论文标题
硬球的泄漏细胞模型
Leaky Cell Model of Hard Spheres
论文作者
论文摘要
我们研究晶格上硬球的包装。分区函数以及因此压力可以仅根据可访问的自由音量（即球体可以探索的空间量而无需接触另一个球体）编写。我们使用泄漏的单元模型计算这些自由体积，在该模型中，可访问的空间解释了球体可能从格子邻居的局部笼子中逃脱的可能性。我们描述了如何使用基本几何形状来计算二维晶格包装中的这种泄漏细胞模型的自由体积，并将结果与众所周知的Carnahan-Starling和Percus-Yevick液体模型进行比较。我们为各种晶格的自由体积提供公式，并使用常见的切线结构来识别它们在泄漏的细胞状态下它们之间的几个相变，表明结晶材料中存在共存的可能性。
We study packings of hard spheres on lattices. The partition function, and therefore the pressure, may be written solely in terms of the accessible free volume, i.e. the volume of space that a sphere can explore without touching another sphere. We compute these free volumes using a leaky cell model, in which the accessible space accounts for the possibility that spheres may escape from the local cage of lattice neighbors. We describe how elementary geometry may be used to calculate the free volume exactly for this leaky cell model in two- and three-dimensional lattice packings and compare the results to the well-known Carnahan-Starling and Percus-Yevick liquid models. We provide formulas for the free volumes of various lattices and use the common tangent construction to identify several phase transitions between them in the leaky cell regime, indicating the possibility of coexistence in crystalline materials.
