The effect of strong surface energy anisotropy on migrating grain-boundary grooves

Abstract

Grain growth during material processing and synthesis is controlled by grain-boundary migration. When a grain boundary ends at a free surface, a groove will develop at the tip to reduce the combined surface and grain-boundary energies. This groove may hinder the movement of the grain boundary and its effect needs to be understood. Previous studies of migrating grooves have focused mainly on isotropic surface energy. We investigate the effect of strong surface energy anisotropy on the groove motion. We assume that the groove evolves by surface diffusion and moves at constant speed. A recently developed delta-function facet model is used to prescribe the surface energy at temperatures above the roughening temperature of the bicrystal. We find that a migrating groove tilts the grain-boundary tip by angle θ away from being perpendicular to the free surface. The angle θ depends on the crystallographic orientations of the bicrystal and is studied systematically for the full range of orientations. Most orientations yield faceted grooves; the remaining few cases generate smooth grooves that have the same shape as the corresponding isotropic grooves, but the size is much smaller. For a given bicrystal, the migrating-groove problem may have a unique solution or multiple solutions. We also show that a migrating-groove profile measured on a polycrystalline alumina surface can be well fitted by our anisotropic model.