We propose a two dimensional frame-invariant phase field model of grain
impingement and coarsening. One dimensional analytical solutions for a stable
grain boundary in a bicrystal are obtained, and equilibrium energies are
computed. We are able to calculate the rotation rate for a free grain between
two grains of fixed orientation. For a particular choice of functional
dependencies in the model the grain boundary energy takes the same analytic
form as the microscopic (dislocation) model of Read and Shockley.Comment: 4 pages, 2 figure