Aste T, Saadatfar M, Senden T J
Department of Applied Mathematics, Research School of Physical Sciences and Engineering, The Australian National University, Canberra ACT 0200, Australia.
Phys Rev E Stat Nonlin Soft Matter Phys. 2005 Jun;71(6 Pt 1):061302. doi: 10.1103/PhysRevE.71.061302. Epub 2005 Jun 20.
The three-dimensional structure of large packings of monosized spheres with volume fractions ranging between 0.58 and 0.64 has been studied with x-ray computed tomography. We search for signatures of organization, classifying local arrangements and exploring the effects of local geometrical constrains on the global packing. This study is the largest and the most accurate empirical analysis of disordered packings at the grain-scale to date, mapping over 380,000 sphere coordinates with precision within 0.1% of the sphere diameters. We discuss topological and geometrical methods to characterize and classify these systems emphasizing the implications that local geometry can have on the mechanisms of formation of these amorphous structures. Some of the main results are (1) the observation that the average number of contacts increases with the volume fraction; (2) the discovery that these systems have a very compact contact network; (3) the finding that disordered packing can be locally more efficient than crystalline packings; (4) the observation that the peaks of the radial distribution function follow power law divergences; (5) the discovery that geometrical frustration plays no role in the formation of such amorphous packings.
利用X射线计算机断层扫描技术研究了体积分数在0.58至0.64之间的单尺寸球体大堆积的三维结构。我们寻找组织特征，对局部排列进行分类，并探索局部几何约束对整体堆积的影响。这项研究是迄今为止在晶粒尺度上对无序堆积进行的规模最大、最精确的实证分析，精确绘制了超过380,000个球体坐标，精度在球体直径的0.1%以内。我们讨论了表征和分类这些系统的拓扑和几何方法，强调了局部几何对这些无定形结构形成机制的影响。一些主要结果包括：（1）观察到平均接触数随体积分数增加；（2）发现这些系统具有非常紧密的接触网络；（3）发现无序堆积在局部可能比晶体堆积更有效；（4）观察到径向分布函数的峰值遵循幂律发散；（5）发现几何挫折在这种无定形堆积的形成中不起作用。
