On the coarse-grained density and compressibility of non-ideal crystals: general theory and an application to cluster crystals

TL;DR

This paper develops a general theoretical framework using classical density functional theory to analyze the density and compressibility of non-ideal, defect-rich crystals, with a focus on cluster crystals with multiple site occupancy.

Contribution

It introduces a coarse-grained approach to connect microscopic density correlations with macroscopic elastic and thermodynamic properties, specifically applied to cluster crystals.

Findings

The long wavelength limit of microscopic density correlation differs from the isothermal compressibility.

The theory reveals that static structure factors do not directly give compressibility in these systems.

Cluster crystals exhibit strong local disorder and unique fluctuation behaviors.

Abstract

The isothermal compressibility of a general crystal is analyzed within classical density functional theory. Our approach can be used for homogeneous and unstrained crystals containing an arbitrarily high density of local defects. We start by coarse-graining the microscopic particle density and then obtain the long wavelength limits of the correlation functions of elasticity theory and the thermodynamic derivatives. We explicitly show that the long wavelength limit of the microscopic density correlation function differs from the isothermal compressibility. It also cannot be obtained from the static structure factor measured in a scattering experiment. We apply our theory to crystals consisting of soft particles which can multiply occupy lattice sites ('cluster crystals'). The multiple occupancy results in a strong local disorder over an extended range of temperatures. We determine the cluster crystals' isothermal compressibility, the fluctuations of the lattice occupation numbers and their correlation functions, and the dispersion relations. We also discuss their low-temperature phase diagram.