TY - JOUR
T1 - Dense crystalline packings of ellipsoids
AU - Jin, Weiwei
AU - Jiao, Yang
AU - Liu, Lufeng
AU - Yuan, Ye
AU - Li, Shuixiang
N1 - Publisher Copyright:
© 2017 American Physical Society.
PY - 2017/3/22
Y1 - 2017/3/22
N2 - 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.
AB - 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.
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U2 - 10.1103/PhysRevE.95.033003
DO - 10.1103/PhysRevE.95.033003
M3 - Article
C2 - 28415357
AN - SCOPUS:85016459051
SN - 2470-0045
VL - 95
JO - Physical Review E
JF - Physical Review E
IS - 3
M1 - 033003
ER -