Number of clusters formed in nucleation-growth processes

The number of clusters, N, formed in nucleation-growth processes in. first-order phase transformations, and their average size, (R), at the end of the stage of independent growth of the supercritical clusters are determined analytically. It is shown that the number of clusters, N, depends only on the thermodynamic parameters like initial supersaturation, specific interfacial energy etc. but not on the values of kinetic parameters Like the diffusion coefficient. In addition, estimates are given for the duration of the different stages of the nucleation-growth process. In this way, a complete quantitative description of the basic characteristics of first-order phase transformations (e.g., segregation in solid or liquid solutions, vapor condensation, etc.) is established. The results are in excellent agreement both with experimental results as well as with computer calculations modelling nucleation and growth based on the numerical solution of the set of kinetic equations describing this process in the framework of classical nucleation theory. (C) 1996 American Institute of Physics.