Statistical-Kinetic Theory of Phase Change

Reaction rate kinetics is applied to the phenomenon of phase change. Two rate constants, one for nucleation and the other for growth processes, are embodied in the theory. These microscopic parameters are of a basic nature, with a significance quite distinct from the macroscopic quantities employed by Johnson-Mehl and Avrami (JMA) in the conventional phenomenological formulation. Expressions for the nucleation rate and the degree of transformation are established once the basic properties of the Poisson exponential binomial limit distribution have been determined. The statistical kinetic theory does indeed lead to a sigmoid-shaped transformation curve commonly observed in phase changes. An essential ingredient of the present theory, not incorporated in the JMA phenomenological theory, is the role of nuclei and specimen size; unusual behavior may be expected in small particles undergoing transformation.