Mode expansion for the density profile of crystal-fluid interfaces: Hard spheres as a test case

TL;DR

This paper introduces a mode expansion technique to analyze three-dimensional density profiles of crystal-fluid interfaces, providing a new way to connect microscopic density data with coarse-grained models.

Contribution

It develops a novel mode expansion method for density profiles and relates them to crystallinity order parameters used in phase field models.

Findings

Mode expansion effectively characterizes density profiles.

Connection established between microscopic densities and coarse-grained order parameters.

Application demonstrated on hard sphere system using density functional theory.

Abstract

We present a technique for analyzing the full three-dimensional density profiles of a planar crystal-fluid interface in terms of density modes. These density modes can also be related to crystallinity order parameter profiles which are used in coarse-grained, phase field type models of the statics and dynamics of crystal-fluid interfaces and are an alternative to crystallinity order parameters extracted from simulations using local crystallinity criteria. We illustrate our results for the hard sphere system using finely-resolved, three-dimensional density profiles from density functional theory of fundamental measure type.