Structural properties of dense hard sphere packings

TL;DR

This paper investigates the structural properties of dense random packings of identical hard spheres, introducing a new order parameter to characterize crystallization and analyzing how local structures evolve with increasing packing density.

Contribution

A novel order parameter based on the $w_6$ invariant is proposed to better characterize crystallization in dense hard sphere packings.

Findings

Crystallization leads to the formation of crystalline clusters and eventually a global 3D structure.

Further densification results in layered structures with different lattice types.

The bond order parameter method reveals detailed local structural changes with packing density.

Abstract

The structural properties of dense random packings of identical hard spheres (HS) are investigated. The bond order parameter method is used to obtain detailed information on the local structural properties of the system for different packing fractions $\phi$, in the range between $\phi=0.53$ and $\phi=0.72$. A new order parameter, based on the cumulative properties of spheres distribution over the rotational invariant $w_6$, is proposed to characterize crystallization of randomly packed HS systems. It is shown that an increase in the packing fraction of the crystallized HS system first results in the transformation of the individual crystalline clusters into the global three-dimensional crystalline structure, which, upon further densification, transforms into alternating planar layers formed by different lattice types.