Theory of shape bifurcation during nucleation in solids

Abstract

The shape bifurcation theory of Johnson and Cahn [su1] is extended to a solid-state nucleation in order to predict the critical nucleus shape as a function of the nucleation driving force. For the case of homogeneous nucleation, the relationship between the nucleation driving force and the nucleus shape reveals characteristics similar to the well-known temperature effects on the isothermal pressure-volume variations of a van der Waals fluid. When the elastic strain energy is a strong function of the nucleus aspect ratio in the neighborhood of a high-symmetry morphology, such as a sphere or a cube, the shape transition is a continuous type, analogous to a smooth pressure-volume change in a van der Waals fluid above the critical temperature. On the other hand, if the elastic energy changes significantly only with small aspect ratios, the shape transition becomes a discontinuous type, analogous to the first-order liquid-to-vapor phase transition below the critical temperature. Results of an elementary model for heterogeneous nucleation also exhibit a similar bifurcation nature, here the potency of a heterogeneous nucleation site replacing the role of the temperature in the phase diagram of a van der Waals fluid.