Understanding of small particles shapes in crystalline materialswith a pseudo-polyhedral approximation

小的晶体颗粒通常形成为具有圆形边缘的近多面体形状。当分析和讨论近多面体形状时，如果这些形状可以用参数简单的方程来表示，将是很方便的。伪多面体是在多面体和球体之间表现各种形状的固体。在这项研究中，使用伪多面体形状近似来考虑小晶体颗粒的形态。由结晶学上的低折射率平面组成的各种近多面体形状用与形状有关的参数的简单方程来描述。本研究处理的是立方晶体结构的颗粒。结果表明，伪多面体近似是评价小颗粒形貌的一种有用的几何工具。

Small crystalline particles are often formed comprising near-polyhedral shapes with round edges. When near-polyhedral shapes are analyzed and discussed, it is convenient if these shapes can be expressed by equations with simple parameters. Pseudo-polyhedra are solids expressing various shapes between those of polyhedra and spheres. The pseudo-polyhedral-shape approximation is used in this study to consider the morphology of small crystalline particles. Various near-polyhedral shapes composed of crystallographically low-index planes are described using a simple equation with shape-related parameters. Cubic crystal structure particles are treated in the present study. It is shown that the pseudo-polyhedral-shape approximation is a useful geometrical tool for evaluating the morphology of small crystalline particles.