Leonardi Alberto, Neder Reinhard, Engel Michael
Institute for Multiscale Simulation, IZNF, Friedrich-Alexander-Universität Erlangen-Nürnberg, Cauerstrasse 3, Erlangen, Bavaria 91058, Germany.
Institut für Physik der Kondensierten Materie, Friedrich-Alexander-Universität Erlangen-Nürnberg, Staudstrasse 3, Erlangen, Bavaria 91058, Germany.
J Appl Crystallogr. 2022 Mar 18;55(Pt 2):329-339. doi: 10.1107/S1600576722001261. eCollection 2022 Apr 1.
Structural characterization of powder samples via total scattering methods, in either real or reciprocal space, must take into account the effect of particle shape. Here, the shape contribution of a set of ideally isolated particles to the small-angle scattering (SAS) component of the intensity profile is modelled using the shape function [Svergun & Koch (2003). , 1735-1782]. The shape function is obtained by orientational averaging of common volume functions (CVFs) for a discrete set of directions. The effects of particle size and size dispersity are accounted for via scaling of the CVFs and their convolution with the underlying probability distribution. The method is applied to shapes with CVFs expressed analytically or by using discrete tables. The accurate calculation of SAS particle shape contributions up to large momentum transfer demonstrates the reliability and flexibility of modelling shape functions from sets of CVFs. The algorithm presented here is computationally efficient and can be directly incorporated into existing routines for analysis of powder total scattering data.
通过全散射方法对粉末样品进行结构表征，无论是在实空间还是倒易空间，都必须考虑颗粒形状的影响。在此，使用形状函数[Svergun和Koch（2003年），1735 - 1782页]对一组理想孤立颗粒对强度分布的小角散射（SAS）分量的形状贡献进行建模。形状函数是通过对离散方向集的公共体积函数（CVF）进行取向平均得到的。颗粒尺寸和尺寸分散性的影响通过CVF的缩放及其与基础概率分布的卷积来考虑。该方法适用于具有解析表示或使用离散表格表示的CVF的形状。在大动量转移下对SAS颗粒形状贡献的精确计算证明了从CVF集建模形状函数的可靠性和灵活性。这里提出的算法计算效率高，可直接纳入现有的粉末全散射数据分析程序中。
