Vorotis: Software for Voronoi tessellation analysis using the polyhedron code

The atoms in disordered structures such as liquids and glasses are arranged in a complex manner. Their atomic arrangements are often studied using the Voronoi tessellation method. This method divides the space containing atoms into regions called Voronoi polyhedra. Each polyhedron contains one atom. From the structure of the polyhedron, we can know the bond network, or the topology, of the cluster composed of the atoms in the polyhedron and its neighbors. Thus, the topological order can be characterized by identifying the most dominant Voronoi polyhedron. For this purpose, the Voronoi index has long been used. However, it does not specify how polygons are arranged in the polyhedron. Therefore, polyhedra with different graph structures can have the same index. This problem can lead to failure in characterizing the topological order. In addition, the Voronoi index does not tell anything about the chemical arrangement, namely how different types of atoms are arranged in the cluster. To characterize both of the topological and chemical order of disordered structures, a polyhedron-naming system called the polyhedron code has been developed and implemented in the Vorotis software. This paper presents the essential features of Vorotis.诸如液体与玻璃这类无序结构中的原子，其排布方式极为复杂。针对这类结构的原子排布，研究人员常借助沃罗诺伊镶嵌（Voronoi tessellation）方法开展研究。该方法将包含原子的空间划分为多个被称为沃罗诺伊多面体（Voronoi polyhedra）的区域，每个区域恰好包含一个原子。通过分析该多面体的结构，我们可以获取该多面体内部原子及其近邻原子所构成团簇的键合网络（或称拓扑结构）。因此，可通过识别占比最高的沃罗诺伊多面体来表征该体系的拓扑有序性。长期以来，研究人员常借助沃罗诺伊指数（Voronoi index）实现这一表征目标，但该指数无法指明多面体内多边形的排布方式。因此，具有不同图结构的多面体可能拥有相同的沃罗诺伊指数，这一缺陷会导致拓扑有序性表征失效。此外，沃罗诺伊指数无法提供任何关于化学排布的信息，即无法说明团簇内不同种类原子的排布情况。为了同时表征无序结构的拓扑有序性与化学有序性，研究人员开发了一种被称为多面体编码（polyhedron code）的多面体命名系统，并将其集成至Vorotis软件中。本文介绍了Vorotis软件的核心特性。