Description of hard sphere crystals and crystal-fluid interfaces: a critical comparison between density functional approaches and a phase field crystal model

TL;DR

This paper compares density functional theory and phase field crystal models in describing hard sphere crystals and interfaces, analyzing their accuracy and applicability through theoretical approximations and simulation comparisons.

Contribution

It provides a systematic derivation of phase field crystal models from density functional theory and evaluates their limits using hard sphere systems.

Findings

Density functional theory accurately predicts coexistence densities.

Phase field crystal models can be fitted to match interfacial properties.

Comparison reveals strengths and limitations of each modeling approach.

Abstract

In materials science the phase field crystal approach has become popular to model crystallization processes. Phase field crystal models are in essence Landau-Ginzburg-type models, which should be derivable from the underlying microscopic description of the system in question. We present a study on classical density functional theory in three stages of approximation leading to a specific phase field crystal model, and we discuss the limits of applicability of the models that result from these approximations. As a test system we have chosen the three--dimensional suspension of monodisperse hard spheres. The levels of density functional theory that we discuss are fundamental measure theory, a second-order Taylor expansion thereof, and a minimal phase-field crystal model. We have computed coexistence densities, vacancy concentrations in the crystalline phase, interfacial tensions and interfacial order parameter profiles, and we compare these quantities to simulation results. We also suggest a procedure to fit the free parameters of the phase field crystal model.