If there is a sulhcient amount of l

If there is a sulhcient amount of liquid, the deformation of the grains due to the impingement between them will not occur. In this case, the grain shape will be determined by the requirement to minimize the solid-liquid interfacial energy (Wulff’s theorem) [6] and the dependence of the growth (dissolution) rate on the grain surface orientation (Frank’s theorem) [7,8]. The Wulff theorem predicts that the cquilibrium grain shape is dctcrrnincd by the orientation dependence of interfacial energy, while the Frank theorem predicts that the grain shape is dctcrmincd by the orientation dependence of the growth (dissolution) rate of a grain surface. In either case. the grain shape can change with tcmpernture because as the surfaces become atomically rough at elevated temperatures [9-I I]. the interfacial energy and the growth (dissolution) rate will become isotropic.