Vol. 7, 2012

2849

between sample and resin was coated with Bostik Quickset, a polyacrelate resin. The total exposed

surface area of the working electrode was 1.0 cm 2 .

2.2.2. Electrochemical methods

Electrochemical experiments were performed by using an Autolab Potentiostat (PGSTAT20

computer controlled) operated by the general purpose electrochemical software (GPES) version 4.9.

The CPP curves were obtained by scanning the potential in the forward direction from -1800 to -500

mV against Ag/AgCl at a scan rate of 3.0mV/s; the potential was then reversed in the backward

direction. Chronoamperometric current-time experiments were carried out by stepping the potential of

the AA 1050 rods at – 630 mV versus Ag/AgCl; in some experiments this potential value was applied

after stepping the potential of Al to -1000mV vs. Ag/AgCl for 20 min. EIS tests were performed at

corrosion potentials (ECorr) over a frequency range of 100 kHz – 100 mHz, with an ac wave of  5 mV

peak-to-peak overlaid on a dc bias potential, and the impedance data were collected using Powersine

software at a rate of 10 points per decade change in frequency. ZSimpWin software was used to fit the

EIS data to best equivalent circuit for Al rods in AGW. All the electrochemical experiments were

recorded after the electrode immersion in the test solution for 20 min and in some cases the electrodes

were immersed for 10 days before measurements. All measurements were also carried out at room

temperature in freely aerated stagnant solutions.

3. RESULTS AND DISCUSSION

3.1. Cyclic potentiodynamic polarization (CPP) data

In order to study the effect of the number of ECAP pass time on the corrosion behavior of AA

1050 in AGW solution, CPP experiments were carried out. The CPP curves for (1) 0 pass, (2) 1 pass,

(3) 2 passes, and (4) 4 passes ECAPed AA 1050, respectively after 20 min immersion in AGW

solutions are shown in Fig. 2. It has been reported [12, 13] that the cathodic reaction for Al in aerated

near neutral pH solutions is the oxygen reduction followed by its adsorption i.e.

)1(4OH 4O2H O 22

  e

The presence of oxygen enhances the cathodic reaction due to oxygen reduction and transforms

aluminum to aluminum hydroxide as follows,

)2(3 Al(OH) 3OH Al ads.3,(S)

  e

The aluminum hydroxide, Al(OH)3, is transformed to Al2O3.3H2O,

Int. J. Electrochem. Sci., Vol. 7, 2012

2850

)3(O.3HOAl 2Al(OH) 232ads.3,



The formed 32

OAl is of a dual nature and consists of an adherent, compact, and stable inner

oxide film covered with a porous, less stable outer layer, which is more susceptible to corrosion [21,

29, 30].

10 -1

10 0

10 1

10 2

10 3

10 4

j / 

A c

m -2

j / 

A c

m -2 (b)

(a)

10 -1

10 0

10 1

10 2

10 3

10 4

-1.8 -1.6 -1.4 -1.2 -1.0 -0.8 -0.6 -0.4

E / V (Ag/AgCl)

(d)(c)

-1.8 -1.6 -1.4 -1.2 -1.0 -0.8 -0.6 -0.4

Figure 2. CPP curves obtained for (a) annealed, (b) 1 pass, (c) 2 passes, and (d) 4 passes ECAPed AA

1050 electrode, respectively after its immersion in AGW for 20 minutes.

It is clearly seen from Fig. 2, curve 1, that the anodic reaction of Al started from the corrosion

potential (‒1285 mV vs. Ag/AgCl) towards the less negative potential values to show a passive region

at an average current density of 62.2 µA/cm 2 , extending from −1150 to −680 mV. In this potential

range, aluminum oxide is formed on the surface according to reaction (3). After which the current

shows an abrupt increase in its values with increasing the applied potential due to the breakdown of the

formed oxide film and the occurrence of pitting corrosion, accordingly the dissolution of aluminum

can be expressed by the reaction [11-13, 31, 32];

)4(3e .Al Al 3  

This occurs under the influence of the attack of the aggressive chloride ions that present in the

seawater to the aluminum in the flawed areas of the oxide film, which leads to the formation of the

soluble aluminum chloride complex;

Int. J. Electrochem. Sci., Vol. 7, 2012

2851

Al 3+

+ 4Cl ‒ = AlCl4

‒ (5)

Here, there are two points of views explaining the mechanism of pitting corrosion at this

condition. The first claims [32, 33] that a salt barrier of AlCl3 is formed within the pits on their

formation, which could lead to the formation of AlCl4 − as repersented by Eq. 5, and diffuses into the

bulk of the solution. While, the second [34] has proposed that the chloride ions do not enter into the

oxide film but they are chemisorbed onto the oxide surface and act as a reaction partner, aiding the

oxide to dissolve via the formation of oxy-chloride complexes as follows:

Al 3+

(in crystal lattice of the oxide) + 2Cl ‒ + 2OH

‒ = Al(OH)2Cl2

‒ (6)

The occurrence of pitting corrosion was also indicated by the appearance of the hysteresis loop

on reversing the potential scan in the backward direction towards the more negative values. This loop

appeared due to higher current values in the reverse scan than the forward values. The bigger the area

of the loop the more severe is the pitting corrosion.

The CPP curves of ECAPed alloy show almost similar behavior but with lower corrosion rates

and higher corrosion resistances. This was indicating by recording the values of the corrosion potential

(ECorr), corrosion current (jCorr), cathodic (βc) and anodic Tafel slopes (βa), passivation current (jPass),

protection potential (EProt), pitting potential (EPit), polarization resistance (RP), and corrosion rate

(KCorr), obtained from CPP curves (Fig. 2) for the annealed and ECAPed AA 1050 alloys after their

immersion in AGW solutions for 20 min and shown in Table 1. The values of the corrosion potential

and corrosion current were obtained from the extrapolation of anodic and cathodic Tafel lines located

next to the linearized current regions. The pitting potential was determined from the forward anodic

polarization curves where a stable increase in the current density occurs. The protection potential was

determined from the backward anodic polarization curve at the intersection point with the forward

polarization curve. The values of RP and KCorr were calculated from the polarization data as reported in

our previous work [35-44].

It is seen from Fig. 2 and Table 1 that the AA 1050 alloy pressed by ECAP shifted the values of

ECorr to less negative values, lowered the values of jCorr, jPass, and KCorr, and increased the values of RP.

This effect is significantly increased with increasing the number of pass time to reach its maximum

after 4 passes. For that CPP behavior of the annealed AA 1050 alloy was compared to the fabricated

alloy by ECAPed for 4 passes after 10 days immersion in sea water before measurements as

repersented by Fig. 3a and Fig. 3b, respectively. The corrosion parameters obtained from Fig. 3 are

shown in Table 1. Fig. 3 and Table 1 show that the ECAPed alloy recorded lower corrosion rate and

higher corrosion resistance than the annealed alloy and both of the alloys showed better performance

compared to their CPP behavior when the immersion time was only 20 min. This indicates that the

increase of immersion time decreases the corrosion of annealed and ECAPed AA 1050 alloys.

According to Chung et al. [6] the increase of ECAP pass number increases the corrosion resistance of

AA 1050 due to the decreasing of the size of the Si-containing impurities on the alloy surface. Where,

the presence of these Si-containing impurities induced the micro-galvanic reaction by its reaction with

the Al matrix and also between the Al matrix and the Si-containing oxide.

Int. J. Electrochem. Sci., Vol. 7, 2012

2852

-1.8 -1.6 -1.4 -1.2 -1.0 -0.8 -0.6 -0.4 10

-1

10 0

10 1

10 2

10 3

10 4

(b)

(a)

10 -1

10 0

10 1

10 2

10 3

10 4

-1.8 -1.6 -1.4 -1.2 -1.0 -0.8 -0.6 -0.4

j / 

A c

m -2

E / V (Ag/AgCl)

j / 

A c

m -2

Figure 3. CPP curves obtained for (a) annealed and (b) 4 passes ECAPed AA 1050 electrode after its

immersion in AGW for 10 days before measurement.

Table 1. Corrosion parameters obtained from polarization curves shown in Fig. 2 and Fig. 3 for AA

1050 after 20 min and 10 days of the electrode immersion in Arabian Gulf water.

AA 1050 alloy

Parameter

βc / mV

dec -1

ECorr/ mV

jCorr/

Acm -2

βa/ mV

dec -1

jPass/

Acm -2

EProt/

EPit/

Rp/

Ωcm 2

KCorr/ mmy

-1

0 pass (20 min) 100 -1285 27 110 62.2 -720 -655 0.84 0.294

1 pass (20 min) 105 -1270 22 115 50.0 -710 -645 1.10 0.240

2 pass (20 min) 110 -1260 18 120 49.9 -705 -643 1.37 0.196

4 pass (20 min) 110 -1255 15 125 42.1 -710 -640 1.70 0.164

0 pass (10 days) 135 -1225 19 153 89.7 -680 -610 1.64 0.207

4 pass (10 days) 140 -1210 13 155 61.6 -680 -620 2.46 0.142

3.2. Chronoamperometric current-time (CT) measurements

In order to shed more light on the effect of ECAP pass time on the pitting corrosion of Al AA

1050 after 20 min and 10 days immersion in AGW at more anodic constant potential value,

chronoamperometric experiments were carried out. Fig. 4 represents the variation of the measured

dissolution currents versus time at ‒630 mV vs. Ag/AgCl for the annealed (1) and ECAPed (2) 1 pass,

(3) 2 passes, and (4) 4 passes AA 1050 alloy, respectively after 20 min immersion in AGW. The same

experiments were conducted on the different Al rods after applying ‒1000 mV (this potential was

chosen from the CPP curves, where it allows the alloy to develop a compact passive layer) for 10 min

Int. J. Electrochem. Sci., Vol. 7, 2012

2853

before stepping the potential to ‒630 mV and the curves are shown in Fig. 5. It is seen from Fig. 4 that

the highest current values were recorded for the annealed alloy (curve 1), where the current increased

upon applying the potential in the first hundreds of seconds, the current then decreased slightly with

time for the whole time of the experiment. For the ECAPed alloys, the current-time curves showed the

same behavior with lower absolute currents. This effect increases with increasing the pass time

number, where the ECAPed alloy fabricated at 4 passes showed the lowest absolute current with time.

This behavior indicates that the increase of pass time number to 4 passes decreased the uniform

corrosion of AA 1050 in AGW.

0 500 1000 1500 2000 2500

time / sec

j /

m A

c m

-2

4 3

Figure 4. Chronoamperometric curves obtained for (1) annealed, (2) 1 pass, (3) 2 passes, and (4) 4

passes ECAPed AA 1050 electrode after its immersion in AGW solutions for 20 minutes

followed by stepping the potential to ‒630mV vs. Ag/AgCl.

The current-time curves depicted in Fig. 5 showed similar behavior to those shown in Fig. 4 at

the same potential, with possible occurrence of pitting corrosion due to the attack of the aggressive

ions present in the AGW to the flawed area of the passive layer that was formed at ‒1000 mV. From

the chronoamperometric experiments the annealed alloy showed the worst corrosion resistance, while

the best performance was recorded for the ECAPed alloy after 4 passes, for that the CT curves at ‒630

mV for (1) annealed and (2) 4 passes ECAPed AA 1050, respectively after 10 days immersion in the

AGW were carried out as shown in Fig. 6. The current for annealed alloy recorded very low values at

the few seconds of the measurement due to the formed corrosion products and oxide layer on the

surface during the 10 days immersion. The current then started to increase rapidly accompanied by

large fluctuations, which indicate on the occurrence of severe pitting corrosion. On the other hand, the

current for the ECAPed alloy recorded very low current values (few microamperes) for the whole time

of the experiment, which indicate that the formed passive layer during the immersion time was

compact enough to protect the surface from being pitted and attacked by the corrosive species that

present in the Gulf water at the applied potential. This also agrees with the work reported by Chung et

al. [6] that the increase of ECAP pass time number increases the pitting resistance of the alloy.

Int. J. Electrochem. Sci., Vol. 7, 2012

2854

0 500 1000 1500 2000 2500

-630 mV

time / sec

3 2

j /

m A

c m

-2

-1000 mV

Figure 5. Chronoamperometric curves obtained for (1) annealed and (2) 1 pass, (3) 2 passes, and (4) 4

passes ECAPed AA 1050 electrodes after their immersion in AGW solutions for 20 min

followed by stepping the potential to ‒1000 mV for 10 minutes and finally fix it to ‒630mV vs.

Ag/AgCl.

0 10 20 30 40 50 60

time / min

j / 

A c m

-2

Figure 6. Chronoamperometric curves obtained for (1) annealed and (2) 4 passes ECAPed AA 1050

rods after their immersion in AGW for 10 days before stepping the potential to ‒630mV vs.

Ag/AgCl.

3.3. Electrochemical impedance spectroscopy (EIS) measurements

The EIS has successfully employed to explain the corrosion and corrosion inhibition of several

metals and alloys in chloride media [45-55]. The method was used to determine kinetic parameters for

electron transfer reactions at the alloy/electrolyte interface. The EIS Nyquist plots obtained for (1)

annealed, (2) ECAPed 1 pass, (3) ECAPed 2 passes, and (4) ECAPed 4 passes AA 1050 alloy,

respectively after 20 min immersion in AGW are shown in Fig. 7. The Nyquist (a), Bode (b) and phase

Int. J. Electrochem. Sci., Vol. 7, 2012

2855

angle (c) plots for (1) annealed and (2) ECAPed 4 passes AA 1050 alloy, respectively after 10 days are

also shown in Fig. 8. The EIS data of the Nyquist spectra shown in Fig. 7 and Fig. 8a were analysed by

fitting to the equivalent circuit model shown in Fig. 9. The parameters obtained by fitting the

equivalent circuit are listed in Table 2. Here, RS represents the solution resistance between the alloy

surface and the counter (platinum) electrode, Q the constant phase elements (CPEs) and contain two

parameters; a pseudo capacitance and an exponent (an exponent of less than unity indicates a

dispersion of capacitor effects [12, 13]), the RP1 accounts for the resistance of a film layer formed on

the alloy surface, Cdl is the double layer capacitance, Cdl is the double layer capacitance, and RP2

accounts for the charge transfer resistance at the alloy surface, i.e. the polarization resistance.

0 2 4 6 8 10 12

-Z " /

k 

c m

Z' / kcm2

3 2

Figure 7. Nyquist plots obtained for (1) annealed, (2) 1 pass, (3) 2 passes, and (4) 4 passes ECAPed

AA 1050 electrode at an open circuit potential after its immersion in AGW for 20 min.

Nyquist spectra shown in Fig. 7 and Fig. 8a with the parameters recorded in Table 2 clearly

revealed that the values of RS, RP1 and RP2 increased with increasing the pass time number for the AA

1050 alloy. This is attributed to the formation of a passive film and/or corrosion products, which gets

thicker with time and could lead to the decrease in jCorr and KCorr and also the increase in RP values we

have seen in polarization data (Fig. 2, Fig. 3 and Table 1) under the same conditions. The semicircles

at high frequencies in Fig. 7 and Fig. 8a are generally associated with the relaxation of electrical

double layer capacitors and the diameters of the high frequency semicircles can be considered as the

charge transfer resistance (RP = RP1 + RP2) [37].

The polarization resistance measured by EIS is a measure of the uniform corrosion rate as

opposed to tendency towards localized corrosion. The decrease Cdl values with ECAP pass time is due

to the reduced access of charged species to the surface suggest that the dissolution of the alloy via

mass transport decreases. The CPEs (Q) with their n values > 0.5 and close to 1.0 represent double

Int. J. Electrochem. Sci., Vol. 7, 2012

2856

layer capacitors with some pores; the decrease of CPEs with the increase of number of ECAP passes

provides another indication on the increased passivation of AA 1050.

0 10 20 30 40 0

10 -1

10 0

10 1

10 2

10 3

10 4

10 5

10 1

10 2

10 3

10 4

10 5

10 -1

10 0

10 1

10 2

10 3

10 4

10 5

(c)

(b)

(a) 2

-Z " /

k 

.c m

Z' / k.cm 2

|Z | 

.c m

Frequency / Hz

P h

a se

o f

Z (

d e g

)

Figure 8. Nyquist (a), Bode (b) and phase angle (c) plots for (1) annealed alloy and (2) 4 passes

ECAPed AA 1050 electrode at an open circuit potential after its immersion in AGW for 10

days.

Figure 9. The equivalent circuit model used to fit the experimental data presented in Fig. 7 and Fig.

8a. See text for symbols used in the circuit.

Int. J. Electrochem. Sci., Vol. 7, 2012

2857

Table 2. EIS parameters obtained by fitting the Nyquist plots shown in Fig. 7 and Fig. 8a with the

equivalent circuit shown in Fig. 9 for AA 1050 electrodes after 20 min and 10 days of

immersion in Arabian Gulf water.

AA 1050 alloy

Parameter

RS /

Ω cm 2

Q RP1 /

k Ω cm 2

Cdl /

µF cm -2

RP2 /

k Ω cm 2 YQ/ µF cm

-2 n

0 pass (20 min) 6.23 32.89 0.83 0.201 26.14 5.51

1 pass (20 min) 8.81 25.34 0.80 0.860 19.01 7.75

2 passes (20 min) 9.45 14.30 0.80 2.86 16.75 9.19

4 passes (20 min) 11.28 5.48 0.76 1.731 13.07 11.39

0 pass (10 days) 8.90 0.56 0.80 1.91 2.79 9.58

4 passes (10 days) 12.49 0.19 0.88 3.28 1.89 23.98

Increasing the immersion time from 20 min to 10 days also enhances the values of RS, RP1, and

RP2 and decreases the values of CPEs and Cdl, which means the alloy surface gets more passivated as

the exposure time before measurements increases. Elongation of immersion period leads to

accumulation of corrosion products and protective oxide layers on the alloy surface and thus decreases

the uniform corrosion. This was also confirmed by the increase in the impedance of the interface (Fig.

8b) and the maximum phase angle (Fig. 8c) with increasing the immersion time. In general, EIS results

agree with CPP and CT measurements that the corrosion AA 1050 decreases with increasing the ECAP

pass time number as well as the immersion time of the alloy in the test solution before measurement.

4. CONCLUSIONS

A series of aluminum alloy 1050 was fabricated by using ECAP process after 0, 1, 2, and 4

passes. The electrochemical behavior of the annealed and the ECAPed AA 1050 in Arabian Gulf water

was investigated using variety of electrochemical methods. Cyclic polarization tests after 20 min and

10 days immersion in AGW indicated that the increase of ECAP passes time as well as immersion time

decrease the uniform corrosion of the alloy. The variation of current against time at – 630 mV vs.

Ag/AgCl after 20 min and 10 days also revealed that the dissolution of AA 1050 decreased with

increasing the pass time number, while increasing the exposure time increases the pitting corrosion of

the annealed alloy. Electrochemical impedance spectra proved that the solution and polarization

resistances decreased with increasing the pass time number up to 4 and immersion intervals. The

results together were internally consistent with each other, indicating clearly that the dissolution of the

alloy decreased with increasing the number of ECAP pass time and the best performance was shown

by 4 passes ECAPed AA 1050 and this effect increased with increasing the immersion time from 20

minutes to 10 days.

ACKNOWLEDGEMENT

The authors are grateful to the Center of Excellence for Research in Engineering Materials (CEREM)

for the financial support.

Int. J. Electrochem. Sci., Vol. 7, 2012

2858

References

1. Cheng Xu, S.V. Dobatkin, Z. Horita, T.G. Langdon, Mater. Sci. Eng. A, 500 (2009) 170–175. 2. Ehab A. El-Danaf, Mater. Sci. Eng. A, 487 (2008) 189–200. 3. K. Nakashima, Z. Horita, M. Nemoto, T.G. Langdon, Acta Mater., 46 (1998) 1589–99. 4. S. Rusz, K. Malaník, J. Kedroŉ, Arch. Mater. Sci. Eng., 34 (2008) 52‒56. 5. Jiang Jing-hua, Ma Ai-bin, Song Dan, N. Saito, Yuan Yu-chun, Y. Nishida, Trans. Nonferrous

Met. Soc. China, 20 (2010) 195‒200.

6. Min-Kyong Chung, Yoon-Seok Choi, Jung-Gu Kim, Young-Man Kim, Jae-Chul Lee, Mater. Sci. Eng. A, 366 (2004) 282–291.

7. Zhang Jing, Zhang Ke-shi, Wu Hwai-Chung, YU Mei-hua, Trans. Nonferrous Met. Soc. China, 19 (2009) 1303‒1311.

8. A. Vinogradov, A. Washikita, K. Kitagawa, V.I. Kopylov, Mater. Sci. Eng. A, 349 (2003) 218– 326.

9. Dan Song, AiBin Ma, Jinghua Jiang, Pinghua Lin, Donghui Yang, Junfeng Fan, Corros. Sci., 52 (2010) 481‒490.

10. R.Z. Valiev, T.G. Langdon, Prog. Mater. Sci., 51 (2006) 881–981. 11. El-Sayed M. Sherif, Int. J. Electrochem. Sci., 6 (2011) 1479. 12. E.M. Sherif, S.-M. Park, Electrochim. Acta, 51 (2006) 1313. 13. E.M. Sherif, S.-M. Park, J. Electrochem. Soc., 152 (2005) B205. 14. N.A. Ogurtsov, A.A. Pud, P. Kamarchik, G.S. Shapoval, Synth. Met., 143 (2004) 43. 15. I.B. Obot1, N.O. Obi-Egbedi, Int. J. Electrochem. Sci., 4 (2009) 1277. 16. A.Y. El-Etre, Corros. Sci., 43 (2001) 1031. 17. S.B. Saidman, J.B. Bessone, J. Electroanal. Chem., 521 (2002) 87. 18. R. Zandi-zand, A. Ershad-langroudi, A. Rahimi, J. Non-Crystalline Solids, 351 (2005) 1307–1311. 19. J.M. Vega, N. Granizo, D. de la Fuente, J. Simancas, M. Morcillo, Prog. Org. Coat. 70 (2011) 213. 20. P.M. Natishan, E. McCafferty, G.K. Hubler, J. Electrochem. Soc., 135 (1988) 321. 21. C.M.A. Brett, I.A.R. Gomes, J.P.S. Martins, Corros. Sci., 36 (1994) 915. 22. S.S.A. Rehim, H.H. Hassan, M.A. Amin, Appl. Surf. Sci., 187 (2002) 279. 23. S. Zein El Abedin, J. Appl. Electrochem., 31 (2001) 711. 24. M. Fujda, T. Kvačkaj, K. Nagyová, J. Met. Mater. Miner., 18 (2008) 81‒87. 25. Eiji Akiyama, Zuogui Zhang, Yoshimi Watanabe, Kaneaki Tsuzaki, J. Solid State Electrochem., 13

(2009) 277‒282.

26. M. Furukawa, Z. Horita, M. Nemoto, T.G. Langdon, J. Mater. Sci. 36 (2001) 2835 – 2843. 27. M. Furukawa, Z. Horita, T. G. Langdon, Adv. Eng. Mater., 3 (2001) 121 – 125. 28. Z. Horita, S. Lee, S. Ota, K. Neishi, T.G. Langdon, Mater. Sci. Forum. 357–359 (2001) 471–476. 29. G.Y. Elewady, I.A. El-Said, A.S. Fouda, Int. J. Electrochem. Sci., 3 (2008) 177. 30. F.D. Wall, M.A. Martinez, J.J. Vandenavyle, J. Electrochem. Soc., 151 (2004) B354. 31. El-Sayed M. Sherif, A.A. Almajid, F.H. Latif, H. Junaedi, Int. J. Electrochem. Sci., 6 (2011) 1085-

1099.

32. F.H. Latief, El-Sayed M. Sherif, A.A. Almajid, H. Junaedi, J. Anal. Appl. Pyrol., 92 (2011) 485- 492.

33. F. Hunkeler, G.S. Frankel, H. Bohni, Corrosion (Houston), 43 (1987) 189. 34. L. Tomcsanyi, K. Varga, I. Bartik, G. Horanyi, E. Maleczki, Electrochim. Acta, 34 (1989) 855. 35. E.M. Sherif, S.-M. Park, Corros. Sci., 48 (2006) 4065. 36. E.M. Sherif, S.-M. Park, J. Electrochem. Soc., 152 (2005) B428. 37. E.M. Sherif, S.-M. Park, Electrochim. Acta, 51 (2006) 6556. 38. El-Sayed M. Sherif, J.H. Potgieter, J.D. Comins, L. Cornish, P.A. Olubambi, C.N. Machio, J. Appl.

Electrochem., 39 (2009) 1385.

Int. J. Electrochem. Sci., Vol. 7, 2012

2859

39. El-Sayed M. Sherif, J.H. Potgieter, J.D. Comins, L. Cornish, P.A. Olubambi, C.N. Machio, Corros. Sci., 51 (2009) 1364.

40. El-Sayed M. Sherif, A.A. Almajid, J. Appl. Electrochem., 40 (2010) 1555. 41. El-Sayed M. Sherif, R.M. Erasmus, J.D. Comins, J. Electrochim. Acta, 55 (2010) 3657. 42. El-Sayed M. Sherif, R.M. Erasmus, J.D. Comins, J. Appl. Electrochem., 39 (2009) 83. 43. El-Sayed M. Sherif, R.M. Erasmus, J.D. Comins, Corros. Sci., 50 (2008) 3439. 44. El-Sayed M. Sherif, R.M. Erasmus, J.D. Comins, J. Colloid Inter. Sci., 209 (2007) 470. 45. El-Sayed M. Sherif, A.A. Almajid, Int. J. Electrochem. Sci., 6 (2011) 2131-2148. 46. E.M. Sherif, S.-M. Park, J. Electrochim. Acta, 51 (2006) 4665. 47. El-Sayed M. Sherif, R.M. Erasmus, J.D. Comins, J. Colloid Interface Sci., 306 (2007) 96. 48. El-Sayed M. Sherif, R.M. Erasmus, J.D. Comins, J. Colloid Interface Sci., 311 (2007) 144. 49. El-Sayed M. Sherif, Int. J. Electrochem. Sci., 6 (2011) 2284-2298. 50. El-Sayed M. Sherif, Mater. Chem. Phys., 129 (2011) 961-967. 51. El-Sayed M. Sherif, Int. J. Electrochem. Sci., 6 (2011) 2077-3092. 52. El-Sayed M. Sherif, A.A. Almajid, A.K. Bairamov, Eissa Al-Zahrani, Int. J. Electrochem. Sci., 6

(2011) 5430-5444.

53. El-Sayed M. Sherif, Int. J. Electrochem. Sci., 6 (2011) 5372-5387. 54. Khalil A. Khalil, El-Sayed M. Sherif, A.A. Almajid, Int. J. Electrochem. Sci., 6 (2011) 6184-6199. 55. El-Sayed M. Sherif, Int. J. Electrochem. Sci., 7 (2012) 1482-1495.

http://www.electrochemsci.org/

Chapter 6 Recommendation and Future work

Abstract

Aluminum is widely used in a plenty of industrial applications such as constructions, electrical engineering, transport and especially in aircraft industry for the manufacturing and production of different equipment and machineries. Despite the good properties of aluminum and its alloys, they are not perfect materials for engineering applications in all environments, since they suffer from corrosion caused by chemical interaction with their surroundings. Pitting corrosion is one of the major problems faced by aluminum components used in aircraft. In this project an experimental investigation is taken on the corrosion analysis of aluminum alloy material used in aircraft components. At present the nose landing gear undergoes severe corrosion problem and leads to failure of component. Pitting corrosion is localized accelerated dissolution of metal that occurs as a result of a breakdown of the protective passive film on the metal surface. This project provides a study about corrosion analysis of aluminum alloy (7076) used in aircraft components. Identification of material details, preparing test samples out of collected material and scope of improvements corrosion resistant recognized as key enabling to reduce the impact of corrosion on the integrity of critical aircraft assets. Hence three different types of coatings are developed and their corrosion resistance been tested.

In this project two types of heat treatment experiments been used to test the samples with coating condition and without coating condition. The material behavior was examined using, Hardness testing (before and after Heat treatment), corrosion test with dry and wet conditions and surface roughness measurement. Finally, the objective of the project is achieved successfully by the analysis of these results.

Keywords: Aluminum alloy (7076), Pitting corrosion, Hardness testing, Heat treatment.

Acknowledgements

Firstly I would like to thank my Supervisor Mr. Abhishek Mohandas to help me get a lot of information related to this project work and for his feedbacks during the process of report writing and organizing the project.

The amount of knowledge and information that I obtained from him was the pathway to the completion of this work. I would also like to thank Dr. Elansezhian Rasu, Mr.Mutlag, and Mr. Siram for their extended supports on metallic coatings inspection of samples, Hardness testing and roughness measurement at CCE-Mechanical & Dynamic labs.

I would like to thank all the teachers and staff at Caledonian College of Engineering who have made my project work in this college so enjoyable.

DECLARATION BY THE STUDENT ii Abstract iii Acknowledgements iv List of figures vii List of tables viiiError! Bookmark not defined. CHAPTER 1: INTRODUCTION 1 1.1 Problem statement: 2 1.2 The aim of the project: 2 1.3 The main objectives of the project are 2 1.4 Scope of studies 2 CHAPTER 2: LITERATURE REVIEW 3 2.1 Introduction: 3 2.2 Chapter Summary 4 CHAPTER 3: EXPERIMENTAL SETUP 5 3.1 Introduction: 5 3.2 Samples preparation: 5 3.3 Samples preparation before doing coating done by 6 3.3.1 Numbering of samples 6 3.3.2 Measuring the weight 6 3.3.3 Metalic coating of samples 7 3.3.4 Samples preparation for coating 7 3.3.5 Coatings Procedures 10 3.3.6 Chromium (Cr) coating 10 3.3.7 Zinc spray coating 11 3.4 Heat treatment of coated samples 12 3.4.1 Annealing. 13 3.4.2 Precipitation hardening……………………………………………………....13 3.5 Hardness testing………………………………………………………………..14 3.6 Corrosion test with wet conditions……………….……………………………16 3.7 Surface Roughness Measurement……………………………..……………..18 3.8 Chapter Summary…………………………………………………………..…18 CHAPTER 4 : RESULT AND DISCUSSION 19 4.1 Hardness testing. 19 4.2 Corrosion test with wet conditions 21 4.3 Surface Roughness Measurement. 22 4.4 Chapter Summary……………………………………………………………….24 CHAPTER 5: CONCLUSION 25 CHAPTER 6: RECOMMENDATION AND FUTURE WORK 26 6.1 Recommendation 26 6.2 Future Work 27 References: 28-29

LIST OF FIGURES

List of Figures: Page No

Figure 1.1 Corrosion Circle …………………………….………………….………….…....1

Figure 3.1 Samples before prepared …………………………………..………………….3

Figure 3.2 Samples after prepared …………………..…….…………………………..... 4

Figure 3.3 Paint Remover Acid ……………………………………………………………8 Figure 3.4 Wire Brush …………………...…………..……….…………………..……..….9

Figure 3.5 Samples Numbering …………………………………………………….…....10

Figure 3.6 Digital analytical balance………………………...………………….……..... 15

Figure 3.7 Acetone………………………………………………………………….….… 16

Figure 3.8 Samples with acetone……… ……………………………….………....…... 18

Figure 3.9 Distilled water …………...………………..……………………..... …..…..... 20

Figure 3.10 Aluminum paint, Aluminum oxide, Brush and Lab specimen container………………………………………………………………………………….... 21

Figure 3.11 Quantity of Aluminum paint in lab container …………….…..…..……... .21

Figure 3.12 Quantity of oxide Nano powder on Digital analytical balance …………. 21

Figure 3.13 Aluminum Oxide on Mixture Rotary Shaker ……………………..….…. 22

Figure 3.14 Preparation before start and during coating apply ………….……….… 23

Figure 3.15 Sample after coating …………….………………………………........…… 24

Figure 3.16 Chromium (Cr) coating ………………………………….……………....… 25

Figure 3.17 Samples before Zinc coating…...…………………………………….…… 26

Figure 3.18 Zinc spray can ……………………………………………..…………….… 27

Figure 3.19 Samples after Zinc coating.………..………………..………………....…. 28

Figure 3.20 Furnace used for annealing process …….…….……….…………….…. 29

Figure 3.21 Furnace used for Precipitation hardening………………….……….…… 30

Figure 3.22 Samples during quenching in cold water………….………………….…. 31

Figure 3.23 Rockwell hardness tester.…………………………….……………….….. 33

Figure 3.24 Different Rockwell Hardness Scales …………………………………….. 35

Figure 3.25 During load selection and Data Display after scale setting ….….…….. 35

Figure 3.26 Coated samples in the test aquarium …………………..……………….. 36

Figure 3.27 Hydrochloric Acid (Hcl).……………………………………………………. 36

Figure 3.28 Preparation of (Hcl) solution ……………………...………….….....….. 40

Figure 3.29 Samples during (Hcl) solution reaction …….……………...………...….. 40

Figure 3.30 Comparative of Samples weight …….……………...………...………..... 40

Figure 4.1 Comparative Hardness scale for Aluminum alloy 7075

before heat treatment…………………………………………………………………… 40

Figure 4.2 Comparative Hardness scale for Aluminum alloy 7075

after heat treatment.…….……………...………...……………………………...……... 40

Figure 4.3 Colum chart of the Removal Rate after168 hours in mm/h after calculated

……………………………………………………………………………………….……... 40

Figure 4.4 Chromium coated surface roughness profile…….……………........…..... 40

Figure 4.5 Zinc coated surface roughness profile…….……………..................…..... 40

Figure 4.6 Aluminum oxide coated surface roughness profile…….……….……....... 40

Figure 4.7 Colum chart of the measurements of surface roughness Rz and Rq in um…......................................................................................................................... 40

LIST OF TABLES

List of Tables: Page No

Table 4.1 Comparative Hardness scale for Aluminum alloy 7075 before heat treatment………………………………………………………………………………...5

Table 4.2 Comparative Hardness scale for Aluminum alloy 7075 after heat treatment…………………………….……………………………………………….….6

Table 4.3 Weights of coated samples after 168 hours of corrosion test in Seawater……………….…………………………………………………………….….5

Table 4.4 Parameters of surface roughness Rz and Rq…………………………...6

5 | Page

CHAPTER 1: INTRODUCTION

· Corrosion is the deterioration of materials by chemical interaction with their environment. Corrosion is a metallic cancer that can be controlled by recognizing the early warning signs and by correcting the condition at an early stage. In aerospace sector, Water or water vapour containing salt combines with oxygen in the atmosphere to produce the main source of corrosion in aircraft. Pitting corrosion is one of the major problems faced by aluminum components used in aircraft. In this project an experimental investigation has been taken on the corrosion analysis of aluminum alloy material used in aircraft component.

Figure.1.1 Corrosion Circle

Problem statement:

Due to the high speed heavy landing at a dusty runway. The high potential sand particles has removed the protective coating which lead to subjected the naked metals to sand blasting process allowing pitting corrosion to develop with the assist of oxidation due to the salty atmospheric environment at Seeb air base.

This project focuses on corrosion analysis of aluminum alloy material used in aircraft component.

The aim of the project:

This project provides a study about corrosion analysis of aluminum alloy material used in an aircraft component. Also, Implement corrosion resistance process experimentally. Furthermore, Heat treatment; conducted these operations to change the properties of metals.

The main objectives of the project are:

· To identify the major causes of corrosion.

· Implement corrosion resistance process.

· Analyze the results.

Scope of studies:

· Review most of the literature about corrosion in aluminum alloy material.

· Research on different engineering aspects of corrosion in aluminum alloy material and effect of heat treatment in change of metal properties.

· Study and understand the principle work of the metal coating and heat treatment to reduce the corrosion in aluminum alloy.

· Carry out roughness measurement of the coated samples. Followed by corrosion test with wet condition.

CHAPTER 2: LITERATURE REVIEW

2.1 Introduction:

In this study there are many references works have been referred to:-

As reported by Go swami& Lucadamo (2010) that “the presence of intermetallic precipitation in the alloy matrix improves the mechanical properties of the alloy but leads to a higher susceptibility to local corrosion .Since the second phase particles are usually preferred sites of cathodic or anodic activity. Severe localized attack always occurs due to the galvanic coupling between the active intermetallic phases and the nobler aluminum alloy matrix The alloy intermetallic influence the film structure as well as the corrosion resistance. It is crucial to understand the relative contributions of the solid solution matrix and intermetallic to the film behavior.”

(Go swami & Lucadamo, 2010)

AS suggested by Davis (1999) “relatively pure aluminum presents good corrosion resistance due to the formation of a barrier oxide film that is bonded strongly to its surface (passive layer) and, that if damaged, reforms immediately in most environments; i.e. re-passivation. This protective oxide layer is especially stable in near-neutral solutions of most non-halide salts leading to excellent pitting resistance. Nevertheless, in open air solutions containing halide ions, with Cl- being the most common, aluminum is susceptible to pitting corrosion. This process occurs, because in the presence of oxygen, the metal is readily polarized to its pitting potential and because chlorides contribute to the formation of soluble chlorinated aluminum (Hydr) oxide which interferes with the formation of a stable oxide on the aluminum surface.”

(Davis, 1999)

As indicated by Small man & White (1985) that “Aluminum and its alloys are used in a variety of cast and wrought forms and conditions of heat treatment. For over 70 years, it ranks next to iron and steel in the metal market. The demand for aluminum grows rapidly because of its unique combination of properties which makes it becomes one of the most versatile of engineering and construction material the optimum properties of aluminum are achieved by alloying additions and heat treatments. This promotes the formation of small hard precipitates which interfere with the motion of dislocations and improve its mechanical properties”.

(Small man & White, 1985)

AS stated by Heinz & Cough ran (2000) that “One of the most commonly used aluminum alloy for structural applications is 7075 Al alloy due to its attractive comprehensive properties such as low density, high strength, ductility, toughness and resistance to fatigue. The formation of these micro segregations (hard precipitates) and inherent residual stresses that are associated with their fabrication methods have serious negative effect on their mechanical properties. Hence, this study is aimed at resolving the problems of micro segregations and inherent residual stresses that are associated with aluminum-zinc for improved service performance.” (Heinz& Cough ran, 2000)

This supports Shyann & Chung (2000) “It has been extensively utilized in aircraft structural parts and other highly stressed structural applications. But aluminum-zinc alloy as it is in 7075 Al alloy is susceptible to embrittlement because of micro segregation of MgZn2 precipitates which may lead to catastrophic failure of components produced from it. The alloy is also susceptibility to stress corrosion cracking. This is due to inhomogeneity of the alloy and inherent residual stresses associated with its fabrication methods” (Shyann & Chung, 2000)

As reported by Adeyemi Dayo & Isa area (2012) that “Since the aluminum and its alloys are widely used in aerospace and automobiles, it is more essential to analyze the wear behavior of alloys. Wear is a removal of material from one or both of two solid surfaces in contact with each other under load and speed. Aluminum alloys of the 7075 series have been considered for structural applications in the automotive industry. The effects of annealing and age hardening heat treatments on the microstructural morphology and mechanical properties of 7075 Al alloy. The alloying elements lead to increase in the strength through formation of MgZn2 precipitate within the structure as the result of aging heat treatment. It was found that yield strength, ultimate tensile strength and hardness values increases but lowers the ductility and impact strength. The significant features of the heat treating process are the solution treatment temperature, the quench rate, the aging temperature and again time”. (Adeyemi Dayo & Isa area, 2012)

As reported by Juffs & Hughes (2001) that” The surface of a wrought or cast alloy is

likely to contain not only aluminum oxide alone, but may for example contain a fragment of a mixed Al-Mg oxide for alloys rich in Mg. This is primarily because of the heat of segregation of Mg is high and it has a favorable free energy for oxide formation. If however an Al surface is mechanically undisturbed - then the surface oxide is relatively protective. Though, most real surfaces have some sort of mechanical finishing which results in the formation of a near surface deformed layer (NSDL) and shingling. Shingling occurs where the alloy matrix is spread across the surface including IM particles in abrasion and milling. (Juffs & Hughes, 2001)

As noted by Aremo & Adeyemi (2012) that “aluminum and its alloys are used in a variety of cast and wrought forms and conditions of heat treatment. For over 70 years, it ranks next to iron and steel in the metal market. The demand for aluminum grows rapidly because of its unique combination of properties which makes it becomes one of the most versatile of engineering and construction material. The optimum properties of aluminum are achieved by alloying additions and heat treatments. This promotes the formation of small hard precipitates which interfere with the motion of dislocations and improve its mechanical properties. One of the most commonly used aluminum alloy for structural applications is 7075 Al alloy due to its attractive comprehensive properties such as low density, high strength, ductility, toughness and resistance to fatigue. It has been extensively utilized in aircraft structural parts and other highly stressed structural applications. But aluminum-zinc alloy as it is in 7075 Al alloy is susceptible to embrittlement because of micro segregation of MgZn2 precipitates which may lead to catastrophic failure of components produced from it. The alloy is also susceptibility to stress corrosion cracking. This is due to inhomogeneity of the alloy and inherent residual stresses associated with its fabrication methods”. (Aremo& Adeyemi, 2012)

Chapter 1 Introduction

2.2 Chapter Summary

This section included past studies and works in corrosion investigation and implement corrosion resistance process. The presence of intermetallic precipitation in the alloy matrix improves the mechanical properties of the alloy and were utilized as a part of this task as result and direction, on the grounds that it is vital to allude to old studies and attempts to expand the effectiveness of the venture.

Chapter 2 Literature Review

CHAPTER 3: EXPERIMENTAL SETUP

3.1 Introduction:

This study is concerned with treatment of the corrosion, which affects the outer layer of aluminum alloy using three different types of metal coating, and to study the effect of heat-treating operation on the corrosion resistance process. Likewise will be the work to reduce the occurrence of disasters resulting from corrosion which may affect the components, especially in the aviation sector because the human and material losses would be extremely critical. In this project, investigations are carried out by:

· Applying three different types of metallic coating.

· Heat treatment of coated samples (3 numbers, 1 from each coating type).

· Hardness testing (before and after Heat treatment).

· Corrosion test with wet condition.

· Surface roughness measurement.

3.2 Samples preparation:

In the beginning, samples are prepared in correct dimension of “20mm*20mm” and "50 mm *50 mm ".

$C:\Users\Administrator\Desktop\IMG_0773.JPG$

Figure 3.1 Samples before prepared. Figure 3.2 Samples After prepared.

Followed by, surface preparation/cleaning of samples is done with wire brush and paint remover acid.

$C:\Users\Administrator\Desktop\wire brush.jpg$ Figure 3.3 Paint Remover Acid Figure 3.4 Wire Brush

3.3 Samples preparation before doing coating done by:

Numbering of samples:

Basic method of numbering systems is included, that is important to know and identify the samples after coating in extraction of results.

$D:\T.Project ,Sep2015\T.Project images NOV 2015\IMG_3341.JPG$ $D:\T.Project ,Sep2015\T.Project images NOV 2015\IMG_3343.JPG$

Figure 3.5 Samples Numbering

Measuring the weight:

Weighing the samples before and after the coating to get the difference in weight by using digital analytical balance as shown in figures below.

$F:\T.Project ,Sep2015\T.Project images NOV 2015\IMG_3346.JPG$ $C:\Users\Administrator\AppData\Local\Microsoft\Windows\Temporary Internet Files\Content.Word\IMG_3348.jpg$

$C:\Users\Administrator\AppData\Local\Microsoft\Windows\Temporary Internet Files\Content.Word\IMG_4538.jpg$ $C:\Users\Administrator\AppData\Local\Microsoft\Windows\Temporary Internet Files\Content.Word\IMG_4540.jpg$

Figure 3.6 Digital analytical balance

METALLIC COATINGS OF SAMPLES:

I used mainly 3 types of metallic coatings in this project. They are Nano aluminum oxide (Al2o3), Chromium (Cr) and zinc coating.

Sample preparation for coating:

Surface preparation is the vital first step treatment of a substrate before the application of any coating. The performance of a coating is significantly affected by its ability to obey properly to the substrate material. It is usually well recognized that precise surface preparation is the most series factor affecting the total success of surface treatment. The existence of even small quantities of surface contaminants, grease, cutting oil, oxides etc. can physically damage and decrease coating adhesion to the substrate. The following are the procedures of samples preparation:

· Using personal protective equipment (PPE) to reduce our exposure to hazards.

· Cleaning the samples by using acetone, followed that by using distilled water as shown in figures below.

$C:\Users\yousuf111115\AppData\Local\Microsoft\Windows\Temporary Internet Files\Content.Word\IMG_3331.jpg$

Figure 3.7 Acetone and Cleaning samples with acetone

$C:\Users\yousuf111115\AppData\Local\Microsoft\Windows\Temporary Internet Files\Content.Word\IMG_3337.jpg$ $C:\Users\yousuf111115\AppData\Local\Microsoft\Windows\Temporary Internet Files\Content.Word\IMG_3351.jpg$

Figure 3.8 Samples with Acetone Figure 3.9 Distilled water

· Prepare a mixture of 50 ml of aluminum paint with 0.500 (g) of aluminum oxide in Lab specimen container then put the container on the rotary shaker for two hours until the mixing process well. As shown in figures below.

$C:\Users\yousuf111115\AppData\Local\Microsoft\Windows\Temporary Internet Files\Content.Word\IMG_3471.jpg$ $C:\Users\yousuf111115\AppData\Local\Microsoft\Windows\Temporary Internet Files\Content.Word\IMG_3475.jpg$

Figure 3.10 Al, paint, Al, oxide, Figure 3.11 Quantity of Al paint in lab container Brush and Lab specimen container.

$C:\Users\yousuf111115\AppData\Local\Microsoft\Windows\Temporary Internet Files\Content.Word\IMG_3480.jpg$ $C:\Users\yousuf111115\AppData\Local\Microsoft\Windows\Temporary Internet Files\Content.Word\IMG_3484.jpg$

Figure 3.12 Quantity of oxide Nano powder on Digital analytical balance

$C:\Users\yousuf111115\AppData\Local\Microsoft\Windows\Temporary Internet Files\Content.Word\IMG_3488.jpg$

Figure 3.13 Aluminum Oxide on Mixture Rotary Shaker

Coatings Procedures:

Aluminum oxide layer above the aluminum samples is to prevent oxygen and water, which they are in the air, to contact the metal located below them. So that is going to stop the oxidation process at an early stage. The following are the steps of samples coating with Aluminum oxide:

1. After cleaning the samples, followed by scratching process to them with emery paper to let coating layer contact with samples metal.

2. Equally apply the aluminum oxide mixture to all sides of the samples.

3. Expose coated samples to exposure area for dry to a period of time about 2 hours.

4. Repeat steps (1),(2)and (3) until obtain the proper thickness of aluminum oxide coating on the samples.

Figure 3.14 Preparation before start and During coating apply

Figure 3.15 Sample after coating

Chromium (Cr) coating:

Chrome coating is used to provide a very high degree of hardness on the surface of a metal to improve wear resistance, reduce friction, and in some cases, improve corrosion resistance. Chrome coating is an electrolytic process that can be applied to regular aluminum, and other materials. This case details the applying of chrome coating to aluminum alloy surfaces as shown in figure 3.16.

1. Proper cleaning of the samples prior to coating.

2. Surfaces after coating should be homogeneous and uniform in color.

Samples before (Cr) coating Samples after (Cr) coating

Figure 3.16 Chromium (Cr) coating

Zinc spray coating:

Zinc spray provides all metals surfaces; it forms a quick draying, adhesive, protective layer of micro fine flakes. Metal parts sprayed with zinc spray showed no corrosion even after more than 550 hours. The innovative zinc flakes form a highly protective layer even against extreme weather and environmental influences.

Following procedures were carried out for zinc spray coating process:

1. Shake can before use until the mixing ball can be heard clearly.

2. Spray on evenly and crosswise at room temperature and at about 25 cm distances from the surface.

3. Dust-dry after approx. 15 minutes, fully hardened after approx. 10-12 hours.

4. Repeat steps (2) and (3) until obtain the proper thickness of zinc spray on the samples.

Figure 3.17 Samples before Zinc coating Figure 3.18 Zinc spray can

Figure 3.19 Samples after Zinc coating

3.4 Heat treatment of coated samples (3 samples, 1 from each coating type):

The heat treatment contains heating and cooling operations or the sequence of two or more such operations applied to any material in order to modify its metallurgical structure and change its physical, chemical and mechanical properties. In this project have been used two types of heat treatment to investigate the effects of annealing and precipitation hardening heat treatment on the hardness, and impact strength of aluminum alloy7075, details as follows:

Apparatus:

· Furnace.

· Bath with Cold Water.

· Long Reach Hose Grip Pliers to hold the samples.

· Watch.

· Gloves.

Annealing :

Metallographic and hardness test piece samples to 470 °C, soaking them at this temperature for 2 hours and then furnace cooled. As shown in figure below.

Figure 3.20 Furnace used for annealing process

Precipitation hardening:

Metallographic and hardness test piece samples at a temperature of 465 °C for 2 hours followed by rapid quenching in cold water. These quenched samples were then subjected to a precipitation hardening treatment (age hardening) by heating them to 120 °C, holding them at this temperature for 3 hours and then followed by air cooling to room temperature. As shown in figures below.

Figure 3.21 Furnace used for Precipitation hardening.

Figure 3.22 During Quenching in cold water

3.5 Hardness testing (before and after Heat treatment):

Figure 3.23 Rockwell hardness tester.

This test is done with Rockwell hardness test. It is characterizes the indentation Hardness of materials (Al 7075) through the scale of penetration of a diamond come or hardened steel ball indenter, loaded on a material test-piece. It is one of several definitions of hardness in material science.

· Procedures of Test :

1. Select the proper scale from Rockwell hardness scale plate been displayed on the device to suit to aluminum alloy samples. The scale is consisting of the correct indicator and load.

2. Place the surface area to be measured close to the indenter. It is important for the accuracy of the test that the sample

be held securely during the application of load.

3. Slowly move down the anvil of device to touch flat surface of the sample, therefore automatic display of the Rockwell hardness number on its screen.

4. Repeat step (3) in various parts of test samples, then take the average of readings been taken.

Figure 3.24 Different Rockwell Hardness Scales

Figure 3.25 During load selection and Data Display after scale setting

3.6 Corrosion test with wet conditions:-

Test in sea water depends on the simulation of the actual environmental conditions being experienced by the metal, this is widely variable environmental conditions, as controlled by the temperature, the amount of dissolved oxygen, type and amount of biological pollution and natural reproduction of microbes.

In this test ,a total of 4 samples of 3 different coatings and one without coating were completely immersed in an aquarium contains seawater with oxygen supply for 7 days at room temperature .Followed by, followed by treatment of the samples with solution of Hydrochloric Acid (Hcl) and water to get proper readings of weight. Therefore, to obtain data for comparison with weight loss corrosion data.

· Procedures of Test :

1. Put the samples in the aquarium and fill it with a certain amount of sea water.

2. Provide an oxygen to the aquarium during test by using electrical air pump.

3. Leave the Samples for a period of 7 days, then take it out and observe the results.

4. Solution is prepared (9:1), 100ml of Hydrochloric Acid (Hcl) and 900ml of (water) H2O.

5. Coated samples were treated with Hcl solution for 5 minutes.

6. Measure the weight of all samples after test by using digital analytical balance, monitor loss of weight.

Figure 3.26 Coated samples in the test aquarium.

$C:\Users\Administrator\AppData\Local\Microsoft\Windows\Temporary Internet Files\Content.Word\IMG_4752.jpg$ $C:\Users\Administrator\AppData\Local\Microsoft\Windows\Temporary Internet Files\Content.Word\IMG_4753.jpg$

Figure 3.27 Hydrochloric Acid (Hcl).

$C:\Users\Administrator\AppData\Local\Microsoft\Windows\Temporary Internet Files\Content.Word\IMG_4760.jpg$ $C:\Users\Administrator\AppData\Local\Microsoft\Windows\Temporary Internet Files\Content.Word\IMG_4771.jpg$ Figure 3.28 Preparation of solution Figure 3.29 During solution reaction

$C:\Users\Administrator\AppData\Local\Microsoft\Windows\Temporary Internet Files\Content.Word\IMG_4652.jpg$ $C:\Users\Administrator\AppData\Local\Microsoft\Windows\Temporary Internet Files\Content.Word\IMG_4772.jpg$ Initial weight Weight after test After Hcl treatment

Figure 3.30 Comparative of Samples weight

3.7 Surface Roughness Measurement:

The most important parameter describing surface integrity is surface roughness. Surface must be within certain limits of roughness. Therefore, measuring surface roughness is vital to quality control of machining work piece. In this test, we have been used Statistical descriptors for measuring roughness of samples.

3.8 Chapter Summary:

This chapter is talked about seven different types of tests and tasks which are:

initial samples preparation, samples preparation for coating, three different types of coatings procedures, two different types of Heat treatment to coated samples, Hardness testing (before and after Heat treatment), Corrosion test in seawater and Surface Roughness Measurement. Each one of those tests and tasks contains subtle elements of the methodology and obliged strategy.

Chapter 3 Experimental Setup

30 | Page

CHAPTER 4: RESULT AND DISCUSSION

This project is consisting of two major steps of experiments namely:

· Implement corrosion resistance process.

· Investigation & Analysis of the results.

Each experiment will be discussed clearly with investigation of their results.

4.1 Hardness testing (before and after Heat treatment):

As previously been explained for this test in the third chapter of this project, it was concluded that the hardness of aluminum increases after heat treatment process than before and the following results as in tables below,

Type of coating	Reading 1 in (g)	Reading 2 in (g)	Reading 3 in (g)	Average Readings in (g)
zinc	95	97.7	92.1	94.93
aluminum	85	88.4	86	86.46667
chrome	89.3	88.4	85.2	87.63333
Al without coating	85.2	86.6	87	86.26667

Table 4. 1 Comparative Hardness scale for Aluminum alloy 7075 before heat treatment

Type of coating	Reading 1 in (g)	Reading 2 in (g)	Reading 3 in (g)	Average Readings in (g)
zinc	104	101.3	100	101.7667
aluminum	88	89.7	90	89.23333
chrome	89.6	89.4	86.7	88.56667
Al without coating	85.2	86.6	87	86.26667

Table 4. 2 Comparative Hardness scale for Aluminum alloy 7075 after heat treatment

Figure 4.1 Comparative Hardness scale for Aluminum alloy 7075

before heat treatment.

Figure 4.2 Comparative Hardness scale for Aluminum alloy 7075

after heat treatment.

Through graphics above we notice that, hardness of sample been coated with chrome was more than others after heat treatment, therefore it improves properties of metal in corrosion resistance.

4.2 Corrosion test with wet conditions:

As previously been explained for this test in the chapter three of this project, it was concluded that samples of aluminum after 168 hours start loss of their weight with different types of coating and the following results as in tables below,

Type of coating	Initial weight (g) of samples before testing	Weight (g) of samples after 168 hours of testing	Removal Rate in mm/h After calculated
zinc	27.174	27.095	0.264
aluminum	24.829	24.823	0.00452
chrome	19.33	19.252	0.0696
Al without coating	20.129	20.035	0.0815

Table 4. 3 Weights of coated samples after 168 hours of corrosion test in Seawater

Figure 4. 4 Colum chart of the Removal Rate after168 hours in mm/h after calculated

From these results in terms of taking weights of tested samples by Digital analytical balance, we note that the sample with zinc coating was lost weight more than other comparative samples, while the sample coated with aluminum oxide lost the least weight and this shows it is the most resistant to corrosion.

4.3 Surface Roughness Measurement:

As previously been explained for this test in the chapter three of this project, it was concluded that by Surface Roughness Tester measured the surface roughness of samples gives root mean square deviation of the profile (Rq) and ten-point mean roughness (Rz), following results as in tables below :

Type of coating	Rz	Rq
zinc	65.99	18.22
aluminum	8.45	2.70
chrome	0.25	0.05

Table 4. 4 Parameters of surface roughness Rz and Rq

Figure 4. 5 Chromium coated surface roughness profile

Figure 4. 2 Zinc coated surface roughness profile

Figure 4. 7 Aluminum oxide coated surface roughness profile

Figure 4. 8 Colum chart of the measurements of surface roughness Rz and Rq in um

Through these results it is clear to us that the surface roughness of the sample with chrome coating is softer when compared to the rest of samples, and thus less likely to be friction which leads to the metal corrosion. On the other side, we found that sample with zinc coating was more surface roughness.

4.4 Chapter Summary:

This chapter is talked about results of all tests and tasks been carried out in this project which are:

Heat treatment to coated samples, Hardness testing (before and after Heat treatment), Corrosion test in seawater and Surface Roughness of coated samples. All scientific experiments are acceptable in terms of objective and iterative, where it does not affect the results if we repeated these experiments again and this ensures that the test or its result not be random and occur once.

Chapter 4 Result and Discussion

CHAPTER 5: CONCLUSION

The purpose of this project provides a study about corrosion analysis of aluminum alloy material used in an aircraft component. This is possible only by resisting the corrosion in aircraft components happens at high speed heavy landing at a dusty runway. The high potential sand particles has removed the protective coating which lead to subjected the naked metals to sand blasting process allowing pitting corrosion to develop with the assist of oxidation due to the salty atmospheric environment at Seeb Air Base.

The objectives of this project were achieved by three steps, identifying the major causes of corrosion, implement corrosion resistance process and analyze the results perfectly. I used three different types of coating followed by different types of testing for its analysis. The heat treatment of coated samples proved that hardness of sample been coated with chrome was more than others after heat treatment, therefore it improves properties of metal in corrosion resistance. Furthermore, results showed that sample with zinc coating was lost weight more than other comparative samples, while the sample coated with aluminum oxide lost the least weight and this shows it is the most resistant to corrosion. Also results showed that sample with chrome coating is softer when compared to the rest of samples, and thus less likely to be friction which leads to the metal corrosion. On the other side, we found that sample with zinc coating was more surface roughness.

Metal coatings and their thickness are vital in making the samples resist corrosion. From corrosion test results, it’s been noticed that samples with aluminum oxide coated sample showing the least corrosion values. These results and their comparisons are used for achieving the objectives of this project successfully.

Chapter 5 Conclusion

CHAPTER 6: RECOMMENDATIONS AND FUTURE WORK

6.1 Recommendation

The following details will explain the major issues and the recommendations in relation with this project work:

· Difficulty in finding specimens of the same parts used in aircraft but after a try has been taking a permit to use them for study purpose. Initial approval prior to starting work is recommended for the availability of materials.

· Time was not enough to carry out corrosion test with dry condition, so the time frame for the project execution has to be planned accordingly.

· Difficulty to find all the types of coating required to carry out coating process.

· Difficulty to carry out erosion tests due to the small sample size and therefore advised to increase their size.

6.2 Future Work

The current work has investigated some aspects of corrosion testing for Aluminum alloy using in aircraft components. However, there is still a room to conduct the corrosion analysis in terms of chemical and material properties. Few of such suggestions are listed below so that they can be carried out as an extension of this project work, so that key findings of this work could be justified.

· Analysis by optical microscopy, will conducted to help elucidate corrosion initiation sites, and degradation of coating.

· For corrosion test with dry condition, samples will be removed and analyzed for a longer exposure period.

· Conducting the same work using different metallic coating so that key results could be compared and a more relevant material coating could be identified.

References:

Royal Air Force of Oman, 2014.Corrosion prevention

And control manual. Lockheed Martin Corporation.

Mahesh, B. & Raman, R., 2014. Role of Nanostructure in Electrochemical Corrosion and High Temperature Oxidation: A Review. The Minerals, Metals & Materials Society and ASM International.45 (A). p. 5799-5818.

Tahamtan, S. & Halvaee, A., 2013.Fabrication of Al/A206–Al2O3 nano/micro composite by combining ball milling and stir casting technology. Mater Des 49:347

Pacheco, T., 1997.A comparison of two Nextel 440 fiber reinforced aluminum composites using acoustic emission. J Mater Sci 32:3135–3142

Parker, E., 1999. Pipe Line Corrosion and cathodic Protection.3rd edition.USA: Elsevier science.

Davis, J.R., 1999.Corrosion of Aluminum and Aluminum alloys.1St edition.USA: ASM International.

Newman Roger, 1976. Pitting Corrosion of Metals.

[Online]. Available from: http://www.electrochem.org/dl/interface/spr/spr10/spr10_p033-038.pdf. [Accessed: 27 Nov 2015].

Vereecken, J., & Vrije Universiteit Brussels, 1994. Corrosion Control of Aluminum-Forms of Corrosion and Prevention.

[Online].Available from: http://www.elinorcorp.com/uploads/TALAT_Lectures_Corrosion_Control_of_Aluminum.pdf. [Accessed: 27 Nov l 2015].

Jones, K., & Hoeppner, D.W., 2009.The Interaction between Pitting Corrosion, Grain Boundaries, and Constituent Particles during Corrosion Fatigue of 7075-T6 Aluminum Alloy. International Journal of Fatigue. 31. p. 686-692.

Włodarczyk, A., & Dobrzanski, LA., 2007. Influence of heat treatment on corrosion resistance of PM composite materials. J Achiev Mater Manuf Eng 24:127

Huang, X., & Quan, X., 2012. 3D analysis for pit evolution and pit-to-crack transition during corrosion fatigue. Journal of Zhejiang University.14. p. 292-299.

Abd El-aziz, K. & Hassam, M., 2015. Wear and Corrosion Behavior of Al–Si Matrix Composite Reinforced with Alumina. Journal of Bio- and Tribo-Corrosion . 1. p. 1-10.

Scrivener, K., & Young, J., 1997.Mechanisms of Chemical Degradation of Aluminum alloys.1st edition.UK: E&FN Spon.

Isadarea, A., Aremob, B., & Mosobalaje, O., 2013. Effect of Heat Treatment on Some Mechanical Properties of 7075 Aluminum Alloy. Prototype Engineering Development Institute Ilesha.1.p.190-194.

Kciuk, M., Kurc, A.,& Szewczenko, J.,2010. Structure and corrosion resistance of aluminum alloys. Institute of Engineering Materials and Biomaterials .41.p 74-81.

Sudhangshu, B., 2011.High Temperature Coatings.1st edition. Butterworth-Heinemann.

Joseph,R.,1999.Corrosion of Aluminum and Aluminum Alloys.1st edition.ASM International.

Buffalo, N., 1946.Relation between Inelastic Deformability and Thermal Expansion of Glass in Its Annealing Range. The American Ceramic Society.29.p 240–253

2 Chromium Reading 1 Reading 2 Reading 3 Average Reading 95 97.7 92.1 94.93 5 aluminum Oxide Reading 1 Reading 2 Reading 3 Average Reading 85 88.4 86 86.466666666666654 1 Zinc Reading 1 Reading 2 Reading 3 Average Reading 89.3 88.4 85.2 87.633333333333326 4 Al,with Out coating Reading 1 Reading 2 Reading 3 Average Reading 85.2 86.6 87 86.266666666666666 2 Chromium Reading 1 Reading 2 Reading 3 Average Reading 104 101.3 100 101.76666666666667 5 aluminum Oxide Reading 1 Reading 2 Reading 3 Average Reading 88 89.7 90 89.233333333333334 1 Zinc Reading 1 Reading 2 Reading 3 Average Reading 89.6 89.4 86.7 88.566666666666663 4 Al,with Out coating Reading 1 Reading 2 Reading 3 Average Reading 85.2 86.6 87 86.266666666666666 Removal Rate in mm/h After calculated zinc aluminum chrome Al without coating 0.26400000000000001 4.5199999999999997E-3 6.9599999999999995E-2 8.1500000000000003E-2

RProfile

5.0000000000000001E-4 1E-3 1.5E-3 2E-3 2.5000000000000001E-3 3.0000000000000001E-3 3.5000000000000001E-3 4.0000000000000001E-3 4.4999999999999997E-3 5.0000000000000001E-3 5.4999999999999997E-3 6.0000000000000001E-3 6.4999999999999997E-3 7.0000000000000001E-3 7.4999999999999997E-3 8.0000000000000002E-3 8.5000000000000006E-3 8.9999999999999993E-3 9.4999999999999998E-3 0.01 1.0500000000000001E-2 1.0999999999999999E-2 1.15E-2 1.2E-2 1.2500000000000001E-2 1.2999999999999999E-2 1.35E-2 1.4E-2 1.4500000000000001E-2 1.4999999999999999E-2 1.55E-2 1.6E-2 1.6500000000000001E-2 1.7000000000000001E-2 1.7500000000000002E-2 1.7999999999999999E-2 1.8499999999999999E-2 1.9E-2 1.95E-2 0.02 2.0500000000000001E-2 2.1000000000000001E-2 2.1499999999999998E-2 2.1999999999999999E-2 2.2499999999999999E-2 2.3E-2 2.35E-2 2.4E-2 2.4500000000000001E-2 2.5000000000000001E-2 2.5499999999999998E-2 2.5999999999999999E-2 2.6499999999999999E-2 2.7E-2 2.75E-2 2.8000000000000001E-2 2.8500000000000001E-2 2.9000000000000001E-2 2.9499999999999998E-2 0.03 3.0499999999999999E-2 3.1E-2 3.15E-2 3.2000000000000001E-2 3.2500000000000001E-2 3.3000000000000002E-2 3.3500000000000002E-2 3.4000000000000002E-2 3.4500000000000003E-2 3.5000000000000003E-2 3.5499999999999997E-2 3.5999999999999997E-2 3.6499999999999998E-2 3.6999999999999998E-2 3.7499999999999999E-2 3.7999999999999999E-2 3.85E-2 3.9E-2 3.95E-2 0.04 4.0500000000000001E-2 4.1000000000000002E-2 4.1500000000000002E-2 4.2000000000000003E-2 4.2500000000000003E-2 4.2999999999999997E-2 4.3499999999999997E-2 4.3999999999999997E-2 4.4499999999999998E-2 4.4999999999999998E-2 4.5499999999999999E-2 4.5999999999999999E-2 4.65E-2 4.7E-2 4.7500000000000001E-2 4.8000000000000001E-2 4.8500000000000001E-2 4.9000000000000002E-2 4.9500000000000002E-2 0.05 5.0500000000000003E-2 5.0999999999999997E-2 5.1499999999999997E-2 5.1999999999999998E-2 5.2499999999999998E-2 5.2999999999999999E-2 5.3499999999999999E-2 5.3999999999999999E-2 5.45E-2 5.5E-2 5.5500000000000001E-2 5.6000000000000001E-2 5.6500000000000002E-2 5.7000000000000002E-2 5.7500000000000002E-2 5.8000000000000003E-2 5.8500000000000003E-2 5.8999999999999997E-2 5.9499999999999997E-2 0.06 6.0499999999999998E-2 6.0999999999999999E-2 6.1499999999999999E-2 6.2E-2 6.25E-2 6.3E-2 6.3500000000000001E-2 6.4000000000000001E-2 6.4500000000000002E-2 6.5000000000000002E-2 6.5500000000000003E-2 6.6000000000000003E-2 6.6500000000000004E-2 6.7000000000000004E-2 6.7500000000000004E-2 6.8000000000000005E-2 6.8500000000000005E-2 6.9000000000000006E-2 6.9500000000000006E-2 7.0000000000000007E-2 7.0499999999999993E-2 7.0999999999999994E-2 7.1499999999999994E-2 7.1999999999999995E-2 7.2499999999999995E-2 7.2999999999999995E-2 7.3499999999999996E-2 7.3999999999999996E-2 7.4499999999999997E-2 7.4999999999999997E-2 7.5499999999999998E-2 7.5999999999999998E-2 7.6499999999999999E-2 7.6999999999999999E-2 7.7499999999999999E-2 7.8E-2 7.85E-2 7.9000000000000001E-2 7.9500000000000001E-2 0.08 8.0500000000000002E-2 8.1000000000000003E-2 8.1500000000000003E-2 8.2000000000000003E-2 8.2500000000000004E-2 8.3000000000000004E-2 8.3500000000000005E-2 8.4000000000000005E-2 8.4500000000000006E-2 8.5000000000000006E-2 8.5500000000000007E-2 8.5999999999999993E-2 8.6499999999999994E-2 8.6999999999999994E-2 8.7499999999999994E-2 8.7999999999999995E-2 8.8499999999999995E-2 8.8999999999999996E-2 8.9499999999999996E-2 0.09 9.0499999999999997E-2 9.0999999999999998E-2 9.1499999999999998E-2 9.1999999999999998E-2 9.2499999999999999E-2 9.2999999999999999E-2 9.35E-2 9.4E-2 9.4500000000000001E-2 9.5000000000000001E-2 9.5500000000000002E-2 9.6000000000000002E-2 9.6500000000000002E-2 9.7000000000000003E-2 9.7500000000000003E-2 9.8000000000000004E-2 9.8500000000000004E-2 9.9000000000000005E-2 9.9500000000000005E-2 0.1 0.10050000000000001 0.10100000000000001 0.1015 0000000000001 0.10199999999999999 0.10249999999999999 0.10299999999999999 0.10349999999999999 0.104 0.1045 0.105 0.1055 0.106 0.1065 0.107 0.1075 0.108 0.1085 0.109 0.1095 0.11 0.1105 0.111 0.1115 0.112 0.1125 0.113 0.1135 0.114 0.1145 0.115 0.11550000000000001 0.11600000000000001 0.11650000000000001 0.11700000000000001 0.11749999999999999 0.11799999999999999 0.11849999999999999 0.11899999999999999 0.1195 0.12 0.1205 0.121 0.1215 0.122 0.1225 0.123 0.1235 0.124 0.1245 0.125 0.1255 0.126 0.1265 0.127 0.1275 0.128 0.1285 0.129 0.1295 0.13 0.1305 0.13100000000000001 0.13150000000000001 0.13200000000000001 0.13250000000000001 0.13300000000000001 0.13350000000000001 0.13400000000000001 0.13450000000000001 0.13500000000000001 0.13550000000000001 0.13600000000000001 0.13650000000000001 0.13700000000000001 0.13750000000000001 0.13800000000000001 0.13850000000000001 0.13900000000000001 0.13950000000000001 0.14000000000000001 0.14050000000000001 0.14099999999999999 0.14149999999999999 0.14199999999999999 0.14249999999999999 0.14299999999999999 0.14349999999999999 0.14399999999999999 0.14449999999999999 0.14499999999999999 0.14549999999999999 0.1459999 9999999999 0.14649999999999999 0.14699999999999999 0.14749999999999999 0.14799999999999999 0.14849999999999999 0.14899999999999999 0.14949999999999999 0.15 0.15049999999999999 0.151 0.1515 0.152 0.1525 0.153 0.1535 0.154 0.1545 0.155 0.1555 0.156 0.1565 0.157 0.1575 0.158 0.1585 0.159 0.1595 0.16 0.1605 0.161 0.1615 0.16200000000000001 0.16250000000000001 0.16300000000000001 0.16350000000000001 0.16400000000000001 0.16450000000000001 0.16500000000000001 0.16550000000000001 0.16600000000000001 0.16650000000000001 0.16700000000000001 0.16750000000000001 0.16800000000000001 0.16850000000000001 0.16900000000000001 0.16950000000000001 0.17 0.17050000000000001 0.17100000000000001 0.17150000000000001 0.17199999999999999 0.17249999999999999 0.17299999999999999 0.17349999999999999 0.17399999999999999 0.17449999999999999 0.17499999999999999 0.17549999999999999 0.17599999999999999 0.17649999999999999 0.17699999999999999 0.17749999999999999 0.17799999999999999 0.17849999999999999 0.17899999999999999 0.17949999999999999 0.18 0.18049999999999999 0.18099999999999999 0.18149999999999999 0.182 0.1825 0.183 0.1835 0.184 0.1845 0.185 0.1855 0.186 0.1865 0.187 0.1875 0.188 0.1885 0.189 0.1895 0.19 0.1905 0.191 0.1915 0.192 0.1925 0.193 0.19350000000000001 0.19400000000000001 0.19450000000000001 0.19500000000000001 0.19550000000000001 0.19600000000000001 0.19650000000000001 0.19700000000000001 0.19750000000000001 0.19800000000000001 0.19850000000000001 0.19900000000000001 0.19950000000000001 0.2 0.20050000000000001 0.20100000000000001 0.20150000000000001 0.20200000000000001 0.20250000000000001 0.20300000000000001 0.20349999999999999 0.20399999999999999 0.20449999999999999 0.20499999999999999 0.20549999999999999 0.20599999999999999 0.20649999999999999 0.20699999999999999 0.20749999999999999 0.20799999999999999 0.20849999999999999 0.20899999999999999 0.20949999999999999 0.21 0. 21049999999999999 0.21099999999999999 0.21149999999999999 0.21199999999999999 0.21249999999999999 0.21299999999999999 0.2135 0.214 0.2145 0.215 0.2155 0.216 0.2165 0.217 0.2175 0.218 0.2185 0.219 0.2195 0.22 0.2205 0.221 0.2215 0.222 0.2225 0.223 0.2235 0.224 0.22450000000000001 0.22500000000000001 0.22550000000000001 0.22600000000000001 0.22650000000000001 0.22700000000000001 0.22750000000000001 0.22800000000000001 0.22850000000000001 0.22900000000000001 0.22950000000000001 0.23 0.23050000000000001 0.23100000000000001 0.23150000000000001 0.23200000000000001 0.23250000000000001 0.23300000000000001 0.23350000000000001 0.23400000000000001 0.23449999999999999 0.23499999999999999 0.23549999999999999 0.23599999999999999 0.23649999999999999 0.23699999999999999 0.23749999999999999 0.23799999999999999 0.23849999999999999 0.23899999999999999 0.23949999999999999 0.24 0.24049999999999999 0.24099999999999999 0.24149999999999999 0.24199999999999999 0.24249999999999999 0.24299999999999999 0.24349999999999999 0.24399999999999999 0.2445 0.245 0.2455 0.246 0.2465 0.247 0.2475 0.248 0.2485 0.249 0.2495 0.25 0.2505 0.251 0.2515 0.252 0.2525 0.253 0.2535 0.254 0.2545 0.255 0.2555 0.25600000000000001 0.25650000000000001 0.25700000000000001 0.25750000000000001 0.25800000000000001 0.25850000000000001 0.25900000000000001 0.25950000000000001 0.26 0.26050000000000001 0.26100000000000001 0.26150000000000001 0.26200000000000001 0.26250000000000001 0.26300000000000001 0.26350000000000001 0.26400000000000001 0.26450000000000001 0.26500000000000001 0.26550000000000001 0.26600000000000001 0.26650000000000001 0.26700000000000002 0.26750000000000002 0.26800000000000002 0.26850000000000002 0.26900000000000002 0.26950000000000002 0.27 0.27050000000000002 0.27100000000000002 0.27150000000000002 0.27200000000000002 0.27250000000000002 0.27300000000000002 0.27350000000000002 0.27400000000000002 0.27450000000000002 0.27500000000000002 0.27550000000000002 0.27600000000000002 0.27650000000000002 0.27700000000000002 0.27750000000000002 0.27800000000000002 0.27850000000000003 0.27900000000000003 0.27950000000000003 0.28000000000000003 0.28050000000000003 0.28100000000000003 0.28149999999999997 0.28199999999999997 0.28249999999999997 0.28299999999999997 0.28349999999999997 0.28399999999999997 0.28449999999999998 0.28499999999999998 0.28549999999999998 0.28599999999999998 0.28649999999999998 0.28699999999999998 0.28749999999999998 0.28799999999999998 0.28849999999999998 0.28899999999999998 0.28949999999999998 0.28999999999999998 0.29049999999999998 0.29099999999999998 0.29149999999999998 0.29199999999999998 0.29249999999999998 0.29299999999999998 0.29349999999999998 0.2939999999 9999998 0.29449999999999998 0.29499999999999998 0.29549999999999998 0.29599999999999999 0.29649999999999999 0.29699999999999999 0.29749999999999999 0.29799999999999999 0.29849999999999999 0.29899999999999999 0.29949999999999999 0.3 0.30049999999999999 0.30099999999999999 0.30149999999999999 0.30199999999999999 0.30249999999999999 0.30299999999999999 0.30349999999999999 0.30399999999999999 0.30449999999999999 0.30499999999999999 0.30549999999999999 0.30599999999999999 0.30649999999999999 0.307 0.3075 0.308 0.3085 0.309 0.3095 0.31 0.3105 0.311 0.3115 0.312 0.3125 0.313 0.3135 0.314 0.3145 0.315 0.3155 0.316 0.3165 0.317 0.3175 0.318 0.31850000000000001 0.31900000000000001 0.31950000000000001 0.32 0.32050000000000001 0.32100000000000001 0.32150000000000001 0.32200000000000001 0.32250000000000001 0.32300000000000001 0.32350000000000001 0.32400000000000001 0.32450000000000001 0.32500000000000001 0.32550000000000001 0.32600000000000001 0.32650000000000001 0.32700000000000001 0.32750000000000001 0.32800000000000001 0.32850000000000001 0.32900000000000001 0.32950000000000002 0.33 0.33050000000000002 0.33100000000000002 0.33150000000000002 0.33200000000000002 0.33250000000000002 0.33300000000000002 0.33350000000000002 0.33400000000000002 0.33450000000000002 0.33500000000000002 0.33550000000000002 0.336000000 00000002 0.33650000000000002 0.33700000000000002 0.33750000000000002 0.33800000000000002 0.33850000000000002 0.33900000000000002 0.33950000000000002 0.34 0.34050000000000002 0.34100000000000003 0.34150000000000003 0.34200000000000003 0.34250000000000003 0.34300000000000003 0.34350000000000003 0.34399999999999997 0.34449999999999997 0.34499999999999997 0.34549999999999997 0.34599999999999997 0.34649999999999997 0.34699999999999998 0.34749999999999998 0.34799999999999998 0.34849999999999998 0.34899999999999998 0.34949999999999998 0.35 0.35049999999999998 0.35099999999999998 0.35149999999999998 0.35199999999999998 0.35249999999999998 0.35299999999999998 0.35349999999999998 0.35399999999999998 0.35449999999999998 0.35499999999999998 0.35549999999999998 0.35599999999999998 0.35649999999999998 0.35699999999999998 0.35749999999999998 0.35799999999999998 0.35849999999999999 0.35899999999999999 0.35949999999999999 0.36 0.36049999999999999 0.36099999999999999 0.36149999999999999 0.36199999999999999 0.36249999999999999 0.36299999999999999 0.36349999999999999 0.36399999999999999 0.36449999999999999 0.36499999999999999 0.36549999999999999 0.36599999999999999 0.36649999999999999 0.36699999999999999 0.36749999999999999 0.36799999999999999 0.36849999999999999 0.36899999999999999 0.3695 0.37 0.3705 0.371 0.3715 0.372 0.3725 0.373 0.3735 0.374 0.3745 0.375 0.3755 0.376 0.3765 0.377 0.3775 0.378 0.3785 0.379 0.3795 0.38 0.3805 0.38100000000000001 0.38150000000000001 0.38200000000000001 0.38250000000000001 0.38300000000000001 0.38350000000000001 0.38400000000000001 0.38450000000000001 0.38500000000000001 0.38550000000000001 0.38600000000000001 0.38650000000000001 0.38700000000000001 0.38750000000000001 0.38800000000000001 0.38850000000000001 0.38900000000000001 0.38950000000000001 0.39 0.39050000000000001 0.39100000000000001 0.39150000000000001 0.39200000000000002 0.39250000000000002 0.39300000000000002 0.39350000000000002 0.39400000000000002 0.39450000000000002 0.39500000000000002 0.39550000000000002 0.39600000000000002 0.39650000000000002 0.39700000000000002 0.3975 0000000000002 0.39800000000000002 0.39850000000000002 0.39900000000000002 0.39950000000000002 0.4 0.40050000000000002 0.40100000000000002 0.40150000000000002 0.40200000000000002 0.40250000000000002 0.40300000000000002 0.40350000000000003 0.40400000000000003 0.40450000000000003 0.40500000000000003 0.40550000000000003 0.40600000000000003 0.40649999999999997 0.40699999999999997 0.40749999999999997 0.40799999999999997 0.40849999999999997 0.40899999999999997 0.40949999999999998 0.41 0.41049999999999998 0.41099999999999998 0.41149999999999998 0.41199999999999998 0.41249999999999998 0.41299999999999998 0.41349999999999998 0.41399999999999998 0.41449999999999998 0.41499999999999998 0.41549999999999998 0.41599999999999998 0.41649999999999998 0.4169999999999999 8 0.41749999999999998 0.41799999999999998 0.41849999999999998 0.41899999999999998 0.41949999999999998 0.42 0.42049999999999998 0.42099999999999999 0.42149999999999999 0.42199999999999999 0.42249999999999999 0.42299999999999999 0.42349999999999999 0.42399999999999999 0.42449999999999999 0.42499999999999999 0.42549999999999999 0.42599999999999999 0.42649999999999999 0.42699999999999999 0.42749999999999999 0.42799999999999999 0.42849999999999999 0.42899999999999999 0.42949999999999999 0.43 0.43049999999999999 0.43099999999999999 0.43149999999999999 0.432 0.4325 0.433 0.4335 0.434 0.4345 0.435 0.4355 0.436 0.4365 0.437 0.4375 0.438 0.4385 0.439 0.4395 0.44 0.4405 0.441 0.4415 0.442 0.4425 0.443 0.44350000000000001 0.44400000000000001 0.44450000000000001 0.44500000000000001 0.44550000000000001 0.44600000000000001 0.44650000000000001 0.44700000000000001 0.44750000000000001 0.44800000000000001 0.44850000000000001 0.44900000000000001 0.44950000000000001 0.45 0.45050000000000001 0.45100000000000001 0.45150000000000001 0.45200000000000001 0.45250000000000001 0.45300000000000001 0.45350000000000001 0.45400000000000001 0.45450000000000002 0.45500000000000002 0.45550000000000002 0.45600000000000002 0.45650000000000002 0.45700000000000002 0.45750000000000002 0.45800000000000002 0.45850000000000002 0.45900000000000002 0.45950000000000002 0.46 0.46050000000000002 0.46100000000000002 0.46150000000000002 0.46200000000000002 0.46250000000000002 0.46300000000000002 0.46350000000000002 0.46400000000000002 0.46450000000000002 0.46500000000000002 0.46550000000000002 0.46600000000000003 0.46650000000000003 0.46700000000000003 0.46750000000000003 0.46800000000000003 0.46850000000000003 0.46899999999999997 0.46949999999999997 0.47 0.47049999999999997 0.47099999999999997 0.47149999999999997 0.47199999999999998 0.47249999999999998 0.47299999999999998 0.47349999999999998 0.47399999999999998 0.47449999999999998 0.47499999999999998 0.47549999999999998 0.47599999999999998 0.47649999999999998 0.47699999999999998 0.47749999999999998 0.47799999999999998 0.47849999999999998 0.47899999999999998 0.47949999999999998 0.48 0.48049999999999998 0.48099999999999998 0.48149999999999998 0.48199999999999998 0.48249999999999998 0.48299999999999998 0.48349999999999999 0.48399999999999999 0.48449999999999999 0.48499999999999999 0.48549999999999999 0.48599999999999999 0.48649999999999999 0.48699999999999999 0.48749999999999999 0.48799999999999999 0.48849999999999999 0.48899999999999999 0.48949999999999999 0.49 0.49049999999999999 0.49099999999999999 0.49149999999999999 0.49199999999999999 0.49249999999999999 0.49299999999999999 0.49349999999999999 0.49399999999999999 0.4945 0.495 0.4955 0.496 0.4965 0.497 0.4975 0.498 0.4985 0.499 0.4995 0.5 0.50049999999999994 0.501 0.50149999999999995 0.502 0.50249999999999995 0.503 0.50349999999999995 0.504 0.50449999999999995 0.505 0.50549999999999995 0.50600000000000001 0.50649999999999995 0.50700000000000001 0.50749999999999995 0.50800000000000001 0.50849999999999995 0.50900000000000001 0.50949999999999995 0.51 0.51049999999999995 0.51100000000000001 0.51149999999999995 0.51200000000000001 0.51249999999999996 0.51300000000000001 0.51349999999999996 0.51400000000000001 0.51449999999999996 0.51500000000000001 0.51549999999999996 0.51600000000000001 0.51649999999999996 0.51700000000000002 0.51749999999999996 0.51800000000000002 0.51849999999999996 0.51900000000000002 0.519499999999999 96 0.52 0.52049999999999996 0.52100000000000002 0.52149999999999996 0.52200000000000002 0.52249999999999996 0.52300000000000002 0.52349999999999997 0.52400000000000002 0.52449999999999997 0.52500000000000002 0.52549999999999997 0.52600000000000002 0.52649999999999997 0.52700000000000002 0.52749999999999997 0.52800000000000002 0.52849999999999997 0.52900000000000003 0.52949999999999997 0.53 0.53049999999999997 0.53100000000000003 0.53149999999999997 0.53200000000000003 0.53249999999999997 0.53300000000000003 0.53349999999999997 0.53400000000000003 0.53449999999999998 0.53500000000000003 0.53549999999999998 0.53600000000000003 0.53649999999999998 0.53700000000000003 0.53749999999999998 0.53800000000000003 0.53849999999999998 0.53900000000000003 0.53949999999999998 0.54 0.54049999999999998 0.54100000000000004 0.54149999999999998 0.54200000000000004 0.54249999999999998 0.54300000000000004 0.54349999999999998 0.54400000000000004 0.54449999999999998 0.54500000000000004 0.54549999999999998 0.54600000000000004 0.54649999999999999 0.54700000000000004 0.54749999999999999 0.54800000000000004 0.54849999999999999 0.54900000000000004 0.54949999999999999 0.55000000000000004 0.55049999999999999 0.55100000000000005 0.55149999999999999 0.55200000000000005 0.55249999999999999 0.55300000000000005 0.55349999999999999 0.55400000000000005 0.55449999999999999 0.55500000000000005 0.55549999999999999 0.55600000000000005 0.55649999999999999 0.55700000000000005 0.5575 0.55800000000 000005 0.5585 0.55900000000000005 0.5595 0.56000000000000005 0.5605 0.56100000000000005 0.5615 0.56200000000000006 0.5625 0.56299999999999994 0.5635 0.56399999999999995 0.5645 0.56499999999999995 0.5655 0.56599999999999995 0.5665 0.56699999999999995 0.5675 0.56799999999999995 0.56850000000000001 0.56899999999999995 0.56950000000000001 0.56999999999999995 0.57050000000000001 0.57099999999999995 0.57150000000000001 0.57199999999999995 0.57250000000000001 0.57299999999999995 0.57350000000000001 0.57399999999999995 0.57450000000000001 0.57499999999999996 0.57550000000000001 0.57599999999999996 0.57650000000000001 0.57699999999999996 0.57750000000000001 0.57799999999999996 0.57850000000000001 0.57899999999999996 0.57950000000000002 0.57999999999999996 0.58050000000000002 0.58099999999999996 0.58150000000000002 0.58199999999999996 0.58250000000000002 0.58299999999999996 0.58350000000000002 0.58399999999999996 0.58450000000000002 0.58499999999999996 0.58550000000000002 0.58599999999999997 0.58650000000000002 0.58699999999999997 0.58750000000000002 0.58799999999999997 0.58850000000000002 0.58899999999999997 0.58950000000000002 0.59 0.59050000000000002 0.59099999999999997 0.59150000000000003 0.59199999999999997 0.59250000000000003 0.59299999999999997 0.59350000000000003 0.59399999999999997 0.59450000000000003 0.59499999999999997 0.59550000000000003 0.59599999999999997 0.59650000000000003 0.59699999999999998 0.59750000000000003 0.59799999999999998 0.59850000000000003 0.59899999999999998 0.59950000000000003 0.6 0.60050000000000003 0.60099999999999998 0.60150000000000003 0.60199999999999998 0.60250000000000004 0.60299999999999998 0.60350000000000004 0.60399999999999998 0.60450000000000004 0.60499999999999998 0.60550000000000004 0.60599999999999998 0.60650000000000004 0.60699999999999998 0.60750000000000004 0.60799999999999998 0.60850000000000004 0.60899999999999999 0.60950000000000004 0.61 0.61050000000000004 0.61099999999999999 0.61150000000000004 0.61199999999999999 0.61250000000000004 0.61299999999999999 0.61350000000000005 0.61399999999999999 0.61450000000000005 0.61499999999999999 0.61550000000000005 0.61599999999999999 0.6165000000000 0005 0.61699999999999999 0.61750000000000005 0.61799999999999999 0.61850000000000005 0.61899999999999999 0.61950000000000005 0.62 0.62050000000000005 0.621 0.62150000000000005 0.622 0.62250000000000005 0.623 0.62350000000000005 0.624 0.62450000000000006 0.625 0.62549999999999994 0.626 0.62649999999999995 0.627 0.62749999999999995 0.628 0.62849999999999995 0.629 0.62949999999999995 0.63 0.63049999999999995 0.63100000000000001 0.63149999999999995 0.63200000000000001 0.63249999999999995 0.63300000000000001 0.63349999999999995 0.63400000000000001 0.63449999999999995 0.63500000000000001 0.63549999999999995 0.63600000000000001 0.63649999999999995 0.637 00000000000001 0.63749999999999996 0.63800000000000001 0.63849999999999996 0.63900000000000001 0.63949999999999996 0.64 0.64049999999999996 0.64100000000000001 0.64149999999999996 0.64200000000000002 0.64249999999999996 0.64300000000000002 0.64349999999999996 0.64400000000000002 0.64449999999999996 0.64500000000000002 0.64549999999999996 0.64600000000000002 0.64649999999999996 0.64700000000000002 0.64749999999999996 0.64800000000000002 0.64849999999999997 0.64900000000000002 0.64949999999999997 0.65 0.65049999999999997 0.65100000000000002 0.65149999999999997 0.65200000000000002 0.65249999999999997 0.65300000000000002 0.65349999999999997 0.65400000000000003 0.65449999999999997 0.65500000000000003 0.65549999999999997 0.65600000000000003 0.65649999999999997 0.65700000000000003 0.65749999999999997 0.65800000000000003 0.65849999999999997 0.65900000000000003 0.65949999999999998 0.66 0.66049999999999998 0.66100000000000003 0.66149999999999998 0.66200000000000003 0.66249999999999998 0.66300000000000003 0.66349999999999998 0.66400000000000003 0.66449999999999998 0.66500000000000004 0.66549999999999998 0.66600000000000004 0.66649999999999998 0.66700000000000004 0.66749999999999998 0.66800000000000004 0.66849999999999998 0.66900000000000004 0.66949999999999998 0.67 0.67049999999999998 0.67100000000000004 0.67149999999999999 0.67200000000000004 0.67249999999999999 0.67300000000000004 0.67349999999999999 0.67400000000000004 0.67449999999999999 0.67500000000000004 0.6 7549999999999999 0.67600000000000005 0.67649999999999999 0.67700000000000005 0.67749999999999999 0.67800000000000005 0.67849999999999999 0.67900000000000005 0.67949999999999999 0.68 0.68049999999999999 0.68100000000000005 0.68149999999999999 0.68200000000000005 0.6825 0.68300000000000005 0.6835 0.68400000000000005 0.6845 0.68500000000000005 0.6855 0.68600000000000005 0.6865 0.68700000000000006 0.6875 0.68799999999999994 0.6885 0.68899999999999995 0.6895 0.69 0.6905 0.69099999999999995 0.6915 0.69199999999999995 0.6925 0.69299999999999995 0.69350000000000001 0.69399999999999995 0.69450000000000001 0.69499999999999995 0.69550000000000001 0.69599999 999999995 0.69650000000000001 0.69699999999999995 0.69750000000000001 0.69799999999999995 0.69850000000000001 0.69899999999999995 0.69950000000000001 0.7 0.70050000000000001 0.70099999999999996 0.70150000000000001 0.70199999999999996 0.70250000000000001 0.70299999999999996 0.70350000000000001 0.70399999999999996 0.70450000000000002 0.70499999999999996 0.70550000000000002 0.70599999999999996 0.70650000000000002 0.70699999999999996 0.70750000000000002 0.70799999999999996 0.70850000000000002 0.70899999999999996 0.70950000000000002 0.71 0.71050000000000002 0.71099999999999997 0.71150000000000002 0.71199999999999997 0.71250000000000002 0.71299999999999997 0.71350000000000002 0.71399999999999997 0.71450000000000002 0.71499999999999997 0.71550000000000002 0.71599999999999997 0.71650000000000003 0.71699999999999997 0.71750000000000003 0.71799999999999997 0.71850000000000003 0.71899999999999997 0.71950000000000003 0.72 0.72050000000000003 0.72099999999999997 0.72150000000000003 0.72199999999999998 0.72250000000000003 0.72299999999999998 0.72350000000000003 0.72399999999999998 0.72450000000000003 0.72499999999999998 0.72550000000000003 0.72599999999999998 0.72650000000000003 0.72699999999999998 0.72750000000000004 0.72799999999999998 0.72850000000000004 0.72899999999999998 0.72950000000000004 0.73 0.73050000000000004 0.73099999999999998 0.73150000000000004 0.73199999999999998 0.73250000000000004 0.73299999999999998 0.73350000000000004 0.73399999999999999 0.734 50000000000004 0.73499999999999999 0.73550000000000004 0.73599999999999999 0.73650000000000004 0.73699999999999999 0.73750000000000004 0.73799999999999999 0.73850000000000005 0.73899999999999999 0.73950000000000005 0.74 0.74050000000000005 0.74099999999999999 0.74150000000000005 0.74199999999999999 0.74250000000000005 0.74299999999999999 0.74350000000000005 0.74399999999999999 0.74450000000000005 0.745 0.74550000000000005 0.746 0.74650000000000005 0.747 0.74750000000000005 0.748 0.74850000000000005 0.749 0.74950000000000006 0.75 0.75049999999999994 0.751 0.75149999999999995 0.752 0.75249999999999995 0.753 0.75349999999999995 0.754 0.75449999999999995 0.755 0.75549999999999995 0.75600000000000001 0.75649999999999995 0.75700000000000001 0.75749999999999995 0.75800000000000001 0.75849999999999995 0.75900000000000001 0.75949999999999995 0.76 0.76049999999999995 0.76100000000000001 0.76149999999999995 0.76200000000000001 0.76249999999999996 0.76300000000000001 0.76349999999999996 0.76400000000000001 0.76449999999999996 0.76500000000000001 0.76549999999999996 0.76600000000000001 0.76649999999999996 0.76700000000000002 0.76749999999999996 0.76800000000000002 0.76849999999999996 0.76900000000000002 0.76949999999999996 0.77 0.77049999999999996 0.77100000000000002 0.77149999999999996 0.77200000000000002 0.77249999999999996 0.77300000000000002 0.77349999999999997 0.77400000000000002 0.77449999999999997 0.77500000000000002 0.77549999999999997 0.77600000000000002 0.77649999999999997 0.77700000000000002 0.77749999999999997 0.77800000000000002 0.77849999999999997 0.77900000000000003 0.77949999999999997 0.78 0.78049999999999997 0.78100000000000003 0.78149999999999997 0.78200000000000003 0.78249999999999997 0.78300000000000003 0.78349999999999997 0.78400000000000003 0.78449999999999998 0.78500000000000003 0.78549999999999998 0.78600000000000003 0.78649999999999998 0.78700000000000003 0.78749999999999998 0.78800000000000003 0.78849999999999998 0.78900000000000003 0.78949999999999998 0.79 0.79049999999999998 0.79100000000000004 0.79149999999999998 0.79200000000000004 0.79249999999999998 0.79300000000000004 0.793 49999999999998 0.79400000000000004 0.79449999999999998 0.79500000000000004 0.79549999999999998 0.79600000000000004 0.79649999999999999 0.79700000000000004 0.79749999999999999 0.79800000000000004 0.79849999999999999 0.79900000000000004 0.79949999999999999 0.8 0.80049999999999999 0.80100000000000005 0.80149999999999999 0.80200000000000005 0.80249999999999999 0.80300000000000005 0.80349999999999999 0.80400000000000005 0.80449999999999999 0.80500000000000005 0.80549999999999999 0.80600000000000005 0.80649999999999999 0.80700000000000005 0.8075 0.80800000000000005 0.8085 0.80900000000000005 0.8095 0.81 0.8105 0.81100000000000005 0.8115 0.81200000000000006 0.8125 0.81299999999999994 0. 8135 0.81399999999999995 0.8145 0.81499999999999995 0.8155 0.81599999999999995 0.8165 0.81699999999999995 0.8175 0.81799999999999995 0.81850000000000001 0.81899999999999995 0.81950000000000001 0.82 0.82050000000000001 0.82099999999999995 0.82150000000000001 0.82199999999999995 0.82250000000000001 0.82299999999999995 0.82350000000000001 0.82399999999999995 0.82450000000000001 0.82499999999999996 0.82550000000000001 0.82599999999999996 0.82650000000000001 0.82699999999999996 0.82750000000000001 0.82799999999999996 0.82850000000000001 0.82899999999999996 0.82950000000000002 0.83 0.83050000000000002 0.83099999999999996 0.83150000000000002 0.83199999999999996 0.83250000000000002 0.83299999999999996 0.83350000000000002 0.83399999999999996 0.83450000000000002 0.83499999999999996 0.83550000000000002 0.83599999999999997 0.83650000000000002 0.83699999999999997 0.83750000000000002 0.83799999999999997 0.83850000000000002 0.83899999999999997 0.83950000000000002 0.84 0.84050000000000002 0.84099999999999997 0.84150000000000003 0.84199999999999997 0.84250000000000003 0.84299999999999997 0.84350000000000003 0.84399999999999997 0.84450000000000003 0.84499999999999997 0.84550000000000003 0.84599999999999997 0.84650000000000003 0.84699999999999998 0.84750000000000003 0.84799999999999998 0.84850000000000003 0.84899999999999998 0.84950000000000003 0.85 0.85050000000000003 0.85099999999999998 0.85150000000000003 0.85199999999999998 0.85250000 000000004 0.85299999999999998 0.85350000000000004 0.85399999999999998 0.85450000000000004 0.85499999999999998 0.85550000000000004 0.85599999999999998 0.85650000000000004 0.85699999999999998 0.85750000000000004 0.85799999999999998 0.85850000000000004 0.85899999999999999 0.85950000000000004 0.86 0.86050000000000004 0.86099999999999999 0.86150000000000004 0.86199999999999999 0.86250000000000004 0.86299999999999999 0.86350000000000005 0.86399999999999999 0.86450000000000005 0.86499999999999999 0.86550000000000005 0.86599999999999999 0.86650000000000005 0.86699999999999999 0.86750000000000005 0.86799999999999999 0.86850000000000005 0.86899999999999999 0.86950000000000005 0.87 0.87050000000000005 0.871 0.87150000000000005 0.872 0.87250000000000005 0.873 0.87350000000000005 0.874 0.87450000000000006 0.875 0.87549999999999994 0.876 0.87649999999999995 0.877 0.87749999999999995 0.878 0.87849999999999995 0.879 0.87949999999999995 0.88 0.88049999999999995 0.88100000000000001 0.88149999999999995 0.88200000000000001 0.88249999999999995 0.88300000000000001 0.88349999999999995 0.88400000000000001 0.88449999999999995 0.88500000000000001 0.88549999999999995 0.88600000000000001 0.88649999999999995 0.88700000000000001 0.88749999999999996 0.88800000000000001 0.88849999999999996 0.88900000000000001 0.88949999999999996 0.89 0.89049999999999996 0.89100000000000001 0.89149999999999996 0.89200000000000002 0.89249999999999996 0.89300000000000002 0.89349999999999996 0.89400000000000002 0.89449999999999996 0.89500000000000002 0.89549999999999996 0.89600000000000002 0.89649999999999996 0.89700000000000002 0.89749999999999996 0.89800000000000002 0.89849999999999997 0.89900000000000002 0.89949999999999997 0.9 0.90049999999999997 0.90100000000000002 0.90149999999999997 0.90200000000000002 0.90249999999999997 0.90300000000000002 0.90349999999999997 0.90400000000000003 0.90449999999999997 0.90500000000000003 0.90549999999999997 0.90600000000000003 0.90649999999999997 0.90700000000000003 0.90749999999999997 0.90800000000000003 0.90849999999999997 0.90900000000000003 0.90949999999999998 0.91 0.91049999999999998 0.91100000000000003 0.91149999999999998 0.91200000000000003 0.91249999999999998 0.91300000000000003 0.91349999999999998 0.91400000000000003 0.91449999999999998 0.91500000000000004 0.91549999999999998 0.91600000000000004 0.91649999999999998 0.91700000000000004 0.91749999999999998 0.91800000000000004 0.91849999999999998 0.91900000000000004 0.91949999999999998 0.92 0.92049999999999998 0.92100000000000004 0.92149999999999999 0.92200000000000004 0.92249999999999999 0.92300000000000004 0.92349999999999999 0.92400000000000004 0.92449999999999999 0.92500000000000004 0.92549999999999999 0.92600000000000005 0.92649999999999999 0.92700000000000005 0.92749999999999999 0.92800000000000005 0.92849999999999999 0.92900000000000005 0.92949999999999999 0.93 0.93049999999999999 0.93100000000000005 0.93149999999999999 0.93200000000000005 0.9325 0.93300000000000005 0.9335 0.93400000000000005 0.9345 0.93500000000000005 0.9355 0.93600000000000005 0.9365 0.93700000000000006 0.9375 0.93799999999999994 0.9385 0.93899999999999995 0.9395 0.94 0.9405 0.94099999999999995 0.9415 0.94199999999999995 0.9425 0.94299999999999995 0.94350000000000001 0.94399999999999995 0.94450000000000001 0.94499999999999995 0.94550000000000001 0.94599999999999995 0.94650000000000001 0.94699999999999995 0.94750000000000001 0.94799999999999995 0.94850000000000001 0.94899999999999995 0.94950000000000001 0.95 0.95050000000000001 0.95099999999999996 0.95150000000000001 0.95199999999999996 0.95250000000000001 0.95299999999999996 0.95350000000000001 0.95399999999999996 0.95450000000000002 0.95499999999999996 0.95550000000000002 0.95599999999999996 0.95650000000000002 0.95699999999999996 0.95750000000000002 0.95799999999999996 0.95850000000000002 0.95899999999999996 0.95950000000000002 0.96 0.96050000000000002 0.96099999999999997 0.96150000000000002 0.96199999999999997 0.96250000000000002 0.96299999999999997 0.96350000000000002 0.96399999999999997 0.96450000000000002 0.96499999999999997 0.96550000000000002 0.96599999999999997 0.96650000000000003 0.96699999999999997 0.96750000000000003 0.96799999999999997 0.96850000000000003 0.96899999999999997 0.96950000000000003 0.97 0.97050000000000003 0.97099999999999997 0.97150000000000003 0.97199999999999998 0.97250000000000003 0.97299999999999998 0.97350000000000003 0.97399999999999998 0.97450000000000003 0.97499999999999998 0.97550000000000003 0.97599999999999998 0.97650000000000003 0.97699999999999998 0.97750000000000004 0.97799999999999998 0.97850000000000004 0.97899999999999998 0.97950000000000004 0.98 0.98050000000000004 0.98099999999999998 0.98150000000000004 0.98199999999999998 0.98250000000000004 0.98299999999999998 0.98350000000000004 0.98399999999999999 0.98450000000000004 0.98499999999999999 0.98550000000000004 0.98599999999999999 0.98650000000000004 0.98699999999999999 0.98750000000000004 0.98799999999999999 0.98850000000000005 0.98899999999999999 0.98950 000000000005 0.99 0.99050000000000005 0.99099999999999999 0.99150000000000005 0.99199999999999999 0.99250000000000005 0.99299999999999999 0.99350000000000005 0.99399999999999999 0.99450000000000005 0.995 0.99550000000000005 0.996 0.99650000000000005 0.997 0.99750000000000005 0.998 0.99850000000000005 0.999 0.99950000000000006 1 1.0004999999999999 1.0009999999999999 1.0015000000000001 1.002 1.0024999999999999 1.0029999999999999 1.0035000000000001 1.004 1.0044999999999999 1.0049999999999999 1.0055000000000001 1.006 1.0065 1.0069999999999999 1.0075000000000001 1.008 1.0085 1.0089999999999999 1.0095000000000001 1.01 1.0105 1.0109999999999999 1.0115000000000001 1.012 1.0125 1.0129999999999999 1.0135000000000001 1.014 1.0145 1.0149999999999999 1.0155000000000001 1.016 1.0165 1.0169999999999999 1.0175000000000001 1.018 1.0185 1.0189999999999999 1.0195000000000001 1.02 1.0205 1.0209999999999999 1.0215000000000001 1.022 1.0225 1.0229999999999999 1.0235000000000001 1.024 1.0245 1.0249999999999999 1.0255000000000001 1.026 1.0265 1.0269999999999999 1.0275000000000001 1.028 1.0285 1.0289999999999999 1.0295000000000001 1.03 1.0305 1.0309999999999999 1.0315000000000001 1.032 1.0325 1.0329999999999999 1.0335000000000001 1.034 1.0345 1.0349999999999999 1.0355000000000001 1.036 1.0365 1.0369999999999999 1.0375000000000001 1.038 1.0385 1.0389999999999999 1.0395000000000001 1.04 1.0405 1.0409999999999999 1.0415000000000001 1.042 1.0425 1.0429999999999999 1.0435000000000001 1.044 1.0445 1.0449999999999999 1.0455000000000001 1.046 1.0465 1.0469999999999999 1.0475000000000001 1.048 1.0485 1.0489999999999999 1.0495000000000001 1.05 1.0505 1.0509999999999999 1.0515000000000001 1.052 1.0525 1.0529999999999999 1.0535000000000001 1.054 1.0545 1.0549999999999999 1.0555000000000001 1.056 1.0565 1.0569999999999999 1.0575000000000001 1.0580000000000001 1.0585 1.0589999999999999 1.0595000000000001 1.06 1.0605 1.0609999999999999 1.0615000000000001 1.0620000000000001 1.0625 1.0629999999999999 1.0634999999999999 1.0640000000000001 1.0645 1.0649999999999999 1.0654999999999999 1.0660000000000001 1.0665 1.0669999999999999 1.0674999999999999 1.0680000000000001 1.0685 1.069 1.0694999999999999 1.07 1.0705 1.071 1.0714999999999999 1.0720000000000001 1.0725 1.073 1.0734999999999999 1.0740000000000001 1.0745 1.075 1.0754999999999999 1.0760000000000001 1.0765 1.077 1.0774999999999999 1.0780000000000001 1.0785 1.079 1.0794999999999999 1.08 1.0805 1.081 1.0814999999999999 1.0820000000000001 1.0825 1.083 1.0834999999999999 1.0840000000000001 1.0845 1.085 1.0854999999999999 1.0860000000000001 1.0865 1.087 1.0874999999999999 1.0880000000000001 1.0885 1.089 1.0894999999999999 1.0900000000000001 1.0905 1.091 1.0914999999999999 1.0920000000000001 1.0925 1.093 1.0934999999999999 1.0940000000000001 1.0945 1.095 1.0954999999999999 1.0960000000000001 1.0965 1.097 1.0974999999999999 1.0980000000000001 1.0985 1.099 1.0994999999999999 1.1000000000000001 1.1005 1.101 1.1014999999999999 1.1020000000000001 1.1025 1.103 1.1034999999999999 1.1040000000000001 1.1045 1.105 1.1054999999999999 1.1060000000000001 1.1065 1.107 1.1074999999999999 1.1080000000000001 1.1085 1.109 1.1094999999999999 1.1100000000000001 1.1105 1.111 1.1114999999999999 1.1120000000000001 1.1125 1.113 1.1134999999999999 1.1140000000000001 1.1145 1.115 1.1154999999999999 1.1160000000000001 1.1165 1.117 1.1174999999999999 1.1180000000000001 1.1185 1.119 1.1194999999999999 1.1200000000000001 1.1205000000000001 1.121 1.1214999999999999 1.1220000000000001 1.1225000000000001 1.123 1.1234999999999999 1.1240000000000001 1.1245000000000001 1.125 1.1254999999999999 1.1259999999999999 1.1265000000000001 1.127 1.1274999999999999 1.1279999999999999 1.1285000000000001 1.129 1.1294999999999999 1.1299999999999999 1.1305000000000001 1.131 1.1315 1.1319999999999999 1.1325000000000001 1.133 1.1335 1.1339999999999999 1.1345000000000001 1.135 1.1355 1.1359999999999999 1.1365000000000001 1.137 1.1375 1.1379999999999999 1.1385000000000001 1.139 1.1395 1.1399999999999999 1.1405000000000001 1.141 1.1415 1.1419999999999999 1.1425000000000001 1.143 1.1435 1.1439999999999999 1.1445000000000001 1.145 1.1455 1.1459999999999999 1.1465000000000001 1.147 1.1475 1.1479999999999999 1.1485000000000001 1.149 1.1495 1.1499999999999999 1.1505000000000001 1.151 1.1515 1.1519999999999999 1.1525000000000001 1.153 1.1535 1.1539999999999999 1.1545000000000001 1.155 1.1555 1.1559999999999999 1.1565000000000001 1.157 1.1575 1.1579999999999999 1.1585000000000001 1.159 1.1595 1.1599999999999999 1.1605000000000001 1.161 1.1615 1.1619999999999999 1.1625000000000001 1.163 1.1635 1.1639999999999999 1.1645000000000001 1.165 1.1655 1.1659999999999999 1.1665000000000001 1.167 1.1675 1.1679999999999999 1.1685000000000001 1.169 1.1695 1.17 1.1705000000000001 1.171 1.1715 1.1719999999999999 1.1725000000000001 1.173 1.1735 1.1739999999999999 1.1745000000000001 1.175 1.1755 1.1759999999999999 1.1765000000000001 1.177 1.1775 1.1779999999999999 1.1785000000000001 1.179 1.1795 1.18 1.1805000000000001 1.181 1.1815 1.1819999999999999 1.1825000000000001 1.1830000000000001 1.1835 1.1839999999999999 1.1845000000000001 1.1850000000000001 1.1855 1.1859999999999999 1.1865000000000001 1.1870000000000001 1.1875 1.1879999999999999 1.1884999999999999 1.1890000000000001 1.1895 1.19 1.1904999999999999 1.1910000000000001 1.1915 1.1919999999999999 1.1924999999999999 1.1930000000000001 1.1935 1.194 1.1944999999999999 1.1950000000000001 1.1955 1.196 1.1964999999999999 1.1970000000000001 1.1975 1.198 1.1984999999999999 1.1990000000000001 1.1995 1.2 1.2004999999999999 1.2010000000000001 1.2015 1.202 1.2024999999999999 1.2030000000000001 1.2035 1.204 1.2044999999999999 1.2050000000000001 1.2055 1.206 1.2064999999999999 1.2070000000000001 1.2075 1.208 1.2084999999999999 1.2090000000000001 1.2095 1.21 1.2104999999999999 1.2110000000000001 1.2115 1.212 1.2124999999999999 1.2130000000000001 1.2135 1.214 1.2144999999999999 1.2150000000000001 1.2155 1.216 1.2164999999999999 1.2170000000000001 1.2175 1.218 1.2184999999999999 1.2190000000000001 1.2195 1.22 1.2204999999999999 1.2210000000000001 1.2215 1.222 1.2224999999999999 1.2230000000000001 1.2235 1.224 1.2244999999999999 1.2250000000000001 1.2255 1.226 1.2264999999999999 1.2270000000000001 1.2275 1.228 1.2284999999999999 1.2290000000000001 1.2295 1.23 1.2304999999999999 1.2310000000000001 1.2315 1.232 1.2324999999999999 1.2330000000000001 1.2335 1.234 1.2344999999999999 1.2350000000000001 1.2355 1.236 1.2364999999999999 1.2370000000000001 1.2375 1.238 1.2384999999999999 1.2390000000000001 1.2395 1.24 1.2404999999999999 1.2410000000000001 1.2415 1.242 1.2424999999999999 1.2430000000000001 1.2435 1.244 1.2444999999999999 1.2450000000000001 1.2455000000000001 1.246 1.2464999999999999 1.2470000000000001 1.2475000000000001 1.248 1.2484999999999999 1.2490000000000001 1.2495000000000001 1.25 1.2504999999999999 1.2509999999999999 1.2515000000000001 1.252 1.2524999999999999 1.2529999999999999 1.2535000000000001 1.254 1.2544999999999999 1.2549999999999999 1.2555000000000001 1.256 1.2565 1.2569999999999999 1.2575000000000001 1.258 1.2585 1.2589999999999999 1.2595000000000001 1.26 1.2605 1.2609999999999999 1.2615000000000001 1.262 1.2625 1.2629999999999999 1.2635000000000001 1.264 1.2645 1.2649999999999999 1.2655000000000001 1.266 1.2665 1.2669999999999999 1.2675000000000001 1.268 1.2685 1.2689999999999999 1.2695000000000001 1.27 1.2705 1.2709999999999999 1.2715000000000001 1.272 1.2725 1.2729999999999999 1.2735000000000001 1.274 1.2745 1.2749999999999999 1.2755000000000001 1.276 1.2765 1.2769999999999999 1.2775000000000001 1.278 1.2785 1.2789999999999999 1.2795000000000001 1.28 1.2805 1.2809999999999999 1.2815000000000001 1.282 1.2825 1.2829999999999999 1.2835000000000001 1.284 1.2845 1.2849999999999999 1.2855000000000001 1.286 1.2865 1.2869999999999999 1.2875000000000001 1.288 1.2885 1.2889999999999999 1.2895000000000001 1.29 1.2905 1.2909999999999999 1.2915000000000001 1.292 1.2925 1.2929999999999999 1.2935000000000001 1.294 1.2945 1.2949999999999999 1.2955000000000001 1.296 1.2965 1.2969999999999999 1.2975000000000001 1.298 1.2985 1.2989999999999999 1.2995000000000001 1.3 1.3005 1.3009999999999999 1.3015000000000001 1.302 1.3025 1.3029999999999999 1.3035000000000001 1.304 1.3045 1.3049999999999999 1.3055000000000001 1.306 1.3065 1.3069999999999999 1.3075000000000001 1.3080000000000001 1.3085 1.3089999999999999 1.3095000000000001 1.31 1.3105 1.3109999999999999 1.3115000000000001 1.3120000000000001 1.3125 1.3129999999999999 1.3134999999999999 1.3140000000000001 1.3145 1.3149999999999999 1.3154999999999999 1.3160000000000001 1.3165 1.3169999999999999 1.3174999999999999 1.3180000000000001 1.3185 1.319 1.3194999999999999 1.32 1.3205 1.321 1.3214999999999999 1.3220000000000001 1.3225 1.323 1.3234999999999999 1.3240000000000001 1.3245 1.325 1.3254999999999999 1.3260000000000001 1.3265 1.327 1.3274999999999999 1.3280000000000001 1.3285 1.329 1.3294999999999999 1.33 1.3305 1.331 1.3314999999999999 1.3320000000000001 1.3325 1.333 1.3334999999999999 1.3340000000000001 1.3345 1.335 1.3354999999999999 1.3360000000000001 1.3365 1.337 1.3374999999999999 1.3380000000000001 1.3385 1.339 1.3394999999999999 1.34 1.3405 1.341 1.3414999999999999 1.3420000000000001 1.3425 1.343 1.3434999999999999 1.3440000000000001 1.3445 1.345 1.3454999999999999 1.3460000000000001 1.3465 1.347 1.3474999999999999 1.3480000000000001 1.3485 1.349 1.3494999999999999 1.35 1.3505 1.351 1.3514999999999999 1.3520000000000001 1.3525 1.353 1.3534999999999999 1.3540000000000001 1.3545 1.355 1.3554999999999999 1.3560000000000001 1.3565 1.357 1.3574999999999999 1.3580000000000001 1.3585 1.359 1.3594999999999999 1.36 1.3605 1.361 1.3614999999999999 1.3620000000000001 1.3625 1.363 1.3634999999999999 1.3640000000000001 1.3645 1.365 1.3654999999999999 1.3660000000000001 1.3665 1.367 1.3674999999999999 1.3680000000000001 1.3685 1.369 1.3694999999999999 1.37 1.3705000000000001 1.371 1.3714999999999999 1.3720000000000001 1.3725000000000001 1.373 1.3734999999999999 1.3740000000000001 1.3745000000000001 1.375 1.3754999999999999 1.3759999999999999 1.3765000000000001 1.377 1.3774999999999999 1.3779999999999999 1.3785000000000001 1.379 1.3794999999999999 1.38 1.380 5000000000001 1.381 1.3815 1.3819999999999999 1.3825000000000001 1.383 1.3835 1.3839999999999999 1.3845000000000001 1.385 1.3855 1.3859999999999999 1.3865000000000001 1.387 1.3875 1.3879999999999999 1.3885000000000001 1.389 1.3895 1.39 1.3905000000000001 1.391 1.3915 1.3919999999999999 1.3925000000000001 1.393 1.3935 1.3939999999999999 1.3945000000000001 1.395 1.3955 1.3959999999999999 1.3965000000000001 1.397 1.3975 1.3979999999999999 1.3985000000000001 1.399 1.3995 1.4 1.4005000000000001 1.401 1.4015 1.4019999999999999 1.4025000000000001 1.403 1.4035 1.4039999999999999 1.4045000000000001 1.405 1.4055 1.4059999999999999 1.4065000000000001 1.407 1.4075 1.4079999999999999 1.4085000000000001 1.409 1.4095 1.41 1.4105000000000001 1.411 1.4115 1.4119999999999999 1.4125000000000001 1.413 1.4135 1.4139999999999999 1.4145000000000001 1.415 1.4155 1.4159999999999999 1.4165000000000001 1.417 1.4175 1.4179999999999999 1.4185000000000001 1.419 1.4195 1.42 1.4205000000000001 1.421 1.4215 1.4219999999999999 1.4225000000000001 1.423 1.4235 1.4239999999999999 1.4245000000000001 1.425 1.4255 1.4259999999999999 1.4265000000000001 1.427 1.4275 1.4279999999999999 1.4285000000000001 1.429 1.4295 1.43 1.4305000000000001 1.431 1.4315 1.4319999999999999 1.4325000000000001 1.4330000000000001 1.4335 1.4339999999999999 1.4345000000000001 1.4350000000000001 1.4355 1.4359999999999999 1.4365000000000001 1.4370000000000001 1.4375 1.4379999999999999 1.4384999999999999 1.4390000000000001 1.4395 1.44 1.4404999999999999 1.4410000000000001 1.4415 1.4419999999999999 1.4424999999999999 1.4430000000000001 1.4435 1.444 1.4444999999999999 1.4450000000000001 1.4455 1.446 1.4464999999999999 1.4470000000000001 1.4475 1.448 1.4484999999999999 1.4490000000000001 1.4495 1.45 1.4504999999999999 1.4510000000000001 1.4515 1.452 1.4524999999999999 1.4530000000000001 1.4535 1.454 1.4544999999999999 1.4550000000000001 1.4555 1.456 1.4564999999999999 1.4570000000000001 1.4575 1.458 1.4584999999999999 1.4590000000000001 1.4595 1.46 1.4604999999999999 1.4610000000000001 1.4615 1.462 1.4624999999999999 1.4630000000000001 1.4635 1.464 1.4644999999999999 1.4650000000000001 1.4655 1.466 1.4664999999999999 1.4670000000000001 1.4675 1.468 1.4684999999999999 1.4690000000000001 1.4695 1.47 1.4704999999999999 1.4710000000000001 1.4715 1.472 1.4724999999999999 1.4730000000000001 1.4735 1.474 1.4744999999999999 1.4750000000000001 1.4755 1.476 1.4764999999999999 1.4770000000000001 1.4775 1.478 1.4784999999999999 1.4790000000000001 1.4795 1.48 1.4804999999999999 1.4810000000000001 1.4815 1.482 1.4824999999999999 1.4830000000000001 1.4835 1.484 1.4844999999999999 1.4850000000000001 1.4855 1.486 1.4864999999999999 1.4870000000000001 1.4875 1.488 1.4884999999999999 1.4890000000000001 1.4895 1.49 1.4904999999999999 1.4910000000000001 1.4915 1.492 1.4924999999999999 1.4930000000000001 1.4935 1.494 1.4944999999999999 1.4950000000000001 1.4955000000000001 1.496 1.4964999999999999 1.4970000000000001 1.4975000000000001 1.498 1.4984999999999999 1.4990000000000001 1.4995000000000001 1.5 1.5004999999999999 1.5009999999999999 1.5015000000000001 1.502 1.5024999999999999 1.5029999999999999 1.5035000000000001 1.504 1.5044999999999999 1.5049999999999999 1.5055000000000001 1.506 1.5065 1.5069999999999999 1.5075000000000001 1.508 1.5085 1.5089999999999999 1.5095000000000001 1.51 1.5105 1.5109999999999999 1.5115000000000001 1.512 1.5125 1.5129999999999999 1.5135000000000001 1.514 1.5145 1.5149999999999999 1.5155000000000001 1.516 1.5165 1.5169999999999999 1.5175000000000001 1.518 1.5185 1.5189999999999999 1.5195000000000001 1.52 1.5205 1.5209999999999999 1.5215000000000001 1.522 1.5225 1.5229999999999999 1.5235000000000001 1.524 1.5245 1.5249999999999999 1.5255000000000001 1.526 1.5265 1.5269999999999999 1.5275000000000001 1.528 1.5285 1.5289999999999999 1.5295000000000001 1.53 1.5305 1.5309999999999999 1.5315000000000001 1.532 1.5325 1.5329999999999999 1.5335000000000001 1.534 1.5345 1.5349999999999999 1.5355000000000001 1.536 1.5365 1.5369999999999999 1.5375000000000001 1.538 1.5385 1.5389999999999999 1.5395000000000001 1.54 1.5405 1.5409999999999999 1.5415000000000001 1.542 1.5425 1.5429999999999999 1.5435000000000001 1.544 1.5445 1.5449999999999999 1.5455000000000001 1.546 1.5465 1.5469999999999999 1.5475000000000001 1.548 1.5485 1.5489999999999999 1.5495000000000001 1.55 1.5505 1.5509999999999999 1.5515000000000001 1.552 1.5525 1.5529999999999999 1.5535000000000001 1.554 1.5545 1.5549999999999999 1.5555000000000001 1.556 1.5565 1.5569999999999999 1.5575000000000001 1.5580000000000001 1.5585 1.5589999999999999 1.5595000000000001 1.56 1.5605 1.5609999999999999 1.5615000000000001 1.5620000000000001 1.5625 1.5629999999999999 1.5634999999999999 1.5640000000000001 1.5645 1.5649999999999999 1.5654999999999999 1.5660000000000001 1.5665 1.5669999999999999 1.5674999999999999 1.5680000000000001 1.5685 1.569 1.5694999999999999 1.57 1.5705 1.571 1.5714999999999999 1.5720000000000001 1.5725 1.573 1.5734999999999999 1.5740000000000001 1.5745 1.575 1.5754999999999999 1.5760000000000001 1.5765 1.577 1.5774999999999999 1.5780000000000001 1.5785 1.579 1.5794999999999999 1.58 1.5805 1.581 1.5814999999999999 1.5820000000000001 1.5825 1.583 1.5834999999999999 1.5840000000000001 1.5845 1.585 1.5854999999999999 1.5860000000000001 1.5865 1.587 1.5874999999999999 1.5880000000000001 1.5885 1.589 1.5894999999999999 1.59 1.5905 1.591 1.5914999999999999 1.5920000000000001 1.5925 1.593 1.5934999999999999 1.5940000000000001 1.5945 1.595 1.5954999999999999 1.5960000000000001 1.5965 1.597 1.5974999999999999 1.5980000000000001 1.5985 1.599 1.5994999999999999 1.6 1.6005 1.601 1.6014999999999999 1.6020000000000001 1.6025 1.603 1.6034999999999999 1.6040000000000001 1.6045 1.605 1.6054999999999999 1.6060000000000001 1.6065 1.607 1.6074999999999999 1.6080000000000001 1.6085 1.609 1.6094999999999999 1.61 1.6105 1.611 1.6114999999999999 1.6120000000000001 1.6125 1.613 1.6134999999999999 1.6140000000000001 1.6145 1.615 1.6154999999999999 1.6160000000000001 1.6165 1.617 1.6174999999999999 1.6180000000000001 1.6185 1.619 1.6194999999999999 1.62 1.6205000000000001 1.621 1.6214999999999999 1.6220000000000001 1.6225000000000001 1.623 1.6234999999999999 1.6240000000000001 1.6245000000000001 1.625 1.6254999999999999 1.6259999999999999 1.6265000000000001 1.627 1.6274999999999999 1.6279999999999999 1.6285000000000001 1.629 1.6294999999999999 1.63 1.6305000000000001 1.631 1.6315 1.6319999999999999 1.6325000000000001 1.633 1.6335 1.6339999999999999 1.6345000000000001 1.635 1.6355 1.6359999999999999 1.6365000000000001 1.637 1.6375 1.6379999999999999 1.6385000000000001 1.639 1.6395 1.64 1.6405000000000001 1.641 1.6415 1.6419999999999999 1.6425000000000001 1.643 1.6435 1.6439999999999999 1.6445000000000001 1.645 1.6455 1.6459999999999999 1.6465000000000001 1.647 1.6475 1.6479999999999999 1.6485000000000001 1.649 1.6495 1.65 1.6505000000000001 1.651 1.6515 1.6519999999999999 1.6525000000000001 1.653 1.6535 1.6539999999999999 1.6545000000000001 1.655 1.6555 1.6559999999999999 1.6565000000000001 1.657 1.6575 1.6579999999999999 1.6585000000000001 1.659 1.6595 1.66 1.6605000000000001 1.661 1.6615 1.6619999999999999 1.6625000000000001 1.663 1.6635 1.6639999999999999 1.6645000000000001 1.665 1.6655 1.6659999999999999 1.6665000000000001 1.667 1.6675 1.6679999999999999 1.6685000000000001 1.669 1.6695 1.67 1.6705000000000001 1.671 1.6715 1.6719999999999999 1.6725000000000001 1.673 1.6735 1.6739999999999999 1.6745000000000001 1.675 1.6755 1.6759999999999999 1.6765000000000001 1.677 1.6775 1.6779999999999999 1.6785000000000001 1.679 1.6795 1.68 1.6805000000000001 1.681 1.6815 1.6819999999999999 1.6825000000000001 1.6830000000000001 1.6835 1.6839999999999999 1.6845000000000001 1.6850000000000001 1.6855 1.6859999999999999 1.6865000000000001 1.6870000000000001 1.6875 1.6879999999999999 1.6884999999999999 1.6890000000000001 1.6895 1.69 1.6904999999999999 1.6910000000000001 1.6915 1.6919999999999999 1.6924999999999999 1.6930000000000001 1.6935 1.694 1.6944999999999999 1.6950000000000001 1.6955 1.696 1.6964999999999999 1.6970000000000001 1.6975 1.698 1.6984999999999999 1.6990000000000001 1.6995 1.7 1.7004999999999999 1.7010000000000001 1.7015 1.702 1.7024999999999999 1.7030000000000001 1.7035 1.704 1.7044999999999999 1.7050000000000001 1.7055 1.706 1.7064999999999999 1.7070000000000001 1.7075 1.708 1.7084999999999999 1.7090000000000001 1.7095 1.71 1.7104999999999999 1.7110000000000001 1.7115 1.712 1.7124999999999999 1.7130000000000001 1.7135 1.714 1.7144999999999999 1.7150000000000001 1.7155 1.716 1.7164999999999999 1.7170000000000001 1.7175 1.718 1.7184999999999999 1.7190000000000001 1.7195 1.72 1.7204999999999999 1.7210000000000001 1.7215 1.722 1.7224999999999999 1.7230000000000001 1.7235 1.724 1.7244999999999999 1.7250000000000001 1.7255 1.726 1.7264999999999999 1.7270000000000001 1.7275 1.728 1.7284999999999999 1.7290000000000001 1.7295 1.73 1.7304999999999999 1.7310000000000001 1.7315 1.732 1.7324999999999999 1.7330000000000001 1.7335 1.734 1.7344999999999999 1.7350000000000001 1.7355 1.736 1.7364999999999999 1.7370000000000001 1.7375 1.738 1.7384999999999999 1.7390000000000001 1.7395 1.74 1.7404999999999999 1.7410000000000001 1.7415 1.742 1.7424999999999999 1.7430000000000001 1.7435 1.744 1.7444999999999999 1.7450000000000001 1.7455000000000001 1.746 1.7464999999999999 1.7470000000000001 1.7475000000000001 1.748 1.7484999999999999 1.7490000000000001 1.7495000000000001 1.75 1.7504999999999999 1.7509999999999999 1.7515000000000001 1.752 1.7524999999999999 1.7529999999999999 1.7535000000000001 1.754 1.7544999999999999 1.7549999999999999 1.7555000000000001 1.756 1.7565 1.7569999999999999 1.7575000000000001 1.758 1.7585 1.7589999999999999 1.7595000000000001 1.76 1.7605 1.7609999999999999 1.7615000000000001 1.762 1.7625 1.7629999999999999 1.7635000000000001 1.764 1.7645 1.7649999999999999 1.7655000000000001 1.766 1.7665 1.7669999999999999 1.7675000000000001 1.768 1.7685 1.7689999999999999 1.7695000000000001 1.77 1.7705 1.7709999999999999 1.7715000000000001 1.772 1.7725 1.7729999999999999 1.7735000000000001 1.774 1.7745 1.7749999999999999 1.7755000000000001 1.776 1.7765 1.7769999999999999 1.7775000000000001 1.778 1.7785 1.7789999999999999 1.7795000000000001 1.78 1.7805 1.7809999999999999 1.7815000000000001 1.782 1.7825 1.7829999999999999 1.7835000000000001 1.784 1.7845 1.7849999999999999 1.7855000000000001 1.786 1.7865 1.7869999999999999 1.7875000000000001 1.788 1.7885 1.7889999999999999 1.7895000000000001 1.79 1.7905 1.7909999999999999 1.7915000000000001 1.792 1.7925 1.7929999999999999 1.7935000000000001 1.794 1.7945 1.7949999999999999 1.7955000000000001 1.796 1.7965 1.7969999999999999 1.7975000000000001 1.798 1.7985 1.7989999999999999 1.7995000000000001 1.8 1.8005 1.8009999999999999 1.8015000000000001 1.802 1.8025 1.8029999999999999 1.8035000000000001 1.804 1.8045 1.8049999999999999 1.8055000000000001 1.806 1.8065 1.8069999999999999 1.8075000000000001 1.8080000000000001 1.8085 1.8089999999999999 1.8095000000000001 1.81 1.8105 1.8109999999999999 1.8115000000000001 1.8120000000000001 1.8125 1.8129999999999999 1.8134999999999999 1.8140000000000001 1.8145 1.8149999999999999 1.8154999999999999 1.8160000000000001 1.8165 1.8169999999999999 1.8174999999999999 1.8180000000000001 1.8185 1.819 1.8194999999999999 1.82 1.8205 1.821 1.8214999999999999 1.8220000000000001 1.8225 1.823 1.8234999999999999 1.8240000000000001 1.8245 1.825 1.8254999999999999 1.8260000000000001 1.8265 1.827 1.8274999999999999 1.8280000000000001 1.8285 1.829 1.8294999999999999 1.83 1.8305 1.831 1.8314999999999999 1.8320000000000001 1.8325 1.833 1.8334999999999999 1.8340000000000001 1.8345 1.835 1.8354999999999999 1.8360000000000001 1.8365 1.837 1.8374999999999999 1.8380000000000001 1.8385 1.839 1.8394999999999999 1.84 1.8405 1.841 1.8414999999999999 1.8420000000000001 1.8425 1.843 1.8434999999999999 1.8440000000000001 1.8445 1.845 1.8454999999999999 1.8460000000000001 1.8465 1.847 1.8474999999999999 1.8480000000000001 1.8485 1.849 1.8494999999999999 1.85 1.8505 1.851 1.8514999999999999 1.8520000000000001 1.8525 1.853 1.8534999999999999 1.8540000000000001 1.8545 1.855 1.8554999999999999 1.8560000000000001 1.8565 1.857 1.8574999999999999 1.8580000000000001 1.8585 1.859 1.8594999999999999 1.86 1.8605 1.861 1.8614999999999999 1.8620000000000001 1.8625 1.863 1.8634999999999999 1.8640000000000001 1.8645 1.865 1.8654999999999999 1.8660000000000001 1.8665 1.867 1.8674999999999999 1.8680000000000001 1.8685 1.869 1.8694999999999999 1.87 1.8705000000000001 1.871 1.8714999999999999 1.8720000000000001 1.8725000000000001 1.873 1.8734999999999999 1.8740000000000001 1.8745000000000001 1.875 1.8754999999999999 1.8759999999999999 1.8765000000000001 1.877 1.8774999999999999 1.8779999999999999 1.8785000000000001 1.879 1.8794999999999999 1.88 1.8805000000000001 1.881 1.8815 1.8819999999999999 1.8825000000000001 1.883 1.8835 1.8839999999999999 1.8845000000000001 1.885 1.8855 1.8859999999999999 1.8865000000000001 1.887 1.8875 1.8879999999999999 1.8885000000000001 1.889 1.8895 1.89 1.8905000000000001 1.891 1.8915 1.8919999999999999 1.8925000000000001 1.893 1.8935 1.8939999999999999 1.8945000000000001 1.895 1.8955 1.8959999999999999 1.8965000000000001 1.897 1.8975 1.8979999999999999 1.8985000000000001 1.899 1.8995 1.9 1.9005000000000001 1.901 1.9015 1.9019999999999999 1.9025000000000001 1.903 1.9035 1.9039999999999999 1.9045000000000001 1.905 1.9055 1.9059999999999999 1.9065000000000001 1.907 1.9075 1.9079999999999999 1.9085000000000001 1.909 1.9095 1.91 1.9105000000000001 1.911 1.9115 1.9119999999999999 1.9125000000000001 1.913 1.9135 1.9139999999999999 1.9145000000000001 1.915 1.9155 1.9159999999999999 1.9165000000000001 1.917 1.9175 1.9179999999999999 1.9185000000000001 1.919 1.9195 1.92 1.9205000000000001 1.921 1.9215 1.9219999999999999 1.9225000000000001 1.923 1.9235 1.9239999999999999 1.9245000000000001 1.925 1.9255 1.9259999999999999 1.9265000000000001 1.927 1.9275 1.9279999999999999 1.9285000000000001 1.929 1.9295 1.93 1.9305000000000001 1.931 1.9315 1.9319999999999999 1.9325000000000001 1.9330000000000001 1.9335 1.9339999999999999 1.9345000000000001 1.9350000000000001 1.9355 1.9359999999999999 1.9365000000000001 1.9370000000000001 1.9375 1.9379999999999999 1.9384999999999999 1.9390000000000001 1.9395 1.94 1.9404999999999999 1.9410000000000001 1.9415 1.9419999999999999 1.9424999999999999 1.9430000000000001 1.9435 1.944 1.9444999999999999 1.9450000000000001 1.9455 1.946 1.9464999999999999 1.9470000000000001 1.9475 1.948 1.948499999999999 9 1.9490000000000001 1.9495 1.95 1.9504999999999999 1.9510000000000001 1.9515 1.952 1.9524999999999999 1.9530000000000001 1.9535 1.954 1.9544999999999999 1.9550000000000001 1.9555 1.956 1.9564999999999999 1.9570000000000001 1.9575 1.958 1.9584999999999999 1.9590000000000001 1.9595 1.96 1.9604999999999999 1.9610000000000001 1.9615 1.962 1.9624999999999999 1.9630000000000001 1.9635 1.964 1.9644999999999999 1.9650000000000001 1.9655 1.966 1.9664999999999999 1.9670000000000001 1.9675 1.968 1.9684999999999999 1.9690000000000001 1.9695 1.97 1.970499999 9999999 1.9710000000000001 1.9715 1.972 1.9724999999999999 1.9730000000000001 1.9735 1.974 1.9744999999999999 1.9750000000000001 1.9755 1.976 1.9764999999999999 1.9770000000000001 1.9775 1.978 1.9784999999999999 1.9790000000000001 1.9795 1.98 1.9804999999999999 1.9810000000000001 1.9815 1.982 1.9824999999999999 1.9830000000000001 1.9835 1.984 1.9844999999999999 1.9850000000000001 1.9855 1.986 1.9864999999999999 1.9870000000000001 1.9875 1.988 1.9884999999999999 1.9890000000000001 1.9895 1.99 1.9904999999999999 1.9910000000000001 1.9915 1.992 1.99 24999999999999 1.9930000000000001 1.9935 1.994 1.9944999999999999 1.9950000000000001 1.9955000000000001 1.996 1.9964999999999999 1.9970000000000001 1.9975000000000001 1.998 1.9984999999999999 1.9990000000000001 1.9995000000000001 2 -0.08 -0.08 -0.09 -0.1 -0.09 -0.09 -7.0000000000000007E-2 -0.05 -0.06 -0.08 -0.1 -0.11 -0.09 -0.04 -0.02 -0.02 -0.03 -0.04 -0.06 -0.06 -7.0000000000000007E-2 -0.08 -7.0000000000000007E-2 -7.0000000000000007E-2 -0.06 -0.09 -0.09 -7.0000000000000007E-2 -0.03 0.02 0.05 0.04 0.01 0.01 0 -0.02 -0.06 -0.08 -0.1 -0.09 -7.0000000000000007E-2 -7.0000000000000007E-2 -7.0000000000000007E-2 -7.0000000000000007E-2 -0.08 -0.08 -0.09 -7.0000000000000007E-2 -0.06 -0.03 -0.01 0.01 0 -0.01 -0.03 -0.04 -0.03 -0.01 -0.01 -0.03 -0.05 -7.0000000000000007E-2 -0.08 -7.0000000000000007E-2 -0.05 -0.03 -0.01 -0.01 -0.04 -0.08 -7.0000000000000007E-2 -7.0000000000000007E-2 -0.06 -0.05 -0.03 -0.01 0.03 0.04 0. 03 0 -0.03 -0.04 -0.04 -0.03 0 0.02 0.01 0 0 -0.02 -0.02 -0.02 -0.02 0.01 0.05 0.04 0 -0.04 -0.08 -7.0000000000000007E-2 -0.03 0 0.01 0.01 0.01 0.01 0.01 -0.01 0.01 0.01 0.01 0.01 0.02 0.01 0.01 0.02 0.04 0.06 7.0000000000000007E-2 0.05 0.01 -0.02 -0.03 -0.02 0.01 0.02 0.02 -0.01 -0.02 -0.03 -0.03 -0.03 -0.02 -0.02 -0.02 -0.01 -0.01 -0.01 0 0.01 0.02 0.02 0 -0.01 0.02 0.05 0.08 7.0000000000000007E-2 0.06 0.04 0.02 0 -0.01 0 0.01 0.02 0.02 0.02 0 0.01 0.02 0.05 7.0000000000000007E-2 7.0000000000000007E-2 7.0000000000000007E-2 0.05 0.03 0.02 0.01 0.01 0.04 0.06 7.0000000000000007E-2 0.08 0.05 0.01 0.01 0.04 0.04 0.03 0.02 0.02 0.02 0.03 0.05 0.05 0.02 -0.03 -0.03 -0.01 0.01 0.04 0.04 0.03 0.02 0.03 0.04 0.04 0.03 0.03 0.03 0.03 0.02 0.03 0.04 0.06 0.06 0.06 0.06 0.05 0.03 0 -0.01 0 0.02 0.03 0.06 0.08 0.09 7.0000000000000007E-2 0.06 0.06 0.05 0.03 0.02 0.01 0.03 0.04 0.03 0.01 -0.01 -0.03 -0.02 -0.02 -0.01 0 0.01 0.03 0.06 7.0000000000000007E-2 0.05 0.04 0.04 0.04 0.04 0.03 0.01 -0.02 -0.02 0 0.03 0.04 0.05 0.08 0.12 0.12 0.09 0.06 0.02 0 0 0.01 0.02 0.02 0.03 0.04 0.03 0.01 0.01 0.03 0.05 7.0000000000000007E-2 7.0000000000000007E-2 0.05 0.03 0.02 0.03 0.02 0.03 0.02 0.02 0.01 0.01 0.01 0.02 0.03 0.05 0.06 7.0000000000000007E-2 0.06 0.03 0 0 0 0.02 0.04 0.03 0.03 0.04 7.0000000000000007E-2 0.08 0.06 0.04 0.02 0.02 0.01 -0.02 -0.02 -0.01 0.01 0.02 0.02 0.02 0.01 -0.01 -0.01 0 0.02 0.02 0.02 0 -0.01 -0.01 0 0.02 0.04 0.02 -0.01 -0.01 0 0.02 0.04 0.02 0 -0.01 -0.01 -0.01 -0.01 -0.01 -0.02 0 0.01 0 -0.03 -0.04 -0.06 -0.04 -0.02 0 0.02 0 -0.02 -0.02 -0.02 -0.02 0 0.02 0.02 0 -0.04 -0.06 -0.06 -0.05 -0.03 -0.02 0.01 0.01 0 -0.02 -0.02 -0.03 -0.03 -0.04 -0.04 -0.05 -0.05 -0.04 -0.03 0 0.02 0.02 0 -0.02 -0.04 -0.05 -0.05 -0.08 -0.09 -0.08 -0.05 -0.04 -0.03 -0.02 -0.02 -0.02 -0.02 -0.03 -0.04 -0.04 -0.05 -0.03 -0.02 -0.01 -0.01 0.01 0.03 0.04 0.04 0.01 -0.02 -0.04 -0.05 -0.06 -0.06 -0.05 -0.04 -0.03 -0.05 -0.05 -0.05 -0.04 -0.01 0.02 0.02 0.03 0.03 0.02 0.02 0.02 0.03 0.03 0.03 0.02 0.01 -0.01 -0.04 -0.05 -0.04 -0.02 0 0 0.02 0.02 0.03 0.01 -0.01 0 0.04 0.04 0.03 0.01 -0.01 -0.03 -0.04 -0.03 0 0.02 0.02 0.03 0.02 0 0 0 -0.01 -0.01 -0.01 -0.01 0.01 0.03 0.04 0.01 -0.01 -0.05 -0.05 -0.06 -0.06 -0.06 -0.03 0.01 0.06 0.06 0.04 0.02 0.03 0.01 0 0 0.02 0.04 0.06 0.04 0.01 0.01 0.03 0.03 0.04 0.03 0.02 0.03 0.05 0.03 0.01 0.01 -0.01 -0.02 -0.04 -0.03 -0.02 0.01 0.02 0.02 0.03 0.05 0.04 0.04 0.04 0.04 0.06 0.06 0.08 0.11 0.12 0.11 0.09 7.0000000000000007E-2 0.06 0.05 0.02 0 0 0.01 0.02 0.02 0.04 0.04 0.04 0.03 0.03 0.06 0.08 0.06 0.04 0.04 0.05 7.0000000000000007E-2 0.09 0.1 0.1 0.1 0.1 0.11 0.13 0.12 0.11 0.11 0.12 0.1 0.06 0.03 0.01 0 0.02 0.04 0.06 0.08 7.0000000000000007E-2 0.06 0.04 0.03 0.05 7.0000000000000007E-2 0.08 0.09 0.05 0.01 0.01 0.02 0.06 0.09 0.08 0.06 0.05 0.06 0.05 0.05 7.0000000000000007E-2 0.08 0.08 0.08 0.09 0.11 0.12 0.11 0.1 0.09 7.0000000000000007E-2 0.05 0.04 0.06 0.1 0.12 0.13 0.12 0.11 0.09 0.09 0.08 0.06 0.06 0.05 0.05 0.06 7.0000000000000007E-2 0.08 0.08 0.06 0.06 0.06 7.0000000000000007E-2 7.0000000000000007E-2 7.0000000000000007E-2 0.06 0.06 0.06 0.06 7.0000000000000007E-2 0.08 0.1 0.1 0.12 0.12 0.1 0.08 7.0000000000000007E-2 0.08 7.0000000000000007E-2 7.0000000000000007E-2 0.06 0.05 0.05 0.04 0.06 0.06 0.06 0.08 0.11 0.1 0.1 0.08 0.06 0.04 0.04 0.05 0.08 0.06 0.04 0.02 0.01 0.04 7.000000000 0000007E-2 0.08 7.0000000000000007E-2 7.0000000000000007E-2 7.0000000000000007E-2 7.0000000000000007E-2 0.06 0.05 0.05 0.05 0.05 7.0000000000000007E-2 0.06 0.03 0.01 0.02 0.04 7.0000000000000007E-2 0.09 0.11 0.09 0.08 0.06 0.04 0.05 0.05 0.08 0.09 0.09 0.08 0.06 0.02 0 -0.01 -0.02 -0.02 -0.02 -0.01 0.01 0.02 0.05 0.06 0.05 0.03 -0.02 -0.04 -0.04 -0.01 0.03 0.04 0.04 0.05 0.05 0.06 7.0000000000000007E-2 7.0000000000000007E-2 0.09 7.0000000000000007E-2 0.06 0.04 0.02 0.02 0.04 0.08 0.08 7.0000000000000007E-2 0.06 0.05 0.04 0.06 0.08 0.09 7.0000000000000007E-2 0.03 0.01 0 0.04 0.08 0.08 7.0000000000000007E-2 0.06 0.04 0.05 0.06 7.0000000000000007E-2 7.0000000000000007E-2 0.06 0.04 0.04 0.05 0.08 0.08 7.0000000000000007E-2 7.0000000000000007E-2 0.08 0.08 7.0000000000000007E-2 0.06 0.05 0.05 0.05 0.04 0.01 0.01 0.02 0.03 0.04 0.04 0.03 0.02 0 0 0 0.03 0.06 7.0000000000000007E-2 0.05 0.04 0.03 0.05 0.05 0.06 0.06 0.06 0.05 0.06 0.06 0.04 0.02 0 0.01 0.03 0.06 0.06 0.06 0.05 0.04 0.03 0.05 7.0000000000000007E-2 0.1 0.12 0.13 0.11 0.09 0.08 0.08 0.09 0.08 0.06 0.03 0.02 0.03 0.04 0.05 0.05 0.05 0.06 0.06 0.06 0.05 0.05 0.05 0.05 0.05 0.06 7.0000000000000007E-2 0.08 7.0000000000000007E-2 0.08 0.06 0.06 0.04 0.02 0 -0.02 -0.02 -0.02 0.01 0.03 0.04 0.04 0.06 0.08 0.08 0.06 0.05 0.02 0.02 0.01 0.01 0.02 0.04 0.04 0.05 0.06 0.08 7.0000000000000007E-2 0.06 0.06 0.05 0.05 0.04 0.03 0.04 0.05 7.0000000000000007E-2 0.09 7.0000000000000007E-2 0.02 -0.02 -0.05 -0.06 -0.05 -0.02 0.03 7.0000000000000007E-2 0.1 0.1 0.09 0.08 7.0000000000000007E-2 0.06 0.03 0.02 0 0.02 0.04 0.06 0.08 0.08 0.05 -0.01 -0.04 -0.04 -0.01 0.03 0.06 0.08 0.08 0.08 7.0000000000000007E-2 7.0000000000000007E-2 0.08 7.0000000000000007E-2 0.05 0.04 0.04 0.04 0.05 0.06 0.05 0.03 0.01 -0.01 0 0 0.01 0.02 0.06 0.09 0.08 7.0000000000000007E-2 0.08 0.08 7.0000000000000007E-2 0.05 0.02 -0.02 -0.03 -0.03 0 0.01 0.03 0.02 0.01 -0.01 -0.02 -0.02 -0.02 -0.01 0 0.01 -0.01 -0.02 -0.04 -0.03 -0.01 0.01 0.01 0.02 0 0 0.02 0.01 0 -0.02 -0.04 -0.04 -0.03 0 0.01 0.02 0.01 0 0.01 0 0.01 0 -0.02 -0.04 -0.05 -0.05 -0.02 0.01 0.03 0.06 0.05 0.02 0 -0.02 0 0 -0.01 -0.01 -0.01 -0.01 0.01 0.02 0.03 0.03 0.03 0.02 0 -0.01 0 -0.02 0 0.02 0.03 0.05 0.05 0.03 0 0 -0.02 -0.01 0 0.02 0.03 0.01 0.01 0 -0.01 -0.03 -0.04 -0.04 -0.03 -0.01 0.01 0.04 0.05 0.05 0.04 0.02 -0.01 -0.02 -0.04 -0.03 -0.03 -0.02 -0.02 -0.03 -0.04 -0.04 -0.03 -0.02 -0.01 0 0 0 0 0.01 0.02 0 -0.03 -0.06 -0.08 -7.0000000000000007E-2 -0.04 -0.02 -0.03 -0.03 -0.03 0 0.04 0.06 0.04 0 -0.04 -7.0000000000000007E-2 -7.0000000000000007E-2 -0.06 -0.04 -0.02 0.01 0.01 0 -0.02 -0.03 -0.03 -0.02 -0.01 -0.01 -0.01 -0.01 -0.02 -0.01 -0.02 -0.03 -0.06 -0.08 -0.08 -0.06 -0.03 -0.02 -0.03 -0.06 -7.0000000000000007E-2 -0.08 -7.0000000000000007E-2 -0.05 -0.03 0 0 0 0 -0.01 -0.02 -0.02 -0.01 -0.01 -0.01 -0.01 0 0.01 0.03 0.02 0 -0.02 -0.02 -0.01 0.01 0.03 0.03 0.02 0 0 -0.01 0.01 0 0 -0.02 -0.04 -0.06 -0.06 -0.05 -0.03 -0.01 -0.02 -0.04 -7.0000000000000007E-2 -0.06 -0.05 -0.04 -0.02 0 0.01 0.02 0.02 0.02 0.01 -0.01 -0.03 -0.03 -0.04 -0.03 -0.01 0.01 0.02 0 -0.01 -0.02 -0.03 -0.02 0 0.01 0.01 0 -0.02 -0.04 -0.06 -7.0000000000000007E-2 -0.08 -0.08 -0.06 -0.02 0.01 -0.02 -0.03 -0.03 -0.02 -0.01 0.01 0.02 0.01 -0.02 -0.03 -0.05 -0.06 -7.0000000000000007E-2 -0.05 -0.02 -0.01 -0.01 -0.02 -0.01 0 0 0.02 0 -0.02 -0.02 -0.01 -0.01 -0.01 -0.02 -0.02 -0.04 -0.05 -0.04 -0.02 0.02 0.03 0.03 0.01 -0.01 -0.05 -0.06 -0.06 -0.04 -0.04 -0.05 -0.03 -0.02 -0.01 -0.01 -0.01 -0.02 -0.01 -0.01 0 -0.01 0 -0.01 0.01 0.01 0.01 0.01 0 0 -0.02 0 0 0 -0.03 -0.04 -0.03 -0.04 -0.04 -0.04 -0.04 -0.03 -0.01 0 -0.01 -0.03 -0.06 -0.06 -0.06 -0.03 0.01 0.04 7.0000000000000007E-2 0.08 7.0000000000000007E-2 0.05 0.03 0 -0.02 -0.03 -0.01 0.02 0.04 0.06 7.0000000000000007E-2 0.05 0.02 -0.01 -0.01 0 0.01 0.03 0.03 0.03 0.02 0 -0.01 -0.01 -0.01 0.01 0.04 0.04 0.02 -0.01 -0.01 -0.01 0.01 0.02 0.04 0.05 0.04 0.01 -0.02 -0.02 0 0.02 0.06 0.08 0.08 7.0000000000000007E-2 0.05 0.02 0.01 0.01 0.01 0.02 0.03 0.06 0.06 0.04 0.02 0.03 0.01 0.01 0.02 0.04 0.06 0.05 0.04 0.05 0.05 0.05 0.05 0.03 0.01 0.01 0.04 7.0000000000000007E-2 0.08 0.06 0. 05 0.03 0.02 0.02 0.03 0.04 0.03 0.02 0.02 0.01 0 -0.03 -0.04 -0.04 -0.05 -0.04 -0.02 -0.01 0 0 0.01 0.01 0.01 0.02 0.02 0.03 0.02 0.01 0 0 -0.02 -0.02 0 0.04 7.0000000000000007E-2 0.08 7.0000000000000007E-2 0.06 0.05 0.04 0.04 0.05 0.03 0 -0.01 0 0.02 0.02 0.01 -0.02 -0.01 0.02 0.08 0.09 0.06 0.04 0.02 0.01 0 0 -0.01 -0.01 -0.02 -0.01 -0.03 -0.02 -0.02 0 0 0.01 0.01 0.02 0.01 0.01 0 -0.01 -0.01 -0.01 0 -0.01 -0.03 -0.05 -7.0000000000000007E-2 -0.06 -0.04 -0.03 -0.02 -0.02 -0.02 0 0.01 0.01 0.01 0.01 0.02 0.03 0.05 0.06 0.05 0.02 0 -0.01 0.01 0.03 0.03 0.03 0.02 0.03 0.03 0.04 0.03 0.02 0 -0.01 -0.03 -0.04 -0.03 -0.01 0 -0.01 -0.03 -0.05 -0.05 -0.05 -0.05 -0.03 -0.02 0.01 0.02 0.02 0.01 -0.01 -0.04 -0.06 -7.0000000000000007E-2 -0.05 -0.02 0.01 0.03 0.03 0.02 -0.01 -0.02 -0.02 -0.01 0 0.02 0.05 0.03 0 -0.03 -0.04 -0.04 -0.03 -0.01 -0.01 -0.01 -0.03 -0.03 -0.03 -0.02 0 -0.01 0 0 0.01 0.03 0.04 0.04 0.04 0.01 -0.01 -0.01 0 -0.01 -0.02 -0.01 0.01 0.03 0.04 0.05 0.06 0.05 0.05 0.03 0.02 0.01 0.03 0.05 7.0000000000000007E-2 0.09 7.0000000000000007E-2 0.05 0.01 0 -0.01 -0.01 -0.03 -0.02 -0.04 -0.04 -0.05 -0.04 -0.02 -0.02 -0.02 -0.01 0 0.02 0.03 0.02 -0.01 -0.04 -0.05 -0.03 -0.01 0.02 0.05 0.03 0.02 0.01 0.01 0 -0.02 -0.05 -0.06 -0.05 0 0.02 0.02 0 0 0.01 0.03 0.03 0.02 0.01 0.01 0.01 0.01 0.03 0.05 0.04 0.03 0.02 0.02 0.01 0 0 0 0.02 0.01 0 0 0 -0.01 0 0.01 0.01 0 -0.01 0 0.01 0.02 0.02 0.03 0.05 0.05 0.03 0.03 -0.01 -0.02 -0.04 -0.06 -0.05 -0.03 -0.01 0 0.01 -0.01 -0.02 -0.03 -0.03 -0.01 0 -0.01 -0.03 -0.04 -0.06 -0.06 -0.04 -0.01 0 0.01 0 -0.03 -0.03 0 0.01 0.01 0.02 -0.01 -0.03 -0.04 -0.04 -0.04 -0.04 -0.05 -0.04 -0.02 0.01 0.01 0 -0.01 -0.01 0 -0.01 -0.01 0.01 0.02 0.02 0.01 0.01 0.01 0 0 -0.01 -0.02 -0.02 0 0 0 -0.03 -0.04 -0.04 -0.02 0.02 0.05 7.0000000000000007E-2 7.0000000000000007E-2 0.05 0.04 0.05 0.06 0.06 0.05 0.06 0.04 0.02 0 0.01 0.02 0.02 0.02 0.04 0.05 0.05 0.05 0.04 0.03 0.03 0.01 0.02 0.03 0.02 0 -0.02 -0.02 -0.01 0 0.04 0.04 0.01 -0.01 -0.04 -0.03 -0.01 0 0.02 0.04 0.05 0.06 0.03 0.02 -0.01 -0.02 -0.02 -0.02 -0.03 -0.04 -0.03 -0.01 0 0 -0.01 -0.01 -0.02 -0.03 -0.03 -0.02 -0.03 -0.05 -0.05 -0.05 -0.04 -0.05 -0.05 -0.04 -0.05 -0.03 -0.02 -0.01 -0.02 -0.04 -0.05 -0.06 -7.0000000000000007E- 2 -7.0000000000000007E-2 -0.06 -0.04 -0.02 -0.01 0 -0.01 -0.03 -0.03 -0.04 -0.03 -0.01 0.01 -0.01 -0.01 -0.03 -0.03 -0.04 -0.04 -0.04 -0.03 0 0.02 0.04 0.03 0 -0.02 -0.01 -0.02 -0.01 0 -0.01 -0.01 -0.02 -0.02 0 0.02 0.04 0.05 0.02 0 -0.04 -0.06 -0.05 -0.03 0 0.01 0.01 -0.01 -0.02 -0.03 -0.03 -0.03 0 -0.01 -0.02 -0.04 -0.05 -0.05 -0.04 -0.01 0 0.02 0.04 0.06 0.06 0.05 0.03 0 -0.01 -0.04 -7.0000000000000007E-2 -7.0000000000000007E-2 -0.08 -7.0000000000000007E-2 -7.0000000000000007E-2 -7.0000000000000007E-2 -0.09 -7.0000000000000007E-2 -0.06 -0.04 -0.03 -0.03 -0.02 -0.02 -0.01 0 0.01 -0.01 -0.03 -0.06 -0.06 -7.0000000000000007E-2 -7.0000000000000007E-2 -0.08 -0.08 -0.08 -7.0000000000000007E-2 -7.0000000000000007E-2 -0.08 -0.09 -0.09 -0.09 -0.08 -7.0000000000000007E-2 -0.06 -7.0000000000000007E-2 -7.0000000000000007E-2 -0.06 -0.05 -0.04 -0.04 -0.04 -0.03 -0.02 -0.02 -0.04 -7.0000000000000007E-2 -0.08 -7.0000000000000007E-2 -0.06 -0.04 -0.02 -0.01 -0.01 -0.03 -7.0000000000000007E-2 -0.08 -7.0000000000000007E-2 -0.04 -0.02 0 -0.01 -0.03 -0.05 -0.06 -0.05 -0.04 -0.01 0 -0.01 -0.03 -0.06 -7.0000000000000007E-2 -0.06 -0.05 -0.03 0 0.02 0.05 0.04 0 -0.05 -0.09 -0.11 -0.1 -0.08 -0.05 -0.02 -0.02 -0.02 0.01 0 -0.01 -0.03 -0.03 -0.03 -0.02 -0.03 -0.04 -0.03 -0.02 0.01 0.03 0.03 0.02 -0.02 -0.05 -0.03 -0.03 -0.04 -0.05 -0.04 -0.04 -0.05 -7.0000000000000007E-2 -0.06 -7.0000000000000007E-2 -0.08 -7.0000000000000007E-2 -0.04 -0.03 -0.02 0 -0.01 -0.03 -0.03 -0.03 -0.03 -0.03 -0.03 -0.03 -0.02 -0.01 0 0.03 0.03 0.04 0.02 0 -0.01 -0.02 -0.02 -0.03 -0.04 -0.05 -0.05 -0.04 -0.03 -0.03 -0.02 -0.02 0 0.01 0.02 0 -0.02 -0.04 -0.03 -0.01 0.01 0.03 0.06 0.06 7.0000000000000007E-2 7.0000000000000007E-2 0.06 0.04 0.01 -0.01 0 0.02 0.05 0.06 0.04 0.02 0 -0.01 -0.01 0.01 0.02 0.01 0 0.02 0.04 0.04 0.04 0.05 0.03 0 -0.04 -0.05 -0.04 -0.02 0 0 -0.01 -0.01 -0.01 -0.02 -0.02 -0.01 0.02 0.04 0.02 0 -0.02 -0.03 -0.01 0.02 0.02 0.01 0.01 0.01 0 -0.01 -0.02 -0.03 -0.02 -0.01 -0.01 -0.01 -0.01 -0.02 -0.01 0 0.01 0.01 0.02 0.03 0.04 0.04 0.02 0.02 0.03 0.04 0.04 0.02 0 -0.01 -0.01 0 -0.01 -0.01 -0.02 0 0.01 0.01 0 0 -0.01 0 0.01 0.01 0.01 0.01 0.03 0.03 0.03 0.03 0 -0.03 -0.04 -0.06 -0.04 -0.02 0 0.03 0.04 0.03 0.01 -0.01 -0.01 -0.02 0 0 0.01 0.01 0.02 0.02 0 0.01 0.01 0.01 -0.01 -0.03 -0.06 -0.08 -7.0000000000000007E-2 -0.05 -0.04 -0.03 -0.02 -0.01 -0.01 -0.01 -0.01 -0.01 -0.02 -0.02 -0.02 -0.02 -0.02 -0.04 -0.03 -0.02 0 0.01 0.01 -0.02 -0.04 -0.05 -0.02 0 0.02 0.04 0.04 0.03 0.01 -0.02 -0.02 -0.04 -0.04 -0.04 -0.04 -0.03 -0.01 0 0.01 0.01 -0.01 -0.02 -0.01 0 0.01 0.01 0.02 0.01 0 -0.02 -0.03 -0.02 0 -0.01 0 0.02 0.04 0.02 0.01 0.01 -0.01 -0.02 -0.03 -0.04 -0.05 -7.0000000000000007E-2 -0.08 -0.08 -0.04 -0.01 -0.01 -0.03 -0.05 -0.06 -0.05 -0.04 -0.02 -0.03 -0.03 -0.01 0.01 0.03 0.03 0.02 0 -0.01 -0.03 -0.03 -0.02 -0.03 -0.04 -7.0000000000000007E-2 -0.08 -0.09 -7.0000000000000007E-2 -0.03 0 -0.01 -0.04 -0.06 -0.08 -0.06 -0.04 -0.03 -0.03 -0.03 -0.02 -0.01 0.01 0 -0.01 -0.02 -0.01 -0.02 -0.03 -0.02 -0.03 -0.03 -0.03 -0.02 0 0 0 0 -0.02 -0.04 -0.06 -7.0000000000000007E-2 -0.06 -0.04 -0.04 -0.03 -0.04 -0.06 -7.0000000000000007E-2 -0.04 -0.01 0.02 0.03 0.03 0.02 0 -0.03 -0.05 -0.04 -0.02 -0.01 -0.01 0 0 -0.01 -0.04 -0.06 -7.0000000000000007E-2 -0.06 -0.04 -0.02 -0.03 -0.04 -0.04 -0.05 -0.04 -0.05 -0.03 -0.02 -0.04 -0.06 -7.0000000000000007E-2 -7.0000000000000007E-2 -0.06 -0.05 -0.04 -0.05 -0.04 -0.03 -0.03 -0.03 -0.05 -0.1 -0.11 -0.11 -0.08 -0.05 -0.06 -7.0000000000000007E-2 -0.09 -0.09 -7.0000000000000007E-2 -0.05 -0.05 -0.05 -0.06 -0.05 -0.05 -0.03 -0.02 -0.02 -0.01 0 -0.01 0 -0.01 -0.01 0 -0.01 -0.05 -0.09 -0.08 -0.05 -0.02 0.01 0.01 -0.03 -7.0000000000000007E-2 -0.09 -0.09 -7.0000000000000007E-2 -7.0000000000000007E-2 -0.05 -0.04 -0.03 -0.04 -0.06 -0.06 -0.06 -0.05 -0.04 -0.03 -0.03 -0.02 -0.02 -0.01 -0.01 -0.03 -0.04 -0.04 -0.01 0 -0.02 -0.04 -7.0000000000000007E-2 -0.1 -0.08 -0.06 -0.01 0 0.02 0.01 0.01 0 -0.02 -0.03 -0.03 -0.04 -0.04 -0.05 -0.06 -7.0000000000000007E-2 -0.06 -0.05 -0.03 -0.01 -0.01 -0.02 -0.02 -0.03 -0.02 0.01 0.05 0.05 0.05 0.04 0.02 0.02 0.04 0.03 0.02 0.02 0.02 0.01 -0.01 -0.02 -0.02 -0.02 -0.02 -0.02 -0.04 -0.03 -0.01 0.02 0.02 0.01 0 -0.03 -0.03 -0.02 -0.01 0 0.01 0.01 0.02 0.02 0.01 0 -0.01 -0.03 -0.04 -0.04 -0.02 -0.01 0 -0.01 -0.01 -0.01 -0.03 -0.05 -7.0000000000000007E-2 -0.06 -0.04 -0.01 -0.01 0.01 0.02 0.02 0.01 0.02 0.01 -0.02 -0.04 -0.03 -0.03 0 0.02 0.03 0.03 0.02 0 -0.01 0 0.02 0 -0.01 0 0 0.02 0.05 0.06 0.05 0.04 0.04 0.05 0.04 0.01 -0.01 -0.02 -0.02 -0.02 -0.01 0.01 0.01 0.02 0.02 0.02 0.02 0.02 0.02 0.04 0.03 0.02 0.01 0.01 -0.01 -0.02 -0.03 -0.02 -0.02 -0.02 -0.02 -0.02 -0.01 0 -0.01 0 0.01 0.01 0 -0.02 -0.04 -0.06 -0.06 -0.06 -0.03 -0.01 0.01 0.02 0.02 0 -0.01 -0.03 -0.01 0.02 0.06 7.0 000000000000007E-2 0.06 0.04 0.03 0.03 0.03 0.01 0.01 0.01 0.01 0 0 -0.02 -0.03 -0.05 -0.03 -0.01 0.01 0.04 0.05 0.05 0.04 -0.02 -0.06 -0.06 -0.05 -0.02 -0.01 -0.02 -0.01 -0.01 -0.01 -0.02 -0.01 -0.02 -0.03 -0.04 -0.03 -0.02 0.02 0.04 0.05 0.05 0.05 0.02 0.01 -0.02 -0.03 -0.04 -0.03 -0.02 -0.03 -0.02 -0.03 -0.03 -0.01 -0.01 -0.01 -0.01 -0.03 -0.05 -0.06 -7.0000000000000007E-2 -0.08 -0.06 -0.05 -0.02 0 0.02 0.04 0.02 -0.01 -0.01 -0.02 -0.02 -0.04 -0.06 -0.08 -0.09 -7.0000000000000007E-2 -7.0000000000000007E-2 -0.05 -0.03 0 0 0 -0.03 -0.04 -0.04 -0.02 0.01 0.03 0.02 0 -0.03 -0.04 -0.04 -0.03 -0.01 0.01 0 -0.03 -0.04 -0.04 -0.04 -0.04 -0.03 -0.03 0.01 0.03 0.03 0.02 -0.01 -0.04 -0.06 -0.09 -0.09 -0.08 -0.05 -0.03 -0.01 0 0 -0.01 -0.04 -0.04 -0.04 -0.05 -0.06 -0.04 -0.02 0.01 0.01 0.02 0.04 0.04 0.03 0.02 0 -0.01 -0.02 0 0.02 0 -0.02 -0.02 -0.01 0 0.01 0.02 0.01 0 -0.01 -0.03 -0.04 -0.06 -0.06 -7.0000000000000007E-2 -0.04 -0.01 0.02 0.01 0 -0.03 -0.06 -0.08 -0.06 -0.03 0 0.01 0.01 0.01 0.02 0.03 0.01 -0.02 -0.05 -7.0000000000000007E-2 -7.0000000000000007E-2 -0.04 -0.02 0.01 0.03 0.02 -0.01 -0.03 -0.05 -0.06 -0.05 -0.04 -0.05 -0.06 -0.04 0 0.04 0.05 0.02 -0.01 -0.04 -0.04 -0.04 -0.05 -0.05 -0.06 -0.04 0. 02 0.02 0.01 -0.04 -0.06 -0.04 0 0 0 0.01 0 -0.02 -0.03 -0.03 -0.01 -0.01 -0.01 -0.01 -0.01 -0.01 -0.03 -0.05 -7.0000000000000007E-2 -7.0000000000000007E-2 -0.04 0.01 0.03 0.04 0.02 0 -0.01 0.01 0.01 0.02 0.03 0.03 0.03 0.02 0.01 0.01 -0.02 -0.03 -0.02 -0.01 0.01 0.02 0 -0.02 -0.05 -7.0000000000000007E-2 -0.05 -0 .01 0.04 0.04 0.05 0.03 0.03 0.01 -0.01 0 -0.01 -0.02 -0.05 -0.06 -0.06 -0.04 -0.03 0 -0.01 -0.03 -0.06 -7.0000000000000007E-2 -0.05 -0.02 0.01 0.04 0.04 0.01 -0.02 -0.05 -0.06 -0.04 -0.01 0 0 -0.02 -0.04 -0.05 -0.03 -0.01 0 -0.01 -0.03 -0.05 -0.04 -0.04 -0.05 -0.04 -0.03 -0.01 -0.02 -0.02 -0.04 -0.05 -0.05 -0.06 -0.08 -7.0000000000000007E-2 -7.0000000000000007E-2 -0.06 -0.05 -0.06 -7.0000000000000007E-2 -7.0000000000000007E-2 -7.0000000000000007E-2 -0.05 -0.04 -0.05 -0.06 -0.05 -0.03 -0.03 -0.04 -0.06 -0.08 -0.09 -0.08 -0.08 -0.08 -0.09 -0.08 -7.0000000000000007E-2 -0.05 -0.04 -0.01 0 -0.02 -0.06 -0.08 -0.08 -0.06 -0.03 -0.01 -0.02 -0.03 -0.06 -0.09 -7.0000000000000007E-2 -0.04 -0.03 -0.03 -0.04 -0.05 -0.06 -0.06 -0.04 0 0.01 0 -0.03 -0.06 -0.08 -0.09 -0.1 -0.09 -0.06 -0.05 -0.06 -7.0000000000000007E-2 -0.09 -0.09 -0.09 -7.0000000000000007E-2 -0.06 -7.0000000000000007E-2 -0.09 -0.09 -7.0000000000000007E-2 -0.06 -0.05 -0.03 -0.02 -0.05 -0.08 -0.1 -0.11 -0.1 -0.09 -7.0000000000000007E-2 -0.05 -0.03 -0.04 -0.05 -0.06 -0.06 -0.06 -0.05 -0.05 -0.05 -0.05 -0.06 -0.06 -0.08 -7.0000000000000007E-2 -0.06 -0.03 -0.04 -0.05 -0.08 -0.11 -0.12 -0.1 -7.0000000000000007E-2 -0.04 -0.02 -0.02 -0.03 -0.04 -0.03 -0.02 -0.02 -0.03 -0.05 -0.06 -0.06 -0.05 -0.05 -0.04 -0.05 -0.05 -0.04 -0.03 -0.04 -0.05 -0.04 0 0.04 0.04 0.04 0.03 0.01 -0.03 -0.06 -0.08 -7.0000000000000007E-2 -0.08 -7.0000000000000007E-2 -7.0000000000000007E-2 -0.08 -0.09 -0.08 -0.05 -0.02 0 0 -0.03 -0.05 -0.06 -7.0000000000000007E-2 -0.09 -0.09 -7.0000000000000007E-2 -7.0000000000000007E-2 -0.06 -7.0000000000000007E-2 -0.08 -0.11 -0.11 -0.12 -0.12 -0.1 -0.09 -7.0000000000000007E-2 -0.06 -0.06 -7.0000000000000007E-2 -0.06 -0.06 -0.06 -0.09 -0.1 -0.11 -0.09 -0.08 -7.0000000000000007E-2 -0.08 -0.09 -0.11 -0.1 -0.1 -0.09 -7.0000000000000007E-2 -7.0000000000000007E-2 -7.0000000000000007E-2 -0.06 -0.06 -0.05 -0.05 -0.04 -0.08 -0.12 -0.13 -0.12 -0.09 -0.06 -0.05 -0.05 -0.09 -0.13 -0.14000000000000001 -0.14000000000000001 -0.11 -0.1 -0.1 -0.1 -0.08 -7.0000000000000007E-2 -0.06 -0.04 -0.03 -0.04 -7.0000000000000007E-2 -0.09 -0.1 -0.1 -0.09 -0.08 -0.09 -0.09 -0.1 -0.12 -0.11 -0.11 -0.09 -0.09 -0.09 -7.0000000000000007E-2 -0.05 -0.06 -0.06 -0.09 -0.11 -0.1 -0.08 -7.0000000000000007E-2 -0.06 -0.04 -0.02 0 -0.01 -0.02 -0.04 -0.06 -0.08 -7.0000000000000007E-2 -0.06 -0.04 -0.06 -7.0000000000000007E-2 -0.09 -0.08 -0.06 -0.04 -0.02 -0.03 -0.03 -0.05 -0.06 -7.0000000000000007E-2 -0.05 -0.03 -0.01 -0.01 -0.02 -0.05 -7.0000000000000007E-2 -0.05 -0.03 0.01 0 -0.03 -0.08 -0.11 -0.12 -0.09 -0.05 -0.02 -0.02 -0.02 -0.01 0 0.01 -0.01 -0.04 -0.08 -0.1 -0.1 -0.08 -7.0000000000000007E-2 -0.05 -0.04 -0.03 -0.04 -0.05 -0.04 -0.02 0.01 0.01 0 0 -0.01 -0.02 -0.05 -0.08 -0.08 -0.05 -0.04 -0.02 -0.02 -0.05 -0.06 -0.08 -0.08 -0.06 -0.05 -0.02 -0.02 -0.02 -0.05 -7.0000000000000007E-2 -0.09 -0.09 -0.08 -0.06 -0.05 -0.05 -0.04 -0.03 -0.02 -0.02 -0.02 -0.06 -0.08 -7.0000000000000007E-2 -0.04 -0.02 -0.02 -0.02 -0.02 -0.04 -7.0000000000000007E-2 -0.09 -0.09 -0.09 -0.1 -0.1 -0.11 -0.1 -0.1 -0.11 -0.11 -0.12 -0.11 -0.1 -0.09 -7.0000000000000007E-2 -0.06 -0.04 -0.04 -0.05 -0.06 -7.0000000000000007E-2 -0.06 -0.04 -0.04 -0.05 -7.0000000000000007E-2 -0.08 -0.08 -0.09 -0.06 -0.02 0 0.02 -0.01 -0.05 -7.0000000000000007E-2 -0.08 -0.05 -0.03 -0.04 -0.03 -0.05 -7.0000000000000007E-2 -7.0000000000000007E -2 -0.06 -0.03 -0.01 -0.01 -0.01 -0.04 -0.06 -0.06 -7.0000000000000007E-2 -0.08 -0.08 -0.08 -0.06 -0.05 -0.05 -0.05 -0.08 -0.1 -0.1 -0.08 -7.0000000000000007E-2 -7.0000000000000007E-2 -0.08 -0.09 -0.1 -0.1 -0.11 -0.1 -0.08 -0.05 -0.03 -0.04 -7.0000000000000007E-2 -7.0000000000000007E-2 -0.09 -0.09 -0.06 -0.05 -0.05 -0.04 -0.04 -0.05 -0.09 -0.11 -0.1 -7.0000000000000007E-2 -0.05 -0.05 -0.06 -7.0000000000000007E-2 -0.09 -0.11 -0.13 -0.15 -0.14000000000000001 -0.13 -0.12 -0.08 -0.06 -0.04 -0.02 0 -0.02 -0.04 -0.04 -0.05 -0.05 -0.05 -0.06 -0.08 -0.08 -0.09 -0.08 -0.05 -0.03 -0.02 -0.05 -0.06 -0.06 -0.05 -0.03 0 0.02 -0.02 -0.04 -0.04 -0.03 -0.01 0.01 0.02 0.01 0 0 0.02 0.02 0.01 -0.02 -0.04 -0.06 -0.03 0 0.04 0.06 0.08 0.1 0.1 0.1 0.08 0.02 -0.01 -0.02 0 0 -0.01 -0.02 -0.03 -0.03 -0.02 0.01 0.02 0.02 0 -0.01 -0.02 -0.03 -0.05 -0.06 -0.06 -0.06 -0.06 -0.04 -0.02 -0.01 0 -0.01 -0.01 0 0 0.01 0.01 0.02 0.01 0.01 0 0.01 0.01 0.01 0.01 0 0 -0.01 0.01 0.02 0.04 0.04 0.03 0.03 0.02 0.02 0.03 0.04 0.03 0.03 0 -0.03 -0.04 -0.04 -0.01 0.01 0.04 0.04 0 -0.03 -0.05 -0.05 -0.04 -0.01 0.02 0.05 0.05 0.06 0.04 0 -0.02 -0.02 -0.03 -0.02 -0.03 -0.04 -0.04 -0.03 -0.03 -0.01 -0.01 0 0 -0.01 -0.04 -7.0000000000000007E-2 -7.0000000000000007E-2 -0.05 -0.02 0.01 0.01 0.01 -0.02 -0.05 -7.0000000000000007E-2 -7.0000000000000007E-2 -0.05 -0.03 0 0.01 0.03 0.02 0 -0.03 -0.04 -0.03 -0.02 -0.02 -0.02 -0.02 -0.03 -0.04 -0.05 -0.03 -0.01 0 0 0 0 0 0 -0.01 -0.02 -0.02 0.01 0 -0.02 -0.04 -0.04 -0.04 -0.03 -0.01 0 0.01 0.01 0.01 0 0 0.02 0.02 0.02 0.01 -0.02 -0.06 -0.06 -7.0000000000000007E-2 -0.06 -0.04 -0.02 -0.01 0 -0.02 -0.04 -0.04 -0.04 -0.02 -0.01 0 -0.02 -0.04 -0.06 -0.06 -0.05 -0.04 -0.05 -0.05 -0.05 -0.04 -0.03 -0.04 -0.04 -0.03 -0.03 -0.03 -0.06 -0.1 -0.11 -0.11 -0.08 -7.0000000000000007E-2 -0.04 -0.01 0 -0.01 -0.02 -0.04 -7.0000000000000007E-2 -0.1 -0.11 -0.1 -0.06 -0.03 -0. 04 -7.0000000000000007E-2 -0.08 -0.08 -0.08 -0.06 -0.02 -0.03 -0.05 -0.05 -0.03 -0.04 -0.04 -0.03 -0.04 -0.04 -0.06 -7.0000000000000007E-2 -7.0000000000000007E-2 -0.06 -0.06 -0.03 -0.02 0 0.01 0 0 -0.02 -0.05 -0.06 -0.04 -0.03 -0.02 -0.02 0 0.01 0.02 0.02 0.03 0.01 0 -0.02 -0.03 -0.04 -0.03 -0.03 -0.03 -0.05 -7.0000000000000007E-2 -0.08 -7.000000 0000000007E-2 -0.05 -0.04 -0.04 -0.04 -0.03 0.01 0.02 0.01 -0.02 -0.04 -0.04 -0.03 -0.01 0 0.03 0.04 0.04 0.02 -0.01 -0.04 -0.04 -0.02 -0.01 0.01 0.01 0.01 0.01 0.01 -0.01 -0.03 -0.04 -0.05 -0.04 -0.03 -0.03 -0.04 -0.06 -0.06 -0.06 -0.05 -0.04 -0.03 -0.03 -0.03 -0.04 -0.01 0.01 0.03 0.03 0 -0.06 -0.1 -0.09 -0.04 -0.01 0.02 0.01 0 -0.01 0 0 0 0 -0.02 -0.04 -0.06 -0.04 -0.02 -0.01 -0.01 -0.01 0 0.01 0 -0.01 -0.02 -0.03 -0.02 -0.01 -0.02 -0.02 -0.03 -0.05 -0.06 -7.0000000000000007E-2 -7.0000000000000007E-2 -0.08 -7.0000000000000007E-2 -7.0000000000000007E-2 -0.05 -0.05 -0.04 -0.02 -0.01 -0.01 -0.05 -0.08 -0.12 -0.11 -0.09 -0.06 -0.06 -0.06 -7.0000000000000007E-2 -0.08 -7.0000000000000007E-2 -0.04 -0.01 -0.01 -0.02 0 -0.01 -0.01 -0.04 -0.05 -0.08 -0.1 -0.1 -7.0000000000000007E-2 -0.04 -0.03 -0.05 -7.0000000000000007E-2 -0.06 -7.0000000000000007E-2 -0.06 -0.05 -0.04 -0.04 -0.05 -0.05 -0.05 -0.06 -7.0000000000000007E-2 -0.09 -0.1 -0.11 -0.1 -0.08 -0.05 -0.03 -0.01 0 0 -0.03 -0.06 -7.0000000000000007E-2 -7.0000000000000007E-2 -0.06 -0.04 -0.04 -0.04 -0.04 -0.04 -0.03 -0.03 -0.02 -0.01 -0.03 -0.05 -0.03 -0.02 -0.01 -0.02 -0.04 -0.06 -0.08 -0.1 -0.09 -0.08 -0.05 -0.05 -0.05 -0.06 -0.08 -0.09 -7.0000000000000007E-2 -0.04 0 0 -0.01 -0.02 -0.03 -0.03 -0.03 -0.01 -0.01 -0.01 -0.04 -0.04 -0.06 -0.06 -0.06 -0.04 -0.02 -0.02 -0.02 -0.02 -0.01 -0.01 -0.02 -0.03 -0.04 -0.06 -0.08 -0.08 -7.0000000000000007E-2 -0.05 -0.05 -0.05 -0.05 -0.05 -0.04 -0.04 -0.04 -0.02 -0.01 0 0.04 0.05 0.03 0 -0.04 -0.06 -0.06 -0.05 -0.03 -0.02 -0.02 -0.03 -0.03 -0.03 -0.01 0.01 0.02 0.02 -0.01 -0.02 -0.03 -0.03 -0.03 -0.04 -0.06 -7.0000000000000007E-2 -7.0000000000000007E-2 -7.0000000000000007E-2 -0.05 -0.04 -0.04 -0.04 -0.03 -0.01 -0.01 -0.02 -0.03 -0.02 -0.01 0 0.01 0.02 0.02 0.02 0 -0.02 -0.02 -0.01 0.01 0.04 0.04 0.02 -0.01 -0.03 -0.05 -0.05 -0.04 -0.01 0.02 0.01 0.01 0 -0.01 -0.01 -0.01 -0.03 -0.03 -0.01 -0.01 0 0.02 0 -0.02 -0.02 -0.01 0 0.01 0.02 0.01 0.02 0.04 0.05 0.05 0.05 0.04 0.04 0.04 0.04 0.03 0.01 -0.01 -0.01 0.02 0.03 0.01 -0.01 -0.02 0 0.02 0.01 0.01 -0.02 -0.02 -0.02 0 0.01 0.02 0.05 0.08 0.09 7.0000000000000007E-2 0.04 0 -0.02 -0.03 -0.02 0 0.01 0.02 0.03 0.04 0.06 0.04 0.02 0 0 0.04 0.04 7.0000000000000007E-2 0.09 0.09 0.09 0.08 0.06 0.04 0.03 0.03 0.05 0.04 0.05 0.04 0.04 0.06 0.08 0.1 0.11 0.1 0.09 0.09 0.1 0.08 0.05 0.03 0.03 0.04 0.06 0.09 0.1 0.08 0.05 0.03 0 0 0 0.01 0.01 0.01 0.01 0.04 0.06 0.06 0.05 0.04 0.05 7.0000000000000007E-2 0.08 0.08 0.04 0.02 0.02 0.03 0.05 0.06 0.06 0.04 0.02 0.01 0.02 0.03 0.05 0.06 0.08 0.08 0.1 0.11 0.11 0.09 7.0000000000000007E-2 0.05 0.04 0.02 0.01 0.02 0.04 7.0000000000000007E-2 0.08 0.09 0.09 0.1 0.09 0.11 0.12 0.1 0.08 0.08 7.0000000000000007E-2 0.09

[mm]

[um]

RProfile

5.0000000000000001E-4 1E-3 1.5E-3 2E-3 2.5000000000000001E-3 3.0000000000000001E-3 3.5000000000000001E-3 4.0000000000000001E-3 4.4999999999999997E-3 5.0000000000000001E-3 5.4999999999999997E-3 6.0000000000000001E-3 6.4999999999999997E-3 7.0000000000000001E-3 7.4999999999999997E-3 8.0000000000000002E-3 8.5000000000000006E-3 8.9999999999999993E-3 9.4999999999999998E-3 0.01 1.0500000000000001E-2 1.0999999999999999E-2 1.15E-2 1.2E-2 1.2500000000000001E-2 1.2999999999999999E-2 1.35E-2 1.4E-2 1.4500000000000001E-2 1.4999999999999999E-2 1.55E-2 1.6E-2 1.6500000000000001E-2 1.7000000000000001E-2 1.7500000000000002E-2 1.7999999999999999E-2 1.8499999999999999E-2 1.9E-2 1.95E-2 0.02 2.0500000000000001E-2 2.1000000000000001E-2 2.1499999999999998E-2 2.1999999999999999E-2 2.2499999999999999E-2 2.3E-2 2.35E-2 2.4E-2 2.4500000000000001E-2 2.5000000000000001E-2 2.5499999999999998E-2 2.5999999999999999E-2 2.6499999999999999E-2 2.7E-2 2.75E-2 2.8000000000000001E-2 2.8500000000000001E-2 2.9000000000000001E-2 2.9499999999999998E-2 0.03 3.0499999999999999E-2 3.1E-2 3.15E-2 3.2000000000000001E-2 3.2500000000000001E-2 3.3000000000000002E-2 3.3500000000000002E-2 3.4000000000000002E-2 3.4500000000000003E-2 3.5000000000000003E-2 3.5499999999999997E-2 3.5999999999999997E-2 3.6499999999999998E-2 3.6999999999999998E-2 3.7499999999999999E-2 3.7999999999999999E-2 3.85E-2 3.9E-2 3.95E-2 0.04 4.0500000000000001E-2 4.1000000000000002E-2 4.1500000000000002E-2 4.2000000000000003E-2 4.2500000000000003E-2 4.2999999999999997E-2 4.3499999999999997E-2 4.3999999999999997E-2 4.4499999999999998E-2 4.4999999999999998E-2 4.5499999999999999E-2 4.5999999999999999E-2 4.65E-2 4.7E-2 4.7500000000000001E-2 4.8000000000000001E-2 4.8500000000000001E-2 4.9000000000000002E-2 4.9500000000000002E-2 0.05 5.0500000000000003E-2 5.0999999999999997E-2 5.1499999999999997E-2 5.1999999999999998E-2 5.2499999999999998E-2 5.2999999999999999E-2 5.3499999999999999E-2 5.3999999999999999E-2 5.45E-2 5.5E-2 5.5500000000000001E-2 5.6000000000000001E-2 5.6500000000000002E-2 5.7000000000000002E-2 5.7500000000000002E-2 5.8000000000000003E-2 5.8500000000000003E-2 5.8999999999999997E-2 5.9499999999999997E-2 0.06 6.0499999999999998E-2 6.0999999999999999E-2 6.1499999999999999E-2 6.2E-2 6.25E-2 6.3E-2 6.3500000000000001E-2 6.4000000000000001E-2 6.4500000000000002E-2 6.5000000000000002E-2 6.5500000000000003E-2 6.6000000000000003E-2 6.6500000000000004E-2 6.7000000000000004E-2 6.7500000000000004E-2 6.8000000000000005E-2 6.8500000000000005E-2 6.9000000000000006E-2 6.9500000000000006E-2 7.0000000000000007E-2 7.0499999999999993E-2 7.0999999999999994E-2 7.1499999999999994E-2 7.1999999999999995E-2 7.2499999999999995E-2 7.2999999999999995E-2 7.3499999999999996E-2 7.3999999999999996E-2 7.4499999999999997E-2 7.4999999999999997E-2 7.5499999999999998E-2 7.5999999999999998E-2 7.6499999999999999E-2 7.6999999999999999E-2 7.7499999999999999E-2 7.8E-2 7.85E-2 7.9000000000000001E-2 7.9500000000000001E-2 0.08 8.0500000000000002E-2 8.1000000000000003E-2 8.1500000000000003E-2 8.2000000000000003E-2 8.2500000000000004E-2 8.3000000000000004E-2 8.3500000000000005E-2 8.4000000000000005E-2 8.4500000000000006E-2 8.5000000000000006E-2 8.5500000000000007E-2 8.5999999999999993E-2 8.6499999999999994E-2 8.6999999999999994E-2 8.7499999999999994E-2 8.7999999999999995E-2 8.8499999999999995E-2 8.8999999999999996E-2 8.9499999999999996E-2 0.09 9.0499999999999997E-2 9.0999999999999998E-2 9.1499999999999998E-2 9.1999999999999998E-2 9.2499999999999999E-2 9.2999999999999999E-2 9.35E-2 9.4E-2 9.4500000000000001E-2 9.5000000000000001E-2 9.5500000000000002E-2 9.6000000000000002E-2 9.6500000000000002E-2 9.7000000000000003E-2 9.7500000000000003E-2 9.8000000000000004E-2 9.8500000000000004E-2 9.9000000000000005E-2 9.9500000000000005E-2 0.1 0.10050000000000001 0.10100000000000001 0.1015 0000000000001 0.10199999999999999 0.10249999999999999 0.10299999999999999 0.10349999999999999 0.104 0.1045 0.105 0.1055 0.106 0.1065 0.107 0.1075 0.108 0.1085 0.109 0.1095 0.11 0.1105 0.111 0.1115 0.112 0.1125 0.113 0.1135 0.114 0.1145 0.115 0.11550000000000001 0.11600000000000001 0.11650000000000001 0.11700000000000001 0.11749999999999999 0.11799999999999999 0.11849999999999999 0.11899999999999999 0.1195 0.12 0.1205 0.121 0.1215 0.122 0.1225 0.123 0.1235 0.124 0.1245 0.125 0.1255 0.126 0.1265 0.127 0.1275 0.128 0.1285 0.129 0.1295 0.13 0.1305 0.13100000000000001 0.13150000000000001 0.13200000000000001 0.13250000000000001 0.13300000000000001 0.13350000000000001 0.13400000000000001 0.13450000000000001 0.13500000000000001 0.13550000000000001 0.13600000000000001 0.13650000000000001 0.13700000000000001 0.13750000000000001 0.13800000000000001 0.13850000000000001 0.13900000000000001 0.13950000000000001 0.14000000000000001 0.14050000000000001 0.14099999999999999 0.14149999999999999 0.14199999999999999 0.14249999999999999 0.14299999999999999 0.14349999999999999 0.14399999999999999 0.14449999999999999 0.14499999999999999 0.14549999999999999 0.1459999 9999999999 0.14649999999999999 0.14699999999999999 0.14749999999999999 0.14799999999999999 0.14849999999999999 0.14899999999999999 0.14949999999999999 0.15 0.15049999999999999 0.151 0.1515 0.152 0.1525 0.153 0.1535 0.154 0.1545 0.155 0.1555 0.156 0.1565 0.157 0.1575 0.158 0.1585 0.159 0.1595 0.16 0.1605 0.161 0.1615 0.16200000000000001 0.16250000000000001 0.16300000000000001 0.16350000000000001 0.16400000000000001 0.16450000000000001 0.16500000000000001 0.16550000000000001 0.16600000000000001 0.16650000000000001 0.16700000000000001 0.16750000000000001 0.16800000000000001 0.16850000000000001 0.16900000000000001 0.16950000000000001 0.17 0.17050000000000001 0.17100000000000001 0.17150000000000001 0.17199999999999999 0.17249999999999999 0.17299999999999999 0.17349999999999999 0.17399999999999999 0.17449999999999999 0.17499999999999999 0.17549999999999999 0.17599999999999999 0.17649999999999999 0.17699999999999999 0.17749999999999999 0.17799999999999999 0.17849999999999999 0.17899999999999999 0.17949999999999999 0.18 0.18049999999999999 0.18099999999999999 0.18149999999999999 0.182 0.1825 0.183 0.1835 0.184 0.1845 0.185 0.1855 0.186 0.1865 0.187 0.1875 0.188 0.1885 0.189 0.1895 0.19 0.1905 0.191 0.1915 0.192 0.1925 0.193 0.19350000000000001 0.19400000000000001 0.19450000000000001 0.19500000000000001 0.19550000000000001 0.19600000000000001 0.19650000000000001 0.19700000000000001 0.19750000000000001 0.19800000000000001 0.19850000000000001 0.19900000000000001 0.19950000000000001 0.2 0.20050000000000001 0.20100000000000001 0.20150000000000001 0.20200000000000001 0.20250000000000001 0.20300000000000001 0.20349999999999999 0.20399999999999999 0.20449999999999999 0.20499999999999999 0.20549999999999999 0.20599999999999999 0.20649999999999999 0.20699999999999999 0.20749999999999999 0.20799999999999999 0.20849999999999999 0.20899999999999999 0.20949999999999999 0.21 0. 21049999999999999 0.21099999999999999 0.21149999999999999 0.21199999999999999 0.21249999999999999 0.21299999999999999 0.2135 0.214 0.2145 0.215 0.2155 0.216 0.2165 0.217 0.2175 0.218 0.2185 0.219 0.2195 0.22 0.2205 0.221 0.2215 0.222 0.2225 0.223 0.2235 0.224 0.22450000000000001 0.22500000000000001 0.22550000000000001 0.22600000000000001 0.22650000000000001 0.22700000000000001 0.22750000000000001 0.22800000000000001 0.22850000000000001 0.22900000000000001 0.22950000000000001 0.23 0.23050000000000001 0.23100000000000001 0.23150000000000001 0.23200000000000001 0.23250000000000001 0.23300000000000001 0.23350000000000001 0.23400000000000001 0.23449999999999999 0.23499999999999999 0.23549999999999999 0.23599999999999999 0.23649999999999999 0.23699999999999999 0.23749999999999999 0.23799999999999999 0.23849999999999999 0.23899999999999999 0.23949999999999999 0.24 0.24049999999999999 0.24099999999999999 0.24149999999999999 0.24199999999999999 0.24249999999999999 0.24299999999999999 0.24349999999999999 0.24399999999999999 0.2445 0.245 0.2455 0.246 0.2465 0.247 0.2475 0.248 0.2485 0.249 0.2495 0.25 0.2505 0.251 0.2515 0.252 0.2525 0.253 0.2535 0.254 0.2545 0.255 0.2555 0.25600000000000001 0.25650000000000001 0.25700000000000001 0.25750000000000001 0.25800000000000001 0.25850000000000001 0.25900000000000001 0.25950000000000001 0.26 0.26050000000000001 0.26100000000000001 0.26150000000000001 0.26200000000000001 0.26250000000000001 0.26300000000000001 0.26350000000000001 0.26400000000000001 0.26450000000000001 0.26500000000000001 0.26550000000000001 0.26600000000000001 0.26650000000000001 0.26700000000000002 0.26750000000000002 0.26800000000000002 0.26850000000000002 0.26900000000000002 0.26950000000000002 0.27 0.27050000000000002 0.27100000000000002 0.27150000000000002 0.27200000000000002 0.27250000000000002 0.27300000000000002 0.27350000000000002 0.27400000000000002 0.27450000000000002 0.27500000000000002 0.27550000000000002 0.27600000000000002 0.27650000000000002 0.27700000000000002 0.27750000000000002 0.27800000000000002 0.27850000000000003 0.27900000000000003 0.27950000000000003 0.28000000000000003 0.28050000000000003 0.28100000000000003 0.28149999999999997 0.28199999999999997 0.28249999999999997 0.28299999999999997 0.28349999999999997 0.28399999999999997 0.28449999999999998 0.28499999999999998 0.28549999999999998 0.28599999999999998 0.28649999999999998 0.28699999999999998 0.28749999999999998 0.28799999999999998 0.28849999999999998 0.28899999999999998 0.28949999999999998 0.28999999999999998 0.29049999999999998 0.29099999999999998 0.29149999999999998 0.29199999999999998 0.29249999999999998 0.29299999999999998 0.29349999999999998 0.2939999999 9999998 0.29449999999999998 0.29499999999999998 0.29549999999999998 0.29599999999999999 0.29649999999999999 0.29699999999999999 0.29749999999999999 0.29799999999999999 0.29849999999999999 0.29899999999999999 0.29949999999999999 0.3 0.30049999999999999 0.30099999999999999 0.30149999999999999 0.30199999999999999 0.30249999999999999 0.30299999999999999 0.30349999999999999 0.30399999999999999 0.30449999999999999 0.30499999999999999 0.30549999999999999 0.30599999999999999 0.30649999999999999 0.307 0.3075 0.308 0.3085 0.309 0.3095 0.31 0.3105 0.311 0.3115 0.312 0.3125 0.313 0.3135 0.314 0.3145 0.315 0.3155 0.316 0.3165 0.317 0.3175 0.318 0.31850000000000001 0.31900000000000001 0.31950000000000001 0.32 0.32050000000000001 0.32100000000000001 0.32150000000000001 0.32200000000000001 0.32250000000000001 0.32300000000000001 0.32350000000000001 0.32400000000000001 0.32450000000000001 0.32500000000000001 0.32550000000000001 0.32600000000000001 0.32650000000000001 0.32700000000000001 0.32750000000000001 0.32800000000000001 0.32850000000000001 0.32900000000000001 0.32950000000000002 0.33 0.33050000000000002 0.33100000000000002 0.33150000000000002 0.33200000000000002 0.33250000000000002 0.33300000000000002 0.33350000000000002 0.33400000000000002 0.33450000000000002 0.33500000000000002 0.33550000000000002 0.336000000 00000002 0.33650000000000002 0.33700000000000002 0.33750000000000002 0.33800000000000002 0.33850000000000002 0.33900000000000002 0.33950000000000002 0.34 0.34050000000000002 0.34100000000000003 0.34150000000000003 0.34200000000000003 0.34250000000000003 0.34300000000000003 0.34350000000000003 0.34399999999999997 0.34449999999999997 0.34499999999999997 0.34549999999999997 0.34599999999999997 0.34649999999999997 0.34699999999999998 0.34749999999999998 0.34799999999999998 0.34849999999999998 0.34899999999999998 0.34949999999999998 0.35 0.35049999999999998 0.35099999999999998 0.35149999999999998 0.35199999999999998 0.35249999999999998 0.35299999999999998 0.35349999999999998 0.35399999999999998 0.35449999999999998 0.35499999999999998 0.35549999999999998 0.35599999999999998 0.35649999999999998 0.35699999999999998 0.35749999999999998 0.35799999999999998 0.35849999999999999 0.35899999999999999 0.35949999999999999 0.36 0.36049999999999999 0.36099999999999999 0.36149999999999999 0.36199999999999999 0.36249999999999999 0.36299999999999999 0.36349999999999999 0.36399999999999999 0.36449999999999999 0.36499999999999999 0.36549999999999999 0.36599999999999999 0.36649999999999999 0.36699999999999999 0.36749999999999999 0.36799999999999999 0.36849999999999999 0.36899999999999999 0.3695 0.37 0.3705 0.371 0.3715 0.372 0.3725 0.373 0.3735 0.374 0.3745 0.375 0.3755 0.376 0.3765 0.377 0.3775 0.378 0.3785 0.379 0.3795 0.38 0.3805 0.38100000000000001 0.38150000000000001 0.38200000000000001 0.38250000000000001 0.38300000000000001 0.38350000000000001 0.38400000000000001 0.38450000000000001 0.38500000000000001 0.38550000000000001 0.38600000000000001 0.38650000000000001 0.38700000000000001 0.38750000000000001 0.38800000000000001 0.38850000000000001 0.38900000000000001 0.38950000000000001 0.39 0.39050000000000001 0.39100000000000001 0.39150000000000001 0.39200000000000002 0.39250000000000002 0.39300000000000002 0.39350000000000002 0.39400000000000002 0.39450000000000002 0.39500000000000002 0.39550000000000002 0.39600000000000002 0.39650000000000002 0.39700000000000002 0.3975 0000000000002 0.39800000000000002 0.39850000000000002 0.39900000000000002 0.39950000000000002 0.4 0.40050000000000002 0.40100000000000002 0.40150000000000002 0.40200000000000002 0.40250000000000002 0.40300000000000002 0.40350000000000003 0.40400000000000003 0.40450000000000003 0.40500000000000003 0.40550000000000003 0.40600000000000003 0.40649999999999997 0.40699999999999997 0.40749999999999997 0.40799999999999997 0.40849999999999997 0.40899999999999997 0.40949999999999998 0.41 0.41049999999999998 0.41099999999999998 0.41149999999999998 0.41199999999999998 0.41249999999999998 0.41299999999999998 0.41349999999999998 0.41399999999999998 0.41449999999999998 0.41499999999999998 0.41549999999999998 0.41599999999999998 0.41649999999999998 0.4169999999999999 8 0.41749999999999998 0.41799999999999998 0.41849999999999998 0.41899999999999998 0.41949999999999998 0.42 0.42049999999999998 0.42099999999999999 0.42149999999999999 0.42199999999999999 0.42249999999999999 0.42299999999999999 0.42349999999999999 0.42399999999999999 0.42449999999999999 0.42499999999999999 0.42549999999999999 0.42599999999999999 0.42649999999999999 0.42699999999999999 0.42749999999999999 0.42799999999999999 0.42849999999999999 0.42899999999999999 0.42949999999999999 0.43 0.43049999999999999 0.43099999999999999 0.43149999999999999 0.432 0.4325 0.433 0.4335 0.434 0.4345 0.435 0.4355 0.436 0.4365 0.437 0.4375 0.438 0.4385 0.439 0.4395 0.44 0.4405 0.441 0.4415 0.442 0.4425 0.443 0.44350000000000001 0.44400000000000001 0.44450000000000001 0.44500000000000001 0.44550000000000001 0.44600000000000001 0.44650000000000001 0.44700000000000001 0.44750000000000001 0.44800000000000001 0.44850000000000001 0.44900000000000001 0.44950000000000001 0.45 0.45050000000000001 0.45100000000000001 0.45150000000000001 0.45200000000000001 0.45250000000000001 0.45300000000000001 0.45350000000000001 0.45400000000000001 0.45450000000000002 0.45500000000000002 0.45550000000000002 0.45600000000000002 0.45650000000000002 0.45700000000000002 0.45750000000000002 0.45800000000000002 0.45850000000000002 0.45900000000000002 0.45950000000000002 0.46 0.46050000000000002 0.46100000000000002 0.46150000000000002 0.46200000000000002 0.46250000000000002 0.46300000000000002 0.46350000000000002 0.46400000000000002 0.46450000000000002 0.46500000000000002 0.46550000000000002 0.46600000000000003 0.46650000000000003 0.46700000000000003 0.46750000000000003 0.46800000000000003 0.46850000000000003 0.46899999999999997 0.46949999999999997 0.47 0.47049999999999997 0.47099999999999997 0.47149999999999997 0.47199999999999998 0.47249999999999998 0.47299999999999998 0.47349999999999998 0.47399999999999998 0.47449999999999998 0.47499999999999998 0.47549999999999998 0.47599999999999998 0.47649999999999998 0.47699999999999998 0.47749999999999998 0.47799999999999998 0.47849999999999998 0.47899999999999998 0.47949999999999998 0.48 0.48049999999999998 0.48099999999999998 0.48149999999999998 0.48199999999999998 0.48249999999999998 0.48299999999999998 0.48349999999999999 0.48399999999999999 0.48449999999999999 0.48499999999999999 0.48549999999999999 0.48599999999999999 0.48649999999999999 0.48699999999999999 0.48749999999999999 0.48799999999999999 0.48849999999999999 0.48899999999999999 0.48949999999999999 0.49 0.49049999999999999 0.49099999999999999 0.49149999999999999 0.49199999999999999 0.49249999999999999 0.49299999999999999 0.49349999999999999 0.49399999999999999 0.4945 0.495 0.4955 0.496 0.4965 0.497 0.4975 0.498 0.4985 0.499 0.4995 0.5 0.50049999999999994 0.501 0.50149999999999995 0.502 0.50249999999999995 0.503 0.50349999999999995 0.504 0.50449999999999995 0.505 0.50549999999999995 0.50600000000000001 0.50649999999999995 0.50700000000000001 0.50749999999999995 0.50800000000000001 0.50849999999999995 0.50900000000000001 0.50949999999999995 0.51 0.51049999999999995 0.51100000000000001 0.51149999999999995 0.51200000000000001 0.51249999999999996 0.51300000000000001 0.51349999999999996 0.51400000000000001 0.51449999999999996 0.51500000000000001 0.51549999999999996 0.51600000000000001 0.51649999999999996 0.51700000000000002 0.51749999999999996 0.51800000000000002 0.51849999999999996 0.51900000000000002 0.519499999999999 96 0.52 0.52049999999999996 0.52100000000000002 0.52149999999999996 0.52200000000000002 0.52249999999999996 0.52300000000000002 0.52349999999999997 0.52400000000000002 0.52449999999999997 0.52500000000000002 0.52549999999999997 0.52600000000000002 0.52649999999999997 0.52700000000000002 0.52749999999999997 0.52800000000000002 0.52849999999999997 0.52900000000000003 0.52949999999999997 0.53 0.53049999999999997 0.53100000000000003 0.53149999999999997 0.53200000000000003 0.53249999999999997 0.53300000000000003 0.53349999999999997 0.53400000000000003 0.53449999999999998 0.53500000000000003 0.53549999999999998 0.53600000000000003 0.53649999999999998 0.53700000000000003 0.53749999999999998 0.53800000000000003 0.53849999999999998 0.53900000000000003 0.53949999999999998 0.54 0.54049999999999998 0.54100000000000004 0.54149999999999998 0.54200000000000004 0.54249999999999998 0.54300000000000004 0.54349999999999998 0.54400000000000004 0.54449999999999998 0.54500000000000004 0.54549999999999998 0.54600000000000004 0.54649999999999999 0.54700000000000004 0.54749999999999999 0.54800000000000004 0.54849999999999999 0.54900000000000004 0.54949999999999999 0.55000000000000004 0.55049999999999999 0.55100000000000005 0.55149999999999999 0.55200000000000005 0.55249999999999999 0.55300000000000005 0.55349999999999999 0.55400000000000005 0.55449999999999999 0.55500000000000005 0.55549999999999999 0.55600000000000005 0.55649999999999999 0.55700000000000005 0.5575 0.55800000000 000005 0.5585 0.55900000000000005 0.5595 0.56000000000000005 0.5605 0.56100000000000005 0.5615 0.56200000000000006 0.5625 0.56299999999999994 0.5635 0.56399999999999995 0.5645 0.56499999999999995 0.5655 0.56599999999999995 0.5665 0.56699999999999995 0.5675 0.56799999999999995 0.56850000000000001 0.56899999999999995 0.56950000000000001 0.56999999999999995 0.57050000000000001 0.57099999999999995 0.57150000000000001 0.57199999999999995 0.57250000000000001 0.57299999999999995 0.57350000000000001 0.57399999999999995 0.57450000000000001 0.57499999999999996 0.57550000000000001 0.57599999999999996 0.57650000000000001 0.57699999999999996 0.57750000000000001 0.57799999999999996 0.57850000000000001 0.57899999999999996 0.57950000000000002 0.57999999999999996 0.58050000000000002 0.58099999999999996 0.58150000000000002 0.58199999999999996 0.58250000000000002 0.58299999999999996 0.58350000000000002 0.58399999999999996 0.58450000000000002 0.58499999999999996 0.58550000000000002 0.58599999999999997 0.58650000000000002 0.58699999999999997 0.58750000000000002 0.58799999999999997 0.58850000000000002 0.58899999999999997 0.58950000000000002 0.59 0.59050000000000002 0.59099999999999997 0.59150000000000003 0.59199999999999997 0.59250000000000003 0.59299999999999997 0.59350000000000003 0.59399999999999997 0.59450000000000003 0.59499999999999997 0.59550000000000003 0.59599999999999997 0.59650000000000003 0.59699999999999998 0.59750000000000003 0.59799999999999998 0.59850000000000003 0.59899999999999998 0.59950000000000003 0.6 0.60050000000000003 0.60099999999999998 0.60150000000000003 0.60199999999999998 0.60250000000000004 0.60299999999999998 0.60350000000000004 0.60399999999999998 0.60450000000000004 0.60499999999999998 0.60550000000000004 0.60599999999999998 0.60650000000000004 0.60699999999999998 0.60750000000000004 0.60799999999999998 0.60850000000000004 0.60899999999999999 0.60950000000000004 0.61 0.61050000000000004 0.61099999999999999 0.61150000000000004 0.61199999999999999 0.61250000000000004 0.61299999999999999 0.61350000000000005 0.61399999999999999 0.61450000000000005 0.61499999999999999 0.61550000000000005 0.61599999999999999 0.6165000000000 0005 0.61699999999999999 0.61750000000000005 0.61799999999999999 0.61850000000000005 0.61899999999999999 0.61950000000000005 0.62 0.62050000000000005 0.621 0.62150000000000005 0.622 0.62250000000000005 0.623 0.62350000000000005 0.624 0.62450000000000006 0.625 0.62549999999999994 0.626 0.62649999999999995 0.627 0.62749999999999995 0.628 0.62849999999999995 0.629 0.62949999999999995 0.63 0.63049999999999995 0.63100000000000001 0.63149999999999995 0.63200000000000001 0.63249999999999995 0.63300000000000001 0.63349999999999995 0.63400000000000001 0.63449999999999995 0.63500000000000001 0.63549999999999995 0.63600000000000001 0.63649999999999995 0.637 00000000000001 0.63749999999999996 0.63800000000000001 0.63849999999999996 0.63900000000000001 0.63949999999999996 0.64 0.64049999999999996 0.64100000000000001 0.64149999999999996 0.64200000000000002 0.64249999999999996 0.64300000000000002 0.64349999999999996 0.64400000000000002 0.64449999999999996 0.64500000000000002 0.64549999999999996 0.64600000000000002 0.64649999999999996 0.64700000000000002 0.64749999999999996 0.64800000000000002 0.64849999999999997 0.64900000000000002 0.64949999999999997 0.65 0.65049999999999997 0.65100000000000002 0.65149999999999997 0.65200000000000002 0.65249999999999997 0.65300000000000002 0.65349999999999997 0.65400000000000003 0.65449999999999997 0.65500000000000003 0.65549999999999997 0.65600000000000003 0.65649999999999997 0.65700000000000003 0.65749999999999997 0.65800000000000003 0.65849999999999997 0.65900000000000003 0.65949999999999998 0.66 0.66049999999999998 0.66100000000000003 0.66149999999999998 0.66200000000000003 0.66249999999999998 0.66300000000000003 0.66349999999999998 0.66400000000000003 0.66449999999999998 0.66500000000000004 0.66549999999999998 0.66600000000000004 0.66649999999999998 0.66700000000000004 0.66749999999999998 0.66800000000000004 0.66849999999999998 0.66900000000000004 0.66949999999999998 0.67 0.67049999999999998 0.67100000000000004 0.67149999999999999 0.67200000000000004 0.67249999999999999 0.67300000000000004 0.67349999999999999 0.67400000000000004 0.67449999999999999 0.67500000000000004 0.6 7549999999999999 0.67600000000000005 0.67649999999999999 0.67700000000000005 0.67749999999999999 0.67800000000000005 0.67849999999999999 0.67900000000000005 0.67949999999999999 0.68 0.68049999999999999 0.68100000000000005 0.68149999999999999 0.68200000000000005 0.6825 0.68300000000000005 0.6835 0.68400000000000005 0.6845 0.68500000000000005 0.6855 0.68600000000000005 0.6865 0.68700000000000006 0.6875 0.68799999999999994 0.6885 0.68899999999999995 0.6895 0.69 0.6905 0.69099999999999995 0.6915 0.69199999999999995 0.6925 0.69299999999999995 0.69350000000000001 0.69399999999999995 0.69450000000000001 0.69499999999999995 0.69550000000000001 0.69599999 999999995 0.69650000000000001 0.69699999999999995 0.69750000000000001 0.69799999999999995 0.69850000000000001 0.69899999999999995 0.69950000000000001 0.7 0.70050000000000001 0.70099999999999996 0.70150000000000001 0.70199999999999996 0.70250000000000001 0.70299999999999996 0.70350000000000001 0.70399999999999996 0.70450000000000002 0.70499999999999996 0.70550000000000002 0.70599999999999996 0.70650000000000002 0.70699999999999996 0.70750000000000002 0.70799999999999996 0.70850000000000002 0.70899999999999996 0.70950000000000002 0.71 0.71050000000000002 0.71099999999999997 0.71150000000000002 0.71199999999999997 0.71250000000000002 0.71299999999999997 0.71350000000000002 0.71399999999999997 0.71450000000000002 0.71499999999999997 0.71550000000000002 0.71599999999999997 0.71650000000000003 0.71699999999999997 0.71750000000000003 0.71799999999999997 0.71850000000000003 0.71899999999999997 0.71950000000000003 0.72 0.72050000000000003 0.72099999999999997 0.72150000000000003 0.72199999999999998 0.72250000000000003 0.72299999999999998 0.72350000000000003 0.72399999999999998 0.72450000000000003 0.72499999999999998 0.72550000000000003 0.72599999999999998 0.72650000000000003 0.72699999999999998 0.72750000000000004 0.72799999999999998 0.72850000000000004 0.72899999999999998 0.72950000000000004 0.73 0.73050000000000004 0.73099999999999998 0.73150000000000004 0.73199999999999998 0.73250000000000004 0.73299999999999998 0.73350000000000004 0.73399999999999999 0.734 50000000000004 0.73499999999999999 0.73550000000000004 0.73599999999999999 0.73650000000000004 0.73699999999999999 0.73750000000000004 0.73799999999999999 0.73850000000000005 0.73899999999999999 0.73950000000000005 0.74 0.74050000000000005 0.74099999999999999 0.74150000000000005 0.74199999999999999 0.74250000000000005 0.74299999999999999 0.74350000000000005 0.74399999999999999 0.74450000000000005 0.745 0.74550000000000005 0.746 0.74650000000000005 0.747 0.74750000000000005 0.748 0.74850000000000005 0.749 0.74950000000000006 0.75 0.75049999999999994 0.751 0.75149999999999995 0.752 0.75249999999999995 0.753 0.75349999999999995 0.754 0.75449999999999995 0.755 0.75549999999999995 0.75600000000000001 0.75649999999999995 0.75700000000000001 0.75749999999999995 0.75800000000000001 0.75849999999999995 0.75900000000000001 0.75949999999999995 0.76 0.76049999999999995 0.76100000000000001 0.76149999999999995 0.76200000000000001 0.76249999999999996 0.76300000000000001 0.76349999999999996 0.76400000000000001 0.76449999999999996 0.76500000000000001 0.76549999999999996 0.76600000000000001 0.76649999999999996 0.76700000000000002 0.76749999999999996 0.76800000000000002 0.76849999999999996 0.76900000000000002 0.76949999999999996 0.77 0.77049999999999996 0.77100000000000002 0.77149999999999996 0.77200000000000002 0.77249999999999996 0.77300000000000002 0.77349999999999997 0.77400000000000002 0.77449999999999997 0.77500000000000002 0.77549999999999997 0.77600000000000002 0.77649999999999997 0.77700000000000002 0.77749999999999997 0.77800000000000002 0.77849999999999997 0.77900000000000003 0.77949999999999997 0.78 0.78049999999999997 0.78100000000000003 0.78149999999999997 0.78200000000000003 0.78249999999999997 0.78300000000000003 0.78349999999999997 0.78400000000000003 0.78449999999999998 0.78500000000000003 0.78549999999999998 0.78600000000000003 0.78649999999999998 0.78700000000000003 0.78749999999999998 0.78800000000000003 0.78849999999999998 0.78900000000000003 0.78949999999999998 0.79 0.79049999999999998 0.79100000000000004 0.79149999999999998 0.79200000000000004 0.79249999999999998 0.79300000000000004 0.793 49999999999998 0.79400000000000004 0.79449999999999998 0.79500000000000004 0.79549999999999998 0.79600000000000004 0.79649999999999999 0.79700000000000004 0.79749999999999999 0.79800000000000004 0.79849999999999999 0.79900000000000004 0.79949999999999999 0.8 0.80049999999999999 0.80100000000000005 0.80149999999999999 0.80200000000000005 0.80249999999999999 0.80300000000000005 0.80349999999999999 0.80400000000000005 0.80449999999999999 0.80500000000000005 0.80549999999999999 0.80600000000000005 0.80649999999999999 0.80700000000000005 0.8075 0.80800000000000005 0.8085 0.80900000000000005 0.8095 0.81 0.8105 0.81100000000000005 0.8115 0.81200000000000006 0.8125 0.81299999999999994 0. 8135 0.81399999999999995 0.8145 0.81499999999999995 0.8155 0.81599999999999995 0.8165 0.81699999999999995 0.8175 0.81799999999999995 0.81850000000000001 0.81899999999999995 0.81950000000000001 0.82 0.82050000000000001 0.82099999999999995 0.82150000000000001 0.82199999999999995 0.82250000000000001 0.82299999999999995 0.82350000000000001 0.82399999999999995 0.82450000000000001 0.82499999999999996 0.82550000000000001 0.82599999999999996 0.82650000000000001 0.82699999999999996 0.82750000000000001 0.82799999999999996 0.82850000000000001 0.82899999999999996 0.82950000000000002 0.83 0.83050000000000002 0.83099999999999996 0.83150000000000002 0.83199999999999996 0.83250000000000002 0.83299999999999996 0.83350000000000002 0.83399999999999996 0.83450000000000002 0.83499999999999996 0.83550000000000002 0.83599999999999997 0.83650000000000002 0.83699999999999997 0.83750000000000002 0.83799999999999997 0.83850000000000002 0.83899999999999997 0.83950000000000002 0.84 0.84050000000000002 0.84099999999999997 0.84150000000000003 0.84199999999999997 0.84250000000000003 0.84299999999999997 0.84350000000000003 0.84399999999999997 0.84450000000000003 0.84499999999999997 0.84550000000000003 0.84599999999999997 0.84650000000000003 0.84699999999999998 0.84750000000000003 0.84799999999999998 0.84850000000000003 0.84899999999999998 0.84950000000000003 0.85 0.85050000000000003 0.85099999999999998 0.85150000000000003 0.85199999999999998 0.85250000 000000004 0.85299999999999998 0.85350000000000004 0.85399999999999998 0.85450000000000004 0.85499999999999998 0.85550000000000004 0.85599999999999998 0.85650000000000004 0.85699999999999998 0.85750000000000004 0.85799999999999998 0.85850000000000004 0.85899999999999999 0.85950000000000004 0.86 0.86050000000000004 0.86099999999999999 0.86150000000000004 0.86199999999999999 0.86250000000000004 0.86299999999999999 0.86350000000000005 0.86399999999999999 0.86450000000000005 0.86499999999999999 0.86550000000000005 0.86599999999999999 0.86650000000000005 0.86699999999999999 0.86750000000000005 0.86799999999999999 0.86850000000000005 0.86899999999999999 0.86950000000000005 0.87 0.87050000000000005 0.871 0.87150000000000005 0.872 0.87250000000000005 0.873 0.87350000000000005 0.874 0.87450000000000006 0.875 0.87549999999999994 0.876 0.87649999999999995 0.877 0.87749999999999995 0.878 0.87849999999999995 0.879 0.87949999999999995 0.88 0.88049999999999995 0.88100000000000001 0.88149999999999995 0.88200000000000001 0.88249999999999995 0.88300000000000001 0.88349999999999995 0.88400000000000001 0.88449999999999995 0.88500000000000001 0.88549999999999995 0.88600000000000001 0.88649999999999995 0.88700000000000001 0.88749999999999996 0.88800000000000001 0.88849999999999996 0.88900000000000001 0.88949999999999996 0.89 0.89049999999999996 0.89100000000000001 0.89149999999999996 0.89200000000000002 0.89249999999999996 0.89300000000000002 0.89349999999999996 0.89400000000000002 0.89449999999999996 0.89500000000000002 0.89549999999999996 0.89600000000000002 0.89649999999999996 0.89700000000000002 0.89749999999999996 0.89800000000000002 0.89849999999999997 0.89900000000000002 0.89949999999999997 0.9 0.90049999999999997 0.90100000000000002 0.90149999999999997 0.90200000000000002 0.90249999999999997 0.90300000000000002 0.90349999999999997 0.90400000000000003 0.90449999999999997 0.90500000000000003 0.90549999999999997 0.90600000000000003 0.90649999999999997 0.90700000000000003 0.90749999999999997 0.90800000000000003 0.90849999999999997 0.90900000000000003 0.90949999999999998 0.91 0.91049999999999998 0.91100000000000003 0.91149999999999998 0.91200000000000003 0.91249999999999998 0.91300000000000003 0.91349999999999998 0.91400000000000003 0.91449999999999998 0.91500000000000004 0.91549999999999998 0.91600000000000004 0.91649999999999998 0.91700000000000004 0.91749999999999998 0.91800000000000004 0.91849999999999998 0.91900000000000004 0.91949999999999998 0.92 0.92049999999999998 0.92100000000000004 0.92149999999999999 0.92200000000000004 0.92249999999999999 0.92300000000000004 0.92349999999999999 0.92400000000000004 0.92449999999999999 0.92500000000000004 0.92549999999999999 0.92600000000000005 0.92649999999999999 0.92700000000000005 0.92749999999999999 0.92800000000000005 0.92849999999999999 0.92900000000000005 0.92949999999999999 0.93 0.93049999999999999 0.93100000000000005 0.93149999999999999 0.93200000000000005 0.9325 0.93300000000000005 0.9335 0.93400000000000005 0.9345 0.93500000000000005 0.9355 0.93600000000000005 0.9365 0.93700000000000006 0.9375 0.93799999999999994 0.9385 0.93899999999999995 0.9395 0.94 0.9405 0.94099999999999995 0.9415 0.94199999999999995 0.9425 0.94299999999999995 0.94350000000000001 0.94399999999999995 0.94450000000000001 0.94499999999999995 0.94550000000000001 0.94599999999999995 0.94650000000000001 0.94699999999999995 0.94750000000000001 0.94799999999999995 0.94850000000000001 0.94899999999999995 0.94950000000000001 0.95 0.95050000000000001 0.95099999999999996 0.95150000000000001 0.95199999999999996 0.95250000000000001 0.95299999999999996 0.95350000000000001 0.95399999999999996 0.95450000000000002 0.95499999999999996 0.95550000000000002 0.95599999999999996 0.95650000000000002 0.95699999999999996 0.95750000000000002 0.95799999999999996 0.95850000000000002 0.95899999999999996 0.95950000000000002 0.96 0.96050000000000002 0.96099999999999997 0.96150000000000002 0.96199999999999997 0.96250000000000002 0.96299999999999997 0.96350000000000002 0.96399999999999997 0.96450000000000002 0.96499999999999997 0.96550000000000002 0.96599999999999997 0.96650000000000003 0.96699999999999997 0.96750000000000003 0.96799999999999997 0.96850000000000003 0.96899999999999997 0.96950000000000003 0.97 0.97050000000000003 0.97099999999999997 0.97150000000000003 0.97199999999999998 0.97250000000000003 0.97299999999999998 0.97350000000000003 0.97399999999999998 0.97450000000000003 0.97499999999999998 0.97550000000000003 0.97599999999999998 0.97650000000000003 0.97699999999999998 0.97750000000000004 0.97799999999999998 0.97850000000000004 0.97899999999999998 0.97950000000000004 0.98 0.98050000000000004 0.98099999999999998 0.98150000000000004 0.98199999999999998 0.98250000000000004 0.98299999999999998 0.98350000000000004 0.98399999999999999 0.98450000000000004 0.98499999999999999 0.98550000000000004 0.98599999999999999 0.98650000000000004 0.98699999999999999 0.98750000000000004 0.98799999999999999 0.98850000000000005 0.98899999999999999 0.98950 000000000005 0.99 0.99050000000000005 0.99099999999999999 0.99150000000000005 0.99199999999999999 0.99250000000000005 0.99299999999999999 0.99350000000000005 0.99399999999999999 0.99450000000000005 0.995 0.99550000000000005 0.996 0.99650000000000005 0.997 0.99750000000000005 0.998 0.99850000000000005 0.999 0.99950000000000006 1 1.0004999999999999 1.0009999999999999 1.0015000000000001 1.002 1.0024999999999999 1.0029999999999999 1.0035000000000001 1.004 1.0044999999999999 1.0049999999999999 1.0055000000000001 1.006 1.0065 1.0069999999999999 1.0075000000000001 1.008 1.0085 1.0089999999999999 1.0095000000000001 1.01 1.0105 1.0109999999999999 1.0115000000000001 1.012 1.0125 1.0129999999999999 1.0135000000000001 1.014 1.0145 1.0149999999999999 1.0155000000000001 1.016 1.0165 1.0169999999999999 1.0175000000000001 1.018 1.0185 1.0189999999999999 1.0195000000000001 1.02 1.0205 1.0209999999999999 1.0215000000000001 1.022 1.0225 1.0229999999999999 1.0235000000000001 1.024 1.0245 1.0249999999999999 1.0255000000000001 1.026 1.0265 1.0269999999999999 1.0275000000000001 1.028 1.0285 1.0289999999999999 1.0295000000000001 1.03 1.0305 1.0309999999999999 1.0315000000000001 1.032 1.0325 1.0329999999999999 1.0335000000000001 1.034 1.0345 1.0349999999999999 1.0355000000000001 1.036 1.0365 1.0369999999999999 1.0375000000000001 1.038 1.0385 1.0389999999999999 1.0395000000000001 1.04 1.0405 1.0409999999999999 1.0415000000000001 1.042 1.0425 1.0429999999999999 1.0435000000000001 1.044 1.0445 1.0449999999999999 1.0455000000000001 1.046 1.0465 1.0469999999999999 1.0475000000000001 1.048 1.0485 1.0489999999999999 1.0495000000000001 1.05 1.0505 1.0509999999999999 1.0515000000000001 1.052 1.0525 1.0529999999999999 1.0535000000000001 1.054 1.0545 1.0549999999999999 1.0555000000000001 1.056 1.0565 1.0569999999999999 1.0575000000000001 1.0580000000000001 1.0585 1.0589999999999999 1.0595000000000001 1.06 1.0605 1.0609999999999999 1.0615000000000001 1.0620000000000001 1.0625 1.0629999999999999 1.0634999999999999 1.0640000000000001 1.0645 1.0649999999999999 1.0654999999999999 1.0660000000000001 1.0665 1.0669999999999999 1.0674999999999999 1.0680000000000001 1.0685 1.069 1.0694999999999999 1.07 1.0705 1.071 1.0714999999999999 1.0720000000000001 1.0725 1.073 1.0734999999999999 1.0740000000000001 1.0745 1.075 1.0754999999999999 1.0760000000000001 1.0765 1.077 1.0774999999999999 1.0780000000000001 1.0785 1.079 1.0794999999999999 1.08 1.0805 1.081 1.0814999999999999 1.0820000000000001 1.0825 1.083 1.0834999999999999 1.0840000000000001 1.0845 1.085 1.0854999999999999 1.0860000000000001 1.0865 1.087 1.0874999999999999 1.0880000000000001 1.0885 1.089 1.0894999999999999 1.0900000000000001 1.0905 1.091 1.0914999999999999 1.0920000000000001 1.0925 1.093 1.0934999999999999 1.0940000000000001 1.0945 1.095 1.0954999999999999 1.0960000000000001 1.0965 1.097 1.0974999999999999 1.0980000000000001 1.0985 1.099 1.0994999999999999 1.1000000000000001 1.1005 1.101 1.1014999999999999 1.1020000000000001 1.1025 1.103 1.1034999999999999 1.1040000000000001 1.1045 1.105 1.1054999999999999 1.1060000000000001 1.1065 1.107 1.1074999999999999 1.1080000000000001 1.1085 1.109 1.1094999999999999 1.1100000000000001 1.1105 1.111 1.1114999999999999 1.1120000000000001 1.1125 1.113 1.1134999999999999 1.1140000000000001 1.1145 1.115 1.1154999999999999 1.1160000000000001 1.1165 1.117 1.1174999999999999 1.1180000000000001 1.1185 1.119 1.1194999999999999 1.1200000000000001 1.1205000000000001 1.121 1.1214999999999999 1.1220000000000001 1.1225000000000001 1.123 1.1234999999999999 1.1240000000000001 1.1245000000000001 1.125 1.1254999999999999 1.1259999999999999 1.1265000000000001 1.127 1.1274999999999999 1.1279999999999999 1.1285000000000001 1.129 1.1294999999999999 1.1299999999999999 1.1305000000000001 1.131 1.1315 1.1319999999999999 1.1325000000000001 1.133 1.1335 1.1339999999999999 1.1345000000000001 1.135 1.1355 1.1359999999999999 1.1365000000000001 1.137 1.1375 1.1379999999999999 1.1385000000000001 1.139 1.1395 1.1399999999999999 1.1405000000000001 1.141 1.1415 1.1419999999999999 1.1425000000000001 1.143 1.1435 1.1439999999999999 1.1445000000000001 1.145 1.1455 1.1459999999999999 1.1465000000000001 1.147 1.1475 1.1479999999999999 1.1485000000000001 1.149 1.1495 1.1499999999999999 1.1505000000000001 1.151 1.1515 1.1519999999999999 1.1525000000000001 1.153 1.1535 1.1539999999999999 1.1545000000000001 1.155 1.1555 1.1559999999999999 1.1565000000000001 1.157 1.1575 1.1579999999999999 1.1585000000000001 1.159 1.1595 1.1599999999999999 1.1605000000000001 1.161 1.1615 1.1619999999999999 1.1625000000000001 1.163 1.1635 1.1639999999999999 1.1645000000000001 1.165 1.1655 1.1659999999999999 1.1665000000000001 1.167 1.1675 1.1679999999999999 1.1685000000000001 1.169 1.1695 1.17 1.1705000000000001 1.171 1.1715 1.1719999999999999 1.1725000000000001 1.173 1.1735 1.1739999999999999 1.1745000000000001 1.175 1.1755 1.1759999999999999 1.1765000000000001 1.177 1.1775 1.1779999999999999 1.1785000000000001 1.179 1.1795 1.18 1.1805000000000001 1.181 1.1815 1.1819999999999999 1.1825000000000001 1.1830000000000001 1.1835 1.1839999999999999 1.1845000000000001 1.1850000000000001 1.1855 1.1859999999999999 1.1865000000000001 1.1870000000000001 1.1875 1.1879999999999999 1.1884999999999999 1.1890000000000001 1.1895 1.19 1.1904999999999999 1.1910000000000001 1.1915 1.1919999999999999 1.1924999999999999 1.1930000000000001 1.1935 1.194 1.1944999999999999 1.1950000000000001 1.1955 1.196 1.1964999999999999 1.1970000000000001 1.1975 1.198 1.1984999999999999 1.1990000000000001 1.1995 1.2 1.2004999999999999 1.2010000000000001 1.2015 1.202 1.2024999999999999 1.2030000000000001 1.2035 1.204 1.2044999999999999 1.2050000000000001 1.2055 1.206 1.2064999999999999 1.2070000000000001 1.2075 1.208 1.2084999999999999 1.2090000000000001 1.2095 1.21 1.2104999999999999 1.2110000000000001 1.2115 1.212 1.2124999999999999 1.2130000000000001 1.2135 1.214 1.2144999999999999 1.2150000000000001 1.2155 1.216 1.2164999999999999 1.2170000000000001 1.2175 1.218 1.2184999999999999 1.2190000000000001 1.2195 1.22 1.2204999999999999 1.2210000000000001 1.2215 1.222 1.2224999999999999 1.2230000000000001 1.2235 1.224 1.2244999999999999 1.2250000000000001 1.2255 1.226 1.2264999999999999 1.2270000000000001 1.2275 1.228 1.2284999999999999 1.2290000000000001 1.2295 1.23 1.2304999999999999 1.2310000000000001 1.2315 1.232 1.2324999999999999 1.2330000000000001 1.2335 1.234 1.2344999999999999 1.2350000000000001 1.2355 1.236 1.2364999999999999 1.2370000000000001 1.2375 1.238 1.2384999999999999 1.2390000000000001 1.2395 1.24 1.2404999999999999 1.2410000000000001 1.2415 1.242 1.2424999999999999 1.2430000000000001 1.2435 1.244 1.2444999999999999 1.2450000000000001 1.2455000000000001 1.246 1.2464999999999999 1.2470000000000001 1.2475000000000001 1.248 1.2484999999999999 1.2490000000000001 1.2495000000000001 1.25 1.2504999999999999 1.2509999999999999 1.2515000000000001 1.252 1.2524999999999999 1.2529999999999999 1.2535000000000001 1.254 1.2544999999999999 1.2549999999999999 1.2555000000000001 1.256 1.2565 1.2569999999999999 1.2575000000000001 1.258 1.2585 1.2589999999999999 1.2595000000000001 1.26 1.2605 1.2609999999999999 1.2615000000000001 1.262 1.2625 1.2629999999999999 1.2635000000000001 1.264 1.2645 1.2649999999999999 1.2655000000000001 1.266 1.2665 1.2669999999999999 1.2675000000000001 1.268 1.2685 1.2689999999999999 1.2695000000000001 1.27 1.2705 1.2709999999999999 1.2715000000000001 1.272 1.2725 1.2729999999999999 1.2735000000000001 1.274 1.2745 1.2749999999999999 1.2755000000000001 1.276 1.2765 1.2769999999999999 1.2775000000000001 1.278 1.2785 1.2789999999999999 1.2795000000000001 1.28 1.2805 1.2809999999999999 1.2815000000000001 1.282 1.2825 1.2829999999999999 1.2835000000000001 1.284 1.2845 1.2849999999999999 1.2855000000000001 1.286 1.2865 1.2869999999999999 1.2875000000000001 1.288 1.2885 1.2889999999999999 1.2895000000000001 1.29 1.2905 1.2909999999999999 1.2915000000000001 1.292 1.2925 1.2929999999999999 1.2935000000000001 1.294 1.2945 1.2949999999999999 1.2955000000000001 1.296 1.2965 1.2969999999999999 1.2975000000000001 1.298 1.2985 1.2989999999999999 1.2995000000000001 1.3 1.3005 1.3009999999999999 1.3015000000000001 1.302 1.3025 1.3029999999999999 1.3035000000000001 1.304 1.3045 1.3049999999999999 1.3055000000000001 1.306 1.3065 1.3069999999999999 1.3075000000000001 1.3080000000000001 1.3085 1.3089999999999999 1.3095000000000001 1.31 1.3105 1.3109999999999999 1.3115000000000001 1.3120000000000001 1.3125 1.3129999999999999 1.3134999999999999 1.3140000000000001 1.3145 1.3149999999999999 1.3154999999999999 1.3160000000000001 1.3165 1.3169999999999999 1.3174999999999999 1.3180000000000001 1.3185 1.319 1.3194999999999999 1.32 1.3205 1.321 1.3214999999999999 1.3220000000000001 1.3225 1.323 1.3234999999999999 1.3240000000000001 1.3245 1.325 1.3254999999999999 1.3260000000000001 1.3265 1.327 1.3274999999999999 1.3280000000000001 1.3285 1.329 1.3294999999999999 1.33 1.3305 1.331 1.3314999999999999 1.3320000000000001 1.3325 1.333 1.3334999999999999 1.3340000000000001 1.3345 1.335 1.3354999999999999 1.3360000000000001 1.3365 1.337 1.3374999999999999 1.3380000000000001 1.3385 1.339 1.3394999999999999 1.34 1.3405 1.341 1.3414999999999999 1.3420000000000001 1.3425 1.343 1.3434999999999999 1.3440000000000001 1.3445 1.345 1.3454999999999999 1.3460000000000001 1.3465 1.347 1.3474999999999999 1.3480000000000001 1.3485 1.349 1.3494999999999999 1.35 1.3505 1.351 1.3514999999999999 1.3520000000000001 1.3525 1.353 1.3534999999999999 1.3540000000000001 1.3545 1.355 1.3554999999999999 1.3560000000000001 1.3565 1.357 1.3574999999999999 1.3580000000000001 1.3585 1.359 1.3594999999999999 1.36 1.3605 1.361 1.3614999999999999 1.3620000000000001 1.3625 1.363 1.3634999999999999 1.3640000000000001 1.3645 1.365 1.3654999999999999 1.3660000000000001 1.3665 1.367 1.3674999999999999 1.3680000000000001 1.3685 1.369 1.3694999999999999 1.37 1.3705000000000001 1.371 1.3714999999999999 1.3720000000000001 1.3725000000000001 1.373 1.3734999999999999 1.3740000000000001 1.3745000000000001 1.375 1.3754999999999999 1.3759999999999999 1.3765000000000001 1.377 1.3774999999999999 1.3779999999999999 1.3785000000000001 1.379 1.3794999999999999 1.38 1.380 5000000000001 1.381 1.3815 1.3819999999999999 1.3825000000000001 1.383 1.3835 1.3839999999999999 1.3845000000000001 1.385 1.3855 1.3859999999999999 1.3865000000000001 1.387 1.3875 1.3879999999999999 1.3885000000000001 1.389 1.3895 1.39 1.3905000000000001 1.391 1.3915 1.3919999999999999 1.3925000000000001 1.393 1.3935 1.3939999999999999 1.3945000000000001 1.395 1.3955 1.3959999999999999 1.3965000000000001 1.397 1.3975 1.3979999999999999 1.3985000000000001 1.399 1.3995 1.4 1.4005000000000001 1.401 1.4015 1.4019999999999999 1.4025000000000001 1.403 1.4035 1.4039999999999999 1.4045000000000001 1.405 1.4055 1.4059999999999999 1.4065000000000001 1.407 1.4075 1.4079999999999999 1.4085000000000001 1.409 1.4095 1.41 1.4105000000000001 1.411 1.4115 1.4119999999999999 1.4125000000000001 1.413 1.4135 1.4139999999999999 1.4145000000000001 1.415 1.4155 1.4159999999999999 1.4165000000000001 1.417 1.4175 1.4179999999999999 1.4185000000000001 1.419 1.4195 1.42 1.4205000000000001 1.421 1.4215 1.4219999999999999 1.4225000000000001 1.423 1.4235 1.4239999999999999 1.4245000000000001 1.425 1.4255 1.4259999999999999 1.4265000000000001 1.427 1.4275 1.4279999999999999 1.4285000000000001 1.429 1.4295 1.43 1.4305000000000001 1.431 1.4315 1.4319999999999999 1.4325000000000001 1.4330000000000001 1.4335 1.4339999999999999 1.4345000000000001 1.4350000000000001 1.4355 1.4359999999999999 1.4365000000000001 1.4370000000000001 1.4375 1.4379999999999999 1.4384999999999999 1.4390000000000001 1.4395 1.44 1.4404999999999999 1.4410000000000001 1.4415 1.4419999999999999 1.4424999999999999 1.4430000000000001 1.4435 1.444 1.4444999999999999 1.4450000000000001 1.4455 1.446 1.4464999999999999 1.4470000000000001 1.4475 1.448 1.4484999999999999 1.4490000000000001 1.4495 1.45 1.4504999999999999 1.4510000000000001 1.4515 1.452 1.4524999999999999 1.4530000000000001 1.4535 1.454 1.4544999999999999 1.4550000000000001 1.4555 1.456 1.4564999999999999 1.4570000000000001 1.4575 1.458 1.4584999999999999 1.4590000000000001 1.4595 1.46 1.4604999999999999 1.4610000000000001 1.4615 1.462 1.4624999999999999 1.4630000000000001 1.4635 1.464 1.4644999999999999 1.4650000000000001 1.4655 1.466 1.4664999999999999 1.4670000000000001 1.4675 1.468 1.4684999999999999 1.4690000000000001 1.4695 1.47 1.4704999999999999 1.4710000000000001 1.4715 1.472 1.4724999999999999 1.4730000000000001 1.4735 1.474 1.4744999999999999 1.4750000000000001 1.4755 1.476 1.4764999999999999 1.4770000000000001 1.4775 1.478 1.4784999999999999 1.4790000000000001 1.4795 1.48 1.4804999999999999 1.4810000000000001 1.4815 1.482 1.4824999999999999 1.4830000000000001 1.4835 1.484 1.4844999999999999 1.4850000000000001 1.4855 1.486 1.4864999999999999 1.4870000000000001 1.4875 1.488 1.4884999999999999 1.4890000000000001 1.4895 1.49 1.4904999999999999 1.4910000000000001 1.4915 1.492 1.4924999999999999 1.4930000000000001 1.4935 1.494 1.4944999999999999 1.4950000000000001 1.4955000000000001 1.496 1.4964999999999999 1.4970000000000001 1.4975000000000001 1.498 1.4984999999999999 1.4990000000000001 1.4995000000000001 1.5 1.5004999999999999 1.5009999999999999 1.5015000000000001 1.502 1.5024999999999999 1.5029999999999999 1.5035000000000001 1.504 1.5044999999999999 1.5049999999999999 1.5055000000000001 1.506 1.5065 1.5069999999999999 1.5075000000000001 1.508 1.5085 1.5089999999999999 1.5095000000000001 1.51 1.5105 1.5109999999999999 1.5115000000000001 1.512 1.5125 1.5129999999999999 1.5135000000000001 1.514 1.5145 1.5149999999999999 1.5155000000000001 1.516 1.5165 1.5169999999999999 1.5175000000000001 1.518 1.5185 1.5189999999999999 1.5195000000000001 1.52 1.5205 1.5209999999999999 1.5215000000000001 1.522 1.5225 1.5229999999999999 1.5235000000000001 1.524 1.5245 1.5249999999999999 1.5255000000000001 1.526 1.5265 1.5269999999999999 1.5275000000000001 1.528 1.5285 1.5289999999999999 1.5295000000000001 1.53 1.5305 1.5309999999999999 1.5315000000000001 1.532 1.5325 1.5329999999999999 1.5335000000000001 1.534 1.5345 1.5349999999999999 1.5355000000000001 1.536 1.5365 1.5369999999999999 1.5375000000000001 1.538 1.5385 1.5389999999999999 1.5395000000000001 1.54 1.5405 1.5409999999999999 1.5415000000000001 1.542 1.5425 1.5429999999999999 1.5435000000000001 1.544 1.5445 1.5449999999999999 1.5455000000000001 1.546 1.5465 1.5469999999999999 1.5475000000000001 1.548 1.5485 1.5489999999999999 1.5495000000000001 1.55 1.5505 1.5509999999999999 1.5515000000000001 1.552 1.5525 1.5529999999999999 1.5535000000000001 1.554 1.5545 1.5549999999999999 1.5555000000000001 1.556 1.5565 1.5569999999999999 1.5575000000000001 1.5580000000000001 1.5585 1.5589999999999999 1.5595000000000001 1.56 1.5605 1.5609999999999999 1.5615000000000001 1.5620000000000001 1.5625 1.5629999999999999 1.5634999999999999 1.5640000000000001 1.5645 1.5649999999999999 1.5654999999999999 1.5660000000000001 1.5665 1.5669999999999999 1.5674999999999999 1.5680000000000001 1.5685 1.569 1.5694999999999999 1.57 1.5705 1.571 1.5714999999999999 1.5720000000000001 1.5725 1.573 1.5734999999999999 1.5740000000000001 1.5745 1.575 1.5754999999999999 1.5760000000000001 1.5765 1.577 1.5774999999999999 1.5780000000000001 1.5785 1.579 1.5794999999999999 1.58 1.5805 1.581 1.5814999999999999 1.5820000000000001 1.5825 1.583 1.5834999999999999 1.5840000000000001 1.5845 1.585 1.5854999999999999 1.5860000000000001 1.5865 1.587 1.5874999999999999 1.5880000000000001 1.5885 1.589 1.5894999999999999 1.59 1.5905 1.591 1.5914999999999999 1.5920000000000001 1.5925 1.593 1.5934999999999999 1.5940000000000001 1.5945 1.595 1.5954999999999999 1.5960000000000001 1.5965 1.597 1.5974999999999999 1.5980000000000001 1.5985 1.599 1.5994999999999999 1.6 1.6005 1.601 1.6014999999999999 1.6020000000000001 1.6025 1.603 1.6034999999999999 1.6040000000000001 1.6045 1.605 1.6054999999999999 1.6060000000000001 1.6065 1.607 1.6074999999999999 1.6080000000000001 1.6085 1.609 1.6094999999999999 1.61 1.6105 1.611 1.6114999999999999 1.6120000000000001 1.6125 1.613 1.6134999999999999 1.6140000000000001 1.6145 1.615 1.6154999999999999 1.6160000000000001 1.6165 1.617 1.6174999999999999 1.6180000000000001 1.6185 1.619 1.6194999999999999 1.62 1.6205000000000001 1.621 1.6214999999999999 1.6220000000000001 1.6225000000000001 1.623 1.6234999999999999 1.6240000000000001 1.6245000000000001 1.625 1.6254999999999999 1.6259999999999999 1.6265000000000001 1.627 1.6274999999999999 1.6279999999999999 1.6285000000000001 1.629 1.6294999999999999 1.63 1.6305000000000001 1.631 1.6315 1.6319999999999999 1.6325000000000001 1.633 1.6335 1.6339999999999999 1.6345000000000001 1.635 1.6355 1.6359999999999999 1.6365000000000001 1.637 1.6375 1.6379999999999999 1.6385000000000001 1.639 1.6395 1.64 1.6405000000000001 1.641 1.6415 1.6419999999999999 1.6425000000000001 1.643 1.6435 1.6439999999999999 1.6445000000000001 1.645 1.6455 1.6459999999999999 1.6465000000000001 1.647 1.6475 1.6479999999999999 1.6485000000000001 1.649 1.6495 1.65 1.6505000000000001 1.651 1.6515 1.6519999999999999 1.6525000000000001 1.653 1.6535 1.6539999999999999 1.6545000000000001 1.655 1.6555 1.6559999999999999 1.6565000000000001 1.657 1.6575 1.6579999999999999 1.6585000000000001 1.659 1.6595 1.66 1.6605000000000001 1.661 1.6615 1.6619999999999999 1.6625000000000001 1.663 1.6635 1.6639999999999999 1.6645000000000001 1.665 1.6655 1.6659999999999999 1.6665000000000001 1.667 1.6675 1.6679999999999999 1.6685000000000001 1.669 1.6695 1.67 1.6705000000000001 1.671 1.6715 1.6719999999999999 1.6725000000000001 1.673 1.6735 1.6739999999999999 1.6745000000000001 1.675 1.6755 1.6759999999999999 1.6765000000000001 1.677 1.6775 1.6779999999999999 1.6785000000000001 1.679 1.6795 1.68 1.6805000000000001 1.681 1.6815 1.6819999999999999 1.6825000000000001 1.6830000000000001 1.6835 1.6839999999999999 1.6845000000000001 1.6850000000000001 1.6855 1.6859999999999999 1.6865000000000001 1.6870000000000001 1.6875 1.6879999999999999 1.6884999999999999 1.6890000000000001 1.6895 1.69 1.6904999999999999 1.6910000000000001 1.6915 1.6919999999999999 1.6924999999999999 1.6930000000000001 1.6935 1.694 1.6944999999999999 1.6950000000000001 1.6955 1.696 1.6964999999999999 1.6970000000000001 1.6975 1.698 1.6984999999999999 1.6990000000000001 1.6995 1.7 1.7004999999999999 1.7010000000000001 1.7015 1.702 1.7024999999999999 1.7030000000000001 1.7035 1.704 1.7044999999999999 1.7050000000000001 1.7055 1.706 1.7064999999999999 1.7070000000000001 1.7075 1.708 1.7084999999999999 1.7090000000000001 1.7095 1.71 1.7104999999999999 1.7110000000000001 1.7115 1.712 1.7124999999999999 1.7130000000000001 1.7135 1.714 1.7144999999999999 1.7150000000000001 1.7155 1.716 1.7164999999999999 1.7170000000000001 1.7175 1.718 1.7184999999999999 1.7190000000000001 1.7195 1.72 1.7204999999999999 1.7210000000000001 1.7215 1.722 1.7224999999999999 1.7230000000000001 1.7235 1.724 1.7244999999999999 1.7250000000000001 1.7255 1.726 1.7264999999999999 1.7270000000000001 1.7275 1.728 1.7284999999999999 1.7290000000000001 1.7295 1.73 1.7304999999999999 1.7310000000000001 1.7315 1.732 1.7324999999999999 1.7330000000000001 1.7335 1.734 1.7344999999999999 1.7350000000000001 1.7355 1.736 1.7364999999999999 1.7370000000000001 1.7375 1.738 1.7384999999999999 1.7390000000000001 1.7395 1.74 1.7404999999999999 1.7410000000000001 1.7415 1.742 1.7424999999999999 1.7430000000000001 1.7435 1.744 1.7444999999999999 1.7450000000000001 1.7455000000000001 1.746 1.7464999999999999 1.7470000000000001 1.7475000000000001 1.748 1.7484999999999999 1.7490000000000001 1.7495000000000001 1.75 1.7504999999999999 1.7509999999999999 1.7515000000000001 1.752 1.7524999999999999 1.7529999999999999 1.7535000000000001 1.754 1.7544999999999999 1.7549999999999999 1.7555000000000001 1.756 1.7565 1.7569999999999999 1.7575000000000001 1.758 1.7585 1.7589999999999999 1.7595000000000001 1.76 1.7605 1.7609999999999999 1.7615000000000001 1.762 1.7625 1.7629999999999999 1.7635000000000001 1.764 1.7645 1.7649999999999999 1.7655000000000001 1.766 1.7665 1.7669999999999999 1.7675000000000001 1.768 1.7685 1.7689999999999999 1.7695000000000001 1.77 1.7705 1.7709999999999999 1.7715000000000001 1.772 1.7725 1.7729999999999999 1.7735000000000001 1.774 1.7745 1.7749999999999999 1.7755000000000001 1.776 1.7765 1.7769999999999999 1.7775000000000001 1.778 1.7785 1.7789999999999999 1.7795000000000001 1.78 1.7805 1.7809999999999999 1.7815000000000001 1.782 1.7825 1.7829999999999999 1.7835000000000001 1.784 1.7845 1.7849999999999999 1.7855000000000001 1.786 1.7865 1.7869999999999999 1.7875000000000001 1.788 1.7885 1.7889999999999999 1.7895000000000001 1.79 1.7905 1.7909999999999999 1.7915000000000001 1.792 1.7925 1.7929999999999999 1.7935000000000001 1.794 1.7945 1.7949999999999999 1.7955000000000001 1.796 1.7965 1.7969999999999999 1.7975000000000001 1.798 1.7985 1.7989999999999999 1.7995000000000001 1.8 1.8005 1.8009999999999999 1.8015000000000001 1.802 1.8025 1.8029999999999999 1.8035000000000001 1.804 1.8045 1.8049999999999999 1.8055000000000001 1.806 1.8065 1.8069999999999999 1.8075000000000001 1.8080000000000001 1.8085 1.8089999999999999 1.8095000000000001 1.81 1.8105 1.8109999999999999 1.8115000000000001 1.8120000000000001 1.8125 1.8129999999999999 1.8134999999999999 1.8140000000000001 1.8145 1.8149999999999999 1.8154999999999999 1.8160000000000001 1.8165 1.8169999999999999 1.8174999999999999 1.8180000000000001 1.8185 1.819 1.8194999999999999 1.82 1.8205 1.821 1.8214999999999999 1.8220000000000001 1.8225 1.823 1.8234999999999999 1.8240000000000001 1.8245 1.825 1.8254999999999999 1.8260000000000001 1.8265 1.827 1.8274999999999999 1.8280000000000001 1.8285 1.829 1.8294999999999999 1.83 1.8305 1.831 1.8314999999999999 1.8320000000000001 1.8325 1.833 1.8334999999999999 1.8340000000000001 1.8345 1.835 1.8354999999999999 1.8360000000000001 1.8365 1.837 1.8374999999999999 1.8380000000000001 1.8385 1.839 1.8394999999999999 1.84 1.8405 1.841 1.8414999999999999 1.8420000000000001 1.8425 1.843 1.8434999999999999 1.8440000000000001 1.8445 1.845 1.8454999999999999 1.8460000000000001 1.8465 1.847 1.8474999999999999 1.8480000000000001 1.8485 1.849 1.8494999999999999 1.85 1.8505 1.851 1.8514999999999999 1.8520000000000001 1.8525 1.853 1.8534999999999999 1.8540000000000001 1.8545 1.855 1.8554999999999999 1.8560000000000001 1.8565 1.857 1.8574999999999999 1.8580000000000001 1.8585 1.859 1.8594999999999999 1.86 1.8605 1.861 1.8614999999999999 1.8620000000000001 1.8625 1.863 1.8634999999999999 1.8640000000000001 1.8645 1.865 1.8654999999999999 1.8660000000000001 1.8665 1.867 1.8674999999999999 1.8680000000000001 1.8685 1.869 1.8694999999999999 1.87 1.8705000000000001 1.871 1.8714999999999999 1.8720000000000001 1.8725000000000001 1.873 1.8734999999999999 1.8740000000000001 1.8745000000000001 1.875 1.8754999999999999 1.8759999999999999 1.8765000000000001 1.877 1.8774999999999999 1.8779999999999999 1.8785000000000001 1.879 1.8794999999999999 1.88 1.8805000000000001 1.881 1.8815 1.8819999999999999 1.8825000000000001 1.883 1.8835 1.8839999999999999 1.8845000000000001 1.885 1.8855 1.8859999999999999 1.8865000000000001 1.887 1.8875 1.8879999999999999 1.8885000000000001 1.889 1.8895 1.89 1.8905000000000001 1.891 1.8915 1.8919999999999999 1.8925000000000001 1.893 1.8935 1.8939999999999999 1.8945000000000001 1.895 1.8955 1.8959999999999999 1.8965000000000001 1.897 1.8975 1.8979999999999999 1.8985000000000001 1.899 1.8995 1.9 1.9005000000000001 1.901 1.9015 1.9019999999999999 1.9025000000000001 1.903 1.9035 1.9039999999999999 1.9045000000000001 1.905 1.9055 1.9059999999999999 1.9065000000000001 1.907 1.9075 1.9079999999999999 1.9085000000000001 1.909 1.9095 1.91 1.9105000000000001 1.911 1.9115 1.9119999999999999 1.9125000000000001 1.913 1.9135 1.9139999999999999 1.9145000000000001 1.915 1.9155 1.9159999999999999 1.9165000000000001 1.917 1.9175 1.9179999999999999 1.9185000000000001 1.919 1.9195 1.92 1.9205000000000001 1.921 1.9215 1.9219999999999999 1.9225000000000001 1.923 1.9235 1.9239999999999999 1.9245000000000001 1.925 1.9255 1.9259999999999999 1.9265000000000001 1.927 1.9275 1.9279999999999999 1.9285000000000001 1.929 1.9295 1.93 1.9305000000000001 1.931 1.9315 1.9319999999999999 1.9325000000000001 1.9330000000000001 1.9335 1.9339999999999999 1.9345000000000001 1.9350000000000001 1.9355 1.9359999999999999 1.9365000000000001 1.9370000000000001 1.9375 1.9379999999999999 1.9384999999999999 1.9390000000000001 1.9395 1.94 1.9404999999999999 1.9410000000000001 1.9415 1.9419999999999999 1.9424999999999999 1.9430000000000001 1.9435 1.944 1.9444999999999999 1.9450000000000001 1.9455 1.946 1.9464999999999999 1.9470000000000001 1.9475 1.948 1.948499999999999 9 1.9490000000000001 1.9495 1.95 1.9504999999999999 1.9510000000000001 1.9515 1.952 1.9524999999999999 1.9530000000000001 1.9535 1.954 1.9544999999999999 1.9550000000000001 1.9555 1.956 1.9564999999999999 1.9570000000000001 1.9575 1.958 1.9584999999999999 1.9590000000000001 1.9595 1.96 1.9604999999999999 1.9610000000000001 1.9615 1.962 1.9624999999999999 1.9630000000000001 1.9635 1.964 1.9644999999999999 1.9650000000000001 1.9655 1.966 1.9664999999999999 1.9670000000000001 1.9675 1.968 1.9684999999999999 1.9690000000000001 1.9695 1.97 1.970499999 9999999 1.9710000000000001 1.9715 1.972 1.9724999999999999 1.9730000000000001 1.9735 1.974 1.9744999999999999 1.9750000000000001 1.9755 1.976 1.9764999999999999 1.9770000000000001 1.9775 1.978 1.9784999999999999 1.9790000000000001 1.9795 1.98 1.9804999999999999 1.9810000000000001 1.9815 1.982 1.9824999999999999 1.9830000000000001 1.9835 1.984 1.9844999999999999 1.9850000000000001 1.9855 1.986 1.9864999999999999 1.9870000000000001 1.9875 1.988 1.9884999999999999 1.9890000000000001 1.9895 1.99 1.9904999999999999 1.9910000000000001 1.9915 1.992 1.99 24999999999999 1.9930000000000001 1.9935 1.994 1.9944999999999999 1.9950000000000001 1.9955000000000001 1.996 1.9964999999999999 1.9970000000000001 1.9975000000000001 1.998 1.9984999999999999 1.9990000000000001 1.9995000000000001 2 4.57 4.45 4.55 4.58 4.57 4.55 4.54 4.58 4.7699999999999996 4.99 5.47 5.53 5.66 5.76 5.91 5.9 5.77 5.87 5.92 6.02 6.26 6.11 6.24 6.07 6.2 6.05 6.27 6.23 5.87 5.72 5.69 5.66 5.58 5.3 4.91 4.45 4.2300000000000004 3.94 3.55 3.01 2.48 1.76 1.24 0.69 0.23 -0.32 -0.84 -1.56 -2.08 -2.56 -2.83 -3.26 -3.65 -4.43 -4.91 -5.7 -6.55 -7.27 -8.31 -8.93 -9.91 -10.78 -11.2 -11.33 -11.54 -12.1 -12.37 -12.61 -12.75 -12.97 -13.19 -13.64 -13.98 -14.22 -14.68 -15.07 -15.35 -15.45 -15.61 -16.07 -16.53 -17.07 -17.47 -17.739999999999998 -17.86 -18.079999999999998 -18.64 -18.86 -18.97 -19.18 -19.399999999999999 -19.850000000000001 -20.18 -20.3 -20.45 -20.84 -21.06 -21.34 -21.63 -21.91 -22.48 -22.71 -22.9 -23.39 -23.93 -24.31 -25.08 -25.83 -26.09 -26.34 -26.94 -27.29 -27.37 -27.8 -28.18 -28.14 -28.6 -29.28 -29.58 -29.9 -30.29 -30.75 -30.89 -30.8 -30.46 -30.36 -30.35 -30.32 -30.17 -30.13 -30.07 -29.78 -29.3 -28.89 -28.45 -28.22 -27.88 -27.76 -27.58 -26.98 -26.45 -25.82 -25.45 -24.86 -24.5 -24.23 -23.58 -22.99 -22.6 -22.24 -21.78 -21.47 -21.23 -20.68 -20.329999999999998 -19.72 -19.329999999999998 -19.04 -18.68 -17.73 -17.190000000000001 -16.77 -16.18 -15.53 -15.23 -14.85 -14.56 -13.96 -13.46 -12.85 -12.13 -11.69 -11.24 -10.53 -9.94 -9.56 -9.17 -8.57 -7.87 -7.51 -7.35 -6.92 -6.07 -5.58 -5.6 -5.07 -4.5 -4.1100000000000003 -3.69 -3.09 -2.7 -1.97 -1.27 -1.03 -0.83 -0.57999999999999996 0.13 0.84 1.0900000000000001 1.29 1.5 2.02 2.27 2.64 3.24 3.6 4.1399999999999997 4.32 4.51 5.03 5.31 5.62 5.59 5.71 5.86 6.21 6.39 6.7 7.16 7.44 7.44 7.3 7.38 7.41 7.48 7.74 8.01 7.79 7.84 8.33 8.44 8.32 8.41 8.44 8.48 8.58 8.5 8.6 8.6300000000000008 8.6199999999999992 8.59 8.57 8.5399999999999991 8.52 8.49 8.4700000000000006 8.44 8.42 8.39 8.3699999999999992 8.35 8.32 8.3000000000000007 8.27 8.18 7.97 7.83 7.59 7.32 6.8 6.65 6.27 5.95 5.36 5.01 4.46 3.81 3.08 2.2799999999999998 1.7 1.1599999999999999 1.2 1.06 1.27 1.17 0.63 0.39 0.21 -0.22 -0.49 -0.48 -0.71 -1.0900000000000001 -1.55 -1.77 -1.97 -2.0099999999999998 -2 -2.4300000000000002 -2.79 -2.62 -2.66 -3.01 -3.16 -3.21 -3.29 -3.48 -3.51 -3.42 -3.56 -3.63 -3.66 -3.67 -3.61 -3.34 -3.05 -3.17 -2.94 -2.83 -2.71 -2.37 -2.2599999999999998 -2.2400000000000002 -2.08 -1.61 -1.56 -1.42 -1.33 -1.1499999999999999 -0.97 -0.55000000000000004 -0.27 -0.18 -7.0000000000000007E-2 0.27 0.39 0.45 0.62 0.74 1.02 1.32 1.21 1.45 1.59 1.72 1.65 1.78 1.94 2.2999999999999998 2.41 2.42 2.46 2.56 2.4300000000000002 2.4300000000000002 2.57 2.58 2.5099999999999998 2.74 2.72 2.86 3.03 3.4 3.57 3.75 3.81 3.95 4.43 4.8899999999999997 5.05 5.25 5.86 6.34 6.81 7.11 7.66 7.91 8.18 8.5500000000000007 9.0299999999999994 9.36 9.6 10.09 10.23 10.67 11.14 11.36 11.68 12.17 12.53 12.78 12.86 13 13.41 13.7 13.79 13.87 14.17 14.58 14.7 14.74 14.92 15.47 15.72 15.98 16.149999999999999 16.12 16.37 16.84 17.18 17.45 18 18.239999999999998 18.46 18.649999999999999 19.09 19.54 20.100000000000001 20.59 20.75 20.96 21.58 22.06 22.54 22.87 23.49 23.86 24.02 24.36 24.98 25.72 26.11 26.28 26.6 27.14 27.67 28.02 28.71 29.33 29.73 30.01 30.27 30.83 31.15 31.63 32.14 32.840000000000003 33.36 33.880000000000003 34.28 34.74 35.44 35.950000000000003 36.47 36.81 37.090000000000003 37.729999999999997 38.29 38.950000000000003 39.340000000000003 39.94 40.32 40.99 41.55 42.21 42.61 43.26 43.69 43.99 44.28 45.03 45.79 46.21 46.81 47.17 47.65 47.68 48.21 48.7 49.19 49.53 50.11 50.36 50.59 50.75 51.13 51.7 51.86 52.23 52.54 53.05 53.08 53.14 53.45 53.89 54.06 54.15 54.28 54.18 54.15 54.16 54.19 54.2 54.07 53.53 52.82 52.43 52.17 51.64 51.42 51.23 51.13 50.97 50.93 50.93 50.85 50.62 50.76 50.53 50.37 50.07 49.67 49.49 49.23 48.84 48.29 48.1 47.57 47.3 47.36 47.26 47.18 47 46.84 46.49 46.33 46.15 46.01 45.78 45.85 45.44 45.24 45.07 45.02 44.93 44.58 44.36 44.02 43.91 43.8 43.4 42.99 42.51 42.14 41.74 41.21 41.04 40.56 40.28 39.79 39.270000000000003 38.86 38.44 38.200000000000003 37.72 37.159999999999997 36.659999999999997 36.35 35.71 35.19 34.93 34.479999999999997 34.01 33.71 33.119999999999997 32.72 32.340000000000003 31.77 31.12 30.81 30.26 29.43 28.52 27.64 26.78 25.63 24.76 23.82 22.74 21.76 20.81 19.760000000000002 18.420000000000002 17.13 15.84 14.36 12.42 9.01 3.57 -2.97 -9.0500000000000007 -13.49 -15 .98 -16.809999999999999 -17.3 -17.8 -18.760000000000002 -19.8 -20.97 -22.14 -23.13 -24.04 -24.81 -25.23 -25.61 -26.17 -26.81 -27.04 -27.2 -27.2 -27.1 -26.93 -26.94 -26.77 -26.66 -26.48 -26.06 -25.83 -25.56 -25.26 -24.6 -24.19 -24.04 -23.86 -23.37 -22.89 -22.34 -21.97 -21.76 -21.34 -20.68 -20.3 -19.8 -19.43 -19.13 -18.649999999999999 -18.649999999999999 -18.27 -17.86 -17.420000000000002 -16.86 -16.37 -15.79 -15.24 -14.57 -14.27 -14 -13.76 -13.26 -12.72 -12.04 -11.71 -11.26 -10.62 -10.37 -10.24 -9.99 -9.69 -9.08 -8.7799999999999994 -8.5299999999999994 -8.4 -8.2100000000000009 -7.74 -7.39 -7.26 -7.18 -7.03 -6.73 -6.79 -6.48 -6.27 -6.02 -5.88 -5.64 -5.04 -4.74 -4.47 -4.22 -3.74 -3.39 -3.25 -3.14 -2.89 -2.65 -2.16 -1.8 -1.61 -1.35 -1.1200000000000001 -0.7 -0.51 -0.38 -0.16 -0.05 0.02 0.21 0.68 1.05 1.23 1.42 1.41 1.6 1.84 2.2400000000000002 2.2799999999999998 1.93 1.73 1.88 1.99 2.0499999999999998 2.12 2.2799999999999998 2.57 2.38 2.3199999999999998 2.35 2.4 2.46 2.5099999999999998 2.56 2.63 2.79 3.07 2.91 2.96 3.22 3.04 2.99 3 3 2.94 3.11 3.21 3.27 3.32 3.37 3.42 3.46 3.46 3.4 3.55 3.61 3.54 3.64 3.56 3.57 3.68 3.9 3.94 3.77 3.64 3.78 3.84 3.77 3.88 3.8 3.8 3.82 3.75 3.44 3.36 3.39 3.44 3.5 3.55 3.59 3.59 3.49 3.48 3.18 3.41 3.54 3.49 3.16 3.03 2.93 3.04 2.97 2.96 3 3.05 3.09 3.09 3.02 3.16 3.1 2.72 2.81 2.5299999999999998 2.2999999999999998 2.25 2.09 1.53 1.08 0.59 0.11 -0.66 -1.49 -2.2200000000000002 -3.02 -3.8 -4.76 -5.49 -6.17 -6.95 -7.64 -8.31 -8.67 -9.3800000000000008 -10.130000000000001 -10.69 -11.58 -12.84 -14.3 -15.24 -16.18 -17.18 -17.93 -18.73 -19.86 -20.65 -21.34 -22.12 -22.85 -23.69 -24.47 -24.94 -25.41 -25.76 -26.16 -26.75 -27.09 -27.7 -28.14 -28.57 -28.85 -29.37 -29.57 -29.74 -29.82 -29.97 -29.98 -29.95 -29.89 -29.82 -29.77 -30.08 -29.84 -29.65 -29.47 -29.54 -29.49 -29.28 -29.18 -29.12 -29.09 -29.05 -29.01 -28.96 -28.86 -28.71 -28.78 -28.71 -28.38 -27.93 -27.87 -28.04 -27.71 -27.45 -27.44 -27.26 -27.06 -26.76 -26.84 -26.54 -26.33 -26.03 -25.75 -25.62 -25.45 -25.06 -24.9 -24.83 -24.74 -24.53 -24.41 -24.23 -23.77 -23.43 -23.32 -23.27 -23.18 -22.95 -22.72 -22.32 -22.15 -22.03 -21.83 -21.79 -21.87 -21.78 -21.81 -21.65 -21.57 -21.59 -21.74 -21.77 -21.75 -21.71 -21.68 -21.65 -21.61 -21.57 -21.56 -21.66 -22 -22.15 -22.25 -22.1 -22.01 -21.98 -22 -22.1 -22.02 -22.11 -22.07 -21.87 -21.78 -21.72 -21.57 -21.18 -21.02 -20.97 -20.88 -20.68 -20.58 -20.48 -20.27 -20.16 -20 -19.64 -19.59 -19.77 -19.45 -19.14 -19.02 -18.989999999999998 -18.98 -19.02 -19.16 -19.14 -18.95 -18.86 -18.8 -18.649999999999999 -18.27 -18.12 -18.079999999999998 -18.05 -17.96 -17.760000000000002 -17.66 -17.579999999999998 -17.43 -17.45 -17.18 -16.73 -16.489999999999998 -16.14 -15.7 -15.53 -15.43 -15.32 -15.54 -15.93 -16.059999999999999 -16.12 -16.27 -16.309999999999999 -16.32 -16.420000000000002 -16.739999999999998 -16.739999999999998 -16.5 -16.71 -16.79 -16.8 -16.84 -17.010000000000002 -17.11 -17.3 -17.47 -17.91 -18.32 -18.739999999999998 -18.86 -18.93 -19.149 999999999999 -19.37 -19.440000000000001 -19.55 -19.899999999999999 -20.079999999999998 -20.32 -20.55 -20.74 -21.17 -21.58 -22.02 -22.27 -22.76 -23.32 -23.81 -24.44 -24.81 -25.37 -25.59 -25.8 -25.97 -26.32 -26.43 -26.51 -26.73 -26.97 -27.16 -27.51 -27.63 -27.7 -27.85 -27.9 -27.92 -28.09 -28.62 -28.8 -28.88 -29.04 -29.1 -29.22 -29.57 -29.69 -29.76 -29.93 -29.99 -30.04 -30.14 -30.01 -29.88 -29.66 -29.46 -29.05 -28.73 -28.16 -27.97 -27.92 -27.77 -27.27 -26.77 -26.55 -26.25 -25.82 -25.26 -25.14 -24.74 -23.94 -23.54 -23.06 -22.61 -22.08 -21.57 -20.92 -20.52 -19.86 -19.29 -18.59 -18.12 -17.66 -17.02 -16.61 -15.81 -14.89 -14.12 -13.84 -13.54 -13.09 -12.33 -11.65 -11.11 -10.75 -10 -9.24 -8.73 -7.78 -6.93 -6.51 -6.29 -5.81 -5.12 -3.94 -3.4 -2.85 -2.2799999999999998 -1.76 -1.06 -0.54 0.06 0.71 1.41 2.15 2.58 2.93 3.73 4.32 4.9800000000000004 5.74 6.33 7.04 7.55 8.09 8.6 9.3000000000000007 9.82 10.36 10.88 11.63 12.2 12.51 13.08 13.76 14.11 14.64 15.2 15.66 16.2 16.68 17.2 17.260000000000002 17.899999999999999 18.61 18.84 18.93 19.13 19.32 19.7 19.91 20.18 20.420000000000002 20.5 20.51 20.53 20.65 20.91 20.81 21.07 21.18 21.19 21.07 20.72 20.6 20.58 20.53 20.350000000000001 20.21 19.899999999999999 19.489999999999998 19.36 19.350000000000001 19.38 19.489999999999998 19.670000000000002 19.29 19.3 19.690000000000001 19.53 19.440000000000001 19.440000000000001 19.55 19.82 19.72 19.98 20.100000000000001 20.18 20.3 20.2 20.22 20.399999999999999 20.47 20.49 20.5 20.5 20.51 20.51 20.46 20.28 20.239999999999998 20.29 20.43 20.45 20.77 20.89 20.93 21.07 21.5 21.84 22.04 22.31 22.2 22.46 22.58 22.61 22.68 22.87 22.95 23.02 23.16 23.14 23.38 23.68 23.46 23.36 23.35 23.36 23.37 23.4 23.52 23.78 23.67 23.82 23.7 23.97 24.09 24.11 23.99 23.63 23.54 23.64 23.89 23.66 23.51 23.38 23.44 23.33 23.29 23.3 23.31 23.31 23.27 23.1 23.03 22.91 22.55 22.39 22.26 22.32 22.08 21.67 21.48 21.23 20.99 20.81 20.45 20.28 20.09 19.96 19.66 19.25 19.05 18.739999999999998 18.25 17.760000000000002 17.13 16.760000000000002 16.2 15.89 15.37 14.71 13.97 13.52 13.07 12.4 11.91 11.47 11.3 11.1 10.93 10.58 10.46 10.4 10.32 10.56 10.89 10.81 11.06 11.07 10.87 11.12 11.24 11.28 11.3 11.32 11.31 11.2 10.88 10.87 11.12 11.02 11.18 11.07 11.34 11.47 11.57 11.79 11.98 12.23 12.01 11.94 12.06 12.45 12.66 12.87 12.96 13.07 13.37 13.7 13.63 13.96 14.26 14.37 14.47 14.8 15.25 15.46 15.68 15.77 15.92 16.309999999999999 16.52 16.739999999999998 16.89 17.09 17.190000000000001 17.32 17.59 17.510000000000002 17.84 18.09 18.09 18.34 18.670000000000002 18.59 18.84 18.86 18.66 18.920000000000002 19.04 19.09 19.170000000000002 19.38 19.53 19.73 19.760000000000002 19.670000000000002 19.809999999999999 19.87 19.850000000000001 19.75 19.82 19.73 19.75 19.88 19.78 19.75 19.760000000000002 19.79 19.8 19.77 19.670000000000002 19.75 19.68 19.64 19.2 19.14 19.37 19.190000000000001 19.22 19.46 19.21 18.940000000000001 18.420000000000002 18.36 18.579999999999998 18.329999999999998 18.11 18.11 17.829999999999998 17.72 17.57 17.07 16.53 16.579999999999998 16.28 15.93 15.5 14.83 14.34 13.86 13.54 13.22 12.38 11.72 11.26 10.78 10.42 10.06 9.6300000000000008 9.34 8.8000000000000007 8.5399999999999991 8.11 7.27 6.64 5.83 5.03 4.45 3.71 3.11 2.74 2.52 2.46 2.34 1.94 1.67 1.6 1.54 1.25 0.8 0.54 0.48 0.02 -0.14000000000000001 -0.21 -0.36 -0.48 -0.78 -1.26 -1.66 -1.98 -1.93 -2.38 -2.65 -2.62 -2.85 -3.24 -3.41 -3.53 -3.44 -3.57 -3.79 -4.32 -4.47 -4.43 -4.34 -4.5599999999999996 -4.54 -4.6500000000000004 -4.67 -4.68 -4.78 -5.12 -5.23 -5.3 -5.51 -5.73 -5.8 -5.92 -6.23 -6.22 -5.99 -6.28 -6.67 -7.1 -7.28 -7.46 -7.55 -7.74 -7.9 -8.26 -8.42 -8.6199999999999992 -8.7799999999999994 -9.1199999999999992 -9.23 -9.3000000000000007 -9.5399999999999991 -9.86 -10.17 -10.11 -10.54 -10.82 -11.25 -11.54 -11.68 -11.98 -12.44 -12.74 -12.88 -13.17 -13.65 -14.08 -14.56 -14.88 -15.2 -16.05 -16.78 -17.489999999999998 -18.37 -19.36 -20.49 -21.64 -23.17 -25.07 -27.21 -29.22 -30.64 -31.65 -32.380000000000003 -32.630000000000003 -32.869999999999997 -33.1 -33.29 -33.71 -33.99 -34.06 -34.049999999999997 -34.03 -34 -33.92 -33.71 -33.5 -33.11 -32.96 -32.869999999999997 -32.68 -32.520000000000003 -32.19 -31.66 -31.13 -30.42 -29.89 -29.35 -28.89 -28.29 -27.65 -27.07 -26.65 -26.25 -25.73 -25.27 -24.75 -24.34 -23.94 -23.42 -22.96 -22.43 -22.03 -21.62 -21.1 -20.65 -20.190000000000001 -19.98 -19.71 -19.43 -19.16 -18.59 -18.329999999999998 -18.09 -17.899999999999999 -17.510000000000002 -17.3 -16.96 -16.52 -16.309999999999999 -16.09 -15.97 -15.89 -16.12 -16.04 -15.92 -15.72 -15.62 -15.5 -15.26 -15.46 -15.43 -15.1 -15.07 -15.28 -15.03 -14.92 -14.89 -14.87 -14.81 -14.67 -14.73 -14.66 -14.76 -14.74 -14.56 -14.5 -14.53 -14.65 -14.59 -14.71 -14.75 -14.77 -14.87 -15.11 -14.98 -15.11 -14.98 -15.29 -15.57 -15.65 -15.66 -15.7 -15.82 -15.75 -15.87 -15.93 -16.059999999999999 -16.420000000000002 -16.53 -16.55 -16.600000000000001 -16.79 -16.98 -17.350000000000001 -17.53 -17.73 -17.84 -17.97 -17.899999999999999 -18.04 -18.21 -18.579999999999998 -18.71 -18.78 -18.96 -19.100000000000001 -19.41 -19.82 -19.96 -20.03 -20.22 -20.399999999999999 -20.86 -21.36 -22.04 -22.42 -22.63 -23.08 -23.59 -24.4 -25.22 -25.82 -26.7 -27.73 -28.64 -30.14 -31.1 -31.9 -32.770000000000003 -33.159999999999997 -33.54 -33.6 -33.479999999999997 -33.520000000000003 -33.340000000000003 -33.159999999999997 -33.14 -32.75 -32.31 -31.73 -31.11 -30.58 -30.24 -29.62 -29.18 -28.76 -28.14 -27.4 -26.93 -26.53 -26.04 -25.65 -25.26 -24.75 -24.24 -23.54 -23.03 -22.51 -22.07 -21.54 -21.05 -20.43 -20.14 -19.75 -19.07 -18.57 -18.05 -17.66 -17.190000000000001 -16.39 -15.63 -15.24 -14.65 -14.28 -13.62 -13.01 -12.17 -11.73 -11.16 -10.89 -10.5 -9.82 -9.26 -8.6 -8.16 -7.39 -6.94 -6.25 -5.69 -5.4 -4.90 00000000000004 -4.34 -3.89 -3.39 -3 -2.5499999999999998 -1.85 -1.28 -0.52 0.1 0.51 0.89 1.4 1.9 2.6 3.1 3.63 4.13 4.83 5.34 5.9 6.41 6.75 7.44 8.07 8.58 9.2200000000000006 9.6 10.23 10.67 11.08 11.62 12.13 12.47 13.16 13.79 14.31 15.01 15.5 15.95 16.22 16.72 17.28 17.739999999999998 18.3 18.809999999999999 19.149999999999999 19.760000000000002 20.14 20.41 20.98 21.35 21.92 22.16 22.38 22.64 23.31 23.87 24.09 24.34 24.59 24.79 25.2 25.45 25.43 25.67 26.08 26.21 26.23 26.23 26.28 26.39 26.28 26.29 26.45 26.5 26.46 26.33 26.38 26.25 26.18 26.04 25.68 25.55 25.53 25.45 25.14 24.71 24.57 24.48 24.24 23.98 23.78 23.4 23.21 23 22.8 22.37 22.12 22.15 22.02 21.9 1 21.78 21.83 21.7 21.66 21.7 21.82 21.68 21.52 21.25 21.36 21.1 20.99 20.99 21.11 21.48 21.6 21.62 21.61 21.61 21.62 21.67 21.79 21.68 21.66 21.65 21.3 21.49 21.59 21.58 21.39 20.85 20.64 20.49 20.12 19.93 19.68 19.420000000000002 19.190000000000001 18.57 17.64 17.059999999999999 16.52 16 15.18 14.32 13.71 13.23 12.17 11.3 10.51 9.98 9.35 8.59 7.99 7.18 6.42 6.08 5.7 5.58 5.57 5.57 5.58 5.65 5.83 5.89 5.9 5.9 5.9 5.9 5.96 6.14 6.22 6.37 6.79 7.09 7.19 7.33 7.68 7.82 7.89 8.08 8.23 8.5299999999999994 8.82 8.59 8.5 8.6 8.98 9.17 9.3699999999999992 9.43 9.44 9.43 9.3699999999999992 9.27 9.5 9.81 9.6999999999999993 9.83 9.56 9.4 9.25 9.32 9.26 9.39 9.3800000000000008 9.1999999999999993 9 8.57 8.32 8.3699999999999992 8.24 8.1 7.73 7.13 6.91 6.76 6.4 6.22 6.09 6.21 6.27 6.28 6.28 6.3 6.4 6.66 6.56 6.88 7.17 7.24 7.22 7.21 7.56 7.37 7.22 7.09 7.2 7.18 6.91 6.59 6.68 6.37 6.08 5.95 5.8 5.74 5.25 5.01 4.8 4.66 4.26 3.53 2.98 2.83 2.82 2.83 2.74 2.38 1.78 1.57 1.46 1.19 0.88 0.97 0.66 0.37 0.22 0.04 -0.01 0.04 0.16 0.06 0 -0.16 -0.8 -1.93 -3.19 -4.34 -5.13 -5.77 -6.27 -6.46 -6.66 -6.85 -7.28 -7.66 -8.0500000000000007 -8.56 -9 -9.5299999999999994 -10.029999999999999 -10.65 -10.9 -11.13 -11.37 -11.94 -12.32 -12.89 -13.13 -13.36 -13.61 -14.24 -1 4.73 -15.18 -15.38 -15.65 -16.02 -16.53 -16.97 -17.48 -17.87 -18.260000000000002 -18.690000000000001 -18.89 -19.07 -19.079999999999998 -18.97 -19.07 -19.04 -18.77 -18.45 -18.54 -18.29 -18.190000000000001 -18.16 -18.09 -17.86 -17.670000000000002 -17.71 -17.59 -17.54 -17.510000000000002 -17.38 -17.02 -16.89 -16.87 -16.87 -16.87 -16.87 -16.89 -17.02 -17.440000000000001 -17.760000000000002 -17.899999999999999 -18.100000000000001 -18.29 -18.66 -18.850000000000001 -19.059999999999999 -19.18 -19.37 -19.43 -19.43 -19.45 -19.559999999999999 -19.79 -19.55 -19.47 -19.55 -19.8 -19.7 -19.95 -20.05 -20.079999999999998 -20.13 -20.260000000000002 -20.2 -20.329999999999998 -20.399999999999999 -20.52 -20.75 -20.53 -20.55 -20.89 -21.02 -21.04 -21.04 -21.04 -21.11 -21.29 -21.36 -21.36 -21.28 -20.97 -20.55 -20.41 -20.309999999999999 -20.010000000000002 -19.59 -19.38 -19.13 -18.87 -18.66 -18.170000000000002 -17.670000000000002 -17.39999999999 9999 -16.940000000000001 -16.510000000000002 -16.010000000000002 -15.69 -15.53 -15.22 -14.74 -14.41 -14.2 -13.76 -13.39 -13.14 -13.06 -12.92 -12.5 -12.18 -11.97 -11.6 -11.42 -11.27 -11.28 -11.03 -11.02 -10.78 -10.47 -10.5 -10.07 -9.9 -9.81 -9.64 -9.58 -9.5500000000000007 -9.43 -9.07 -8.9499999999999993 -8.93 -8.93 -8.94 -8.94 -8.94 -8.94 -8.94 -8.9499999999999993 -8.9499999999999993 -8.9499999999999993 -8.9499999999999993 -8.9499999999999993 -8.9499999999999993 -8.9 -8.7799999999999994 -8.81 -8.5500000000000007 -8.09 -7.83 -7.87 -7.74 -7.63 -7.42 -7.24 -6.87 -6.66 -6.34 -5.92 -5.79 -5.68 -5.32 -4.72 -4.51 -4.43 -4.24 -4.05 -3.62 -3.31 -3.15 -2.83 -2.35 -2.0299999999999998 -1.87 -1.56 -1.1399999999999999 -0.92 -0.59 -0.1 0.27 0.54 0.73 1.1299999999999999 1.44 2 2.25 2.48 2.72 3.27 3.54 3.88 4.37 4.74 5.0199999999999996 5.22 5.65 5.95 6.03 6.12 6.43 6.94 7.43 8 8.1 8.43 9.02 9.2200000000000006 9.34 9.6999999999999993 10.29 10.52 10.75 11.33 11.65 11.69 12.01 12.23 12.51 12.46 12.91 13.21 13.6 13.72 13.74 13.74 13.81 14.05 14.23 14.13 14.13 14.32 14.52 14.95 15.28 15.49 15.86 15.99 16.07 16.260000000000002 16.37 16.510000000000002 16.47 16.73 17.21 17.55 17.760000000000002 18.14 18.32 18.52 18.579999999999998 18.600000000000001 18.66 18.86 19.059999999999999 19.43 19.57 19.649999999999999 19.829999999999998 19.89 19.91 19.98 20.18 20.36 20.63 20.51 20.63 20.38 20.29 20.41 20.78 20.89 20.81 20.56 20.67 20.440000000000001 20.440000000000001 20.66 20.45 20.47 20.83 21.02 21.25 21.44 21.81 21.96 22.12 22.59 22.98 22.96 23.42 23.78 24.38 24.76 25.34 25.62 26.02 26.63 26.91 27.26 27.75 28.08 28.22 28.43 28.64 29.06 29.33 29.44 30 30.44 30.86 31.38 31.81 32.15 32.119999999999997 32.56 32.799999999999997 33.04 33.299999999999997 33.86 34.07 34.24 34.6 34.74 34.840000000000003 35.08 35.270000000000003 35.25 35.51 35.950000000000003 36.15 36.369999999999997 36.5 36.700000000000003 36.79 36.93 37.31 37.53 37.85 38.15 37.9500 00000000003 37.979999999999997 38.33 38.47 38.57 38.76 38.840000000000003 38.85 38.799999999999997 38.6 38.369999999999997 37.840000000000003 37.71 37.68 37.1 36.51 35.89 34.49 30.05 20.99 8.56 -3.15 -10.89 -13.55 -12.48 -10.31 -8.4 -7.69 -7.66 -8.0399999999999991 -8.7100000000000009 -9.01 -8.83 -8.44 -7.92 -7.59 -7.5 -7.46 -7.26 -6.7 -6.5 -6.46 -6.42 -6.24 -5.81 -5.97 -6.05 -6.06 -6.05 -6.03 -6.02 -6 -5.98 -5.98 -6.03 -6.19 -6.23 -6.18 -6.11 -6.39 -6.49 -6.49 -6.49 -6.6 -6.95 -7.06 -7.07 -7.05 -7.03 -7.02 -6.98 -6.86 -6.59 -6.71 -6.61 -6.84 -6.45 -6.22 -6.04 -6.07 -5.88 -5.69 -5.73 -5.57 -5.37 -4.9000000000000004 -4.46 -3.99 -3.75 -3.38 -2.87 -2.89 -2.5299999999999998 -2.11 -1.65 -1.44 -1.2 -0.94 -0.36 -0.03 0.39 0.66 1.1100000000000001 1.45 1.67 2.06 2.27 2.56 2.92 3.26 3.18 3.53 3.95 4.41 4.57 4.66 4.8600000000000003 5 5.2 5.3 5.45 5.83 6.03 6.25 6.34 6.5 6.85 6.87 6.54 6.45 6.54 6.74 6.4 6.36 6.24 6.24 6.25 5.78 5.54 5.29 5.05 4.8600000000000003 4.43 4.0199999999999996 3.58 3.32 2.83 2.38 2.35 2.54 2.2000000000000002 2.17 2.02 1.85 1.5 1.39 1.38 1.35 1.24 1.3 1.2 1.23 1.41 1.43 1.27 1.22 1.22 1.18 1.07 1.1499999999999999 1.1000000000000001 1.24 1.23 0.94 0.47 0.17 0.03 -0.31 -0.96 -1.8 -2.14 -2.56 -3.33 -4.1399999999999997 -4.7300000000000004 -5.48 -6.08 -6.46 -6.72 -6.96 -7.49 -7.75 -8.1300000000000008 -8.74 -9.11 -9.75 -10.3 -11.07 -11.87 -12.82 -13.52 -14.54 -15.53 -16.48 -17.36 -18.07 -18.760000000000002 -19.489999999999998 -19.95 -20.38 -21 -21.38 -21.99 -22.37 -22.64 -23.16 -23.29 -23.18 -23.2 -22.93 -22.49 -22.22 -21.81 -21.55 -21.15 -20.94 -20.61 -20.170000000000002 -19.96 -19.66 -19.22 -18.579999999999998 -18.239999999999998 -17.78 -17.38 -16.989999999999998 -16.55 -16.399999999999999 -16.309999999999999 -16.11 -15.9 -15.46 -15.13 -14.99 -14.85 -14.9 -14.76 -14.68 -14.56 -14.3 -14.39 -14.13 -14.01 -13.98 -14 -14.1 -14.33 -14.07 -13.9 -13.77 -13.98 -14.28 -14.17 -14.43 -14.59 -14.83 -15.03 -15.1 -15.58 -15.76 -15.83 -15.94 -15.89 -16.13 -16.55 -16.739999999999998 -16.940000000000001 -16.989999999999998 -16.989999999999998 -16.98 -16.97 -16.96 -16.96 -16.940000000000001 -16.87 -16.66 -16.489999999999998 -16.309999999999999 -16.72 -16.87 -16.850000000000001 -16.71 -16.760000000000002 -16.63 -16.55 -16.43 -16.16 -16.29 -16.16 -16.39 -16.39 -16.149999999999999 -16.239999999999998 -15.93 -15.69 -15.73 -15.6 -15.52 -15.38 -15.02 -14.89 -14.87 -14.85 -14.73 -14.38 -14.28 -14.25 -13.77 -13.59 -13.54 -13.49 -13.37 -13.48 -13.56 -13.67 -13.9 -13.67 -13.56 -13.53 -13.53 -13.52 -13.46 -13.27 -13.21 -13.2 -13.2 -13.19 -13.13 -12.93 -12.74 -12.36 -12.18 -12.04 -12.07 -11.82 -11.41 -11.27 -11.25 -11.25 -11.19 -11.06 -11.13 -11.06 -11.21 -11.37 -11.61 -11.4 -11.48 -12.02 -12.31 -12.59 -12.48 -12.74 -12.9 -13.11 -13.23 -13.44 -13.64 -14.06 -14.32 -14.34 -14.66 -14.91 -15.35 -15.6 -15.56 -15.7 -15.87 -16.25 -16.45 -16.73 -17.100000000000001 -17.54 -17.73 -17.95 -18.13 -18.510000000000002 -18.71 -18.96 -19.22 -19.43 -19.86 -20.18 -20.399999999999999 -20.83 -21.15 -21.31 -21.61 -21.92 -21.82 -22.09 -22.26 -22.46 -22.53 -22.53 -22.47 -22.29 -22.21 -22.1 -21.85 -21.96 -21.74 -21.75 -21.97 -21.72 -21.49 -21.13 -21.04 -21.03 -20.55 -20.29 -19.95 -19.489999999999998 -19.23 -19.2 -18.77 -18.21 -17.7 -17.079999999999998 -16.809999999999999 -16.48 -15.99 -15.54 -14.98 -14.47 -14.21 -13.77 -13.39 -12.98 -12.39 -11.84 -11.86 -11.46 -10.87 -10.31 -9.98 -9.77 -9.26 -8.66 -8.15 -7.96 -7.76 -7.57 -7.14 -6.76 -6.38 -5.95 -5.76 -5.56 -5.43 -5.13 -4.7 -4.5 -4.17 -3.7 -3.36 -3.09 -2.4900000000000002 -2.13 -2.02 -1.84 -1.31 -1.1100000000000001 -0.9 -0.34 0.01 0.47 0.47 0.93 1.29 1.93 2.35 2.61 2.69 2.88 3.43 3.74 4.1900000000000004 4.49 4.6500000000000004 4.95 5.36 5.5 5.59 5.89 6.31 6.5 6.69 6.84 7.21 7.8 8.01 8.17 8.58 8.8800000000000008 9.0299999999999994 9.35 9.84 10.199999999999999 10.47 10.67 11.11 11.54 12.05 12.44 12.82 13.25 13.43 13.64 13.83 14.27 14.62 14.82 14.76 14.9 15.08 15.51 15.81 15.95 16.149999999999999 16.350000000000001 16.760000000000002 17 16.899999999999999 16.920000000000002 17.21 17.63 17.760000000000002 17.78 17.84 18.02 18.13 18.27 18.2 18.32 18.39 18.52 18.88 19.010000000000002 19.03 19 18.87 18.52 18.5 18.72 18.48 18.309999999999999 18.100000000000001 17.97 17.77 17.57 17.12 16.7 16.239999999999998 15.95 15.38 14.64 14.12 13.59 13.06 12.25 11.44 10.9 10.3 9.6300000000000008 8.93 8.52 7.75 6.88 6.1 5.27 4.5599999999999996 3.85 3.03 2.3199999999999998 1.68 1.04 0.39 -0.32 -1.1200000000000001 -1.7 -2.0699999999999998 -2.81 -3.59 -4 -4.24 -4.79 -5.46 -5.73 -5.94 -6.06 -6.24 -6.32 -6.46 -6.8 -6.8 -6.45 -6.31 -6.22 -5.99 -5.8 -5.82 -5.57 -5.15 -5.0199999999999996 -4.99 -4.92 -4.74 -4.68 -4.67 -4.66 -4.5199999999999996 -4.09 -3.7 -3.3 -2.8 -2.4700000000000002 -2.2599999999999998 -1.83 -1.5 -1.22 -0.59 -0.08 0.43 0.78 1.05 1.61 1.86 2.0699999999999998 2.2200000000000002 2.5 4 3.03 3.37 3.65 4.21 4.46 4.6900000000000004 4.88 5.26 5.45 5.68 5.87 6.24 6.39 6.54 6.92 7.18 7.57 7.76 7.98 8.19 8.6199999999999992 8.93 9.0299999999999994 9.1300000000000008 9.41 9.76 9.7899999999999991 10.41 10.65 10.71 10.87 11.4 11.97 11.95 12.23 12.42 12.68 12.93 13.03 13.18 13.61 13.95 14.17 14.55 14.69 14.78 14.97 15.04 15.07 15.14 15.35 15.55 15.94 16.14 16.36 16.48 16.649999999999999 16.73 17.23 17.43 17.47 17.54 17.75 17.96 18.34 18.489999999999998 18.579999999999998 18.71 18.68 18.88 19.149999999999999 19.36 19.75 19.89 19.989999999999998 20.21 20.47 21.04 21.26 21.36 21.55 21.64 21.8 22.24 22.57 22.68 22.83 23.22 23.43 23.64 23.72 23.76 23.83 23.98 23.93 24.02 23.91 23.88 23.89 23.9 23.87 23.69 23.52 23.16 23.01 22.89 22.95 22.65 22.02 21.64 21.37 20.71 20.04 19.43 18.95 18.739999999999998 18.38 17.72 17.239999999999998 16.809999999999999 16.7 16.66 16.559999999999999 16.649999999999999 16.55 16.510000000000002 16.46 16.32 16.329999999999998 16.47 16.38 16.36 16.440000000000001 16.649999999999999 16.739999999999998 16.78 16.72 16.440000000000001 16.04 15.93 15.94 15.98 16 15.97 15.82 15.77 15.65 15.26 14.98 14.87 14.75 14.73 14.4 14.61 14.72 14.67 14.46 14.71 14.74 14.56 14.82 14.96 15.01 15.05 15.14 15.36 15.45 15.49 15.52 15.56 15.66 15.87 15.96 16.03 16.190000000000001 16.579999999999998 16.739999999999998 16.8 16.89 17.12 17.350000000000001 17.75 17.91 17.96 18 18.11 18.37 18.59 18.55 18.7 19.13 19.02 19.09 19.53 19.88 20.059999999999999 20.29 20.399999999999999 20.56 20.84 20.75 20.94 20.92 21.39 21.6 21.66 21.7 21.75 21.9 22.19 22.12 22.42 22.56 22.62 22.66 22.7 22.75 22.79 22.8 22.66 22.23 22.26 22.25 22 21.62 21.46 21.3 21.2 20.93 20.55 20.46 20.43 20.27 20.059999999999999 19.47 18.96 18.260000000000002 17.61 16.59 16.05 15.68 15.24 14.97 14.88 14.72 14.58 14.25 14.09 13.82 13.43 13.22 12.86 12.6 12.07 11.8 11.46 11.31 11.1 10.89 10.74 10.35 10.1 10.050000000000001 9.9600000000000009 9.64 9.51 9.43 9.6 9.69 9.69 9.5500000000000007 9.5500000000000007 9.64 9.81 9.75 9.74 9.7100000000000009 9.56 9.42 9.1 9.02 8.99 8.86 8.84 8.82 8.69 8.68 8.73 8.76 8.7100000000000009 8.5 8.66 8.4600000000000009 8.39 8.39 8.43 8.85 8.85 9.17 9.33 9.4600000000000009 9.6199999999999992 9.5500000000000007 9.56 9.66 9.9 10.01 10.09 10.19 10.35 10.23 10.050000000000001 10.01 9.93 9.61 9.48 9.34 9.31 9.23 8.93 8.84 8.76 8.43 8.24 7.9 7.77 7.61 7.5 7.29 7.46 7.26 7.2 7.18 7.04 6.98 6.85 6.82 6.73 6.37 6.12 6.07 5.92 5.44 5.3 5.27 5.13 5 4.68 4.54 4.33 4.1500000000000004 4.12 4.04 3.73 3.6 3.44 3.31 3 2.86 2.66 2.46 2.31 1.92 1.53 1.01 0.45 -0.04 -0.37 -1.05 -1.26 -1.44 -1.98 -2.2999999999999998 -2.39 -2.5499999999999998 -2.73 -3.17 -3.19 -3.26 -3.19 -2.98 -2.91 -2.94 -2.66 -2.29 -2.36 -2.23 -2.63 -2.88 -3.21 -3.28 -3.24 -3.18 -3.13 -3.06 -2.87 -2.37 -1.88 -1.37 -1.1100000000000001 -0.78 -0.36 0.11 0.2 0.1 0.56000000000000005 0.78 0.88 1.01 1.37 1.85 2.06 2.1800000000000002 2.36 2.35 2.48 2.4700000000000002 2.57 2.39 2.13 2.31 2.2400000000000002 2.56 2.78 2.98 2.98 3.16 3.27 3.33 3.39 3.44 3.5 3.56 3.61 3.6 3.48 3.46 3.37 3 2.74 2.66 2.5099999999999998 2.38 2 1.67 1.34 0.88 0.4 -0.36 -1.1200000000000001 -1.59 -2.04 -2.38 -2.79 -3.47 -4.0599999999999996 -4.53 -5.18 -5.69 -6.35 -6.85 -7.45 -7.87 -8.77 -9.6999999999999993 -10.48 -10.9 -11.23 -11.62 -11.82 -12.21 -12.54 -12.9 -13.46 -14.1 -14.37 -14.72 -14.92 -15.29 -15.51 -15.54 -15.99 -16.23 -16.5 -16.47 -16.690000000000001 -17.12 -17.440000000000001 -17.649999999999999 -17.68 -17.77 -18.14 -18.41 -18.54 -18.75 -18.59 -18.8 -18.91 -19.059999999999999 -19.07 -19.03 -19.04 -19.16 -19.2 -19.34 -19.78 -19.79 -19.91 -20.03 -20.36 -20.49 -20.58 -20.48 -20.55 -20.55 -20.51 -20.47 -20.48 -20.61 -20.62 -20.6 -20.68 -20.97 -20.94 -20.68 -20.92 -21.1 -21.02 -21.09 -21.09 -21.07 -21.16 -21.53 -21.79 -21.83 -21.87 -22.11 -22.38 -22.23 -22.43 -22.5 -22.6 -22.93 -23.13 -23.49 -23.74 -24.14 -24. 05 -24.27 -24.39 -24.55 -24.62 -24.78 -24.93 -25.33 -25.73 -26.19 -26.52 -26.75 -26.92 -27.44 -28.12 -28.47 -28.61 -28.94 -29.49 -29.64 -29.72 -30.03 -30.62 -30.95 -31.43 -31.51 -31.75 -31.83 -32.29 -32.49 -32.65 -32.69 -32.78 -33.1 -33.18 -33.159999999999997 -33.119999999999997 -33.14 -33.229999999999997 -33.11 -33 -32.47 -32.25 -32.18 -32.15 -32.11 -31.99 -31.64 -31.11 -30.69 -30.37 -30.13 -29.67 -29.32 -29.07 -28.57 -28.03 -27.31 -26.89 -26.69 -26.32 -25.67 -24.95 -24.64 -24.34 -24.05 -23.81 -23.33 -22.87 -22.37 -22.06 -21.55 -21.11 -20.98 -20.14 -19.75 -19.489999999999998 -19.39 -19.27 -18.940000000000001 -18.47 -18.23 -17.940000000000001 -17.649999999999999 -17.41 -16.93 -16.48 -16.100000000000001 -16.12 -15.72 -15.69 -15.63 -15.42 -15.28 -15.09 -14.99 -14.47 -14.17 -13.8 -13.35 -13.18 -13.07 -12.85 -12.68 -12.35 -12.01 -12.07 -11.71 -11.26 -10.79 -10.62 -10.57 -10.47 -10.199999999999999 -9.93 -9.81 -9.64 -9.25 -9.1 -9.0399999999999991 -8.9499999999999993 -8.74 -8.58 -8.36 -8.27 -8.2100000000000009 -8.02 -7.61 -7.75 -7.4 -7.34 -7.14 -6.93 -6.53 -6.3 -6.09 -6.06 -6.21 -6.24 -6.16 -5.95 -5.85 -5.81 -5.78 -5.77 -5.8 -5.95 -5.99 -5.97 -5.93 -5.85 -5.7 -5.79 -5.82 -5.8 -5.78 -5.74 -5.65 -5.43 -5.28 -5.0599999999999996 -4.9800000000000004 -4.9400000000000004 -4.9000000000000004 -4.76 -4.5 -4.6900000000000004 -4.67 -4.41 -4.51 -4.34 -4.4400000000000004 -4.16 -4.03 -3.98 -3.95 -3.86 -3.66 -3.57 -3.53 -3.5 -3.48 -3.46 -3.5 -3.66 -3.69 -3.61 -3.41 -3.37 -3.46 -3.38 -3.48 -3.53 -3.62 -3.85 -3.71 -3.94 -4 -3.89 -3.63 -3.83 -3.92 -3.91 -3.89 -3.86 -3.84 -3.88 -4.03 -4.01 -3.81 -3.72 -3.69 -3.66 -3.62 -3.5 -3.29 -3.62 -3.58 -3.53 -3.5 -3.47 -3.43 -3.27 -2.91 -2.87 -3.06 -2.8 -2.61 -2.39 -2.2799999999999998 -2.12 -1.73 -1.52 -1.29 -1.1399999999999999 -0.93 -0.84 -0.82 -0.8 -0.75 -0.53 0.02 0.18 0.12 0.27 0.46 0.8 0.84 1.06 1.33 1.56 1.95 2.1 2.14 2.23 2.44 2.59 2.8 2.88 2.93 3.08 3.47 3.62 3.67 3.67 3.57 3.23 3.12 3.06 2.9 2.81 2.7 2.78 2.69 2.65 2.5299999999999998 2.12 1.77 1.47 1.24 1.1100000000000001 0.76 0.18 -7.0000000000000007E-2 -0.38 -0.87 -1.34 -1.94 -2.2000000000000002 -2.57 -3.16 -3.46 -3.89 -4.17 -4.28 -4.46 -4.62 -4.97 -5.07 -5.0599999999999996 -5.03 -5 -4.9800000000000004 -4.9400000000000004 -4.79 -4.3899999999999997 -4.18 -3.95 -3.86 -3.76 -3.56 -3.46 -3.29 -2.85 -2.56 -2.4300000000000002 -1.86 -1.48 -1.28 -0.92 -0.28000000000000003 0.42 0.72 0.98 1.32 2.0699999999999998 2.42 2.75 3.21 3.85 4.1399999999999997 4.45 4.8499999999999996 5.38 5.86 6.39 6.82 7.31 8.07 8.75 9.3000000000000007 9.9499999999999993 10.23 10.54 10.96 11.61 12.37 12.81 13.14 13.91 14.72 15.18 15.48 16.05 16.350000000000001 16.78 17.489999999999998 18.03 18.57 19 19.489999999999998 20.27 20.91 21.3 21.6 22.25 22.77 23.27 23.56 23.99 24.32 24.85 24.96 25.27 25.78 26.19 26.5 26.74 27.26 27.77 27.98 28.22 28.78 29 29.08 29.23 29.62 29.79 29.9 30.11 30.21 30.26 30.34 30.5 30.47 30.58 30.5 5 30.69 30.67 30.41 30.5 30.51 30.35 30.14 29.69 29.71 29.73 29.58 29.41 28.96 28.49 28.24 27.78 27.32 27.07 26.54 25.83 25.26 24.41 23.44 22.82 22.09 21.51 21.12 20.71 20.09 19.809999999999999 19.86 19.649999999999999 19.27 19.12 19.03 19.16 19.07 18.57 18.350000000000001 18.170000000000002

[mm]

[um]

RProfile

5.0000000000000001E-4 1E-3 1.5E-3 2E-3 2.5000000000000001E-3 3.0000000000000001E-3 3.5000000000000001E-3 4.0000000000000001E-3 4.4999999999999997E-3 5.0000000000000001E-3 5.4999999999999997E-3 6.0000000000000001E-3 6.4999999999999997E-3 7.0000000000000001E-3 7.4999999999999997E-3 8.0000000000000002E-3 8.5000000000000006E-3 8.9999999999999993E-3 9.4999999999999998E-3 0.01 1.0500000000000001E-2 1.0999999999999999E-2 1.15E-2 1.2E-2 1.2500000000000001E-2 1.2999999999999999E-2 1.35E-2 1.4E-2 1.4500000000000001E-2 1.4999999999999999E-2 1.55E-2 1.6E-2 1.6500000000000001E-2 1.7000000000000001E-2 1.7500000000000002E-2 1.7999999999999999E-2 1.8499999999999999E-2 1.9E-2 1.95E-2 0.02 2.0500000000000001E-2 2.1000000000000001E-2 2.1499999999999998E-2 2.1999999999999999E-2 2.2499999999999999E-2 2.3E-2 2.35E-2 2.4E-2 2.4500000000000001E-2 2.5000000000000001E-2 2.5499999999999998E-2 2.5999999999999999E-2 2.6499999999999999E-2 2.7E-2 2.75E-2 2.8000000000000001E-2 2.8500000000000001E-2 2.9000000000000001E-2 2.9499999999999998E-2 0.03 3.0499999999999999E-2 3.1E-2 3.15E-2 3.2000000000000001E-2 3.2500000000000001E-2 3.3000000000000002E-2 3.3500000000000002E-2 3.4000000000000002E-2 3.4500000000000003E-2 3.5000000000000003E-2 3.5499999999999997E-2 3.5999999999999997E-2 3.6499999999999998E-2 3.6999999999999998E-2 3.7499999999999999E-2 3.7999999999999999E-2 3.85E-2 3.9E-2 3.95E-2 0.04 4.0500000000000001E-2 4.1000000000000002E-2 4.1500000000000002E-2 4.2000000000000003E-2 4.2500000000000003E-2 4.2999999999999997E-2 4.3499999999999997E-2 4.3999999999999997E-2 4.4499999999999998E-2 4.4999999999999998E-2 4.5499999999999999E-2 4.5999999999999999E-2 4.65E-2 4.7E-2 4.7500000000000001E-2 4.8000000000000001E-2 4.8500000000000001E-2 4.9000000000000002E-2 4.9500000000000002E-2 0.05 5.0500000000000003E-2 5.0999999999999997E-2 5.1499999999999997E-2 5.1999999999999998E-2 5.2499999999999998E-2 5.2999999999999999E-2 5.3499999999999999E-2 5.3999999999999999E-2 5.45E-2 5.5E-2 5.5500000000000001E-2 5.6000000000000001E-2 5.6500000000000002E-2 5.7000000000000002E-2 5.7500000000000002E-2 5.8000000000000003E-2 5.8500000000000003E-2 5.8999999999999997E-2 5.9499999999999997E-2 0.06 6.0499999999999998E-2 6.0999999999999999E-2 6.1499999999999999E-2 6.2E-2 6.25E-2 6.3E-2 6.3500000000000001E-2 6.4000000000000001E-2 6.4500000000000002E-2 6.5000000000000002E-2 6.5500000000000003E-2 6.6000000000000003E-2 6.6500000000000004E-2 6.7000000000000004E-2 6.7500000000000004E-2 6.8000000000000005E-2 6.8500000000000005E-2 6.9000000000000006E-2 6.9500000000000006E-2 7.0000000000000007E-2 7.0499999999999993E-2 7.0999999999999994E-2 7.1499999999999994E-2 7.1999999999999995E-2 7.2499999999999995E-2 7.2999999999999995E-2 7.3499999999999996E-2 7.3999999999999996E-2 7.4499999999999997E-2 7.4999999999999997E-2 7.5499999999999998E-2 7.5999999999999998E-2 7.6499999999999999E-2 7.6999999999999999E-2 7.7499999999999999E-2 7.8E-2 7.85E-2 7.9000000000000001E-2 7.9500000000000001E-2 0.08 8.0500000000000002E-2 8.1000000000000003E-2 8.1500000000000003E-2 8.2000000000000003E-2 8.2500000000000004E-2 8.3000000000000004E-2 8.3500000000000005E-2 8.4000000000000005E-2 8.4500000000000006E-2 8.5000000000000006E-2 8.5500000000000007E-2 8.5999999999999993E-2 8.6499999999999994E-2 8.6999999999999994E-2 8.7499999999999994E-2 8.7999999999999995E-2 8.8499999999999995E-2 8.8999999999999996E-2 8.9499999999999996E-2 0.09 9.0499999999999997E-2 9.0999999999999998E-2 9.1499999999999998E-2 9.1999999999999998E-2 9.2499999999999999E-2 9.2999999999999999E-2 9.35E-2 9.4E-2 9.4500000000000001E-2 9.5000000000000001E-2 9.5500000000000002E-2 9.6000000000000002E-2 9.6500000000000002E-2 9.7000000000000003E-2 9.7500000000000003E-2 9.8000000000000004E-2 9.8500000000000004E-2 9.9000000000000005E-2 9.9500000000000005E-2 0.1 0.10050000000000001 0.10100000000000001 0.1015 0000000000001 0.10199999999999999 0.10249999999999999 0.10299999999999999 0.10349999999999999 0.104 0.1045 0.105 0.1055 0.106 0.1065 0.107 0.1075 0.108 0.1085 0.109 0.1095 0.11 0.1105 0.111 0.1115 0.112 0.1125 0.113 0.1135 0.114 0.1145 0.115 0.11550000000000001 0.11600000000000001 0.11650000000000001 0.11700000000000001 0.11749999999999999 0.11799999999999999 0.11849999999999999 0.11899999999999999 0.1195 0.12 0.1205 0.121 0.1215 0.122 0.1225 0.123 0.1235 0.124 0.1245 0.125 0.1255 0.126 0.1265 0.127 0.1275 0.128 0.1285 0.129 0.1295 0.13 0.1305 0.13100000000000001 0.13150000000000001 0.13200000000000001 0.13250000000000001 0.13300000000000001 0.13350000000000001 0.13400000000000001 0.13450000000000001 0.13500000000000001 0.13550000000000001 0.13600000000000001 0.13650000000000001 0.13700000000000001 0.13750000000000001 0.13800000000000001 0.13850000000000001 0.13900000000000001 0.13950000000000001 0.14000000000000001 0.14050000000000001 0.14099999999999999 0.14149999999999999 0.14199999999999999 0.14249999999999999 0.14299999999999999 0.14349999999999999 0.14399999999999999 0.14449999999999999 0.14499999999999999 0.14549999999999999 0.1459999 9999999999 0.14649999999999999 0.14699999999999999 0.14749999999999999 0.14799999999999999 0.14849999999999999 0.14899999999999999 0.14949999999999999 0.15 0.15049999999999999 0.151 0.1515 0.152 0.1525 0.153 0.1535 0.154 0.1545 0.155 0.1555 0.156 0.1565 0.157 0.1575 0.158 0.1585 0.159 0.1595 0.16 0.1605 0.161 0.1615 0.16200000000000001 0.16250000000000001 0.16300000000000001 0.16350000000000001 0.16400000000000001 0.16450000000000001 0.16500000000000001 0.16550000000000001 0.16600000000000001 0.16650000000000001 0.16700000000000001 0.16750000000000001 0.16800000000000001 0.16850000000000001 0.16900000000000001 0.16950000000000001 0.17 0.17050000000000001 0.17100000000000001 0.17150000000000001 0.17199999999999999 0.17249999999999999 0.17299999999999999 0.17349999999999999 0.17399999999999999 0.17449999999999999 0.17499999999999999 0.17549999999999999 0.17599999999999999 0.17649999999999999 0.17699999999999999 0.17749999999999999 0.17799999999999999 0.17849999999999999 0.17899999999999999 0.17949999999999999 0.18 0.18049999999999999 0.18099999999999999 0.18149999999999999 0.182 0.1825 0.183 0.1835 0.184 0.1845 0.185 0.1855 0.186 0.1865 0.187 0.1875 0.188 0.1885 0.189 0.1895 0.19 0.1905 0.191 0.1915 0.192 0.1925 0.193 0.19350000000000001 0.19400000000000001 0.19450000000000001 0.19500000000000001 0.19550000000000001 0.19600000000000001 0.19650000000000001 0.19700000000000001 0.19750000000000001 0.19800000000000001 0.19850000000000001 0.19900000000000001 0.19950000000000001 0.2 0.20050000000000001 0.20100000000000001 0.20150000000000001 0.20200000000000001 0.20250000000000001 0.20300000000000001 0.20349999999999999 0.20399999999999999 0.20449999999999999 0.20499999999999999 0.20549999999999999 0.20599999999999999 0.20649999999999999 0.20699999999999999 0.20749999999999999 0.20799999999999999 0.20849999999999999 0.20899999999999999 0.20949999999999999 0.21 0. 21049999999999999 0.21099999999999999 0.21149999999999999 0.21199999999999999 0.21249999999999999 0.21299999999999999 0.2135 0.214 0.2145 0.215 0.2155 0.216 0.2165 0.217 0.2175 0.218 0.2185 0.219 0.2195 0.22 0.2205 0.221 0.2215 0.222 0.2225 0.223 0.2235 0.224 0.22450000000000001 0.22500000000000001 0.22550000000000001 0.22600000000000001 0.22650000000000001 0.22700000000000001 0.22750000000000001 0.22800000000000001 0.22850000000000001 0.22900000000000001 0.22950000000000001 0.23 0.23050000000000001 0.23100000000000001 0.23150000000000001 0.23200000000000001 0.23250000000000001 0.23300000000000001 0.23350000000000001 0.23400000000000001 0.23449999999999999 0.23499999999999999 0.23549999999999999 0.23599999999999999 0.23649999999999999 0.23699999999999999 0.23749999999999999 0.23799999999999999 0.23849999999999999 0.23899999999999999 0.23949999999999999 0.24 0.24049999999999999 0.24099999999999999 0.24149999999999999 0.24199999999999999 0.24249999999999999 0.24299999999999999 0.24349999999999999 0.24399999999999999 0.2445 0.245 0.2455 0.246 0.2465 0.247 0.2475 0.248 0.2485 0.249 0.2495 0.25 0.2505 0.251 0.2515 0.252 0.2525 0.253 0.2535 0.254 0.2545 0.255 0.2555 0.25600000000000001 0.25650000000000001 0.25700000000000001 0.25750000000000001 0.25800000000000001 0.25850000000000001 0.25900000000000001 0.25950000000000001 0.26 0.26050000000000001 0.26100000000000001 0.26150000000000001 0.26200000000000001 0.26250000000000001 0.26300000000000001 0.26350000000000001 0.26400000000000001 0.26450000000000001 0.26500000000000001 0.26550000000000001 0.26600000000000001 0.26650000000000001 0.26700000000000002 0.26750000000000002 0.26800000000000002 0.26850000000000002 0.26900000000000002 0.26950000000000002 0.27 0.27050000000000002 0.27100000000000002 0.27150000000000002 0.27200000000000002 0.27250000000000002 0.27300000000000002 0.27350000000000002 0.27400000000000002 0.27450000000000002 0.27500000000000002 0.27550000000000002 0.27600000000000002 0.27650000000000002 0.27700000000000002 0.27750000000000002 0.27800000000000002 0.27850000000000003 0.27900000000000003 0.27950000000000003 0.28000000000000003 0.28050000000000003 0.28100000000000003 0.28149999999999997 0.28199999999999997 0.28249999999999997 0.28299999999999997 0.28349999999999997 0.28399999999999997 0.28449999999999998 0.28499999999999998 0.28549999999999998 0.28599999999999998 0.28649999999999998 0.28699999999999998 0.28749999999999998 0.28799999999999998 0.28849999999999998 0.28899999999999998 0.28949999999999998 0.28999999999999998 0.29049999999999998 0.29099999999999998 0.29149999999999998 0.29199999999999998 0.29249999999999998 0.29299999999999998 0.29349999999999998 0.2939999999 9999998 0.29449999999999998 0.29499999999999998 0.29549999999999998 0.29599999999999999 0.29649999999999999 0.29699999999999999 0.29749999999999999 0.29799999999999999 0.29849999999999999 0.29899999999999999 0.29949999999999999 0.3 0.30049999999999999 0.30099999999999999 0.30149999999999999 0.30199999999999999 0.30249999999999999 0.30299999999999999 0.30349999999999999 0.30399999999999999 0.30449999999999999 0.30499999999999999 0.30549999999999999 0.30599999999999999 0.30649999999999999 0.307 0.3075 0.308 0.3085 0.309 0.3095 0.31 0.3105 0.311 0.3115 0.312 0.3125 0.313 0.3135 0.314 0.3145 0.315 0.3155 0.316 0.3165 0.317 0.3175 0.318 0.31850000000000001 0.31900000000000001 0.31950000000000001 0.32 0.32050000000000001 0.32100000000000001 0.32150000000000001 0.32200000000000001 0.32250000000000001 0.32300000000000001 0.32350000000000001 0.32400000000000001 0.32450000000000001 0.32500000000000001 0.32550000000000001 0.32600000000000001 0.32650000000000001 0.32700000000000001 0.32750000000000001 0.32800000000000001 0.32850000000000001 0.32900000000000001 0.32950000000000002 0.33 0.33050000000000002 0.33100000000000002 0.33150000000000002 0.33200000000000002 0.33250000000000002 0.33300000000000002 0.33350000000000002 0.33400000000000002 0.33450000000000002 0.33500000000000002 0.33550000000000002 0.336000000 00000002 0.33650000000000002 0.33700000000000002 0.33750000000000002 0.33800000000000002 0.33850000000000002 0.33900000000000002 0.33950000000000002 0.34 0.34050000000000002 0.34100000000000003 0.34150000000000003 0.34200000000000003 0.34250000000000003 0.34300000000000003 0.34350000000000003 0.34399999999999997 0.34449999999999997 0.34499999999999997 0.34549999999999997 0.34599999999999997 0.34649999999999997 0.34699999999999998 0.34749999999999998 0.34799999999999998 0.34849999999999998 0.34899999999999998 0.34949999999999998 0.35 0.35049999999999998 0.35099999999999998 0.35149999999999998 0.35199999999999998 0.35249999999999998 0.35299999999999998 0.35349999999999998 0.35399999999999998 0.35449999999999998 0.35499999999999998 0.35549999999999998 0.35599999999999998 0.35649999999999998 0.35699999999999998 0.35749999999999998 0.35799999999999998 0.35849999999999999 0.35899999999999999 0.35949999999999999 0.36 0.36049999999999999 0.36099999999999999 0.36149999999999999 0.36199999999999999 0.36249999999999999 0.36299999999999999 0.36349999999999999 0.36399999999999999 0.36449999999999999 0.36499999999999999 0.36549999999999999 0.36599999999999999 0.36649999999999999 0.36699999999999999 0.36749999999999999 0.36799999999999999 0.36849999999999999 0.36899999999999999 0.3695 0.37 0.3705 0.371 0.3715 0.372 0.3725 0.373 0.3735 0.374 0.3745 0.375 0.3755 0.376 0.3765 0.377 0.3775 0.378 0.3785 0.379 0.3795 0.38 0.3805 0.38100000000000001 0.38150000000000001 0.38200000000000001 0.38250000000000001 0.38300000000000001 0.38350000000000001 0.38400000000000001 0.38450000000000001 0.38500000000000001 0.38550000000000001 0.38600000000000001 0.38650000000000001 0.38700000000000001 0.38750000000000001 0.38800000000000001 0.38850000000000001 0.38900000000000001 0.38950000000000001 0.39 0.39050000000000001 0.39100000000000001 0.39150000000000001 0.39200000000000002 0.39250000000000002 0.39300000000000002 0.39350000000000002 0.39400000000000002 0.39450000000000002 0.39500000000000002 0.39550000000000002 0.39600000000000002 0.39650000000000002 0.39700000000000002 0.3975 0000000000002 0.39800000000000002 0.39850000000000002 0.39900000000000002 0.39950000000000002 0.4 0.40050000000000002 0.40100000000000002 0.40150000000000002 0.40200000000000002 0.40250000000000002 0.40300000000000002 0.40350000000000003 0.40400000000000003 0.40450000000000003 0.40500000000000003 0.40550000000000003 0.40600000000000003 0.40649999999999997 0.40699999999999997 0.40749999999999997 0.40799999999999997 0.40849999999999997 0.40899999999999997 0.40949999999999998 0.41 0.41049999999999998 0.41099999999999998 0.41149999999999998 0.41199999999999998 0.41249999999999998 0.41299999999999998 0.41349999999999998 0.41399999999999998 0.41449999999999998 0.41499999999999998 0.41549999999999998 0.41599999999999998 0.41649999999999998 0.4169999999999999 8 0.41749999999999998 0.41799999999999998 0.41849999999999998 0.41899999999999998 0.41949999999999998 0.42 0.42049999999999998 0.42099999999999999 0.42149999999999999 0.42199999999999999 0.42249999999999999 0.42299999999999999 0.42349999999999999 0.42399999999999999 0.42449999999999999 0.42499999999999999 0.42549999999999999 0.42599999999999999 0.42649999999999999 0.42699999999999999 0.42749999999999999 0.42799999999999999 0.42849999999999999 0.42899999999999999 0.42949999999999999 0.43 0.43049999999999999 0.43099999999999999 0.43149999999999999 0.432 0.4325 0.433 0.4335 0.434 0.4345 0.435 0.4355 0.436 0.4365 0.437 0.4375 0.438 0.4385 0.439 0.4395 0.44 0.4405 0.441 0.4415 0.442 0.4425 0.443 0.44350000000000001 0.44400000000000001 0.44450000000000001 0.44500000000000001 0.44550000000000001 0.44600000000000001 0.44650000000000001 0.44700000000000001 0.44750000000000001 0.44800000000000001 0.44850000000000001 0.44900000000000001 0.44950000000000001 0.45 0.45050000000000001 0.45100000000000001 0.45150000000000001 0.45200000000000001 0.45250000000000001 0.45300000000000001 0.45350000000000001 0.45400000000000001 0.45450000000000002 0.45500000000000002 0.45550000000000002 0.45600000000000002 0.45650000000000002 0.45700000000000002 0.45750000000000002 0.45800000000000002 0.45850000000000002 0.45900000000000002 0.45950000000000002 0.46 0.46050000000000002 0.46100000000000002 0.46150000000000002 0.46200000000000002 0.46250000000000002 0.46300000000000002 0.46350000000000002 0.46400000000000002 0.46450000000000002 0.46500000000000002 0.46550000000000002 0.46600000000000003 0.46650000000000003 0.46700000000000003 0.46750000000000003 0.46800000000000003 0.46850000000000003 0.46899999999999997 0.46949999999999997 0.47 0.47049999999999997 0.47099999999999997 0.47149999999999997 0.47199999999999998 0.47249999999999998 0.47299999999999998 0.47349999999999998 0.47399999999999998 0.47449999999999998 0.47499999999999998 0.47549999999999998 0.47599999999999998 0.47649999999999998 0.47699999999999998 0.47749999999999998 0.47799999999999998 0.47849999999999998 0.47899999999999998 0.47949999999999998 0.48 0.48049999999999998 0.48099999999999998 0.48149999999999998 0.48199999999999998 0.48249999999999998 0.48299999999999998 0.48349999999999999 0.48399999999999999 0.48449999999999999 0.48499999999999999 0.48549999999999999 0.48599999999999999 0.48649999999999999 0.48699999999999999 0.48749999999999999 0.48799999999999999 0.48849999999999999 0.48899999999999999 0.48949999999999999 0.49 0.49049999999999999 0.49099999999999999 0.49149999999999999 0.49199999999999999 0.49249999999999999 0.49299999999999999 0.49349999999999999 0.49399999999999999 0.4945 0.495 0.4955 0.496 0.4965 0.497 0.4975 0.498 0.4985 0.499 0.4995 0.5 0.50049999999999994 0.501 0.50149999999999995 0.502 0.50249999999999995 0.503 0.50349999999999995 0.504 0.50449999999999995 0.505 0.50549999999999995 0.50600000000000001 0.50649999999999995 0.50700000000000001 0.50749999999999995 0.50800000000000001 0.50849999999999995 0.50900000000000001 0.50949999999999995 0.51 0.51049999999999995 0.51100000000000001 0.51149999999999995 0.51200000000000001 0.51249999999999996 0.51300000000000001 0.51349999999999996 0.51400000000000001 0.51449999999999996 0.51500000000000001 0.51549999999999996 0.51600000000000001 0.51649999999999996 0.51700000000000002 0.51749999999999996 0.51800000000000002 0.51849999999999996 0.51900000000000002 0.519499999999999 96 0.52 0.52049999999999996 0.52100000000000002 0.52149999999999996 0.52200000000000002 0.52249999999999996 0.52300000000000002 0.52349999999999997 0.52400000000000002 0.52449999999999997 0.52500000000000002 0.52549999999999997 0.52600000000000002 0.52649999999999997 0.52700000000000002 0.52749999999999997 0.52800000000000002 0.52849999999999997 0.52900000000000003 0.52949999999999997 0.53 0.53049999999999997 0.53100000000000003 0.53149999999999997 0.53200000000000003 0.53249999999999997 0.53300000000000003 0.53349999999999997 0.53400000000000003 0.53449999999999998 0.53500000000000003 0.53549999999999998 0.53600000000000003 0.53649999999999998 0.53700000000000003 0.53749999999999998 0.53800000000000003 0.53849999999999998 0.53900000000000003 0.53949999999999998 0.54 0.54049999999999998 0.54100000000000004 0.54149999999999998 0.54200000000000004 0.54249999999999998 0.54300000000000004 0.54349999999999998 0.54400000000000004 0.54449999999999998 0.54500000000000004 0.54549999999999998 0.54600000000000004 0.54649999999999999 0.54700000000000004 0.54749999999999999 0.54800000000000004 0.54849999999999999 0.54900000000000004 0.54949999999999999 0.55000000000000004 0.55049999999999999 0.55100000000000005 0.55149999999999999 0.55200000000000005 0.55249999999999999 0.55300000000000005 0.55349999999999999 0.55400000000000005 0.55449999999999999 0.55500000000000005 0.55549999999999999 0.55600000000000005 0.55649999999999999 0.55700000000000005 0.5575 0.55800000000 000005 0.5585 0.55900000000000005 0.5595 0.56000000000000005 0.5605 0.56100000000000005 0.5615 0.56200000000000006 0.5625 0.56299999999999994 0.5635 0.56399999999999995 0.5645 0.56499999999999995 0.5655 0.56599999999999995 0.5665 0.56699999999999995 0.5675 0.56799999999999995 0.56850000000000001 0.56899999999999995 0.56950000000000001 0.56999999999999995 0.57050000000000001 0.57099999999999995 0.57150000000000001 0.57199999999999995 0.57250000000000001 0.57299999999999995 0.57350000000000001 0.57399999999999995 0.57450000000000001 0.57499999999999996 0.57550000000000001 0.57599999999999996 0.57650000000000001 0.57699999999999996 0.57750000000000001 0.57799999999999996 0.57850000000000001 0.57899999999999996 0.57950000000000002 0.57999999999999996 0.58050000000000002 0.58099999999999996 0.58150000000000002 0.58199999999999996 0.58250000000000002 0.58299999999999996 0.58350000000000002 0.58399999999999996 0.58450000000000002 0.58499999999999996 0.58550000000000002 0.58599999999999997 0.58650000000000002 0.58699999999999997 0.58750000000000002 0.58799999999999997 0.58850000000000002 0.58899999999999997 0.58950000000000002 0.59 0.59050000000000002 0.59099999999999997 0.59150000000000003 0.59199999999999997 0.59250000000000003 0.59299999999999997 0.59350000000000003 0.59399999999999997 0.59450000000000003 0.59499999999999997 0.59550000000000003 0.59599999999999997 0.59650000000000003 0.59699999999999998 0.59750000000000003 0.59799999999999998 0.59850000000000003 0.59899999999999998 0.59950000000000003 0.6 0.60050000000000003 0.60099999999999998 0.60150000000000003 0.60199999999999998 0.60250000000000004 0.60299999999999998 0.60350000000000004 0.60399999999999998 0.60450000000000004 0.60499999999999998 0.60550000000000004 0.60599999999999998 0.60650000000000004 0.60699999999999998 0.60750000000000004 0.60799999999999998 0.60850000000000004 0.60899999999999999 0.60950000000000004 0.61 0.61050000000000004 0.61099999999999999 0.61150000000000004 0.61199999999999999 0.61250000000000004 0.61299999999999999 0.61350000000000005 0.61399999999999999 0.61450000000000005 0.61499999999999999 0.61550000000000005 0.61599999999999999 0.6165000000000 0005 0.61699999999999999 0.61750000000000005 0.61799999999999999 0.61850000000000005 0.61899999999999999 0.61950000000000005 0.62 0.62050000000000005 0.621 0.62150000000000005 0.622 0.62250000000000005 0.623 0.62350000000000005 0.624 0.62450000000000006 0.625 0.62549999999999994 0.626 0.62649999999999995 0.627 0.62749999999999995 0.628 0.62849999999999995 0.629 0.62949999999999995 0.63 0.63049999999999995 0.63100000000000001 0.63149999999999995 0.63200000000000001 0.63249999999999995 0.63300000000000001 0.63349999999999995 0.63400000000000001 0.63449999999999995 0.63500000000000001 0.63549999999999995 0.63600000000000001 0.63649999999999995 0.637 00000000000001 0.63749999999999996 0.63800000000000001 0.63849999999999996 0.63900000000000001 0.63949999999999996 0.64 0.64049999999999996 0.64100000000000001 0.64149999999999996 0.64200000000000002 0.64249999999999996 0.64300000000000002 0.64349999999999996 0.64400000000000002 0.64449999999999996 0.64500000000000002 0.64549999999999996 0.64600000000000002 0.64649999999999996 0.64700000000000002 0.64749999999999996 0.64800000000000002 0.64849999999999997 0.64900000000000002 0.64949999999999997 0.65 0.65049999999999997 0.65100000000000002 0.65149999999999997 0.65200000000000002 0.65249999999999997 0.65300000000000002 0.65349999999999997 0.65400000000000003 0.65449999999999997 0.65500000000000003 0.65549999999999997 0.65600000000000003 0.65649999999999997 0.65700000000000003 0.65749999999999997 0.65800000000000003 0.65849999999999997 0.65900000000000003 0.65949999999999998 0.66 0.66049999999999998 0.66100000000000003 0.66149999999999998 0.66200000000000003 0.66249999999999998 0.66300000000000003 0.66349999999999998 0.66400000000000003 0.66449999999999998 0.66500000000000004 0.66549999999999998 0.66600000000000004 0.66649999999999998 0.66700000000000004 0.66749999999999998 0.66800000000000004 0.66849999999999998 0.66900000000000004 0.66949999999999998 0.67 0.67049999999999998 0.67100000000000004 0.67149999999999999 0.67200000000000004 0.67249999999999999 0.67300000000000004 0.67349999999999999 0.67400000000000004 0.67449999999999999 0.67500000000000004 0.6 7549999999999999 0.67600000000000005 0.67649999999999999 0.67700000000000005 0.67749999999999999 0.67800000000000005 0.67849999999999999 0.67900000000000005 0.67949999999999999 0.68 0.68049999999999999 0.68100000000000005 0.68149999999999999 0.68200000000000005 0.6825 0.68300000000000005 0.6835 0.68400000000000005 0.6845 0.68500000000000005 0.6855 0.68600000000000005 0.6865 0.68700000000000006 0.6875 0.68799999999999994 0.6885 0.68899999999999995 0.6895 0.69 0.6905 0.69099999999999995 0.6915 0.69199999999999995 0.6925 0.69299999999999995 0.69350000000000001 0.69399999999999995 0.69450000000000001 0.69499999999999995 0.69550000000000001 0.69599999 999999995 0.69650000000000001 0.69699999999999995 0.69750000000000001 0.69799999999999995 0.69850000000000001 0.69899999999999995 0.69950000000000001 0.7 0.70050000000000001 0.70099999999999996 0.70150000000000001 0.70199999999999996 0.70250000000000001 0.70299999999999996 0.70350000000000001 0.70399999999999996 0.70450000000000002 0.70499999999999996 0.70550000000000002 0.70599999999999996 0.70650000000000002 0.70699999999999996 0.70750000000000002 0.70799999999999996 0.70850000000000002 0.70899999999999996 0.70950000000000002 0.71 0.71050000000000002 0.71099999999999997 0.71150000000000002 0.71199999999999997 0.71250000000000002 0.71299999999999997 0.71350000000000002 0.71399999999999997 0.71450000000000002 0.71499999999999997 0.71550000000000002 0.71599999999999997 0.71650000000000003 0.71699999999999997 0.71750000000000003 0.71799999999999997 0.71850000000000003 0.71899999999999997 0.71950000000000003 0.72 0.72050000000000003 0.72099999999999997 0.72150000000000003 0.72199999999999998 0.72250000000000003 0.72299999999999998 0.72350000000000003 0.72399999999999998 0.72450000000000003 0.72499999999999998 0.72550000000000003 0.72599999999999998 0.72650000000000003 0.72699999999999998 0.72750000000000004 0.72799999999999998 0.72850000000000004 0.72899999999999998 0.72950000000000004 0.73 0.73050000000000004 0.73099999999999998 0.73150000000000004 0.73199999999999998 0.73250000000000004 0.73299999999999998 0.73350000000000004 0.73399999999999999 0.734 50000000000004 0.73499999999999999 0.73550000000000004 0.73599999999999999 0.73650000000000004 0.73699999999999999 0.73750000000000004 0.73799999999999999 0.73850000000000005 0.73899999999999999 0.73950000000000005 0.74 0.74050000000000005 0.74099999999999999 0.74150000000000005 0.74199999999999999 0.74250000000000005 0.74299999999999999 0.74350000000000005 0.74399999999999999 0.74450000000000005 0.745 0.74550000000000005 0.746 0.74650000000000005 0.747 0.74750000000000005 0.748 0.74850000000000005 0.749 0.74950000000000006 0.75 0.75049999999999994 0.751 0.75149999999999995 0.752 0.75249999999999995 0.753 0.75349999999999995 0.754 0.75449999999999995 0.755 0.75549999999999995 0.75600000000000001 0.75649999999999995 0.75700000000000001 0.75749999999999995 0.75800000000000001 0.75849999999999995 0.75900000000000001 0.75949999999999995 0.76 0.76049999999999995 0.76100000000000001 0.76149999999999995 0.76200000000000001 0.76249999999999996 0.76300000000000001 0.76349999999999996 0.76400000000000001 0.76449999999999996 0.76500000000000001 0.76549999999999996 0.76600000000000001 0.76649999999999996 0.76700000000000002 0.76749999999999996 0.76800000000000002 0.76849999999999996 0.76900000000000002 0.76949999999999996 0.77 0.77049999999999996 0.77100000000000002 0.77149999999999996 0.77200000000000002 0.77249999999999996 0.77300000000000002 0.77349999999999997 0.77400000000000002 0.77449999999999997 0.77500000000000002 0.77549999999999997 0.77600000000000002 0.77649999999999997 0.77700000000000002 0.77749999999999997 0.77800000000000002 0.77849999999999997 0.77900000000000003 0.77949999999999997 0.78 0.78049999999999997 0.78100000000000003 0.78149999999999997 0.78200000000000003 0.78249999999999997 0.78300000000000003 0.78349999999999997 0.78400000000000003 0.78449999999999998 0.78500000000000003 0.78549999999999998 0.78600000000000003 0.78649999999999998 0.78700000000000003 0.78749999999999998 0.78800000000000003 0.78849999999999998 0.78900000000000003 0.78949999999999998 0.79 0.79049999999999998 0.79100000000000004 0.79149999999999998 0.79200000000000004 0.79249999999999998 0.79300000000000004 0.793 49999999999998 0.79400000000000004 0.79449999999999998 0.79500000000000004 0.79549999999999998 0.79600000000000004 0.79649999999999999 0.79700000000000004 0.79749999999999999 0.79800000000000004 0.79849999999999999 0.79900000000000004 0.79949999999999999 0.8 0.80049999999999999 0.80100000000000005 0.80149999999999999 0.80200000000000005 0.80249999999999999 0.80300000000000005 0.80349999999999999 0.80400000000000005 0.80449999999999999 0.80500000000000005 0.80549999999999999 0.80600000000000005 0.80649999999999999 0.80700000000000005 0.8075 0.80800000000000005 0.8085 0.80900000000000005 0.8095 0.81 0.8105 0.81100000000000005 0.8115 0.81200000000000006 0.8125 0.81299999999999994 0. 8135 0.81399999999999995 0.8145 0.81499999999999995 0.8155 0.81599999999999995 0.8165 0.81699999999999995 0.8175 0.81799999999999995 0.81850000000000001 0.81899999999999995 0.81950000000000001 0.82 0.82050000000000001 0.82099999999999995 0.82150000000000001 0.82199999999999995 0.82250000000000001 0.82299999999999995 0.82350000000000001 0.82399999999999995 0.82450000000000001 0.82499999999999996 0.82550000000000001 0.82599999999999996 0.82650000000000001 0.82699999999999996 0.82750000000000001 0.82799999999999996 0.82850000000000001 0.82899999999999996 0.82950000000000002 0.83 0.83050000000000002 0.83099999999999996 0.83150000000000002 0.83199999999999996 0.83250000000000002 0.83299999999999996 0.83350000000000002 0.83399999999999996 0.83450000000000002 0.83499999999999996 0.83550000000000002 0.83599999999999997 0.83650000000000002 0.83699999999999997 0.83750000000000002 0.83799999999999997 0.83850000000000002 0.83899999999999997 0.83950000000000002 0.84 0.84050000000000002 0.84099999999999997 0.84150000000000003 0.84199999999999997 0.84250000000000003 0.84299999999999997 0.84350000000000003 0.84399999999999997 0.84450000000000003 0.84499999999999997 0.84550000000000003 0.84599999999999997 0.84650000000000003 0.84699999999999998 0.84750000000000003 0.84799999999999998 0.84850000000000003 0.84899999999999998 0.84950000000000003 0.85 0.85050000000000003 0.85099999999999998 0.85150000000000003 0.85199999999999998 0.85250000 000000004 0.85299999999999998 0.85350000000000004 0.85399999999999998 0.85450000000000004 0.85499999999999998 0.85550000000000004 0.85599999999999998 0.85650000000000004 0.85699999999999998 0.85750000000000004 0.85799999999999998 0.85850000000000004 0.85899999999999999 0.85950000000000004 0.86 0.86050000000000004 0.86099999999999999 0.86150000000000004 0.86199999999999999 0.86250000000000004 0.86299999999999999 0.86350000000000005 0.86399999999999999 0.86450000000000005 0.86499999999999999 0.86550000000000005 0.86599999999999999 0.86650000000000005 0.86699999999999999 0.86750000000000005 0.86799999999999999 0.86850000000000005 0.86899999999999999 0.86950000000000005 0.87 0.87050000000000005 0.871 0.87150000000000005 0.872 0.87250000000000005 0.873 0.87350000000000005 0.874 0.87450000000000006 0.875 0.87549999999999994 0.876 0.87649999999999995 0.877 0.87749999999999995 0.878 0.87849999999999995 0.879 0.87949999999999995 0.88 0.88049999999999995 0.88100000000000001 0.88149999999999995 0.88200000000000001 0.88249999999999995 0.88300000000000001 0.88349999999999995 0.88400000000000001 0.88449999999999995 0.88500000000000001 0.88549999999999995 0.88600000000000001 0.88649999999999995 0.88700000000000001 0.88749999999999996 0.88800000000000001 0.88849999999999996 0.88900000000000001 0.88949999999999996 0.89 0.89049999999999996 0.89100000000000001 0.89149999999999996 0.89200000000000002 0.89249999999999996 0.89300000000000002 0.89349999999999996 0.89400000000000002 0.89449999999999996 0.89500000000000002 0.89549999999999996 0.89600000000000002 0.89649999999999996 0.89700000000000002 0.89749999999999996 0.89800000000000002 0.89849999999999997 0.89900000000000002 0.89949999999999997 0.9 0.90049999999999997 0.90100000000000002 0.90149999999999997 0.90200000000000002 0.90249999999999997 0.90300000000000002 0.90349999999999997 0.90400000000000003 0.90449999999999997 0.90500000000000003 0.90549999999999997 0.90600000000000003 0.90649999999999997 0.90700000000000003 0.90749999999999997 0.90800000000000003 0.90849999999999997 0.90900000000000003 0.90949999999999998 0.91 0.91049999999999998 0.91100000000000003 0.91149999999999998 0.91200000000000003 0.91249999999999998 0.91300000000000003 0.91349999999999998 0.91400000000000003 0.91449999999999998 0.91500000000000004 0.91549999999999998 0.91600000000000004 0.91649999999999998 0.91700000000000004 0.91749999999999998 0.91800000000000004 0.91849999999999998 0.91900000000000004 0.91949999999999998 0.92 0.92049999999999998 0.92100000000000004 0.92149999999999999 0.92200000000000004 0.92249999999999999 0.92300000000000004 0.92349999999999999 0.92400000000000004 0.92449999999999999 0.92500000000000004 0.92549999999999999 0.92600000000000005 0.92649999999999999 0.92700000000000005 0.92749999999999999 0.92800000000000005 0.92849999999999999 0.92900000000000005 0.92949999999999999 0.93 0.93049999999999999 0.93100000000000005 0.93149999999999999 0.93200000000000005 0.9325 0.93300000000000005 0.9335 0.93400000000000005 0.9345 0.93500000000000005 0.9355 0.93600000000000005 0.9365 0.93700000000000006 0.9375 0.93799999999999994 0.9385 0.93899999999999995 0.9395 0.94 0.9405 0.94099999999999995 0.9415 0.94199999999999995 0.9425 0.94299999999999995 0.94350000000000001 0.94399999999999995 0.94450000000000001 0.94499999999999995 0.94550000000000001 0.94599999999999995 0.94650000000000001 0.94699999999999995 0.94750000000000001 0.94799999999999995 0.94850000000000001 0.94899999999999995 0.94950000000000001 0.95 0.95050000000000001 0.95099999999999996 0.95150000000000001 0.95199999999999996 0.95250000000000001 0.95299999999999996 0.95350000000000001 0.95399999999999996 0.95450000000000002 0.95499999999999996 0.95550000000000002 0.95599999999999996 0.95650000000000002 0.95699999999999996 0.95750000000000002 0.95799999999999996 0.95850000000000002 0.95899999999999996 0.95950000000000002 0.96 0.96050000000000002 0.96099999999999997 0.96150000000000002 0.96199999999999997 0.96250000000000002 0.96299999999999997 0.96350000000000002 0.96399999999999997 0.96450000000000002 0.96499999999999997 0.96550000000000002 0.96599999999999997 0.96650000000000003 0.96699999999999997 0.96750000000000003 0.96799999999999997 0.96850000000000003 0.96899999999999997 0.96950000000000003 0.97 0.97050000000000003 0.97099999999999997 0.97150000000000003 0.97199999999999998 0.97250000000000003 0.97299999999999998 0.97350000000000003 0.97399999999999998 0.97450000000000003 0.97499999999999998 0.97550000000000003 0.97599999999999998 0.97650000000000003 0.97699999999999998 0.97750000000000004 0.97799999999999998 0.97850000000000004 0.97899999999999998 0.97950000000000004 0.98 0.98050000000000004 0.98099999999999998 0.98150000000000004 0.98199999999999998 0.98250000000000004 0.98299999999999998 0.98350000000000004 0.98399999999999999 0.98450000000000004 0.98499999999999999 0.98550000000000004 0.98599999999999999 0.98650000000000004 0.98699999999999999 0.98750000000000004 0.98799999999999999 0.98850000000000005 0.98899999999999999 0.98950 000000000005 0.99 0.99050000000000005 0.99099999999999999 0.99150000000000005 0.99199999999999999 0.99250000000000005 0.99299999999999999 0.99350000000000005 0.99399999999999999 0.99450000000000005 0.995 0.99550000000000005 0.996 0.99650000000000005 0.997 0.99750000000000005 0.998 0.99850000000000005 0.999 0.99950000000000006 1 1.0004999999999999 1.0009999999999999 1.0015000000000001 1.002 1.0024999999999999 1.0029999999999999 1.0035000000000001 1.004 1.0044999999999999 1.0049999999999999 1.0055000000000001 1.006 1.0065 1.0069999999999999 1.0075000000000001 1.008 1.0085 1.0089999999999999 1.0095000000000001 1.01 1.0105 1.0109999999999999 1.0115000000000001 1.012 1.0125 1.0129999999999999 1.0135000000000001 1.014 1.0145 1.0149999999999999 1.0155000000000001 1.016 1.0165 1.0169999999999999 1.0175000000000001 1.018 1.0185 1.0189999999999999 1.0195000000000001 1.02 1.0205 1.0209999999999999 1.0215000000000001 1.022 1.0225 1.0229999999999999 1.0235000000000001 1.024 1.0245 1.0249999999999999 1.0255000000000001 1.026 1.0265 1.0269999999999999 1.0275000000000001 1.028 1.0285 1.0289999999999999 1.0295000000000001 1.03 1.0305 1.0309999999999999 1.0315000000000001 1.032 1.0325 1.0329999999999999 1.0335000000000001 1.034 1.0345 1.0349999999999999 1.0355000000000001 1.036 1.0365 1.0369999999999999 1.0375000000000001 1.038 1.0385 1.0389999999999999 1.0395000000000001 1.04 1.0405 1.0409999999999999 1.0415000000000001 1.042 1.0425 1.0429999999999999 1.0435000000000001 1.044 1.0445 1.0449999999999999 1.0455000000000001 1.046 1.0465 1.0469999999999999 1.0475000000000001 1.048 1.0485 1.0489999999999999 1.0495000000000001 1.05 1.0505 1.0509999999999999 1.0515000000000001 1.052 1.0525 1.0529999999999999 1.0535000000000001 1.054 1.0545 1.0549999999999999 1.0555000000000001 1.056 1.0565 1.0569999999999999 1.0575000000000001 1.0580000000000001 1.0585 1.0589999999999999 1.0595000000000001 1.06 1.0605 1.0609999999999999 1.0615000000000001 1.0620000000000001 1.0625 1.0629999999999999 1.0634999999999999 1.0640000000000001 1.0645 1.0649999999999999 1.0654999999999999 1.0660000000000001 1.0665 1.0669999999999999 1.0674999999999999 1.0680000000000001 1.0685 1.069 1.0694999999999999 1.07 1.0705 1.071 1.0714999999999999 1.0720000000000001 1.0725 1.073 1.0734999999999999 1.0740000000000001 1.0745 1.075 1.0754999999999999 1.0760000000000001 1.0765 1.077 1.0774999999999999 1.0780000000000001 1.0785 1.079 1.0794999999999999 1.08 1.0805 1.081 1.0814999999999999 1.0820000000000001 1.0825 1.083 1.0834999999999999 1.0840000000000001 1.0845 1.085 1.0854999999999999 1.0860000000000001 1.0865 1.087 1.0874999999999999 1.0880000000000001 1.0885 1.089 1.0894999999999999 1.0900000000000001 1.0905 1.091 1.0914999999999999 1.0920000000000001 1.0925 1.093 1.0934999999999999 1.0940000000000001 1.0945 1.095 1.0954999999999999 1.0960000000000001 1.0965 1.097 1.0974999999999999 1.0980000000000001 1.0985 1.099 1.0994999999999999 1.1000000000000001 1.1005 1.101 1.1014999999999999 1.1020000000000001 1.1025 1.103 1.1034999999999999 1.1040000000000001 1.1045 1.105 1.1054999999999999 1.1060000000000001 1.1065 1.107 1.1074999999999999 1.1080000000000001 1.1085 1.109 1.1094999999999999 1.1100000000000001 1.1105 1.111 1.1114999999999999 1.1120000000000001 1.1125 1.113 1.1134999999999999 1.1140000000000001 1.1145 1.115 1.1154999999999999 1.1160000000000001 1.1165 1.117 1.1174999999999999 1.1180000000000001 1.1185 1.119 1.1194999999999999 1.1200000000000001 1.1205000000000001 1.121 1.1214999999999999 1.1220000000000001 1.1225000000000001 1.123 1.1234999999999999 1.1240000000000001 1.1245000000000001 1.125 1.1254999999999999 1.1259999999999999 1.1265000000000001 1.127 1.1274999999999999 1.1279999999999999 1.1285000000000001 1.129 1.1294999999999999 1.1299999999999999 1.1305000000000001 1.131 1.1315 1.1319999999999999 1.1325000000000001 1.133 1.1335 1.1339999999999999 1.1345000000000001 1.135 1.1355 1.1359999999999999 1.1365000000000001 1.137 1.1375 1.1379999999999999 1.1385000000000001 1.139 1.1395 1.1399999999999999 1.1405000000000001 1.141 1.1415 1.1419999999999999 1.1425000000000001 1.143 1.1435 1.1439999999999999 1.1445000000000001 1.145 1.1455 1.1459999999999999 1.1465000000000001 1.147 1.1475 1.1479999999999999 1.1485000000000001 1.149 1.1495 1.1499999999999999 1.1505000000000001 1.151 1.1515 1.1519999999999999 1.1525000000000001 1.153 1.1535 1.1539999999999999 1.1545000000000001 1.155 1.1555 1.1559999999999999 1.1565000000000001 1.157 1.1575 1.1579999999999999 1.1585000000000001 1.159 1.1595 1.1599999999999999 1.1605000000000001 1.161 1.1615 1.1619999999999999 1.1625000000000001 1.163 1.1635 1.1639999999999999 1.1645000000000001 1.165 1.1655 1.1659999999999999 1.1665000000000001 1.167 1.1675 1.1679999999999999 1.1685000000000001 1.169 1.1695 1.17 1.1705000000000001 1.171 1.1715 1.1719999999999999 1.1725000000000001 1.173 1.1735 1.1739999999999999 1.1745000000000001 1.175 1.1755 1.1759999999999999 1.1765000000000001 1.177 1.1775 1.1779999999999999 1.1785000000000001 1.179 1.1795 1.18 1.1805000000000001 1.181 1.1815 1.1819999999999999 1.1825000000000001 1.1830000000000001 1.1835 1.1839999999999999 1.1845000000000001 1.1850000000000001 1.1855 1.1859999999999999 1.1865000000000001 1.1870000000000001 1.1875 1.1879999999999999 1.1884999999999999 1.1890000000000001 1.1895 1.19 1.1904999999999999 1.1910000000000001 1.1915 1.1919999999999999 1.1924999999999999 1.1930000000000001 1.1935 1.194 1.1944999999999999 1.1950000000000001 1.1955 1.196 1.1964999999999999 1.1970000000000001 1.1975 1.198 1.1984999999999999 1.1990000000000001 1.1995 1.2 1.2004999999999999 1.2010000000000001 1.2015 1.202 1.2024999999999999 1.2030000000000001 1.2035 1.204 1.2044999999999999 1.2050000000000001 1.2055 1.206 1.2064999999999999 1.2070000000000001 1.2075 1.208 1.2084999999999999 1.2090000000000001 1.2095 1.21 1.2104999999999999 1.2110000000000001 1.2115 1.212 1.2124999999999999 1.2130000000000001 1.2135 1.214 1.2144999999999999 1.2150000000000001 1.2155 1.216 1.2164999999999999 1.2170000000000001 1.2175 1.218 1.2184999999999999 1.2190000000000001 1.2195 1.22 1.2204999999999999 1.2210000000000001 1.2215 1.222 1.2224999999999999 1.2230000000000001 1.2235 1.224 1.2244999999999999 1.2250000000000001 1.2255 1.226 1.2264999999999999 1.2270000000000001 1.2275 1.228 1.2284999999999999 1.2290000000000001 1.2295 1.23 1.2304999999999999 1.2310000000000001 1.2315 1.232 1.2324999999999999 1.2330000000000001 1.2335 1.234 1.2344999999999999 1.2350000000000001 1.2355 1.236 1.2364999999999999 1.2370000000000001 1.2375 1.238 1.2384999999999999 1.2390000000000001 1.2395 1.24 1.2404999999999999 1.2410000000000001 1.2415 1.242 1.2424999999999999 1.2430000000000001 1.2435 1.244 1.2444999999999999 1.2450000000000001 1.2455000000000001 1.246 1.2464999999999999 1.2470000000000001 1.2475000000000001 1.248 1.2484999999999999 1.2490000000000001 1.2495000000000001 1.25 1.2504999999999999 1.2509999999999999 1.2515000000000001 1.252 1.2524999999999999 1.2529999999999999 1.2535000000000001 1.254 1.2544999999999999 1.2549999999999999 1.2555000000000001 1.256 1.2565 1.2569999999999999 1.2575000000000001 1.258 1.2585 1.2589999999999999 1.2595000000000001 1.26 1.2605 1.2609999999999999 1.2615000000000001 1.262 1.2625 1.2629999999999999 1.2635000000000001 1.264 1.2645 1.2649999999999999 1.2655000000000001 1.266 1.2665 1.2669999999999999 1.2675000000000001 1.268 1.2685 1.2689999999999999 1.2695000000000001 1.27 1.2705 1.2709999999999999 1.2715000000000001 1.272 1.2725 1.2729999999999999 1.2735000000000001 1.274 1.2745 1.2749999999999999 1.2755000000000001 1.276 1.2765 1.2769999999999999 1.2775000000000001 1.278 1.2785 1.2789999999999999 1.2795000000000001 1.28 1.2805 1.2809999999999999 1.2815000000000001 1.282 1.2825 1.2829999999999999 1.2835000000000001 1.284 1.2845 1.2849999999999999 1.2855000000000001 1.286 1.2865 1.2869999999999999 1.2875000000000001 1.288 1.2885 1.2889999999999999 1.2895000000000001 1.29 1.2905 1.2909999999999999 1.2915000000000001 1.292 1.2925 1.2929999999999999 1.2935000000000001 1.294 1.2945 1.2949999999999999 1.2955000000000001 1.296 1.2965 1.2969999999999999 1.2975000000000001 1.298 1.2985 1.2989999999999999 1.2995000000000001 1.3 1.3005 1.3009999999999999 1.3015000000000001 1.302 1.3025 1.3029999999999999 1.3035000000000001 1.304 1.3045 1.3049999999999999 1.3055000000000001 1.306 1.3065 1.3069999999999999 1.3075000000000001 1.3080000000000001 1.3085 1.3089999999999999 1.3095000000000001 1.31 1.3105 1.3109999999999999 1.3115000000000001 1.3120000000000001 1.3125 1.3129999999999999 1.3134999999999999 1.3140000000000001 1.3145 1.3149999999999999 1.3154999999999999 1.3160000000000001 1.3165 1.3169999999999999 1.3174999999999999 1.3180000000000001 1.3185 1.319 1.3194999999999999 1.32 1.3205 1.321 1.3214999999999999 1.3220000000000001 1.3225 1.323 1.3234999999999999 1.3240000000000001 1.3245 1.325 1.3254999999999999 1.3260000000000001 1.3265 1.327 1.3274999999999999 1.3280000000000001 1.3285 1.329 1.3294999999999999 1.33 1.3305 1.331 1.3314999999999999 1.3320000000000001 1.3325 1.333 1.3334999999999999 1.3340000000000001 1.3345 1.335 1.3354999999999999 1.3360000000000001 1.3365 1.337 1.3374999999999999 1.3380000000000001 1.3385 1.339 1.3394999999999999 1.34 1.3405 1.341 1.3414999999999999 1.3420000000000001 1.3425 1.343 1.3434999999999999 1.3440000000000001 1.3445 1.345 1.3454999999999999 1.3460000000000001 1.3465 1.347 1.3474999999999999 1.3480000000000001 1.3485 1.349 1.3494999999999999 1.35 1.3505 1.351 1.3514999999999999 1.3520000000000001 1.3525 1.353 1.3534999999999999 1.3540000000000001 1.3545 1.355 1.3554999999999999 1.3560000000000001 1.3565 1.357 1.3574999999999999 1.3580000000000001 1.3585 1.359 1.3594999999999999 1.36 1.3605 1.361 1.3614999999999999 1.3620000000000001 1.3625 1.363 1.3634999999999999 1.3640000000000001 1.3645 1.365 1.3654999999999999 1.3660000000000001 1.3665 1.367 1.3674999999999999 1.3680000000000001 1.3685 1.369 1.3694999999999999 1.37 1.3705000000000001 1.371 1.3714999999999999 1.3720000000000001 1.3725000000000001 1.373 1.3734999999999999 1.3740000000000001 1.3745000000000001 1.375 1.3754999999999999 1.3759999999999999 1.3765000000000001 1.377 1.3774999999999999 1.3779999999999999 1.3785000000000001 1.379 1.3794999999999999 1.38 1.380 5000000000001 1.381 1.3815 1.3819999999999999 1.3825000000000001 1.383 1.3835 1.3839999999999999 1.3845000000000001 1.385 1.3855 1.3859999999999999 1.3865000000000001 1.387 1.3875 1.3879999999999999 1.3885000000000001 1.389 1.3895 1.39 1.3905000000000001 1.391 1.3915 1.3919999999999999 1.3925000000000001 1.393 1.3935 1.3939999999999999 1.3945000000000001 1.395 1.3955 1.3959999999999999 1.3965000000000001 1.397 1.3975 1.3979999999999999 1.3985000000000001 1.399 1.3995 1.4 1.4005000000000001 1.401 1.4015 1.4019999999999999 1.4025000000000001 1.403 1.4035 1.4039999999999999 1.4045000000000001 1.405 1.4055 1.4059999999999999 1.4065000000000001 1.407 1.4075 1.4079999999999999 1.4085000000000001 1.409 1.4095 1.41 1.4105000000000001 1.411 1.4115 1.4119999999999999 1.4125000000000001 1.413 1.4135 1.4139999999999999 1.4145000000000001 1.415 1.4155 1.4159999999999999 1.4165000000000001 1.417 1.4175 1.4179999999999999 1.4185000000000001 1.419 1.4195 1.42 1.4205000000000001 1.421 1.4215 1.4219999999999999 1.4225000000000001 1.423 1.4235 1.4239999999999999 1.4245000000000001 1.425 1.4255 1.4259999999999999 1.4265000000000001 1.427 1.4275 1.4279999999999999 1.4285000000000001 1.429 1.4295 1.43 1.4305000000000001 1.431 1.4315 1.4319999999999999 1.4325000000000001 1.4330000000000001 1.4335 1.4339999999999999 1.4345000000000001 1.4350000000000001 1.4355 1.4359999999999999 1.4365000000000001 1.4370000000000001 1.4375 1.4379999999999999 1.4384999999999999 1.4390000000000001 1.4395 1.44 1.4404999999999999 1.4410000000000001 1.4415 1.4419999999999999 1.4424999999999999 1.4430000000000001 1.4435 1.444 1.4444999999999999 1.4450000000000001 1.4455 1.446 1.4464999999999999 1.4470000000000001 1.4475 1.448 1.4484999999999999 1.4490000000000001 1.4495 1.45 1.4504999999999999 1.4510000000000001 1.4515 1.452 1.4524999999999999 1.4530000000000001 1.4535 1.454 1.4544999999999999 1.4550000000000001 1.4555 1.456 1.4564999999999999 1.4570000000000001 1.4575 1.458 1.4584999999999999 1.4590000000000001 1.4595 1.46 1.4604999999999999 1.4610000000000001 1.4615 1.462 1.4624999999999999 1.4630000000000001 1.4635 1.464 1.4644999999999999 1.4650000000000001 1.4655 1.466 1.4664999999999999 1.4670000000000001 1.4675 1.468 1.4684999999999999 1.4690000000000001 1.4695 1.47 1.4704999999999999 1.4710000000000001 1.4715 1.472 1.4724999999999999 1.4730000000000001 1.4735 1.474 1.4744999999999999 1.4750000000000001 1.4755 1.476 1.4764999999999999 1.4770000000000001 1.4775 1.478 1.4784999999999999 1.4790000000000001 1.4795 1.48 1.4804999999999999 1.4810000000000001 1.4815 1.482 1.4824999999999999 1.4830000000000001 1.4835 1.484 1.4844999999999999 1.4850000000000001 1.4855 1.486 1.4864999999999999 1.4870000000000001 1.4875 1.488 1.4884999999999999 1.4890000000000001 1.4895 1.49 1.4904999999999999 1.4910000000000001 1.4915 1.492 1.4924999999999999 1.4930000000000001 1.4935 1.494 1.4944999999999999 1.4950000000000001 1.4955000000000001 1.496 1.4964999999999999 1.4970000000000001 1.4975000000000001 1.498 1.4984999999999999 1.4990000000000001 1.4995000000000001 1.5 1.5004999999999999 1.5009999999999999 1.5015000000000001 1.502 1.5024999999999999 1.5029999999999999 1.5035000000000001 1.504 1.5044999999999999 1.5049999999999999 1.5055000000000001 1.506 1.5065 1.5069999999999999 1.5075000000000001 1.508 1.5085 1.5089999999999999 1.5095000000000001 1.51 1.5105 1.5109999999999999 1.5115000000000001 1.512 1.5125 1.5129999999999999 1.5135000000000001 1.514 1.5145 1.5149999999999999 1.5155000000000001 1.516 1.5165 1.5169999999999999 1.5175000000000001 1.518 1.5185 1.5189999999999999 1.5195000000000001 1.52 1.5205 1.5209999999999999 1.5215000000000001 1.522 1.5225 1.5229999999999999 1.5235000000000001 1.524 1.5245 1.5249999999999999 1.5255000000000001 1.526 1.5265 1.5269999999999999 1.5275000000000001 1.528 1.5285 1.5289999999999999 1.5295000000000001 1.53 1.5305 1.5309999999999999 1.5315000000000001 1.532 1.5325 1.5329999999999999 1.5335000000000001 1.534 1.5345 1.5349999999999999 1.5355000000000001 1.536 1.5365 1.5369999999999999 1.5375000000000001 1.538 1.5385 1.5389999999999999 1.5395000000000001 1.54 1.5405 1.5409999999999999 1.5415000000000001 1.542 1.5425 1.5429999999999999 1.5435000000000001 1.544 1.5445 1.5449999999999999 1.5455000000000001 1.546 1.5465 1.5469999999999999 1.5475000000000001 1.548 1.5485 1.5489999999999999 1.5495000000000001 1.55 1.5505 1.5509999999999999 1.5515000000000001 1.552 1.5525 1.5529999999999999 1.5535000000000001 1.554 1.5545 1.5549999999999999 1.5555000000000001 1.556 1.5565 1.5569999999999999 1.5575000000000001 1.5580000000000001 1.5585 1.5589999999999999 1.5595000000000001 1.56 1.5605 1.5609999999999999 1.5615000000000001 1.5620000000000001 1.5625 1.5629999999999999 1.5634999999999999 1.5640000000000001 1.5645 1.5649999999999999 1.5654999999999999 1.5660000000000001 1.5665 1.5669999999999999 1.5674999999999999 1.5680000000000001 1.5685 1.569 1.5694999999999999 1.57 1.5705 1.571 1.5714999999999999 1.5720000000000001 1.5725 1.573 1.5734999999999999 1.5740000000000001 1.5745 1.575 1.5754999999999999 1.5760000000000001 1.5765 1.577 1.5774999999999999 1.5780000000000001 1.5785 1.579 1.5794999999999999 1.58 1.5805 1.581 1.5814999999999999 1.5820000000000001 1.5825 1.583 1.5834999999999999 1.5840000000000001 1.5845 1.585 1.5854999999999999 1.5860000000000001 1.5865 1.587 1.5874999999999999 1.5880000000000001 1.5885 1.589 1.5894999999999999 1.59 1.5905 1.591 1.5914999999999999 1.5920000000000001 1.5925 1.593 1.5934999999999999 1.5940000000000001 1.5945 1.595 1.5954999999999999 1.5960000000000001 1.5965 1.597 1.5974999999999999 1.5980000000000001 1.5985 1.599 1.5994999999999999 1.6 1.6005 1.601 1.6014999999999999 1.6020000000000001 1.6025 1.603 1.6034999999999999 1.6040000000000001 1.6045 1.605 1.6054999999999999 1.6060000000000001 1.6065 1.607 1.6074999999999999 1.6080000000000001 1.6085 1.609 1.6094999999999999 1.61 1.6105 1.611 1.6114999999999999 1.6120000000000001 1.6125 1.613 1.6134999999999999 1.6140000000000001 1.6145 1.615 1.6154999999999999 1.6160000000000001 1.6165 1.617 1.6174999999999999 1.6180000000000001 1.6185 1.619 1.6194999999999999 1.62 1.6205000000000001 1.621 1.6214999999999999 1.6220000000000001 1.6225000000000001 1.623 1.6234999999999999 1.6240000000000001 1.6245000000000001 1.625 1.6254999999999999 1.6259999999999999 1.6265000000000001 1.627 1.6274999999999999 1.6279999999999999 1.6285000000000001 1.629 1.6294999999999999 1.63 1.6305000000000001 1.631 1.6315 1.6319999999999999 1.6325000000000001 1.633 1.6335 1.6339999999999999 1.6345000000000001 1.635 1.6355 1.6359999999999999 1.6365000000000001 1.637 1.6375 1.6379999999999999 1.6385000000000001 1.639 1.6395 1.64 1.6405000000000001 1.641 1.6415 1.6419999999999999 1.6425000000000001 1.643 1.6435 1.6439999999999999 1.6445000000000001 1.645 1.6455 1.6459999999999999 1.6465000000000001 1.647 1.6475 1.6479999999999999 1.6485000000000001 1.649 1.6495 1.65 1.6505000000000001 1.651 1.6515 1.6519999999999999 1.6525000000000001 1.653 1.6535 1.6539999999999999 1.6545000000000001 1.655 1.6555 1.6559999999999999 1.6565000000000001 1.657 1.6575 1.6579999999999999 1.6585000000000001 1.659 1.6595 1.66 1.6605000000000001 1.661 1.6615 1.6619999999999999 1.6625000000000001 1.663 1.6635 1.6639999999999999 1.6645000000000001 1.665 1.6655 1.6659999999999999 1.6665000000000001 1.667 1.6675 1.6679999999999999 1.6685000000000001 1.669 1.6695 1.67 1.6705000000000001 1.671 1.6715 1.6719999999999999 1.6725000000000001 1.673 1.6735 1.6739999999999999 1.6745000000000001 1.675 1.6755 1.6759999999999999 1.6765000000000001 1.677 1.6775 1.6779999999999999 1.6785000000000001 1.679 1.6795 1.68 1.6805000000000001 1.681 1.6815 1.6819999999999999 1.6825000000000001 1.6830000000000001 1.6835 1.6839999999999999 1.6845000000000001 1.6850000000000001 1.6855 1.6859999999999999 1.6865000000000001 1.6870000000000001 1.6875 1.6879999999999999 1.6884999999999999 1.6890000000000001 1.6895 1.69 1.6904999999999999 1.6910000000000001 1.6915 1.6919999999999999 1.6924999999999999 1.6930000000000001 1.6935 1.694 1.6944999999999999 1.6950000000000001 1.6955 1.696 1.6964999999999999 1.6970000000000001 1.6975 1.698 1.6984999999999999 1.6990000000000001 1.6995 1.7 1.7004999999999999 1.7010000000000001 1.7015 1.702 1.7024999999999999 1.7030000000000001 1.7035 1.704 1.7044999999999999 1.7050000000000001 1.7055 1.706 1.7064999999999999 1.7070000000000001 1.7075 1.708 1.7084999999999999 1.7090000000000001 1.7095 1.71 1.7104999999999999 1.7110000000000001 1.7115 1.712 1.7124999999999999 1.7130000000000001 1.7135 1.714 1.7144999999999999 1.7150000000000001 1.7155 1.716 1.7164999999999999 1.7170000000000001 1.7175 1.718 1.7184999999999999 1.7190000000000001 1.7195 1.72 1.7204999999999999 1.7210000000000001 1.7215 1.722 1.7224999999999999 1.7230000000000001 1.7235 1.724 1.7244999999999999 1.7250000000000001 1.7255 1.726 1.7264999999999999 1.7270000000000001 1.7275 1.728 1.7284999999999999 1.7290000000000001 1.7295 1.73 1.7304999999999999 1.7310000000000001 1.7315 1.732 1.7324999999999999 1.7330000000000001 1.7335 1.734 1.7344999999999999 1.7350000000000001 1.7355 1.736 1.7364999999999999 1.7370000000000001 1.7375 1.738 1.7384999999999999 1.7390000000000001 1.7395 1.74 1.7404999999999999 1.7410000000000001 1.7415 1.742 1.7424999999999999 1.7430000000000001 1.7435 1.744 1.7444999999999999 1.7450000000000001 1.7455000000000001 1.746 1.7464999999999999 1.7470000000000001 1.7475000000000001 1.748 1.7484999999999999 1.7490000000000001 1.7495000000000001 1.75 1.7504999999999999 1.7509999999999999 1.7515000000000001 1.752 1.7524999999999999 1.7529999999999999 1.7535000000000001 1.754 1.7544999999999999 1.7549999999999999 1.7555000000000001 1.756 1.7565 1.7569999999999999 1.7575000000000001 1.758 1.7585 1.7589999999999999 1.7595000000000001 1.76 1.7605 1.7609999999999999 1.7615000000000001 1.762 1.7625 1.7629999999999999 1.7635000000000001 1.764 1.7645 1.7649999999999999 1.7655000000000001 1.766 1.7665 1.7669999999999999 1.7675000000000001 1.768 1.7685 1.7689999999999999 1.7695000000000001 1.77 1.7705 1.7709999999999999 1.7715000000000001 1.772 1.7725 1.7729999999999999 1.7735000000000001 1.774 1.7745 1.7749999999999999 1.7755000000000001 1.776 1.7765 1.7769999999999999 1.7775000000000001 1.778 1.7785 1.7789999999999999 1.7795000000000001 1.78 1.7805 1.7809999999999999 1.7815000000000001 1.782 1.7825 1.7829999999999999 1.7835000000000001 1.784 1.7845 1.7849999999999999 1.7855000000000001 1.786 1.7865 1.7869999999999999 1.7875000000000001 1.788 1.7885 1.7889999999999999 1.7895000000000001 1.79 1.7905 1.7909999999999999 1.7915000000000001 1.792 1.7925 1.7929999999999999 1.7935000000000001 1.794 1.7945 1.7949999999999999 1.7955000000000001 1.796 1.7965 1.7969999999999999 1.7975000000000001 1.798 1.7985 1.7989999999999999 1.7995000000000001 1.8 1.8005 1.8009999999999999 1.8015000000000001 1.802 1.8025 1.8029999999999999 1.8035000000000001 1.804 1.8045 1.8049999999999999 1.8055000000000001 1.806 1.8065 1.8069999999999999 1.8075000000000001 1.8080000000000001 1.8085 1.8089999999999999 1.8095000000000001 1.81 1.8105 1.8109999999999999 1.8115000000000001 1.8120000000000001 1.8125 1.8129999999999999 1.8134999999999999 1.8140000000000001 1.8145 1.8149999999999999 1.8154999999999999 1.8160000000000001 1.8165 1.8169999999999999 1.8174999999999999 1.8180000000000001 1.8185 1.819 1.8194999999999999 1.82 1.8205 1.821 1.8214999999999999 1.8220000000000001 1.8225 1.823 1.8234999999999999 1.8240000000000001 1.8245 1.825 1.8254999999999999 1.8260000000000001 1.8265 1.827 1.8274999999999999 1.8280000000000001 1.8285 1.829 1.8294999999999999 1.83 1.8305 1.831 1.8314999999999999 1.8320000000000001 1.8325 1.833 1.8334999999999999 1.8340000000000001 1.8345 1.835 1.8354999999999999 1.8360000000000001 1.8365 1.837 1.8374999999999999 1.8380000000000001 1.8385 1.839 1.8394999999999999 1.84 1.8405 1.841 1.8414999999999999 1.8420000000000001 1.8425 1.843 1.8434999999999999 1.8440000000000001 1.8445 1.845 1.8454999999999999 1.8460000000000001 1.8465 1.847 1.8474999999999999 1.8480000000000001 1.8485 1.849 1.8494999999999999 1.85 1.8505 1.851 1.8514999999999999 1.8520000000000001 1.8525 1.853 1.8534999999999999 1.8540000000000001 1.8545 1.855 1.8554999999999999 1.8560000000000001 1.8565 1.857 1.8574999999999999 1.8580000000000001 1.8585 1.859 1.8594999999999999 1.86 1.8605 1.861 1.8614999999999999 1.8620000000000001 1.8625 1.863 1.8634999999999999 1.8640000000000001 1.8645 1.865 1.8654999999999999 1.8660000000000001 1.8665 1.867 1.8674999999999999 1.8680000000000001 1.8685 1.869 1.8694999999999999 1.87 1.8705000000000001 1.871 1.8714999999999999 1.8720000000000001 1.8725000000000001 1.873 1.8734999999999999 1.8740000000000001 1.8745000000000001 1.875 1.8754999999999999 1.8759999999999999 1.8765000000000001 1.877 1.8774999999999999 1.8779999999999999 1.8785000000000001 1.879 1.8794999999999999 1.88 1.8805000000000001 1.881 1.8815 1.8819999999999999 1.8825000000000001 1.883 1.8835 1.8839999999999999 1.8845000000000001 1.885 1.8855 1.8859999999999999 1.8865000000000001 1.887 1.8875 1.8879999999999999 1.8885000000000001 1.889 1.8895 1.89 1.8905000000000001 1.891 1.8915 1.8919999999999999 1.8925000000000001 1.893 1.8935 1.8939999999999999 1.8945000000000001 1.895 1.8955 1.8959999999999999 1.8965000000000001 1.897 1.8975 1.8979999999999999 1.8985000000000001 1.899 1.8995 1.9 1.9005000000000001 1.901 1.9015 1.9019999999999999 1.9025000000000001 1.903 1.9035 1.9039999999999999 1.9045000000000001 1.905 1.9055 1.9059999999999999 1.9065000000000001 1.907 1.9075 1.9079999999999999 1.9085000000000001 1.909 1.9095 1.91 1.9105000000000001 1.911 1.9115 1.9119999999999999 1.9125000000000001 1.913 1.9135 1.9139999999999999 1.9145000000000001 1.915 1.9155 1.9159999999999999 1.9165000000000001 1.917 1.9175 1.9179999999999999 1.9185000000000001 1.919 1.9195 1.92 1.9205000000000001 1.921 1.9215 1.9219999999999999 1.9225000000000001 1.923 1.9235 1.9239999999999999 1.9245000000000001 1.925 1.9255 1.9259999999999999 1.9265000000000001 1.927 1.9275 1.9279999999999999 1.9285000000000001 1.929 1.9295 1.93 1.9305000000000001 1.931 1.9315 1.9319999999999999 1.9325000000000001 1.9330000000000001 1.9335 1.9339999999999999 1.9345000000000001 1.9350000000000001 1.9355 1.9359999999999999 1.9365000000000001 1.9370000000000001 1.9375 1.9379999999999999 1.9384999999999999 1.9390000000000001 1.9395 1.94 1.9404999999999999 1.9410000000000001 1.9415 1.9419999999999999 1.9424999999999999 1.9430000000000001 1.9435 1.944 1.9444999999999999 1.9450000000000001 1.9455 1.946 1.9464999999999999 1.9470000000000001 1.9475 1.948 1.948499999999999 9 1.9490000000000001 1.9495 1.95 1.9504999999999999 1.9510000000000001 1.9515 1.952 1.9524999999999999 1.9530000000000001 1.9535 1.954 1.9544999999999999 1.9550000000000001 1.9555 1.956 1.9564999999999999 1.9570000000000001 1.9575 1.958 1.9584999999999999 1.9590000000000001 1.9595 1.96 1.9604999999999999 1.9610000000000001 1.9615 1.962 1.9624999999999999 1.9630000000000001 1.9635 1.964 1.9644999999999999 1.9650000000000001 1.9655 1.966 1.9664999999999999 1.9670000000000001 1.9675 1.968 1.9684999999999999 1.9690000000000001 1.9695 1.97 1.970499999 9999999 1.9710000000000001 1.9715 1.972 1.9724999999999999 1.9730000000000001 1.9735 1.974 1.9744999999999999 1.9750000000000001 1.9755 1.976 1.9764999999999999 1.9770000000000001 1.9775 1.978 1.9784999999999999 1.9790000000000001 1.9795 1.98 1.9804999999999999 1.9810000000000001 1.9815 1.982 1.9824999999999999 1.9830000000000001 1.9835 1.984 1.9844999999999999 1.9850000000000001 1.9855 1.986 1.9864999999999999 1.9870000000000001 1.9875 1.988 1.9884999999999999 1.9890000000000001 1.9895 1.99 1.9904999999999999 1.9910000000000001 1.9915 1.992 1.99 24999999999999 1.9930000000000001 1.9935 1.994 1.9944999999999999 1.9950000000000001 1.9955000000000001 1.996 1.9964999999999999 1.9970000000000001 1.9975000000000001 1.998 1.9984999999999999 1.9990000000000001 1.9995000000000001 2 -9.06 -9 -8.92 -8.84 -8.77 -8.7200000000000006 -8.65 -8.57 -8.48 -8.3800000000000008 -8.31 -8.27 -8.24 -8.19 -8.14 -8.07 -7.98 -7.86 -7.69 -7.52 -7.35 -7.16 -6.99 -6.85 -6.72 -6.5 -6.37 -6.26 -6.16 -6.03 -5.92 -5.82 -5.73 -5.67 -5.6 -5.51 -5.42 -5.35 -5.27 -5.23 -5.15 -5.08 -5 -4.93 -4.8600000000000003 -4.87 -4.8899999999999997 -4.84 -4.7699999999999996 -4.6500000000000004 -4.59 -4.51 -4.38 -4.2699999999999996 -4.18 -4.1100000000000003 -4.0599999999999996 -3.98 -3.89 -3.83 -3.76 -3.71 -3.69 -3.63 -3.6 -3.6 -3.57 -3.51 -3.54 -3.54 -3.45 -3.43 -3.4 -3.35 -3.27 -3.2 -3.09 -3.04 -2.96 -2.88 -2.79 -2.7 -2.57 -2.52 -2.46 -2.4 -2.31 -2.23 -2.15 -2.09 -2.06 -2.0299999999999998 -2.02 -1.99 -1.97 -1.93 -1.86 -1.79 -1.71 -1.64 -1.57 -1.52 -1.47 -1.47 -1.44 -1.45 -1.42 -1.37 -1.34 -1.29 -1.23 -1.1499999999999999 -1.0900000000000001 -1.04 -1.04 -1.01 -1.01 -0.98 -0.98 -1 -1 -0.95 -0.9 -0.84 -0.81 -0.81 -0.79 -0.79 -0.76 -0.73 -0.74 -0.76 -0.71 -0.62 -0.52 -0.47 -0.41 -0.34 -0.27 -0.22 -0.15 -0.1 -0.06 0.01 0.13 0.2 0.23 0.3 0.38 0.49 0.52 0.53 0.53 0.6 0.72 0.82 0.91 0.97 1.04 1.1299999999999999 1.24 1.3 1.32 1.34 1.37 1.44 1.52 1.61 1.67 1.72 1.75 1.81 1.87 1.91 1.96 2 2.0299999999999998 2.0699999999999998 2.14 2.16 2.17 2.23 2.2799999999999998 2.2799999999999998 2.33 2.38 2.44 2.5 2.5299999999999998 2.54 2.6 2.65 2.69 2.79 2.81 2.84 2.9 2.95 3.02 3.05 3.13 3.17 3.24 3.32 3.41 3.4 3.34 3.31 3.35 3.4 3.44 3.43 3.43 3.46 3.51 3.56 3.61 3.61 3.65 3.66 3.67 3.66 3.69 3.73 3.75 3.76 3.79 3.77 3.75 3.8 3.84 3.83 3.84 3.88 3.89 3.9 3.9 3.95 4.01 4.04 4.0199999999999996 4.0199999999999996 4.0599999999999996 4.07 4.08 4.1100000000000003 4.12 4.0599999999999996 4.09 4.1399999999999997 4.17 4.21 4.21 4.1900000000000004 4.1900000000000004 4.2 4.1500000000000004 4.1500000000000004 4.17 4.16 4.18 4.2300000000000004 4.25 4.26 4.2300000000000004 4.18 4.16 4.1900000000000004 4.26 4.2699999999999996 4.24 4.22 4.21 4.22 4.18 4.17 4.2300000000000004 4.21 4.2 4.2 4.1900000000000004 4.1900000000000004 4.18 4.16 4.0999999999999996 4.0999999999999996 4.12 4.0999999999999996 4.0999999999999996 4.1399999999999997 4.1500000000000004 4.16 4.16 4.1500000000000004 4.16 4.16 4.1500000000000004 4.13 4.1500000000000004 4.1100000000000003 4.0999999999999996 4.13 4.18 4.2 4.2300000000000004 4.25 4.24 4.2 4.21 4.1900000000000004 4.21 4.2 4.2300000000000004 4.29 4.3 4.34 4.41 4.41 4.38 4.33 4.3 4.3099999999999996 4.33 4.4000000000000004 4.49 4.4800000000000004 4.4400000000000004 4.45 4.46 4.38 4.32 4.3099999999999996 4.26 4.24 4.22 4.2300000000000004 4.1900000000000004 4.21 4.2300000000000004 4.21 4.18 4.12 4.07 4.0599999999999996 4.0599999999999996 4.07 4.03 3.95 3.88 3.87 3.87 3.86 3.85 3.8 3.77 3.76 3.66 3.54 3.44 3.37 3.27 3.26 3.21 3.15 3.16 3.21 3.23 3.25 3.26 3.29 3.33 3.32 3.32 3.31 3.31 3.29 3.27 3.18 3.08 3.05 3.03 2.98 2.92 2.88 2.82 2.82 2.89 2.87 2.82 2.82 2.8 2.81 2.78 2.71 2.63 2.6 2.54 2.48 2.48 2.44 2.35 2.2799999999999998 2.23 2.17 2.08 1.98 2 2.0299999999999998 2.0499999999999998 2.0299999999999998 2.02 1.95 1.91 1.9 1.86 1.83 1.75 1.7 1.58 1.5 1.46 1.39 1.35 1.25 1.2 1.1299999999999999 1.08 1.06 1.03 0.95 0.92 0.92 0.95 0.92 0.9 0.82 0.73 0.69 0.64 0.57999999999999996 0.49 0.44 0.38 0.32 0.25 0.16 0.08 0.01 -0.06 -0.13 -0.19 -0.25 -0.33 -0.41 -0.45 -0.47 -0.53 -0.61 -0.67 -0.72 -0.77 -0.83 -0.89 -0.95 -1.07 -1.1399999999999999 -1.18 -1.2 -1.29 -1.32 -1.37 -1.41 -1.52 -1.61 -1.66 -1.72 -1.77 -1.81 -1.9 -2.04 -2.13 -2.2000000000000002 -2.2400000000000002 -2.2799999999999998 -2.37 -2.4300000000000002 -2.5299999999999998 -2.62 -2.72 -2.83 -2.95 -3.03 -3.13 -3.17 -3.24 -3.28 -3.34 -3.49 -3.62 -3.69 -3.76 -3.84 -3.92 -3.96 -3.95 -3.94 -4.03 -4.0599999999999996 -4.08 -4.2300000000000004 -4.33 -4.37 -4.41 -4.5 -4.63 -4.71 -4.72 -4.8099999999999996 -4.97 -5.05 -5.12 -5.15 -5.15 -5.13 -5.17 -5.22 -5.3 -5.41 -5.52 -5.55 -5.65 -5.72 -5.82 -5.85 -5.93 -5.96 -6.06 -6.13 -6.23 -6.26 -6.34 -6.34 -6.35 -6.38 -6.47 -6.58 -6.6 -6.67 -6.74 -6.78 -6.83 -6.95 -7.03 -7.03 -7.07 -7.07 -7.1 -7.12 -7.2 -7.22 -7.28 -7.36 -7.4 -7.43 -7.48 -7.5 -7.57 -7.56 -7.54 -7.6 -7.67 -7.69 -7.78 -7.83 -7.87 -7.92 -7.94 -8.0399999999999991 -8.06 -8.0299999999999994 -8.02 -8.1199999999999992 -8.19 -8.2899999999999991 -8.3000000000000007 -8.34 -8.44 -8.4700000000000006 -8.52 -8.4600000000000009 -8.5 -8.49 -8.57 -8.6 -8.58 -8.6 -8.67 -8.7200000000000006 -8.7899999999999991 -8.83 -8.8699999999999992 -8.93 -8.9700000000000006 -9.01 -9.06 -9.0399999999999991 -9.0299999999999994 -9.1199999999999992 -9.18 -9.27 -9.49 -9.6999999999999993 -10 -10.37 -10.77 -10.98 -11.03 -10.97 -10.88 -10.85 -10.82 -10.79 -10.82 -10.75 -10.58 -10.5 -10.36 -10.17 -10.09 -9.9499999999999993 -9.75 -9.6199999999999992 -9.4499999999999993 -9.2100000000000009 -9.09 -8.93 -8.89 -8.77 -8.69 -8.64 -8.61 -8.61 -8.4700000000000006 -8.31 -8.25 -8.16 -8.11 -8.1 -8.08 -8.0500000000000007 -7.97 -7.91 -7.86 -7.84 -7.76 -7.71 -7.7 -7.66 -7.65 -7.7 -7.7 -7.6 -7.49 -7.52 -7.46 -7.41 -7.37 -7.34 -7.26 -7.2 -7.16 -7.14 -7.07 -7.04 -6.97 -6.95 -6.9 -6.82 -6.8 -6.74 -6.67 -6.65 -6.59 -6.47 -6.34 -6.35 -6.33 -6.28 -6.23 -6.18 -6.13 -6.08 -6.05 -6.03 -5.95 -5.89 -5.85 -5.83 -5.76 -5.71 -5.72 -5.73 -5.71 -5.71 -5.83 -5.92 -5.93 -5.93 -5.9 -5.84 -5.78 -5.79 -5.72 -5.65 -5.57 -5.54 -5.47 -5.41 -5.27 -5.29 -5.31 -5.29 -5.27 -5.29 -5.31 -5.21 -5.26 -5.26 -5.26 -5.2 -5.19 -5.18 -5.2 -5.0999999999999996 -5.0599999999999996 -5.0999999999999996 -5.09 -5.0599999999999996 -5.07 -5.05 -5.05 -5.01 -4.9400000000000004 -4.93 -4.93 -4.9800000000000004 -4.96 -4.93 -4.9000000000000004 -4.93 -4.97 -4.9000000000000004 -4.92 -4.9000000000000004 -4.88 -4.9000000000000004 -4.9000000000000004 -4.8499999999999996 -4.84 -4.8099999999999996 -4.7699999999999996 -4.72 -4.67 -4.5999999999999996 -4.62 -4.68 -4.71 -4.7699999999999996 -4.8 -4.8899999999999997 -4.8499999999999996 -4.84 -4.8899999999999997 -4.7699999999999996 -4.74 -4.7 -4.67 -4.66 -4.71 -4.74 -4.8 -4.84 -4.9400000000000004 -4.9800000000000004 -5.01 -4.93 -4.91 -4.76 -4.68 -4.63 -4.6100000000000003 -4.5999999999999996 -4.55 -4.54 -4.51 -4.46 -4.4000000000000004 -4.42 -4.4800000000000004 -4.45 -4.3600000000000003 -4.37 -4.34 -4.26 -4.33 -4.3499999999999996 -4.3499999999999996 -4.3 -4.33 -4.3899999999999997 -4.3600000000000003 -4.2699999999999996 -4.29 -4.29 -4.29 -4.2300000000000004 -4.1900000000000004 -4.2 -4.18 -4.1399999999999997 -4.1100000000000003 -4.07 -4.07 -4.12 -4.12 -4.1100000000000003 -4.12 -4.0999999999999996 -4.0599999999999996 -4.03 -3.98 -3.91 -3.91 -3. 89 -3.87 -3.88 -3.85 -3.82 -3.87 -3.82 -3.81 -3.71 -3.74 -3.68 -3.69 -3.63 -3.67 -3.57 -3.59 -3.6 -3.61 -3.59 -3.55 -3.49 -3.5 -3.51 -3.46 -3.45 -3.38 -3.36 -3.4 -3.44 -3.35 -3.29 -3.26 -3.26 -3.32 -3.33 -3.34 -3.29 -3.28 -3.23 -3.21 -3.16 -3.15 -3.1 -3.1 -3.09 -3.09 -3.15 -3.16 -3.13 -3.1 -3.07 -3.04 -3.02 -3.03 -2.98 -2.97 -2.9 -2.87 -2.86 -2.91 -2.87 -2.84 -2.86 -2.87 -2.9 -2.82 -2.8 -2.85 -2.86 -2.85 -2.85 -2.8 -2.8 -2.92 -2.99 -2.99 -2.97 -2.99 -2.98 -2.99 -3.05 -3.06 -3.03 -3 -2.94 -2.83 -2.8 -2.87 -2.91 -2.89 -2.94 -2.95 -2.97 -3.07 -3.06 -3.06 -3.04 -3.11 -3.07 -3.13 -3.17 -3.17 -3.16 -3.16 -3.11 -3.09 -3.11 -3.13 -3.2 -3.22 -3.28 -3.36 -3.37 -3.37 -3.4 -3.44 -3.46 -3.5 -3.45 -3.51 -3.55 -3.56 -3.58 -3.7 -3.74 -3.8 -3.84 -3.77 -3.75 -3.81 -3.84 -3.88 -3.91 -3.9 -3.97 -3.93 -4 -4.08 -4.16 -4.18 -4.17 -4.2 -4.2 -4.2300000000000004 -4.26 -4.32 -4.3099999999999996 -4.25 -4.3099999999999996 -4.3 -4.32 -4.32 -4.34 -4.4400000000000004 -4.42 -4.41 -4.43 -4.4400000000000004 -4.47 -4.4400000000000004 -4.3899999999999997 -4.4000000000000004 -4.51 -4.53 -4.49 -4.38 -4.3600000000000003 -4.42 -4.4400000000000004 -4.47 -4.5599999999999996 -4.5199999999999996 -4.54 -4.4800000000000004 -4.53 -4.54 -4.54 -4.5599999999999996 -4.5599999999999996 -4.5199999999999996 -4.46 -4.43 -4.43 -4.4800000000000004 -4.42 -4.41 -4.38 -4.29 -4.17 -4.1399999999999997 -4.16 -4.04 -4 -4.0199999999999996 -4 -3.9 -3.76 -3.67 -3.63 -3.59 -3.49 -3.37 -3.32 -3.28 -3.21 -3.15 -3.02 -2.93 -2.89 -2.85 -2.76 -2.62 -2.52 -2.4500000000000002 -2.34 -2.2799999999999998 -2.19 -2.09 -1.99 -2 -1.88 -1.71 -1.56 -1.45 -1.39 -1.31 -1.33 -1.28 -1.29 -1.21 -1.1599999999999999 -1.1000000000000001 -1.1000000000000001 -1.07 -1.0900000000000001 -1.0900000000000001 -1.08 -1.1100000000000001 -1.21 -1.17 -1.1000000000000001 -1.17 -1.17 -1.18 -1.18 -1.29 -1.32 -1.31 -1.31 -1.34 -1.36 -1.4 -1.45 -1.58 -1.67 -1.71 -1.81 -1.89 -1.96 -1.94 -2.0299999999999998 -2.08 -2.15 -2.27 -2.36 -2.46 -2.48 -2.4700000000000002 -2.4700000000000002 -2.52 -2.57 -2.61 -2.68 -2.7 -2.72 -2.77 -2.83 -2.76 -2.73 -2.74 -2.82 -2.85 -2.88 -2.85 -2.85 -2.81 -2.8 -2.82 -2.79 -2.69 -2.74 -2.7 -2.62 -2.68 -2.72 -2.69 -2.66 -2.64 -2.6 -2.5 -2.4900000000000002 -2.5299999 999999998 -2.44 -2.36 -2.34 -2.36 -2.31 -2.2599999999999998 -2.1800000000000002 -2.2000000000000002 -2.16 -2.2200000000000002 -2.23 -2.19 -2.09 -2.0299999999999998 -1.98 -1.98 -1.93 -1.86 -1.83 -1.83 -1.85 -1.78 -1.7 -1.74 -1.73 -1.63 -1.58 -1.53 -1.41 -1.41 -1.33 -1.3 -1.27 -1.23 -1.23 -1.21 -1.21 -1.1499999999999999 -1.05 -0.96 -0.98 -0.91 -0.87 -0.86 -0.84 -0.82 -0.78 -0.8 -0. 79 -0.73 -0.68 -0.61 -0.66 -0.64 -0.55000000000000004 -0.5 -0.48 -0.56000000000000005 -0.51 -0.48 -0.46 -0.45 -0.43 -0.37 -0.33 -0.28000000000000003 -0.25 -0.24 -0.23 -0.22 -0.19 -0.11 -0.13 -7.0000000000000007E-2 -0.06 -0.13 -0.12 -0.02 -7.0000000000000007E-2 -0.01 0.02 0.03 0.04 0.06 0.1 0.08 0.09 0.16 0.21 0.19 0.18 0.19 0.18 0.16 0.2 0.22 0.22 0.22 0.18 0.17 0.17 0.18 0.21 0.24 0.18 0.1 0.11 0.18 7.0000000000000007E-2 7.0000000000000007E-2 0.08 0.1 0.14000000000000001 0.23 0.24 0.15 0.11 0.09 0.12 0.14000000000000001 0.14000000000000001 0.11 0.15 0.14000000000000001 0.08 0.12 0.08 0.09 0.06 0.05 0.06 0.06 7.0000000000000007E-2 0.08 0.08 0.06 0.02 0.08 -0.02 -0.09 -0.08 -0.11 -0.14000000000000001 -0.19 -0.12 -0.17 -0.12 -7.0000000000000007E-2 -0.01 0.04 0.11 0.08 0.12 0.1 0.18 0.24 0.24 0.28000000000000003 0.31 0.35 0.31 0.27 0.3 0.32 0.33 0.34 0.36 0.41 0.41 0.39 0.41 0.4 0.42 0.45 0.56999999999999995 0.62 0.6 0.51 0.48 0.47 0.45 0.51 0.59 0.54 0.52 0.55000000000000004 0.61 0.59 0.66 0.69 0.66 0.57999999999999996 0.57999999999999996 0.64 0.62 0.69 0.72 0.73 0.73 0.7 0.62 0.62 0.69 0.66 0.7 0.64 0.61 0.61 0.62 0.62 0.62 0.62 0.69 0.62 0.62 0.6 0.62 0.59 0.57999999999999996 0.56999999999999995 0.52 0.49 0.46 0.57999999999999996 0.56999999999999995 0.6 0.63 0.66 0.62 0.56000000000000005 0.55000000000000004 0.55000000000000004 0.56999999999999995 0.63 0.67 0.62 0.65 0.69 0.62 0.53 0.61 0.64 0.61 0.6 0.61 0.65 0.62 0.57999999999999996 0.52 0.57999999999999996 0.61 0.59 0.53 0.56000000000000005 0.51 0.51 0.56999999999999995 0.52 0.49 0.44 0.3 0.24 0.19 0.18 0.18 0.17 0.09 -0.01 -0.04 -0.04 -0.04 -0.05 -0.09 -0.11 -0.1 -0.11 -0.13 -0.22 -0.25 -0.25 -0.27 -0.31 -0.32 -0.32 -0.31 -0.3 -0.27 -0.31 -0.36 -0.36 -0.32 -0.3 -0.28999999999999998 -0.28999999999999998 -0.28999999999999998 -0.28999999999999998 -0.28000000000000003 -0.28000000000000003 -0.3 -0.34 -0.35 -0.34 -0.3 -0.31 -0.3 -0.33 -0.34 -0.33 -0.32 -0.28999999999999998 -0.31 -0.32 -0.31 -0.28000000000000003 -0.3 -0.3 -0.27 -0.28000000000000003 -0.26 -0.28000000000000003 -0.26 -0.28999999999999998 -0.34 -0.42 -0.42 -0.36 -0.39 -0.32 -0.28999999999999998 -0.27 -0.22 -0.21 -0.22 -0.24 -0.19 -0.1 -0.04 -0.12 -0.12 -0.13 -0.17 -0.16 -0.11 -0.06 0.03 0.03 -0.02 0.03 0.03 -0.02 0.04 7.0000000000000007E-2 0.08 0.08 0.08 0.08 0.09 0.09 0.08 0.05 -0.03 -0.03 0.06 0.09 0.1 0.1 0.1 0.1 0.11 0.12 0.17 0.19 0.19 0.19 0.18 0.15 0.18 0.19 0.18 0.16 0.22 0.28000000000000003 0.18 0.15 0.14000000000000001 0.06 0.1 0.1 0.04 0.1 0.13 0.14000000000000001 0.14000000000000001 0.14000000000000001 0.16 0.24 0.31 0.26 0.26 0.32 0.24 0.19 0.22 0.23 0.22 0.17 0.16 0.2 0.28999999999999998 0.22 0.23 0.22 0.2 0.23 0.24 0.23 0.21 0.26 0.34 0.28000000000000003 0.25 0.23 0.19 0.19 0.24 0.25 0.25 0.24 0.21 0.24 0.26 0.24 0.16 0.06 0.03 0.06 0.17 0.24 0.25 0.22 0.24 0.2 0.16 0.09 0.11 0.05 0.11 0.1 0.16 0.16 0.1 0.13 0.06 0.02 -0.01 0.02 0.03 0.02 -0.01 0.01 -0.01 0.03 0.04 0.02 -0.04 -0.1 -0.1 -0.06 -0.04 -0.03 -0.03 -0.03 -0.03 -0.03 -0.03 -0.03 -0.03 -0.03 -0.03 -0.03 -0.05 -0.09 -0.09 -7.0000000000000007E-2 -0.1 -0.11 -0.11 -0.11 -0.11 -0.14000000000000001 -0.23 -0.23 -0.18 -0.24 -0.26 -0.27 -0.28999999999999998 -0.36 -0.43 -0.36 -0.31 -0.37 -0.48 -0.55000000000000004 -0.54 -0.55000000000000004 -0.52 -0.51 -0.51 -0.52 -0.55000000000000004 -0.52 -0.53 -0.56999999999999995 -0.56999999999999995 -0.54 -0.57999999999999996 -0.61 -0.54 -0.51 -0.52 -0.56999999999999995 -0.56999999999999995 -0.54 -0.55000000000000004 -0.52 -0.5 -0.48 -0.41 -0.44 -0.41 -0.47 -0.47 -0.38 -0.34 -0.3 -0.33 -0.33 -0.31 -0.36 -0.42 -0.32 -0.28000000000000003 -0.27 -0.27 -0.28999999999999998 -0.33 -0.35 -0.35 -0.34 -0.28999999999999998 -0.27 -0.27 -0.28999999999999998 -0.33 -0.34 -0.31 -0.34 -0.35 -0.34 -0.3 -0.28000000000000003 -0.28000000000000003 -0.27 -0.25 -0.19 -0.24 -0.24 -0.19 -0.25 -0.28000000000000003 -0.28000000000000003 -0.28000000000000003 -0.28000000000000003 -0.28999999999999998 -0.28999999999999998 -0.28999999999999998 -0.28999999999999998 -0.28000000000000003 -0.26 -0.2 -0.22 -0.14000000000000001 -0.09 -0.15 -0.22 -0.17 -0.14000000000000001 -0.13 -0.13 -0.12 -0.09 -0.1 -7.0000000000000007E-2 -0.06 -0.08 -0.12 -0.12 -0.1 -0.11 -0.09 -0.11 -0.1 -0.16 -0.23 -0.16 -0.11 -0.12 -0.1 -0.14000000000000001 -0.18 -0.24 -0.19 -0.16 -0.15 -0.14000000000000001 -0.11 -0.14000000000000001 -0.14000000000000001 -0.1 -0.1 -0.15 -0.16 -0.16 -0.13 -7.0000000000000007E-2 -0.12 -0.12 -0.16 -0.17 -0.17 -0.14000000000000001 -7.0000000000000007E-2 -0.1 -0.15 -0.16 -0.12 -0. 12 -0.16 -0.18 -0.17 -0.12 -0.13 -0.17 -0.18 -0.17 -0.13 -0.11 -0.11 -0.11 -0.12 -0.12 -0.13 -0.15 -0.11 -0.2 -0.28999999999999998 -0.27 -0.3 -0.24 -0.21 -0.2 -0.2 -0.32 -0.37 -0.38 -0.38 -0.38 -0.38 -0.35 -0.28999999999999998 -0.35 -0.38 -0.39 -0.39 -0.39 -0.39 -0.4 -0.4 -0.39 -0.37 -0.31 -0.39 -0.44 -0.39 -0.32 -0.38 -0.41 -0.41 -0.42 -0.44 -0.48 -0.48 -0.46 -0.49 -0.49 -0.47 -0.53 -0.63 -0.64 -0.55000000000000004 -0.52 -0.52 -0.56000000000000005 -0.65 -0.68 -0.71 -0.75 -0.77 -0.77 -0.76 -0.73 -0.76 -0.73 -0.65 -0.72 -0.73 -0.76 -0.73 -0.72 -0.73 -0.76 -0.75 -0.77 -0.76 -0.79 -0.8 -0.8 -0.77 -0.78 -0.75 -0.74 -0.74 -0.71 -0.62 -0.59 -0.59 -0.63 -0.7 1 -0.72 -0.67 -0.69 -0.62 -0.56000000000000005 -0.59 -0.6 -0.61 -0.61 -0.61 -0.62 -0.62 -0.62 -0.62 -0.62 -0.63 -0.63 -0.66 -0.72 -0.67 -0.64 -0.64 -0.67 -0.74 -0.71 -0.78 -0.81 -0.83 -0.87 -0.85 -0.88 -0.85 -0.75 -0.8 -0.8 -0.74 -0.77 -0.71 -0.68 -0.68 -0.69 -0.69 -0.67 -0.63 -0.63 -0.66 -0.64 -0.62 -0.62 -0.63 -0.63 -0.63 -0.6 -0.51 -0.46 -0.42 -0.4 -0.41 -0.43 -0.47 -0.48 -0.45 -0.47 -0.43 -0.41 -0.37 -0.38 -0.46 -0.45 -0.44 -0.44 -0.43 -0.4 -0.43 -0.45 -0.45 -0.46 -0.46 -0.44 -0.4 -0.41 -0.45 -0.47 -0.46 -0.42 -0.42 -0.48 -0.51 -0.48 -0.54 -0.55000000000000004 -0.51 -0.5 -0.48 -0.46 -0.49 -0.5 -0.49 -0.45 -0.44 -0.46 -0.5 -0.51 -0.47 -0.45 -0.47 -0.5 -0.48 -0.46 -0.46 -0.44 -0.38 -0.44 -0.44 -0.39 -0.42 -0.38 -0.41 -0.32 -0.32 -0.31 -0.28000000000000003 -0.26 -0.26 -0.27 -0.28999999999999998 -0.33 -0.3 -0.21 -0.27 -0.33 -0.3 -0.26 -0.2 -0.23 -0.17 -0.18 -0.24 -0.21 -0.25 -0.19 -0.16 -0.14000000000000001 -0.12 -0.13 -0.1 -0.08 -0.05 -0.06 -0.04 -0.03 -0.03 -0.03 -0.03 -0.03 0 0.08 0.11 0.11 0.11 0.11 0.1 0.11 0.14000000000000001 0.12 0.14000000000000001 0.12 0.15 0.16 0.19 0.28000000000000003 0.31 0.31 0.32 0.36 0.38 0.38 0.39 0.43 0.44 0.45 0.47 0.53 0.47 0.47 0.55000000000000004 0.55000000000000004 0.51 0.59 0.59 0.57999999999999996 0.59 0.65 0.7 0.72 0.7 0.67 0.7 0.73 0.8 0.77 0.83 0.86 0.9 1 0.94 0.88 0.91 0.95 1.03 1.04 0.97 0.99 0.93 0.94 1.03 1.1100000000000001 1.1200000000000001 1.1100000000000001 1.06 1.04 1.05 1.0900000000000001 1.1000000000000001 1.1000000000000001 1.1000000000000001 1.1100000000000001 1.1499999999999999 1.17 1.2 1.29 1.32 1.31 1.28 1.24 1.32 1.31 1.3 1.3 1.34 1.45 1.43 1.46 1.39 1.37 1.38 1.44 1.41 1.47 1.5 1.5 1.5 1.49 1.49 1.48 1.48 1.49 1.52 1.49 1.47 1.46 1.46 1.48 1.53 1.58 1.55 1.53 1.52 1.52 1.5 1.47 1.51 1.57 1.57 1.52 1.51 1.52 1.44 1.41 1.42 1.45 1.43 1.44 1.41 1.41 1.43 1.41 1.4 1.3 1.31 1.24 1.21 1.18 1.1499999999999999 1.1599999999999999 1.1399999999999999 1.1599999999999999 1.1200000000000001 1.1000000000000001 1.06 0.97 0.93 0.92 0.91 0.87 0.88 0.85 0.83 0.83 0.82 0.82 0.82 0.83 0.86 0.87 0.96 0.91 0.86 0.81 0.79 0.8 0.83 0.79 0.76 0.71 0.69 0.7 0.73 0.69 0.68 0.67 0.66 0.63 0.56999999999999995 0.63 0.64 0.62 0.52 0.49 0.47 0.46 0.41 0.41 0.45 0.44 0.36 0.28000000000000003 0.34 0.36 0.37 0.37 0.37 0.24 0.19 0.18 0.18 0.18 0.16 0.12 0.13 0.1 0.08 0.09 0.13 0.13 0.1 0.12 0.12 7.0000000000000007E-2 7.0000000000000007E-2 0.09 7.0000000000000007E-2 0.1 0.11 0.09 0.04 0.02 0 -0.05 -7.0000000000000007E-2 -7.0000000000000007E-2 -0.08 -0.08 -7.0000000000000007E-2 -0.03 -0.01 -0.02 -0.04 -0.12 -0.23 -0.27 -0.24 -0.16 -0.16 -0.25 -0.25 -0.18 -0.18 -0.26 -0.27 -0.23 -0.32 -0.47 -0.57999999999999996 -0.56000000000000005 -0.62 -0.62 -0.56999999999999995 -0.6 -0.57999999999999996 -0.64 -0.64 -0.61 -0.72 -0.76 -0.78 -0.81 -0.88 -0.85 -0.92 -0.95 -0.96 -0.96 -0.93 -0.85 -0.82 -0.86 -0.95 -0.96 -0.91 -0.97 -1 -1.04 -1.1200000000000001 -1.1299999999999999 -1.1499999999999999 -1.1399999999999999 -1.17 -1.2 -1.24 -1.33 -1.37 -1.37 -1.35 -1.29 -1.37 -1.45 -1.48 -1.48 -1.47 -1.48 -1.57 -1.53 -1.51 -1.54 -1.63 -1.64 -1.59 -1.62 -1.57 -1.58 -1.67 -1.72 -1.76 -1.73 -1.74 -1.8 -1.86 -1.85 -1.89 -1.9 -1.92 -1.95 -2.0099999999999998 -1.96 -1.94 -1.97 -2.06 -2.0699999999999998 -2.02 -2.09 -2.13 -2.17 -2.14 -2.11 -2.0499999999999998 -2.12 -2.16 -2.2000000000000002 -2.1800000000000002 -2.1800000000000002 -2.19 -2.2200000000000002 -2.17 -2.12 -2.2000000000000002 -2.1800000000000002 -2.12 -2.2000000000000002 -2.2799999999999998 -2.2999999999999998 -2.31 -2.2999999999999998 -2.2599999999999998 -2.2400000000000002 -2.2200000000000002 -2.13 -2.11 -2.11 -2.11 -2.12 -2.13 -2.13 -2.12 -2.08 -2.0699999999999998 -2.0699999999999998 -2.08 -2.0699999999999998 -2.0299999999999998 -2.02 -2.04 -2.0699999999999998 -2.02 -1.96 -2.0299999999999998 -2.11 -2.12 -2.0499999999999998 -1.95 -1.96 -2.0499999999999998 -2.09 -2.09 -2.0699999999999998 -1.98 -1.96 -1.96 -1.97 -1.97 -1.98 -1.98 -1.97 -1.94 -1.94 -1.99 -2 -1.96 -1.95 -1.96 -1.96 -1.97 -1.98 -2 -2.0499999999999998 -2.06 -2.04 -2.0699999999999998 -2.09 -2.09 -2.06 -2.08 -2.06 -2.0499999999999998 -2.0499999999999998 -2.06 -2.0699999999999998 -2.08 -2.08 -2.06 -2 -2.0299999999999998 -1.96 -1.9 -1.94 -2.0699999999999998 -2.1 -2.06 -2.12 -2.15 -2.13 -2.08 -2.11 -2.04 -1.97 -1.94 -1.92 -1.97 -2.04 -2.0699999999999998 -2.0699999999999998 -2.06 -2.0299999999999998 -2.02 -2.02 -2.0099999999999998 -1.99 -2.0099999999999998 -1.98 -1.95 -1.91 -2.02 -2.0699999999999998 -2.09 -2.08 -2.0499999999999998 -2.0499999999999998 -1.98 -2.08 -2.11 -2.08 -2.09 -2.11 -2.0699999999999998 -2 -2.0699999999999998 -2.09 -2.09 -2.06 -2.19 -2.17 -2.16 -2.08 -2.12 -2.12 -2.0499999999999998 -2.06 -2.15 -2.15 -2.0699999999999998 -2.13 -2.09 -2.0699999999999998 -2.06 -2.04 -2.06 -2.0299999999999998 -2 -1.94 -2.0099999999999998 -2.0499999999999998 -2.08 -2.11 -2.06 -1.96 -1.93 -1.94 -1.98 -2.08 -2.12 -2.1 -2.0499999999999998 -2.12 -2.15 -2.13 -2.0299999999999998 -1.96 -1.95 -1.97 -2.0099999999999998 -1.97 -1.92 -1.91 -1.87 -1.76 -1.76 -1.76 -1.71 -1.66 -1.64 -1.63 -1.59 -1.7 -1.7 -1.59 -1.58 -1.63 -1.59 -1.57 -1.57 -1.58 -1.59 -1.6 -1.59 -1.52 -1.4 -1.35 -1.38 -1.39 -1.34 -1.28 -1.24 -1.1399999999999999 -1.07 -1.08 -1.1200000000000001 -1.1100000000000001 -1.1399999999999999 -1.1100000000000001 -1.1000000000000001 -1.06 -0.94 -0.91 -0.94 -0.92 -0.92 -0.92 -0.92 -0.88 -0.88 -0.88 -0.86 -0.77 -0.73 -0.69 -0.65 -0.56999999999999995 -0.54 -0.53 -0.48 -0.43 -0.44 -0.47 -0.42 -0.38 -0.46 -0.44 -0.34 -0.28000000000000003 -0.3 -0.25 -0.17 -0.08 -0.08 -0.14000000000000001 -0.08 -0.02 -0.01 -0.02 -0.03 0.08 0.12 0.11 0.11 0.11 0.15 0.17 0.21 0.22 0.24 0.33 0.36 0.41 0.46 0.54 0.48 0.53 0.6 0.62 0.64 0.62 0.65 0.69 0.78 0.83 0.8 0.78 0.78 0.82 0.84 0.88 0.92 1 1 0.94 1 1.04 0.98 0.9 0.94 0.98 1.02 1.03 1.02 1.04 1.1299999999999999 1.1599999999999999 1.19 1.1499999999999999 1.1499 999999999999 1.19 1.23 1.19 1.19 1.22 1.23 1.22 1.21 1.2 1.19 1.18 1.1599999999999999 1.1000000000000001 1.06 1 0.98 0.97 0.97 1 0.97 0.98 0.91 0.83 0.87 0.85 0.76 0.72 0.74 0.84 0.89 0.86 0.83 0.79 0.72 0.77 0.81 0.85 0.86 0.85 0.84 0.83 0.84 0.87 0.88 0.88 0.9 0.99 1.01 0.89 0.87 0.94 0.93 0.84 0.8 0.78 0.77 0.77 0.79 0.84 0.77 0.77 0.81 0.74 0.71 0.67 0.62 0.61 0.65 0.69 0.79 0.86 0.87 0.86 0.85 0.83 0.79 0.81 0.81 0.8 0.79 0.87 0.84 0.87 0.79 0.76 0.78 0.88 0.95 0.96 0.94 0.9 0.9 0.85 0.81 0.74 0.79 0.8 0.8 0.81 0.85 0.85 0.85 0.84 0.83 0.82 0.83 0.86 0.85 0.82 0.88 0.97 0.96 0.9 0.95 0.97 0.96 0.96 0.95 0.94 0.95 0.98 0.99 0.99 1.01 1.0900000000000001 1.1100000000000001 1.07 0.98 0.97 1.05 1.0900000000000001 1.1299999999999999 1.1399999999999999 1.1399999999999999 1.1499999999999999 1.1000000000000001 1.1499999999999999 1.1499999999999999 1.1200000000000001 1.1399999999999999 1.1499999999999999 1.1399999999999999 1.1399999999999999 1.1599999999999999 1.24 1.27 1.28 1.3 1.27 1.28 1.24 1.23 1.25 1.22 1.23 1.29 1.27 1.25 1.24 1.23 1.22 1.22 1.22 1.23 1.1599999999999999 1.18 1.23 1.24 1.24 1.27 1.34 1.33 1.24 1.2 1.22 1.3 1.33 1.33 1.33 1.37 1.41 1.5 1.52 1.52 1.51 1.53 1.58 1.55 1.6 1.63 1.65 1.69 1.59 1.56 1.5 1.44 1.45 1.51 1.48 1.44 1.49 1.45 1.4 1.42 1.41 1.38 1.4 1.42 1.45 1.42 1.43 1.39 1.39 1.42 1.43 1.41 1.37 1.39 1.4 1.39 1.39 1.38 1.4 1.45 1.39 1.35 1.34 1.33 1.31 1.31 1.41 1.42 1.37 1.42 1.45 1.48 1.46 1.48 1.49 1.46 1.42 1.44 1.54 1.51 1.52 1.43 1.45 1.51 1.49 1.55 1.57 1.48 1.52 1.53 1.53 1.53 1.53 1.56 1.54 1.56 1.59 1.62 1.62 1.57 1.54 1.53 1.53 1.52 1.51 1.5 1.5 1.51 1.55 1.55 1.55 1.58 1.66 1.65 1.56 1.5 1.46 1.48 1.49 1.49 1.48 1.48 1.5 1.55 1.48 1.45 1.44 1.46 1.5 1.39 1.35 1.39 1.43 1.52 1.54 1.53 1.5 1.43 1.48 1.51 1.5 1.49 1.45 1.36 1.32 1.31 1.28 1.23 1.21 1.2 1.19 1.19 1.18 1.18 1.17 1.1499999999999999 1.1000000000000001 1.08 0.99 1.04 1.1000000000000001 1.1100000000000001 1.07 1.08 1.05 1.06 1.02 1.01 0.99 0.95 0.86 0.87 1 1.06 1.1299999999999999 1.2 1.1399999999999999 1.1000000000000001 1.0900000000000001 1.08 1.08 1.1100000000000001 1.19 1.18 1.0900000000000001 1.03 0.97 0.95 0.96 0.99 1 1.08 1.03 1 1.02 1.05 0.96 0.99 1.05 0.99 0.96 0.97 1.02 0.96 0.93 0.95 1.04 1.08 1.1100000000000001 1.08 1.0900000000000001 1.05 1.03 1.03 1.01 0.98 0.92 0.97 1 1.04 1.02 1.04 1.04 1.04 1.1399999999999999 1.1299999999999999 1 0.96 0.97 0.94 0.94 0.97 0.98 0.99 1.01 1.06 1 0.99 1.04 1.01 1.06 1.06 1 1.04 1.03 0.94 0.88 0.83 0.83 0.9 1 1.02 0.99 0.88 0.81 0.81 0.77 0.75 0.76 0.78 0.75 0.75 0.78 0.79 0.77 0.72 0.7 0.68 0.65 0.57999999999999996 0.6 0.53 0.5 0.47 0.42 0.4 0.39 0.39 0.38 0.37 0.35 0.28999999999999998 0.25 0.17 0.2 0.13 0.09 7.0000000000000007E-2 0.03 0.05 0.05 -0.01 -0.08 -0.22 -0.27 -0.27 -0.25 -0.27 -0.26 -0.32 -0.41 -0.53 -0.57999999999999996 -0.62 -0.6 -0.61 -0.69 -0.77 -0.73 -0.75 -0.87 -0.88 -0.9 -0.94 -0.95 -0.91 -0.94 -1.03 -1.07 -1.1200000000000001 -1.21 -1.22 -1.17 -1.23 -1.29 -1.35 -1.41 -1.44 -1.57 -1.62 -1.63 -1.64 -1.7 -1.84 -1.89 -1.91 -1.93 -1.98 -2.0099999999999998 -2.06 -2.08 -2.21 -2.2799999999999998 -2.34 -2.35 -2.3199999999999998 -2.36 -2.41 -2.48 -2.48 -2.58 -2.6 -2.64 -2.68 -2.73 -2.75 -2.76 -2.77 -2.81 -2.88 -2.85 -2.89 -2.86 -2.91 -2.9 -3.01 -3.06 -3.08 -3.08 -3.09 -3.13 -3.2 -3.17 -3.22 -3.19 -3.26 -3.29 -3.27 -3.19 -3.16 -3.17 -3.17 -3.18 -3.19 -3.18 -3.16 -3.2 -3.25 -3.32 -3.26 -3.24 -3.24 -3.23 -3.2 -3.19 -3.2 -3.2 -3.17 -3.09 -3.05 -3.02 -3.04 -3.02 -3.03 -3.07 -3.04 -3.02 -2.94 -2.85 -2.82 -2.8 -2.77 -2.76 -2.76 -2.74 -2.65 -2.61 -2.57 -2.56 -2.5499999999999998 -2.46 -2.3199999999999998 -2.29 -2.3199999999999998 -2.27 -2.17 -2.14 -2.11 -2.0299999999999998 -2 -1.96 -1.83 -1.79 -1.78 -1.73 -1.68 -1.57 -1.55 -1.49 -1.38 -1.29 -1.23 -1.19 -1.1100000000000001 -1.07 -1.02 -0.96 -0.82 -0.75 -0.76 -0.71 -0.64 -0.67 -0.62 -0.61 -0.64 -0.7 -0.65 -0.63 -0.64 -0.64 -0.65 -0.64 -0.6 -0.56999999999999995 -0.51 -0.57999999999999996 -0.63 -0.68 -0.67 -0.71 -0.73 -0.72 -0.7 -0.74 -0.79 -0.87 -0.85 -0.92 -0.96 -0.98 -1.02 -1 -1.01 -1.04 -1.04 -1.0900000000000001 -1.1299999999999999 -1.08 -1.1100000000000001 -1.1200000000000001 -1.1299999999999999 -1.1499999999999999 -1.17 -1.22 -1.23 -1.21 -1.25 -1.25 -1.2 -1.17 -1.2 -1.22 -1.24 -1.25 -1.27 -1.31 -1.28 -1.26 -1.24 -1.26 -1.25 -1.27 -1.22 -1.1599999999999999 -1.24 -1.31 -1.29 -1.25 -1.1499999999999999 -1.1000000000000001 -1.1299999999999999 -1.1499999999999999 -1.17 -1.17 -1.17 -1.1299999999999999 -1.0900000000000001 -1 -0.98 -0.98 -0.98 -0.96 -0.98 -0.97 -1.01 -1.02 -0.99 -0.99 -1.03 -0.99 -0.96 -0.99 -1 -0.97 -0.95 -0.93 -0.85 -0.82 -0.81 -0.79 -0.81 -0.79 -0.79 -0.8 -0.82 -0.88 -0.9 -0.89 -0.85 -0.83 -0.79 -0.8 -0.84 -0.81 -0.78 -0.69 -0.66 -0.63 -0.67 -0.68 -0.66 -0.68 -0.67 -0.69 -0.64 -0.57999999999999996 -0.61 -0.56000000000000005 -0.56999999999999995 -0.64 -0.61 -0.65 -0.59 -0.66 -0.61 -0.56999999999999995 -0.5 -0.54 -0.56999999999999995 -0.51 -0.49 -0.49 -0.47 -0.38 -0.36 -0.37 -0.38 -0.39 -0.39 -0.39 -0.35 -0.36 -0.4 -0.38 -0.37 -0.38 -0.38 -0.36 -0.28000000000000003 -0.26 -0.26 -0.26 -0.24 -0.28000000000000003 -0.3 -0.28999999999999998 -0.24 -0.19 -0.18 -0.18 -0.2 -0.2 -0.16 -0.05 -0.09 -0.17 -0.16 -0.25 -0.33 -0.35 -0.32 -0.22 -0.24 -0.18 -0.17 -0.17 -0.16 -0.09 -0.03 -0.06 0 0.05 0.12 0.09 7.0000000000000007E-2 0.06 0.06 0.09 0.19 0.17 0.19 0.12 0.08 0.06 0.06 0.09 0.18 0.23 0.2 0.18 0.16 0.15 0.17 0.25 0.36 0.34 0.4 0.42 0.41 0.4 0.39 0.39 0.39 0.43 0.44 0.43 0.4 0.37 0.42 0.53 0.59 0.59 0.66 0.71 0.79 0.82 0.83 0.86 0.87 0.87 0.88 0.92 0.8 0.77 0.83 0.93 0.97 1 0.96 0.93 0.89 0.82 0.87 0.9 0.92 0.99 0.97 0.96 0.99 1 1 1.02 1.1200000000000001 1.19 1.18 1.1499999999999999 1.1499999999999999 1.1200000000000001 1.1499999999999999 1.19 1.27 1.31 1.34 1.31 1.34 1.34 1.33 1.33 1.33 1.35 1.33 1.36 1.39 1.45 1.41 1.47 1.5 1.53 1.5 1.54 1.6 1.64 1.72 1.74 1.74 1.73 1.72 1.71 1.72 1.76 1.8 1.85 1.78 1.75 1.78 1.89 1.9 1.93 1.95 1.97 1.94 1.91 1.92 1.96 2 2.08 2.11 2.1 2.11 2.15 2.14 2.08 2.0699999999999998 2.1 2.19 2.14 2.11 2.1 2.09 2.08 2.0699999999999998 2.06 2.06 2.08 2.17 2.2000000000000002 2.23 2.19 2.2000000000000002 2.25 2.2000000000000002 2.21 2.23 2.27 2.27 2.25 2.2000000 000000002 2.19 2.2599999999999998 2.35 2.35 2.25 2.2200000000000002 2.23 2.3199999999999998 2.34 2.34 2.33 2.33 2.33 2.23 2.2400000000000002 2.19 2.2200000000000002 2.1800000000000002 2.23 2.25 2.25 2.2599999999999998 2.2799999999999998 2.2599999999999998 2.2599999999999998 2.2200000000000002 2.2000000000000002 2.19 2.15 2.09 2.15 2.2000000000000002 2.17 2.15 2.14 2.13 2.12 2.11 2.1 2.1 2.09 2.08 2.0699999999999998 2.04 1.98 2.06 2.02 1.95 1.99 1.98 1.89 1.85 1.83 1.82 1.82 1.85 1.93 1.95 1.95 1.94 1.9 1.83 1.86 1.81 1.82 1.7 1.65 1.64 1.63 1.62 1.63 1.67 1.68 1.71 1.75 1.67 1.59 1.56 1.55 1.53 1.49 1.52 1.54 1.58 1.59 1.62 1.66 1.58 1.5 1.49 1.51 1.46 1.4 1.41 1.38 1.4 1.37 1.38 1.34 1. 33 1.35 1.32 1.29 1.26 1.19 1.23 1.23 1.17 1.23 1.28 1.22 1.1399999999999999 1.19 1.21 1.21 1.21 1.24 1.2 1.17 1.1399999999999999 1.0900000000000001 1.1599999999999999 1.1299999999999999 1.05 1.1000000000000001 1.08 1 0.98 1.03 0.96 0.93 0.95 1.01 0.97 0.99 0.9 0.82 0.8 0.8 0.84 0.83 0.8 0.82 0.83 0.81 0.75 0.73 0.68 0.59 0.59 0.68 0.73 0.7 0.65 0.56999999999999995 0.6 0.55000000000000004 0.56000000000000005 0.44 0.38 0.34 0.38 0.41 0.38 0.34 0.25 0.12 0.03 -0.03 -0.1 -0.08 -0.15 -0.18 -0.21 -0.28000000000000003 -0.38 -0.47 -0.45 -0.54 -0.63 -0.7 -0.73 -0.78 -0.89 -0.98 -1.04 -1.1499999999999999 -1.24 -1.28 -1.37 -1.5 -1.59 -1.65 -1.77 -1.87 -1.94 -1.96 -1.98 -2.0299999999999998 -2.17 -2.21 -2.2000000000000002 -2.2599999999999998 -2.35 -2.33 -2.41 -2.4700000000000002 -2.57 -2.6 -2.58 -2.65 -2.76 -2.82 -2.88 -2.91 -2.96 -2.95 -3.02 -3.1 -3.1 -3.22 -3.27 -3.29 -3.33 -3.42 -3.43 -3.35 -3.38 -3.52 -3.57 -3.6 -3.64 -3.6 -3.57 -3.62 -3.68 -3.71 -3.71 -3.72 -3.84 -3.9 -3.91 -3.92 -3.89 -3.81 -3.79 -3.82 -3.88 -3.8 -3.71 -3.73 -3.74 -3.74 -3.72 -3.75 -3.73 -3.61 -3.59 -3.64 -3.54 -3.51 -3.51 -3.51 -3.49 -3.42 -3.41 -3.44 -3.28 -3.18 -3.28 -3.28 -3.17 -3.16 -3.22 -3.15 -3.07 -3.01 -2.95 -2.83 -2.8 -2.71 -2.73 -2.66 -2.59 -2.57 -2.5299999999999998 -2.5099999999999998 -2.35 -2.2999999999999998 -2.2599999999999998 -2.16 -2.08 -2.0299999999999998 -2.0099999999999998 -1.99 -1.89 -1.82 -1.77 -1.67 -1.59 -1.53 -1.52 -1.49 -1.38 -1.26 -1.19 -1.07 -1.06 -1 -0.89 -0.82 -0.79 -0.72 -0.62 -0.6 -0.57999999999999996 -0.51 -0.4 -0.33 -0.31 -0.28000000000000003 -0.18 -0.19 -0.12 -0.06 -0.06 -0.1 -0.08 -0.04 0.04 0.09 0.14000000000000001 0.18 0.2 0.32 0.28000000000000003 0.37 0.4 0.42 0.49 0.61 0.71 0.81 0.84 0.85 0.88 0.9 0.93 0.9 0. 93 0.98 1.1000000000000001 1.1399999999999999 1.23 1.2 1.26 1.28 1.29 1.31 1.27 1.27 1.32 1.35 1.3 1.25 1.27 1.28 1.31 1.32 1.44 1.47 1.47 1.46 1.45

[mm]

[um]

Parameters of surface roughness Rz and Rq in um

Rz zinc aluminum chrome 65.989999999999995 8.4499999999999993 0.25 Rq zinc aluminum chrome 18.22 2.7 0.05

Type of Coating

measurement of surface roughness Rz & Ra

i- Engineering services is one of the most important force, which classified under ministry of defense. MODES Cooperated with SAF (Sultan Qaboos armed forces). They are support service directorate of civilian, as well as army, Navy and RAFO due to its several different of engineering sections (example, mechanical, electrical, public health and projects). They are associate of water, electricity, vehicles transport, mechanical and electrical related assistance (example, gas, water, electricity as well as transport). Thus, MODES has established at 1979 as small organization then it starts to develop to become as one of lead organization in the engineering sector, at the beginning the services were provided by contractors but nowadays MODES has its own equipment’s and human resources.

They do have drilling for water and distributed water to the camp. It is as service and support. Also analyzing water quality, to use in standard classification to make sure that all the parapets meets the water regulatory. In addition to that they do maintenance and repair unit for all kind of pumps. According to civilian requirement they do maintain the annual plant maintenance record (example either water production and sewage treatment and electricity). MODES Serving Sultan Qaboos Armed Forces as well as the main responsibility of its customer. Also, whenever the service civilian request for the help and in case of emergency situation such as cyclones.

There is no annual production, but the water treatment plant producing the water as per Oman standard volume of water approx. 3000 M3 per day. Also drilling of new borehole to get water according to the civilian requirement for example, MAM camp B/H NO1 produce 10000 Gallon per hour. in addition to the side of electricity there are gas turbines 46 mw capacity per day.

The Major business on MODES is providing the major living services such as (Electricity, water) for the sultana Qaboos armed forces. Those forces can be provided by neither contracted company or it on human resources and equipment’s.

ii- 1. The first process that I will explain more in detail is Sewage treatment water process which is the process of removing contaminants from wastewater, primarily from household sewage. Sewage treatment water is used for irrigation purpose. This process includes:

· Preliminary process: this process consists of two steps:

1. Screening which is removing the large objects and the suspended matters for example: papers and small pieces of wood that may block and damage the equipment.

2. Grit Chamber is a conically constructed pit in the steam of the sewage input to the sewage plant. The sewage is forced to whirl through two paddles fixed on a shaft that is driven by motor, by the help of both the paddle and the conical shape of the grit chamber when the sewage is whirling the solid materials gather at the bottom center and then the lift pump lifts them along with water and then go to classifier where the separation happens by means of screw shaft mechanism. Sewage water thus separated will be transported for the treatment process.

· Secondary treatment: Sewage composed of 99% water and 1% impurities. However, it contains many types of bacteria. These indigenous water-born micro-organisms are useful for sewage treatment whereas some are harmful to individual general health. The sewage is purified by the beneficial bacteria which digest the pollutant. The sewage become septic once no oxygen left in it. the bacteria then convert the complex organic compound present in the sewage to simpler and more stable compounds resulting in clarifying the water.

Bacteria exists in the sewage can be divided into two categories:

1. Anaerobic bacteria: These bacteria do not need the oxygen to function. These organisms can decompose the sewage in closed air-free tank. These will treat the sewage and remove part of the pollutants and some of the contaminated substances. The effluent from this process still contain significant amount of pollutants and smells badly because of the existence of hydrogen sulphide thus further treatment is required.

2. Aerobic bacteria: In contrast to anaerobic, aerobic bacteria need oxygen (from aeration process) and food which is available in the sewage to live and continue their role removing the contaminated substances from the sewage hence purifying it. this type removes organic matter and convert it to Carbon Dioxide, water and nitrogen and help eliminates the odor. Aerobic bacteria integrate the process of the anaerobic bacteria in clarifying the sewage.

· Final treatment: the water at this step is almost free from harmful substance and chemicals. Then, it will pass through a chlorination step to kill any kind of bacteria where the range of chlorine must be from 3 to 5 ppm. After that, it goes to contact tank where bacteria cells are destruction in 30 minutes. Finally, the filter water is stored in a final tank.

2. The second process is Drilling of borehole which is normally carried out in order to find suitable steady flow of water resource, the procedure for drilling new borehole consist of:

· Site selection: the most important step to ensure uninterrupted production of the borehole drilled. In this step the site selected must not lie near any infrastructure or buried services for example: Electric, Water and Telephone lines.

· Equipment and tools: in this step select the suitable drill bit in relation to the soil formation at that site. We have three types of bits: Teeth, Tricon and Hammering. Usually the Tricon bit is used in the mountainous areas because the formation there is hard, but for soft to medium formation teeth bit is used. Also, the hammering bit is used for the beach formation.

· Method of drilling: there are two methods used for rig(rotary and hammer method), the classification of methods depend on formation example all kind of formation can be drilled by rotary method except beach formation which can be drilled by hammering method.

· Drilling fluids: fluids used while drilling to lubricate the drilling bit , to increase rate of penetration and to prevent borehole from collapse. But selecting the proper fluids for suitable formation is the goal. There are so many types of chemicals to add, but MODES uses three types of chemicals which the formation can control by these chemicals. Foam is the first chemical and fit for soft to medium formation, bentionute is the second chemical and fit for soft- medium and hard formation, final chemical is Easy mud and it is as a treatment for the drilling issue.

· Final process content on drilling activities is casing installation. This process protects the borehole from collapse and maintain the borehole from pollution.

3. The third process I will discuss about is Bacteriological water analysis which is a method of analyzing water to estimate the number of bacteria present. This stage represents one important aspect of water quality. As we know that the presence of bacteria is a concern when considering the safety of drinking water because it can cause intestinal infections, dysentery, typhoid fever and other illnesses. In the laboratory we used IDEXX method because it provides easy, rapid and a very accurate bacterial count. This method is used for the detection of coliforms and E. coil.

So, in order to obtain the right results using this method we have to:

1. First, open snap pack and add reagent to 100 mL of water sample in a sterile vessel.

2. Then, carefully squeeze the upper part of the Quanti-Tray and pull the foil tab away from the well side to open it.

3. Pour the sample into the Quanti-Tray and put it inside the machine.

4. Place the Quanti-Tray in an incubator for 24 hours at 35 ºC.

Then, analyzing the results that has been obtained as follows:

· If no yellow color is observed, the sample is negative for total coliforms and E. coil.

· If the sample has a yellow color, the presence of total coliforms is confirmed.

· If yellow is observed, check vessel for fluorescence by placing the sample in a UV light. If the fluorescence is observed, the presence of E. coil is confirmed.

iii- Water treatment technical issue because of booster pump not working, otherwise membrane shock and blocks. To overcome the issue the membrane shock needs to follow up necessary periodic preventive maintenance record (example 6 month use to replace the membrane, sensor and filters).

Second technical issue is related to water well drilling, as I said that while drilling there are some fluids to be added as a chemical to prevent the borehole from collapses and to increase the rate of penetration, but the formation of ground earth is different and each formation has got special fluid to treat. So, because of the formation changing while drilling the fluid added will not be able to do its function therefore drilling stuck will occur. To overcome that issue MODES employed geologist to study the formation of earth before starting the drilling operation to classify the proper fluid for the suitable formation.

iv- During my training at MODES and as per the schedule program for various section , I have learned that the method of maintenance which MODES follow it is breakdown maintenance and preventive maintenance.

blog7

TABLE OF CONTENTS

LIST OF FIGURES

LIST OF TABLES

Zinc spray coating:

3.4 Heat treatment of coated samples (3 samples, 1 from each coating type):

3.6 Corrosion test with wet conditions:-

3.7 Surface Roughness Measurement:

3.8 Chapter Summary:

4.3 Surface Roughness Measurement:

4.4 Chapter Summary:

References:

Get help from top-rated tutors in any subject.