Cell Dynamics Simulation of Kolmogorov-Johnson-Mehl-Avrami Kinetics of Phase Transformation

TL;DR

This paper employs a simplified cell dynamics simulation to validate the KJMA theory of phase transformation, confirming its predictions on transformation kinetics and demonstrating the method's effectiveness.

Contribution

The study introduces a simplified cell dynamics approach that accurately reproduces KJMA theory predictions for phase transformation kinetics.

Findings

Cell dynamics method reproduces KJMA's time evolution of phase transformation.

Simulation confirms the linearity of the KJMA plot and the predicted Avrami exponents.

The approach is effective for studying pattern formation and basic phase transformation properties.

Abstract

In this study, we use the cell dynamics method to test the validity of the Kormogorov-Johnson-Mehl-Avrami (KJMA) theory of phase transformation. This cell dynamics method is similar to the well-known phase-field model, but it is a more simple and efficient numerical method for studying various scenarios of phase transformation in a unified manner. We find that the cell dynamics method reproduces the time evolution of the volume fraction of the transformed phase predicted by the KJMA theory. Specifically, the cell dynamics simulation reproduces a double-logarithmic linear KJMA plot and confirms the integral Avrami exponents $n$ predicted from the KJMA theory. Our study clearly demonstrates that the cell dynamics approach is not only useful for studying the pattern formation but also for simulating the most basic properties of phase transformation.