Classical nucleation theory in the phase-field crystal model

TL;DR

This paper investigates nucleation processes in the phase-field crystal model, demonstrating qualitative agreement with classical nucleation theory and highlighting the need for an extended, multi-variable nucleation framework for quantitative accuracy.

Contribution

It numerically analyzes homogeneous nucleation in the PFC model, revealing qualitative CNT agreement and identifying limitations that suggest extending CNT to multiple variables.

Findings

PFC model shows qualitative agreement with CNT predictions.

Early lattice structure formation disagrees with CNT assumptions.

Quantitative modeling requires extending CNT to multiple variables.

Abstract

A full understanding of polycrystalline materials requires studying the process of nucleation, a thermally activated phase transition that typically occurs at atomistic scales. The numerical modeling of this process is problematic for traditional numerical techniques: commonly used phase-field methods' resolution does not extend to the atomic scales at which nucleation takes places, while atomistic methods such as molecular dynamics are incapable of scaling to the mesoscale regime where late-stage growth and structure formation takes place following earlier nucleation. Consequently, it is of interest to examine nucleation in the more recently proposed phase-field crystal (PFC) model, which attempts to bridge the atomic and mesoscale regimes in microstructure simulations. In this work, we numerically calculate homogeneous liquid-to-solid nucleation rates and incubation times in the simplest version of the PFC model, for various parameter choices. We show that the model naturally exhibits qualitative agreement with the predictions of classical nucleation theory (CNT) despite a lack of some explicit atomistic features presumed in CNT. We also examine the early appearance of lattice structure in nucleating grains, finding disagreement with some basic assumptions of CNT. We then argue that a quantitatively correct nucleation theory for the PFC model would require extending CNT to a multi-variable theory.