The effect of surface contact conditions on grain boundary interdiffusion in a semi-infinite bicrystal

The Kirkendall effect is conditioned by active diffusion as well as by active sources and sinks for vacancies. In the case of grain boundaries under the condition of negligible bulk diffusion, the Kirkendall effect is highly localized and responsible for the formation of an extra material wedge in the grain boundary, which may lead to high stress concentrations. The Kirkendall effect in grain boundaries of a binary system is described by a set of partial differential equations for the mole fraction of one of the diffusing components and for the stress component normal to the grain boundary completed with the respective initial and boundary conditions. The contact conditions of the grain boundary with the surface layer acting as source of one of the diffusing components can be considered as equilibrium ones ensuring the continuity of generalized chemical potentials of both diffusing components. Thus, the boundary conditions are determined by the difference in chemistry (i.e. how the thermodynamic parameters depend on chemical composition) of the grain boundaries and of the surface layer. The simulations based on the present model indicate a drastic influence of the chemistry on the grain boundary interdiffusion and Kirkendall effect.