Abstract

The equilibrium pressure in a crystal composed of hard spheres or disks may be determined from the statistical geometry of a single isolated monocavity (one large enough for addition of only one particle). Additional knowledge of the equilibrium concentration of monocavities permits evaluation of the chemical potential and absolute entropy. We have used Monte Carlo simulation to examine isolated monocavities in the rigid-disk crystal near close packing. The resulting pressures compare very favorably with those from previous simulations, and with asymptotic high-compression equations of state. The monocavities exhibit fluctuating polygonal shapes; the number of sides varies from three to six, with four the most probable occurrence.