Salvatore Torquato
Department of Chemistry, Princeton University, Princeton, New Jersey 08544, USA, Program in Applied and Computational Mathematics, Princeton University, Princeton, New Jersey 08544, USA, Princeton Institute for the Science and Technology of Materials, Princeton University, Princeton, New Jersey 08544, USA, and Princeton Center for Theoretical Physics, Princeton University, Princeton, New Jersey 08544, USA

Frank H. Stillinger
Department of Chemistry, Princeton University, Princeton, New Jersey 08544, USA

J. Appl. Phys. 102, 093511 (2007).

Received 28 July 2007; accepted 6 September 2007; published 6 November 2007.

Abstract

We have discovered a family of three-dimensional crystal sphere packings that are strictly jammed (i.e., mechanically stable) and yet possess an anomalously low density. This family constitutes an uncountably infinite number of crystal packings that are subpackings of the densest crystal packings and are characterized by a high concentration of self-avoiding "tunnels" (chains of vacancies) that permeate the structures. The fundamental geometric characteristics of these tunneled crystals command interest in their own right and are described here in some detail. These include the lattice vectors (that specify the packing configurations), coordination structure, Voronoi cells, and density fluctuations. The tunneled crystals are not only candidate structures for achieving the jamming threshold (lowest-density rigid packing), but may have substantially broader significance for condensed matter physics and materials science.