Structural properties of dense hard spheres near random close packing

TL;DR

This study investigates the structural properties of dense hard sphere packings near the random close packing density, revealing a disorder-order transition and formation of crystalline and layered structures.

Contribution

It provides detailed structural analysis across a range of densities, identifying a phase transition at RCP and characterizing the evolution of local symmetries.

Findings

Disorder-order phase transition at $\,\phi_{c} \simeq 0.64$

Formation of 3D crystalline nuclei above RCP

Presence of icosahedral symmetry near RCP

Abstract

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.