Equilibrium crystal shapes and their application to nucleation in solids

A major aim of theoretical calculations of nucleation rates, for diffusional phase transformations involving solids, is to obtain the equilibrium crystal shape (ECS) of the critical nucleus of the precipitating phase in the surrounding medium (matrix). The importance of the ECS arises from the fact that, in phase transformations involving negligible strain energy, the homogeneous nucleation rate is strongly dependent on the anisotropic interfacial energy of the precipitate-matrix interphase interface. The ECS is determined by this interfacial energy which, in turn, depends on the concentration profile at the interface. Equations obtained on the basis of the discrete lattice plane (DLP) model for the composition profile at a structurally sharp, compositionally diffuse interface between two crystal structures in a binary system, are presented in this paper. The results of application of the DLP model to determine the ECS of an h.c.p. precipitate in an f.c.c. matrix are also described. Good agreement is obtained on comparing the ECS obtained by this model with experiments which reveal the ECS. These results, as well as the computed temperature dependence of the ECS are discussed.