# An Electrochemical Impedance Study of AISI 321 Stainless Steel in 0.5 M H2SO4

Authors: A. Fattah-Alhosseini; M. Mosavi; A. Allahdadi
Journal: International Journal of Electrochemistry
 (2011)

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## Abstract

The electrochemical behavior of passive films formed on AISI 321 has been examined using electrochemical impedance spectroscopy. AISI 321 is characterized by high interfacial impedance, thereby illustrating its high corrosion resistance. Results showed that the interfacial impedance and the polarization resistance initially increase with applied potential, within the low potential. However, at a sufficiently high potential (E>0.6 V), the interfacial impedance and the polarization resistance decrease with increasing potential. The impedance data were adequately represented by an equivalent electrical circuit model based on point defect model, which described the behavior of the passive film on stainless steel more satisfactorily than the proposed models.


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## Body

## 1. Introduction

The excellent corrosion resistance of stainless steels is largely due to the protective oxide passive films formed on the surface. Many analytical studies have agreed that the passive film on stainless steels consists of Cr-enriched (Fe, Cr) oxide/hydroxide, which in many cases are no thicker than a few nanometers, act as a reactivity barrier between the stainless steel and the environment [1–3]. The electrochemical polarization method, including anodic passivation, enhances the preferential dissolution of iron into solution and the enrichment of chromium in the passive film, and hence this method is effective for increasing stability, compaction, and corrosion resistance of the passive films [4, 5]. The anodic current density of anodic films is lowered by several orders of magnitude than that of naturally grown oxide films. The chemical composition, the structure, and the thickness of electrochemically formed passive films on stainless steel change not only with environment but especially with passivation potential [6–9].Compared with many theories qualitatively describing the passive state, the point defect model (PDM) provides a microscopic description of the growth and breakdown of a passive film and an analytical expression for the flux and the concentration of vacancies within the passive film, and hence which afford an opportunity for quantitative analysis [10, 14–18].The PDM assumes that the transport of matter through the film takes place via ionic point defects. This model further postulates that the point defects present in a passive film are, in general, cation vacancies (VMχ-), oxygen vacancies (VO··), and cation interstitials (Miχ+), as designated by the Kroger-Vink notation. The defect structure of the passive film can be understood in terms of the set of defect generation and annihilation reactions occurring at the metal/passive film interface and at the passive film/solution interface, as depicted in Figure 1 [11–13].Figure 1
Interfacial defect generation-annihilation reactions that are postulated to occur in the growth of anodic barrier oxide films according to the PDM.m = metal atom, VMχ- = cation vacancy on the metal sublattice of the barrier layer, Miχ+ = interstitial cation, MM = metal cation on the metal sublattice of the barrier layer, VO·· = oxygen vacancy on the oxygen sublattice of the barrier layer, OO = oxygen anion on the oxygen sublattice of the barrier layer, MΓ+ = metal cation in solution [10–13].This transport is necessary for any growth of the film. The presence of point defects also provides a path for the cations formed from the substrate metal to pass through the film into the solution. Point defects are formed and annihilated in reactions proceeding at the metal/film and film/solution interfaces. The rates of these reactions and of the defect transport determine to a great extent the electrical and electrochemical properties of the film [11–13].Electrochemical impedance spectroscopy (EIS) has been widely used for studying the electrochemical mechanisms occurring on the electrodes. EIS data can be used to establish an equivalent electrical circuit model for the electrochemical processes of electrodes. The various elements in this equivalent circuit are related to the metal/film and film/solution interfaces and the phenomena occurring inside the passive film [19, 20]. EIS measurements make it possible to obtain some information on the mechanism, establishing a theoretical transfer function, and developing the passive film growth model [21, 22].AISI 321 stainless steel is a most popular alloy, used extensively because of its good corrosion resistance; its passive films have been the subject of many investigations. In spite of the relatively large amount of research on the electrical properties of passive films anodically formed; however, few papers have been published on a systematic study of the impedance behavior. The great complexity of the metal/passive film/electrolyte system of stainless steels makes the clarification of the passive film difficult. In this work, EIS measurements were made in a large range of frequencies in order to get more information on the passive film electrochemically grown on AISI 321 stainless steel/solution properties.


## 2. Experimental Procedures

Specimens were fabricated from 1 cm diameter rods of AISI 321 stainless steel; the nominal composition is given in Table1. The samples were placed in stainless steel sacks and were annealed in inert environment (Ar gas) to eliminate the cold work effect due to cutting process. The annealing was performed at 1050°C for 90 min followed by water quenching. The pretreatment applied on specimens consisted of mechanical polishing using emery papers up to 1200 grade, degreasing and rinsing in distilled water. 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. Prior to each experiment, the working electrode was catholically polarized at −1.2 V for 5 min.Table 1
Nominal chemical composition of AISI 321 stainless steel.
ElementsCrNiMnSiCTiNbSMoCuFeAISI 321/wt%19.19.851.650.2970.0860.680.0350.050.160.172BalImpedance investigations were performed using an EG&G Model 273A potentiostat/galvanostat controlled by a personal computer at ambient temperature (23–25°C). Passive films on AISI 321 stainless steel were formed potentiostatically at DC potentials selected based on the passive region of anodic curve for 1 h and then EIS measurements were done. Each electrochemical measurement was repeated at least three times. An excitation voltage of 10 mV (peak-to-peak) and an applied frequency ranging from 100 kHz to 10 mHz have been used. For EIS data modeling and curve-fitting method,Z-View2 impedance software “Equivalent Circuit” was used. This program is based on the method of nonlinear least squares, which allows nonideal electrochemical behavior to be modeled.


## 3. Results and Discussion

### 3.1. Polarization Behavior

The potentidynamic polarization curve of AISI 321 stainless steel in 0.5 M H2SO4 solution is shown in Figure 2. According to Figure 2, two stages of the passive process can be distinguished in the curve. The low potential passive region ranges from about −0.15 to 0.6 V (region I). In region II, the comparatively slow increase of the current in the potential range 0.6–0.9 V could be connected to the formation of high valency Cr [23] in the film prior to transpassive dissolution. The steeper increase in the range 0.9 to 1.1 V is most probably related to the onset of the transpassive dissolution.Figure 2
Potentiodynamic polarization curve for AISI 321 stainless steel in 0.5 M H2SO4.


### 3.2. EIS Measurements

The electrochemical behavior of the anodic passive films on AISI 321 stainless steel in 0.5 M H2SO4 have been evaluated by means of EIS measurements. For this purpose, passive films on stainless steel electrode were formed potentiostatically at DC potentials selected based on the passive region of anodic curve for 1 h and then EIS measurements were done.Typical Nyquist and Bode plots for anodic oxide films are presented in Figure3. 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.Impedance spectra for AISI 321 stainless steel in 0.5 M H2SO4 solution as a function of film formation potential: (a) Nyquist plots and (b) Bode plots.
(a)(b)Figure4 indicates that the impedance magnitude at low frequencies initially increase with film formation potential, within the low passive potential. However, at a sufficiently high passive potential (E>0.6 V) the impedance magnitude decrease with increasing potential. The high impedance values in this low-frequency region can be associated with the presence of the barrier layer of the passive film.Figure 4
Effect of film formation potential on impedance magnitude of AISI 321 stainless steel in 0.5 M H2SO4 at low frequencies.


### 3.3. The Physical and Mathematical Passivation Models

For many years, a great number of models have been put forward through the research and analysis of the EIS of different systems. Among these models, the six main ones are as follows.Model A
The interface resistanceR and the capacitance C are simply paralleled to represent the passive electrode system [24–30]. When measuring the impedance of the actual system, the obtained capacitance sometimes may deviate from the ‘‘pure capacitance.’’ Therefore, a constant phase element (Q) is introduced for the fitting to replace capacitor C [31–33]. In Figure 5(a), Rs is the uncompensated solution resistance; R1 and Q1 are the interface resistance and the interface constant phase element, respectively. The mathematical expression of the impedance of the electrode system in this model is
(1)Z=Rs+11/R1+Y0(jω)n.
The impedance of the constant phase element Q is presented by
(2)ZQ=[Y0(jω)n]-1,
where n is associated with the roughness of the electrode surface and Y0 is a frequency-independent real constant representing the total capacitance of the Q. When n=1, it means that Q is equivalent to a pure capacitor and Y0=C [34–38].Physical models for metal/passive film/solution system: (a) Model A, (b) Model B, (c) Model C, (d) Model D, (e) Model E, and (f) Model F.
(a)(b)(c)(d)(e)(f)Model B
It is believed that the impedance of the passive films of metals comes from the migration of metal and oxygen vacancies within the film. According to this statement, the process of migration of metal and oxygen vacancies within the passive film has the form of a Warburg impedance. When the oxygen vacancies are dominant in the passive film, the impedance of the film isZf=σ0ω-1/2(1-j) [39, 40]. Figure 5(b) shows the equivalent circuit of this model [41–44]; here R1 is the charge transfer resistance. The mathematic expression of the impedance of this electrode system is
(3)Z=Rs+1Y0(jω)n+1/(R1+ZD).Model C
A constant phase element (Q2) is used to represent the transfer of the charged particles within the passive film, shown in Figure 5(c). It is believed that the passive film has capacitive characters. Jamnik et al. [45] postulate that, in the Nyquist plot, the diffusion of the charged particles in a solid must be combined with a reaction impedance that may result in a slope greater than 45°, but not 90°. The mathematic expression of the impedance of the electrode system is
(4)Z=Rs+11/R1+Y01(jω)n1+1Y02(jω)n2.Model D
TwoR//Q parallel circuits are used, to represent the electrochemical activities of the passive film and the film/solution interface, respectively (Figure 5(d)) [46]. In this figure, R1 and Q1 are the charge transfer resistance and the double layer capacitance, respectively. R2 and Q2 are the film resistance and the film capacitance, or the resistance and capacitance of the space charge layer, respectively. The mathematical expression of the impedance of the electrode system in this model is
(5)Z=Rs+11/R1+Y01(jω)n1+11/R2+Y02(jω)n2.Model E
Figure5(e) shows a graphical representation of the electrochemical system and the equivalent circuit [47]. C1 and R1 represent the capacitive and resistive contributions of the passive film/metal interface, CP and RP represent the bulk passive film, Q and R2 represent the solution/passive film interface, and Rs is the uncompensated solution resistance. The mathematical expression of the impedance of the electrode system in this model is
(6)Z=Rs+11/R1+Y01(jω)n1+11/RP+CP(jω)n+11/R2+C2(jω)n.Model F
Figure5(f) shows a graphical representation of the electrochemical system and the equivalent circuit [48]. The equivalent circuit is a combination of three branches, including the uncompensated solution resistance, Rs. Rct and Qdl are the charge-transfer resistance of the interfacial reaction and the double-layer capacitance. RP and QP are related to the electronic charging in the passive oxide film. ZD represents the impedance diffusion, which can be related to ionic defect transport through the passive film. R1 and Q1 indicate the contribution of surface states. According to Cahan and Chen [47], in some passivation conditions an excess proton creates a corresponding Fe2+ and a deficient proton causes an equivalent Fe3+ in the film, and these ions play the role of surface states. The mathematical expression of the impedance of the electrode system in this model is
(7)Z=Rs+11/Rct+Y0dl(jω)ndl+11/(RP+ZD)+Y0P(jω)nP+11/R1+Y01(jω)n1.
The impedance of diffusion is given by
(8)ZD=RDtanh(jω(δ2/D))n′(jω(δ2/D))n′,
where RD is the diffusion resistance, δ is the effective diffusion thickness, D is the effective diffusion coefficient, and n′ is the generalized finite Warburg exponent.According to the PDM, at the metal/passive film interface, the annihilation of metal vacancies (reaction (9)), formation of oxygen vacancies (reaction (10)) and injection of metal interstitials (reaction (11)) take place [16]:(9)M+VM3-→r1MM+3e-(10)M→r2MM+32VO2++3e-(11)M→r3Mi2++2e-
In the passive film, high-field assisted migration of defects is assumed to proceed. At the passive film/solution interface, metal vacancies are generated via abstraction of metal positions in the oxide lattice (reaction (12)), the interstitials are dissolved (reaction (13)) and the oxygen vacancies react with adsorbed water (reaction (14)). Reaction (14), together with reaction (10) and transport of oxygen vacancies outwards (i.e., motion of oxygen ions inwards as indicated above), result in film growth [16]:(12)MM→r4VM3-+Maq3+(13)Mi2+→r5Maqx++(χ-2)e-(14)32H2O+32VO2+→r632OO+3H+
In order to preserve the steady-state thickness of the film at a given potential, the growth reaction has to be balanced by chemical dissolution of the film(15)M2O3+6H+→r72Maq3++3H2O
The overall impedance of the metal/passive film/solution (Z) is defined as the sum of the interfacial impedances at the metal/passive film (Zm/f) and passive film/solution (Zf/s) interfaces and the transport impedance in the passive film (Zf) [49]:(16)Z=Zm/f+Zf+Zf/s.
The faradic impedances of the metal/passive film and passive film/solution interfaces have in general the form of charge transfer resistances which are functions of the rate constants and Tafel coefficients of the interfacial reactions [12, 49]:(17)Zm/f-1=Rm/f-1+jωCm/f,Zf/s-1=Rf/s-1+jωCf/s.
Assuming the transport of both ionic and electronic defects contribute to the passive film impedance, it can be shown that [50, 51](18)Zf-1=(Ze-1+Zion-1).
Where Ze is impedance due to electron transport through the passive film and Zion is impedance due to ion transport through the passive film. Therefore it is observed clearly that the impedance data were adequately represented by an equivalent electrical circuit model (Model F) based on PDM, which described the behavior of the passive film on stainless steel more satisfactorily than the proposed models.


### 3.4. The Fitting Results

Figure6 shows the fitting results of typical Nyquist plots for passive films on AISI 321 electrodes were formed potentiostatically at 0.4 V using the five models. It is found that the fitting errors of Models A, B, C, and D are relatively high. In Model A, the EIS is corresponding to a capacitive loop. When fitting the data, the fitting error increases remarkably. In Model B, diffusion process occurs at low frequency and has a form of Warburg impedance. When fitting with this model, large errors occur in the low-frequency region. Therefore, Models A and B are not suitable for this system.Figure 6
The fitting results of typical Nyquist plots for passive films on AISI 321 electrodes were formed potentiostatically at 0.4 V using the five models.In Model C,R1 is the charge transfer resistance. Q1 and Q2, respectively, reflect the double-layer capacitance and the substance transfer processes in the passive film. From the physical point of view, it is not reasonable to represent the substance transfer within the passive film simply by a capacitor. Model D consists of two (R-Q) parallel circuits, which represent the contribution of the interfacial reaction and a passivating film. When fitting with this model, large errors occur in the low-frequency region and no significant variations of the different electrical-circuit element were found. Therefore, Models C and D are not suitable for this system either. When fitting with Model E, small errors occur in the low-frequency region.The above six models were used to fit the impedance data obtained; it was found that the fitting results of model F are suitable to the actual passivation process. When fitting our theoretical electrical-equivalent circuit, a value of Chi-quadrate (χ2) of approximately 10−4 was found and the fitting errors were quite small. Figure 7 shows, in all cases, that the correlation between experimental data and simulated data is very good.Nyquist plots for AISI 321 stainless steel in 0.5 M H2SO4 and as a function of potential showing a comparison between the experimental and simulated data.
(a)(b)(c)(d)(e)The Bode plots and admittance plots (not shown) also displayed an acceptable agreement between experimental and simulated data, thereby validating the selected equivalent circuit model. Table2 summarizes the values of the circuit parameters obtained from the best fit with the experimental impedance diagrams.Table 2
Passive element values for the equivalent circuit of Model F obtained from the fitting procedure of types.
ER1Y01n1RPY0Pn2RDδ2/DRctY03n3VΩ cm2μF cm−2kΩ cm2μF cm−2Ω cm2kΩ cm2μF cm−20.00.42954.440.780.76221.250.9548.804.4415.379538.030.890.20.50243.530.681.31172.420.9117.994.4118.68543.890.910.40.52228.710.711.51132.950.8614.495.0122.97443.530.990.60.59181.420.954.93125.460.909.274.1326.85299.030.990.80.39196.660.701.78105.140.8510.524.9629.72362.830.99Same to charge-transfer resistance (Rct), which does vary significantly with film formation potential, passive film resistance (RP) varies with film formation potential. RP increases considerably with film formation potential. This increase of RP is accompanied by a decrease of Y0P at every electrode potential, reflecting the growth and the thickening of the passive film or the decrease in the amount of charge carriers in the film [48]. One can notice the continuous decrease of RP when the film formation potential increases and it highest value at films formed at 0.6 V. These results may be related to the presence and the competition of two kinds of oxides, chromium and iron. At low potentials (potentials lower than the transpassive potential of chromium), passive films are more enriched with chromium, making the films more protective [12]. At high potential in the passive range, chromium decreases continuously and iron increases progressively and hence the protective effect reduces [12, 48].The values of the exponentn2 obtained by fitting our EIS data were between 0.85 and 0.95, which points to a considerable passive film surface homogeneity; therefore, the constant phase element can be assumed to correspond to capacitive behavior while the values of n1 and n3 obtained can be associated with a distribution of the relaxation times as a result of heterogeneities present at the interfaces and static disorders such as porosity [48, 52].The impedance of diffusion is independent of film formation potential. Defect transport is primarily due to migration under the influence of the electric field, and because the field strength is postulated to be independent of the applied potential in the point defect model, the impedance should be insensitive to the film formation potential [48, 53].The variation ofR1 with the film formation potential is characteristic for uniform distribution of surface-states. The values of R1 initially increased with film formation potential in the region I. At a sufficiently high potential (E>0.6 V), which is close to the onset of the transpassive state, R1 is observed to decrease with increasing formation potential [48].The polarization resistance was taken to be the sum ofR1, RP, RD, and Rct. Figure 8 shows the variation of polarization resistance with the film formation potential. The polarization resistance (RPol) initially increased with film formation potential in the region I. This is due to the establishment of the passive oxide layer. At a sufficiently high potential (E>0.6 V), which is close to the onset of the transpassive state (Region II), the polarization resistance is observed to decrease with increasing potential. It has been reported that this is due to the oxidative ejection of Cr (VI) from the passive film [12].Figure 8
Effect of potential on polarization resistance of AISI 321 stainless steel in 0.5 M H2SO4.


## 3.1. Polarization Behavior

The potentidynamic polarization curve of AISI 321 stainless steel in 0.5 M H2SO4 solution is shown in Figure 2. According to Figure 2, two stages of the passive process can be distinguished in the curve. The low potential passive region ranges from about −0.15 to 0.6 V (region I). In region II, the comparatively slow increase of the current in the potential range 0.6–0.9 V could be connected to the formation of high valency Cr [23] in the film prior to transpassive dissolution. The steeper increase in the range 0.9 to 1.1 V is most probably related to the onset of the transpassive dissolution.Figure 2
Potentiodynamic polarization curve for AISI 321 stainless steel in 0.5 M H2SO4.


## 3.2. EIS Measurements

The electrochemical behavior of the anodic passive films on AISI 321 stainless steel in 0.5 M H2SO4 have been evaluated by means of EIS measurements. For this purpose, passive films on stainless steel electrode were formed potentiostatically at DC potentials selected based on the passive region of anodic curve for 1 h and then EIS measurements were done.Typical Nyquist and Bode plots for anodic oxide films are presented in Figure3. 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.Impedance spectra for AISI 321 stainless steel in 0.5 M H2SO4 solution as a function of film formation potential: (a) Nyquist plots and (b) Bode plots.
(a)(b)Figure4 indicates that the impedance magnitude at low frequencies initially increase with film formation potential, within the low passive potential. However, at a sufficiently high passive potential (E>0.6 V) the impedance magnitude decrease with increasing potential. The high impedance values in this low-frequency region can be associated with the presence of the barrier layer of the passive film.Figure 4
Effect of film formation potential on impedance magnitude of AISI 321 stainless steel in 0.5 M H2SO4 at low frequencies.


## 3.3. The Physical and Mathematical Passivation Models

For many years, a great number of models have been put forward through the research and analysis of the EIS of different systems. Among these models, the six main ones are as follows.Model A
The interface resistanceR and the capacitance C are simply paralleled to represent the passive electrode system [24–30]. When measuring the impedance of the actual system, the obtained capacitance sometimes may deviate from the ‘‘pure capacitance.’’ Therefore, a constant phase element (Q) is introduced for the fitting to replace capacitor C [31–33]. In Figure 5(a), Rs is the uncompensated solution resistance; R1 and Q1 are the interface resistance and the interface constant phase element, respectively. The mathematical expression of the impedance of the electrode system in this model is
(1)Z=Rs+11/R1+Y0(jω)n.
The impedance of the constant phase element Q is presented by
(2)ZQ=[Y0(jω)n]-1,
where n is associated with the roughness of the electrode surface and Y0 is a frequency-independent real constant representing the total capacitance of the Q. When n=1, it means that Q is equivalent to a pure capacitor and Y0=C [34–38].Physical models for metal/passive film/solution system: (a) Model A, (b) Model B, (c) Model C, (d) Model D, (e) Model E, and (f) Model F.
(a)(b)(c)(d)(e)(f)Model B
It is believed that the impedance of the passive films of metals comes from the migration of metal and oxygen vacancies within the film. According to this statement, the process of migration of metal and oxygen vacancies within the passive film has the form of a Warburg impedance. When the oxygen vacancies are dominant in the passive film, the impedance of the film isZf=σ0ω-1/2(1-j) [39, 40]. Figure 5(b) shows the equivalent circuit of this model [41–44]; here R1 is the charge transfer resistance. The mathematic expression of the impedance of this electrode system is
(3)Z=Rs+1Y0(jω)n+1/(R1+ZD).Model C
A constant phase element (Q2) is used to represent the transfer of the charged particles within the passive film, shown in Figure 5(c). It is believed that the passive film has capacitive characters. Jamnik et al. [45] postulate that, in the Nyquist plot, the diffusion of the charged particles in a solid must be combined with a reaction impedance that may result in a slope greater than 45°, but not 90°. The mathematic expression of the impedance of the electrode system is
(4)Z=Rs+11/R1+Y01(jω)n1+1Y02(jω)n2.Model D
TwoR//Q parallel circuits are used, to represent the electrochemical activities of the passive film and the film/solution interface, respectively (Figure 5(d)) [46]. In this figure, R1 and Q1 are the charge transfer resistance and the double layer capacitance, respectively. R2 and Q2 are the film resistance and the film capacitance, or the resistance and capacitance of the space charge layer, respectively. The mathematical expression of the impedance of the electrode system in this model is
(5)Z=Rs+11/R1+Y01(jω)n1+11/R2+Y02(jω)n2.Model E
Figure5(e) shows a graphical representation of the electrochemical system and the equivalent circuit [47]. C1 and R1 represent the capacitive and resistive contributions of the passive film/metal interface, CP and RP represent the bulk passive film, Q and R2 represent the solution/passive film interface, and Rs is the uncompensated solution resistance. The mathematical expression of the impedance of the electrode system in this model is
(6)Z=Rs+11/R1+Y01(jω)n1+11/RP+CP(jω)n+11/R2+C2(jω)n.Model F
Figure5(f) shows a graphical representation of the electrochemical system and the equivalent circuit [48]. The equivalent circuit is a combination of three branches, including the uncompensated solution resistance, Rs. Rct and Qdl are the charge-transfer resistance of the interfacial reaction and the double-layer capacitance. RP and QP are related to the electronic charging in the passive oxide film. ZD represents the impedance diffusion, which can be related to ionic defect transport through the passive film. R1 and Q1 indicate the contribution of surface states. According to Cahan and Chen [47], in some passivation conditions an excess proton creates a corresponding Fe2+ and a deficient proton causes an equivalent Fe3+ in the film, and these ions play the role of surface states. The mathematical expression of the impedance of the electrode system in this model is
(7)Z=Rs+11/Rct+Y0dl(jω)ndl+11/(RP+ZD)+Y0P(jω)nP+11/R1+Y01(jω)n1.
The impedance of diffusion is given by
(8)ZD=RDtanh(jω(δ2/D))n′(jω(δ2/D))n′,
where RD is the diffusion resistance, δ is the effective diffusion thickness, D is the effective diffusion coefficient, and n′ is the generalized finite Warburg exponent.According to the PDM, at the metal/passive film interface, the annihilation of metal vacancies (reaction (9)), formation of oxygen vacancies (reaction (10)) and injection of metal interstitials (reaction (11)) take place [16]:(9)M+VM3-→r1MM+3e-(10)M→r2MM+32VO2++3e-(11)M→r3Mi2++2e-
In the passive film, high-field assisted migration of defects is assumed to proceed. At the passive film/solution interface, metal vacancies are generated via abstraction of metal positions in the oxide lattice (reaction (12)), the interstitials are dissolved (reaction (13)) and the oxygen vacancies react with adsorbed water (reaction (14)). Reaction (14), together with reaction (10) and transport of oxygen vacancies outwards (i.e., motion of oxygen ions inwards as indicated above), result in film growth [16]:(12)MM→r4VM3-+Maq3+(13)Mi2+→r5Maqx++(χ-2)e-(14)32H2O+32VO2+→r632OO+3H+
In order to preserve the steady-state thickness of the film at a given potential, the growth reaction has to be balanced by chemical dissolution of the film(15)M2O3+6H+→r72Maq3++3H2O
The overall impedance of the metal/passive film/solution (Z) is defined as the sum of the interfacial impedances at the metal/passive film (Zm/f) and passive film/solution (Zf/s) interfaces and the transport impedance in the passive film (Zf) [49]:(16)Z=Zm/f+Zf+Zf/s.
The faradic impedances of the metal/passive film and passive film/solution interfaces have in general the form of charge transfer resistances which are functions of the rate constants and Tafel coefficients of the interfacial reactions [12, 49]:(17)Zm/f-1=Rm/f-1+jωCm/f,Zf/s-1=Rf/s-1+jωCf/s.
Assuming the transport of both ionic and electronic defects contribute to the passive film impedance, it can be shown that [50, 51](18)Zf-1=(Ze-1+Zion-1).
Where Ze is impedance due to electron transport through the passive film and Zion is impedance due to ion transport through the passive film. Therefore it is observed clearly that the impedance data were adequately represented by an equivalent electrical circuit model (Model F) based on PDM, which described the behavior of the passive film on stainless steel more satisfactorily than the proposed models.


## 3.4. The Fitting Results

Figure6 shows the fitting results of typical Nyquist plots for passive films on AISI 321 electrodes were formed potentiostatically at 0.4 V using the five models. It is found that the fitting errors of Models A, B, C, and D are relatively high. In Model A, the EIS is corresponding to a capacitive loop. When fitting the data, the fitting error increases remarkably. In Model B, diffusion process occurs at low frequency and has a form of Warburg impedance. When fitting with this model, large errors occur in the low-frequency region. Therefore, Models A and B are not suitable for this system.Figure 6
The fitting results of typical Nyquist plots for passive films on AISI 321 electrodes were formed potentiostatically at 0.4 V using the five models.In Model C,R1 is the charge transfer resistance. Q1 and Q2, respectively, reflect the double-layer capacitance and the substance transfer processes in the passive film. From the physical point of view, it is not reasonable to represent the substance transfer within the passive film simply by a capacitor. Model D consists of two (R-Q) parallel circuits, which represent the contribution of the interfacial reaction and a passivating film. When fitting with this model, large errors occur in the low-frequency region and no significant variations of the different electrical-circuit element were found. Therefore, Models C and D are not suitable for this system either. When fitting with Model E, small errors occur in the low-frequency region.The above six models were used to fit the impedance data obtained; it was found that the fitting results of model F are suitable to the actual passivation process. When fitting our theoretical electrical-equivalent circuit, a value of Chi-quadrate (χ2) of approximately 10−4 was found and the fitting errors were quite small. Figure 7 shows, in all cases, that the correlation between experimental data and simulated data is very good.Nyquist plots for AISI 321 stainless steel in 0.5 M H2SO4 and as a function of potential showing a comparison between the experimental and simulated data.
(a)(b)(c)(d)(e)The Bode plots and admittance plots (not shown) also displayed an acceptable agreement between experimental and simulated data, thereby validating the selected equivalent circuit model. Table2 summarizes the values of the circuit parameters obtained from the best fit with the experimental impedance diagrams.Table 2
Passive element values for the equivalent circuit of Model F obtained from the fitting procedure of types.
ER1Y01n1RPY0Pn2RDδ2/DRctY03n3VΩ cm2μF cm−2kΩ cm2μF cm−2Ω cm2kΩ cm2μF cm−20.00.42954.440.780.76221.250.9548.804.4415.379538.030.890.20.50243.530.681.31172.420.9117.994.4118.68543.890.910.40.52228.710.711.51132.950.8614.495.0122.97443.530.990.60.59181.420.954.93125.460.909.274.1326.85299.030.990.80.39196.660.701.78105.140.8510.524.9629.72362.830.99Same to charge-transfer resistance (Rct), which does vary significantly with film formation potential, passive film resistance (RP) varies with film formation potential. RP increases considerably with film formation potential. This increase of RP is accompanied by a decrease of Y0P at every electrode potential, reflecting the growth and the thickening of the passive film or the decrease in the amount of charge carriers in the film [48]. One can notice the continuous decrease of RP when the film formation potential increases and it highest value at films formed at 0.6 V. These results may be related to the presence and the competition of two kinds of oxides, chromium and iron. At low potentials (potentials lower than the transpassive potential of chromium), passive films are more enriched with chromium, making the films more protective [12]. At high potential in the passive range, chromium decreases continuously and iron increases progressively and hence the protective effect reduces [12, 48].The values of the exponentn2 obtained by fitting our EIS data were between 0.85 and 0.95, which points to a considerable passive film surface homogeneity; therefore, the constant phase element can be assumed to correspond to capacitive behavior while the values of n1 and n3 obtained can be associated with a distribution of the relaxation times as a result of heterogeneities present at the interfaces and static disorders such as porosity [48, 52].The impedance of diffusion is independent of film formation potential. Defect transport is primarily due to migration under the influence of the electric field, and because the field strength is postulated to be independent of the applied potential in the point defect model, the impedance should be insensitive to the film formation potential [48, 53].The variation ofR1 with the film formation potential is characteristic for uniform distribution of surface-states. The values of R1 initially increased with film formation potential in the region I. At a sufficiently high potential (E>0.6 V), which is close to the onset of the transpassive state, R1 is observed to decrease with increasing formation potential [48].The polarization resistance was taken to be the sum ofR1, RP, RD, and Rct. Figure 8 shows the variation of polarization resistance with the film formation potential. The polarization resistance (RPol) initially increased with film formation potential in the region I. This is due to the establishment of the passive oxide layer. At a sufficiently high potential (E>0.6 V), which is close to the onset of the transpassive state (Region II), the polarization resistance is observed to decrease with increasing potential. It has been reported that this is due to the oxidative ejection of Cr (VI) from the passive film [12].Figure 8
Effect of potential on polarization resistance of AISI 321 stainless steel in 0.5 M H2SO4.


## 4. Conclusion

The impedance data obtained for AISI 321 in sulphuric acid solution were adequately represented by an equivalent electrical circuit model based on PDM, comprising twoR//Q elements in series with a ZD-R//Q and an uncompensated solution resistance. The interfacial impedance and polarization resistance initially increased with applied potential. At a sufficiently high potential (E>0.6 V), which is close to the initiation of the transpassive state, the interfacial impedance and polarization resistance were observed to decrease with increasing potential. The polarization resistance of AISI 321 stainless steel is of the order of 102 kΩ cm2, commensurate with its high corrosion resistance.



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*Source: 505929-2011-06-08.xml*