Hyperuniformity Order Metric of Barlow Packings

The concept of hyperuniformity has been a useful tool in the study of large-scale density fluctuations 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 $\bar{\Lambda}$. 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 wavevector $K$. 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 $\bar{\Lambda}$ 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 $\bar{\Lambda}$ of all Barlow packings is primarily controlled by the local cluster geometry. These results indicate the special nature of anisotropic stacking disorder, which provides impetus for future research on the development of anisotropic order metrics and hyperuniformity properties.Comment: 13 pages, 7 figure

For the Jubilee of Vladimir Mikhailovich Chernov

On April 25, 2019, Vladimir Chernov celebrated his 70th birthday, Doctor of Physics and Mathematics, Chief Researcher at the Laboratory of Mathematical Methods of Image Processing of the Image Processing Systems Institute of the Russian Academy of Sciences (IPSI RAS), a branch of the Federal Science Research Center "Crystallography and Photonics RAS and part-Time Professor at the Department of Geoinformatics and Information Security of the Samara National Research University named after academician S.P. Korolev (Samara University). The article briefly describes the scientific and pedagogical achievements of the hero of the day. © Published under licence by IOP Publishing Ltd