# Densest binary sphere packings

## Author(s): Hopkins, Adam B.; Stillinger, Frank H.; Torquato, Salvatore

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 Abstract: ©2012 American Physical Society. 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 AlB2 (hexagonal ω), HgBr2, and AuTe2 structures, and to XYn structures composed of close-packed large spheres with small spheres (in a number ratio of nto 1) in the interstices, e.g., the NaCl packing for n=1. However, utilizing an implementation of the Torquato-Jiao sphere-packing algorithm [Torquato and Jiao, Phys. Rev. E 82, 061302 (2010)], 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 [Hopkins et al., Phys. Rev. Lett. 107, 125501 (2011)], 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. Publication Date: Feb-2012 Electronic Publication Date: 22-Feb-2012 Citation: Hopkins, Adam B., Stillinger, Frank H., Torquato, Salvatore. (2012). Densest binary sphere packings. Physical Review E, 85 (2), 10.1103/PhysRevE.85.021130 DOI: doi:10.1103/PhysRevE.85.021130 ISSN: 1539-3755 EISSN: 1550-2376 Pages: 021130-1 - 021130-19 Type of Material: Journal Article Journal/Proceeding Title: Physical Review E Version: Final published version. Article is made available in OAR by the publisher's permission or policy.