Density Profiles and Direct Correlation Functions from Density Functional Theory in Binary Hard-Sphere Crystals: Substitutional Solid and Interstitial Solid Solution

TL;DR

This study uses density functional theory to analyze equilibrium density profiles and direct correlation functions in binary hard-sphere crystals, revealing distinct behaviors in substitutional and interstitial structures.

Contribution

It provides detailed density profiles and correlation functions for binary hard-sphere crystals, highlighting differences between substitutional and interstitial configurations.

Findings

Density profiles are similar to single-component case in substitutional crystals.

Interstitial solutions show delocalized small species within the unit cell.

Large-large correlation components scale with vacancy concentration as ~1/n_vac.

Abstract

We determine the fully resolved equilibrium density profiles for two binary hard-sphere crystal structures using classical density functional theory through the White Bear II functional from fundamental measure theory. While for the substitutional crystal, in which some hard spheres are replaced by spheres of slightly smaller diameter, the density profiles are rather similar to the single-component case (narrow Gaussian peaks centered at fcc lattice sites), we observe a more complex behavior for the case of interstitial solid solutions, where the small species is fairly delocalized in the unit cell. Further, we compute the species-resolved inhomogeneous two-body direct correlation functions for these two types of binary crystals. The large-large components are mainly determined by the vacancy concentration $n_\text{vac}$ and show a characteristic magnitude $~1/n_\text{vac}$. Based on this observation, we propose a simple geometric picture of this six-dimensional function. The components of the direct correlation function involving the small spheres substantially differ in interstitial solid solutions from those of the substitutional crystal.