Using the parameters of Voronoi–Dirichlet (VD) polyhedra the authors have verified the maximum space-filling principle in substructures constructed of actinide atoms (from thorium to einsteinium) in all crystal structures from the Inorganic Crystal Structure Database (ICSD) and Cambridge Structural Database (CSD). It is shown that most of the actinide atoms in such substructures are surrounded by 14 or 12 neighboring atoms. It was discovered that U substructures with greater than or equal to 20 crystallographically independent U atoms in the unit cell feature 15-faceted VD polyhedra as the most common type. Analogous unimodal distributions of VD polyhedra with maxima at 15 faces are observed for F and H substructures and the model system `ideal gas', which has no order in the arrangement of atoms. This similarity allows one to assume that substructures of crystal structures with greater than or equal to 20 crystallographically independent atoms in the unit cell do not possess short-range (local) order in the mutual arrangement of atoms, but feature long-range order (translational symmetry). Thus, crystalline compounds with such substructures can formally be regarded as `antiliquid', that is the antipode of a liquid, whose structure possesses short-range order but lacks translational symmetry.

中文翻译：

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晶体结构中锕系原子亚结构的拓扑方面和反液体的概念

使用 Voronoi-Dirichlet (VD) 多面体参数，作者验证了无机晶体结构数据库 (ICSD) 和剑桥结构数据库中所有晶体结构中锕系原子（从钍到锿）构成的子结构的最大空间填充原理（惩教署）。结果表明，此类子结构中的大多数锕系元素原子被 14 或 12 个相邻原子包围。研究发现，晶胞中具有大于或等于 20 个晶体学独立 U 原子的 U 子结构以 15 面 VD 多面体为最常见的类型。对于 F 和 H 子结构和模型系统“理想气体”，观察到在 15 个面处具有最大值的 VD 多面体的类似单峰分布，其原子排列没有顺序。这种相似性允许人们假设晶胞中具有大于或等于 20 个晶体学独立原子的晶体结构的子结构在原子的相互排列中不具有短程（局部）有序性，但具有长程有序（平移）对称）。因此，具有这种子结构的晶体化合物可以在形式上被视为“反液体”，即液体的对映体，其结构具有短程有序但缺乏平移对称性。