Introduction

We have developed in Chapters V and VIII the knowledge needed to derive rates of nucleation and spinodal decomposition. The steady-state nucleation rate is proportional to the product of the equilibrium distribution of nuclei and the rate of attachment of molecules to the nuclei, which for nucleation in condensed phases involves diffusion or diffusion-like jumps across an interface. The time dependence of the nucleation rate follows from a consideration of the mode of growth and shrinkage of embryos. Experimental verification of the theory is very difficult and to the extent that it has been carried out does not contradict the theory.

The rate of spinodal decomposition depends on the thermodynamic driving force and diffusion over a penetration distance corresponding to a quarter wavelength of a composition wave and can be shown to have a maximum at a particular wavelength of the periodic composition wave developed in this mode of decomposition of a metastable host.

Growth of nuclei to produce precipitates and other product phases needs to consider depletion of the solute in the parent metastable phase for the case of partitioning modes of decomposition of the parent phase and impingement of the product phases. This problem is considered from its original classical analytical treatment to more modern treatments based on the availability of computers to simulate processes as well as to solve non-linear coupled equations numerically.

1. Rate of Heterophase Nucleation