Stable and metastable hard sphere crystals in Fundamental Measure Theory

TL;DR

This paper compares free energies and vacancy concentrations of bcc, fcc, and hcp hard-sphere crystals using fundamental measure theory and Stillinger's approach, revealing stability differences and potential phase instability mechanisms.

Contribution

It introduces a combined analysis using fundamental measure theory and Stillinger's expansion to study crystal stability and vacancy behavior in hard-sphere systems.

Findings

fcc/hcp and one bcc branch agree with Stillinger's n=2 approach

a second bcc branch shows high vacancy concentrations and possible shear instability

hcp is slightly more stable than fcc within the models, contrary to some simulations

Abstract

Using fully minimized fundamental measure functionals, we investigate free energies, vacancy concentrations and density distributions for bcc, fcc and hcp hard-sphere crystals. Results are complemented by an approach due to Stillinger which is based on expanding the crystal partition function in terms of the number n of free particles while the remaining particles are frozen at their ideal lattice positions. The free energies of fcc/hcp and one branch of bcc agree well with Stillinger's approach truncated at n=2. A second branch of bcc solutions features rather spread-out density distributions around lattice sites and large equilibrium vacancy concentrations and is presumably linked to the shear instability of the bcc phase. Within fundamental measure theory and the Stillinger approach (n=2), hcp is more stable than fcc by a free energy per particle of about 0.001 k_{B}T. In previous simulation work, the reverse situation has been found which can be rationalized in terms of effects due to a correlated motion of at least 5 particles in the Stillinger picture.