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International Journal of Electrochemistry
Volume 2011, Article ID 521384, 9 pages
http://dx.doi.org/10.4061/2011/521384
Research Article

The Mechanism of Transpassive Dissolution of AISI 321 Stainless Steel in Sulphuric Acid Solution

1Faculty of Engineering, Bu-Ali Sina University (BASU), Hamedan 65178-38695, Iran
2Department of Materials Engineering, Isfahan University of Technology, Isfahan 84156-83111, Iran

Received 9 August 2010; Accepted 21 October 2010

Academic Editor: Angela Molina

Copyright © 2011 A. Fattah-Alhosseini and N. Attarzadeh. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

The transpassive dissolution mechanism of AISI 321 stainless steel in a 0.5 M sulphate solution was studied using electrochemical impedance spectroscopy (EIS). On the basis of the experimental results, surface charge approach, and point defect model, a kinetic model of the transpassive dissolution process is proposed. The transpassive film is modeled as a highly doped n-type semiconductor—insulator-p-type semiconductor structure. Injection of negative defects at the transpassive film/solution interface results in their accumulation as a negative surface charge. It alters the nonstationary transpassive film growth rate controlled by the transport of positive defects (oxygen vacancies). The model describes the process as dissolution of Cr as Cr (VI) and Fe as Fe (III) through the transpassive film via parallel reaction paths.

1. Introduction

Transpassivation is a phenomenon in which a passivated metal starts rapid dissolution if the electrode potential of the metal becomes too positive [1]. Transpassive dissolution of a metal or alloy can be defined as the formation of chemical species in a valence state higher than that in the primary passive film formed on the material [27]. Transpassive dissolution of a range of alloys is closely related to passive film breakdown and localized corrosion phenomena. It leads to a depletion of alloying elements such as Cr in the first atomic layers near the solution, which are the most susceptible to localized attack by aggressive anions [818]. Two main approaches can serve as a basis for a theoretical treatment of the problem.

The Surface Charge Approach (SCA)
The SCA assumes that transpassive dissolution is a complex process including several reaction stages: formation and growth of a passive film via generation, transport and annihilation of ionic point defects, continuous changes in the stoichiometry of this film and especially of the first atomic layers adjacent to the solution, charge transfer reactions at the film/solution interface, and transport of reaction products in the bulk solution. According to this model the passive film was represented as an n-i-p junction structure with injection of oxygen vacancies from the metal substrate during film growth and metal vacancies from the solution during film dissolution. Assuming that the transport of metal vacancies is slower than the rate of their annihilation at the metal/film interface, they accumulate at the film/solution interface. This accumulation of negative charge enhances the nonstationary transport of positively charged oxygen vacancies, thus explaining the low frequency inductive loop in the impedance response of a range of passive metals [1926].

The Point Defect Model (PDM)
The PDM assumes segregation of alloying elements such as Cr in the film as high valency cations. These cations are assumed to reduce the concentration and diffusivity of cation vacancies in the film by means of forming complexes with them. Macdonald et al. assume that there is an accumulation of oxygen vacancies at the metal/film interface and a corresponding accumulation of cation vacancies at the film/solution interface [2730].
As transpassivation is a rapid dissolution process, it is generally regarded as a type of corrosion damage to a passivated metal. How to prevent transpassivation is an important topic in corrosion science and engineering. In general, stainless steels are more widely used in many corrosive environments and are more likely to suffer from transpassivation damage. Therefore, it seems that an investigation into transpassivation mechanism of stainless steels will be of scientific and practical interest.

2. Experimental

Specimens were fabricated from 1 cm diameter rods of AISI 321 stainless steel; the nominal composition is given in the Table 1. The samples were placed in stainless steel sacks and were annealed to eliminate the cold work effect due to cutting process. The annealing was preformed at 1050°C for 90 min followed by water quenching. The working electrode pretreatment consisted of mechanical polishing on emery paper up to 1200 grade, degreasing and rinsing with distilled water. A three electrode cell featuring a Pt counter electrode and a calomel reference electrode was employed. The solution (0.5 M H2SO4) was prepared from analytical grade 97% H2SO4 and distilled water.

tab1
Table 1: Nominal chemical composition of AISI 321 stainless steel.

All electrochemical measurements were performed using an EG&G PAR Model 273A potentiostat/galvanostat controlled by a personal computer at ambient temperature (23–25°C). A polarization curve was obtained at a potential scan rate of 1 mV/s. To perform impedance measurements, the current versus time curve was recorded at each potential until a steady state current was reached. The impedance spectra were measured at this steady state in a frequency range of 10 mHz–100 KHz at an AC amplitude of 10 mV (rms). The validation of the impedance spectra was performed by checking the linearity condition, that is, measuring spectra at AC signal amplitudes between 5 and 15 mV (rms). For the simulation processing of the impedance data, Zview2 software was employed.

3. Results and Discussion

3.1. Polarization Behavior

The potentiodynamic polarization curve of AISI 321 stainless steel in 0.5 M H2SO4 solution is shown in Figure 1. According to Figure 1, two stages of the passive process can be distinguished in the curve. The low potential passive region ranges from about −0.15 to 0.3 V versus SCE (region I). In region II, the comparatively slow increase of the current in the potential range 0.3–0.9 V versus SCE could be connected to the formation of high valency Cr [31] in the film prior to transpassive dissolution. The steeper increase in the range from 0.9 to 1.1 V versus SCE (region III) is most probably related to the onset of the transpassive dissolution.

521384.fig.001
Figure 1: Potentiodynamic polarization curve for AISI 321 stainless steel in 0.5 M H2SO4. Potential regions: I-:low potential passive, II-:high potential passive, III-:transpassive dissolution.
3.2. EIS Measurements

Typical experimental impedance spectra for the transpassive state on AISI 321 stainless steel are shown in Figure 2, in the form of Nyquist plots, in which the imaginary component of the impedance is plotted against the real component for decreasing frequencies. In all cases, the correlation between experimental data and simulated data is judged to be acceptable. Two time constants—a high frequency capacitive and a low frequency inductive—followed by a capacitive behavior at the lowest frequencies are observed at  V versus SCE. Thus, the high frequency capacitive loop reflects the high field assisted migration of defects in the transpassive film; the inductive loop at intermediate frequencies is due to the relaxation of the negative surface charge formed by the accumulation of cation vacancies at the transpassive film/solution interface and, at the lowest frequencies, the faradaic pseudocapacitance is detected.

fig2
Figure 2: Electrochemical impedance spectra for AISI 321 stainless steel in the transpassive region registered after 30-minute polarization at 0.8 V versus SCE.

Based on the polarization curve and the Nyquist plots, it is clear that the barrier layer in the transpassive region cannot exist since, as Macdonald mentioned, the current density is high. Therefore, the transpassive film must be a nonbarrier layer which has little resistance to current flow [2, 3].

In order to model the transpassive film with electrical analogs, the equivalent electrical circuit of Figure 3 was found to be appropriate [32, 33]. In this circuit, CPE is the high frequency constant phase element of the metal/ transpassive film/solution system, is the defect migration resistance, and are elements associated with the inductive loop observed throughout the investigated potential range, is the Faradaic pseudocapacitance, and is the uncompensated solution resistance. These parameter values characterize the properties of the interface and the rates of the reaction steps involved and they acquire clear physical meaning only when related to a specific kinetic model. The dependences of , , and on the potential are presented in Figures 4(a) and 4(b). According to Figures 4(a) and 4(b), a steep decrease of , , and is observed in the transpassive dissolution region. A more detailed explanation of the circuit elements will be presented in the Section 3.3 on the basis of a kinetic model.

521384.fig.003
Figure 3: Equivalent electrical circuit of the metal/transpassive film/solution interface.
fig4
Figure 4: Potential dependences of (a) and , (b) . These circuit elements are acquired from equivalent electrical circuit of Figure 3.
3.3. A Kinetic Model Based on PDM and SCA

Figure 5 summarizes the physicochemical processes that are envisioned to occur within the transpassive film formed on the AISI 321 stainless steel, according to the PDM [3439]. This model provides microscopic description of the growth and breakdown of the passive film under steady state and transient condition. PDM is based on the migration of the point defects under the influence of the electrostatic field in the film [26]. On the basis of PDM for a given potential at steady state, the continuity equation imposes [711]: Therefore, the impedance of the system will be the sum of the impedances of the two interfaces and the transpassive film [711] According to the PDM [3445] at the metal/transpassive film interface, annihilation of metal vacancies and injection of oxygen vacancies take place as follows: The interfacial rate constants are assumed to be potential dependent in a tafel manner Then the balance of fluxes at the interface gives [19, 20]

521384.fig.005
Figure 5: A Scheme representation of the processes in the metal/transpassive film/solution system, according to PDM.

Based upon the SCA [20], the small sine perturbation does not lead to a significant deviation of from its steady state value. Therefore, the impedance at the metal/transpassive film interface is

According to the SCA [19, 20] in the transpassive film with a thickness , oxygen vacancy motion is driven by the electric field at the metal/transpassive film interface: where [4345] and is a negative surface charge accumulated at the transpassive film/solution interface by the cation vacancies generated mainly by the transpassive dissolution reaction [19, 20]. As for most cases, , , and by setting and , The time dependence of the surface charge is treated in analogy to the SCA [19, 20]: where is a capture cross section for a positive defect by the negative surface charge. The steady-state value of the surface charge is Inserting this in (11) results in the expression [19, 20] From (10) and (13) under a small amplitude AC perturbation, Accordingly, the faradaic impedance of the transpassive film is which is equivalent to where [19, 20]

In order to derive the total impedance, the high frequency constant phase element of the transpassive film and the faradaic pseudocapacitance has to be added in the appropriate manner. Thus, the experimental impedance spectra are well described and will be discussed according to the following transfer function [33]: According to the PDM [3445] at the transpassive film/solution interface, reaction of oxygen vacancies with water and production of metal vacancies take place as follows:

At higher potentials, passivity is observed to break down on many metals and alloys, and the dissolution rate of the substrate increases dramatically as the system transitions into the transpassive state. This process is postulated to be due to the oxidative dissolution of the barrier layer; for example, in the case of stainless steels, which form chromic oxide barrier layers, the onset of transpassive dissolution is due to the reaction [2, 3]

It is noticed that transpassive film on the stainless steels in the transpassive region are assumed to be covered by a mixed Cr (VI) and Fe (III) oxide film and some Mo-containing species. Also it is assumed [4649] that the amount of Ni in the transpassive film on stainless steels is negligible, and no separate reaction path for the dissolution of Mo from the transpassive film as Mo (VI) is included in the present approach. Rather, it is assumed that Mo in the alloy substrate has a catalytic effect on the transpassive dissolution of Cr via the formation of soluble molybdate or Cr–Mo-containing species that accelerate the abstraction of Cr (VI) from the outermost layer of the transpassive film [12]. Therefore, the transpassive dissolution reaction results in an accumulation of cation vacancies near the transpassive film/solution interface in a layer with a thickness and to a depletion of this layer in Cr positions in the transpassive film. The balance of fluxes at the transpassive film/solution interface gives [19, 20] Assuming that the small sine perturbation does not change significantly, the impedance of that interface becomes The impedance response of the system in the transpassive dissolution exhibits only two time constants (one capacitive and one inductive) and a series capacitive features at low frequencies, which is consistent with the impedance defined by (16)–(20). In order to explore these dependences within the frames of the present model, the transpassive film thickness versus potential relationship is taken from the PDM [6] with the assumption that the applied potential is expressed versus the potential of zero film thickness: In transpassive dissolution and , Inserting (26) in (16)–(18), it follows that

The numerators of (28) increase linearly with the potential whereas their denominators increase exponentially with the same parameter. Thus , , and all decrease which is found experimentally in Figures 4(a) and 4(b). From (28)–(36), two important characteristics of the system could be derived, namely [19], and versus the transpassive potential are plotted in Figures 6 and 7. The obtained dependences are consistent with the physical picture given in Figure 5. Due to the accumulation of at the transpassive film/solution interface and the simultaneous Cr depletion of the interface [50], the rate of the transpassive dissolution is slowed down. This leads to a gradual dissipation of the surface charge . As a consequence, the parameter characterizing the part of the applied potential consumed at the transpassive film/solution interface decreases (Figure 6). Similar speculations could explain the potential trend of the capture cross section per charge carrier (Figure 7). This quantity is related to the surface excess of negative carriers by the following equation [20]:

521384.fig.006
Figure 6: Potential dependences of the polarizability of the transpassive film/solution interface. This parameter is acquired from (29).
521384.fig.007
Figure 7: Potential dependences of the capture cross section per positive defect. This parameter is acquired from (29).

The observed decrease of (Figure 7) is caused by the increase of the surface excess of negative carriers due to the gradual dissipation of the surface charge.

4. Conclusions

This study reports an EIS study of transpassive dissolution of AISI 321 stainless steel in 0.5 M H2SO4 solution. The overall impedance of the system was described using the electrical equivalent circuit, Figure 3, and by the corresponding transfer function, (22). Based on the Nyquist plots and the polarization curve, it is clear that the transpassive film must be a nonbarrier layer which has little resistance to current flow. On the basis of the experimental results, SCA, and PDM, a generalized model of the transpassivity is proposed. This model represents the transpassive film as a highly doped n-i-p junction structure. Injection of negative defects at the transpassive film/solution interface results in their accumulation as a negative surface charge. It alters the nonstationary transpassive film growth rate controlled by the transport of positively charge defects. On the basis of the results obtained, a kinetic model including the dissolution of Cr from the outermost cation layer of the transpassive film in parallel reaction paths is deduced.

Nomenclature

:Atomic jump distance, cm
:Polarizability of the transpassive film/solution interface
:Constant in the high field migration equation, Acm-2
:Field coefficient in the high field equation, V-1 cm
:Tafel coefficients of the interfacial reactions (), V-1
:Concentration of oxygen vacancies at the transpassive film/solution interface, mol cm-3
:Concentration of oxygen vacancies at the metal/transpassive film interface, mol cm-3
:Concentration of metal vacancies at the transpassive film/solution interface, mol cm-3
:Concentration of metal vacancies at the metal/transpassive film interface, mol cm-3
:Diffusivity of oxygen vacancies, cm2s-1
:Applied potential, V
:Electric field strength, Vcm-1
:Current density at the metal/transpassive film interface, Acm-2
:Film formation current density, Acm-2
:Current density at the transpassive film/solution interface, Acm-2
:Steady state current density, Acm-2
:Imaginary unit
:Thickness of the transpassive film, cm
:Thickness of the metal vacancy accumulation layer, cm
:Metal atom in the metal phase
:Metal position in the transpassive film
:Oxygen position in the transpassive film
:Negative surface charge at the transpassive film/solution interface, C cm-2
:Charge transfer resistance, Ωcm2
:Uncompensated solution resistance, Ωcm2
:Rate constants of the interfacial reactions () mol cm-2s-1
:Capture cross section for a positive defect, cm2C-1
:Molar volume of the phase in the transpassive film, cm3 mol-1
:Oxygen vacancy in the transpassive film
:Metal vacancy in the transpassive film
:Impedance of the metal/transpassive film interface, Ωcm2
:Impedance of the transpassive film, Ωcm2
:Impedance of the transpassive film/solution interface, Ωcm2
:Maximum surface excess, mol cm-2
:Dielectric constant of the transpassive film
:Dielectric permittivity of vacuum
:Local potential drop at the metal/transpassive film interface, V
:Local potential drop at the transpassive film/solution interface, V
:Valency of transpassive dissolution
:Valency of the cation in the transpassive film.

References

  1. G. Song, “Transpassivation of Fe-Cr-Ni stainless steels,” Corrosion Science, vol. 47, no. 8, pp. 1953–1987, 2005. View at Publisher · View at Google Scholar · View at Scopus
  2. D. D. Macdonald, “On the tenuous nature of passivity and its role in the isolation of HLNW,” Journal of Nuclear Materials, vol. 379, no. 1–3, pp. 24–32, 2008. View at Publisher · View at Google Scholar · View at Scopus
  3. D. D. MacDonald, “On the existence of our metals-based civilization I. Phase-space analysis,” Journal of the Electrochemical Society, vol. 153, no. 7, pp. B213–B224, 2006. View at Publisher · View at Google Scholar · View at Scopus
  4. L. Zhang and D. D. Macdonald, “Segregation of alloying elements in passive systems—II. Numerical simulation,” Electrochimica Acta, vol. 43, no. 18, pp. 2673–2685, 1998. View at Google Scholar · View at Scopus
  5. D. D. Macdonald and M. Urquidi-Macdonald, “Theory of steady-state passive films,” Journal of the Electrochemical Society, vol. 137, no. 8, pp. 2395–2402, 1990. View at Google Scholar · View at Scopus
  6. D. D. Macdonald, “Point defect model for the passive state,” Journal of the Electrochemical Society, vol. 139, no. 12, pp. 3434–3449, 1992. View at Google Scholar · View at Scopus
  7. J. H. W. de Wit and H. J. W. Lenderink, “Electrochemical impedance spectroscopy as a tool to obtain mechanistic information on the passive behaviour of aluminium,” Electrochimica Acta, vol. 41, no. 7-8, pp. 1111–1119, 1996. View at Google Scholar · View at Scopus
  8. M. Bojinov, G. Fabricius, P. Kinnunen et al., “Mechanism of transpassive dissolution of Ni-Cr alloys in sulphate solutions,” Electrochimica Acta, vol. 45, no. 17, pp. 2791–2802, 2000. View at Publisher · View at Google Scholar · View at Scopus
  9. M. Bojinov, G. Fabricius, T. Laitinen, and T. Saario, “Transpassivity mechanism of iron-chromium-molybdenum alloys studied by AC impedance, DC resistance and RRDE measurements,” Electrochimica Acta, vol. 44, no. 24, pp. 4331–4343, 1999. View at Google Scholar · View at Scopus
  10. M. Bojinov, I. Betova, and R. Raicheff, “A model for the transpassivity of molybdenum in acidic sulphate solutions based on ac impedance measurements,” Electrochimica Acta, vol. 41, no. 7-8, pp. 1173–1179, 1996. View at Google Scholar · View at Scopus
  11. M. Bojinov, G. Fabricius, T. Laitinen, and T. Saario, “The mechanism of the transpassive dissolution of chromium in acidic sulfate solutions,” Journal of the Electrochemical Society, vol. 145, no. 6, pp. 2043–2050, 1998. View at Google Scholar · View at Scopus
  12. I. Betova, M. Bojinov, T. Laitinen, K. Mäkelä, P. Pohjanne, and T. Saario, “The transpassive dissolution mechanism of highly alloyed stainless steels I. Experimental results and modelling procedure,” Corrosion Science, vol. 44, no. 12, pp. 2675–2697, 2002. View at Publisher · View at Google Scholar · View at Scopus
  13. I. Betova, M. Bojinov, T. Laitinen, K. Mäkelä, P. Pohjanne, and T. Saario, “The transpassive dissolution mechanism of highly alloyed stainless steels II. Effect of pH and solution anion on the kinetics,” Corrosion Science, vol. 44, no. 12, pp. 2699–2723, 2002. View at Publisher · View at Google Scholar · View at Scopus
  14. T. Piao and S.-M. Park, “Spectroelectrochemical studies of passivation and transpassive breakdown reactions of stainless steel,” Journal of the Electrochemical Society, vol. 144, no. 10, pp. 3371–3377, 1997. View at Google Scholar · View at Scopus
  15. M. Itagaki, A. Matsuzaki, and K. Watanabe, “The electrochemical impedance response of transpassive dissolution of chromium in neutral solutions containing sodium chloride and sodium fluoride,” Corrosion Science, vol. 37, no. 11, pp. 1867–1878, 1995. View at Google Scholar · View at Scopus
  16. R. Knoedler and K. E. Heusler, “The mechanism of oxidation of chromium to chromate,” Electrochimica Acta, vol. 17, no. 2, pp. 197–212, 1972. View at Google Scholar · View at Scopus
  17. M. S. El-Basiouny and S. Haruyama, “The polarization behaviour of chromium in acidic sulphate solutions,” Corrosion Science, vol. 17, no. 5, pp. 405–414, 1977. View at Google Scholar · View at Scopus
  18. N. Sato, “An overview on the passivity of metals,” Corrosion Science, vol. 31, pp. 1–19, 1990. View at Publisher · View at Google Scholar
  19. M. Bojinov, “The ability of a surface charge approach to describe barrier film growth on tungsten in acidic solutions,” Electrochimica Acta, vol. 42, no. 23-24, pp. 3489–3498, 1997. View at Google Scholar · View at Scopus
  20. M. Bojinov, I. Betova, G. Fabricius, T. Laitinen, R. Raicheff, and T. Saario, “The stability of the passive state of iron-chromium alloys in sulphuric acid solution,” Corrosion Science, vol. 41, no. 8, pp. 1557–1584, 1999. View at Publisher · View at Google Scholar
  21. M. Bojinov, I. Betova, and R. Raicheff, “Transpassivity of molybdenum in H2SO4 solution,” Journal of Electroanalytical Chemistry, vol. 381, no. 1-2, pp. 123–131, 1995. View at Google Scholar · View at Scopus
  22. M. Bojinov, I. Betova, and R. Raicheff, “Influence of pH on the anodic dissolution mechanism of Fe-Mo alloys in sulphate solutions,” Electrochimica Acta, vol. 44, no. 5, pp. 721–734, 1998. View at Google Scholar · View at Scopus
  23. I. Betova, M. Bojinov, and TZ. Tzvetkoff, “Transpassive dissolution mechanism of ferrous alloys in phosphoric acid/acetic acid mixtures,” Journal of Solid State Electrochemistry, vol. 9, no. 3, pp. 154–167, 2005. View at Publisher · View at Google Scholar · View at Scopus
  24. M. Bojinov, I. Betova, and R. Raicheff, “Influence of molybdenum on the anodic dissolution of iron in acidic solutions,” Journal of Applied Electrochemistry, vol. 26, no. 9, pp. 939–946, 1996. View at Google Scholar · View at Scopus
  25. I. Betova, M. Bojinov, P. Kinnunen, T. Laitinen, P. Pohjanne, and T. Saario, “Mechanism of transpassive dissolution of nickel-based alloys studied by impedance spectroscopy and rotating ring-disc voltammetry,” Electrochimica Acta, vol. 47, no. 13-14, pp. 2093–2107, 2002. View at Publisher · View at Google Scholar · View at Scopus
  26. I. Betova, M. Bojinov, P. Kinnunen et al., “Transpassive dissolution mechanism of Ni-based alloys in a simulated bleaching solution: Effect of alloying elements,” Journal of the Electrochemical Society, vol. 149, no. 11, pp. B499–B509, 2002. View at Publisher · View at Google Scholar · View at Scopus
  27. D. D. Macdonald, “Passivity—the key to our metals-based civilization,” Pure and Applied Chemistry, vol. 71, no. 6, pp. 951–978, 1999. View at Google Scholar · View at Scopus
  28. L. Zhang and D. D. Macdonald, “Segregation of alloying elements in passive systems—II. Numerical simulation,” Electrochimica Acta, vol. 43, no. 18, pp. 2673–2685, 1998. View at Google Scholar · View at Scopus
  29. A. Fattah-Alhosseini, M. A. Golozar, A. Saatchi, and K. Raeissi, “Effect of solution concentration on semiconducting properties of passive films formed on austenitic stainless steels,” Corrosion Science, vol. 52, p. 205, 2010. View at Publisher · View at Google Scholar · View at Scopus
  30. A. Fattah-Alhosseini, A. Saatchi, M. A. Golozar, and K. Raeissi, “The passivity of AISI 316L stainless steel in 0.05 M H2SO4,” Journal of Applied Electrochemistry, vol. 40, pp. 457–461, 2010. View at Publisher · View at Google Scholar · View at Scopus
  31. J. A. Bardwell, G. I. Sproule, B. MacDougall, M. J. Graham, A. J. Davenport, and H. S. Isaacs, “In situ XANES detection of Cr(VI) in the passive film on Fe-26Cr,” Journal of the Electrochemical Society, vol. 139, no. 2, pp. 371–373, 1992. View at Google Scholar · View at Scopus
  32. G. Vázquez and I. González, “Diffusivity of anion vacancies in WO3 passive films,” Electrochimica Acta, vol. 52, no. 24, pp. 6771–6777, 2007. View at Publisher · View at Google Scholar · View at Scopus
  33. M. Metikoš-Huković and Z. Grubač, “The growth kinetics of thin anodic WO3 films investigated by electrochemical impedance spectroscopy,” Journal of Electroanalytical Chemistry, vol. 556, pp. 167–178, 2003. View at Publisher · View at Google Scholar · View at Scopus
  34. D. D. Macdonald, K. M. Ismail, and E. Sikora, “Characterization of the passive state on zinc,” Journal of the Electrochemical Society, vol. 145, no. 9, pp. 3141–3149, 1998. View at Google Scholar · View at Scopus
  35. D. D. MacDonald and A. Sun, “An electrochemical impedance spectroscopic study of the passive state on Alloy-22,” Electrochimica Acta, vol. 51, no. 8-9, pp. 1767–1779, 2006. View at Publisher · View at Google Scholar · View at Scopus
  36. D. D. Macdonald, A. Sun, N. Priyantha, and P. Jayaweera, “An electrochemical impedance study of Alloy-22 in NaCl brine at elevated temperature: II. Reaction mechanism analysis,” Journal of Electroanalytical Chemistry, vol. 572, no. 2, pp. 421–431, 2004. View at Publisher · View at Google Scholar · View at Scopus
  37. E. Sikora, J. Sikora, and D. D. Macdonald, “A new method for estimating the diffusivities of vacancies in passive films,” Electrochimica Acta, vol. 41, no. 6, pp. 783–789, 1996. View at Publisher · View at Google Scholar · View at Scopus
  38. Z. Lu and D. D. Macdonald, “Transient growth and thinning of the barrier oxide layer on iron measured by real-time spectroscopic ellipsometry,” Electrochimica Acta, vol. 53, no. 26, pp. 7696–7702, 2008. View at Publisher · View at Google Scholar · View at Scopus
  39. D. D. Macdonald, E. Sikora, and J. Sikora, “The kinetics of growth of the passive film on tungsten in acidic phosphate solutions,” Electrochimica Acta, vol. 43, no. 19-20, pp. 2851–2861, 1998. View at Google Scholar · View at Scopus
  40. B. Krishnamurthy, R. E. White, and H. J. Ploehn, “Non-equilibrium point defect model for time-dependent passivation of metal surfaces,” Electrochimica Acta, vol. 46, no. 22, pp. 3387–3396, 2001. View at Publisher · View at Google Scholar · View at Scopus
  41. B. Krishnamurthy, R. E. White, and H. J. Ploehn, “Electric field strength effects on time-dependent passivation of metal surfaces,” Electrochimica Acta, vol. 47, no. 15, pp. 2505–2513, 2002. View at Publisher · View at Google Scholar · View at Scopus
  42. B. Krishnamurthy, R. E. White, and H. J. Ploehn, “Simplified point defect model for growth of anodic passive films on iron,” Electrochimica Acta, vol. 47, no. 20, pp. 3375–3381, 2002. View at Publisher · View at Google Scholar · View at Scopus
  43. L. F. Lin, C. Y. Chao, and D. D. Macdonald, “point defect model for anodic passive films,” Journal of the Electrochemical Society, vol. 128, no. 6, pp. 1187–1194, 1981. View at Google Scholar · View at Scopus
  44. L. F. Lin, C. Y. Chao, and D. D. Macdonald, “point defect model for anodic passive films. 2. Chemical Breakdown and Pit Initiation,” Journal of the Electrochemical Society, vol. 128, no. 6, pp. 1194–1198, 1981. View at Google Scholar · View at Scopus
  45. C. Y. Chao, L. F. Lin, and D. D. Macdonald, “point defect model for anodic passive films,” pp. 1874–1879. View at Google Scholar · View at Scopus
  46. V. Maurice, W. P. Yang, and P. Marcus, “X-ray photoelectron spectroscopy and scanning tunneling microscopy study of passive films formed on (100) Fe-18Cr-13Ni single-crystal surfaces,” Journal of the Electrochemical Society, vol. 145, no. 3, pp. 909–920, 1998. View at Google Scholar · View at Scopus
  47. I. Olefjord and L. Wegrelius, “Surface analysis of passive state,” Corrosion Science, vol. 31, pp. 89–98, 1990. View at Google Scholar · View at Scopus
  48. B. Elsener and A. Rossi, “Effect of pH on electrochemical behaviour and passive film composition of stainless steels,” Materials Science Forum, vol. 192, pp. 225–236, 1995. View at Google Scholar
  49. N. Hara and K. Sugimoto, “In situ analysis of passive films on Fe-Cr-Ni alloy by potential-modulated UV-visible reflection spectroscopy,” Journal of the Electrochemical Society, vol. 138, no. 6, pp. 1594–1599, 1991. View at Google Scholar · View at Scopus
  50. R. Kirchheim, B. Heine, H. Fischmeister, S. Hofmann, H. Knote, and U. Stolz, “The passivity of iron-chromium alloys,” Corrosion Science, vol. 29, no. 7, pp. 899–917, 1989. View at Google Scholar · View at Scopus