Comparative study of approaches based on the differential critical region and correlation functions in modeling phase-transformation kinetics

Massimo Tomellini and Massimo Fanfoni
Phys. Rev. E 90, 052406 – Published 20 November 2014

Abstract

The statistical methods exploiting the “Correlation-Functions” or the “Differential-Critical-Region” are both suitable for describing phase transformation kinetics ruled by nucleation and growth. We present a critical analysis of these two approaches, with particular emphasis to transformations ruled by diffusional growth which cannot be described by the Kolmogorov-Johnson-Mehl-Avrami (KJMA) theory. In order to bridge the gap between these two methods, the conditional probability functions entering the “Differential-Critical-Region” approach are determined in terms of correlation functions. The formulation of these probabilities by means of cluster expansion is also derived, which improves the accuracy of the computation. The model is applied to 2D and 3D parabolic growths occurring at constant value of either actual or phantom-included nucleation rates. Computer simulations have been employed for corroborating the theoretical modeling. The contribution to the kinetics of phantom overgrowth is estimated and it is found to be of a few percent in the case of constant value of the actual nucleation rate. It is shown that for a parabolic growth law both approaches do not provide a closed-form solution of the kinetics. In this respect, the two methods are equivalent and the longstanding overgrowth phenomenon, which limits the KJMA theory, does not admit an exact analytical solution.

  • Figure
  • Figure
  • Figure
  • Figure
  • Figure
  • Figure
  • Figure
5 More
  • Received 30 July 2014
  • Revised 17 October 2014

DOI:https://doi.org/10.1103/PhysRevE.90.052406

©2014 American Physical Society

Authors & Affiliations

Massimo Tomellini*

  • Dipartimento di Scienze e Tecnologie Chimiche, Università di Roma Tor Vergata, Via della Ricerca Scientifica, 00133 Roma, Italy

Massimo Fanfoni

  • Dipartimento di Fisica, Università di Roma Tor Vergata, Via della Ricerca Scientifica, 00133 Roma, Italy

  • *tomellini@uniroma2.it

Article Text (Subscription Required)

Click to Expand

References (Subscription Required)

Click to Expand
Issue

Vol. 90, Iss. 5 — November 2014

Reuse & Permissions
Access Options
Author publication services for translation and copyediting assistance advertisement

Authorization Required


×
×

Images

×

Sign up to receive regular email alerts from Physical Review E

Log In

Cancel
×

Search


Article Lookup

Paste a citation or DOI

Enter a citation
×