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Order metrics and order maps of octahedron packings

Author

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  • Liu, Lufeng
  • Lu, Peng
  • Meng, Lingyi
  • Jin, Weiwei
  • Li, Shuixiang

Abstract

We apply the ideal octahedron model and the relaxation algorithm in generating octahedron packings. The cubatic order parameter [P4]1, bond-orientational order metric Q6, and local cubatic order parameter P4local of the packings are calculated and their correlations with the packing density are investigated in the order maps. The border curve of packing density separates the geometrically feasible and infeasible regions in the order maps. Observing the transition phenomenon on the border curve, we propose the concept of the maximally dense random packing (MDRP) as the densest packing in the random state in which the particle positions and orientations are randomly distributed and there is no nontrivial spatial correlations among particles. The MDRP characterizes the onset of nontrivial spatial correlations among particles. A special packing with a density about 0.7 is found in the order maps and considered to be the MDRP of octahedra. The P4local is proposed as a new order parameter for octahedron packings, which measures the average order degree in the neighborhoods of particles. The [P4]1, Q6 and P4local evaluate the order degree of orientation, bond orientation and local structures, respectively and are applied simultaneously to measure the order degree of the octahedron packings. Their thresholds in the random state are determined by Monte Carlo simulations.

Suggested Citation

  • Liu, Lufeng & Lu, Peng & Meng, Lingyi & Jin, Weiwei & Li, Shuixiang, 2016. "Order metrics and order maps of octahedron packings," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 444(C), pages 870-882.
    • Handle: RePEc:eee:phsmap:v:444:y:2016:i:c:p:870-882
    DOI: 10.1016/j.physa.2015.10.101
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    References listed on IDEAS

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    1. S. Torquato & Y. Jiao, 2009. "Dense packings of the Platonic and Archimedean solids," Nature, Nature, vol. 460(7257), pages 876-879, August.
    2. Amir Haji-Akbari & Michael Engel & Aaron S. Keys & Xiaoyu Zheng & Rolfe G. Petschek & Peter Palffy-Muhoray & Sharon C. Glotzer, 2009. "Disordered, quasicrystalline and crystalline phases of densely packed tetrahedra," Nature, Nature, vol. 462(7274), pages 773-777, December.
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    Cited by:

    1. Yuan, Ye & Jin, Weiwei & Liu, Lufeng & Li, Shuixiang, 2016. "Two typical structure patterns in jammed monodisperse disk packings at high densities," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 461(C), pages 747-755.

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