Crystal growth kinetics and size-probability density function in phase transformations with spatially-correlated nuclei

We present a study on crystal growth kinetics, nucleation kinetics and probability density function of crystal size, in nucleation and growth phase transformations with correlated nuclei.The method used is based on the theory of stochastic processes, for a set of correlated dots, that makes use of correlation functions.The theory is formulated within the framework of second-order approximation in correlation functions and is valid for any growth law of the crystals.It allows determining the rate of appearance of the actual nuclei, I a , and the evolution of the mean crystal volume, v.The crystal-size distribution function is eventually computed using the I a and v parameters.The model has been applied to a system of correlated nuclei according to the hard-sphere model in which the formation of actual nuclei is forbidden in a shell around growing crystals.The numerical results relating to 3D transformations are presented for linear crystal growth.This approach has also been used to describe uncorrelated nuclei (throughout the entire space) for which the exact solutions, for both I a and v, are given by the Kolmogorov-Johnson-Mehl-Avrami (KJMA) theory.Comparison with the KJMA approach provides verification of the model's validity.Poissonian distribution of nuclei has also been investigated in nonsolid-state transformations, specifically in those characterized by a coalescence mechanism.Statistical models on the reduction of