Systematics of fluorite-related structures. I. General principles

The Kang-Eyring system of description of fluorite-related aniondeficient structures is extended to the wide range of fluorite-related structures with vacancies in both anion and cation sites. 22 different types of modules are characterized on the base of the concept of module equivalence and 280 different module orientations are obtained from the symmetry considerations. Possible ways of linking of modules are considered. It is shown that for geometrical description of fluorite-related structures the following characteristics may be used: matrix of transformation from fluorite-related sublattice to real lattice and an average parameter a(f) of fluorite sublattice.