CAVITIES IN THE HARD-SPHERE CRYSTAL AND FLUID

The number, size, surface area and shape of cavities in the hard-sphere crystal and dense fluid were studied by simulation. The number n(c) of cavities per sphere is given over about 60 orders of magnitude by -ln{n(c)} = pV/NkT - 1 + F(z) with F(z) almost-equal-to 0.6 + ln {z} in the crystal and F(z) almost-equal-to -2.5 in the dense fluid. The average cavity volume [v] is given by ln[v] = DELTAS/Nk - ln{N/V} + F(z), where DELTAS is the entropy relative to an ideal gas. z is the density relative to close packing. The equilibrium number of vacancies per sphere in the crystal is n, = n(c)/(1.2z - 0.45). The cavity shape factor a(z), defined by pV/NkT = 1 + a(z)/[v]1/3, is close to the sphere diameter sigma. The assumption that a(z) almost-equal-to sigma predicts the measured values of [v], [s] and n(c), for the crystal, to within their uncertainties.