Dense crystalline packings of ellipsoids

Weiwei Jin, Yang Jiao, Lufeng Liu, Ye Yuan, Shuixiang Li

Research output: Contribution to journalArticlepeer-review

14 Scopus citations


An ellipsoid, the simplest nonspherical shape, has been extensively used as a model for elongated building blocks for a wide spectrum of molecular, colloidal, and granular systems. Yet the densest packing of congruent hard ellipsoids, which is intimately related to the high-density phase of many condensed matter systems, is still an open problem. We discover an unusual family of dense crystalline packings of self-dual ellipsoids (ratios of the semiaxes α:α:1), containing 24 particles with a quasi-square-triangular (SQ-TR) tiling arrangement in the fundamental cell. The associated packing density φ exceeds that of the densest known SM2 crystal [A. Donev, Phys. Rev. Lett. 92, 255506 (2004)10.1103/PhysRevLett.92.255506] for aspect ratios α in (1.365, 1.5625), attaining a maximal φ≈0.75806... at α=93/64. We show that the SQ-TR phase derived from these dense packings is thermodynamically stable at high densities over the aforementioned α range and report a phase diagram for self-dual ellipsoids. The discovery of the SQ-TR crystal suggests organizing principles for nonspherical particles and self-assembly of colloidal systems.

Original languageEnglish (US)
Article number033003
JournalPhysical Review E
Issue number3
StatePublished - Mar 22 2017

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Statistics and Probability
  • Condensed Matter Physics


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