Stochastic modeling of nucleation and growth in a thin layer between two interfaces

A stochastic modeling method is presented for the analysis of nucleation and growth in a thin layer between two interfaces. In this layer, nucleation occurs randomly and growth slops at the interfaces after instantaneous growth. This halting of the growth causes non-random impingement because phantom crystallites in the Kolmogorov-Johnson-Mehl-Avrami (KJMA) model shrink to an effective size. This stochastic model successfully deals with effective size using a factor gamma which accounts for the overlap between a phantom crystallite and a crystallite. This leads to a phenomenological equation for nonrandom impingement: dX(t)/dV(ex) = [1 - X(t)](i), where X(t) is the transformed fraction and V-ex is the KJMA extended volume fraction. It is shown that the exponent is clearly expressed as i = 2 - gamma. An analytical solution of the transformed fraction agrees very well with the numerical simulations. (C) 1997 Acta Metallurgica Inc.