Oxidation and Scale Adhesion of a Type 430 Stainless Steel in Ar–CO₂ Gas Mixtures at 800 °C

Abstract

Biogas is an alternative source of fuel potentially used to run solid oxide fuel cells (SOFCs). It mainly consists of CH₄ and CO₂ which can degrade the SOFC interconnect, which is typically made of stainless steel. To investigate the effect of each gas constituent, we focussed here on the effect of CO₂ on high-temperature oxidation behavior of and scale adhesion on the stainless steel interconnect, Type 430 stainless steel. The samples studied were oxidised in CO₂ at contents of 5–100% at 800 °C. The oxidation kinetics were found to be parabolic with the rate constant increasing when the CO₂ content increased. The scale adhesion was assessed using a tensile-test method. The scale formed in the atmosphere containing higher CO₂ content exhibited poorer scale adhesion, as indicated by a lower strain initiating the first spallation and a larger spallation percentage after the first spallation took place. The worsened scale adhesion relates to pores formed at the scale/steel interface. The adhesion energies were further quantified giving the values of about 40–100 J m^–2. Oxidation mechanisms were suggested based on the dependence of the parabolic rate constant on the oxygen partial pressure and the inward diffusion of carbon-bearing species.

Appendix

The objective of appendix is to derive Eq. (12). Consider the oxide ${\text{M}}_{{\nu_{1} }} {\text{O}}_{{\nu_{2} }}$ thermally grown on the metal M. Equation (16) is the Fick’s first law [47] expressing the molar flux of A standing for M or O as a function of its diffusivity D, molar concentration C, chemical potential μ and absolute temperature T, where x is the diffusing distance measured positively from the metal/oxide interface towards the oxide/gas interface and R is the universal gas constant.

$$j_{{\text{A}}} = - \frac{{D_{{\text{A}}} C_{{\text{A}}} }}{{{\text{R}}T}}\frac{{{\text{d}}\mu_{{\text{A}}} }}{{{\text{d}}x}}$$

(16)

If A is M, the relation between the chemical potential of M and that of O₂ is according to the Gibbs–Duhem relation: ${\text{d}}\mu_{{\text{M}}} = ( - \nu_{2} /2\nu_{1} ){\text{d}}\mu_{{{\text{O}}_{2} }}$ [61]. If A is O, the relation between the chemical potential of O and O₂ is as follows: ${\text{d}}\mu_{{\text{O}}} = (1/2){\text{d}}\mu_{{{\text{O}}_{2} }}$ [38]. With these relations and Eq. (16), Eq. (17) can be obtained with $\phi^{\prime\prime}$ being $\nu_{2} /2\nu_{1}$ for the diffusion of M by the cationic defects and being $- 1/2$ for the diffusion of O by the anionic defects.

$$j_{A} = \phi^{\prime\prime}\frac{{D_{{\text{A}}} C_{{\text{A}}} }}{{{\text{RT}}}}\frac{{{\text{d}}\mu_{{{\text{O}}_{2} }} }}{{{\text{d}}x}}$$

(17)

Consider a part of the flux of A that is from the diffusion of defect $\delta$ ($j_{\delta }$). By inserting the $f_{\delta } D_{{{\text{o}}\delta }} p_{{O_{2} }}^{{\gamma_{\delta } }}$ term from Eq. (11) and the relation ${\text{d}}\mu_{{{\text{O}}_{2} }} = {\text{R}}T{\text{d}}\ln p_{{{\text{O}}_{2} }}$ to Eq. (17), Eq.(18) can be obtained.

$$j_{\delta } = \phi^{\prime\prime}_{\delta } f_{\delta } D_{o\delta } C_{\delta } p_{{O_{2} }}^{{\gamma_{\delta } - 1}} \frac{{{\text{d}}p_{{O_{2} }} }}{{{\text{d}}x}}$$

(18)

By integrating this equation from the metal/oxide to the oxide/gas interface and assuming steady state diffusion, we can obtain Eq. (19) where y is the oxide thickness.

$$j_{\delta } = \frac{{\phi_{\delta }^{\prime \prime } f_{\delta } D_{{{\text{o}}\delta }} C_{\delta } }}{{\gamma_{\delta } }}\left( {\frac{{p_{{{\text{O}}_{2} }}^{{\gamma_{\delta } }} - p_{{{\text{O}}_{2} ,{\text{int}} .}}^{{\gamma_{\delta } }} }}{y}} \right)$$

(19)

The flux due to metal diffusion ($j_{{{\text{M}} }}$) can also be written by Eq. (20) where $C_{{M }}$ is the molar concentration of metal M in the oxide ${\text{M}}_{{\nu_{1} }} {\text{O}}_{{\nu_{2} }}$ [47, 62].

$$j_{{{\text{M}} }} = C_{{{\text{M}} }} \frac{{{\text{d}}y}}{{{\text{d}}t}}$$

(20)

Similarly, if α represents the ratio of the time oxygen spent to diffuse through the entire oxide thickness to the time the metal spent, the flux due to oxygen diffusion can be expressed as –C_O(dy/αdt) where C_O is the molar concentration of oxygen in the oxide. From this relation and Eqs. (19) and (20), Eq. (21) can be obtained where the coefficients $\phi^{\prime}_{\delta }$ are $\nu_{2} /{2}\nu_{1}$ and α/2 for the cationic and anionic defects, respectively.

$$y^{2} = \left( {\sum\limits_{i = 1}^{4} {\frac{{\phi^{\prime}_{{\delta_{i} }} f_{{\delta_{i} }} D_{{o\delta_{i} }} }}{{\gamma_{{\delta_{i} }} }}\left( {p_{{O_{2} }}^{{\gamma_{{\delta_{i} }} }} - p_{{O_{2} ,{\text{int}} .}}^{{\gamma_{{\delta_{i} }} }} } \right)} } \right) \cdot t$$

(21)

By converting the oxide thickness to the mass gain by the relation $(\Delta m/A) = \beta y$, we obtain Eq. (22) where the coefficients $\phi_{\delta }$ are $\nu_{2} \beta^{2} /{2}\nu_{1}$ and $\alpha\beta^{2}/{2}$ for the cationic and anionic defects, respectively. In fact, Eq. (22) is the integrated form of the parabolic rate law with a parabolic rate constant ($k_{{\text{p}}}$) shown in Eq. (23). Each term in the right hand side of Eq. (23) is a part of $k_{{\text{p}}}$ contributed from the diffusion of each defect—the n-type cationic, n-type anionic, p-type cationic and p-type s anionic defects. It is the one reported in Eq. (12).

$$\left( {\frac{\Delta m}{A}} \right)^{2} = \left( {\sum\limits_{i = 1}^{4} {\frac{{\phi_{{\delta_{i} }} f_{{\delta_{i} }} D_{{o\delta_{i} }} }}{{\gamma_{{\delta_{i} }} }}\left( {p_{{O_{2} }}^{{\gamma_{{\delta_{i} }} }} - p_{{O_{2} ,{\text{int}} .}}^{{\gamma_{{\delta_{i} }} }} } \right)} } \right) \cdot t = k_{{\text{p}}} \cdot t$$

(22)

$$k_{{\text{p}}} = \sum\limits_{i = 1}^{4} {\frac{{\phi_{{\delta_{i} }} f_{{\delta_{i} }} D_{{o\delta_{i} }} }}{{\gamma_{{\delta_{i} }} }}\left( {p_{{O_{2} }}^{{\gamma_{{\delta_{i} }} }} - p_{{O_{2} ,{\text{int}} .}}^{{\gamma_{{\delta_{i} }} }} } \right)}$$

(23)