Free-energy functional for freezing transitions: Hard sphere systems   freezing into crystalline and amorphous structures
  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 the molecular dynamics simulations at packing fractions $\eta$ lower than the glass close packing fraction $\eta_{J}$ and investigated their stability compared to that of a homogeneous fluid. The existence of free-energy minimum corresponding to a density distribution of overlapping Gaussians centered around an amorphous lattice depicts the deeply supercooled state with a heterogeneous density profile. 
Swarn Lata Singh, Atul S. Bharadwaj and Yashwant Singh
cond-mat.soft