A new approach was proposed for the description of diffusion-induced grain-boundary migration. The key difference between this approach and previous ones was that the present analysis included diffusion, not only along the grain boundary, but also along free surfaces that were in contact with the grain boundary. The well-posed mathematical problem was formulated by matching the diffusional fields at the triple junction. Account was taken of the elastic effects which arose due to the sharp concentration jump ahead of the moving grain boundary. By means of several simplifications, the closed equation for the steady-state velocity of diffusion-induced grain-boundary migration was derived as a function of the supersaturation and the system parameters. It was found that mass transport at the free surface played a very important role in the diffusion-induced grain boundary migration. The solution revealed an asymmetry between the cases of alloying and de-alloying. In the alloying case, a solution existed even without elastic effects while, in the case of de-alloying, elastic effects were necessary for diffusion-induced grain boundary migration. Diffusion-induced grain-boundary migration in systems consisting of isotopes was also considered, and it was shown that diffusion-induced grain boundary migration did not exist in such systems.

Theory of Diffusion-Induced Grain Boundary Migration - is Mass Transport along Free Surfaces Important? E.A.Brener, D.E.Temkin: Acta Materialia, 2002, 50[7], 1707-16