A Model of Gas Diffusion in a Metal Plate with Phase Transformation

Abstract

A model of gas diffusion in a metal plate has been proposed, in which a phase transformation “metal–gassed metal” takes place, when the gas concentration exceeds a certain critical value, and the properties of the system change qualitatively. The phase transformation is modeled by changing the coefficient of gas diffusion. In particular, a system of two phases with different diffusion coefficients and a moving interface between them is considered. The gas concentrations in both phases at the interface are assumed to be the known constants. An analytical solution is obtained in the approximation that the diffusion in the metal phase (the initial state of a metal layer) is much quicker than that in the gassed-metal one, with the both being much quicker than the motion of the phase interface. In the framework of this model, the spatial distribution of the gas concentration in the gassed-metal phase is calculated, and the analytic formula describing the motion of a phase interface is derived.