Densest binary sphere packings

Adam B. Hopkins, Frank H. Stillinger, Salvatore Torquato

Research output: Contribution to journalArticlepeer-review

66 Scopus citations


The densest binary sphere packings in the α-x plane of small to large sphere radius ratio α and small sphere relative concentration x have historically been very difficult to determine. Previous research had led to the prediction that these packings were composed of a few known "alloy" phases including, for example, the AlB 2 (hexagonal ω), HgBr 2, and AuTe 2 structures, and to XY n structures composed of close-packed large spheres with small spheres (in a number ratio of n to 1) in the interstices, e.g., the NaCl packing for n=1. However, utilizing an implementation of the Torquato-Jiao sphere-packing algorithm, we have discovered that many more structures appear in the densest packings. For example, while all previously known densest structures were composed of spheres in small to large number ratios of one to one, two to one, and very recently three to one, we have identified densest structures with number ratios of seven to three and five to two. In a recent work, we summarized these findings. In this work, we present the structures of the densest-known packings and provide details about their characteristics. Our findings demonstrate that a broad array of different densest mechanically stable structures consisting of only two types of components can form without any consideration of attractive or anisotropic interactions. In addition, the structures that we have identified may correspond to currently unidentified stable phases of certain binary atomic and molecular systems, particularly at high temperatures and pressures.

Original languageEnglish (US)
Article number021130
JournalPhysical Review E - Statistical, Nonlinear, and Soft Matter Physics
Issue number2
StatePublished - Feb 22 2012

All Science Journal Classification (ASJC) codes

  • Condensed Matter Physics
  • Statistical and Nonlinear Physics
  • Statistics and Probability


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