Phase Field Theory of Nucleation and Polycrystalline Pattern Formation

TL;DR

This paper reviews phase field modeling of crystal nucleation and polycrystalline growth, demonstrating accurate predictions of nucleation barriers and diverse pattern formations including spherulites, with implications for understanding solidification processes.

Contribution

It introduces a phase field model that accurately predicts nucleation barriers and captures complex polycrystalline patterns, including spherulite formation, by adjusting a few parameters.

Findings

Phase field theory accurately predicts nucleation barrier heights.

The model reproduces diverse spherulitic growth patterns.

Long-term polycrystalline growth involves nucleation at growth fronts.

Abstract

We review our recent modeling of crystal nucleation and polycrystalline growth using a phase field theory. First, we consider the applicability of phase field theory for describing crystal nucleation in a model hard sphere fluid. It is shown that the phase field theory accurately predicts the nucleation barrier height for this liquid when the model parameters are fixed by independent molecular dynamics calculations. We then address various aspects of polycrystalline solidification and associated crystal pattern formation at relatively long timescales. This late stage growth regime, which is not accessible by molecular dynamics, involves nucleation at the growth front to create new crystal grains in addition to the effects of primary nucleation. Finally, we consider the limit of extreme polycrystalline growth, where the disordering effect due to prolific grain formation leads to isotropic growth patterns at long times, i.e., spherulite formation. Our model of spherulite growth exhibits branching at fixed grain misorientations, induced by the inclusion of a metastable minimum in the orientational free energy. It is demonstrated that a broad variety of spherulitic patterns can be recovered by changing only a few model parameters.