Unusually Dense Crystal Packings of Ellipsoids

Abstract

In this Letter, we report on the densest-known packings of congruent ellipsoids. The family of new packings consists of crystal arrangements of spheroids with a wide range of aspect ratios, and with density $\phi$ always surpassing that of the densest Bravais lattice packing $\phi \approx 0.7405$. A remarkable maximum density of $\varphi \approx 0.7707$ is achieved for maximal aspect ratios larger than $\sqrt{3}$, when each ellipsoid has 14 touching neighbors. Our results are directly relevant to understanding the equilibrium behavior of systems of hard ellipsoids, and, in particular, the solid and glassy phases.