A set of coupled diffusion equations was numerically solved to demonstrate that grain boundary diffusion was significantly enhanced when diffusing atomic species had dissimilar atomic hop frequencies in the bulk. The model was based on a rigorous treatment of two-component substitutional diffusion where vacancies were treated as an additional species. By examining the concentration fields and the eigenvalues of the diffusivity matrix, the origin of the enhanced grain boundary diffusion was explained in terms of the Kirkendall effect.

Theory of Grain Boundary Diffusion Induced by the Kirkendall Effect. H.C.Yu, A.Van der Ven, K.Thornton: Applied Physics Letters, 2008, 93[9], 091908