Hydrogen Absorption into Fe Plates with Rust Layers Containing Various MgCl₂ Amounts during Atmospheric Corrosion with Controlled Humidity

Abstract

Fe plates with rust layers containing various MgCl₂ amount were prepared as specimens. Each specimen was subjected to dry/wet repeat test beyond 50 cycles, and then subjected to electrochemical hydrogen absorption test under atmospheric corrosion in the air with controlled relative humidity (RH). For an MgCl₂ amount of 39.8 g·m⁻², a hydrogen absorption rate (i_H) started to increase from an RH around 15%, steeply increased with an increase in RH up to about 30%, steeply decreased up to about 35%, gradually increased up to 65% and gradually decreased up to about 92%. A decrease in MgCl₂ amount in the range between 0.514 and 39.8 g·m⁻² induced a decrease in i_H in wide RH range. The maximum i_H at an RH around 30% increased with an increase in MgCl₂ amount in the rust layer. Besides, the RH where the maximum i_H was obtained beyond an RH of 40% increased with a decrease in MgCl₂ amount. From theoretical relationship between RH and thickness of MgCl₂ solution film on the Fe plate without rust layer, it is found that the solution film thicknesses at the RHs were about 0.18 mm, almost independent of MgCl₂ amount. In addition, thicknesses of the rust layers containing 25.7 and 39.8 g·m⁻² MgCl₂ were measured to be almost 0.18 mm each other. The trends of i_H depending on MgCl₂ amount were tried to be explained using nature of deliquescence for MgCl₂.

1. Introduction

From the viewpoint of saving and energy and materials, high-strength material has been being desired and developing in the world. High-strength steels were already used for bolt, auto mobile, and so on, and have tried to use. However, it is well-known that the high-strength steels suffer hydrogen embrittlement (HE) when they are used in both aqueous solutions as well as in open air.^1,2) So far, a lot of researchers have investigated HE of the high-strength steels, and revealed some essential evidences as follows. Hydrogen atoms are formed as products of cathodic reaction in accompany with the corrosion of the steel, absorb into the steel, and induce failure of the steel.^3,4) Susceptibility to HE of the steel was enhanced by increase in its strength⁵⁾ and hydrogen concentration in it.⁶⁾ Therefore, most of the researches regarding HE have focused on composition and microstructure of the steel for the sake of developing the steels which perform HE-resistance even at larger hydrogen concentration.^7,8) However, the other important point of developing HE-resistant steels is to understand the way to suppress hydrogen absorption into the steels. There have been few researches investigating the relationship between hydrogen absorption into the steel and environmental factors like corrosion potential as well as solution pH. For example, a logarithm of hydrogen permeability (equal to a hydrogen absorption rate multiplied by a steel thickness) almost linearly decreases with a rise in potential in alkaline solution⁹⁾ as well as in neutral solution with H₂S.^10,11) A hydrogen concentration at the steel surface is fixed in a quite short time after the hydrogen absorption condition charged, a logarithm of hydrogen concentration increases linearly with an increase in a steel hardness as well as in a reverse of diffusion coefficient of hydrogen in the steel, and the hydrogen concentration decreased with a rise of cathodic potential but slightly increased with a rise of anodic potential.^12,13) Many researches on hydrogen absorption including these ones were generally conducted in aqueous solutions. However, the high-strength steel frequently suffers HE during atmospheric corrosion, so that it is also important to accumulate the information on hydrogen absorption relating to the weather conditions like temperature and humidity. There have been the researches that tried to measure hydrogen absorption rate of polished steels during atmospheric corrosion in air open conditions and revealed enhancement of hydrogen absorption at higher temperature and at optimum humidity.^14,15,16,17) Our research group has, on the other hand, focused on hydrogen absorption into the steels with rust layer containing salt during atmospheric corrosion, and investigated the relationship between hydrogen absorption rate and relative humidity (RH) of air at the room temperature using an Fe plate with the rust layer containing NaCl¹⁸⁾ or MgCl₂.¹⁹⁾ As brief results, the hydrogen absorption rate had one and two peaks against RH for NaCl and MgCl₂, respectively. Present research extendedly investigated the effect of MgCl₂ amount in the rust layer on the relationship between the hydrogen absorption rate and RH during atmospheric corrosion for the Fe plate with the rust layer.

2. Experimental Procedure

2.1. Specimen Preparation

Material was Fe sheet (Nilaco Co.) in 2 mm thickness and its purity was 99.5 mass%. The sheet was cut into specimens with shape of 40 mm × 40 mm. The specimen was fully annealed at 1073 K for 1.8 ks followed by furnace cooling. The specimen surface was mechanically polished by SiC papers to #6/0 (corresponding to #800) to remove thick oxide film, and then electrolytically polished to remove deformed layer on the specimen surface introduced by the mechanical polishing. The electrolytic polishing was conducted using a potentiostat (Toho Tech. Res. Co. Ltd., PS-07) with a Pt counter electrode and an Ag/AgCl (sat. KCl, room temp.) reference electrode. The specimen was immersed in the solution containing H₃PO₄ (concentration: 85 mass%) and H₂SO₄ (concentration: 95 mass%) mixed by 75 and 25 vol%, respectively, at 298 K, and then a potential of 1.5 V_Ag/AgCl was applied to the specimen for 84.6 ks. After the polishing, the specimen surface was removed by about 50 µm. Thereafter, electrolytic plating of Ni was conducted to the specimen as described below. Watt bath (NiSO₄·6H₂O: 250 kg·m⁻³, NiCl·6H₂O: 45 kg·m⁻³, H₃BO₃: 40 kg·m⁻³) at 333 K was prepared for the plating. One side of the specimen surface was fully covered with a polytetrafluoroethylene tape, and a current density of −10 A·m⁻² was applied to the other side for 420 s in the bath by a potentiostat (Toho Tech. Res. Co. Ltd., Model 2000). Ni layer of about 15 nm thick was then deposited on the surface after the report by Yoshizawa et al.^20,21)

The specimen surface without Ni plate was fully covered with rust layer by the following procedure. MgCl₂ solutions at various concentrations between 0.002 and 0.1 kmol·m⁻³ were prepared. An O-ring (an inner diameter of 31 mm) was sufficiently contacted to the surface, and the MgCl₂ solution poured in it by 2.0 × 10⁻⁶ m⁻³ followed by drying up for 86.4 ks in a sealed box with silica gel. Subsequently, it was repeated twice that pure water of 2.0 × 10⁻⁶ m⁻³ was poured in it and dried up to produce the rust layer uniformly covering the surface. Amounts of MgCl₂ in the obtained rusts were estimated as 0.514 g·m⁻², 5.14 g·m⁻², 25.7 g·m⁻² and 39.8 g·m⁻².

2.2. Electrochemical Hydrogen Absorption Test

In the hydrogen absorption test, a couple of modified Devanathan-Stachursky type cells^18,22) was employed. Schematic illustration of the system is shown in Fig. 1. The cell was set in the box in which dry air at an RH less than 5% was introduced. The specimen was set between two cells. The cell contacting the surface with the rust layer was the hydrogen absorption cell, in which air with a controlled RH can be introduced. The other cell contacting the Ni-plated surface was the hydrogen detection cell, in which 0.1 kmol·m⁻³ NaOH solution was introduced. In the cell, an Ag/AgCl reference electrode and a Pt counter electrode were equipped, and connected to a potentiostat (Toho Tech. Res. Co. Ltd., Model 2090).

Fig. 1.

Schematic illustration of the system for measurement of hydrogen absorption rate during atmospheric corrosion. (Online version in color.)

Procedure of the test was described as follows: The specimen was set between the two cells, and the NaOH solution was introduced to the hydrogen detection cell. After the solution was fully contacted to the Ni-plated surface, a passivation potential of 0 V_Ag/AgCl was applied to it, and dry air (RH 0%) was introduced to the hydrogen absorption cell. After a passivation current density reached 0.2 mA·m⁻² and become sufficiently stable, a dry/wet repeat test was conducted in the following way. Dry air and air with a controlled RH were introduced to the hydrogen absorption cell each other for 10.8 ks in order to start and stop atmospheric corrosion, respectively. During the test, an RH and a temperature in the hydrogen absorption cell as well as an anodic current density on the hydrogen detection side were monitored simultaneously. After repeating more than 50 cycles, the rusted surface was exposed to dry air, wet air with a controlled RH and then dry air for about 86.4 ks each. During the test, an RH, a temperature and a current density was also monitored. A hydrogen absorption rate (i_H) was defined as a difference between the steady state anodic current density during atmospheric corrosion and that during introduction of dry air.

2.3. Calculation to Obtain Hydrogen Concentration at Hydrogen Absorption Surface of Fe Plate

As described later, when wet air contacts the specimen surface with the rust layer, anodic current density on the opposite hydrogen detection side increases. The fact is explained as that hydrogen atoms are formed as products of cathodic reaction in accompany with atmospheric corrosion, absorb from the hydrogen absorption surface, diffuse into the Fe plate, reach the hydrogen detection surface, and then oxidize to hydrogen ion as follows.   

$$\mathrm{H}\to {\mathrm{H}}^{+}+{\mathrm{e}}^{-}$$(1)

In addition, when the anodic current density on the hydrogen detection surface is under the steady state during atmospheric corrosion, diffusion of hydrogen in the Fe plate is also under steady state. The situation satisfies Fick’s first law as follows.   

$$i_{\mathrm{H}}=FJ=FD{C}_0/L$$(2)

Where, F is a Faraday’s constant, J is a flux of hydrogen in steady state, D is a diffusion coefficient of hydrogen in the Fe plate, C₀ is a hydrogen concentration at the hydrogen absorption surface of the Fe plate and L is a thickness of the Fe plate. Since F is 9.65 × 10⁴ C·mol⁻¹, D is 5.6 × 10⁻⁹ m²·s^{−1 12,13)} and L is a measurable value, C₀ under steady state can be obtained from i_H.

3. Results

The Fe plate specimens with the rust layers containing various amount of MgCl₂ were subjected to the dry/wet repeat test, and an anodic current density on the hydrogen detection side was monitored during the test. An average RH and a dry/wet cycle for each specimen were summarized in Table 1. As the previous study¹¹⁾ revealed, an anodic current density on the hydrogen detection surface, correlating to a hydrogen absorption rate, decreased with an increase in dry/wet cycle, and reached almost steady state beyond about 40 cycles for the specimens containing 25.7 and 39.8 g·m⁻² MgCl₂. Whereas, i_H was monitored for some steels exposed in open-air and similar transients in i_H with an exposure day were obtained.²³⁾ The trends reached the decision of that the following test for evaluation of i_H depending on RH is conducted by the specimen subjected to the dry/wet repeat test beyond 50 cycles, because almost same i_H is expected under the same RH, independent of test frequency, for the specimen beyond the test cycle of 50.

Table 1. An average RH and a dry/wet cycle for each specimen.

Amount of MgCl2, wMgCl2/g·m−2	average RH(%)	End of cycle
0.514	80	60
5.14	70	100
25.7	27	55
39.8	33	100

Effects of RH on i_H as a function of amount of MgCl₂ within the rust were shown in Fig. 2. For an MgCl₂ amount of 39.8 g·m⁻², i_H started to increase from an RH around 15%, steeply increased with an increase in RH up to about 30%, steeply decreased up to about 35%, gradually increased up to 65% and gradually decreased up to about 92%. Totally, i_H had two peaks against RH. Hereafter, the peaks at lower and at higher RH were defined as 1st and 2nd peaks, respectively. As focusing on an MgCl₂ amount, a decrease in MgCl₂ amount induced a decrease in i_H in wide RH range. In particular, the RH at the top of the 1st peak located in a relatively narrow range between 25 and 35%, almost independent of the amount, but the maximum i_H decreased with a decrease in the amount. Figure 3 shows effect of amount of MgCl₂ on the maximum i_H at the 1st peak. It was found that the maximum i_H was almost proportional to the amount. In Fig. 2, whereas, the RH and the maximum i_H of the 2nd peak clearly increased and decreased, respectively, with a decreased in the amount, except for the MgCl₂ amount of 0.514 g·m⁻² at which the 2nd peak was not observed. Effect of amount of MgCl₂ on the RH of the 2nd peak top is shown in Fig. 4. The figure revealed that the RH increased almost linearly with a decrease in the amount, through RH 100% at amount of 0 g·m⁻².

Fig. 2.

Effects of RH on hydrogen absorption rate as a function of amount of MgCl₂ in the rust layer. (Online version in color.)

Fig. 3.

Effect of amount of MgCl₂ on the maximum i_H at the 1st peak.

Fig. 4.

Effect of amount of MgCl₂ on the RH of the 2nd peak top.

4. Discussion

4.1. 1st Peak

As shown in Fig. 2, i_H had two peaks against RH. Now the 1st peak around a smaller RH is focused to be discussed. Figure 5 shows a model of the solution particles in the rust layer on the Fe plate. The previous study¹¹⁾ discussed that generation of the 1st peak is caused by corrosion of the Fe substrate with tiny particles of saturated MgCl₂ solution. In the air of RH 33%, MgCl₂ solid transforms its saturated aqueous solution with flat surface, so called, deliquescence. Below an RH of 33%, MgCl₂ solid should not be deliquescent in general, but may be in some porous materials like rust layer by capillary condensation, as shown in the upper part of Fig. 5. According to Kelvin’s equation²⁴⁾ as shown in Eq. (3), a curvature radius for concave surface of the solution (r) decreases with a decrease in a pressure of water vapor in air (p).   

$$\mathrm{l}\mathrm{n}(p/p_0)=-2\gamma V_{\mathrm{m}}/(rRT)$$(3)

where, p₀ is the pressure of water vapor coexisting with the solution composed of flat surface (r = ∞), γ is a surface tension of the solution, V_m is a molar volume of the solution, R is the gas constant and T is an absolute temperature. Since an RH is a ratio of p to the pressure of water vapor coexisting with the water composed of flat surface, a decrease in RH induces a decrease in the number and a volume of solution particles satisfying the concave radius (r), a decrease in a total contact area between the solution particles and the Fe plate, and then suppression of a corrosion rate corresponding to a hydrogen absorption rate. As shown in Fig. 3, the maximum i_H of the 1st peak decreased with a decrease in amount of MgCl₂, and the tendency is explained by that a smaller amount of MgCl₂ induces a smaller number and volume of the solution particles, a smaller total contact area as shown in the lower part of Fig. 5, and then a smaller corrosion rate corresponding to i_H.

Fig. 5.

A proposed model of saturated MgCl₂ solution particles in the rust layer on the Fe plate for the 1st peak in Fig. 2.

In the previous study,¹¹⁾ a decrease in i_H with an increase in RH for the end of 1st peak was explained as follows. When an RH in air increases, the number as well as a volume of the solution particles increases to promote atmospheric corrosion, and finally the solution particles connect each other to make saturated solution film covering on the Fe plate. Since the concentration of dissolved oxygen in the saturated solution is 8.9 mmol·m⁻³,^25,26) about 1/100 of that in water, a corrosion rate corresponding to i_H suppressed under the solution film. In the present study, film thicknesses of the saturated solution on the flat surface without any rust at an RH of 33% were calculated to be 0.0853, 0.0551, 0.0110 and 0.0011 mm for MgCl₂ amounts of 39.8, 25.7, 5.14 and 0.514 g·m⁻², respectively, under the concentration of the saturated MgCl₂ solution of 4.90 kmol·m⁻³ and the molar mass of MgCl₂ of 95.2 g·mol⁻¹. It is noted from Fig. 2 that the RHs at which i_H started to decrease in the 1st peak are less than 33% for MgCl₂ amounts of 39.8 and 25.7 g·m⁻², suggesting that the RH provides formation of the saturated solution film to cover on the Fe plate and that the film suppresses the corrosion. For an MgCl₂ amount of 5.14 g·m⁻², the RH seems to be 33%, corresponding to the RH for deliquescence of MgCl₂. While, the 1st peak is hardly observed for 0.514 g·m⁻², suggesting that almost no saturated solution film but some solution particles were considered to be formed in the rust layer even though the rust is exposed in the air of RH 33%.

4.2. 2nd Peak

In the previous study,¹¹⁾ formation of the 2nd peak is discussed on the basis of the relationship between a concentration of the MgCl₂ solution film and an RH of air beyond 33%, as follows. As an RH increases beyond 33%, a concentration of MgCl₂ solution film decreases because of maintaining equivalence between activities of water in the air and that in the solution. Since an amount of MgCl₂ in the rust layer remains during the test in which an RH varies, an increase in RH induces an increase in volume as well as thickness of the solution film. On the other hand, concentration of oxygen dissolving in the solution generally decreases as the MgCl₂ concentration increases. Therefore, an increase in RH also induces an increase in concentration of oxygen dissolved in the solution film. Assuming that the atmospheric corrosion rate (i_corr) is controlled by the diffusion-limited cathodic reaction rate of dissolved oxygen, i_corr is expressed as follows,   

$$i_{\mathrm{c}\mathrm{o}\mathrm{r}\mathrm{r}}=4F\mathrm{\hspace{0.17em} }{D}_{\mathrm{O}2}{C}_{\mathrm{O}2}{}^0/L_{\mathrm{s}}$$(4)

where, F is the Faraday’s constant, D_O2 is a diffusion coefficient of dissolved oxygen, C_O2⁰ is a concentration of dissolved oxygen at air-side surface of the solution film, L_s is a solution film thickness. In the case that D_O2 is almost independent of C_O2⁰, then i_corr corresponding to i_H depends on C_O2⁰ and L_s. It was clearly observed in Fig. 2 that i_H increased and then decreased with an increase in RH beyond 33%. The trend is expected to be explained by that an increase in i_H is more strongly controlled by an increase in C_O2⁰, and that a decrease in i_H is more strongly controlled by an increase in L_s. after Eq. (4).

An MgCl₂ solution at a given concentration was set in a sealed container, and a stable RH in it was measured. Figure 6 shows relationship between a solution concentration and an RH. It is obvious that an RH decreased almost linearly with an increase in concentration. Using the relationship, a thickness of the solution film forming on flat surface without any rust was calculated for each specimen and the results were summarized against MgCl₂ amount in Fig. 7. It was noted that a solution film thickness for each specimen was increased with an increase in amount of MgCl₂ and acceleratingly in RH. From Figs. 4 and 7, the thickness at the RH for the top of the 2nd peak was also obtained, and was about 0.18 mm, almost independent of an MgCl₂ amount beyond 5.14 g·m⁻², that is, the maximum i_H of the 2nd peak top appears when the solution film thickness reaches about 0.18 mm. In addition, the RH of the 2nd peak top for the specimen with 0.514 g·m⁻² MgCl₂ is estimated to be 99.4% from Fig. 7, based on the thickness of 0.18 mm. The estimation suggests that there was no 2nd peak in Fig. 2 because of the controlled RH region between 0 and 98%. Thicknesses of the rust layers of the specimens with 39.8 and 5.14 g·m⁻² MgCl₂ was measured using a 3D measurement machine and were about 0.18 mm both as an average. It is very interesting that the measured thickness of the rust layer is quite similar to the estimated thickness of the solution film without the rust layer, and that an amount of MgCl₂ does not affect the solution film thickness of about 0.18 mm corresponding to the RH of the 2nd peak top.

Fig. 6.

Relationship between a MgCl₂ solution concentration and an RH.

Fig. 7.

Effect of RH beyond 33% on thickness of MgCl₂ solution film forming on flat surface. (Online version in color.)

By means of Figs. 2 and 7, i_H was plotted against solution film thickness. The results are summarized in Fig. 8. It was found in this figure that i_H increased with an increase in solution thickness until about 0.18 mm, decreased until about 0.6 mm, and reached in steady-state. In addition, the relationship seemed to be almost independent of amount of MgCl₂ in the rust, but is not clear right now. The shape of the curve seems to be quite similar to that of corrosion rate via solution thickness proposed by Tomashov²⁷⁾ if i_H corresponds to corrosion rate. Tomashov explained the curve which was divided into 4 regions: Region I (dry atmospheric corrosion) induces corrosion by adsorbed water molecules on the metal surface (without continuous film formation), Region II (humid atmospheric corrosion) induces corrosion promoted by formation of quite thin film of electrolyte, Region III (wet atmospheric corrosion) induces corrosion suppressed by thickened solution film causing reduction of oxygen diffusion rate, and Region IV (complete immersion corrosion) induces corrosion independent of solution film thickness due to formation of a constant diffusion layer for oxygen. After the explanation by Tomashov, the trend in the curve of Fig. 8 was tried to be explained as follows. A region of solution thickness until 0.18 mm is a combination of Regions I and II by Tomashov. Tomashov suggested that the maximum of corrosion rate is obtained at a thickness of about 0.001 mm, and Tsuru et al.^28,29) obtained the thickness of about 0.01 mm by electrochemical impedance spectroscopy. On the other hand, the present result from Fig. 8 revealed the thickness of 0.18 mm, 10 to 100 times larger than the previous values. The difference may be caused by the situation of solution film without and with rust layer in the previous and the present result, respectively. In addition, Tomashov explained that Region IV was classified in the solution film thickness more than a constant diffusion layer of oxygen. Although Region IV should be started from the solution layer thickness of 0.4 mm as the general value in the stagnant solution, the present result in Fig. 8 showed the region showing the steady i_H, corresponding to Region IV by Tomashov, beyond about 0.6 mm. Considering the differences from the previous results, a corrosion model for the present results was proposed as shown in Fig. 9. As mentioned before, thin saturated solution film covers the Fe plate with the rust layer at the lowest RH of the 2nd peak in Fig. 2. The situation is expressed in Fig. 9(a). As an RH increases, a thickness solution film increases. Assuming that the rust layer indicates electrical conductivity, thickening the solution film induces widening the cathodic reaction area for dissolved oxygen to enhance corrosion rate corresponding to i_H, as shown in Fig. 9(b). As an RH and an accompanying solution thickness increases beyond the rust layer (c.a., 0.18 mm, the top of the 2nd peak), an oxygen diffusion flux decreases, and then a corrosion rate and then an i_H suppress, as shown in Fig. 9(c). When a thickness of the solution film excluding the rust layer exceeds the diffusion layer for oxygen (c.a., 0.4 mm), that is, a total solution thickness exceeds about 0.58 mm, a corrosion rate corresponding to an i_H reaches a constant as shown in Fig. 8.

Fig. 8.

Effects of solution film thickness on hydrogen absorption rate and hydrogen concentration at hydrogen-absorption surface.

Fig. 9.

A proposed corrosion model for the 2nd peak in Fig. 2.

On the basis of Eq. (2), a hydrogen concentration at the hydrogen absorption surface of the Fe plate (C₀) can be converted from i_H, and C₀ was additionally expressed in Fig. 8. It was found that the range of C₀ under the present atmospheric corrosion condition was between 0 to about 0.15 × 10⁻³ ppm. The previous study⁵⁾ revealed that C₀ of a high-strength (c.a., 1500 MPa class) steel 300 times larger than that of Fe, so it is suggests that atmospheric corrosion induces HE to the high-strength steel. In addition, Region IV indicates the corrosion condition in diluted solution with sufficient volume, so that the corrosion rate is estimated to be 0.2 A·m⁻². The value of C₀ under the condition was about 0.075 × 10⁻³ ppm, in relatively good agreement with that of Fe at the cathodic current density of 0.2 A·m⁻² obtained by the electrochemical hydrogen absorption test with a neutral solution in the previous study.⁴⁾

5. Conclusions

Fe plates with rust layers containing various amount MgCl₂ was prepared. Each specimen was subjected to a dry/wet repeat test beyond 50 cycles, and then subjected to an electrochemical hydrogen absorption test under atmospheric corrosion in air with a controlled relative humidity (RH). The results were briefly summarized as follows.

• In the case for the MgCl₂ amount of 39.8 g·m⁻², hydrogen absorption rate (i_H) started to increase from an RH around 15%, steeply increased with an increase in RH up to about 30%, steeply decreased up to about 35%, gradually increased up to 65% and gradually decreased up to about 92%. A decrease in amount of MgCl₂ in the range between 0.514 and 39.8 g·m⁻² induced a decrease in i_H in wide RH range.

• The maximum i_H at an RH around 30% increased with an increase in MgCl₂ amount. The result was explained as follows. At the RH, saturated MgCl₂ solution particles with concave shape form in the rust, contact and corrode the Fe plate. Therefore, an increase in MgCl₂ amount induces an increase in number and volume of solution particles, in contact area between the particles and the Fe plate, and in corrosion rate corresponding to i_H.

• The RH where the maximum i_H was obtained beyond an RH of 40% increased with an increase in MgCl₂ amount. From theoretical relationship between RH and thickness of MgCl₂ solution film formed on the Fe plate without rust layer, it is found that the solution film thickness at the RH was about 0.18 mm, almost independent of MgCl₂ amount. Thicknesses of the rust layers for 25.7 and 39.8 g·m⁻² MgCl₂ were measured to be almost 0.18 mm both. According to the evidences, it is supposed that an increase in i_H with an increase in RH is caused by an increase in area of cathodic reaction in the rust due to an increase in solution volume, and that a decrease in i_H is caused by a decrease in diffusion flux of oxygen in the solution film over the rust layer.

Acknowledgements

One of the authors thanks the study groups, “Comprehensive Understanding of Hydrogen-Passive Surface on Steels for Prevention of Hydrogen Embrittlement” from 2013 to 2015 and “Corrosion-induced Hydrogen Absorption to Steels” since 2018 in Iron and Steel Institute of Japan for sufficient discussion to our research results and a part of financial support. In addition, One of the authors thanks Grant-in-Aid for Scientific Research (C) (18K04784) of JSPS and Kansai University Fund for Domestic and Overseas Research Fund for a part of financial support.

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