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

physical review. b, condensed matter and materials physics

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