(392d) Nature of the Instability of the Body-Centered-Cubic (bcc) Structure in Classical Hard Sphere Solids

The body-centered cubic (bcc) solid phase of hard spheres is known to be mechanically unstable and also less thermodynamically stable than the face-centered cubic (fcc) and hexagonal close packed (hcp) solids. Yet interest in the bcc hard sphere solid remains, especially in relation to the development of perturbation theories for bcc solids of other model potentials. We employed Monte Carlo simulation in the canonical ensemble, with and without single occupancy cell (SOC) constraints, to explore the nature of the instability in the bcc structure of hard spheres. Starting from a perfect bcc lattice, we observed that the system rapidly evolved into one of four distorted structures, which we named bcc-di with i ranging from 0 to 3, which then persisted for the duration of the simulation. These different structures appeared over a range of densities and were characterized by patterns in the radial distribution function and bond order parameter distribution. The bcc-di were formed by small, well-defined average displacements of the particle centers away from the bcc lattice sites, but none of them comprises a repeating crystalline lattice. None of the traditionally employed SOC constraints, e.g. Wigner-Seitz, octahedral, or spherical, was sufficient to prevent the bcc structure from distorting into one of the bcc-di. Finally, we also ran constant-pressure simulations with box shape fluctuations and observed that the bcc solids evolved into defective fcc structures, passing through one of the bcc-distructures as an intermediate. We conclude that the perfect bcc hard sphere solid is a highly unstable structure surrounded by a set of metastable distorted, noncrystalline structures, and thus is unsuitable for use as a reference system for bcc solids of other interaction potentials.