Free-energy functional for freezing transitions: hard-sphere systems freezing into crystalline and amorphous structures

Abstract

A free-energy functional that contains both the symmetry-conserved and symmetry-broken parts of the direct pair correlation function has been used to investigate the freezing of a system of hard spheres into crystalline and amorphous structures. The freezing parameters for fluid-crystal transition have been found to be in very good agreement with the results found from simulations. We considered amorphous structures found from molecular dynamics simulations at packing fractions η lower than the glass close packing fraction η_J and investigated their stability compared to that of a homogeneous fluid. The existence of a free-energy minimum corresponding to a density distribution of overlapping Gaussians centered around an amorphous lattice depicts a deeply supercooled state with a heterogeneous density profile.