Crystal structure systematics from oxide phase diagrams by contouring them with Zoltai's tetrahedral sharing coefficient

For crystal structures of oxides with tetrahedral coordination polyhedra, the average number of tetrahedra participating in the sharing of a corner, i.e., Zoltai's tetrahedral sharing coefficient, provides a measure of the degree of polymerization of the tetrahedra. By contouring oxide phase diagrams with Zoltai's tetrahedral sharing coefficient, crystal structure systematics can be conveniently displayed and correlated with other physical and thermochemical properties. The advantages of this analysis are (i) a structural map guides exploration for new compounds, (ii) possible structures for existing compounds that are not known are suggested, (iii) the internal consistency of the chemistry of specific compounds is tested by structural constraints, (iv) the physical behavior and properties of a family of compounds in a chemical system can be correlated with the degree of polymerization of the tetrahedra, and (v) the analysis lends itself to computer programming, in that contour templates of tetrahedral sharing coefficients for different types of oxide systems can be easily determined and overlaid on traditional phase diagrams. Shortcomings to this approach are that the tetrahedral sharing coefficient does not define a unique tetrahedral anion topology, ambiguities arise if some of the oxygen atoms are not part of the tetrahedral anion, and many chemical systems contain oxides where one or more of the tetrahedral cations adopt other coordination geometries.