Phase-field model of oxidation: Kinetics

The kinetics of oxidation is examined using a phase-field model of electrochemistry when the oxide film is smaller than the Debye length. As a test of the model, the phase-field approach recovers the results of classical Wagner diffusion-controlled oxide growth when the interfacial mobility of the oxide-metal interface is large and the films are much thicker than the Debye length. However, for small interfacial mobilities, where the growth is reaction controlled, we find that the film increases in thickness linearly in time, and that the phase-field model naturally leads to an electrostatic overpotential at the interface that affects the prefactor of the linear growth law. Since the interface velocity decreases with the distance from the oxide vapor, for a fixed interfacial mobility, the film will transition from reaction- to diffusion-controlled growth at a characteristic thickness. For thin films, we find that in the limit of high interfacial mobility we recover a Wagner-type parabolic growth law in the limit of a composition-independent mobility. A composition-dependent mobility leads to a nonparabolic kinetics at small thickness, but for the materials parameters chosen, the deviation from parabolic kinetics is small. Unlike classical oxidation models, we show that the phase-field model can be used to examine the dynamics of nonplanar oxide interfaces that are routinely observed in experiment. As an illustration, we examine the evolution of nonplanar interfaces when the oxide is growing only by anion diffusion and find that it is morphologically stable.