Clusters can form and grow from a supersaturated vapor by successive reactions in which molecules (or “monomers”) of the vapor collide with the cluster and stick. In general, these reactions are reversible. The net forward rate of each of these reactions is termed the “nucleation current” of clusters of the size formed by the reaction. If a steady-state cluster size distribution exists, then the nucleation currents for clusters of all sizes are identical and can be equated to the steady-state (or “stationary”) nucleation rate. In that case, one can derive a closed-form expression for the nucleation rate in terms of a summation over clusters of all sizes up to some arbitrarily large size. The key terms in this summation are the forward rate constants and the Gibbs free energies of cluster formation from the monomer vapor. Evaluating the summation requires size-dependent values of these terms. For saturation ratios that lie within the condensation–evaporation regime, the free energy of cluster formation has a maximum at the critical cluster size. The nucleation theorem relates this size to the dependence of the nucleation rate on saturation ratio.

Phase transformations often begin by nucleation, where a small but distinct volume of material forms with a structure and composition that differ from those of the parent phase. An unfavorable surface bounds the new phase, giving rise to a barrier that must be overcome before thefluctuation in structure and composition can become a stable, growing region of new phase. Chapter 4 develops the thermodynamics of forming a nucleus, with emphasis on the characteristic size and undercooling that are required. Homogeneous and heterogeneous nucleation are explained. The temperature dependence of nucleation is explained. The time dependence of nucleation is discussed in terms of the shape of the free energy barrier that must be crossed by a growing nucleus. There is some discussion of nucleation in multicomponent alloys.