Vacancy diffusion in colloidal crystals as determined by dynamical density-functional theory and the phase-field-crystal model

TL;DR

This study investigates vacancy diffusion in a 2D colloidal crystal near melting using simulations and models, revealing differences in temperature dependence predictions between dynamical density functional theory and phase-field crystal models.

Contribution

It compares vacancy relaxation dynamics across Brownian dynamics, dynamical density functional theory, and phase-field crystal modeling, highlighting the need for temperature-dependent mobility in phase-field models.

Findings

Vacancy is quickly filled by diffusive hopping.

Diffusion constant decreases with decreasing temperature in simulations.

Phase-field crystal model predicts the opposite temperature trend.

Abstract

A two-dimensional crystal of repulsive dipolar particles is studied in the vicinity of its melting transition by using Brownian dynamics computer simulation, dynamical density functional theory and phase-field crystal modelling. A vacancy is created by taking out a particle from an equilibrated crystal and the relaxation dynamics of the vacancy is followed by monitoring the time-dependent one-particle density. We find that the vacancy is quickly filled up by diffusive hopping of neighbouring particles towards the vacancy center. We examine the temperature dependence of the diffusion constant and find that it decreases with decreasing temperature in the simulations. This trend is reproduced by the dynamical density functional theory. Conversely, the phase field crystal calculations predict the opposite trend. Therefore, the phase-field model needs a temperature-dependent expression for the mobility to predict trends correctly.