The Structural Basis of the Fluorite-Related Rare Earth Higher Oxides

In this paper phenomenological structural principles, and rules for their application are advanced for predicting the ideal structures of the higher oxides of the rare earths that (1) establish a generic formula incorporating all known phases, (2) guide the correct modelling of the established structures of members, (3) demonstrate that structures previously proposed but proven incorrect do not follow the structural principles, (4) predict the structures not yet established for known phases, including polymorphs, (5) provide rationalization for phases fitting the generic formula that have not yet been found. The structural principles flow naturally from the fluorite substructure characteristic of all established phases.