Minkowski Tensors and Local Structure Metrics: Amorphous and Crystalline Sphere Packings
Minkowski Tensors and Local Structure Metrics: Amorphous and Crystalline Sphere Packings
复制标题
闵可夫斯基张量和局部结构度量：非晶球和晶球填料
DOI：
10.1063/1.4811939
复制
发表时间：
2013
影响因子：
8.6
通讯作者：
K. Mecke
中科院分区：
文献类型：
--
作者：
G. Schröder;Richard Schielein;S. Kapfer;F. Schaller;Geoff P. Delaney;T. Senden;M. Saadatfar;T. Aste;K. Mecke
表征局部结构的稳健而灵敏的工具对于颗粒或颗粒物质的研究至关重要。通常，从键网络导出的局部结构度量用于此目的，特别是斯坦哈特的键取向有序参数 ql 。在这里，我们讨论一种替代方法，该方法基于通过 Minkowski 张量和导出的各向异性测量对粒子 Voronoi 单元形状的稳健表征。我们已经成功地应用这些指标来量化随机球体包中的结构变化和结晶的开始。在这里，我们具体讨论了简单晶体单峰球体堆积的这些度量的期望值，这些球体由布拉维晶格点上的单个球体组成。这些数据为讨论通常与粒状系统相关的无序结构的各向异性值提供了重要参考。该分析表明，至少对于高于 φ > 0.61 的足够高的堆积分数，存在结晶球堆积，其 Voronoi 单元相对于体积矩张量的各向异性比随机球堆积中 Voronoi 单元各向异性的平均值更大。
Robust and sensitive tools to characterise local structure are essential for investigations of granular or particulate matter. Often local structure metrics derived from the bond network are used for this purpose, in particular Steinhardt's bond-orientational order parameters ql . Here we discuss an alternative method, based on the robust characterisation of the shape of the particles' Voronoi cells, by Minkowski tensors and derived anisotropy measures. We have successfully applied these metrics to quantify structural changes and the onset of crystallisation in random sphere packs. Here we specifically discuss the expectation values of these metrics for simple crystalline unimodal packings of spheres, consisting of single spheres on the points of a Bravais lattice. These data provide an important reference for the discussion of anisotropy values of disordered structures that are typically of relevance in granular systems. This analysis demonstrates that, at least for sufficiently high packing fractions above φ > 0.61, crystalline sphere packs exist whose Voronoi cells are more anisotropic with respect to a volumetric moment tensor than the average value of Voronoi cell anisotropy in random sphere packs.