Validity of Avrami's kinetics for random and nonrandom distributions of germs

Up to now, the time dependence of the volume fraction during a first-order phase transition has been often described by Avrami's model, in which nucleation is assumed to occur randomly in the infinite volume. In this paper we present a computer simulation of the phase transition in order to verify the validity of Avrami's kinetics in the cases of random and nonrandom distribution of germ nuclei. Our results indicate that Avrami's kinetics is the correct solution, provided the distribution of nuclei is random and the extended volume is computed by including the so-called phantom nuclei. It is also shown that the general solution in the form of a functional of the extended volumes is appropriate for both nucleus distributions.