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Original article
9 (
2_suppl
); S1342-S1348
doi:
10.1016/j.arabjc.2012.02.015

Passivity of AISI 321 stainless steel in 0.5 M H2SO4 solution studied by Mott–Schottky analysis in conjunction with the point defect model

 Faculty of Engineering, Bu-Ali Sina University, Hamedan 65178-38695, Iran

⁎Tel.: +98 811 8257409, mobile: +98 9137066811; fax: +98 811 8257400. a.fattah@basu.ac.ir (A. Fattah-alhosseini)

Received: , Accepted: ,
© The Author(s) 2012
Disclaimer:
This article was originally published by Elsevier and was migrated to Scientific Scholar after the change of Publisher.

Peer review under responsibility of King Saud University.

Abstract

The passivity of AISI 321 stainless steel in 0.5 M H2SO4 solution, in the steady-state condition, has been explored using electrochemical impedance spectroscopy (EIS) and Mott–Schottky analysis. Based on the Mott–Schottky analysis in conjunction with the point defect model (PDM), it was shown that the calculated donor density decreases exponentially with increasing passive film formation potential. The thickness of the passive film was increased linearly with the formation potential. These observations were consistent with the predictions of the PDM, noting that the point defects within the passive film are metal interstitials, oxygen vacancies, or both.

Keywords

Mott–Schottky plot
Stainless steel
Electrochemical impedance spectroscopy
1

1 Introduction

Generally, semiconducting properties are often observed on the surfaces of the passivity metals. Their electrical properties are expected to be crucially important in understanding the protective characters against corrosion. Mott–Schottky analysis has been widely used to study and characterize the semiconducting properties of the passive films, such as the passive films on Cr (Kong et al., 2003; Kim et al., 2001), Ni (Sikora and Macdonald, 2002; Park et al., 2011; Grubač et al., 2010; Ries et al., 2008; Kang et al., 2008; Darowicki et al., 2006; Nakaoka et al., 2004; Da Cunha Belo et al., 1999), Al (Martin et al., 2005; Levine et al., 2008; Zhang et al., 2010; Liu et al., 2009), Co (Pontinha et al., 2006; Kang et al., 2008), Zn (Bohe et al., 1989; Vilche et al., 1990), Ti (Schmidt et al., 2006; Azumi and Seo, 2001; da Fonseca et al., 1994; Radecka et al., 2008; Sellers and Seebauer, 2011), carbon steels (Fujimoto and Tsuchiya, 2007; Wielant et al., 2007; Zeng and Luo, 2003; Li et al., 2008; Zhang and Cheng, 2009) and stainless steels (Amri et al., 2008; Ningshen et al., 2007; Taveira et al., 2010; Feng et al., 2010; Marconnet et al., 2008).

Passivity of stainless steel is usually attributed to the formation on the metal surface of a mixture of iron and chromium oxide film with semiconducting behavior. In the last decade, increasing research on the electronic properties of passive films formed on stainless steels has given an important contribution to the understanding of the corrosion behavior of these alloys (Simões et al., 1990; Olefjord and Wegrelius, 1990; Mischler et al., 1991; Montemor et al., 2000; Sunseri et al., 1990). Depending on the predominant defects present in the passive oxide layer on stainless steels, either p-type or n-type behaviors are observed. The passive oxide films with a deficiency in metal ions or excess with cation vacancies generally behave as p-type. Similarly, n-type is developed in the passive films either by excess cation in interstitial sites or anion vacancies. Mott–Schottky analysis has been shown to be an important in situ method for investigation of the semiconductor properties of passive films (Sikora and Macdonald, 1997; Sikora et al., 2000; Cho et al., 2002; Hakiki et al., 2000; Stimming, 1986).

Compared with many theories describing the passive state qualitatively, the PDM (Macdonald, 2011, 2004, 2006, 2008; Macdonald and Sun, 2006; Fattah-alhosseini et al., 2010, 2009) provides a microscopic description of the growth and breakdown of the passive film, as well as an analytical expression for the flux and concentration of vacancies within the passive film. Therefore this model can also provide an opportunity for quantitative analysis of the passive film. The PDM is based on the migration of point defects under the influence of electrostatic field within the passive film. Because the passive film grows into the metal by the generation of oxygen vacancies at the metal/passive film interface, and by their annihilation at the passive film/solution interface, the transport properties and spatial distribution of oxygen vacancies or metal cations within the passive film are of the great interest.

Diffusivity of the point defects is a key parameter in describing the transport of point defects and hence the kinetics of passive film growth. Inspite of relatively extensive works published on the passive films, there seems to be lack of study on the density and diffusivity of point defects in the passive films formed on stainless steels in acidic solutions. In this work, EIS and Mott–Schottky analysis of AISI 321 have been performed. The ultimate goal of this study is to model experimental data within the PDM. This work includes determination of the passive region for AISI 321 in 0.5 M H2SO4, measurement of steady-state current for the region of passive film formation, determination of the semiconductor character and estimation of the dopant levels in the passive film, as well as the estimation of the film thickness as a function of the formation potential.

2

2 Experimental procedures

Specimens were fabricated from 1 cm diameter rods of AISI 321 stainless steel; the nominal composition is given in Table 1. The Samples were placed in stainless steel sacks and annealed in inert environment (Ar gas) to eliminate the cold work effect due to cutting process. The annealing was preformed at 1050 °C for 90 min followed by water quenching. All samples were ground to 1200 grit and cleaned by ethanol and deionized water prior to tests. A three electrode cell featuring a Pt counter electrode and a saturated calomel electrode (SCE) was employed. All the potential values in the text are relative to the SCE. The solution (0.5 M H2SO4) was prepared from analytical grade 97% H2SO4 and distilled water. Before potentiostatic film growth, the electrode was held at −1.2 V for 5 min to remove the native oxide film.

Table 1 Nominal chemical composition of AISI 321 stainless steel.
Elements Cr Ni Mn Si C Ti Nb S Mo Cu Fe
AISI 321/wt.% 19.1 9.85 1.65 0.297 0.086 0.68 0.035 0.05 0.16 0.172 Bal

All electrochemical measurements were obtained using an EG&G 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. Four potentials within the passive region were chosen for potentiostatic film growth and EIS measurements, 0, 0.2, 0.4 and 0.6 V. Films were gown at each potential for 1 h to ensure that the system was in steady-state. After each film growth period, EIS measurements were performed. The frequency was scanned between 0.01 Hz and 100 kHz and with an excitation potential of 10 mV (peak-to-peak). Mott–Schottky experiments were done by measuring the frequency response at 1 kHz during a 25 mV/s negative potential scan from 0.6 to 0.0 V.

3

3 Results and discussion

3.1

3.1 Polarization measurement

Fig. 1 shows the potentiodynamic curve for the AISI 321 electrode in 0.5 M H2SO4. From the polarization curve, the passive range was determined to be from −0.15 to 0.9 V.

Polarization curve of AISI 321 in 0.5 M H2SO4 in the anodic direction at 1 mV/s.
Figure 1
Polarization curve of AISI 321 in 0.5 M H2SO4 in the anodic direction at 1 mV/s.

During the formation of the oxide films on working electrode, the evolution of the current density measured during the application of different potentials (0.0, 0.2, 0.4, and 0.6 V) in the passive domain was recorded. It was observed that the current density diminishes with time until a constant value is reached and a steady-state is established. Fig. 2 shows the values of the steady-state passive current density (iss) versus the formation potential. The steady-state current density is approximately 4.2 μA cm−2.

Steady-state passive current density obtained during the potentiostatic growth of the passive films; at different film formation potentials for 1 h.
Figure 2
Steady-state passive current density obtained during the potentiostatic growth of the passive films; at different film formation potentials for 1 h.

3.2

3.2 EIS measurements

The impedance spectra were measured at selected potentials in the passive film formation region. Nyquist and Bode plots for passive films are presented in Fig. 3. Bode plots have been added for the representation of the impedance spectra because the magnitude of the impedance at low frequencies is several orders of magnitude higher than that at high frequencies, and thus high-frequency features are difficult to discern in a Nyquist plot. In the frequency range of measurement, all impedance spectra have the same features. As predicted by PDM, the complex plane plot in the low frequency region is a straight line and is insensitive to the formation potential. The constant phase nature of the impedance at low frequencies is a consequence of defect transport in the oxide film being mainly due to migration under the influence of the electric field (Nicic and Macdonald, 2008; Macdonald and Smedley, 1990; Sikora and Macdonald, 2002). Table 2 shows charge transfer resistance and double layer capacitance from the impedance diagrams of AISI 321 stainless steel in 0.5 M H2SO4 solution at selected formation potentials.

Impedance spectra for AISI 321 in 0.5 M H2SO4 as a function of film formation potential: (a) Nyquist plots and (b) Bode plots.
Figure 3
Impedance spectra for AISI 321 in 0.5 M H2SO4 as a function of film formation potential: (a) Nyquist plots and (b) Bode plots.
Table 2 Calculated charge transfer resistance and double layer capacitance from the impedance diagrams of AISI 321 stainless steel in 0.5 M H2SO4 solution (Fig. 3).
E/V Rct/kΩ (cm2) Cdl/μF (cm−2)
0.0 15.45 558.03
0.2 18.47 492.23
0.4 22.65 423.65
0.6 26.34 289.14

3.3

3.3 Mott–Schottky analysis

Mott–Schottky analysis has been employed to determine the semiconductor type and dopant density of the passive film. The equations for Mott–Schottky analysis are (Di Paola, 1989):

(1)
1 C SC 2 = 2 ε ε 0 eN D E - E FB - k B T q for n - type semiconductor
(2)
1 C SC 2 = - 2 ε ε 0 eN A E - E FB - k B T q for p - type semiconductor where e is the electron charge, ND and NA are the donor and acceptor densities (cm−3), ε is the dielectric constant of the passive film (ε = 12 Hakiki et al., 1998; Gaben et al., 2004; Goodlet et al., 2004), ε0 is the vacuum permittivity (8.854 × 10−14 F/cm), KB is the Boltzmann constant (1.38 × 10−23 J/K), T is the absolute temperature and EFB is the flat band potential. The interfacial capacitance, C, is obtained from Sikora and Macdonald (2002):
(3)
C = - 1 ω Z img where Zimg is the imaginary component of the impedance and ω = 2πf is the angular frequency. Assuming that the capacitance of the double layer can be neglected, the measured capacitance C is equal to the space charge capacitance, CSC. Neglecting the double layer capacitance requires that the space charge capacitance be at least one to two orders lower than the specific double layer capacitance and must be significantly higher than the parallel geometric capacitance for this assumption to be valid (Gaben et al., 2004; Raja and Jones, 2006).

Fig. 4 represents C−2 versus potential plots for a passive film formed on AISI 321 in 0.5 M H2SO4 at selected formation potentials. Fig. 4 displays positive slopes, indicative that n-type semiconductor behavior exists at all formation potentials. From the linear part of the slopes a donor density can be estimated. The dopant density calculated with this method indicates the density close to the alloy/passive film interface, where the concentrations of oxygen vacancies and metal interstitials are predicted to be the highest.

Mott– Schottky plots of C−2 as a function of potential for passive films on AISI 321 formed at the potentials of 0.0, 0.2, 0.4 and 0.6 V in 0.5 M H2SO4.
Figure 4
Mott– Schottky plots of C−2 as a function of potential for passive films on AISI 321 formed at the potentials of 0.0, 0.2, 0.4 and 0.6 V in 0.5 M H2SO4.

Fig. 5 displays the donor density as a function of the formation potential. Similar values for the donor density have been observed, and the tendency of the donor density to decrease with increasing potential has been reported by Sikora and Macdonald (Sikora and Macdonald, 1997; Sikora et al., 1996). Other studies have shown that the relationship between donor density and the formation potential can be developed theoretically on the basis of the PDM (Sikora et al., 1996; Ahn and Kwon, 2004; Liu and Macdonald, 2001).

Donor densities of the passive films formed on AISI 321 in 0.5 M H2SO4 as a function of film formation potential.
Figure 5
Donor densities of the passive films formed on AISI 321 in 0.5 M H2SO4 as a function of film formation potential.

According to the PDM, the flux of oxygen vacancy through the passive film is essential to the film growth process, which supports the existence of oxygen vacancy in the film regardless of its concentration. In this concept, the dominant point defects in the passive film are considered to be oxygen vacancies and/or cation interstitials acting as electron donors. However, as it is impossible to separate the contribution of oxygen vacancies and cation interstitials on the measured diffusivity value based on the PDM, the diffusivity is considered to be dependence on the combination effects of these two point defects (Szklarska-Smialowska and Kozlowski, 1983).

This theoretical relationship yields a good fit to the experimental results, and allows the diffusivity of defects in the passive film to be calculated. The relevant equation describing the dependency of the donor density on the formation potential is shown as Eq. (4), where ω1, ω2 and b are unknown constants that are to be determined from the experimental data (Sikora et al., 1996; Ahn and Kwon, 2004):

(4)
N D = ω 1 exp ( bE ) + ω 2 Based on the nonlinear fitting of the experimental data by the software, the exponential relationship between the donor density and the formation potential is derived as:
(5)
N D = 1.913 × 10 22 exp ( - 3.942 E ) + 6.271 × 10 22 ( cm - 3 ) The diffusion coefficient can be calculated from Eq. (6) as follows Sikora et al., 1996; Ahn and Kwon, 2004:
(6)
D O = J O 2 K ω 2 = J O RT 2 F ω 2 k
(7)
J O = - i ss 2 e where K = kF RT , k represents the electric field strength of the passive film, and iss is determined from the Fig. 2. The k was determined to be approximately 1.02 × 106 V/cm by Szklarska-Smialowska and Kozlowski (1983) for the passive film grown on iron . Therefore, it is assumed that the value of k for the passive film on AISI 321 in 0.5 M H2SO4 to be approximately 106 V/cm. Substitution of iss (4.2 × 10−6 A cm−2), e (−1.602 × 10−19 C), k (106 V/cm), ω2 (6.271 × 1022 cm−3), R (8.314 J/mol K), T (298 K) and F (96,500 C mol/e) into Eqs. (6) and (7) yields D0 = 2.6 × 10−17 cm2/s. Taking into account the error caused by the assumption of k in Eq. (6), the diffusion coefficient of defects in the passive film formed on AISI 321 in 0.5 M H2SO4 is estimated to be in the range of 10−17–10−16cm2/s, which is in the order of the results reported for diffusion coefficient of defects in the passive film on carbon steel in borate solution at room temperature (Cheng et al., 2002; Bojinov et al., 2001).

Fig. 6 shows a linear relationship between the steady-state film thickness (Lss) and the formation potential. This relationship between the steady-state film thickness and the formation potential has been reported by Macdonald et al. (Macdonald and Sun, 2006, Macdonald, 2008, Nicic and Macdonald, 2008). The film thickness was calculated from the capacitance measured at 1 kHz after each 1 h constant potential growth. It is assumed that, at this frequency, the electrochemical impedance is largely capacitive in nature, with the measured capacitance being almost independent of frequency. The parallel plate expression was used for calculating the steady-state film thickness from the measured capacitance (Sikora and Macdonald, 1997; Sikora et al., 1996):

(8)
L ss = ε ε 0 C The calculated thickness ranges from about 0.51 nm at 0.0 V to 0.94 nm at 0.6 V. These values of the thickness are considered to be eminently realistic (Macdonald and Sun, 2006; Macdonald, 2008, 2006; Nicic and Macdonald, 2008; Olsson and Landolt, 2003).
Film thickness as a function of the formation potential. Thickness was measured after each 1 h film growth.
Figure 6
Film thickness as a function of the formation potential. Thickness was measured after each 1 h film growth.

According to the PDM, the steady-state passive current density may be used to calculate the general corrosion rate using the formula (Nicic and Macdonald, 2008):

(9)
dL dt = M ‾ z ¯ F ρ i ss where M ‾ and z ¯ are the composition-averaged atomic weight and oxidation number, respectively and ρ is the density of the steel. Noting that
(10)
M ‾ = χ Fe M Fe + χ Cr M Cr + χ Ni M Ni + χ Mn M Mn and
(11)
z ¯ = χ Fe z Fe + χ Cr z Cr + χ Ni z Ni + χ Mn z Mn

where χi is the atomic fraction, Mi is the atomic weight, and zi is the oxidation number of element i in the steel, then the rate of penetration of general corrosion is readily calculated (Nicic and Macdonald, 2008). Thus, taking a generic AISI 321 as having a composition of 67.92 wt.% Fe, 19.1 wt.% Cr, 9.85 wt.% Ni, and 1.65 wt.% Mn, it is obtained that χFe, χCr, χNi, χMn are 0.6894, 0.1938, 0.0999, 0.0167, respectively. The composition averaged atomic weight of the steel, as calculated from Eq. (10), is 55.351 g. Likewise, noting that zFe, zCr, zNi, and zMn are 2, 3, 2, and 2, respectively, the composition-averaged oxidation number is found from Eq. (11) to be 2.1937. Taking the density of AISI 321 as 7.99 g/cm3, the corrosion rate calculated from Eq. (9) corresponding to a steady-state passive current density of 4.2 × 10−6 A/cm2 (Fig. 2) is 1.374 × 10−10 cm/s or 43.338 μm/year. This corresponds to approximately 4.3 mm corrosion penetration in one hundred years service.

4

4 Conclusions

Potentiodynamic polarization studies demonstrate that AISI 321 displays a wide passive range in 0.5 M H2SO4 at ambient temperature. Potentiostatic polarization tests revealed that the steady-state current density through the passive film formed on AISI 321 for 1 h was independent of formation potential, which is well consistent with the postulation of the PDM. Based on the Mott–Schottky analysis, it was shown that the calculated donor density decreases exponentially with increasing formation potential and the thickness of the passive film increases linearly with the formation potential. The experimental data were interpreted in terms of the PDM for the passivity of AISI 321 in 0.5 M H2SO4, assuming that the donors are defects including oxygen vacancies and cation interstitials. The calculated diffusivity of defect was in the range of 10−17 cm2/s. Also no evidence for p-type behavior was obtained, indicating that cation vacancies do not have any significant population density in the passive film.

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