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.

References in corpus (2)

• Numerical model of solid phase transformations governed by nucleation and growth. Microstructure development during isothermal crystallization
• Simple approximate analytical solution for non-isothermal single-step transformations: kinetic analysis

Cited by in corpus (5)

• Time-evolution of grain size distributions in random nucleation and growth crystallization processes
• Grain refinement and partitioning of impurities in the grain boundaries of a colloidal polycrystal
• 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