Kopera Bernd A F, Retsch Markus
Department of Chemistry , University of Bayreuth , Universitätsstraße 30 , 95447 Bayreuth , Germany.
Anal Chem. 2018 Dec 4;90(23):13909-13914. doi: 10.1021/acs.analchem.8b03157. Epub 2018 Nov 16.
The radial distribution function, g( r), is ubiquitously used to analyze the internal structure of particulate systems. However, experimentally derived particle coordinates are always confined to a finite sample volume. This poses a particular challenge on computing g( r): Once the radial distance, r, extends beyond the sample boundaries in at least one dimension, substantial deviations from the true g( r) function can occur. State of the art algorithms for g( r) mitigate this issue for instance by using artificial periodic boundary conditions. However, ignoring the finite nature of the sample volume distorts g( r) significantly. Here, we present a simple, analytic algorithm for the computation of g( r) in finite samples. No additional assumptions about the sample are required. The key idea is to use an analytic solution for the intersection volume between a spherical shell and the sample volume. In addition, we discovered a natural upper bound for the radial distance that only depends on sample size and shape. This analytic approach will prove to be invaluable for the quantitative analysis of the increasing amount of experimentally derived tomography data.
径向分布函数g(r)被广泛用于分析颗粒系统的内部结构。然而，通过实验获得的粒子坐标总是局限于有限的样本体积内。这给g(r)的计算带来了一个特殊的挑战：一旦径向距离r在至少一个维度上超出样本边界，就可能出现与真实g(r)函数的显著偏差。用于g(r)的现有算法通过使用人工周期性边界条件等方法来缓解这个问题。然而，忽略样本体积的有限性质会显著扭曲g(r)。在这里，我们提出了一种简单的解析算法，用于计算有限样本中的g(r)。无需对样本做额外假设。关键思想是使用球壳与样本体积之间相交体积的解析解。此外，我们发现了一个仅取决于样本大小和形状的径向距离自然上限。这种解析方法对于定量分析越来越多的通过实验获得的断层扫描数据将被证明具有极高价值。
