(490h) A Classical Density-Functional Theory Study of the Body-Centered-Cubic and cI16 Solid Phases of Hard Spheres

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) phase, yet there is still interest in the bcc hard sphere solid, especially in relation to the development of perturbation theories for bcc solids of other model potentials. Previous density-functional theory (DFT) calculations of the structural and thermodynamic properties of the bcc phase, utilizing the most accurate functionals for hard spheres, have yielded unphysical results. In a recent Monte Carlo (MC) simulation study, we observed that hard spheres initially arranged in a perfect bcc lattice very rapidly transitioned to one of three disordered structures or the crystalline cI16 structure. The latter is a cubic lattice with a 16-site unit cell that can be mathematically represented, through a single scalar parameter x, as a coherent perturbation of the sites in a 2x2x2 bcc supercell. While the cI16 structure has been observed experimentally for sodium and lithium under high pressures, it is remarkable that a structure with such a large number of atoms per unit cell shows a high degree of mechanical stability for the simple hard sphere potential. In the present study, we revisited the DFT of the bcc hard-sphere solid by allowing for a bcc-to-cI16 transition. More specifically, we included x as a free parameter when minimizing the free energy density functional based on the fundamental measure theory. We found that cI16 (x>0) structures had lower free energy than bcc (x=0) structures at all dimensionless densities above 1.0, and the magnitude of x increased with density up to the close-packing limit, where it was about 3% of the cI16 unit cell side length. For cI16 there were no unphysical trends in the thermodynamic and structural property predictions from DFT, as were seen for bcc, and the results were in excellent agreement with corresponding values from our MC simulations.