Dynamic scaling and stochastic fractal in nucleation and growth processes

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 v & AP; s (t)/t and v & AP; x/tau(x), where s (t) and tau 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 t that are taken to collect data for the distribution function c (x , t) of the domain size x 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 v = const., such as in the classical Kolmogorov-Johnson-Mehl-Avrami model, and for v & AP; 1/t, 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.