THE STATISTICAL PARTICLE GROWTH LAW IN SELF-SIMILAR COARSENING

The classical method of Lifshitz and Slyozov (LS) for the analysis of coarsening is generalized by starting with a statistical particle growth law of the form R(c)gamma<R\R> = f(rho), where R is the volume equivalent radius, R(c) its critical value, rho = R/R(c), and <R\R> is the average value of R = dR/dt for a given R. For a given gamma and function f(rho), the results are the same as obtained from the original deterministic theory based on R in place of <R\R>, but the scope of the statistically based theory is somewhat greater. It is then shown that, under very general assumptions, a statistical growth law of the form stated above must hold for the particular case of the self-similar distribution of any system undergoing self-similar coarsening. Furthermore, a formula is given that allows one to calculate <R\R> from the experimental distribution function P(rho) and the time dependence of <R>. The theoretical results are discussed and illustrated by comparing them with simulation results for a linear bubble model undergoing coarsening.