Direct numerical simulation of homogeneous nucleation and growth in a phase-field model using cell dynamics method

TL;DR

This study uses a phase-field model and cell dynamics method to simulate homogeneous nucleation and growth, confirming the KJMA scenario and analyzing temperature-dependent nucleation rates and incubation times.

Contribution

It provides a detailed numerical analysis of nucleation and growth in a phase-field model, including quantitative extraction of KJMA parameters and temperature dependencies.

Findings

Nucleation and growth follow the KJMA scenario closely.

The Avrami exponent is approximately 3, matching theoretical predictions.

Nucleation rate exhibits activation-type temperature dependence, incubation time does not.

Abstract

Homogeneous nucleation and growth in a simplest two-dimensional phase field model is numerically studied using the cell dynamics method. Whole process from nucleation to growth is simulated and is shown to follow closely the Kolmogorov-Johnson-Mehl-Avrami (KJMA) scenario of phase transformation. Specifically the time evolution of the volume fraction of new stable phase is found to follow closely the KJMA formula. By fitting the KJMA formula directly to the simulation data, not only the Avrami exponent but the magnitude of nucleation rate and, in particular, of incubation time are quantitatively studied. The modified Avrami plot is also used to verify the derived KJMA parameters. It is found that the Avrami exponent is close to the ideal theoretical value m=3. The temperature dependence of nucleation rate follows the activation-type behavior expected from the classical nucleation theory. On the other hand, the temperature dependence of incubation time does not follow the exponential activation-type behavior. Rather the incubation time is inversely proportional to the temperature predicted from the theory of Shneidman and Weinberg [J. Non-Cryst. Solids {\bf 160}, 89 (1993)]. A need to restrict thermal noise in simulation to deduce correct Avrami exponent is also discussed.