A comparative study was made of the free energies and density distributions, in hard-sphere crystals, using Monte Carlo simulations and density functional theory (with fundamental measure functionals). Using the recently introduced technique of Schilling and Schmid (2009), crystal free-energies were obtained to high precision. The free energies from fundamental measure theory were in good agreement with the simulation results and demonstrated the applicability of these functionals to the treatment of other problems involving crystallization. The agreement between fundamental measure theory and simulations on the level of the free energies was also reflected in the density distributions around single lattice sites. Overall, the peak widths and anisotropy signs for different lattice directions agree, however, it was found that fundamental measure theory gave slightly narrower peaks with more anisotropy than seen in the simulations. Among the three types of fundamental measure functionals studied, only the White Bear II functional of Hansen-Goos and Roth (2006) exhibited sensible results for the equilibrium vacancy concentration and a physical behaviour of the chemical potential in crystals constrained by a fixed vacancy concentration.

Free Energies, Vacancy Concentrations, and Density Distribution Anisotropies in Hard-Sphere Crystals: a Combined Density Functional and Simulation Study. M.Oettel, S.Görig, A.Härtel, H.Löwen, M.Radu, T.Schilling: Physical Review E, 2010, 82[5], 051404