Toward the Jamming Threshold of Sphere Packings: Tunneled Crystals

TL;DR

This paper introduces a new family of strictly jammed, low-density crystal sphere packings with tunnel-like vacancies, which are promising candidates for the jamming threshold and have broader implications in physics and materials science.

Contribution

The authors discover an uncountably infinite family of tunneled crystal packings that are strictly jammed and characterized by high vacancy concentration, expanding understanding of low-density rigid packings.

Findings

Existence of an uncountably infinite family of tunneled crystal packings.

These packings are strictly jammed and mechanically stable.

Potential relevance for achieving the jamming threshold and applications in materials science.

Abstract

We have discovered a new 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.