Grain-Boundary Grooving and Migration

1. Grain-Boundary Grooving and Migration 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. In Regime II, the turning relaxes following two different paths depending on s/b, where s is the supplementary dihedral angle and b (<< 1) is the initial inclination angle of the grain boundary. For b >s/6, the groove root positions (x0 ,y0) ~ (t 1/2, t 1/6) as time t → ∞, whereas for b < s/6, (x0, y0) ~ (t1/4, t1/4) as t → ∞. These results come from asymptotic expansions and agree with a finite-difference solution of the coupled equations. They show that the grain boundary is never pinned. • Zhang, H. and H. Wong "Coupled grooving and migration of inclined grain boundaries: Regime I," Acta Materialia50, 1983-1994 (2002). • Zhang, H. and H. Wong "Coupled grooving and migration of inclined grain boundaries: Regime II," Acta Materialia50, 1995-2012 (2002). • Min, D. and H. Wong "A model of migrating grain-boundary grooves with application to two mobility-measurement methods," Acta Materialia50, 5155-5169 (2002).