Comparative study of approaches based on the differential critical region and correlation functions in modeling phase-transformation kinetics

The statistical methods exploiting the “Correlation-Functions” or the “Differential-Critical-Region” are both suitable for describing phase transformation kinetics ruled by nucleation and growth.We present a critical analysis of these two approaches, with particular emphasis to transformations ruled by diffusional growth which cannot be described by the Kolmogorov-Johnson-Mehl-Avrami (KJMA) theory. In order to bridge the gap between these two methods, the conditional probability functions entering the “Differential-Critical-Region” approach are determined in terms of correlation functions. The formulation of these probabilities by means of cluster expansion is also derived, which improves the accuracy of the computation. The model is applied to 2D and 3D parabolic growths occurring at constant value of either actual or phantom-included nucleation rates. Computer simulations have been employed for corroborating the theoretical modeling. The contribution to the kinetics of phantom overgrowth is estimated and it is found to be of a few percent in the case of constant value of the actual nucleation rate. It is shown that for a parabolic growth law both approaches do not provide a closed-form solution of the kinetics. In this respect, the two methods are equivalent and the longstanding overgrowth phenomenon, which limits the KJMA theory, does not admit an exact analytical solution.