Validity of compressibility equation and Kirkwood-Buff theory in crystalline matter

TL;DR

This paper extends Kirkwood-Buff theory to crystalline solids by resolving divergence issues using finite-volume methods, demonstrating the validity of the compressibility equation in harmonic crystals at finite temperature.

Contribution

It introduces a finite-volume approach to apply KBI theory to crystals and derives an analytic peak shape for harmonic interactions, confirming the compressibility equation's validity.

Findings

KBI theory can be generalized to crystals using finite-volume methods.

The compressibility equation holds exactly in harmonic crystals.

An analytic expression for the pair-distribution function peak shape is derived.

Abstract

Volume integrals over the radial pair-distribution function, so-called Kirkwood-Buff integrals (KBI) play a central role in the theory of solutions, by linking structural with thermodynamic information. The simplest example is the compressibility equation, a fundamental relation in statistical mechanics of fluids. Until now, KBI theory could not be applied to crystals, because the integrals strongly diverge when computed in the standard way. We solve the divergence problem and generalize KBI theory to crystalline matter by using the recently proposed finite-volume theory. For crystals with harmonic interaction, we derive an analytic expression for the peak shape of the pair-distribution function at finite temperature. From this we demonstrate that the compressibility equation holds exactly in harmonic crystals.