A family of stochastic models of disordered particles is proposed, obtained by clipping a Gaussian random field with a function that is space dependent. Depending on the shape of the clipping function, dense or hollow particles can be modelled. General expressions are derived for the form factor of the particles, for their average volume and surface area, and for their density and surface-area distributions against the distance to the particle centre. A general approximation for the form factor is also introduced, based on the density and surface-area distributions, which coincides with the Guinier and Porod expressions in the limits of low and high scattering vector magnitude q. The models are illustrated with the fitting of small-angle X-ray scattering (SAXS) data measured on Pt/Ni hollow nanoparticles. The SAXS analysis and modelling notably capture the collapse of the particles' porosity after being used as oxygen-reduction catalysts.

中文翻译：

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致密或空心纳米粒子的随机模型及其散射特性

提出了一系列无序粒子的随机模型，通过使用空间相关的函数裁剪高斯随机场获得。根据剪切函数的形状，可以对密集或空心粒子进行建模。对于颗粒的形状因子、它们的平均体积和表面积以及它们的密度和表面积分布与到颗粒中心的距离的一般表达式是导出的。还介绍了基于密度和表面积分布的形状因子的一般近似值，这与低和高散射矢量幅度 q 限制中的 Guinier 和 Porod 表达式一致。这些模型通过拟合在 Pt/Ni 中空纳米粒子上测量的小角 X 射线散射 (SAXS) 数据进行说明。