Statistical treatment of nucleation and growth in a thin layer between two interfaces

The statistical distribution of phantom crystallites in the Kolmogorov-Johnson-Mehl-Avrami (KJMA) model is corrected to account for the shrinking of phantom crystallites to effective size owing to the halting of crystal growth between two interfaces. In a previous paper, a stochastic treatment of shrinkage led to a kinetic equation, dX(t)l dV_ex = [1 -X(t)]_2-y, where X(t) is the transformed fraction, V_ex is the KJMA extended volume fraction, and y is a overlap probability between a phantom crystallite and a crystallite. The present paper focuses on the statistical meaning of the kinetic equation to find that crystallites of size k and phantom crystallites of different size kγ^m (m = 1, 2, 3,...) are generated according to the Poisson distribution as determined by γ. The other statistical features of the phantom crystallites and crystallites are fully explained in terms of γ.