Dynamic scaling and stochastic fractal in nucleation and growth processes

Abstract

A class of nucleation and growth models of a stable phase is investigated for various different growth velocities. It is shown that for growth velocities [Formula: see text] and [Formula: see text], where [Formula: see text] and [Formula: see text] are the mean domain size of the metastable phase (M-phase) and the mean nucleation time, respectively, the M-phase decays following a power law. Furthermore, snapshots at different time [Formula: see text] that are taken to collect data for the distribution function [Formula: see text] of the domain size [Formula: see text] of the M-phase are found to obey dynamic scaling. Using the idea of data-collapse, we show that each snapshot is a self-similar fractal. However, for [Formula: see text], such as in the classical Kolmogorov–Johnson–Mehl–Avrami model, and for [Formula: see text], the decays of the M-phase are exponential and they are not accompanied by dynamic scaling. We find a perfect agreement between numerical simulation and analytical results.