Cell size distribution in a random tessellation of space governed by the Kolmogorov-Johnson-Mehl-Avrami model: Grain size distribution in crystallization

TL;DR

This paper derives the expected and variance of cell size distributions in random tessellations based on the Kolmogorov-Johnson-Mehl-Avrami model, providing an analytical PDF and applying it to crystallization processes.

Contribution

It introduces a new analytical approach to predict cell size distributions without restrictions on nucleation and growth rates, applicable to crystallization.

Findings

Derived expected value and variance of cell size distributions.

Developed an approximate analytical probability density function.

Applied the model to crystallization under isochronal heating.

Abstract

The space subdivision in cells resulting from a process of random nucleation and growth is a subject of interest in many scientific fields. In this paper, we deduce the expected value and variance of these distributions while assuming that the space subdivision process is in accordance with the premises of the Kolmogorov-Johnson-Mehl-Avrami model. We have not imposed restrictions on the time dependency of nucleation and growth rates. We have also developed an approximate analytical cell size probability density function. Finally, we have applied our approach to the distributions resulting from solid phase crystallization under isochronal heating conditions.