Eur. Phys. J. B 34, 331-341 (2003)
https://doi.org/10.1140/epjb/e2003-00229-9

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

¹ Dipartimento di Fisica Università di Roma Tor Vergata and Istituto Nazionale per la Fisica della Materia, Via della Ricerca Scientifica, 00133 Rome, Italy
² Dipartimento di Scienze e Tecnologie Chimiche, Università di Roma Tor Vergata and Istituto Nazionale per la Fisica della Materia, Via della Ricerca Scientifica, 00133 Rome, Italy

Corresponding authors: ^a massimo.fanfoni@roma2.infn.it - ^b tomellini@uniroma2.it

Received: 27 January 2003
Revised: 10 May 2003
Published online: 11 August 2003

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.