The liquid–solid transition of the hard sphere system from uniformity of the chemical potential

Abstract

The search for solidlike singlet distribution functions in a system of hard spheres is undertaken. The analysis is based on the potential-distribution theory for nonuniform fluids. The ensuing requirement of constancy of the chemical potential throughout the system leads to a nonlinear integro-difference equation for the singlet density which is exact in one dimension. Bifurcations from its uniform solution, occurring before close packing and of an oscillatory nature, are found for both hard disks and hard spheres, but not for hard rods. The branching solution for hard spheres has the symmetry of a hexagonal close packing lattice, whereas that for hard disks is triangular. An investigation is also made of the stability of the fluid states. It is found that fluid instabilities and bifurcation points appear simultaneously.