Disordered, quasicrystalline and crystalline phases of densely packed tetrahedra

Engel M, Haji-Akbari A, Keys AS, Zheng X, Petschek RG, Palffy-Muhoray P, Glotzer SC (2009)

Publication Language: English

Publication Status: Published

Publication Type: Journal article, Original article

Publication year: 2009

Journal

Nature Nature Publishing Group

Publisher: Nature Publishing Group

Book Volume: 462

Pages Range: 773-U91

Journal Issue: 7274

DOI: 10.1038/nature08641

Abstract

All hard, convex shapes are conjectured by Ulam to pack more densely than spheres(1), which have a maximum packing fraction of phi = pi/root 18 approximate to 0.7405. Simple lattice packings of many shapes easily surpass this packing fraction(2,3). For regular tetrahedra, this conjecture was shown to be true only very recently; an ordered arrangement was obtained via geometric construction with phi = 0.7786 (ref. 4), which was subsequently compressed numerically to phi = 0.7820 (ref. 5), while compressing with different initial conditions led to phi = 0.8230 ( ref. 6). Here we show that tetrahedra pack even more densely, and in a completely unexpected way. Following a conceptually different approach, using thermodynamic computer simulations that allow the system to evolve naturally towards high-density states, we observe that a fluid of hard tetrahedra undergoes a first-order phase transition to a dodecagonal quasicrystal(7-10), which can be compressed to a packing fraction of phi = 0.8324. By compressing a crystalline approximant of the quasicrystal, the highest packing fraction we obtain is phi = 0.8503. If quasicrystal formation is suppressed, the system remains disordered, jams and compresses to phi = 0.7858. Jamming and crystallization are both preceded by an entropy-driven transition from a simple fluid of independent tetrahedra to a complex fluid characterized by tetrahedra arranged in densely packed local motifs of pentagonal dipyramids that form a percolating network at the transition. The quasicrystal that we report represents the first example of a quasicrystal formed from hard or non-spherical particles. Our results demonstrate that particle shape and entropy can produce highly complex, ordered structures.

Authors with CRIS profile

Michael Engel Lehrstuhl für Multiscale Simulation of Particulate Systems

Involved external institutions

University of Michigan US United States (USA) (US) Case Western Reserve University US United States (USA) (US)

How to cite

APA:

Engel, M., Haji-Akbari, A., Keys, A.S., Zheng, X., Petschek, R.G., Palffy-Muhoray, P., & Glotzer, S.C. (2009). Disordered, quasicrystalline and crystalline phases of densely packed tetrahedra. Nature, 462(7274), 773-U91. https://dx.doi.org/10.1038/nature08641

MLA:

Engel, Michael, et al. "Disordered, quasicrystalline and crystalline phases of densely packed tetrahedra." Nature 462.7274 (2009): 773-U91.

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