A STATISTICAL-THEORY OF NUCLEATION AND GROWTH IN FINITE SYSTEMS

The Kolmogorov-Avrami-type formulation for both the latent nucleation (inhomogeneous) and the random nucleation (homogeneous) cases is presented for finite systems. In finite systems, there appear three time regimes. For the latent nucleus case the fraction of transformed regions remains as 1 - e(-NV) (N: density of nuclei, V: system volume) and for the random nucleation case it approaches unity in the time dependence as 1 - Ae(-JVt) (A: constant, J: nucleation rate). The growth rate in finite systems is always smaller than that in infinite systems. We present the numerical results of one-dimensional system as an example.