Jammed Spheres: Minkowski Tensors Reveal Onset of Local Crystallinity

TL;DR

This study uses Minkowski tensors to identify a sharp transition to local crystallinity in jammed sphere packings at a critical density around 0.649, challenging previous estimates and highlighting limitations of traditional order metrics.

Contribution

It introduces Minkowski tensor-based metrics to accurately detect local crystallinity and reveals an abrupt transition at a higher packing fraction than previously reported.

Findings

Critical packing fraction   0.649 identified.

Abrupt increase in local crystalline configurations at .

Traditional q_6 metric produces false positives.

Abstract

The local structure of disordered jammed packings of monodisperse spheres without friction, generated by the Lubachevsky-Stillinger algorithm, is studied for packing fractions above and below 64%. The structural similarity of the particle environments to fcc or hcp crystalline packings (local crystallinity) is quantified by order metrics based on rank-four Minkowski tensors. We find a critical packing fraction \phi_c \approx 0.649, distinctly higher than previously reported values for the contested random close packing limit. At \phi_c, the probability of finding local crystalline configurations first becomes finite and, for larger packing fractions, increases by several orders of magnitude. This provides quantitative evidence of an abrupt onset of local crystallinity at \phi_c. We demonstrate that the identification of local crystallinity by the frequently used local bond-orientational order metric q_6 produces false positives, and thus conceals the abrupt onset of local crystallinity. Since the critical packing fraction is significantly above results from mean-field analysis of the mechanical contacts for frictionless spheres, it is suggested that dynamic arrest due to isostaticity and the alleged geometric phase transition in the Edwards framework may be disconnected phenomena.