Interplay between Kolmogorov–Johnson–Mehl–Avrami kinetics and Poisson–Voronoi tessellation

•An integral equation for the distribution function of Voronoi cells is obtained from the KJMA theory.•The exact solution is computed for the 1D Voroni tessellation.•The Gamma distribution has also been obtained for the dD case.•Evolution of the nucleus size distribution function has been derived.

In this paper we investigate the connection between Voronoi tessellation and the KJMA approach of space filling. In particular, we study how nuclei, in their growth, cover a given Voronoi cell. This approach leads to an integral equation for the cell-size distribution function. Starting from the 1D case, that is solved exactly, we extend the results to the dDdD case. The analysis allows to find a rationale to the phenomenological parameter entering the Gamma distribution function and to improve the description of the transformation through the knowledge of the kinetics of grain formation. Moreover, the nucleus size distribution function has been calculated as a function of the transformed fraction.