Perturbation approach to metal surface oxidation considering volume variation

In this article, kinetics equation of the metal surface oxidation is presented using the perturbation approach. A moving boundary is converted into a fixed one by Landau transformation. The perturbation results show that (1) the solution of the zeroth-order stands for the quasi-steady state and that of the first-order is instantaneous and (2) the reaction rate, diffusion coefficient, and the thickness of the initial oxide layer have important effects on the oxidation kinetics. If the chemical reaction is supposed to be instantaneous, our results are reduced to the classical parabolic law, no matter whether there exists the initial oxide layer or not. Moreover, the kinetic coefficient of the parabolic law is analytically presented. The proposed perturbation scheme can be easily extended to the higher order, and the higher order solution will provide a method to correct the error offered by the classical model.