New phase growth in the vicinity of a spherical particle interacting with a matrix with regard mechanical stresses induced by diffusion

Abstract

This paper presents a model of interaction between a solid particle and a metal melt within the framework of the theory of reactive diffusion in the coupled formulation. In the example considered it is assumed that, only one new phase is formed between the original particle and the melt. In quasistationary formulation the diffusion and mechanical equilibrium problem are solved analytically independently. The mechanical stresses accompanying the diffusion and growth of the new phase are calculated and contain the time dependent functions. Approximate analytical solutions of the corresponding diffusion problems with movable interfaces are found. The problem taking into account the explicit dependence of the diffusion coefficient on the stress work has been solved for the first time. Analytical solution makes it possible to clearly distinguish a power dependence of the diffusion coefficient on concentration, which is a consequence of the influence of stresses on diffusion. The consequence is the effect of the mechanical properties of the growing phase on its growth rate. The problem can be generalized to the case of formation of N new phases.