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Jammed spheres: Minkowski tensors reveal onset of local crystallinity

Sebastian C. Kapfer1,*, Walter Mickel1,2,3,†, Klaus Mecke1,‡, and Gerd E. Schröder-Turk1,§

  • 1Institut für Theoretische Physik, Friedrich-Alexander-Universität Erlangen-Nürnberg, Staudtstraße 7, D-91058 Erlangen, Germany
  • 2Université de Lyon, F-69000 Lyon, France; CNRS, UMR5586, Laboratoire PMCN, Lyon, France
  • 3Karlsruhe Institute of Technology, Institut für Stochastik, Kaiserstraße 89, D-76128 Karlsruhe, Germany

  • *sebastian.kapfer@physik.uni-erlangen.de
  • †walter.mickel@physik.uni-erlangen.de
  • ‡klaus.mecke@physik.uni-erlangen.de
  • §gerd.schroeder-turk@physik.uni-erlangen.de
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Phys. Rev. E 85, 030301(R) – Published 6 March, 2012

DOI: https://doi.org/10.1103/PhysRevE.85.030301

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 φc≈0.649, distinctly higher than previously reported values for the contested random close packing limit. At φc, 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 φc. We demonstrate that the identification of local crystallinity by the frequently used local bond-orientational order metric q6 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.

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Phys. Rev. E 85, 030301(R)– Published 6 March, 2012
  • Received 11 August 2011

©2012 American Physical Society

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