Influence of Zn on the oxide layer on AISI 316L(NG) stainless steel in simulated pressurised water reactor coolant

Electrochimica Acta 54 (2009) 1056–1069

Contents lists available at ScienceDirect

Electrochimica Acta journal homepage: www.elsevier.com/locate/electacta

Influence of Zn on the oxide layer on AISI 316L(NG) stainless steel in simulated pressurised water reactor coolant Iva Betova a , Martin Bojinov b,∗ , Petri Kinnunen c , Klas Lundgren d , Timo Saario c a

Department of Chemistry, Technical University of Sofia, Kl. Ohridski Blvd. 8, 1000 Sofia, Bulgaria Department of Physical Chemistry, University of Chemical Technology and Metallurgy, Kl. Ohridski Blvd. 8, 1756 Sofia, Bulgaria c VTT Materials and Building, Technical Research Centre of Finland, P.O. Box 1000, FIN-02044 VTT Espoo, Finland d ALARA Engineering AB, P.O. Box 26, SE-730 50 Skultuna, Sweden b

a r t i c l e

i n f o

Article history: Received 4 June 2008 Received in revised form 19 August 2008 Accepted 22 August 2008 Available online 30 August 2008 Keywords: Stainless steel Pressurised water reactor coolant Oxide film growth Zinc incorporation Kinetic model

a b s t r a c t The oxidation of AISI 316L(NG) stainless steel in simulated pressurised water reactor (PWR) coolant with or without addition of 1 ppm Zn at 280 ◦ C for up to 96 h has been characterised in situ by electrochemical impedance spectroscopy (EIS), both at the corrosion potential and under anodic polarisation up to 0.5 V vs. the reversible hydrogen electrode (RHE). Additional tests were performed in simulated PWR coolant with the addition of 0.01 M Na2 B4 O7 to exclude the effect of pH excursions probably due to Zn hydrolysis reactions. The thickness and in-depth composition of the oxide films formed at open circuit and at 0.5 V vs. RHE in the investigated electrolytes have been estimated from X-ray photoelectron spectroscopy (XPS) depth profiles. The kinetic and transport parameters characterising the oxide layer growth have been estimated using a calculational procedure based on the mixed conduction model for oxide films. Successful simulations of both the EIS and XPS data have been obtained. The parameter estimates are discussed in terms of the effect of Zn on the oxide layers on stainless steel in PWR conditions. © 2008 Elsevier Ltd. All rights reserved.

1. Introduction The ultimate goal of this work is to develop a deterministic model for activity incorporation in coolant circuits of light water reactors (LWRs) and to increase the theoretical understanding of the oxide film build-up and breakdown, controlling the localised corrosion phenomena of structural materials in such reactors. In order to ensure adequate modelling, uncertain or non-determined fundamental parameters are planned to be set or adjusted within the range of reasonable values by evaluating well-defined or wellcontrolled in-plant observations or laboratory experiments. The aim of the present communication is to estimate kinetic parameters of the incorporation of electrolyte originating species such as Zn during the initial stages of film growth on stainless steel in simulated pressurised water reactor (PWR) conditions, as well as the effect of this process on film growth and restructuring. The mechanisms of the influence of the oxide layers on activity incorporation and localised corrosion phenomena have been investigated basically in two ways. The first, related mainly to the study of the role of surface oxides in different forms of material corrosion, has resulted in the elaboration of several models for

∗ Corresponding author. E-mail address: [email protected] (M. Bojinov). 0013-4686/$ – see front matter © 2008 Elsevier Ltd. All rights reserved. doi:10.1016/j.electacta.2008.08.040

film growth and restructuring, as well as corrosion product release [1–7]. These models have been based mainly on surface analytical and morphological data for oxides formed during exposure to a range of (electro)chemical conditions pertinent to different types of operating nuclear power plants. In situ electrochemical, mechanoelectrochemical and analytical methods have started to contribute to the scientific basis of such models only recently, their importance being widely recognized [8–11]. The second type of studies has been mainly promoted by the need to understand the mechanism of radioactivity build-up in primary circuits, as well as that of stress corrosion crack initiation, and has been focused on the interaction of the oxides with coolant-originating cationic and anionic species [12–37]. In these approaches, growth and restructuring of the oxides in LWR conditions have been studied mostly by measuring depth profiles of electrolyte-originating cationic species (Zn, Mn, Mg, Ni, etc.) throughout the oxide film on the construction material. Although during recent years, both ways of investigation have contributed significantly to the increase of our understanding, our opinion is that no significant cross-linking between the two approaches has been attempted in order to combine the gained knowledge in a more quantitative way. Recently, the mixed-conduction model for oxide films (MCM) has been employed to estimate the kinetic and transport parameters of oxide growth, restructuring and metal dissolution through the

I. Betova et al. / Electrochimica Acta 54 (2009) 1056–1069

oxide layer on stainless steels [38] and nickel-based alloys [39] in a high-temperature borate electrolyte. To achieve this, calculational procedures based on a quantitative comparison of the model equations to in situ electrochemical impedance spectroscopic (EIS) [38,39] and ex situ Auger electron spectroscopic data [40] have been devised and validated. Further, the kinetic and transport parameters of film growth and restructuring on AISI 304 stainless steel after prolonged exposures to simulated pressurised water reactor (PWR) water with or without zinc addition were also estimated on the basis of a quantitative comparison of the model predictions [40] and recent literature data [41,42]. In the present paper, the predictions of the MCM are for the first time fitted to both in situ EIS and ex situ XPS data for oxides on AISI 316L(NG) formed in simulated PWR water at 280 ◦ C with or without Zn addition. First, the experimental data are presented and qualitatively discussed in terms of the effect of Zn addition on both the conduction mechanism and the in-depth composition of the oxide layer. Second, the model concepts and the calculational procedure are introduced emphasizing the simplifying assumptions made. Third, calculational results are presented and discussed in terms of different hypotheses for the effect of Zn on the oxide layer on stainless steel during the initial stages of exposure to PWR water. 2. Experimental 2.1. Electrodes and electrolytes The working electrodes have been manufactured from AISI 316 L(NG) stainless steel (its composition as determined by emission spectroscopy is listed in Table 1). PTFE-insulated rectangular samples with a working area of 6.3 cm2 were used for both the impedance measurements and the exposure aimed at a subsequent ex situ XPS characterisation. The working electrode pretreatment consisted of mechanical polishing with emery paper up to grade 4000, rinsing with ultrapure water (resistivity >18 M cm) and drying with hot air. All measurements were performed in a static PTFE-lined autoclave at a temperature of 280 ± 2 ◦ C, the corresponding pressure being ca. 9 MPa. A Pt sheet was used as a counter electrode. All potentials were measured vs. a Pd electrode electrochemically charged with hydrogen to approximate the reversible hydrogen electrode (RHE). The electrolyte was simulated PWR coolant (1200 ppm B as H3 BO3 , 2.2 ppm Li as LiOH) with or without the addition of 1 ppm Zn as Zn(NO3 )2 and/or 0.01 M Na2 B4 O7 which was added to buffer the electrolyte and prevent any pH excursions due to hydrolysis reactions of soluble Zn. The measurements were performed under slow continuous bubbling with N2 (99.999%). According to earlier experience [6,38], a conservative estimate of the maximum hydrogen level in such conditions at high temperatures is ca. 900 ppb (10 cm3 kg−1 at a standard temperature and pressure) and the maximum oxygen level is ca. 10–20 ppb (3–6 × 10−7 mol dm−3 ). Table 1 Composition of the material used in the investigations (weight-%) AISI 316L(NG) C Cr Cu Fe Mn Ni S Si Mo Others

0.015 16.5 0.26 Balance 1.73 10.5 0.002 0.54 2.55 N: 0.056

1057

2.2. Apparatus and procedures Impedance spectra in the alloy/oxide/electrolyte configuration were obtained with a PAR 283/5210 system controlled by PowerSine software (Princeton Applied Research) in a frequency range of 80 kHz to 0.5 mHz at an ac signal amplitude of 30 mV (rms). The validation of the impedance spectra was performed by checking the linearity condition, i.e. measuring spectra at different signal amplitudes. The spectra were also found to be compatible with the Kramers–Kronig transforms within the experimental error (±2% by magnitude and ±4◦ by phase angle). Points that did not comply to the transforms (usually at both ends of the measured frequency range) were rejected. For the simulation and fitting of impedance spectra to the transfer function derived from the kinetic model, an Origin 7.5-based software routine has been employed. XPS spectra were registered using an ESCALAB Mk II (VG Scientific) electron spectrometer with a base pressure of ≈10−7 Pa. The photoelectrons were excited with a Mg K␣ (1253.6 eV) Xray source and the analyzer pass energy was 20 eV. The B1s, C1s, O1s, Fe2p, Cr2p, Ni2p and Zn2p photoelectron lines were recorded and the binding energies were calibrated versus the C1s peak. To obtain depth profiles, Ar ion milling was used and the conversion of the sputtering time to depth has been performed with respect to a Ta2 O5 standard (sputtering rate 0.4 nm min−1 ). The peak positions were determined by Gaussian–Lorentzian peak fitting after Savitzky–Golay smoothing and Shirley background subtraction, and peak areas were converted to atomic concentrations as depending on sputtering depth. The position of the alloy/inner layer interface was estimated by averaging the inflection points of the oxygen profiles and of the iron profiles from the minimum concentration of Fe in the film inward. The boundary between the inner and outer layers, respectively, has been estimated by averaging the inflection points of the Fe profiles from the outer interface to the respective minimum and those of the Cr or Ni profiles from the outer interface to the respective maximum. The corresponding inflection points were calculated via sigmoidal fitting using Origin 7.5 software. The difference between the respective values was at most 10%, thus the proposed estimates were considered reliable and were used for further calculations. The concentrations of the metallic constituents of the oxide were converted to mass fractions by normalising them to the total concentration of metallic constituents. For the simulation of the depth profiles of the mass fractions of the metallic elements according to the MCM, the respective non-steady state differential equations were solved using Maple 8.1 software [40].

3. Results 3.1. Electrochemical impedance spectroscopy Impedance spectra for AISI 316L(NG) stainless steel in simulated PWR coolant at a range of potentials (0–0.5 V vs. RHE) after a 48 h exposure at 280 ◦ C without and with the addition of 1 ppm Zn are presented in Fig. 1a and b. The corresponding spectra in PWR water with the addition of 0.01 M Na2 B4 O7 are shown in Fig. 2a and b, respectively. It is worth mentioning that the oxide layers were allowed to grow for 24 h before any Zn was injected into the electrolyte. Subsequently, the films were allowed to grow for another 24-h period before measuring the impedance spectra as a function of potential. This was repeated for 48 h exposures, and the impedance spectra were found not to change with time of exposure within the reproducibility limit (±2% by impedance magnitude and ±4◦ by phase angle). The conductivity of the electrolyte with 0.01 M Na2 B4 O7 addition was substantially higher than that of the plain

1058

I. Betova et al. / Electrochimica Acta 54 (2009) 1056–1069

Fig. 1. Impedance spectra of AISI 316L(NG) at a range of potentials vs. RHE in simulated PWR water at 280 ◦ C: (a) without Zn, (b) with 1 ppm Zn. Left column: impedance magnitude vs. frequency, right column: phase angle vs. frequency. Points: experimental values, solid lines: best-fit calculation according to the model outlined in the text.

simulated PWR water. Therefore, the electrolyte resistance estimated from the high-frequency intercept of the impedance spectra has been subtracted from the data in order to facilitate the comparison between spectra in the two electrolytes. The obtained spectra are broadly analogous to those published earlier for austenitic stainless steels and nickel-based alloys [38,39]. The impedance magnitude at low frequency, |Z|f→0, that can be assumed to be inversely proportional to the steady-state conductivity of the alloy/oxide/electrolyte system, in general increases with potential in the passive region (from 0 to ca. 0.3–0.4 V), decreasing for higher potentials probably due to the onset of transpassivity and/or oxygen evolution. For the films formed in the simulated PWR water with 1 ppm Zn, the values of |Z|f→0 are somewhat higher at low potentials in the passive range. This indicates a lower steadystate conductivity of the system, i.e. lower rates of the processes of film growth and restructuring in the presence of Zn (Fig. 1a and b). The parameter |Z|f→0 exhibits in general lower values in the Na2 B4 O7 -containing electrolyte when compared to the plain simulated PWR water (Figs. 1a and 2a). This observation could be explained by the different composition of the oxide formed in an electrolyte with higher pH (∼9 vs. 6.4, see also below). However,

the values of |Z|f→0 in the passive range for the films that were subjected to Zn injection are larger also in the Na2 B4 O7 -containing electrolyte, which points to a decelerating effect of Zn on the rates of the processes in this case (Fig. 2a and b). On the other hand, in the transpassive region (above 0.3 V) the values of |Z|f→0 are lower in the presence of Zn than in his absence, which may point out to an earlier onset of transpassivity in the presence of Zn than in its absence. A total of three time constants could be detected in the phase angle vs. frequency curves by preliminary deconvolution of the impedance spectra. The approximate frequency ranges in which these time constants were detected are shown in the figures with arrows. Following previous interpretations of impedance spectra in high-temperature electrolytes [39], the highest frequency time constant is associated with the electronic properties of the inner, continuous layer of the oxide film, the medium frequency time constant most probably reflects the ion and electron transfer processes at the oxide/electrolyte interface and the lowest-frequency time constant is assigned to the transport of point defects in the inner layer of oxide. No contribution of the outer layer was discerned in the spectra most probably due to the fact that it represents a

I. Betova et al. / Electrochimica Acta 54 (2009) 1056–1069

1059

Fig. 2. Impedance spectra of AISI 316L(NG) at a range of potentials vs. RHE in simulated PWR water + 0.01 M Na2 B4 O7 at 280 ◦ C: (a) without Zn, (b) with 1 ppm Zn. Left column: impedance magnitude vs. frequency, right column: phase angle vs. frequency. Points: experimental values, solid lines: best-fit calculation according to the model outlined in the text.

conductive oxide phase consisting of discrete crystallites, as commented also in previous work [38,40]. In what concerns the effect of Zn, it can be stated that its injection leads to significant alterations in the phase angle vs. frequency curves in both electrolytes, affecting the frequency ranges of all the three time constants in the spectra. The effect of Zn seems to be more pronounced in the case of the plain simulated PWR water, which could be due to the fact that a significant pH decrease (down to pH 6, measured at room temperature after autoclave cool down) occurred during the measurements. This decrease most probably leads to a profound alteration in the composition and properties of the oxide layers formed on the stainless steel. Proofs for that statement are sought in the ex situ characterisation of the in-depth composition of the oxides that are described below. However, it is worth noting that the effect of Zn on the phase angle vs. frequency curves is significant also in the tetraborate-containing electrolyte, in which no pH excursion has been observed (the pH at the beginning and at the end of the experiments was close to 9). This allows the conclusion that the effect of Zn on the electrical and electrochemical proper-

ties of the oxides on AISI 316L(NG) in PWR water is not only due to the pH excursion provoked by the hydrolysis reactions of Zn, as commented also by others [37]. 3.2. Estimation of the in-depth composition of the oxide films with XPS The XPS depth profiles of the oxides formed on AISI 316L(NG) in simulated PWR water without Zn for 96 h at open circuit (close to 0 V vs. RHE) and during potentiostatic polarisation at 0.5 V RHE are shown in Fig. 3, and the corresponding profiles for the oxides formed for 24 h in the absence of Zn followed by Zn injection and 72 h oxidation in a Zn-containing electrolyte are presented in Fig. 4. A comparison between the in-depth variations of the contents of metallic constituents normalised to the total metallic content in order to exclude the effect of oxygen on the depth profiles [11,38,40] is shown in the figures. The positions of the alloy/inner layer interface and the boundary between the inner and outer layers, are presented in the figures with solid lines. The respective sigmoidal

1060

I. Betova et al. / Electrochimica Acta 54 (2009) 1056–1069

(more than twice, both at o.c. and at 0.5 V). For the film formed at 0.5 V in the presence of Zn, also the Ni content is increased with respect to the oxide formed in the Zn-free solution. Zn is incorporated in the oxide at both potentials in significant amounts (a normalised content of several %), its concentration being somewhat larger in the film formed at open circuit (Fig. 4). It can be concluded that the injection of 1 ppm Zn to the simulated PWR water causes a dramatic restructuring of the oxide formed on stainless steel for 24 h in Zn-free solution. Part of this effect could be attributed to the decrease of pH due to the hydrolysis reactions of Zn, as discussed already above (a pH decrease would increase the solubility of the main oxide constituents and most notably that of Fe). Thus we tried to isolate the effect of Zn incorporation by performing measurements in PWR water buffered with Na2 B4 O7 . Fig. 5 presents the XPS depth profiles for the films formed in this type of solution at open circuit with and without Zn injection. In the presence of tetraborate, the thicknesses of the films in both Zn-free and Zn-containing electrolytes are more than two times larger than those formed in solutions that did not contain tetraborate. This effect could be related to the decrease of the solubility of Fe with increasing pH. Such an explanation is corroborated by the fact that outer layers (i.e. layers that are formed by a dissolution–precipitation mechanism) are observed in both Zn-free and Zn-containing electrolytes and their thickness is larger than

Fig. 3. XPS depth profiles of the oxides formed on AISI 316L(NG) in simulated PWR water without the addition of Zn at 280 ◦ C at open circuit (a) and at 0.5 V vs. RHE (b). Profiles of the atomic concentration of oxygen and Ni, Cr and Fe contents normalised to the total metallic content of the film are presented. Dashed and dotted lines represent sigmoidal fits to the respective profiles to estimate the alloy/inner layer and inner layer/outer layer interfaces.

fits used to estimate the two boundaries are also shown in the figures with dashed and dotted lines, respectively, to demonstrate the ability of this approach to account for the features of the experimental data. Both the thickness values and the in-depth compositions of the oxides formed in Zn-free simulated PWR water are in general agreement with earlier results by a range of authors [2,41,43,44]. It is worth noting that a hydroxide signal in the O1s spectra has been detected only in the outermost layers of the respective films, thus it can be concluded that the layers consist mostly of oxides. The effect of potential on thickness and in-depth composition is not very significant, the only noticeable change being the decrease of Cr content in the oxide at the potential of 0.5 V when compared to that at open circuit, and the corresponding increase in Ni content of the oxide (Fig. 3). These effects can be explained by the loss of Cr via oxidative dissolution as Cr(VI). On the other hand, the effect of Zn injection on the thickness and composition of the oxides is much more pronounced—the thickness of the oxide decreases ca. 6 times at open circuit and more than 2 times at 0.5 V RHE (cf. Figs. 3 and 4), the outer layer is practically absent (only a very thin layer containing boron is detected at the potential of 0.5 V) and the Cr content of the inner layer is significantly increased

Fig. 4. XPS depth profiles of the oxides formed on AISI 316L(NG) in simulated PWR water with 1 ppm Zn at 280 ◦ C at open circuit (a) and at 0.5 V vs. RHE (b). Profiles of the atomic concentration of oxygen, as well as Ni, Cr, Fe and Zn contents normalised to the total metallic content of the film are presented. Dashed lines represent sigmoidal fits to the respective profiles to estimate the alloy/inner layer interfaces.

I. Betova et al. / Electrochimica Acta 54 (2009) 1056–1069

1061

4. Discussion 4.1. A model for the impedance response The MCM is at the conceptual level quite similar to the point defect model (PDM) proposed and developed by Macdonald and co-workers during the last three decades [45–48] and also on certain commonly held views on passive films as described, e.g. by Schultze and Lohrengel [49]. However, some basic assumptions made in these models differ to a certain extent. Thus it is worth summarising the assumptions made within the frames of the MCM:

Fig. 5. XPS depth profiles of the oxides formed on AISI 316L(NG) in simulated PWR water + 0.01 M Na2 B4 O7 without (a) and with 1 ppm Zn (b) at 280 ◦ C at open circuit. Profiles of the atomic concentration of oxygen, as well as Ni, Cr, Fe and Zn contents normalised to the total metallic content of the film are presented. Dashed and dotted lines represent sigmoidal fits to the respective profiles to estimate the alloy/inner layer and inner layer/outer layer interfaces.

that of the inner layer. The changes of the in-depth composition of the oxide caused by Zn injection are not as drastic as in the plain PWR water, even if the incorporation of Zn especially in the outer layer is really significant (above 20% of normalised content). This probably means that the outer layer formed by restructuring of the oxide following Zn injection is in fact a mixed Fe–Zn oxide containing small amounts of Ni and Cr. On the other hand, the amount of Zn incorporated in the inner layer stays close to that in the plain PWR water (Figs. 4 and 5). A notable effect of Zn injection is that the Ni content of the inner layer formed as a result seems to be larger than that of Cr, which is opposite to the inner layer formed in the absence of Zn. Thus Zn incorporation seems to play an important role in the restructuring of the inner layer also in tetraborate-containing PWR water. Summarising, Zn injection has a significant effect on the oxides formed for 72 h in both unbuffered and buffered PWR water, altering both the thickness and the in-depth composition of the oxide and its electrical and electrochemical properties as reflected by the impedance spectroscopic results. An attempt to quantify these effects is made in Section 4 within the frames of the MCM.

1. The film consists mainly of oxide and the amount of hydroxide in the film is negligible, as demonstrated by the XPS data obtained in the present study. The stoichiometric composition of the oxide varies gradually with potential, whereas its structure remains unchanged, as already noticed by several authors [41–43,2,44]. 2. The ionic transport through the film proceeds either via a vacancy or an interstitial mechanism. 3. A certain concentration of oxygen vacancies is maintained in the film, in order to explain the growth of the film via the inwardmotion of oxygen ions. 4. The electric field strength in the inner layer is assumed to be independent of potential, i.e. the inner layer thickness is proportional to the applied potential, as already shown for AISI 316 in borate solutions in the temperature range 150–300 ◦ C [38]. Physically, the constancy of the electric field strength is supposed to be due to band-to-band tunneling of electrons and holes that effectively buffers the field against any process that would tend to increase the potential gradient [50]. 5. For the transport of ionic species, the high-field approximation is used at room temperature and the low-field approximation at high temperatures, which is due to the fact that field strength decreases with increasing temperature, as already demonstrated in the literature [38,45]. 6. The applied potential is distributed as potential drops at the two  + F/S [38,39,45–48]. interfaces and the film bulk: E = M/F + EL At steady-state, from the assumption that the potential drop at the film/solution interface is proportional to the applied potential (␾F/E = ␣E + const) [38,39,45–48] and the linear dependence of thickness on potential (L = (1 − ˛)E/E + const), it follows that the potential drop at the alloy/oxide interface is independent on the applied potential. 7. Each ionic point defect in the film plays the role of an electron donor or acceptor. In other words, n-type semiconductor behaviour can be regarded as a result of a decrease in the oxidation state of a lattice cation with simultaneous generation of interstitial cations or oxygen vacancies. The extra interstitial cation in the lattice creates a positive electrostatic potential which captures an electron in a bonding orbital close to the conduction band edge. By analogy, an increase in the oxidation state of a cation is accompanied by the formation of cation vacancies and holes, the latter being effectively captured in acceptor orbitals [51]. 8. The model makes use of the general transport equations of Fromhold and Cook [52], which are derived from a microscopic discrete hopping mechanism. By defining the appropriate boundary conditions, the concentration profiles for different ionic charge carriers in the film can be calculated and the ionic contribution to the impedance derived. Further, as at constant mobility of the electronic carriers, the electronic conductivity is proportional to the concentration of defects, the transfer function for the electronic contribution to the film impedance

1062

I. Betova et al. / Electrochimica Acta 54 (2009) 1056–1069

depending on the film thickness and potential derived from the MCM is mathematically equivalent to the formal model of Young [53]. The oxides that form in the inner layer of stainless steels in PWR conditions are spinels, which is largely consistent with both thermodynamic calculations [54] and experimental observations [41–43,2,44]. Thus, a certain excess concentration of octahedral interstitial cations and tetrahedral cation vacancies is present in the lattice. Furthermore, a certain concentration of oxygen vacancies is assumed to exist. This assumption is necessary, so that the model can explain the growth of the film via the inward-motion of oxygen ions m→

•• MM + 1.5VO(M/F)

In turn, the following expressions have been derived for these impedance components as depending on the kinetic parameters of the reactions of generation kg and consumption of point defects kc , the diffusion coefficients of ionic and electronic defects De and Di , the field strength E in the inner layer of steady state thickness L¯ and the polarisability of the inner layer/electrolyte interface ˛:



Ze ≈

p ln j ωC

1 + j ωd εε0 exp

 1 

p 1 + j ωd εε0 − → 1−˛ FE K= , L = LE=0 + − → E, RT E

(6) RT kg d = 2 F De kc

RT



8F 2 KDi kg (1 − ˛) [1/(kc exp(2KL)) + 1/(2KDi )] 1 +

 MM + 1.5H2 O → 0.5M2 O3 + VM(F/E) + 3H+   VM(F/E) → VM(M/F)

(2)

MM + 3e− m

•• •• Mi(M/F) → Mi(F/E)



 1 + j ω/(K 2 Di )

(7) In full analogy to our previous treatments, the impedance that reflects the electronic properties of the oxide has the form of an Young impedance, C being the space-charge layer capacitance of the semiconductor phase in the inner layer, whereas the impedance of ionic transport can be regarded as a generalised Warburg impedance within a layer of finite thickness [38]. With the reasonable assumption of kc exp (2KL) 2KDi , Eq. (7) can be rewritten in a simplified form as Z i = Rt +

•• m → Mi(M/F) + 2e− m

•• Mi(F/E)

(5)

Zi = Rt +

+ 1.5H2 O → 1.5OO + 3H

+m→

−1

(1) +

where M/F stands for the alloy/film interface and F/E for the film/electrolyte interface. The dissolution of metal through the film followed by the redeposition of material to form the outer layer is in turn described by the two sequences of reactions

 VM(M/F)

Zf = (Ze−1 + Zi−1 )

1 p= , 2KL

+ 3e− m

•• •• 1.5VO(M/F) → 1.5VO(F/E) •• 1.5VO(F/E)

defects through it Zi connected in parallel

RT



4F 2 kg (1 − ˛) 1 +



1 + j ω/(K 2 Di )



(8)

(3) +

+ 1.5H2 O → 0.5M2 O3 + 3H

4.2. A model for the in-depth contents of individual metallic constituents

+ e

Although it has been presumed that Cr and Ni are transported through the oxide via vacancies and Fe via interstitial cations [5,7,11], at this point we do not distinguish between the types of the defects via which the respective metallic constituent is transported through the inner layer of oxide. Thus, e.g. the reaction rate constant at the alloy/inner layer interface for Fe can be regarded as a sum of the reaction rate constants of the reactions producing Fe interstitials, normal Fe positions and oxygen vacancies and consuming cation vacancies with the simultaneous production of normal Fe positions, as electrochemical reaction steps proceeding in parallel at the same interface. On the other hand, the diffusion coefficients DCr , DFe and DNi can be regarded as characterising the overall transport of cations through the inner layer resulting either from its growth via generation, transport and consumption of oxygen vacancies or the dissolution of these cations through the inner layer via a vacancy or interstitial mechanism. The impedance response of the alloy/inner layer/electrolyte system can be approximated as sum of the impedances of the inner layer Zf and its interface with the electrolyte ZF/E Z = Rel + Zf + ZF/E = Rel + (Ze−1 + Zi−1 )

−1

+

1 −1 RF/E + jωCF/E

(4)

where the impedance of the outer interface has been represented −1 as a parallel combination of a charge transfer resistance RF/E and an interfacial capacitance CF/E , and Rel is the electrolyte resistance (for a complete list of symbols, the reader is referred to Appendix A). On the other hand, following previous treatments [38], the impedance of the inner layer Zf is taken as a sum of the impedances of its electronic properties Ze and the impedance of transport of

Within the frames of the MCM, the depth profile of a metallic constituent j = Fe, Cr, Ni, or Zn, can be expressed as the dependence of its molar fraction, yj = cj Vm,MO , on the distance within the inner layer, where cj is its molar concentration and Vm,MO the molar volume of the phase in that layer. In order to calculate the depth profiles the respective transient transport equations for each component have to be solved [40]  Fe ∂yFe ∂yFe XF ED ∂2 yFe = DFe + RT ∂t ∂x ∂x2  Cr ∂yCr ∂yCr ∂2 yCr 3F ED = DCr + RT ∂t ∂x ∂x2 2  2F EDNi ∂yNi ∂yNi ∂ yNi + = DNi RT ∂t ∂x ∂x2

(9)

where X stands for the nominal valency of Fe in the oxide, which is close to 2.67 in the passive region and close to 3 in the transpassive region. The relevant boundary conditions at the alloy/film and film/electrolyte interfaces, as well as the initial conditions are given as [40] yFe (x, 0) = yFe,a ,

yCr (x, 0) = yCr,a ,

yNi (x, 0) = yNi,a

yFe (0, t) = yFe,a ,

yCr (0, t) = yCr,a ,

yNi (0, t) = yNi,a





 Fe ) yFe (L, t) = kg,Fe /(Vm,MO ) 1/(kc,Fe ) + RT/(XF ED









 Ni ) yNi (L, t) = kg,Ni /(Vm,MO ) 1/(kc,Ni ) + RT/(2F ED  Cr ) yCr (L, t) = kg,Cr /(Vm,MO ) 1/(kc,Cr ) + RT/(3F ED

(10)

I. Betova et al. / Electrochimica Acta 54 (2009) 1056–1069

1063

Table 2 Kinetic parameters of film growth and restructuring on AISI 316L(NG) at 280 ◦ C in PWR water as estimated by the proposed procedure Parameter

1012 kg,Cr (cm4 mol−1 s−1 ) 1012 kg,Fe (cm4 mol−1 s−1 ) 1012 kg,Ni (cm4 mol−1 s−1 ) 1013 kc,Cr (cm s−1 ) 1013 kc,Fe (cm s−1 ) 1013 kc,Ni (cm s−1 ) E (kV cm−1 ) 1018 DCr (cm2 s−1 ) 1018 DFe (cm2 s−1 ) 1018 DNi (cm2 s−1 ) 1018 DZn (cm2 s−1 ) 1016 DCr ,OL (cm2 s−1) 1016 DFe ,OL (cm2 s−1) 1016 DNi ,OL (cm2 s−1 ) 1016 DZn ,OL (cm2 s−1 )

PWR, no Zn

PWR, 1 ppm Zn

PWR + borate,o.c.

o.c.

0.5 V RHE

o.c.

0.5 V RHE

no Zn

1 ppm Zn

8.0 8.0 4.0 7.0 3.2 7.0 57 3.7 2.5 3.5 – 5.0 6.0 7.0 –

8.0 8.0 5.0 15.0 3.0 6.0 52 3.0 2.2 3.0 – 5.0 6.0 7.0 –

9.0 8.0 2.5 3.0 20.0 5.0 80 0.5 0.7 0.4 0.5 – – – –

6.0 7.0 4.0 3.0 15 3.0 40 4.0 5.0 5.0 3.0 – – – –

9.0 7.0 4.0 15 2.3 6.0 57 3.7 5.0 3.5 – 5.0 6.0 7.0 –

7.0 7.0 4.0 20 2.0 7.0 57 2.7 4.0 2.5 5.5 0.030 0.055 0.030 0.10

Fig. 6. Sensitivity analysis of the fitting procedure to the estimated parameters using a phase angle vs. frequency curve at 0.3 V vs. RHE in simulated PWR water + 0.01 M  Na2 B4 O7 . Closed symbols: experiment, solid lines: best fit, open symbols: spectra calculated with a 10% offset value of the respective parameter (C, p, Di and E).

1064

I. Betova et al. / Electrochimica Acta 54 (2009) 1056–1069

The incorporation of Zn is assumed to proceed either via sequential filling and emptying of available empty cation interstices or cation vacancies: 2+ + Vi Mi •• → Maq

(11)

(dissolution of a divalent cation, e.g. Fe or Ni, and creation of an empty interstice) •• Vi + Zn2+ aq → Zni

(12)

(incorporation of a foreign cation in that interstice) III 3+  → Maq + VM MM

(13)

(dissolution of a trivalent cation, e.g. Fe or Cr, and creation of a cation vacancy)   + Zn2+ VM aq → ZnM

(14)

(incorporation of Zn by filling the vacancy). Regardless of the type of defect via which Zn is incorporated, the associated equation for the transient inward transport of Zn cation is written as  Zn ∂yZn 2F ED ∂2 yZn ∂yZn = DZn − 2 RT ∂t ∂x ∂x

factor of Zn Kenr defined as the ratio between the concentration of Zn at that interface and the Zn concentration in the water, assumed to be independent on the time of exposure. In the absence of representative information on the pore diameter and tortuousity, and also of reliable data on the crystallite size of the outer layer, the growth of this layer is formally treated as a diffusion process in a matrix constituted of outer layer crystals with electrolyte in between [40]. Such a treatment for the oxide layer has already been presented in relation to incorporation of foreign species into the growing film. Since the outer layer is not continuous but rather represents a system of discrete crystallites with electrolyte in the pores, the role of the potential gradient in this layer can be considered negligible with respect to the concentration gradient. Thus, to calculate the depth profile of a certain cation in the outer layer, the following system of equations has to be solved

(15)

with the boundary conditions yZn (x, 0) = 0, yZn (0, t) = 0, yZn (L, t) = Kenr cZn,aq Vm,MO . The boundary condition for Zn at the inner layer/electrolyte interface is given by the enrichment

∂2 yFe,OL ∂yFe,OL = DFe,OL ∂t ∂x2 ∂yCr,OL ∂2 yCr,OL = DCr,OL ∂t ∂x2 ∂yNi,OL ∂t

= DNi,OL

∂yZn,OL = ∂t

∂2 yNi,OL

(16)

∂x2

∂2 yZn,OL DZn,OL ∂x2

Fig. 7. Dependences of the space charge capacitance of the inner layer C (a), the inverse value of the parameter p (b), the parameter d ε (c) and the charge transfer resistance at the film/electrolyte interface RF/E (c) on potential.

I. Betova et al. / Electrochimica Acta 54 (2009) 1056–1069

The boundary conditions at the inner interface of the outer oxide layer are identical to those used as outer boundary conditions at the inner layer/electrolyte interface, which ensures the continuity of the composition of the whole film. At this point, the boundary conditions at the outer layer/electrolyte interface are assumed to be equal to the experimentally found stoichiometry of the outermost layer of oxide as estimated by XPS. In a future refinement of the model, these boundary conditions could be estimated from an independent investigation of the kinetics of sorption of electrolyte originating cations onto the outer layer surface. 4.3. Calculational procedure and parameter estimates As a first step, impedance spectra for AISI 316L(NG) in the studied electrolytes were fitted to Eqs. (4)–(7) and the values of the  RF/E and CF/E have been estimated parameters C, p, d ε, kg , Di , E, as depending on potential. The results of this fitting are shown in Figs. 1 and 2 with solid lines and demonstrate the ability of the model approach to reproduce both the magnitude and the frequency distribution of the impedance in the whole studied range of potentials. As the number of parameters to fit each impedance spectrum is significant, a sensitivity analysis was carried out to assess the relevance of each parameter and its influence in the different regions of the frequency range studied. For the purpose, every individual parameter has been given sequentially values 10% lower and 10%

1065

higher than the values that have been returned as optimal by the fitting procedure, and the corresponding impedance spectra have been calculated. As an example of the effect of the variation of C,  phase angle vs. frequency curves in simulated PWR p, Di and E, water + 0.1 M Na2 B4 O7 at 0.3 V are presented in Fig. 6. It has been found that certain parameters, such as kg , Di , d ε, have an effect on  exert the low-frequency response alone, whereas others, e.g. C, p, E, an influence over a wider frequency range. On the overall, it can be stated that all the studied parameters have a noticeable effect on the phase angle curves and their values can be considered reliable. The fitting results showed that kg , Di , E and CF/E were practically independent on potential. The dependences of charge layer capacitance C, the parameters p and d ε (see Eq. (6)) as well as the charge transfer resistance at the inner layer/electrolyte interface RF/E are plotted vs. potential in Fig. 7. The space charge layer capacitance decreases with potential and the resulting C−2 vs. E dependences are linear (Fig. 7a), suggesting the presence of an ntype semiconductor phase in the inner layer. Notwithstanding all the limitations of the use of a simple Mott–Schottky approach to that layer, it is worth mentioning that the apparent donor densities calculated from the slope of the C−2 vs. E dependences in general decrease in the presence of Zn. This seems to be in accordance with the presumed decrease of the concentration of ionic defects playing the role of electron donors for the films restructured after the injection of Zn to the electrolyte. Additionally, the p−1 vs. E dependences (Fig. 7b) is found to be linear in agreement

Fig. 8. Experimental (points) and calculated (solid lines) mass fractions of the main metallic constituents of the oxides formed on AISI 316L(NG) in simulated PWR water (1200 ppm B, 2 ppm Li) at 280 ◦ C at open circuit (a, c) and at 0.5 V vs. RHE (b, d) without Zn (a, b) and with 1 ppm Zn (c, d).

1066

I. Betova et al. / Electrochimica Acta 54 (2009) 1056–1069

with the predictions of the respective model equation (second row of Eq. (6) above), further demonstrating the validity of the present approach. The d ε dependence (Fig. 7c) is to a certain extent analogous to that obtained earlier for AISI 316L(NG) in 0.1 M Na2 B4 O7 in the temperature interval 250–300 ◦ C [38] and also demonstrates the presence of an n-type semiconductor layer in the most part of the passive region. The values of this parameter are the largest for the film formed and restructured in plain simulated PWR water with Zn injection, which could be correlated to the highest Cr content of this film as evidenced by XPS (Fig. 4). This is corroborated by the fact that the values of d ε are the lowest for the oxides formed in borate containing solutions, i.e. for films in which Cr content is the lowest. The decrease of d ε with potential starts at the lowest potential for the films formed in borate-containing PWR water with Zn addition, which points out once more to an earlier onset of transpassivity in this solution. The dependences of the charge transfer resistance at the film/electrolyte interface RF/E on potential (Fig. 7d) suggest that a redox reaction dominates over the ionic transfer reactions at this interface [39]. The exponential coefficients of the cathodic branch of the curves approximating this dependence (ca. 6 V−1 , Fig. 7d) are larger than those for the anodic branch (ca. 2 V−1 ) which is consistent with a charge transfer reaction on an n-type semiconductor layer. Next, assuming a dielectric constant ε = 25 for the inner layer, and values of the polarisability of the inner layer/electrolyte interface ˛ = 0.9 and the diffusion coefficient of electronic current carriers of 6 × 10−13 cm2 s−1 [38], the rate constant kc has been estimated from the potential dependence of the d ε parameter. Further, estimates for the rate constants and diffusion coefficients of individual metallic constituents of the inner layer, as well as the apparent diffusion coefficients of outer layer growth were sought by a quantitative comparison of the XPS depth profile data with the solutions of Eqs. (10) and (16). The estimates obtained above from the fitting of the electrochemical data were used to introduce the following restrictions: kg = kg,Fe yFe,a + kg,Cr yCr,a + kg,Ni yNi,a kc = kc,Fe yFe (L, t) + kc,Cr yCr (L, t) + kc,Ni yNi (L, t)

(17)

Fig. 9. Sensitivity analysis of the calculational procedure with respect to the kinetic and transport parameters of the individual inner layer constituents: (a) rate constants at the metal/film interface, (b) rate constants at the film/solution interface. The direction of change of the parameters with respect to the optimal values is shown with positive and negative signs, respectively.

Di = DFe yFe,a + DCr yCr,a + DNi yNi,a + DZn yZn (L, t) The contents of the each metallic constituent of the oxide were normalised to the total metallic content to calculate the respective mass fractions. The depth was recalculated as distance from the alloy/oxide interface using the estimates of inner and outer layer thicknesses obtained as described in the Experimental section. The plots of the mass fractions vs. the distance from the alloy/oxide interface are presented in Figs. 8–9 (for AISI 316L(NG) in the plain simulated PWR water) and Fig. 10 (for the PWR water with the addition) of 0.01 M Na2 B4 O7 ). The calculated curves (solid lines) are in good agreement with the experimental data (points), indicating that the model is once again able to account for the essential features of the data. The main kinetic parameters calculated form such a procedure are summarised in Table 2. Sensitivity analyses were performed in analogy to our previous paper [40] by estimating the effect of a ±10% change of the respective kinetic parameters on the calculated depth profiles. As an example, such an analysis involving kg and kc values for the oxide formed in simulated PWR water without Zn addition at open circuit is shown in Fig. 9. It can be concluded that a 10% alteration of the rate constants at both alloy/inner layer and inner layer/electrolyte interfaces has a significant effect on both the shape of the profiles and the values of the respective mass fractions of the components. The alteration of the diffusion coefficients in the inner layer (not

shown for the sake of brevity) has a comparatively weaker, but still well detectable effect on the calculated profiles. Thus the extracted parameter values can be considered reliable and are discussed below. The following conclusions can be drawn from the parameter values: • The field strength in the inner layer preserves rather low values (40–80 kV cm−1 ) indicating that the use of the low-field approximation in the derivation of the transport equation is appropriate for oxide films formed in high-temperature electrolytes, as demonstrated also earlier [38–40]. • The main effect of the injection of 1 ppm Zn is exerted on the rate constants at the inner layer/electrolyte interface and the ionic diffusion coefficients in the inner layer, the parameters at the alloy/inner layer interface being essentially unaffected by Zn which in fact does not reach this interface. Especially for the films formed at open circuit in the plain PWR water, the effect of Zn on the diffusion coefficients of the main inner layer constituents is dramatic (they decrease 6–7 times) which is expressed as a corresponding decrease in film thickness, as observed experimentally. For this specific case, the diffusion coefficient of Zn in the inner layer is rather close to that of Cr and Ni and is somewhat smaller

I. Betova et al. / Electrochimica Acta 54 (2009) 1056–1069

1067

Na2 B4 O7 is drastic (the corresponding decrease of the apparent diffusion coefficients of the outer layer growth is with ca. 2 orders of magnitude). There are two viable explanations to this observation. First, it is possible that the dimensions of the outer layer crystallites are significantly decreased with respect to the case without Zn, as experimentally found for oxide layers formed on AISI 304 upon prolonged exposure to PWR water with or without the addition of 30 ppb Zn [41,42]. On the other hand, it is possible that the nature of the outer layer has changed as a result of Zn injection, and instead of representing a combination of loosely packed individual crystallites, it is transformed into a more compact and homogeneous layer of a mixed Fe–Zn oxide in which the transport is actually governed by a solid-state mechanism to a certain extent analogous to that in the inner layer. Clearly, structural and morphological studies are needed to resolve this issue. The results of such studies will be communicated in the near future.

5. Conclusions

Fig. 10. Experimental (points) and calculated (solid lines) mass fractions of the main metallic constituents of the oxides formed on AISI 316L(NG) in simulated PWR water (1200 ppm B, 2 ppm Li) + 0.1 M Na2 B4 O7 at 280 ◦ C at open circuit without Zn (a) and with 1 ppm Zn (b).

than that of Fe. It is encouraging that the estimated diffusion coefficients agree sufficiently well with those estimated earlier by us [40] for films on AISI 304 after prolonged exposure to a simulated PWR water containing 30 ppb Zn based on the literature data on the corresponding depth profiles [41]. • Conversely, the diffusion coefficients for the films formed at 0.5 V are not significantly affected by Zn injection, the main effect being detected on the rate constants for Fe and Cr dissolution at the film/electrolyte interface. This result is in line with the fact that in the transpassive region, the rate limiting step of the overall process of film growth and restructuring is most probably at the outer interface, whereas in the passive region, transport through the film is probably rate determining. • For the films formed and restructured in PWR water containing 0.01 M Na2 B4 O7 , the effect of Zn on the kinetic and transport parameters is less pronounced, but still noticeable (a 20–30% decrease in the diffusion coefficients of the main inner layer constituents is observed upon Zn injection, and the corresponding alteration of the rate constants at the outer interface is even smaller). Thus a significant part of the effect of Zn on the films is thought to be due to the pH change in the unbuffered electrolyte caused by the hydrolysis reactions of Zn, as discussed also by others [37]. • The effect of Zn on the transport parameters in the outer layer formed upon injection of Zn in the PWR water containing 0.01 M

In the present paper, the MCM was used to obtain values for the kinetic and transport parameters for the oxide on stainless steel formed in simulated PWR water with and without the addition of Zn to the electrolyte. For the first time, this has been achieved by fitting both in situ electrochemical impedance spectra and ex situ XPS depth profiles of main oxide constituents to the relevant model equations. The experimental and calculational results obtained in the present paper have clearly indicated the significant effect of Zn injection in simulated high-temperature PWR water on the initial stages of the growth and restructuring of the oxide film on AISI 316L(NG). In unbuffered PWR water, a drastic decrease of the thickness of the oxide is observed after Zn injection. This is demonstrated to be due to both the change in the pH of the electrolyte as a result of Zn hydrolysis reactions and the Zn adsorption on/incorporation in the oxide film which leads to significant decrease of the rates of ion transport in the inner layer and the interfacial reactions at the inner layer/electrolyte interface. On the other hand, the effect of Zn on film growth and restructuring in buffered PWR water is much less dramatic, but still significant. This effect is demonstrated to be due to both Zn incorporation in the inner layer and the probable formation of a new Zn-rich phase in the outer layer. These findings have been quantified in terms of estimates for the reaction rate constants at the alloy/inner layer and inner layer/electrolyte interfaces, as well as diffusion coefficients for the solid-state transport in the inner layer, all calculated for the individual metallic constituents. The rates of outer layer formation have been also estimated on the basis of a formal model that treats the growth of its crystallites as a process of transport of individual metallic constituents characterised by their apparent diffusion coefficients. In terms of the activity incorporation in oxide films on structural materials in contact with the coolant circuits of LWRs, it has been demonstrated that the proposed approach can account successfully for the interaction between oxides and coolant-originating species. In that respect, an extension of the model to allow for estimates of kinetic and transport parameters during simultaneous incorporation of several species, e.g. Zn and Co, is conceptually straightforward and is expected to bring valuable new information on the mechanisms of activity build-up on such oxide surfaces. The main drawbacks of the proposed approach revolve around the use of empirical values for the oxide stoichiometry at the outer layer/electrolyte interface, as well as the enrichment factors of zinc at both outer layer/electrolyte and inner layer/electrolyte interfaces. These issues are expected to be resolved by an experimental

1068

I. Betova et al. / Electrochimica Acta 54 (2009) 1056–1069

study and the associated modelling of the kinetics of interaction between cations originating from the electrolyte and the surface of the outer layer. Such a study is in progress and its results will be communicated in the near future. Acknowledgements The funding of this work by the FP6 Euratom programme of the European Commission via Contract No. FI6O-036367 “A deterministic model for corrosion and activity incorporation in nuclear power plants (ANTIOXI)” is gratefully acknowledged. Appendix A. Nomenclature

C CF/E DCr De DCr,OL DFe DFe,OL Di DNi DNi,OL DZn DZn,OL e− m e E E F kc kc,Cr kc,Fe kc,Ni kg kg,Cr kg,Fe kg,Ni Kenr L LE=0 Mi•• MM OO p R Rel

capacitance of the space charge layer (F cm−2 ) capacitance at the inner layer/electrolyte interface (F cm−2 ) diffusion coefficient of Cr in the inner layer (cm2 s−1 ) diffusion coefficient of electronic current carrier (cm2 s−1 ) formal diffusion coefficient of Cr in the outer layer (cm2 s−1 ) diffusion coefficient of Fe in the inner layer (cm2 s−1 ) formal diffusion coefficient of Fe in the outer layer (cm2 s−1 ) diffusion coefficient of ionic current carrier (cm2 s−1 ) diffusion coefficient of Ni in the inner layer (cm2 s−1 ) formal diffusion coefficient of Ni in the outer layer (cm2 s−1 ) diffusion coefficient of Zn in the inner layer (cm2 s−1 ) formal diffusion coefficient of Zn in the outer layer (cm2 s−1 ) electron in the metal electron in the oxide film electrode potential (V) field strength in the inner layer (V cm−1 ) Faraday number, 96,487 C mol−1 rate constant of dissolution at the inner layer/electrolyte interface (cm s−1 ) rate constant of dissolution of Cr at the inner layer/electrolyte interface (cm s−1 ) rate constant of dissolution of Fe at the inner layer/electrolyte interface (cm s−1 ) rate constant of dissolution of Ni at the inner layer/electrolyte interface (cm s−1 ) rate constant of oxidation at the alloy/inner layer interface (cm4 mol−1 s−1 ) rate constant of oxidation of Cr at the alloy/inner layer interface (cm4 mol−1 s−1 ) rate constant of oxidation of Fe at the alloy/inner layer interface (cm4 mol−1 s−1 ) rate constant of oxidation of Ni at the alloy/inner layer interface, cm4 mol−1 s−1 enrichment factor of Zn at the inner layer/electrolyte interface inner layer thickness (cm) film thickness at E = 0 (cm) interstitial metal cation in the inner layer normal metal position in the inner layer oxygen anion position in the inner layer relative depth penetration of the concentration profile universal gas constant, 8.314 J mol−1 K−1 electrolyte resistance ( cm2 )

RF/E Rt T Vm,MO  VM VO•• Vl yCr yFe yNi yZn yCr,a yFe,a yNi,a yZn,a Ze Zf ZF/E Zi

charge transfer resistance at the inner layer/electrolyte interface ( cm2 ) charge transfer resistance at the alloy/inner layer interface ( cm2 ) temperature (K) molar volume of the phase in the inner layer (cm3 mol−1 ) cation vacancy in the inner layer oxygen vacancy in the inner layer empty interstice in the inner layer mass fraction of Cr in the oxide mass fraction of Fe in the oxide mass fraction of Ni in the oxide mass fraction of Zn in the oxide mass fraction of Cr in the alloy substrate mass fraction of Fe in the alloy substrate mass fraction of Ni in the alloy substrate mass fraction of Zn in the alloy substrate electronic contribution to the impedance ( cm2 ) impedance of the inner layer ( cm2 ) impedance of the inner layer/electrolyte interface ( cm2 ) ionic contribution to the impedance ( cm2 )

Greek symbols ˛ polarizability of the barrier layer/solution interface ε dielectric constant of the film ε0 dielectric permittivity of vacuum, 8.85419 × 10−14 F cm−1 d defect induced interfacial resistivity ( cm) ω angular frequency (rad s−1 ) References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13]

[14]

[15] [16] [17] [18]

[19] [20]

[21] [22]

L. Tomlinson, Corrosion 37 (1981) 591. D.H. Lister, E. McAlpine, R.D. Davidson, Corros. Sci. 27 (1987) 113. J. Robertson, Corros. Sci. 32 (1991) 443. B. Stellwag, Corros. Sci. 40 (1998) 337. B. Beverskog, M. Bojinov, P. Kinnunen, T. Laitinen, K. Mäkelä, T. Saario, Corros. Sci. 44 (2002) 1923. M. Bojinov, P. Kinnunen, G. Sundholm, Corrosion 59 (2003) 91. I. Betova, M. Bojinov, P. Kinnunen, K. Mäkelä, T. Saario, J. Electroanal. Chem. 572 (2004) 211. C.S. Kumai, T.M. Devine, in: CORROSION ‘2001, NACE International, Houston, 2001 (paper 01150). B. Beverskog, M. Bojinov, P. Kinnunen, T. Laitinen, K. Mäkelä, T. Saario, Corros. Sci. 44 (2002) 1901. Y. Takeda, M. Bojinov, H. Hanninen, P. Kinnunen, T. Laitinen, K. Mäkelä, T. Saario, T. Sakaguchi, T. Shoji, P. Sirkiä, A. Toivonen, Key Eng. Mater. 261–263 (2004) 925. Y. Takeda, T. Shoji, M. Bojinov, P. Kinnunen, T. Saario, Appl. Surf. Sci. 252 (2006) 8580. L.W. Niedrach, W.H. Stoddard, Corrosion 42 (1986) 546. J.N. Esposito, G. Economy, W.A. Byers, J.B. Esposito, F.W. Pement, R.J. Jacko, C.A. Bergmann, Proceedings of the 5th International Symposium on Environmental Degradation of Materials in Nuclear Power Systems—Water Reactors, American Nuclear Society, La Grange Park, USA, 1991, p. 495. W.A. Byers, R.J. Jacko, in: R.E. Gold, E.P. Simonen (Eds.), Proceedings of the 6th International Symposium on Environmental Degradation of Materials in Nuclear Power Systems—Water Reactors, The Minerals, Metals and Materials Society, 1993, p. 837. R.E. Gold, W.A. Byers, R.J. Jacko, Proceedings of the International Symposium Fontevraud III, vol. 1, French Nuclear Society, Paris, 1994, p. 300. S. Ono, M. Haginuma, M. Kumagai, M. Kitamura, K. Tachibana, K. Ishigure, J. Nucl. Sci. Technol. 32 (2) (1995) 125. T.M. Angeliu, P.L. Andresen, Corrosion 52 (1996) 28. M. Haginuma, S. Ono, K. Takamori, K. Takeda, K. Tachibana, K. Ishigure, Water Chemistry of Nuclear Reactor Systems 7, vol. 1, British Nuclear Energy Society, London, 1996, p. 128. P.J. Bennett, P. Gunnerud, J.K. Petersen, A. Harper, Water Chemistry of Nuclear Reactor Systems 7, vol. 1, British Nuclear Energy Society, London, 1996, p. 189. P.J. Bennett, P. Gunnerud, H. Loner, J.K. Petersen, A. Harper, Water Chemistry of Nuclear Reactor Systems 7, vol. 1, British Nuclear Energy Society, London, 1996, p. 293. Y. Hanzawa, K. Ishigure, C. Matsuura, D. Hiroishi, Water Chemistry of Nuclear Reactor Systems 7, vol. 1, British Nuclear Energy Society, London, 1996, p. 301. V.F. Baston, M.F. Garbauskas, H. Ocken, Water Chemistry of Nuclear Reactor Systems 7, vol. 2, British Nuclear Energy Society, London, 1996, p. 558.

I. Betova et al. / Electrochimica Acta 54 (2009) 1056–1069 [23] J. Korb, B. Stellwag, Water Chemistry of Nuclear Reactor Systems 7, vol. 2, British Nuclear Energy Society, London, 1996, p. 566. [24] R. Riess, B. Stellwag, Water Chemistry of Nuclear Reactor Systems 7, vol. 2, British Nuclear Energy Society, London, 1996, p. 573. [25] N. Yoshida, K. Aoki, Y. Saitoh, T. Sakai, Proceedings of the 8th International Symposium on Environmental Degradation of Materials in Nuclear Power Systems—Water Reactors, American Nuclear Society, La Grange Park, USA, 1997, p. 543. [26] B. Beverskog, K. Mäkelä, Proceedings of the JAIF International Conference on Water Chemistry in Nuclear Power Plants, Kashiwazaki, Japan, 1998, p. 89. [27] M. Haginuma, S. Ono, M. Sambongi, K. Takeda, K. Tachibana, K. Ishigure, Proceedings of the JAIF International Conference on Water Chemistry in Nuclear Power Plants, Kashiwazaki, Japan, 1998, p. 122. [28] H. Inagaki, Y. Naruse, S. Ono, M. Haginuma, T. Tsuji, Proceedings of the JAIF International Conference on Water Chemistry in Nuclear Power Plants, Kashiwazaki, Japan, 1998, p. 772. [29] Y.-K. Kim, R.J. Jacko, in: F.P. Ford, S.M. Bruemmer, G.S. Was (Eds.), Proceedings of the 9th International Symposium on Environmental Degradation of Materials in Nuclear Power Systems—Water Reactors, The Minerals, Metals and Materials Society, 1999, p. 477. [30] D.H. Lister, G. Venkateswaran, Nucl. Technol. 125 (1999) 316. [31] G. Repphun, A. Hiltpold, I. Mailand, B. Stellwag, Power Plant Chem. 1 (1999) 18. [32] T. Tatsuki, T. Kikuchi, T. Sakai, Water Chemistry of Nuclear Reactor Systems 7, vol. 1, British Nuclear Energy Society, London, 2000, p. 153. [33] J.H. Harding, W.S. Walters, H.E. Sims, Water Chemistry of Nuclear Reactor Systems 7, vol. 1, British Nuclear Energy Society, London, 2000, p. 302. [34] B. Beverskog, Water Chemistry of Nuclear Reactor Systems 7, vol. 2, British Nuclear Energy Society, London, 2000, p. 420.

1069

[35] H. Inagaki, A. Nishikawa, Y. Sugita, T. Tsuji, J. Nuclear Sci. Technol. 40 (2003) 143. [36] H. Hosogawa, M. Nagase, J. Nuclear Sci. Technol. 41 (2004) 682. [37] B. Beverskog, in: Proceedings of the International Conference “Water Chemistry of Nuclear Reactor Systems”, San Francisco, CA, October 10–14, 2004, paper 2.7 (CD-ROM publication). [38] M. Bojinov, P. Kinnunen, K. Lundgren, G. Wikmark, J. Electrochem. Soc. 152 (2005) B250. [39] M. Bojinov, A. Galtayries, P. Kinnunen, A. Machet, P. Marcus, Electrochim. Acta 52 (2007) 7475. [40] I. Betova, M. Bojinov, P. Kinnunen, K. Lundgren, T. Saario, J. Electrochem. Soc. 155 (2008) C81. [41] S.E. Ziemniak, M. Hanson, Corros. Sci. 44 (2002) 2209. [42] S.E. Ziemniak, M. Hanson, Corros. Sci. 48 (2006) 2525. [43] R.L. Tapping, R.D. Davidson, E. McAlpine, D.H. Lister, Corros. Sci. 26 (1986) 563. [44] Z. Szklarska-Smialowska, K. Chou, Z. Xia, Corros. Sci. 32 (1992) 609. [45] C.Y. Chao, L.F. Lin, D.D. Macdonald, J. Electrochem. Soc. 128 (1981) 1187. [46] D.D. Macdonald, J. Electrochem. Soc. 139 (1992) 3434. [47] D.D. Macdonald, Pure Appl. Chem. 71 (1999) 951. [48] D.D. Macdonald, J. Electrochem. Soc. 153 (2006) B213. [49] J.W. Schultze, M. Lohrengel, Electrochim. Acta 45 (2000) 2499. [50] M. Kamrunnahar, J.E. Bao, D.D. Macdonald, Corros. Sci. 47 (2005) 3111. [51] W. Schmickler, J.W. Schultze, in: J.O’M. Bockris, B.E. Conway, R.E. White (Eds.), Modern Aspects of Electrochemistry, vol. 17, Plenum Press, New York, 1987, pp. 357–410. [52] A.T. Fromhold Jr., E.L. Cook, J. Appl. Phys. 38 (1967) 1546. [53] L. Young, Trans. Faraday Soc. 51 (1955) 1250. [54] B. Beverskog, I. Puigdomenech, Corrosion 55 (1999) 1077.