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On the mechanism of hydrogen permeation in iron in alkaline medium
PII:
Acta mater. Vol. 46, No. 3, pp. 869±879, 1998 # 1998 Acta Metallurgica Inc. Published by Elsevier Science Ltd. All rights reserved Printed in Great Britain 1359-6454/98 $19.00 + 0.00 S1359-6454(97)00311-X
ON THE MECHANISM OF HYDROGEN PERMEATION IN IRON IN ALKALINE MEDIUM A. M. BRASS{ and J. R. COLLET-LACOSTE{ Laboratoire de MeÂtallurgie Structurale, CNRS URA 1107, Universite Paris-Sud, 91405 Orsay Cedex, France (Received 14 August 1997; accepted 26 August 1997) AbstractÐHydrogen permeation tests were performed in pure iron in sodium hydroxide at 298 K, based on the electrochemical technique. Hydrogen charging was conducted under potentiostatic control, simultaneously registering both the permeation (ip) and the cathodic (ic) currents until stabilization. After a ®rst polarization transient at ÿ1105 or ÿ1355 mV/NHE, potential increments or decrements were performed, allowing in both cases the currents to stabilize. Based on the analysis of the experimental data, a model was developed, which takes into account the existence of a 0.5 to 1 nm thick unreduced air-grown oxide ®lm on the input side of the samples in spite of long cathodic polarization times. A good correlation between the potential distribution at the oxide/solution interface and the calculated oxide thickness was obtained. # 1998 Acta Metallurgica Inc. ReÂsumeÂÐLa diusion de l'hydrogeÁne dans du fer pur a eÂte eÂtudieÂe aÁ tempeÂrature ambiante en milieu basique aÁ l'aide de la technique de permeÂation eÂlectrochimique. Le courant total d'hydrogeÁne deÂcharge sur la surface par polarisation cathodique aÁ potential impose (ÿ1105 or ÿ1355 mV/NHE) a eÂte mesure en continu et compare au ¯ux de permeÂation. La concentration d'hydrogeÁne disponible sur la surface a eÂte modi®eÂe par paliers successifs une fois un reÂgime permanent de diusion atteint. Les reÂsultats expeÂrimentaux ont eÂte modeÂliseÂs en consideÂrant une reÂduction incompleÁte de l'oxyde super®ciel naturel sous polarisation cathodique et la diusion d'hydrogeÁne au travers d'un ®lm reÂmanent d'oxy-hydoxyde de treÁs faible eÂpaisseur (0.5 aÁ 1 nm). # 1998 Acta Metallurgica Inc.
1. INTRODUCTION
The knowledge of the diusion coecient of hydrogen in metals and the related problems of trapping and surface eects is necessary in order to improve the understanding of hydrogen embrittlement and stress corrosion cracking phenomena. Trapping eects can be considered to be negligible in well recrystallized pure iron whereas passive and oxide ®lms are unavoidable, namely in alkaline aqueous environments, and may greatly in¯uence the hydrogen ingress at room temperature in metals where the hydrogen diusivity is large. The information required in order to solve Fick's equations for hydrogen permeation in a given system is both the hydrogen concentration or the hydrogen ¯ux at any time (at input and output sides of the plane sheets where hydrogen diusion proceeds) and the initial conditions, i.e. the hydrogen concentration distribution in the metal. Two options are possible regarding the boundary condition at the input surface where hydrogen is discharged: to assume a step increase in concen{To whom all correspondence should be addressed. {On leave from U.A. Quimica. Comision Nacional de Energia Atomica, 8250 Av. del Libertador, 1429 Buenos Aires, Argentina. 869
tration (constant concentration at charged surface) or in ¯ux (constant ¯ux entering at charged surface) at the beginning of the polarization and during the test [1±3]. Some authors [1, 2] suggest that the constant concentration condition can only be applied if the charging condition is potentiostatic, and that the constant ¯ux condition at charged surface is only valid for galvanostatic charging. This is true for Pd [2, 4] but has not been proved for iron [3]. Furthermore some works in the literature report the existence of an oxide ®lm not completely reduced which play the role of a barrier for the penetration of hydrogen in the metal during long cathodic polarizations. Distortions in the hydrogen permeation transients [5±9] are often observed together with non-linear changes in the permeation ¯ux with the square root of the cathodic current as well as values of the exponential factor n connecting the permeation and the cathodic current smaller than 0.5 [5]. An independence of the permeation ¯ux on the cathodic current for very high current values was stated together with a transfer coecient close to 0.5 [10]. Changes in the transfer coecient and in the exchange current during scratching tests were observed [11] with the formation of a mono-layer of adsorbed FeOOH after scratching [12, 13].
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The purpose of this paper is to present a model for the hydrogen penetration in pure iron in alkaline medium. A remnant oxi-hydroxide ®lm on the input surface accounts for experimental relationships between the permeation and the cathodic currents. 2. EXPERIMENTAL
2.1. Material A pure iron bar was homogenized in vacuum for 24 h at 1123 K. The chemical composition (wt. ppm) is the following: C: 40 ppm, S: 35 ppm, O2: 3 ppm, N2: 5 ppm, P: 40 ppm, Si: 40 ppm. 0.25 cm thick slides were given a thermal treatment in vacuum for 24 h at 1453 K followed by water quenching. Electrolytical polishing was then performed before cold working (R.A. 50%). A thermal treatment in vacuum for 24 h at 1053 K was conducted before ®nal polishing to a thickness ranging from 200 to 1070 mm. The large ®nal grain size (200 mm) and the small dislocation density obtained with this heat treatment, together with the very small amount of impurities allowed us to consider that trapping of hydrogen on microstructural defects will be negligible. 2.1.1. Surface preparation. The samples were mechanically polished with a 1200 grid paper on one side and with a 1 mm diamond paste on the other side. Ultrasonic cleaning was successively conducted in trichlorethylene, butanol and acetone. Surface ®nishing was performed just before the set up of the samples in the experimental device. Some iron probes were purposely oxidized at 523 K for 15 h. The oxide thickness (100 nm) was measured by abrasion in an ionic analyzer and measurements of the craters with a talystep device. 2.2. Electrochemical permeation test The permeation cell [14] is composed of two double wall glass compartments separated by the sample (working electrode) clamped in a separate sample holder. Thermostated water is circulated in the double jacket in order to maintain a constant temperature in both chambers (298 20.1 K). In the charging compartment the specimen is the cathode and the anode is a platinum electrode. The reference electrode is immersed in a luggin capillary ®lled with NaOH. Hydrogen production is carried out by cathodic polarization in 0.1 N NaOH at a constant potential value according to: H2O + 2eÿ4H2+2OHÿ. In the detection (anodic) compartment the output side of the sample is polarized in the passive range in 0.1 N NaOH so that hydrogen is oxidized according to: Hads 4H++eÿ. The smallest value (less than 10 nA cmÿ2) of the background current [15] was obtained by applying the rest potential (ED) measured on the output face under open circuit conditions and continuous argon
bubbling until stabilization (15 h). In order to avoid the formation of a passive ®lm on the input side of the sample by contact with the charging solution (0.1 N NaOH) under open circuit conditions before the beginning of the permeation test, the cathodic polarization was started during the introduction of the preheated solution in the charging compartment (instantaneous cathodic polarization). The experiments were carried out by imposing a constant potential E1= ÿ 1105 or ÿ1355 mV/NHE. Both the permeation (ip) and the cathodic (ic) currents were simultaneously registered and allowed to stabilize for more than 20 h. In some experiments potential steps (De = 25 or 50 mV) were then performed, allowing in both cases the currents to stabilize. These steps could involve either increments or decrements from the initial potential value E1. 3. RESULTS AND DISCUSSION
The hydrogen entry condition must be consistent with one of the two physical-chemistry processes (equilibrium or kinetic) that occur on the surface [3]: (i) Equilibrium is reached between the external phase and the hydrogen absorbed in the ®rst metallic layers (C(0,t) = C0) at e = 0 where e is the sample thickness. No condition is imposed on the entrance ¯ux (which is in®nite at t = 0). The hydrogen ¯ux on the input side is dependent on the diusion process beneath the surface. In this way, the external system must be capable of a quick reaction to the demand of hydrogen from the inner metal, so as to maintain equilibrium as hydrogen diuses through the bulk. In this case as input concentration only depends on the thermodynamical state of the external phase, the stationary ¯ux of hydrogen J1 is inversely proportional to the metallic sheet thickness. (ii) The other case involves a constant input ¯ux (J(0,t) = J0) and an input concentration that increases from 0 at t = 0 to a maximum value equal to Cmax=J0 e/D, where D is the diusion coecient of hydrogen. The system is not in equilibrium with the external phase and the amount of hydrogen that penetrates the metal depends on the kinetic parameters of transfer phenomena between the external phase and the metal. The stationary hydrogen ¯ux is then independent on the thickness of the sheet. For both cases, if continuous changes occur in the surface properties during the hydrogen charge (changes in the values of the equilibrium or kinetic constants) or in the concentration of adsorbed or absorbed hydrogen which regulates the concentration or entrance ¯ux, changes in C0 and J0 with time will be observed. Distortions in the permeation curves usually are attributed to changes in C0 with time.
BRASS et al.: MECHANISM OF HYDROGEN PERMEATION
In the case of iron, it was stated that the constants kabs and kdes for the reaction: Hadsorbed\Habsorbed are ®nite, which makes the boundary condition for input: J(0,t) = kabs y ÿ kdes C(0,t). Assuming y is attained instantaneously at t = 0, the input ¯ux decreases with time to reach a stationary state and the concentration a maximum value C1. This model [3] is an example of case (ii) in which the desorption time depends on the entry concentration C(0,t). The inverse of the ¯ux as a function of the thickness is linear (the extrapolation to e = 0 gives 1/kabsy) as a consequence of a dependence of the entry ¯ux on C(0,t). However, this model predicts a constant cathodic current, given that the latter changes as y2 [16] with y considered as constant. 3.1. Experimental observations relative to hydrogen permeation in pure iron in 0.1 N NaOH The permeation curves obtained by cathodic charging at ÿ1105 mV/NHE are distorted whereas a well marked ``plateau'' is observed in the transient of permeation curves resulting from cathodic charging at ÿ1355 mV/MHE (Fig. 1). This ``plateau'' is followed by a much slower increase in the permeation current before the maximum stationary value is attained. An increase in the cathodic current is observed within the ®rst 10 min following the start of the cathodic polarization (Fig. 2(a)). For samples oxidized at 523 K a similar increase is observed immediately after the start of charging (Fig. 2(b)). However, a maximum in (ic) is reached after 5±7 h instead of 10 min or less with probes oxidized in air at 298 K (Fig. 2(a)). The transients of the permeation curves obtained with samples oxidized at 523 K exhibit strong distortions even at ÿ1105 mV/NHE (Fig. 3) with a maximum in the
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hydrogen ¯ux corresponding to the maximum in the cathodic current. A sharp decrease in the cathodic current (Fig. 1) is observed as the permeation current increases, even when the stationary state is reached. The drop in the cathodic current is smaller after a potential step than during the ®rst charging [17]. These experimental observations are inconsistent with discharge±absorption±recombination models [16] since both the permeation and the recombination currents should increase as a consequence of an increase in the fraction y of the sites occupied by hydrogen. The diusion coecient of hydrogen calculated from the ®rst polarization transient yields 4.10ÿ6 cm2/s at 298 K. This value is small when compared to the highest diusivity (8 to 9.5 10 ÿ5 cm2/s) of hydrogen in pure iron reported in the literature [19±23]. However, potential steps [18] conducted after the steady state allowed us to reach 8.10ÿ5 cm2/s. The changes in the reciprocal value of the stationary hydrogen ¯ux (J1) with the sample thickness are shown in Fig. 4 for tests performed at ÿ1105 mV/NHE. In spite of the discrepancy of the results obtained with tests performed for the same thickness, it is clear that the permeation ¯ux increases as the thickness decreases. Nevertheless, the line drawn by the method of least squares does not pass through the origin. This fact is inconsistent with Bockris's model [16] predicting the intercept to be equal to zero (case (i)). Another interesting fact is shown in Fig. 5, where Qc, the total amount of hydrogen discharged on the input side, was plotted as a function of the sample thickness for ®ve dierent values of charging time. It is apparent that the mean cathodic current, which is proportional to Qc, becomes larger as the
Fig. 1. Change in the permeation and cathodic currents during cathodic charging of pure iron at ÿ1355 mV/NHE (0.1 N NaOH, 298 K, e = 830 mm).
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Fig. 2. (a) Cathodic current (3 tests) vs time on iron oxidized at 298 K polarized at ÿ1105 mV/NHE (0.1 N NaOH, 298 K); (b) cathodic current vs time on iron (0.1 N NaOH, 298 K). (a) (b) samples oxidized at 298 K polarized, respectively, at ÿ1105 and ÿ1355 mV/NHE, (c) (d) samples oxidized at 523 K polarized, respectively, at ÿ1105 and ÿ1355 mV/NHE.
thickness of the metal sheet decreases and the polarization time increases. This dependence is inconsistent with a model involving an equilibrium between the external phase and the ®rst metallic layers since under this condition, the input concentration is controlled by the external phase and the hydrogen ¯ux only by the diusion process. Since the cathodic current is ®xed by the physical properties of the surface, the observed results would imply a dependence of the input hydrogen ¯ux with the sample thickness.
3.2. Migration of hydrogen through an oxide ®lm The potentials for the reactions: 2Fe3 O4 H2 O , 3Fe2 O3 2H 2eÿ and 2Fe 4H2 O , 3Fe3 O4 8H 8eÿ are, respectively, equal to ÿ550 mV/NHE and ÿ855 mV/NHE in a solution at pH 13. From a
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Fig. 3. Normalized hydrogen ¯ux vs t (Dt/e2) in pure iron cathodically charged at ÿ1105 mV/NHE (0.1 N NaOH, 298 K), (a) samples oxidized in air at 298 K (standard deviation of 10 tests), (b) samples oxidized in air at 523 K (2 tests).
thermodynamical point of view, oxide ®lms grown in air at room temperature on iron are thus unstable at potentials more cathodic than ÿ855 mV/ NHE at this pH. Though neither structure nor composition of these ®lms are exactly known, their thickness lies between 6 and 18 nm [24], depending on the medium where they are formed. Some authors arm [25, 26] that after a period of time ranging between a few seconds and 5 min the air grown oxide is completely reduced under cathodic discharge. Nevertheless, other works [5, 6, 11] show that at this pH a non-reduced oxide ®lm remains on the surface, even under cathodic polarization. In order to analyze our experimental results we assume the surface air grown oxide to be reduced
to a very thin layer of remanent oxy-hydroxide with a thickness (eox) which does not change with time, or has actually a very slow dissolution kinetics through all the test duration. Figure 6 shows the assumed potential distribution between the solution, the oxide and the metal. The basic assumptions involve: Ðpotential in the solution and in the metal is considered as constant, given the high conductivity with respect to the interfaces 1/2 and 2/3, and the oxide ®lm. Ða large potential drop D V produced on the ®lm, which leads to a high electric ®eld Ef equal to: Ef=(D V/e).
Fig. 4. Change in the inverse stationary ¯ux of hydrogen as a function of the sample thickness for cathodic polarization of pure iron at ÿ1105 mV/NHE (0.1 N NaOH, 298 K).
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Fig. 5. Change in the amount of hydrogen discharged on pure iron as a function of the sample thickness for dierent values of polarization time at ÿ1105 mV/NHE (0.1 N NaOH, 298 K).
Ðpotential drops e1,2 and e2,3 at the interfaces which are equal to the addition of the equilibrium potential e81,2 and e82,3 (current equal to zero) and the drops in the overpotentials that de®ne the current passing through the interfaces. The oxide is considered to behave as a semi-conductor in which a redistribution of the applied charge due to the applied potential leads to a potential drop inside the ®lm. According to high-®eld conduction equations [27± 30] the permeation current in the oxide can be expressed as: ip ip;0 exp BEf
1
where ip,0 is the exchange current density proportional to the amount of charge carriers inside the ®lm (protons), B is a parameter equal to (qa/ 2kT), q being the charge of the current transporting species under the electric ®eld Ef and a the distance separating two potential barriers. An expression for ip,0 can be obtained from the equation for high ®eld transport in the presence of a concentration gradient [30]: ip;0 4a exp ÿW=RT
C0H ÿCeHox exp qE0 eox =RT ; 1 ÿ exp qE0 eox =RT
Fig. 6. Possible potential distribution at the solution/oxide/metal interfaces.
BRASS et al.: MECHANISM OF HYDROGEN PERMEATION
where C H is the hydrogen concentration at the 0 input side, dependent on potential e2,3 and C H eox the proton concentration when the distance x is equal to the oxide thickness (eox). The latter concentration can be considered to be in equilibrium with the hydrogen concentration on the ®rst layers beneath the surface (C0), thus: ip;0 4a exp ÿW=RT
C0H ÿC0 k exp qE0 eox =RT : 1 ÿ exp qE0 eox =RT
This equation predicts, as in [3], the dependence between J1 and the sample thickness. It is considered in this model, that the total cathodic current measured on the input surface is the sum of the current produced by the reduction of water at the solution/oxide interface plus the current corresponding to the injection of protons in the ®lm. More details on the behavior of hydrogen in oxides (solution/oxide interactions and mechanism on proton conduction) can be found elsewhere [31]. Given that the permeation current is two to three orders of magnitude smaller than the cathodic current (Fig. 1), we write, taking Tafel's equation into account: ic ic;0 exp be2;3 ip 1ic;0 exp be2;3
2
b = Fb0/RT, b0 being the transfer coecient for the cathodic reaction. The following condition is imposed for potentiostatic charge: e e1;2 e2;3 Ef eox E1 cte;
3
where e* is a constant which depends on the type of reference electrode, and E1 is the initially applied potential. The electrical potential in the metal is constant and imposed by the potentiostat. The tension drop e1,2 at the metal/oxide interface is considered to be constantly equal to the equilibrium value (e01,2) owing to a very high exchange current in the electron transfer reaction: H++1 eÿ4H0. When a cathodic potential is applied to the sample, tension is distributed between the oxide and the interface in a proportion which depends on the transport properties and the thickness of the oxide. If the ®lm is reduced during a time dt, with a decrease in thickness deox, the fraction of the tension applied to the ®lm will be redistributed between the ®lm and the interface and both the cathodic and the permeation currents will increase (Fig. 2). Once a stable thickness is reached, there will be a transfer of the applied potential from the interface to the oxide, giving origin, as experimentally observed (Figs 1 and 3), to a decrease in the cathodic current and an increase in the permeation current. Once the most stable condition for the distribution of potential has been attained between the metal/solution interface and the ®lm, the fact of
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imposing a new increase in the potential (E1 4E1+De) will force a new potential distribution between the oxide and the oxide/solution interface. This potential distribution will depend on the ®lm thickness, on the intrinsic transport properties of the oxide, and indirectly on the properties of the metal/solution interface. According to this model a galvanostatic control of the input metal surface would lead to a constant potential dierence at the oxide/solution interface during all the test (ip<
6
where ic(E1) is the cathodic current measured at potential E1. The changes in the cathodic current as a function of the potential increments are shown in Fig. 8.
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Fig. 7. Logarithm of the stationary permeation current through pure iron vs applied potential steps (0.1 N NaOH, 298 K). ip (E1) is the permeation current measured at potential equal to E1. Potential increments are expressed as overpotentials De (mV) relative to the potential E1.
The experimental data of Figs 7 and 8 allow us to obtain, for each test, the values of (Ba)/eox and b(1 ÿ a) reported in Table 1. Tests no. 6 and 7 were performed on 250 mm thick samples and test no. 1 on iron coated with palladium on the output side [18]. As shown by Fig. 1, the cathodic current recorded during cathodic polarization at ÿ1355 mV/NHE decreases before and during the ``plateau''. After the ``plateau'' (arrow on Fig. 1) the cathodic current starts to decrease with a steeper slope. The change in the permeation ¯ux is, however, slow enough to allow us to consider that the hydrogen concentration pro®le in the sheet is quasi-linear at every moment. As a matter of fact
the comparison of the constant d(DJ/J)/ dt for the time necessary to reach a constant hydrogen concentration on the input surface (maximum change in the experimental ¯ux with time) with the time constant for the diusion process D/e2 gives evidence that the change in the permeation ¯ux is at most 30 times larger than the change in the hydrogen concentration on the input surface. At the end of the ``plateau'' the ®lm is supposed to have a constant thickness eox and the constant tension applied between the ®lm and the oxide/solution interface begins to redistribute until a stationary value is reached for both currents. From equations (1)±(3) we can write:
Fig. 8. Logarithm of the cathodic current on pure iron vs applied potential steps (0.1 N NaOH, 298 K). ic (E1) is the cathodic current measured at potential equal to E1. Potential increments are expressed as overpotentials De (mV) relative to the potential E1.
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Table 1. Values of parameters a, b0, B, n and eox computed from the change in the hydrogen permeation ¯ux and the cathodic current density induced by potential increments in 0.1 N NaOH (298 K) Test a
1 2 3 4 5 6 7 8 9 10 11 12 13a 14a
Ba/eox (mVÿ1) ÿ3
5.755 10 4.642 10ÿ3 3.434 10ÿ3 4.145 10ÿ3 3.601 10ÿ3 1.312 10ÿ3 1.431 10ÿ3 1.927 10ÿ3 Ð Ð Ð Ð Ð Ð
b (1 ÿ a) (mVÿ1)
B/eoxb
ÿ2
1.038 10 1.092 10ÿ2 9.590 10ÿ3 1.041 10ÿ2 1.503 10ÿ2 8.983 10ÿ3 8.095 10ÿ3 6.884 10ÿ3 Ð Ð Ð Ð Ð Ð
0.687 0.607 Ð Ð Ð Ð Ð Ð 0.491 0.534 1.325 1.165 1.762 1.306
b0 0.475 0.471 0.473b 0.473b 0.473b 0.473b 0.473b 0.473b 0.473b 0.473b 0.473b 0.473b 0.473b 0.473b
a 0.447 0.412 0.485 0.441 0.193 0.518 0.565 0.630 Ð Ð Ð Ð Ð Ð
B/eox (mVÿ1) 1.29 1.13 7.08 9.40 1.86 2.53 2.53 3.06 9.15 9.95 2.47 2.17 3.28 2.43
ÿ2
10 10ÿ2 10ÿ3 10ÿ2 10ÿ2 10ÿ3 10ÿ3 10ÿ3 10ÿ3 10ÿ3 10ÿ2 10ÿ2 10ÿ2 10ÿ2
eox (nm) 0.63 0.73 1.16 0.88 0.44 3.25 3.26 2.70 0.90 0.83 0.33 0.38 0.26 0.34
n 0.555 0.425 0.358 0.396 0.230 0.146 0.177 0.280 Ð Ð Ð Ð Ð Ð
a
With palladium on the detection side. Mean value of b0 obtained from tests 1 and 2.
b
ln ip ln ip;0 ic;0 B=eox b exp
B E1 ÿ e ÿ e12 B ÿ ln ic : eox eox b
7
The inverse relationship between the cathodic and the permeation currents predicted by equation (7) is veri®ed by our experimental results as shown in Figs 1 and 9. Tests reported in Fig. 9 were conducted at ÿ1355 mV/NHE without subsequent increase or decrease in the applied potential (tests no. 9±12). The data plotted in Fig. 9 were taken after the ``plateau'' observed on the permeation curve (Fig. 1). In this case the change in (ip) and (ic) is due to a redistribution of the tension between the
oxide and the metal surface in order to maintain the potential constant. Results obtained with samples coated with palladium on the output side (tests no. 13 and 14) are also reported in Fig. 9. As already seen in Fig. 7 (test no. 1) the stationary hydrogen current through coated samples is larger.
3.3. Relationship between cathodic and permeation currents on pure iron oxidized in air at 298 K From equations (5) and (6) the value of De can be obtained as a function of (ip) and (ic): eox ip E1 1 ic E1 De ln : 8 ln Ba ip Ex 1 ÿ ab ic Ex Rearranging terms in equation (8) leads to:
Fig. 9. Logarithm of the permeation current (ip) through pure iron vs cathodic current (ic) after the ``plateau'' observed on permeation curves (cf. Fig. 1). Full symbols are relative to tests performed on samples coated with palladium on the output surface (0.1 N NaOH, 298 K).
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Fig. 10. Stationary permeation current through pure iron vs cathodic current (ic) after the potential steps (0.1 N NaOH, 298 K). The permeation current is normalized for a 1 cm thickness.
ln ip E1 ln ip Ex ÿ ln ic Ex
Ba beox 1 ÿ a Ba ln ic E1 9 beox 1 ÿ a
Fig. 10 shows the changes in the permeation current with respect to the cathodic current corresponding to additional increments in potential once the steady state has been reached. The exponential factor n connecting the permeation to the cathodic current according to ip=k. (ic)n can be drawn from equation (9): n
Ba : beox 1 ÿ a
10
The value of n computed from the data of Fig. 10 are given in the last column of Table 1. B/eoxb can be calculated from the slope of the graphs of Fig. 9. The estimation of B is possible according to the high-®eld theory. B = 8.25.10ÿ10 cm/mV with q = 1 (proton migration in the oxide ®lm). a is the distance between two crystallographic planes in Fe2O3 and was considered to be equal to 0.25 nm [32, 33]. The lack of accuracy in the determination of B which is due to the estimate of the parameter a can lead to an error of about 50% in the values of (eox) which can, however, be compared amongst themselves. The values of a, b0, B/eox and eox are given in Table 1. The complete set of parameters b0, a, eox and n could be calculated for tests no. 1 and 2. In this case a plateau was observed on the permeation curves and potential steps were performed after the steady state. Taking for b0 the mean value of tests
no. 1 and 2, a was calculated for tests no. 1±8 and eox for each test. The values of b0 (0.473) computed from tests no. 1 and 2 are close to 0.5, which corresponds to the theoretical value for a symmetrical potential barrier for the electron transfer. The changes in the cathodic current with the applied potential will indirectly depend on the oxide ®lm thickness through the term (1 ÿ a) in equation (6). This accounts for the large discrepancy in the values of the transfer coecients in alkaline media given in the literature. Although the values for a listed in Table 1 dier from one test to another, there is a very good correlation between the oxide ®lm thickness and the tension transfer coecient a. The experimental relationship between 1/a and 1/eox: 1/a = 1.02 + 1.37 10ÿ7 (cm)/eox is in favour of a hydrogen migration process through an oxide ®lm, given that the potential distribution in the electrochemical system is a function of the resistance of each phase to the mass transfer. The larger the oxide thickness the larger the fraction of potential applied in the oxide. It is apparent from the relationship between 1/a and 1/eox that for large values of the thickness of the remanent oxide, a tends to 1, which may be an explanation for cases where no intermediate ``plateau'' is observed in the permeation transient. Once the stationary regime is over, the remaining oxide ®lm is still so thick that the potential distribution is in its most stable condition, and this, from the beginning of the polarization. As a matter of fact the remanent oxide thickness computed from tests no. 2 and 8 show that eox
BRASS et al.: MECHANISM OF HYDROGEN PERMEATION
is larger when the permeation transient does not exhibit a ``plateau''. The thickness of the remanent oxide ranges 0.5 to 1.2 nm except for thin samples. This is qualitatively correlated with the results of Fig. 5 showing an increase in the cathodic current when sample thickness decreases. 4. CONCLUSIONS
The thin oxide layer grown in air at room temperature on pure iron with a negligible trap density leads to a small apparent diusion coecient of hydrogen when compared to the lattice diusivity. The hydrogen permeation in 0.1 N NaOH through pure iron oxidized in air at room temperature or at 523 K gives rise to distorted diusion pro®les correlated with a non-monotonic decrease in the cathodic current. The diusion coecient of hydrogen yields the lattice diusivity only if potential steps are imposed to the sample once a steady state is reached. A clear relationship is found between the cathodic and the permeation currents of tests performed at ÿ1355 mV/NHE on pure iron oxidized at 298 or 523 K. The experimental data cannot be explained by a discharge±adsorption±recombination mechanism. Hydrogen penetration in alkaline medium proceeds by proton migration across an oxide ®lm which is not reduced in spite of potentiostatic cathodic polarization. The model presented in this work allows us to assess the thickness of the remanent oxy-hydroxide ®lm which depends on the initial surface properties (thickness and nature of the air-grown oxide). This thickness ranges 0.5 to 1 nm. A very good correlation was found between the oxide thickness and the coecient of tension distribution between the ®lm and the oxide/metal interface. The in¯uence of passive layers, corrosion products or oxides formed at high temperature has to be taken into account in the assessment of the diusivity of hydrogen in iron base materials. REFERENCES 1. Fullenwider, M. A., J. electrochem. Soc., 1975, 122. 2. Early, J. G., Acta met., 1978, 26. 3. Pumphrey, P. H., Scripta met., 1980, 14.
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4. Brass, A. M. and Collet-Lacoste, J. J. electrochem. Soc. Submitted. 5. Zakroczymski, T. and Szklarska-Smialowska, Z., J. electrochem. Soc., 1985, 132. 6. Zakroczymski, T., Fan, Chwei-Jer and SzklarskaSmialowska, Z., J. electrochem. Soc., 1985, 132. 7. Brass, A. M. and Collet-Lacoste, J., Proc. 5th International Conference on Hydrogen Eects in Materials Behavior, ed. N Moody, A Thompson. 1994, p. 189. 8. Hagi, H., Hayashi, Y. and Othani, N., Trans. Japan Inst. Metals, 1979, 20. 9. Dillard, J. L., MeÂm. Sci. Rev. Met., 1970, 67. 10. Daft, E. G., Bohnenkamp, K. and Engell, H. J., Corros. Sci., 1979, 19. 11. Burstein, G. T. and Kearns, M. A., J. electrochem. Soc., 1984, 131. 12. Burstein, G. T. and Davis, D. H., Corros. Sci., 1980, 20. 13. Burstein, G. T. and Davis, D. H., J. electrochem. Soc., 1981, 33. 14. Devanathan, M. A. V. and Stachurski, Z., Proc. R. Soc., 1962, A270. 15. Charbonnier, J. C., Margot-Marette, H., Brass, A. M. and Aucouturier, M., Metall. Trans., 1985, 16A. 16. Bockris, J. O'. M, McBreen, J. and Nanis, L., J. electrochem. Soc., 1965, 112. 17. Collet-Lacoste, J., TheÁse de Doctorat es Sciences, Universite Paris-Sud, Orsay, 1993. 18. Brass, A. M. and Collet-Lacoste, J., in Hydrogen Transport and Cracking in Metals, 142, ed. A. Turnbull. Japan Inst. Mat., 1995. 19. Riecke, E. and Bohnenkamp, K., Z. Metallk., 1984, 75. 20. Kiuchi, K. and McLellan, R. B., Acta met., 1983, 31. 21. Quick, N. R. and Johnson, H. H., Acta met., 1978, 26. 22. Hashimoto, M. and Latanision, R. M., Metall. Trans., 1988, 19A. 23. Zakroczymski, T., Scripta met., 1985, 19. 24. Brass, A. M., Nevot, L., Aucouturier, M. and Berneron, R., Corros. Sci., 1984, 24. 25. Sewell, P. B., Stockbridge, C. D. and Cohen, M., J. electrochem. Soc., 1961, 108. 26. Berkowitz, B. J. and Horowitz, H. H., J. Electrochem. Soc., 1982, 129. 27. Kirchheim, R., Electrochim. Acta, 1987, 32. 28. Vetter, J. K. and Gorn, F., Electrochem. Acta, 1973, 18. 29. Vetter, J. K., Z. Elektrochem., 1954, 58. 30. Fromhold, A. T. Jr and Cook, E. L., J. appl Phys., 1967, 38. 31. Brass, A. M., Ann. Chim. Fr., 1989, 14. 32. Keddam, M., Lizee, J. F., Pallotta, C. D. and Takenouti, H., J. electrochem. Soc., 1981, 128. 33. Keddam, M. and Pallotta, C. D., Electrochim. Acta, 1985, 30.
Acta mater. Vol. 46, No. 3, pp. 869±879, 1998 # 1998 Acta Metallurgica Inc. Published by Elsevier Science Ltd. All rights reserved Printed in Great Britain 1359-6454/98 $19.00 + 0.00 S1359-6454(97)00311-X
ON THE MECHANISM OF HYDROGEN PERMEATION IN IRON IN ALKALINE MEDIUM A. M. BRASS{ and J. R. COLLET-LACOSTE{ Laboratoire de MeÂtallurgie Structurale, CNRS URA 1107, Universite Paris-Sud, 91405 Orsay Cedex, France (Received 14 August 1997; accepted 26 August 1997) AbstractÐHydrogen permeation tests were performed in pure iron in sodium hydroxide at 298 K, based on the electrochemical technique. Hydrogen charging was conducted under potentiostatic control, simultaneously registering both the permeation (ip) and the cathodic (ic) currents until stabilization. After a ®rst polarization transient at ÿ1105 or ÿ1355 mV/NHE, potential increments or decrements were performed, allowing in both cases the currents to stabilize. Based on the analysis of the experimental data, a model was developed, which takes into account the existence of a 0.5 to 1 nm thick unreduced air-grown oxide ®lm on the input side of the samples in spite of long cathodic polarization times. A good correlation between the potential distribution at the oxide/solution interface and the calculated oxide thickness was obtained. # 1998 Acta Metallurgica Inc. ReÂsumeÂÐLa diusion de l'hydrogeÁne dans du fer pur a eÂte eÂtudieÂe aÁ tempeÂrature ambiante en milieu basique aÁ l'aide de la technique de permeÂation eÂlectrochimique. Le courant total d'hydrogeÁne deÂcharge sur la surface par polarisation cathodique aÁ potential impose (ÿ1105 or ÿ1355 mV/NHE) a eÂte mesure en continu et compare au ¯ux de permeÂation. La concentration d'hydrogeÁne disponible sur la surface a eÂte modi®eÂe par paliers successifs une fois un reÂgime permanent de diusion atteint. Les reÂsultats expeÂrimentaux ont eÂte modeÂliseÂs en consideÂrant une reÂduction incompleÁte de l'oxyde super®ciel naturel sous polarisation cathodique et la diusion d'hydrogeÁne au travers d'un ®lm reÂmanent d'oxy-hydoxyde de treÁs faible eÂpaisseur (0.5 aÁ 1 nm). # 1998 Acta Metallurgica Inc.
1. INTRODUCTION
The knowledge of the diusion coecient of hydrogen in metals and the related problems of trapping and surface eects is necessary in order to improve the understanding of hydrogen embrittlement and stress corrosion cracking phenomena. Trapping eects can be considered to be negligible in well recrystallized pure iron whereas passive and oxide ®lms are unavoidable, namely in alkaline aqueous environments, and may greatly in¯uence the hydrogen ingress at room temperature in metals where the hydrogen diusivity is large. The information required in order to solve Fick's equations for hydrogen permeation in a given system is both the hydrogen concentration or the hydrogen ¯ux at any time (at input and output sides of the plane sheets where hydrogen diusion proceeds) and the initial conditions, i.e. the hydrogen concentration distribution in the metal. Two options are possible regarding the boundary condition at the input surface where hydrogen is discharged: to assume a step increase in concen{To whom all correspondence should be addressed. {On leave from U.A. Quimica. Comision Nacional de Energia Atomica, 8250 Av. del Libertador, 1429 Buenos Aires, Argentina. 869
tration (constant concentration at charged surface) or in ¯ux (constant ¯ux entering at charged surface) at the beginning of the polarization and during the test [1±3]. Some authors [1, 2] suggest that the constant concentration condition can only be applied if the charging condition is potentiostatic, and that the constant ¯ux condition at charged surface is only valid for galvanostatic charging. This is true for Pd [2, 4] but has not been proved for iron [3]. Furthermore some works in the literature report the existence of an oxide ®lm not completely reduced which play the role of a barrier for the penetration of hydrogen in the metal during long cathodic polarizations. Distortions in the hydrogen permeation transients [5±9] are often observed together with non-linear changes in the permeation ¯ux with the square root of the cathodic current as well as values of the exponential factor n connecting the permeation and the cathodic current smaller than 0.5 [5]. An independence of the permeation ¯ux on the cathodic current for very high current values was stated together with a transfer coecient close to 0.5 [10]. Changes in the transfer coecient and in the exchange current during scratching tests were observed [11] with the formation of a mono-layer of adsorbed FeOOH after scratching [12, 13].
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The purpose of this paper is to present a model for the hydrogen penetration in pure iron in alkaline medium. A remnant oxi-hydroxide ®lm on the input surface accounts for experimental relationships between the permeation and the cathodic currents. 2. EXPERIMENTAL
2.1. Material A pure iron bar was homogenized in vacuum for 24 h at 1123 K. The chemical composition (wt. ppm) is the following: C: 40 ppm, S: 35 ppm, O2: 3 ppm, N2: 5 ppm, P: 40 ppm, Si: 40 ppm. 0.25 cm thick slides were given a thermal treatment in vacuum for 24 h at 1453 K followed by water quenching. Electrolytical polishing was then performed before cold working (R.A. 50%). A thermal treatment in vacuum for 24 h at 1053 K was conducted before ®nal polishing to a thickness ranging from 200 to 1070 mm. The large ®nal grain size (200 mm) and the small dislocation density obtained with this heat treatment, together with the very small amount of impurities allowed us to consider that trapping of hydrogen on microstructural defects will be negligible. 2.1.1. Surface preparation. The samples were mechanically polished with a 1200 grid paper on one side and with a 1 mm diamond paste on the other side. Ultrasonic cleaning was successively conducted in trichlorethylene, butanol and acetone. Surface ®nishing was performed just before the set up of the samples in the experimental device. Some iron probes were purposely oxidized at 523 K for 15 h. The oxide thickness (100 nm) was measured by abrasion in an ionic analyzer and measurements of the craters with a talystep device. 2.2. Electrochemical permeation test The permeation cell [14] is composed of two double wall glass compartments separated by the sample (working electrode) clamped in a separate sample holder. Thermostated water is circulated in the double jacket in order to maintain a constant temperature in both chambers (298 20.1 K). In the charging compartment the specimen is the cathode and the anode is a platinum electrode. The reference electrode is immersed in a luggin capillary ®lled with NaOH. Hydrogen production is carried out by cathodic polarization in 0.1 N NaOH at a constant potential value according to: H2O + 2eÿ4H2+2OHÿ. In the detection (anodic) compartment the output side of the sample is polarized in the passive range in 0.1 N NaOH so that hydrogen is oxidized according to: Hads 4H++eÿ. The smallest value (less than 10 nA cmÿ2) of the background current [15] was obtained by applying the rest potential (ED) measured on the output face under open circuit conditions and continuous argon
bubbling until stabilization (15 h). In order to avoid the formation of a passive ®lm on the input side of the sample by contact with the charging solution (0.1 N NaOH) under open circuit conditions before the beginning of the permeation test, the cathodic polarization was started during the introduction of the preheated solution in the charging compartment (instantaneous cathodic polarization). The experiments were carried out by imposing a constant potential E1= ÿ 1105 or ÿ1355 mV/NHE. Both the permeation (ip) and the cathodic (ic) currents were simultaneously registered and allowed to stabilize for more than 20 h. In some experiments potential steps (De = 25 or 50 mV) were then performed, allowing in both cases the currents to stabilize. These steps could involve either increments or decrements from the initial potential value E1. 3. RESULTS AND DISCUSSION
The hydrogen entry condition must be consistent with one of the two physical-chemistry processes (equilibrium or kinetic) that occur on the surface [3]: (i) Equilibrium is reached between the external phase and the hydrogen absorbed in the ®rst metallic layers (C(0,t) = C0) at e = 0 where e is the sample thickness. No condition is imposed on the entrance ¯ux (which is in®nite at t = 0). The hydrogen ¯ux on the input side is dependent on the diusion process beneath the surface. In this way, the external system must be capable of a quick reaction to the demand of hydrogen from the inner metal, so as to maintain equilibrium as hydrogen diuses through the bulk. In this case as input concentration only depends on the thermodynamical state of the external phase, the stationary ¯ux of hydrogen J1 is inversely proportional to the metallic sheet thickness. (ii) The other case involves a constant input ¯ux (J(0,t) = J0) and an input concentration that increases from 0 at t = 0 to a maximum value equal to Cmax=J0 e/D, where D is the diusion coecient of hydrogen. The system is not in equilibrium with the external phase and the amount of hydrogen that penetrates the metal depends on the kinetic parameters of transfer phenomena between the external phase and the metal. The stationary hydrogen ¯ux is then independent on the thickness of the sheet. For both cases, if continuous changes occur in the surface properties during the hydrogen charge (changes in the values of the equilibrium or kinetic constants) or in the concentration of adsorbed or absorbed hydrogen which regulates the concentration or entrance ¯ux, changes in C0 and J0 with time will be observed. Distortions in the permeation curves usually are attributed to changes in C0 with time.
BRASS et al.: MECHANISM OF HYDROGEN PERMEATION
In the case of iron, it was stated that the constants kabs and kdes for the reaction: Hadsorbed\Habsorbed are ®nite, which makes the boundary condition for input: J(0,t) = kabs y ÿ kdes C(0,t). Assuming y is attained instantaneously at t = 0, the input ¯ux decreases with time to reach a stationary state and the concentration a maximum value C1. This model [3] is an example of case (ii) in which the desorption time depends on the entry concentration C(0,t). The inverse of the ¯ux as a function of the thickness is linear (the extrapolation to e = 0 gives 1/kabsy) as a consequence of a dependence of the entry ¯ux on C(0,t). However, this model predicts a constant cathodic current, given that the latter changes as y2 [16] with y considered as constant. 3.1. Experimental observations relative to hydrogen permeation in pure iron in 0.1 N NaOH The permeation curves obtained by cathodic charging at ÿ1105 mV/NHE are distorted whereas a well marked ``plateau'' is observed in the transient of permeation curves resulting from cathodic charging at ÿ1355 mV/MHE (Fig. 1). This ``plateau'' is followed by a much slower increase in the permeation current before the maximum stationary value is attained. An increase in the cathodic current is observed within the ®rst 10 min following the start of the cathodic polarization (Fig. 2(a)). For samples oxidized at 523 K a similar increase is observed immediately after the start of charging (Fig. 2(b)). However, a maximum in (ic) is reached after 5±7 h instead of 10 min or less with probes oxidized in air at 298 K (Fig. 2(a)). The transients of the permeation curves obtained with samples oxidized at 523 K exhibit strong distortions even at ÿ1105 mV/NHE (Fig. 3) with a maximum in the
871
hydrogen ¯ux corresponding to the maximum in the cathodic current. A sharp decrease in the cathodic current (Fig. 1) is observed as the permeation current increases, even when the stationary state is reached. The drop in the cathodic current is smaller after a potential step than during the ®rst charging [17]. These experimental observations are inconsistent with discharge±absorption±recombination models [16] since both the permeation and the recombination currents should increase as a consequence of an increase in the fraction y of the sites occupied by hydrogen. The diusion coecient of hydrogen calculated from the ®rst polarization transient yields 4.10ÿ6 cm2/s at 298 K. This value is small when compared to the highest diusivity (8 to 9.5 10 ÿ5 cm2/s) of hydrogen in pure iron reported in the literature [19±23]. However, potential steps [18] conducted after the steady state allowed us to reach 8.10ÿ5 cm2/s. The changes in the reciprocal value of the stationary hydrogen ¯ux (J1) with the sample thickness are shown in Fig. 4 for tests performed at ÿ1105 mV/NHE. In spite of the discrepancy of the results obtained with tests performed for the same thickness, it is clear that the permeation ¯ux increases as the thickness decreases. Nevertheless, the line drawn by the method of least squares does not pass through the origin. This fact is inconsistent with Bockris's model [16] predicting the intercept to be equal to zero (case (i)). Another interesting fact is shown in Fig. 5, where Qc, the total amount of hydrogen discharged on the input side, was plotted as a function of the sample thickness for ®ve dierent values of charging time. It is apparent that the mean cathodic current, which is proportional to Qc, becomes larger as the
Fig. 1. Change in the permeation and cathodic currents during cathodic charging of pure iron at ÿ1355 mV/NHE (0.1 N NaOH, 298 K, e = 830 mm).
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Fig. 2. (a) Cathodic current (3 tests) vs time on iron oxidized at 298 K polarized at ÿ1105 mV/NHE (0.1 N NaOH, 298 K); (b) cathodic current vs time on iron (0.1 N NaOH, 298 K). (a) (b) samples oxidized at 298 K polarized, respectively, at ÿ1105 and ÿ1355 mV/NHE, (c) (d) samples oxidized at 523 K polarized, respectively, at ÿ1105 and ÿ1355 mV/NHE.
thickness of the metal sheet decreases and the polarization time increases. This dependence is inconsistent with a model involving an equilibrium between the external phase and the ®rst metallic layers since under this condition, the input concentration is controlled by the external phase and the hydrogen ¯ux only by the diusion process. Since the cathodic current is ®xed by the physical properties of the surface, the observed results would imply a dependence of the input hydrogen ¯ux with the sample thickness.
3.2. Migration of hydrogen through an oxide ®lm The potentials for the reactions: 2Fe3 O4 H2 O , 3Fe2 O3 2H 2eÿ and 2Fe 4H2 O , 3Fe3 O4 8H 8eÿ are, respectively, equal to ÿ550 mV/NHE and ÿ855 mV/NHE in a solution at pH 13. From a
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873
Fig. 3. Normalized hydrogen ¯ux vs t (Dt/e2) in pure iron cathodically charged at ÿ1105 mV/NHE (0.1 N NaOH, 298 K), (a) samples oxidized in air at 298 K (standard deviation of 10 tests), (b) samples oxidized in air at 523 K (2 tests).
thermodynamical point of view, oxide ®lms grown in air at room temperature on iron are thus unstable at potentials more cathodic than ÿ855 mV/ NHE at this pH. Though neither structure nor composition of these ®lms are exactly known, their thickness lies between 6 and 18 nm [24], depending on the medium where they are formed. Some authors arm [25, 26] that after a period of time ranging between a few seconds and 5 min the air grown oxide is completely reduced under cathodic discharge. Nevertheless, other works [5, 6, 11] show that at this pH a non-reduced oxide ®lm remains on the surface, even under cathodic polarization. In order to analyze our experimental results we assume the surface air grown oxide to be reduced
to a very thin layer of remanent oxy-hydroxide with a thickness (eox) which does not change with time, or has actually a very slow dissolution kinetics through all the test duration. Figure 6 shows the assumed potential distribution between the solution, the oxide and the metal. The basic assumptions involve: Ðpotential in the solution and in the metal is considered as constant, given the high conductivity with respect to the interfaces 1/2 and 2/3, and the oxide ®lm. Ða large potential drop D V produced on the ®lm, which leads to a high electric ®eld Ef equal to: Ef=(D V/e).
Fig. 4. Change in the inverse stationary ¯ux of hydrogen as a function of the sample thickness for cathodic polarization of pure iron at ÿ1105 mV/NHE (0.1 N NaOH, 298 K).
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BRASS et al.: MECHANISM OF HYDROGEN PERMEATION
Fig. 5. Change in the amount of hydrogen discharged on pure iron as a function of the sample thickness for dierent values of polarization time at ÿ1105 mV/NHE (0.1 N NaOH, 298 K).
Ðpotential drops e1,2 and e2,3 at the interfaces which are equal to the addition of the equilibrium potential e81,2 and e82,3 (current equal to zero) and the drops in the overpotentials that de®ne the current passing through the interfaces. The oxide is considered to behave as a semi-conductor in which a redistribution of the applied charge due to the applied potential leads to a potential drop inside the ®lm. According to high-®eld conduction equations [27± 30] the permeation current in the oxide can be expressed as: ip ip;0 exp BEf
1
where ip,0 is the exchange current density proportional to the amount of charge carriers inside the ®lm (protons), B is a parameter equal to (qa/ 2kT), q being the charge of the current transporting species under the electric ®eld Ef and a the distance separating two potential barriers. An expression for ip,0 can be obtained from the equation for high ®eld transport in the presence of a concentration gradient [30]: ip;0 4a exp ÿW=RT
C0H ÿCeHox exp qE0 eox =RT ; 1 ÿ exp qE0 eox =RT
Fig. 6. Possible potential distribution at the solution/oxide/metal interfaces.
BRASS et al.: MECHANISM OF HYDROGEN PERMEATION
where C H is the hydrogen concentration at the 0 input side, dependent on potential e2,3 and C H eox the proton concentration when the distance x is equal to the oxide thickness (eox). The latter concentration can be considered to be in equilibrium with the hydrogen concentration on the ®rst layers beneath the surface (C0), thus: ip;0 4a exp ÿW=RT
C0H ÿC0 k exp qE0 eox =RT : 1 ÿ exp qE0 eox =RT
This equation predicts, as in [3], the dependence between J1 and the sample thickness. It is considered in this model, that the total cathodic current measured on the input surface is the sum of the current produced by the reduction of water at the solution/oxide interface plus the current corresponding to the injection of protons in the ®lm. More details on the behavior of hydrogen in oxides (solution/oxide interactions and mechanism on proton conduction) can be found elsewhere [31]. Given that the permeation current is two to three orders of magnitude smaller than the cathodic current (Fig. 1), we write, taking Tafel's equation into account: ic ic;0 exp be2;3 ip 1ic;0 exp be2;3
2
b = Fb0/RT, b0 being the transfer coecient for the cathodic reaction. The following condition is imposed for potentiostatic charge: e e1;2 e2;3 Ef eox E1 cte;
3
where e* is a constant which depends on the type of reference electrode, and E1 is the initially applied potential. The electrical potential in the metal is constant and imposed by the potentiostat. The tension drop e1,2 at the metal/oxide interface is considered to be constantly equal to the equilibrium value (e01,2) owing to a very high exchange current in the electron transfer reaction: H++1 eÿ4H0. When a cathodic potential is applied to the sample, tension is distributed between the oxide and the interface in a proportion which depends on the transport properties and the thickness of the oxide. If the ®lm is reduced during a time dt, with a decrease in thickness deox, the fraction of the tension applied to the ®lm will be redistributed between the ®lm and the interface and both the cathodic and the permeation currents will increase (Fig. 2). Once a stable thickness is reached, there will be a transfer of the applied potential from the interface to the oxide, giving origin, as experimentally observed (Figs 1 and 3), to a decrease in the cathodic current and an increase in the permeation current. Once the most stable condition for the distribution of potential has been attained between the metal/solution interface and the ®lm, the fact of
875
imposing a new increase in the potential (E1 4E1+De) will force a new potential distribution between the oxide and the oxide/solution interface. This potential distribution will depend on the ®lm thickness, on the intrinsic transport properties of the oxide, and indirectly on the properties of the metal/solution interface. According to this model a galvanostatic control of the input metal surface would lead to a constant potential dierence at the oxide/solution interface during all the test (ip<
6
where ic(E1) is the cathodic current measured at potential E1. The changes in the cathodic current as a function of the potential increments are shown in Fig. 8.
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BRASS et al.: MECHANISM OF HYDROGEN PERMEATION
Fig. 7. Logarithm of the stationary permeation current through pure iron vs applied potential steps (0.1 N NaOH, 298 K). ip (E1) is the permeation current measured at potential equal to E1. Potential increments are expressed as overpotentials De (mV) relative to the potential E1.
The experimental data of Figs 7 and 8 allow us to obtain, for each test, the values of (Ba)/eox and b(1 ÿ a) reported in Table 1. Tests no. 6 and 7 were performed on 250 mm thick samples and test no. 1 on iron coated with palladium on the output side [18]. As shown by Fig. 1, the cathodic current recorded during cathodic polarization at ÿ1355 mV/NHE decreases before and during the ``plateau''. After the ``plateau'' (arrow on Fig. 1) the cathodic current starts to decrease with a steeper slope. The change in the permeation ¯ux is, however, slow enough to allow us to consider that the hydrogen concentration pro®le in the sheet is quasi-linear at every moment. As a matter of fact
the comparison of the constant d(DJ/J)/ dt for the time necessary to reach a constant hydrogen concentration on the input surface (maximum change in the experimental ¯ux with time) with the time constant for the diusion process D/e2 gives evidence that the change in the permeation ¯ux is at most 30 times larger than the change in the hydrogen concentration on the input surface. At the end of the ``plateau'' the ®lm is supposed to have a constant thickness eox and the constant tension applied between the ®lm and the oxide/solution interface begins to redistribute until a stationary value is reached for both currents. From equations (1)±(3) we can write:
Fig. 8. Logarithm of the cathodic current on pure iron vs applied potential steps (0.1 N NaOH, 298 K). ic (E1) is the cathodic current measured at potential equal to E1. Potential increments are expressed as overpotentials De (mV) relative to the potential E1.
BRASS et al.: MECHANISM OF HYDROGEN PERMEATION
877
Table 1. Values of parameters a, b0, B, n and eox computed from the change in the hydrogen permeation ¯ux and the cathodic current density induced by potential increments in 0.1 N NaOH (298 K) Test a
1 2 3 4 5 6 7 8 9 10 11 12 13a 14a
Ba/eox (mVÿ1) ÿ3
5.755 10 4.642 10ÿ3 3.434 10ÿ3 4.145 10ÿ3 3.601 10ÿ3 1.312 10ÿ3 1.431 10ÿ3 1.927 10ÿ3 Ð Ð Ð Ð Ð Ð
b (1 ÿ a) (mVÿ1)
B/eoxb
ÿ2
1.038 10 1.092 10ÿ2 9.590 10ÿ3 1.041 10ÿ2 1.503 10ÿ2 8.983 10ÿ3 8.095 10ÿ3 6.884 10ÿ3 Ð Ð Ð Ð Ð Ð
0.687 0.607 Ð Ð Ð Ð Ð Ð 0.491 0.534 1.325 1.165 1.762 1.306
b0 0.475 0.471 0.473b 0.473b 0.473b 0.473b 0.473b 0.473b 0.473b 0.473b 0.473b 0.473b 0.473b 0.473b
a 0.447 0.412 0.485 0.441 0.193 0.518 0.565 0.630 Ð Ð Ð Ð Ð Ð
B/eox (mVÿ1) 1.29 1.13 7.08 9.40 1.86 2.53 2.53 3.06 9.15 9.95 2.47 2.17 3.28 2.43
ÿ2
10 10ÿ2 10ÿ3 10ÿ2 10ÿ2 10ÿ3 10ÿ3 10ÿ3 10ÿ3 10ÿ3 10ÿ2 10ÿ2 10ÿ2 10ÿ2
eox (nm) 0.63 0.73 1.16 0.88 0.44 3.25 3.26 2.70 0.90 0.83 0.33 0.38 0.26 0.34
n 0.555 0.425 0.358 0.396 0.230 0.146 0.177 0.280 Ð Ð Ð Ð Ð Ð
a
With palladium on the detection side. Mean value of b0 obtained from tests 1 and 2.
b
ln ip ln ip;0 ic;0 B=eox b exp
B E1 ÿ e ÿ e12 B ÿ ln ic : eox eox b
7
The inverse relationship between the cathodic and the permeation currents predicted by equation (7) is veri®ed by our experimental results as shown in Figs 1 and 9. Tests reported in Fig. 9 were conducted at ÿ1355 mV/NHE without subsequent increase or decrease in the applied potential (tests no. 9±12). The data plotted in Fig. 9 were taken after the ``plateau'' observed on the permeation curve (Fig. 1). In this case the change in (ip) and (ic) is due to a redistribution of the tension between the
oxide and the metal surface in order to maintain the potential constant. Results obtained with samples coated with palladium on the output side (tests no. 13 and 14) are also reported in Fig. 9. As already seen in Fig. 7 (test no. 1) the stationary hydrogen current through coated samples is larger.
3.3. Relationship between cathodic and permeation currents on pure iron oxidized in air at 298 K From equations (5) and (6) the value of De can be obtained as a function of (ip) and (ic): eox ip E1 1 ic E1 De ln : 8 ln Ba ip Ex 1 ÿ ab ic Ex Rearranging terms in equation (8) leads to:
Fig. 9. Logarithm of the permeation current (ip) through pure iron vs cathodic current (ic) after the ``plateau'' observed on permeation curves (cf. Fig. 1). Full symbols are relative to tests performed on samples coated with palladium on the output surface (0.1 N NaOH, 298 K).
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Fig. 10. Stationary permeation current through pure iron vs cathodic current (ic) after the potential steps (0.1 N NaOH, 298 K). The permeation current is normalized for a 1 cm thickness.
ln ip E1 ln ip Ex ÿ ln ic Ex
Ba beox 1 ÿ a Ba ln ic E1 9 beox 1 ÿ a
Fig. 10 shows the changes in the permeation current with respect to the cathodic current corresponding to additional increments in potential once the steady state has been reached. The exponential factor n connecting the permeation to the cathodic current according to ip=k. (ic)n can be drawn from equation (9): n
Ba : beox 1 ÿ a
10
The value of n computed from the data of Fig. 10 are given in the last column of Table 1. B/eoxb can be calculated from the slope of the graphs of Fig. 9. The estimation of B is possible according to the high-®eld theory. B = 8.25.10ÿ10 cm/mV with q = 1 (proton migration in the oxide ®lm). a is the distance between two crystallographic planes in Fe2O3 and was considered to be equal to 0.25 nm [32, 33]. The lack of accuracy in the determination of B which is due to the estimate of the parameter a can lead to an error of about 50% in the values of (eox) which can, however, be compared amongst themselves. The values of a, b0, B/eox and eox are given in Table 1. The complete set of parameters b0, a, eox and n could be calculated for tests no. 1 and 2. In this case a plateau was observed on the permeation curves and potential steps were performed after the steady state. Taking for b0 the mean value of tests
no. 1 and 2, a was calculated for tests no. 1±8 and eox for each test. The values of b0 (0.473) computed from tests no. 1 and 2 are close to 0.5, which corresponds to the theoretical value for a symmetrical potential barrier for the electron transfer. The changes in the cathodic current with the applied potential will indirectly depend on the oxide ®lm thickness through the term (1 ÿ a) in equation (6). This accounts for the large discrepancy in the values of the transfer coecients in alkaline media given in the literature. Although the values for a listed in Table 1 dier from one test to another, there is a very good correlation between the oxide ®lm thickness and the tension transfer coecient a. The experimental relationship between 1/a and 1/eox: 1/a = 1.02 + 1.37 10ÿ7 (cm)/eox is in favour of a hydrogen migration process through an oxide ®lm, given that the potential distribution in the electrochemical system is a function of the resistance of each phase to the mass transfer. The larger the oxide thickness the larger the fraction of potential applied in the oxide. It is apparent from the relationship between 1/a and 1/eox that for large values of the thickness of the remanent oxide, a tends to 1, which may be an explanation for cases where no intermediate ``plateau'' is observed in the permeation transient. Once the stationary regime is over, the remaining oxide ®lm is still so thick that the potential distribution is in its most stable condition, and this, from the beginning of the polarization. As a matter of fact the remanent oxide thickness computed from tests no. 2 and 8 show that eox
BRASS et al.: MECHANISM OF HYDROGEN PERMEATION
is larger when the permeation transient does not exhibit a ``plateau''. The thickness of the remanent oxide ranges 0.5 to 1.2 nm except for thin samples. This is qualitatively correlated with the results of Fig. 5 showing an increase in the cathodic current when sample thickness decreases. 4. CONCLUSIONS
The thin oxide layer grown in air at room temperature on pure iron with a negligible trap density leads to a small apparent diusion coecient of hydrogen when compared to the lattice diusivity. The hydrogen permeation in 0.1 N NaOH through pure iron oxidized in air at room temperature or at 523 K gives rise to distorted diusion pro®les correlated with a non-monotonic decrease in the cathodic current. The diusion coecient of hydrogen yields the lattice diusivity only if potential steps are imposed to the sample once a steady state is reached. A clear relationship is found between the cathodic and the permeation currents of tests performed at ÿ1355 mV/NHE on pure iron oxidized at 298 or 523 K. The experimental data cannot be explained by a discharge±adsorption±recombination mechanism. Hydrogen penetration in alkaline medium proceeds by proton migration across an oxide ®lm which is not reduced in spite of potentiostatic cathodic polarization. The model presented in this work allows us to assess the thickness of the remanent oxy-hydroxide ®lm which depends on the initial surface properties (thickness and nature of the air-grown oxide). This thickness ranges 0.5 to 1 nm. A very good correlation was found between the oxide thickness and the coecient of tension distribution between the ®lm and the oxide/metal interface. The in¯uence of passive layers, corrosion products or oxides formed at high temperature has to be taken into account in the assessment of the diusivity of hydrogen in iron base materials. REFERENCES 1. Fullenwider, M. A., J. electrochem. Soc., 1975, 122. 2. Early, J. G., Acta met., 1978, 26. 3. Pumphrey, P. H., Scripta met., 1980, 14.
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4. Brass, A. M. and Collet-Lacoste, J. J. electrochem. Soc. Submitted. 5. Zakroczymski, T. and Szklarska-Smialowska, Z., J. electrochem. Soc., 1985, 132. 6. Zakroczymski, T., Fan, Chwei-Jer and SzklarskaSmialowska, Z., J. electrochem. Soc., 1985, 132. 7. Brass, A. M. and Collet-Lacoste, J., Proc. 5th International Conference on Hydrogen Eects in Materials Behavior, ed. N Moody, A Thompson. 1994, p. 189. 8. Hagi, H., Hayashi, Y. and Othani, N., Trans. Japan Inst. Metals, 1979, 20. 9. Dillard, J. L., MeÂm. Sci. Rev. Met., 1970, 67. 10. Daft, E. G., Bohnenkamp, K. and Engell, H. J., Corros. Sci., 1979, 19. 11. Burstein, G. T. and Kearns, M. A., J. electrochem. Soc., 1984, 131. 12. Burstein, G. T. and Davis, D. H., Corros. Sci., 1980, 20. 13. Burstein, G. T. and Davis, D. H., J. electrochem. Soc., 1981, 33. 14. Devanathan, M. A. V. and Stachurski, Z., Proc. R. Soc., 1962, A270. 15. Charbonnier, J. C., Margot-Marette, H., Brass, A. M. and Aucouturier, M., Metall. Trans., 1985, 16A. 16. Bockris, J. O'. M, McBreen, J. and Nanis, L., J. electrochem. Soc., 1965, 112. 17. Collet-Lacoste, J., TheÁse de Doctorat es Sciences, Universite Paris-Sud, Orsay, 1993. 18. Brass, A. M. and Collet-Lacoste, J., in Hydrogen Transport and Cracking in Metals, 142, ed. A. Turnbull. Japan Inst. Mat., 1995. 19. Riecke, E. and Bohnenkamp, K., Z. Metallk., 1984, 75. 20. Kiuchi, K. and McLellan, R. B., Acta met., 1983, 31. 21. Quick, N. R. and Johnson, H. H., Acta met., 1978, 26. 22. Hashimoto, M. and Latanision, R. M., Metall. Trans., 1988, 19A. 23. Zakroczymski, T., Scripta met., 1985, 19. 24. Brass, A. M., Nevot, L., Aucouturier, M. and Berneron, R., Corros. Sci., 1984, 24. 25. Sewell, P. B., Stockbridge, C. D. and Cohen, M., J. electrochem. Soc., 1961, 108. 26. Berkowitz, B. J. and Horowitz, H. H., J. Electrochem. Soc., 1982, 129. 27. Kirchheim, R., Electrochim. Acta, 1987, 32. 28. Vetter, J. K. and Gorn, F., Electrochem. Acta, 1973, 18. 29. Vetter, J. K., Z. Elektrochem., 1954, 58. 30. Fromhold, A. T. Jr and Cook, E. L., J. appl Phys., 1967, 38. 31. Brass, A. M., Ann. Chim. Fr., 1989, 14. 32. Keddam, M., Lizee, J. F., Pallotta, C. D. and Takenouti, H., J. electrochem. Soc., 1981, 128. 33. Keddam, M. and Pallotta, C. D., Electrochim. Acta, 1985, 30.