Monte Carlo studies of grain growth on curved surfaces

Monte Carlo simulations have been carried out to study the effect of surface curvature on normal grain growth. As predicted by a recent theory of kinetics of coarsening on curved surfaces, we find that the stability properties of stationary grains are sensitive to the Gaussian curvature of the surface. In particular, it is found that on a spherical surface, the normalized grain-size distribution is not stationary in time. In regions of positive curvature, grains that are much larger than the mean are unstable and grow faster than the mean and engulf the entire surface. In regions of negative curvature, all stationary grains are stable and the final configuration consists of many grains which have established a stable size. These observations are in agreement with results of experimental studies of the growth of grains in polycrystalline films on curved surfaces. © 1993 The American Physical Society.