Path-integral Monte Carlo study of the structural and mechanical properties of quantum fcc and bcc hard-sphere solids

Abstract

Path-integral Monte Carlo simulations involving the Cao–Berne’s hard-sphere propagator and aimed at exploring the high-density region (ρ*=0.8, 0.9) of the quantum hard-sphere (QHS) system are reported. By starting from single cubic (sc), body-centered cubic (bcc), and face-centered cubic (fcc) lattices, the following range of temperatures defined by the reduced de Broglie’s wavelengths 0.116⩽λB*⩽0.5 is studied. The r-space structural quantities computed are pair radial correlation functions (instantaneous, linear response, and necklace center of mass) and necklace radii of gyration. In addition, the following quantities related to the necklace centers of mass are calculated: maximal structure factor values, Steinhardt et al.’s orientational order parameters, and Lindemann’s index. The thermodynamic properties evaluated are energies and pressures. Comparison with Scheraga et al.’s results available in the literature [J. Chem. Phys. 96, 7005 (1992)] is made wherever possible. As shown, only the fcc lattice maintains its features under the strong QHS repulsions, whereas bcc and sc cannot cope with these effects transforming into striking partially crystalline [bcc(q)] and fluid phases, respectively. Conclusions on the features of the resulting phases which can help to explain the stages of the partial crystallization of the QHS fluid are also drawn.