Derivation of the phase field crystal model for colloidal solidification

TL;DR

This paper derives a phase-field crystal model for colloidal solidification from microscopic theory, compares it with density functional theory, and proposes a less approximate variant, validating it through simulations of crystal growth.

Contribution

It introduces a derivation of the phase-field crystal model from microscopic density functional theory tailored for colloidal systems, and proposes a less approximate variant.

Findings

Good agreement with density functional theory after free energy scaling

The derived model accurately predicts crystal front velocities

A less approximate phase-field crystal variant improves modeling accuracy

Abstract

The phase-field crystal model is by now widely used in order to predict crystal nucleation and growth. For colloidal solidification with completely overdamped individual particle motion, we show that the phase-field crystal dynamics can be derived from the microscopic Smoluchowski equation via dynamical density functional theory. The different underlying approximations are discussed. In particular, a variant of the phase-field crystal model is proposed which involves less approximations than the standard phase-field crystal model. We finally test the validity of these phase-field crystal models against dynamical density functional theory. In particular, the velocities of a linear crystal front from the undercooled melt are compared as a function of the undercooling for a two-dimensional colloidal suspension of parallel dipoles. Good agreement is only obtained by a drastic scaling of the free energies in the phase-field crystal model in order to match the bulk freezing transition point.