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

Abstract

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 longrange 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.

Uranyl Coordination Compounds with Alkaline Earth Metals and Crotonate Ligands

“…this means that in the process of crystallization such clusters/aquacations tend to arrange in a manner minimizing the overlap of outer electron shells of neighboring species. Thus, the title compounds are another examples showing the relevancy and generality of the 14‐neighbor rule being developed by us within the stereoatomic model of crystal structures . Note, that similar coexistence of 13‐ and 15‐faceted VD polyhedra in U‐substructures was earlier observed for uranyl acetate compounds with divalent secondary metals, while the M ‐substructures of the same compounds were also found to be represented by the CTT [4 6 6 8 ] …”

“…One of the most efficient ways to study packing of complexes is to analyze VD polyhedra of central atoms of such complexes in crystal substructures. This type of analysis of crystal structures was carried out by our group many times providing valuable insights into the structure of matter (See for example, refs …”

“…Finally, the strictest characteristic showing different packing motifs is the combinatorial‐topological type ( CTT ) of polyhedra, depicting the number of faces of VD polyhedra with given number of vertices. Thus, the VD polyhedra of both U atoms in U‐substructure of compound 1 which does not feature clustering have 14 faces and belong to a widespread CTT [4 4 5 4 6 6 ]‐2, designating that these VD polyhedra have four quadrangular, four pentagonal and six hexagonal faces . On the other hand, the VD polyhedra of U atoms in U‐substructures of compounds 2–4 feature odd numbers of faces (13 or 15) and are very rare .…”

“…Thus, the VD polyhedra of both U atoms in U‐substructure of compound 1 which does not feature clustering have 14 faces and belong to a widespread CTT [4 4 5 4 6 6 ]‐2, designating that these VD polyhedra have four quadrangular, four pentagonal and six hexagonal faces . On the other hand, the VD polyhedra of U atoms in U‐substructures of compounds 2–4 feature odd numbers of faces (13 or 15) and are very rare . Especially VD polyhedra of U atoms in U‐substructures of compounds 3 and 4 are very complex, containing rare faces with 7 and 8 vertices and different CTT's for every independent U atom, what shows difficult to perceive packing of [UO 2 L 3 ] – complexes in these structures.…”

“…This type of arrangement (the CTT [4 6 6 8 ]) is topologically equal to the bcc lattice, which in turn represents the thinnest covering of the 3D space. According to the paper in ref . this means that in the process of crystallization such clusters/aquacations tend to arrange in a manner minimizing the overlap of outer electron shells of neighboring species.…”