Klatt Michael A, Torquato Salvatore
Department of Chemistry, Department of Physics, Princeton University, Princeton, New Jersey 08544, USA and Friedrich-Alexander-Universität Erlangen-Nürnberg (FAU), Institut für Theoretische Physik, Staudtstraße 7, 91058 Erlangen, Germany.
Department of Chemistry, Department of Physics, Princeton Institute for the Science and Technology of Materials, and Program in Applied and Computational Mathematics, Princeton University, Princeton, New Jersey 08544, USA.
Phys Rev E Stat Nonlin Soft Matter Phys. 2014 Nov;90(5-1):052120. doi: 10.1103/PhysRevE.90.052120. Epub 2014 Nov 13.
We characterize the structure of maximally random jammed (MRJ) sphere packings by computing the Minkowski functionals (volume, surface area, and integrated mean curvature) of their associated Voronoi cells. The probability distribution functions of these functionals of Voronoi cells in MRJ sphere packings are qualitatively similar to those of an equilibrium hard-sphere liquid and partly even to the uncorrelated Poisson point process, implying that such local statistics are relatively structurally insensitive. This is not surprising because the Minkowski functionals of a single Voronoi cell incorporate only local information and are insensitive to global structural information. To improve upon this, we introduce descriptors that incorporate nonlocal information via the correlation functions of the Minkowski functionals of two cells at a given distance as well as certain cell-cell probability density functions. We evaluate these higher-order functions for our MRJ packings as well as equilibrium hard spheres and the Poisson point process. It is shown that these Minkowski correlation and density functions contain visibly more information than the corresponding standard pair-correlation functions. We find strong anticorrelations in the Voronoi volumes for the hyperuniform MRJ packings, consistent with previous findings for other pair correlations [A. Donev et al., Phys. Rev. Lett. 95, 090604 (2005)PRLTAO0031-900710.1103/PhysRevLett.95.090604], indicating that large-scale volume fluctuations are suppressed by accompanying large Voronoi cells with small cells, and vice versa. In contrast to the aforementioned local Voronoi statistics, the correlation functions of the Voronoi cells qualitatively distinguish the structure of MRJ sphere packings (prototypical glasses) from that of not only the Poisson point process but also the correlated equilibrium hard-sphere liquids. Moreover, while we did not find any perfect icosahedra (the locally densest possible structure in which a central sphere contacts 12 neighbors) in the MRJ packings, a preliminary Voronoi topology analysis indicates the presence of strongly distorted icosahedra.
我们通过计算最大随机堵塞（MRJ）球体堆积相关的Voronoi胞元的闵可夫斯基泛函（体积、表面积和积分平均曲率）来表征其结构。MRJ球体堆积中Voronoi胞元的这些泛函的概率分布函数在定性上与平衡硬球液体的相似，甚至部分与不相关的泊松点过程相似，这意味着这种局部统计在结构上相对不敏感。这并不奇怪，因为单个Voronoi胞元的闵可夫斯基泛函仅包含局部信息，对全局结构信息不敏感。为了改进这一点，我们引入了描述符，这些描述符通过给定距离处两个胞元的闵可夫斯基泛函的相关函数以及某些胞元 - 胞元概率密度函数来纳入非局部信息。我们对我们的MRJ堆积以及平衡硬球和泊松点过程评估这些高阶函数。结果表明，这些闵可夫斯基相关函数和密度函数比相应的标准对相关函数包含明显更多的信息。我们发现超均匀MRJ堆积的Voronoi体积中存在强烈的反相关，这与之前关于其他对相关的研究结果一致[A. Donev等人，《物理评论快报》95, 090604 (2005)PRLTAO0031 - 900710.1103/PhysRevLett.95.090604]，表明大规模体积波动通过大的Voronoi胞元与小胞元相伴而受到抑制，反之亦然。与上述局部Voronoi统计相反，Voronoi胞元的相关函数在定性上不仅将MRJ球体堆积（典型的玻璃态）的结构与泊松点过程区分开来，而且与相关的平衡硬球液体区分开来。此外，虽然我们在MRJ堆积中没有发现任何完美的二十面体（中心球体与12个邻居接触的局部最密结构），但初步的Voronoi拓扑分析表明存在严重扭曲的二十面体。
