Stochastic Geometry and Transformation Kinetics Theories: Basics and Results

Aim of this paper is to show the application of Stochastic Geometry in transformation kinetics theories. We generalize the early Kolmogorov, Johnson, Mehl and Avrami theory, to more general nucleation-and-growth processes. In particular the notion of point process will be introduced to model various kinds of nucleation processes, for instance inhomogeneous nucleation, cluster nucleation and nucleation on lower dimensional sets. Volume fraction, mean volume and surface densities of the transformed phase are studied by methods of Stochastic Geometry making use of the notion of causal cone.