Dense crystalline packings of ellipsoids

Weiwei Jin, Yang Jiao, Lufeng Liu, Ye Yuan, and Shuixiang Li
Phys. Rev. E 95, 033003 – Published 22 March 2017
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Abstract

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 et al., Phys. Rev. Lett. 92, 255506 (2004)] for aspect ratios α in (1.365, 1.5625), attaining a maximal ϕ0.75806... 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.

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  • Received 21 October 2016
  • Revised 2 March 2017

DOI:https://doi.org/10.1103/PhysRevE.95.033003

©2017 American Physical Society

Physics Subject Headings (PhySH)

Statistical Physics & ThermodynamicsCondensed Matter, Materials & Applied PhysicsPolymers & Soft Matter

Authors & Affiliations

Weiwei Jin1, Yang Jiao2, Lufeng Liu1, Ye Yuan1, and Shuixiang Li1,*

  • 1Department of Mechanics and Engineering Science, Peking University, Beijing 100871, China
  • 2Materials Science and Engineering, Arizona State University, Tempe, Arizona 85287, USA

  • *Corresponding author: lsx@pku.edu.cn

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Issue

Vol. 95, Iss. 3 — March 2017

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