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

Abstract 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, d X ( t )/ d V ex =[1− X ( t )] 2− γ , where X ( t ) is the transformed fraction, V ex is the KJMA extended volume fraction, and γ 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 .