Specific features of the stereochemistry of cerium in the structures of oxygen-containing compounds

Voronoi-Dirichlet (VD) polyhedra and the intersecting spheres method were used to perform crystal-chemical analysis of 218 compounds containing 306 crystallographic types of cerium atoms in CeO eta coordination polyhedra. With respect to oxygen atoms, the coordination numbers (CNs) of Ce(IV) atoms are 6-10 and 12 and those of Ce(III) atoms are 4 and 6-12. For a fixed valence state of a cerium atom, the volume of its VD polyhedron is virtually independent of the CN, although the Ce-O bond lengths change by 0.8 angstrom. In going from Ce(IV) to Ce(III), the volume of their VD polyhedra increases, on average, by 2.1 angstrom(3). The characteristics of the VD polyhedra of cerium atoms can be used for determining their valence states in crystals structures.