A compositional and structural rationalization of the higher oxides of Ce, Pr, and Tb

Cerium, praseodymium and terbium exhibit a family of related mixed-valent binary oxides which are anion-deficient and fluorite-related. The recent structural refinement of five members of this series from neutron diffraction data have made it possible for the first time to generalize the main features of their structures, and to propose a structural principle as well as a generic formula covering all known members of the homologous series and their polymorphs. The structural principle also permits the modeling of the five refined structures correctly (and it is believed uniquely), hence, the confident prediction of the, as yet undetermined, structures of series members for which the composition and suitable diffraction patterns are available. The principle flows from the way fluorite unit-cell modules which may contain vacant oxygen sites can pack together. Rules for packing these modules and examples of their application are presented.