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

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.

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• Grain refinement and partitioning of impurities in the grain boundaries of a colloidal polycrystal
• Geometric order parameters derived from the Voronoi tessellation show signatures of the jamming transition
• Beyond the constraints underlying Kolmogorov-Johnson-Mehl-Avrami theory related to the growth laws
• Nucleation and growth of micellar polycrystals under time-dependent volume fraction conditions
• Fokker-Planck equation for the particle size distribution function in KJMA transformations
• Cell-size distribution and scaling in a one-dimensional KJMA lattice model with continuous nucleation
• Nonequilibrium grain size distribution with generalized growth and nucleation rates
• Kinetics of island growth in the framework of planar diffusion zones and 3D nucleation and growth models for electrodeposition