It was recalled that thermal grooving at a grain boundary was well understood when the surface of the groove was entirely rough (finite surface stiffness) at its root. In this situation, the grain-boundary energy was uniquely related to the surface energy of the groove at its root via the dihedral angle that was obtained by imposing an equilibrium balance of capillary forces at the triple-junction. However, when a groove-root was faceted, the non-analyticity of the surface energy at the facet orientation led to ambiguities in the enforcement of equilibrium at the groove-root and in the relationship between facet energy and grain-boundary energy. It was shown here that equilibrium at the groove-root required careful consideration of the torque; which could adjust itself so as to maintain a fixed facet orientation for a range of grain-boundary energies; thus achieving a net balance of capillary forces. This contrasted sharply with the case of a rough root where the grain-boundary energy was in 1-to-1 correspondence with the observed dihedral angle. By using this insight, it was shown - via a simple graphical method - that the grain-boundary energy and surface-energy function were adequate for determining whether a groove-root was faceted or rough; thus avoiding the need for any ad hoc specification of the dihedral angle as a boundary condition. The evolution of thermal grooves was studied by using a variational approach that could handle infinite surface stiffness and naturally allowed for facet formation. The mobility of the triple-junction, which was know to lead to deviations from Mullins’ t1/4 scaling law, was also explicitly included in the model. A key observation was that low junction-mobilities could lead to the formation of kinetic groove-shapes. In particular, groove-roots that were expected to be rough (from energetic considerations alone) were instead seen to exhibit nearby facet orientations at low junction mobilities. Such kinetically limited facets at groove-roots could not be obtained if the equilibrium angle were prescribed as a routine boundary condition for the evolution equation. The analysis was also extended to the more realistic case of asymmetrical grooves, and a graphical procedure was presented that clarified their structure.

On the Evolution of Faceted Grain-Boundary Grooves by Surface Diffusion. A.Ramasubramaniam, V.B.Shenoy: Acta Materialia, 2005, 53[10], 2943-56