Abstract
Grain-boundary migration controls the growth and shrinkage of crystalline grains and is important in materials synthesis and processing. A grain boundary ending at a free surface forms a groove at the tip, which affects its migration. This coupled grooving and migration is studied for an initially straight, inclined grain boundary intercepting a horizontal free surface. The groove deepens by surface diffusion. Previous work on a groove migrating at constant speed suggests that the grain boundary is pinned if the inclination angle is small. We find that the grain boundary is never pinned. The coupled motion can be separated into two time regimes. In Regime I, both the groove and grain-boundary profiles grow with time following similarity laws. The groove profile is symmetric about the groove root which turns the grain boundary tip vertically. This bending drives the migration. The self-similar profiles are shown to be linearly stable, and they grow continuously into Regime II.
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