An analytical model for isothermal and isochronal transformation kinetics

An analytical model for the kinetics of phase transformations has been discussed that combines three overlapping processes: nucleation, growth, and impingement. Two kinds of nucleation have been considered in particular: a mixture of site saturation and continuous nucleation and Avrami nucleation. In combination with either interface-controlled growth or volume diffusion controlled growth, and incorporating the effect of impingement of the growing particles, a general analytical description of the transformation kinetics has been given for both isothermally and isochronally conducted transformations. The corresponding kinetic parameters are time and temperature dependent. In specific, limiting cases, the model reduces to the so-called Johnson-Mehl-Avrami description of transformation kinetics. The analytical model has been verified by exact results obtained from numerical calculations. The influences of the different nucleation and growth modes on the time and temperature dependencies of the transformation rate and the kinetic parameters have been demonstrated.