Eighth-order phase-field-crystal model for two-dimensional crystallization

TL;DR

This paper derives and tests an eighth-order phase-field-crystal model for 2D crystallization, demonstrating its accuracy and efficiency in replicating density functional theory results for static and dynamic properties.

Contribution

The paper introduces a new eighth-order phase-field-crystal model that improves accuracy and computational efficiency over previous models for 2D crystallization.

Findings

The eighth-order model aligns well with density functional theory results.

It accurately captures static and dynamic properties of 2D crystallization.

The model is computationally efficient compared to earlier approaches.

Abstract

We present a derivation of the recently proposed eighth order phase field crystal model [Jaatinen et al., Phys. Rev. E 80, 031602 (2009)] for the crystallization of a solid from an undercooled melt. The model is used to study the planar growth of a two dimensional hexagonal crystal, and the results are compared against similar results from dynamical density functional theory of Marconi and Tarazona, as well as other phase field crystal models. We find that among the phase field crystal models studied, the eighth order fitting scheme gives results in good agreement with the density functional theory for both static and dynamic properties, suggesting it is an accurate and computationally efficient approximation to the density functional theory.