Transformation kinetics for nucleus clusters

A rigorous mathematical approach based on stochastic geometry concepts is presented to extend previous Johnson-Mehl, Avrami, Kolmogorov treatment of transformation kinetics to situations in which nuclei are not homogeneously located in space but are located in clusters. An exact analytical solution is presented here for the first time assuming that nucleation sites follow a Matérn cluster process. The influence of Matérn cluster process parameters on subsequent growth kinetics and the microstructural path are illustrated by means of numerical examples. Moreover, using the superposition principle, exact analytical solutions are also obtained when nucleation takes place by a combination of a Matérn cluster process and an inhomogeneous Poisson point process. The new solutions presented here significantly increase the number of exactly solvable cases available to formal kinetics.