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Disordered, quasicrystalline and crystalline phases of densely packed tetrahedra

Author

Listed:
  • Amir Haji-Akbari

    (Department of Chemical Engineering,)

  • Michael Engel

    (Department of Chemical Engineering,)

  • Aaron S. Keys

    (Department of Chemical Engineering,)

  • Xiaoyu Zheng

    (Department of Mathematical Sciences,)

  • Rolfe G. Petschek

    (Case Western Reserve University, Cleveland, Ohio 44106, USA)

  • Peter Palffy-Muhoray

    (Liquid Crystal Institute, Kent State University, Kent, Ohio 44242, USA)

  • Sharon C. Glotzer

    (Department of Chemical Engineering,
    University of Michigan, Ann Arbor, Michigan 48109, USA)

Abstract

A surprise package One of the simplest shapes for which the densest packing arrangement remains unresolved is the regular tetrahedron — despite much theoretical, computational and experimental effort. Using a novel approach involving thermodynamic computer simulations that allow the system to evolve naturally towards high-density states, Sharon Glotzer and colleagues have worked out the densest ordered packing yet for tetrahedra, a configuration with a packing fraction of 0.8324. Unexpectedly, the structure is a dodecagonal quasicrystal, the first example of a quasicrystal formed from hard particles or from non-spherical building blocks.

Suggested Citation

  • 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.
    • Handle: RePEc:nat:nature:v:462:y:2009:i:7274:d:10.1038_nature08641
    DOI: 10.1038/nature08641
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    Citations

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    Cited by:

    1. Jin, Yuliang & Makse, Hernán A., 2010. "A first-order phase transition defines the random close packing of hard spheres," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(23), pages 5362-5379.
    2. Zhihua Cheng & Matthew R. Jones, 2022. "Assembly of planar chiral superlattices from achiral building blocks," Nature Communications, Nature, vol. 13(1), pages 1-11, December.
    3. 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.
    4. Sangmin Lee & Sharon C. Glotzer, 2022. "Entropically engineered formation of fivefold and icosahedral twinned clusters of colloidal shapes," Nature Communications, Nature, vol. 13(1), pages 1-10, December.

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