A diffuse-interface kinetic field model for the description of grain-boundary motion was proposed which was based upon the time-dependent Ginzburg-Landau equations, in which grain orientations were described by non-conserved order parameters. As an example, a 2-dimensional circular grain boundary with an isotropic grain-boundary energy was considered. It was shown that, in the sharp-interface limit, the boundary migration velocity did not depend explicitly upon the magnitude of the grain boundary energy, and was linearly proportional to its mean curvature. Numerical simulations demonstrated that, even for a boundary with a finite thickness, its migration velocity was proportional to the mean curvature. It was noted that this conclusion was surprisingly insensitive to the accuracy of the numerical method, although the values for the boundary velocity matched the sharp-interface solution only when there were enough grid points to resolve the boundary region in the simulation.

D.Fan, L.Q.Chen: Philosophical Magazine Letters, 1997, 75[4], 187-96