Cavities in the hard sphere fluid and crystal and the equation of state
Cavities in the hard sphere fluid and crystal and the equation of state
复制标题
硬球流体和晶体中的空腔以及状态方程
DOI：
10.1080/00268979100100741
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发表时间：
1991
影响因子：
1.7
通讯作者：
H. Reiss
中科院分区：
文献类型：
--
作者：
R. J. Speedy;H. Reiss
在硬球系统中，有足够空间容纳另一个球的区域称为空腔。本文评述了空洞的数目、大小、表面积与热力学性质之间的精确关系，并从理论上探讨了通过空洞的统计几何分析发展D维硬球流体和晶体理论以及熔化理论的前景。状态方程表示为pV/RT = 1 + a（z）/ 1/D，其中z是相对于紧密堆积的密度，a（z）是表现良好的空腔形状因子，并且是平均空腔尺寸。在高密度极限下，pV/RT随D/（1 - z）变化.定义一个函数F（z），使得每个球的空穴数nc由lnnc = 1 - pV/RT-F（z）和ln = ΔS/R-ln（N/V）+ F（z）给出，其中ΔS是相对于理想气体的熵。F（z）在一维上是零，我们证明了它是一个行为良好的函数，它趋向于一个有限约束。
In a hard sphere system regions where there is sufficient space to accommodate another sphere are called cavities. Exact relations between the number, size and surface area of cavities, and thermodynamic properties are reviewed, and the prospect of developing a theory of the D-dimensional hard sphere fluid and crystal, and of melting, by analysing the statistical geometry of cavities, is investigated theoretically. The equation of state is expressed as pV/RT = 1 + a(z)/ 1/D , where z is the density relative to close packing, a(z) is a well-behaved cavity shape factor and is the average cavity size. We show that in the high density limit varies as (1 - z) D and pV/RT varies as D/(1 - z). A function F(z) is defined such that the number of cavities per sphere, n c, is given by ln n c = 1 - pV/RT - F(z) and ln = ΔS/R - ln(N/V) + F(z), where ΔS is the entropy relative to the ideal gas. F(z) is exactly zero in one dimension, and we show that it is a well-behaved function that tends to a finite con...