Growth Kinetics of Steady-state Passive Film on Type 304 Stainless Steel Based on Point Defect Model

doi:10.11902/1005.4537.2022.269

Journal of Chinese Society for Corrosion and protection

2023, Vol. 43

Issue (4): 911-921 DOI: 10.11902/1005.4537.2022.269

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Growth Kinetics of Steady-state Passive Film on Type 304 Stainless Steel Based on Point Defect Model

MAO Feixiong¹(

), ZHOU Yuting², YAO Wenqing², SHEN Xiang³, XIAO Long³, LI Minghui³

^1.Key Laboratory of Marine Materials and Related Technologies, Zhejiang Key Laboratory of Marine Materials and Protective Technologies, Ningbo Institute of Materials Technology and Engineering, Chinese Academy of Sciences, Ningbo 315201, China
^2.School of Metallurgy, Northeastern University, Shenyang 110819, China
^3.Ningbo Hangzhou Bay Bridge Development Co. LTD, Ningbo 315201, China

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Abstract

The passivity of type 304 stainless steel in aqueous solution at different pH values has been assessed, and the acquired data suggest that the passive ﬁlm formed on type 304 SS is n-type semiconducting, and the donor density within the passive film is inversely proportional to the applied voltage except those in pH=13.4 solution. The current density in steady-state is voltage-independent in the passive range, while the thickness of the barrier layer has a linear relationship with the applied voltage, which are satisfied with the statements of the point defect model (PDM). EIS data are analyzed with the PDM by optimizing the model on the data using genetic algorithm approach. In addition, the impedance data over the entire passive range can be described by the fitted parameters, which can be utilized to predict the corrosion evolution of the sample as a function of time. The results of the optimization indicate that interstitial cations are the dominant defects in the barrier layer and that the diffusivity of the defect is about 10^-19 cm²·s^-1.

Key words: 304 stainless steel passivity point defect model EIS

Received: 31 August 2022 32134.14.1005.4537.2022.269

ZTFLH:

TG174

Fund: Ningbo Key Scientific and Technological Project(2021Z079);International Partnership Program of Chinese Academy of Sciences(174433KYSB20200006)

Corresponding Authors: MAO Feixiong, E-mail: maofeixiong@nimte.ac.cn

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Cite this article:

MAO Feixiong, ZHOU Yuting, YAO Wenqing, SHEN Xiang, XIAO Long, LI Minghui. Growth Kinetics of Steady-state Passive Film on Type 304 Stainless Steel Based on Point Defect Model. Journal of Chinese Society for Corrosion and protection, 2023, 43(4): 911-921.

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https://www.jcscp.org/EN/10.11902/1005.4537.2022.269 OR https://www.jcscp.org/EN/Y2023/V43/I4/911

Fig.1 Interfacial defect generation/annihilation reactions happened hypothetically in the growth of anodic barrier oxide films according to PDM. For the symbols, m is metal atom, $V M χ'$ is cation vacancy on the metal sublattice of the barrier layer, $M i χ +$ is interstitial cation, $M M$ is metal cation on the metal sublattice of barrier layer, $V O ∙ ∙$ is oxygen vacancy on the oxygen sublattice of barrier layer. $O O$ is oxygen anion on the oxygen sublattice of barrier layer, $M δ +$ is metal cation in solution

Reaction	$a i / V - 1$	$b i / c m - 1$	c_i	Units of $k i 0$
(1) $m + V M χ' → k 1 M M + ν m + χ e'$	$α 1 (1 - α) χ γ$	$- α 1 χ K$	-α₁βχγ	$1 S$
(2) $m → k 2 M i χ + + ν m + χ e'$	$α 2 (1 - α) χ γ$	$- α 2 χ K$	-α₂βχγ	$m o l c m 2 ⋅ s$
(3) $m → k 3 M M + χ 2 V O ∙ ∙ + χ e'$	$α 3 (1 - α) χ γ$	$- α 3 χ K$	-α₃βχγ	$m o l c m 2 ⋅ s$
(4) $M M → k 4 M δ + + (δ - χ) e'$	$α 4 α δ γ$	-	α₄βδγ	$m o l c m 2 ⋅ s$
(5) $M i χ + → k 5 M δ + + (δ - χ) e'$	$α 5 α δ γ$	-	α₅βδγ	$c m s$
(6) $V O ∙ ∙ + H 2 O → k 6 O O + 2 H +$	$2 α 6 α γ$	-	α₆βδγ	$c m s$
(7) $M O χ / 2 + χ H + → k 7 M δ + + χ 2 H 2 O + (δ - χ) e'$	$α 7 α (δ - χ) γ$	-	α₇(δ-χ)βγ	$m o l c m 2 ⋅ s$

Table 1 Various coefficients in the rate constants of the interfacial reactions, i.e.

k i = k i 0 e a i V e b i L e c i p H

Fig.2 Potentiodynamic polarization curves for Type 304 stain steel in the test solutions with different pH values

Fig.3 Steady state (potentiostatic) current densities of 304 stainless steel in the test solutions with different pH values as a function of oxide formation potential. The inset shows the current vs. time curves

Fig.4 Mott-Schottky plots (a, c, e, g) and donor densities (b, d, f, h) for the barrier layer formed on 304 stainless steel passivated for 6 h at different formation potentials in pH 1.4 sulfuric acid solution (a, b), pH 5.4 acetate buffer solution (c, d), pH 9.4 borate buffer solution (e, f) and pH 13.4 H₃BO₃+NaOH solution (g, h)

Fig.5 EIS plots (a) and K-K transforms (b) for 304 stainless steel at a potential of 0.5 V_SCE in pH 1.4 solution

Fig.6 Equivalent circuit used to ﬁt the experimental data of EIS

Fig.7 Nyquist (a, c, e, g) and Bode (b, d, f, h) plots for 304 stainless steel in pH 1.4 sulfuric acid solution (a, b), pH 5.4 acetate buffer solution (c, d), pH 9.4 H₃BO₃+NaOH solution (e, f) and pH 13.4 H₃BO₃+NaOH solution (g, h) at different applied potentials

Parameter	0.3 / V	0.4 / V	0.5 / V	Stage optinization
Polarizability α	0.45	0.45	0.44	Second stage optimization
Transfer coeff. α₂	0.23	0.23	0.23	Average of first stage optimization
Transfer coeff. α₃	0.66	0.66	0.66	Average of first stage optimization
Transfer coeff. α₇	0.49	0.49	0.49	Average of first stage optimization
Rate constant $k 200 /$ mol·cm^-2·s^-1	4.67×10^-13	4.67×10^-13	4.67×10^-13	Average of first stage optimization
Rate constant $k 300$ / mol·cm^-2·s^-1	3.78×10^-17	3.78×10^-17	3.78×10^-17	Average of first stage optimization
Rate constant $k 700$ / mol·cm^-2·s^-1	6.16×10^-15	6.16×10^-15	6.16×10^-15	Average of first stage optimization
CPE-Y / S·s ^α ·cm^-2	4.18×10^-5	3.92×10^-5	3.86×10^-5	Second stage optimization
CPE-α	0.94	0.95	0.95	Second stage optimization
Warburg coeff. σ / Ω·cm²·s^-0.5	3.03×10⁵	2.14×10⁵	1.56×10⁵	Second stage optimization
Electronic resistance R_{e, h} / Ω·cm²	7.82×10⁶	1.72×10⁷	9.93×10¹²	Second stage optimization
Double layer capacitance C_dl / F·cm^-2	1.51×10^-4	9.56×10^-5	6.91×10^-5	Second stage optimization
Charge transfer resistance R_ct / Ω·cm²	1.75×10⁵	2.88×10⁵	4.22×10^-5	Second stage optimization
Strength of electric field ε / V·cm^-1	2.03×10⁶	2.03×10⁶	2.03×10⁶	Average of first stage optimization
Kinetic order of H⁺n	0.5	0.5	0.5	Average of first stage optimization
Current density I_ss / nA·cm^-2	16.15	20.24	24.56	Second stage optimization
Thickness of barrier layer L_ss / nm	1.24	1.47	1.74	Second stage optimization
Diffusivity of principal defect D / cm²·s^-1	1.34×10^-18	8.64×10^-19	6.43×10^-19	Second stage optimization

Table 2 Calculated values of various parameters from optimization of the PDM based on the experimental impedance data for 304 stainless steel in pH 1.4 solution at different applied potentials

Parameter	0.3 / V	0.4 / V	0.5 / V	Stage optinization
Polarizability α	0.34	0.25	0.25	Second stage optimization
Transfer coeff. α₂	0.23	0.23	0.23	Average of first stage optimization
Transfer coeff. α₃	0.66	0.66	0.66	Average of first stage optimization
Transfer coeff. α₇	0.49	0.49	0.49	Average of first stage optimization
Rate constant $k 200$ / mol·cm^-2·s^-1	4.67×10^-13	4.67×10^-13	4.67×10^-13	Average of first stage optimization
Rate constant $k 300$ / mol·cm^-2·s^-1	3.78×10^-17	3.78×10^-17	3.78×10^-17	Average of first stage optimization
Rate constant $k 700$ / mol·cm^-2·s^-1	6.16×10^-15	6.16×10^-15	6.16×10^-15	Average of first stage optimization
CPE-Y / S·s ^α ·cm^-2	7.34×10^-5	3.53×10^-5	4.14×10^-5	Second stage optimization
CPE-α	1	1	0.94	Second stage optimization
Warburg coeff. σ / Ω·cm²·s^-0.5	1.07×10⁴	6.91×10⁴	7.38×10⁴	Second stage optimization
Electronic resistance R_{e, h} / Ω·cm²	3.78×10¹²	7.07×10¹²	7.67×10¹²	Second stage optimization
Double layer capacitance C_dl / F·cm^-2	3.14×10^-5	6.99×10^-5	1.13×10^-4	Second stage optimization
Charge transfer resistance R_ct / Ω·cm²	1.08×10⁶	3.37×10⁵	4.19×10⁵	Second stage optimization
Strength of electric field ε / V·cm^-1	2.03×10⁶	2.03×10⁶	2.03×10⁶	Average of first stage optimization
Kinetic order of H⁺n	0.5	0.5	0.5	Average of first stage optimization
Current density I_ss / nA·cm^-2	15.22	13.4	15.66	Second stage optimization
Thickness of barrier layer L_ss / nm	2.36	2.99	3.33	Second stage optimization
Diffusivity of principal defect D / cm²·s^-1	1.85×10^-10	5.45×10^-19	4.66×10^-19	Second stage optimization

Table 3 Calculated values of various parameters from optimization of the PDM based on the experimental impedance data for 304 stainless steel in pH=5.4 solution at different applied potentials

Parameter	0 / V	-0.1 / V	-0.2 / V	Stage optinization
Polarizability α	0.45	0.282624	0.289249	Second stage optimization
Transfer coeff. α₂	0.23	0.23	0.23	Average of first stage optimization
Transfer coeff. α₃	0.66	0.66	0.66	Average of first stage optimization
Transfer coeff. α₇	0.49	0.49	0.49	Average of first stage optimization
Rate constant $k 200$ / mol·cm^-2·s^-1	4.67×10^-13	4.67×10^-13	4.67×10^-13	Average of first stage optimization
Rate constant $k 300$ / mol·cm^-2·s^-1	3.78×10^-17	3.78×10^-17	3.78×10^-17	Average of first stage optimization
Rate constant $k 700$ / mol·cm^-2·s^-1	6.16×10^-15	6.16×10^-15	6.16×10^-15	Average of first stage optimization
CPE-Y (S·s ^α ·cm^-2	2.39×10^-5	2.70×10^-5	3.97×10^-5	Second stage optimization
CPE-α	0.91	0.91	0.89	Second stage optimization
Warburg coeff. σ / Ω·cm²·s^-0.5	8.48×10⁵	3.82×10⁵	6.28×10⁵	Second stage optimization
Electronic resistance R_{e, h} / Ω·cm²	1.00×10¹³	9.81×10¹²	9.99×10¹²	Second stage optimization
Double layer capacitance C_dl / F·cm^-2	2.23×10^-4	48.99×10^-4	2.32×10^-4	Second stage optimization
Charge transfer resistance R_ct / Ω·cm²	1.18×10⁵	2.03×10⁴	6.02×10⁴	Second stage optimization
Strength of electric field ε / V·cm^-1	2.03×10⁶	2.03×10⁶	2.03×10⁶	Average of first stage optimization
Kinetic order of H⁺n	0.5	0.5	0.5	Average of first stage optimization
Current density I_ss / nA·cm^-2	13.93	9.91	8.62	Second stage optimization
Thickness of barrier layer L_ss / nm	2.08	1.99	1.66	Second stage optimization
Diffusivity of principal defect D / cm²·s^-1	2.32×10^-18	1.08×10^-18	1.34×10^-18	Second stage optimization

Table 4 Calculated values of various parameters from optimization of the PDM based on the experimental impedance data for 304 stainless steel in pH 9.4 solution at different applied potentials

Parameter	-0.2 / V	-0.3 / V	-0.4 / V	Stage optinization
Polarizability α	0.394221	0.449973	0.45	Second stage optimization
Transfer coeff. α₂	0.23	0.23	0.23	Average of first stage optimization
Transfer coeff. α₃	0.66	0.66	0.66	Average of first stage optimization
Transfer coeff. α₇	0.49	0.49	0.49	Average of first stage optimization
Rate constant $k 200$ / mol·cm^-2·s^-1	4.67×10^-13	4.67×10^-13	4.67×10^-13	Average of first stage optimization
Rate constant $k 300$ / mol·cm^-2·s^-1	3.78×10^-17	3.78×10^-17	3.78×10^-17	Average of first stage optimization
Rate constant $k 700$ / mol·cm^-2·s^-1	6.16×10^-15	6.16×10^-15	6.16×10^-15	Average of first stage optimization
CPE-Y / S·s ^α ·cm^-2	4.08×10^-5	3.65×10^-5	3.97×10^-5	Second stage optimization
CPE-α	0.88	0.92	0.92	Second stage optimization
Warburg coeff. σ / Ω·cm²·s^-0.5	3.99×10⁵	2.52×10⁵	2.26×10⁵	Second stage optimization
Electronic resistance R_{e, h} / Ω·cm²	8.28×10¹²	8.28×10¹²	7.42×10¹²	Second stage optimization
Double layer capacitance C_dl / F·cm^-2	1.35×10^-4	1.54×10^-4	2.04×10^-4	Second stage optimization
Charge transfer resistance R_ct / Ω·cm²	2.25×10⁵	1.83×10⁵	1.24×10⁵	Second stage optimization
Strength of electric field ε / V·cm^-1	2.03×10⁶	2.03×10⁶	2.03×10⁶	Average of first stage optimization
Kinetic order of H⁺n	0.5	0.5	0.5	Average of first stage optimization
Current density I_ss / nA·cm^-2	1.15	0.93	0.74	Second stage optimization
Thickness of barrier layer L_ss / nm	2.39	2.15	1.93	Second stage optimization
Diffusivity of principal defect D / cm²·s^-1	5.21×10^-18	1.54×10^-18	7.30×10^-19	Second stage optimization

Table 5 Calculated values of various parameters from optimization of the PDM based on the experimental impedance data for 304 stainless steel in pH 13.4 solution at different applied potentials

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