Theory of the Kirkendall effect during grain boundary interdiffusion

A grain boundary interdiffusion in a semi-infinite bicrystal under the conditions of negligible bulk diffusion is considered. We show that the inequality of the intrinsic grain boundary diffusion coefficients of the two components leads to plating out of additional material at the grain boundary in the form of a wedge of extra material, which generates an elastic stress field in the vicinity of the grain boundary. We solved a coupled diffusion/elasticity problem and determined the time-dependent stress field and concentration distribution in the vicinity of the grain boundary. We show that diffusion of embrittling impurities along the grain boundary generates tensile stresses at the boundary which are high enough to cause intergranular fracture.