Crystallographic shear relations between the structure types α-UO3, CaF2, La2O3and NaCl and a correlation of some lanthanide and actinide oxide structures

When the α-UO3, La2O3 and NaCl structure types are idealized by a topological distortion involving only an extension or contraction of the hexagonal c axis (cubic [111]) it is clear that they are related to each other, and to the CaF2 type, by crystallographic shear. A number of lanthanide and actinide oxide structures are of these types, or derived superstructure types containing ordered anion `vacancies' or `interstitial' anions. The structural relations suggest possible reduction mechanisms.