A Monte Carlo study of the freezing transition of hard spheres

Abstract

A simulation method for fluid–solid transitions, which is based on a modification of theconstrained cell model of Hoover and Ree, is developed and tested on a system of hardspheres. In the fully occupied constrained cell model, each particle is confined in its ownWigner–Seitz cell. Constant-pressure simulations of the constrained cell model for asystem of hard spheres indicate a point of mechanical instability at a densitywhich is about 64% of the density at the close packed limit. Below that point, thesolid is mechanically unstable since without the confinement imposed by thecell walls it will disintegrate to a disordered, fluid-like phase. Hoover and Reeproposed a modified cell model by introducing an external field of variable strength.High values of the external field variable favor configurations with one particleper cell and thus stabilize the solid phase. In this work, the modified cell modelof a hard-sphere system is simulated under constant-pressure conditions usingtempering and histogram reweighting techniques. The simulations indicate that as thestrength of the field is reduced, the transition from the solid to the fluid phaseis continuous below the mechanical instability point and discontinuous above.The fluid–solid transition of the hard-sphere system is determined by analyzingthe field-induced fluid–solid transition of the modified cell model in the limitin which the external field vanishes. The coexistence pressure and densities areobtained through finite-size scaling techniques and are in good accord with previousestimates.