The Kolmogorov-Johnson-Mehl-Avrami model; which is a nucleation and growth Poissonian process in space; has been implemented by taking into account spatial correlation among nuclei. This is achieved through a detailed study of a system of distinguishable and correlated dots (nuclei). The probability that no dots be in a region of the space has been evaluated in terms of correlation functions. The central point of the paper is the application of the theory to describe nucleation and growth in two dimensions under constant nucleation rate, where correlation among nuclei depends upon the size of the nucleus. This is a typical case occurring in transformation governed by particle diffusion. We also propose a simple formula for describing the phase transition kinetics under this circumstance.

Fanfoni, M., Tomellini, M. (2003). Beyond the Kolmogorov Johnson Mehl Avrami kinetics: inclusion of the spatial correlation. THE EUROPEAN PHYSICAL JOURNAL. B, CONDENSED MATTER PHYSICS, 34, 331 [10.1140/epjb/e2003-00229-9].

Beyond the Kolmogorov Johnson Mehl Avrami kinetics: inclusion of the spatial correlation

FANFONI, MASSIMO;TOMELLINI, MASSIMO
2003-01-01

Abstract

The Kolmogorov-Johnson-Mehl-Avrami model; which is a nucleation and growth Poissonian process in space; has been implemented by taking into account spatial correlation among nuclei. This is achieved through a detailed study of a system of distinguishable and correlated dots (nuclei). The probability that no dots be in a region of the space has been evaluated in terms of correlation functions. The central point of the paper is the application of the theory to describe nucleation and growth in two dimensions under constant nucleation rate, where correlation among nuclei depends upon the size of the nucleus. This is a typical case occurring in transformation governed by particle diffusion. We also propose a simple formula for describing the phase transition kinetics under this circumstance.
2003
Pubblicato
Rilevanza internazionale
Articolo
Sì, ma tipo non specificato
Settore FIS/03 - FISICA DELLA MATERIA
English
Correlation methods; Diffusion; Functions; Mathematical transformations; Nucleation; Phase transitions; Poisson distribution; Reaction kinetics; Correlated dots; Nucleation rate; Particle diffusion; Spatial correlation; Mathematical models
Fanfoni, M., Tomellini, M. (2003). Beyond the Kolmogorov Johnson Mehl Avrami kinetics: inclusion of the spatial correlation. THE EUROPEAN PHYSICAL JOURNAL. B, CONDENSED MATTER PHYSICS, 34, 331 [10.1140/epjb/e2003-00229-9].
Fanfoni, M; Tomellini, M
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2108/37587
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