Chapter 9 - Master equation

Abstract

A cluster is considered as a static formation that is in internal thermodynamic equilibrium. In addition, the cluster is considered as being in partial or complete thermodynamic equilibrium with the ambient old phase. It is only a transient formation with a certain lifetime depending on the cluster size and is often as short as a nano- and even a picosecond. A comprehensive description of the nucleation process requires kinetic considerations based on a concrete mechanism by which the clusters grow and decay and thus change their size. The chapter presents the formulation of the master equation of nucleation—the basic kinetic equation that describes the evolution of the process with the help of a generalization of the Szilard model. This generalization is essential because it makes it possible for the so-formulated master equation to describe kinetically all stages of the overall process of first-order phase transition and not only its initial nucleation stage. The considerations are restricted to one component nucleation, which can be either homogeneous or heterogeneous.