Polycrystalline materials typically contain a very large number of grains whose surrounding grain boundaries evolve over time to reducethe overall energy of the microstructure. The evolution of the microstructure is influencedby the motion of the exterior surface since the grain boundaries couple to the exterior surface of the specimen; these effects can be appreciable especially in thin specimens. We model these effects using the classical framework of Mullins, in whichgrain boundaries move by mean curvature motion, Vn =A κ, and the exterior surface evolves by surface diffusion, Vn = -BΔs κ. Here Vn and κ denote the normal velocity and the mean curvature of the respective evolving surfaces, and Δs is the surface Laplacian. A classical way to determine A, the ``reduced mobility," is to make measurements based on the half-loop bicrystalline geometry. In this geometry one of the two grains, which embedded within the other, recedes at a roughly constant rate which can provide an estimate for A. In this note, we report on findings concerning the effects of the exterior surface on grain boundary motion and mobility measurements in the context of the half-loop bicrystalline geometry. We assume that the ratio of grain boundary energy to the exterior surface energy is small, and suitable assumptions are made of the specimen aspect ratio.
An algorithm for Mean Curvature Motion
