A diffusional analysis for the oxidation on a plane metal–oxide interface

Based on the diffusion of oxygen, the oxidation on a plane metal–oxide interface is analyzed using a perturbation scheme. Unlike previous models, the reaction rate and the oxygen dissolution into metal are taken into account. One-dimensional Landau transformation is applied to transform a moving domain by volumetric expansion during oxidation into a fixed domain. We investigate how the oxide thickness depends on the reaction rate, the ratio of diffusion coefficients, the molar density ratio, etc. By comparison of the results with the experimental observations, we compute the diffusion coefficients of oxygen in the metal and oxide, as well as the reaction rate coefficient for silicon and titanium oxidation.