The Influence of the Exterior Surface on Grain Boundary Mobility Measurements

Abstract

Polycrystalline materials typically contain a very large number of grains whose surrounding grain boundaries evolve over time to reduce the overall energy of the microstructure. The evolution of the microstructure is influenced by 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 which grain boundaries move by mean curvature motion, V_n = Aκ, and the exterior surface evolves by surface diffusion, V_n = −BΔ_sκ. Here V_n and κ denote the normal velocity and the mean curvature of the respective evolving surfaces, and Δ_s 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.