Kinetics of transformation with nucleation and growth mechanism: Two- and three-dimensional models

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Abstract
Theoretical results on the kinetics of transformations with nucleation and growth mechanisms in homogeneous systems during isothermal annealing are reported. The present derivations start from a probability calculation in a finite discrete assembly. In the simplest case with a constant growth rate the results of the formulation agree with the classical Avrami equation for two- and three-dimensional systems. Furthermore, by calculating the survival probability step by step for separate occurrences, the relationships between interfering processes and the effects of neighboring nuclei are revealed. In particular, the distribution of nuclei pairs with distance is determined. Various cases of preferred nucleation in specialized regions, such as linear zones (e.g., dislocations), planar areas (e.g., grain boundaries), or three-dimensional partial volumes, are analytically solved and these solutions can be directly used for the interpretation and evaluation of experimental measurements.