Structural properties of dense hard spheres near random close packing

We numerically study structural properties of mechanically stable packings of hard spheres (HS), in a wide range of packing fractions $0.53 \le \phi \le 0.72$. Detailed structural information is obtained from the analysis of orientational order parameters, which clearly reveals a disorder-order phase transition at the random close packing (RCP) density, $\phi_{\rm c} \simeq 0.64$. Above $\phi_{\rm c}$ the crystalline nuclei form 3D-like clusters, which upon further desification, transform into alternating planar-like layers. We also find that particles with icosahedral symmetry survive only in a narrow density range in the vicinity of the RCP transition.