Weighted-density-functional theory calculation of elastic constants for face-centered-cubic and body-centered-cubic hard-sphere crystals

The isothermal elastic constants for the face-centered-cubic (fcc) and body-centered-cubic (bcc) hard-sphere crystal are calculated for a range of densities using the modified weighted-density functional of Denton and Ashcroft [Phys. Rev. A 39, 4701 (1989)]. The fcc elastic constants are shown to be in excellent agreement with the computer simulation data and to represent a significant improvement over the predictions of other density-functional methods. The bcc crystal is predicted correctly to be unstable to shear, in agreement with simulation. This fact supports the conclusion that the bcc hard-sphere solid, even though mechanically unstable, is well described by such methods.