Path integral Monte Carlo study of quantum-hard sphere solids

A path integral study of the fcc, hcp, and bcc quantum hard-sphere solids is presented. Ranges of densities within the interval of reduced de Broglie wavelengths 0.2≤λB(*)≤0.8 have been analyzed using Monte Carlo simulations with Cao-Berne propagator. Energies, pressures, and structural quantities (pair radial correlation functions, centroid structure factors, and Steinhardt order parameters) have been computed. Also, applications of the Einstein crystal technique [L. M. Sesé, J. Chem. Phys. 126, 164508 (2007)] have been made to compute the free energies of the fcc and hcp solids. Some technical points related to the latter technique are discussed, and it is shown that these calculations produce consistent results with increasing sample sizes. The fluid-solid (fcc and hcp) equilibria have been studied, thus completing prior work by this author on the fluid-fcc equilibrium. Within the accuracy attained no significant differences between the relative stabilities of the fcc and hcp lattices have been detected. The bcc case stands apart from the other two lattices, as the simulations lead either to irregular lattices (two types) that keep some traces of bcc-memory, or to spontaneous transitions to hcp-like lattices. The latter transitions make manifestly clear the potential repercussions that the quantum hard-sphere behavior can have on solid-solid equilibria at low temperatures in real systems (e.g., helium).