Diffuse-interface description of grain boundary motion

A diffuse-interface kinetic field model for describing grain boundary motion is proposed. It is based on the time-dependent Ginzburg-Landau equations, in which grain orientations are described by non-conserved order parameters. A simple example, a two-dimensional circular grain boundary with isotropic grain boundary energy, is considered. It is shown that, in the sharp-interface limit, the boundary migration velocity does not explicitly depend on the magnitude of grain boundary energy, and is linearly proportional to its mean curvature. Our numerical simulations demonstrated that, even for a boundary with a finite thickness, its migration velocity is also proportional to the mean curvature, which is, surprisingly, insensitive to the accuracy of the numerical method, although the values for the boundary velocity match the sharp-interface solution only if there are enough grid points to resolve the boundary region in the simulation. The applicability of the diffuse-interface model to simulating microstructural evolution and grain growth kinetics is discussed.