Density-functional approach to the equation of state of a hard-sphere crystal

The equation of state (pressure) of a hard-sphere fcc crystal is computed by means of a classical density-functional theory based on the modified weighted-density approximation and a simple Gaussian approximation for the density distribution. Predictions for the total pressure compare favorably with computer simulation data for packing fractions throughout the range 0.460.68 (i.e., from just below to well above the fluid-solid transition). The ideal-gas and excess contributions are computed individually and found to exhibit physically interesting variations with packing fraction. In particular, whereas the ideal-gas pressure is always positive and generally makes the largest contribution, the excess pressure is relatively small and, for {η}0.63, negative in sign, implying an effective attraction between neighboring hard spheres. Preliminary analysis of available simulation data for mean-square atomic displacements lends support to these predictions. Implications for a recently proposed heuristic model of hard-sphere crystal pressures are also discussed.