Aspects of the topology of actinide atom substructures in crystal structures and the concept of antiliquid

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.