Dense crystalline packings of ellipsoids

An ellipsoid, the simplest non-spherical shape, has been extensively used as models 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 a novel dense crystalline packing of ellipsoids containing 24 particles with a quasi-square-triangular (SQ-TR) tiling arrangement, whose packing density {\phi} exceeds that of the SM2 crystal for aspect ratios {\alpha} in (1.365, 1.5625), attaining a maximal {\phi} about 0.75806 at {\alpha} = 93/64. We show that SQ-TR phase is thermodynamically stable at high densities over the aforementioned {\alpha} range and report a novel phase diagram for self-dual ellipsoids. The discovery of SQ-TR crystal suggests novel organizing principles for non-spherical particles and self-assembly of colloidal systems.