Semiconducting behavior and kinetics of passive film growth on AISI 321 stainless steel in sulfuric acid

3.1 Corrosion behavior of SS and chronoamperometric curves at different potentials

The potentiodynamic polarization curves of SS in 1 m H₂SO₄ are shown in Figure 1. Different regions including passivation were obtained during the wide range of potential scan from −0.6 to 1.8 V. A further inspection illustrated the active-passive transition before the critical pitting potential (E_p=1000 mV vs. SCE). For the study of passive film properties, the current time potentiostatic transients for the oxide growth were recorded at different potentials selected from the passivation range (−0.29 to 1 V). The chronoamperometric measurements were conducted at each formation potential for 1 h to ensure the formation of the oxide film. Figure 2 illustrates the potentiostatic current transients for the passive film obtained at different constant anodic potentials. Transient current decreased rapidly with time before reaching the steady-state passive current density (i_ss) in which the steady state was established. The steady-state passive current density obtained at different anodic formation potentials is presented in Table 2.

Figure 1:

Potentiodynamic polarization curve for AISI 321 SS in 1 m H₂SO₄.

Figure 2:

Potentiostatic current time transients for SS in 1 m H₂SO₄ at different anodic potentials.

3.2 EIS

The impedance spectra of SS-grown passive film in 1 m H₂SO₄ at different formation potentials are depicted in Figures 3 and 4. The impedance plots showed the same features for all selected formation potentials. The corresponding electrochemical parameters are summarized in Table 2. The impedance data were obtained from the experimental results fit using the equivalent circuit illustrated in Figure 3 (inset).

Figure 3:

Nyquist plots for passive film growth of SS in 1 m H₂SO₄ at different formation potentials.

Figure 4:

Bode plots for passive film growth of SS in 1 m H₂SO₄ at different formation potentials.

The double-layer capacitance can be calculated using the following formula (Popova et al., 2015):

where Y₀ is the CPE constant and n is the CPE exponent related to the surface roughness and zero imperfections (Brug et al., 1984; Popova et al., 2015).

The data demonstrated the increase in charge transfer resistance with the anodic potential shift from 0 to 0.6 V. The decrease in double-layer capacitance with the anodic potential indicated the continuous growth of the passive film resulting in the decrease in the local dielectric constant of the interface (Li et al., 2014). To visualize the regions dominated by the resistive elements such as solution resistance, Bode plots of impedance data were collected for the SS passive film formed at different anodic potentials. The analysis of these data gave excellent insights on the different mechanisms or governing phenomena. This representation made it possible to identify the small impedances in the presence of large impedances. Bode plots depicted in Figure 4 exhibits about two time constants that appear to be overlapped (bell-shaped phase maximums). As a further analysis, the phase angle at middle frequencies increased with the formation potential. Generally, the time constant located at higher frequencies was related to the charge transfer process. Meanwhile, the one in the low-frequency range might be linked to the diffusion-controlled process (Li et al., 2014). As described earlier by Macdonald et al., the constant phase of impedance at lower frequencies was a result of the defect transport in the passive film due to the migration under the influence of the electric field (Sikora & Macdonald, 2002).

3.3 Effects of aging and formation potential on the semiconducting behavior of SS

The semiconductor behavior of the passive film grown on SS was studied at high-frequency domain based on the Mott-Schottky theory. The main focus was put on the effect of the formation potential and the aging on the semiconductor properties of the passive film. Mott-Schottky plots were obtained by plotting the space charge capacitances of n- and p-type semiconductor versus the electrode potential E as given by the following Mott-Schottky relationships (Fattah-alhosseini & Imantalab, 2013; Fattah-alhosseini & Vafaeian, 2016):

where e is the electron charge, N_D and N_A are the donor and acceptor densities (cm⁻³), ε is the assumed dielectric constant of the passive film (ε=12), ε₀ is the vacuum permittivity (8.854×10¹⁴ F/cm), K_B is the Boltzmann constant (1.38×10⁻²³ J/K), T is the absolute temperature, and E_FB is the flat band potential. The interfacial capacitance of the passive film (C_I) is considered to be the combination of two series capacitances: the space charge capacitance (C_SC) at the barrier layer-environment interface and the double-layer capacitance (C_dl; Ahn & Kwon, 2006):

According to the Mott-Schottky theory, the double-layer capacitance could be neglected when the space charge capacitance is at least one to two orders lower than the specific double-layer capacitance (Fattah-alhosseini, 2016). Therefore, the interfacial capacitance is assumed to be equal to the space charge capacitance. This assumption is only valid with a selected frequency on the order of kHz (Fattah-alhosseini & Imantalab, 2013). The semiconductor properties of the passive film could be linked to the donor and acceptor densities determined from the slopes of the linear plots of capacitance as function of potential. These data could highlight the charge distribution in the passive layers grown at different conditions of formation. Figure 5 illustrates the semiconductor behavior of the passive film grown on SS in H₂SO₄ at different immersion times. These plots have almost the similar semiconducting behavior with two linear regions characteristic of different types of passive oxide layers. According to the Mott-Schottky theory, the donor density could be determined from the linear segment with the positive slope, whereas the acceptor density is obtained from the linear plot characterized by the negative slope (Fattah-alhosseini & Vafaeian, 2016). At the potential domain between 0.3 and 0.7 V, the formed passive film performs n-type semiconductor for all studied immersion times, whereas the linear plot obtained between 0.8 and 1 V is indicative of p-type semiconductor. Figure 6 shows the semiconductor behavior of the passive film at different selected formation potentials. These plots clearly display two linear regions corresponding to the n- and p-type semiconducting behaviors. Generally, the cation vacancies are the defects performing the p-type semiconductor as acceptors. However, the n-type semiconducting behavior is almost performed by oxygen vacancies and cation interstitials (Macdonald, 2012). Moreover, numerous studies have correlated the semiconducting properties of the passive film with the composition of mixed oxide films Fe₂O₃-Cr₂O₃-N_iO and (Fe,Cr)₂O₃ as well as the predominant defect (Sugimota et al., 1993; Schmuki, 1998). It has been reported that the barrier layer on SS is commonly treated as a defective Cr₂O₃ layer resulting in n-type doping (Fattah-alhosseini et al., 2011a). The observed dual semiconducting behavior of the SS passive film can probably be explained by the formation n-type oxide films Fe₂O₃ and Fe(OH)₃ in the potential range of 0.3−0.7 V, whereas p-type oxide films Fe₃O₄ and NiO are formed in the range between 0.8 and 1 V (Jinlong & Hongyun, 2013; BenSalah et al., 2014).

Figure 5:

Mott-Schottky plots of passive film grown on SS in H₂SO₄ at different immersion times.

Figure 6:

Mott-Schottky plots of passive film grown on SS in H₂SO₄ at different formation potentials.

Table 3 reveals that both donor and acceptor densities decrease as immersion time increases. Table 3 shows the decrease in donor and acceptor densities of the passive film with the formation potential. The obtained N_D values are in the order of 3×10²¹ cm⁻³, which is in accordance with the range of donor densities determined elsewhere (Jinlong & Hongyun, 2013). The density of donor charge carriers appears to decrease exponentially with the increase in formation potential (Table 3). These results are in good agreement with the theory of the PDM described earlier by Macdonald et al. (Sikora et al., 1996). The relationship between donor density and formation potential can be studied theoretically based on the PDM, assuming that the diffusing donor defects are the oxygen vacancies (Sikora et al., 1996). The theoretical expression of N_D versus E yields a good fit to the experimental results [Equation (5)].

It is well recognized that the passive film grown on SS may be described as a highly doped film exhibiting various semiconductor properties. The PDM theory is used to calculate the diffusion coefficient and the steady-state passive film thickness over the range of the anodic potential of passive film formation.

This model microscopically describes passive film growth as well as the breakdown mechanism based on the diffusion of the charge carriers (i.e. oxygen and metal vacancies imparting n- and p-type behaviors, respectively) within the passive film (Sikora et al., 1996). According to the PDM, the flux of oxygen vacancy and/or cation interstitials (Cr³⁺, Fe²⁺, and Ni²⁺) through the passive film is important for its growth (Fattah-alhosseini & Vafaeian, 2016). Also, the passive film is a bilayer structure made of a defective barrier layer and the outer layer is formed by the hydrolysis of cations transmitted within the barrier layer (Mao et al., 2015).

Importantly, Macdonald et al. have reported that the growth of the barrier layer into the metal is essentially related to the oxygen vacancies generated at the interface metal-barrier layer and by their annihilation at the film-solution interface (Liu & Macdonald, 2001). This latter is typically caused by injection of oxide into the barrier layer from solution. Thus, this theory has focused on the distribution and the transport mechanism of oxygen vacancies as a key parameter in describing the growth the passive films onto the metal surface. Therefore, the kinetics of the barrier layer growth could be described in terms of vacancy diffusivity (D). The kinetics of passive film growth has been described elsewhere in terms of five electrochemical reactions occurring in the barrier layer interfaces (Sikora et al., 1996).

The PDM predicts the existence of a steady state when the rates of passive film growth and breakdown are equal in which the thickness of the barrier layer is predicted to vary linearly with the formation potential (Sikora et al., 1996). The steady-state passive film thickness is calculated from capacitance measurements at frequencies above 1 kHz using the capacitance expression (Equation 4), assuming that the impedance is largely capacitive in nature (Fattah-alhosseini, 2016):

Figure 7 displays the linear relationship between the steady-state passive film thickness of the obtained experimental results and the formation potential. Table 4 shows that L_ss values increase with increasing formation voltage. The passive film thickness varies from 0.350 nm at 0 mV to 0.534 nm at 600 mV. These results are highly realistic and in good agreement with the EIS data. The donor and acceptor densities for passive film formed on SS at different immersion times are listed in Table 5.

Figure 7:

Linear relationship between the steady-state passive film thickness and the formation potential.

The dependency of the donor density on the formation potential is described as given in Equation (5), where a₁, b, and a₂ are determined from the exponential fit of the experimental data (Sikora et al., 1996; Fattah-alhosseini, 2016):

From the exponential fit of the experimental data, the exponential relationship of N_D versus E is derived as

The exponential fit of the obtained data is presented in Figure 8, and the corresponding parameters are determined as a₁=−4.93×10¹⁸ cm⁻³ and a₂=3.45×10²¹ cm⁻³.

Figure 8:

Donor density versus formation potential for the growth of passive film grown on SS in H₂SO₄.

The diffusion coefficient (D) is determined from the following equation:

The flux of double-charged oxygen vacancies J can be calculated as

where k is the electric field strength of the passive film, e=−1.602×10⁻¹⁹ C, R=8.314 J/mol K, F=96500C mol/e, and the i_ss value is given in Table 6. According to Fattah-alhosseini, k is assumed be approximately 10⁶ V/cm for the passive film on AISI 321 in 0.5 m H₂SO₄. The electric field strength k could be determined from the linear relationship between steady-state thickness L_ss and formation potential as described elsewhere. The substitution of all calculated parameters summarized in Table 6 in Equations (7) and (8) yields D=1.78×10⁻¹⁵ cm²/s. The calculated diffusion coefficient of oxygen vacancies through the barrier layer is in the order of that reported for the defect diffusion in the passive film of carbon steel (Bojinov et al., 2001) and that of SS in 0.5 m H₂SO₄ (Fattah-alhosseini, 2016).

3.4 Kinetic study of passive film growth and the early stages of pitting process

The current time transients are obtained by polarizing the SS electrode at different anodic potentials E_a selected from the polarization curve. The potentiodynamic polarization (Figure 1) shows the existence of a critical potential E_p shown to be 1 V in which the nucleation of the first pits starts. To describe the kinetic behavior of passive film growth and pitting process in the vicinity of the pitting potential, chronoamperometric curves were recorded for 5 min at each selected anodic potential ranging from 1 to 1.9 V. To account for the early stages of passive film growth, the current time transients of passive film growth and pitting were given within the first 20 s of i/t transient measurement. Figure 9 reveals that, for potentials E_a<1300 mV, the overall transient current decreases rapidly to reach a steady current density value. The decrease could be attributed to the growth of the passive film. For the polarization at constant anodic potential E_a>1200 mV, the current transient decreases to a minimum value I_m corresponding to the induction time t_i before rising steadily with elapse of time. This continuous rise is due to the growth of the pits already initiated. The experimental results of passive film growth are fitted to the Macdonald model [Equation (10)] (Chen et al., 2009; Albrimi et al., 2011).

Figure 9:

Linear scale of chronoamperometric plots for SS in H₂SO₄ obtained at different anodic potentials.

This model is based on the existence and migration of defects in the film-solution interface under the effect of a local electric field. This migration depends on the applied potential and pH of the solutions and is only applicable for thin layers (Chao et al., 1981):

where i represents the current density of SS in 1 m H₂SO₄. A and n are constants depending on the constant anodic potential and the electrolyte concentration, respectively. n constant yields the rate of passive film growth and is given by the first slope of the descending transient current as depicted in Figure 10. The derived parameters listed in Table 7 demonstrate that passive film growth is slowed down with the increase in anodic potential. Also, the minimum attained steady-state transient current increases with potential shift in the positive direction. The continuous increase in transient current after reaching the induction time could be described by Engell Stolica equation [Equation (10)] (Chen et al., 2009; Albrimi et al., 2011):

Figure 10:

Kinetic parameter determination from logarithmic scale of current transients.

where B and b are constants depending on the anodic potential of polarization and the electrolyte concentration.

Figure 10 illustrates the graphical determination of the kinetic parameters for passive film growth and pitting stages. The slopes b₁ and b₂ of the straight lines located after the induction time correspond to the pit initiation and pit propagation, respectively. The reciprocal incubation time (t_i⁻¹) corresponds to the rate of pit initiation. As displayed in Figure 11, the overall current density is given by three contributions, e.g. passive film growth, pit initiation, and growth of metastable pits. Figure 11 illustrates the chronoamperometric plots in logarithmic scale for SS in H₂SO₄ recorded at different anodic potentials and the derived kinetic parameters are summarized in Table 7. It is worth noting that the different regions corresponding to the early stages of passive growth and pit propagation are clearly distinguished in logarithmic scale. It is clearly seen from Table 7 that the rate of pit initiation increases when the formation potential shifts in the positive direction. This indicates that higher anodic potential stimulates the initiation of pitting corrosion of SS in H₂SO₄. The induction time is shortened with the polarization at more positive anodic potentials.

Figure 11:

Logarithmic scale of current transients for polarized SS in H₂SO₄ at different potentials.

3.5 Morphological analysis

The surface morphology of SS polarized at different anodic potentials has been scanned using scanning electron microscopy (SEM) as depicted in Figure 12. For 1900 mV, the SS surface seems to be highly pitted. For lower potentials ranging from 1200 to 1700 mV, the pitting corrosion is initiated at multiple sites on the metal surface, but only few stable pits are able to propagate. For 1800 and 1900 mV, the lateral growth of some broad pits produced by coalescence of the neighboring pits is clearly observed. However, it is clearly seen that, at 1500 mV, the surface appears to have some covered pits with the corrosion products indicating the first stage of transition from metastable pits to the stable phase. The stable growth of the pits is necessary stimulated by the formation of the corrosion product on the pit. The propagation of pits is kinetically promoted with the formation of corrosion products that prevent the oxygen diffusion inside the pit and hinder the subsequent repassivation. Also, for higher potentials, the pits are grown in depth by increasing the applied voltage and have attained the incubation period that makes them visible. Furthermore, the pitting frequency yielding the number of pits per surface area has been increased with the increase in the applied voltage. It could be concluded that the stability of the created pits is likely to be induced by the higher applied voltage. Generally, the growth of stable pits is diffusion controlled, with the diffusion barrier provided by the pit depth (Burstein et al., 1993). Also, Figure 12 shows that the corrosion products in the vicinity of the pits are likely to be removed at more anodic potentials. The openness of the pits is highly promoted with the increase in the applied potential. These statements are in good agreement with the results of Tian et al. (2015).

Figure 12:

Morphological analysis for polarized SS at different anodic potentials.