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 0.46<η<0.68 (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. © 1995 The American Physical Society.