It was recalled that a grain boundary, ending at a free surface, formed a groove at the tip which affected its migration. This coupled grooving and migration was studied for an initially straight inclined grain boundary which intercepted a horizontal free surface. The groove deepened via surface diffusion. Previous work on a groove migrating at constant speed had suggested that the grain boundary was pinned if the inclination angle was small. It was found here that the grain boundary was never pinned. The coupled motion could be separated into 2 time regimes. In regime I, both the groove and the grain-boundary profiles grew with time; obeying similarity laws. The groove profile was symmetrical about the groove root which turned the grain boundary tip vertically. This bending drove the migration. The self-similar profiles were shown to be linearly stable, and grew continuously into regime II.

Coupled Grooving and Migration of Inclined Grain Boundaries - Regime I. H.Zhang, H.Wong: Acta Materialia, 2002, 50[8], 1983-94

A study was made of the coupled grooving and migration of an initially straight inclined grain boundary which ended at a horizontal free surface at an inclination angle, β << 1. The coupled motion was separated into 2 time regimes. In regime I, the grain boundary turned vertically at the groove root. In regime II, the turning relaxed and followed 2 different paths; depending upon α/β, where α was the supplementary dihedral angle. For β > α/6, the groove root positions were described by: (x0,y0) ~ (t1/2, t1/6) as t → ∞. For β < α/6, it was found that (x0, y0) ~ (t1/4, t1/4) as t → ∞. These results arose from asymptotic expansions, and agreed with a finite-difference solution of the coupled equations. They showed that the grain boundary was never pinned. The asymptotic solutions also applied to the Sun-Bauer method of measuring mobility, and predicted grain-boundary profiles that agreed better with experiments.

Coupled Grooving and Migration of Inclined Grain Boundaries - Regime II. H.Zhang, H.Wong: Acta Materialia, 2002, 50[8], 1995-2012