Transformation kinetics for surface and bulk nucleation

Abstract

A rigorous mathematical approach based on the causal cone and stochastic geometry concepts is used to derive new exact expressions for transformation kinetics theory. General expressions for the mean volume density and the volume fraction are derived for both surface and bulk nucleation in a general Borel subset of R 3 . In practice, probably any specimen shape of engineering interest is going to be a Borel set. An expression is also derived for the important case of polyhedral shape, in which surface nucleation may take place on the faces, edges and vertices of the polyhedron as well as within the bulk. Moreover, explicit expressions are given for surface and bulk nucleation for three specific shapes of engineering relevance: two parallel planes, an infinitely long cylinder and a sphere. Superposition is explained in detail and it permits the treatment of situations in which surface and bulk nucleation take place simultaneously. The new exact expressions presented here result in a significant increase in the number of exactly solvable cases available to formal kinetics.