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Hyperuniformity order metric of Barlow packings.

Author(s): Middlemas, T. M.; Stillinger, Frank H.; Torquato, Salvatore

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Abstract: The concept of hyperuniformity has been a useful tool in the study of density fluctuations at large length scales in systems ranging across the natural and mathematical sciences. One can rank a large class of hyperuniform systems by their ability to suppress long-range density fluctuations through the use of a hyperuniformity order metric Λ[over ¯]. We apply this order metric to the Barlow packings, which are the infinitely degenerate densest packings of identical rigid spheres that are distinguished by their stacking geometries and include the commonly known fcc lattice and hcp crystal. The "stealthy stacking" theorem implies that these packings are all stealthy hyperuniform, a strong type of hyperuniformity, which involves the suppression of scattering up to a wave vector K. We describe the geometry of three classes of Barlow packings, two disordered classes and small-period packings. In addition, we compute a lower bound on K for all Barlow packings. We compute Λ[over ¯] for the aforementioned three classes of Barlow packings and find that, to a very good approximation, it is linear in the fraction of fcc-like clusters, taking values between those of least-ordered hcp and most-ordered fcc. This implies that the value of Λ[over ¯] of all Barlow packings is primarily controlled by the local cluster geometry. These results highlight the special nature of anisotropic stacking disorder, which provides impetus for future research on the development of anisotropic order metrics and hyperuniformity properties.
Publication Date: 11-Feb-2019
Citation: Middlemas, T. M., Stillinger, F. H., Torquato, S. (2019). Hyperuniformity order metric of Barlow packings.. Physical review. E, 99 (2-1), 022111 - ?. doi:10.1103/physreve.99.022111
DOI: doi:10.1103/physreve.99.022111
ISSN: 2470-0045
EISSN: 2470-0053
Pages: 99, 022111-1 - 022111-11
Language: eng
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.

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