Fokker–Planck equation for the particle size distribution function in KJMA transformations

Massimo Tomellini

Physica A: Statistical Mechanics and its Applications, 2023, vol. 615, issue C

Abstract: The Fokker–Planck (FP) equation has been derived for describing the temporal evolution of the particle size probability density function (PDF) for KJMA (Kolmogorov–Johnson–Mehl–Avrami) transformations. The classical case of transformations with constant rates of both nucleation and growth, in 3D space, has been treated. Integration of the equation shows that the PDF is given by the superposition of one-parameter gamma distributions with time-dependent mean size given by the KJMA theory. The asymptotic behavior of the FP solution offers a demonstration of the conjecture, previously proposed by Pineda et al. (2004), according to which the set of crystals formed at the same time are gamma-distributed, with the parameter depending on crystal birth time. Computer simulations of the transformation with constant nucleation and growth rates show that the temporal evolution of the PDF, in volume domain, is in good agreement with the Johnson–Mehl PDF. The approach based on the FP equation provides a particle size PDF that exhibits such behavior.

Keywords: Kolmogorov–Johnson–Mehl–Avrami model; Fokker–Planck equation; Phase transformation kinetics; Particle-size distribution function (search for similar items in EconPapers)
Date: 2023
References: View complete reference list from CitEc
Citations:

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0378437123000705
Full text for ScienceDirect subscribers only. Journal offers the option of making the article available online on Science direct for a fee of $3,000

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:615:y:2023:i:c:s0378437123000705

DOI: 10.1016/j.physa.2023.128515

Access Statistics for this article

Physica A: Statistical Mechanics and its Applications is currently edited by K. A. Dawson, J. O. Indekeu, H.E. Stanley and C. Tsallis

More articles in Physica A: Statistical Mechanics and its Applications from Elsevier
Bibliographic data for series maintained by Catherine Liu ().