Contributions to the crystal chemistry of normal and defect tetrahedral structures*

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Abstract
A structure is called a normal tetrahedral structure if every atom of the structure has four nearest neighbors which are located at the vertices of a surrounding tetrahedron. If not all four corners of the surrounding tetrahedron are occupied with an atom, the structure is said to be a defect tetrahedral structure. Normal-tetrahedral structures are formed only if the average valenceelectron concentration per atom is four. Defect tetrahedral structures can be made to fit the valence-electron concentration rule if the number of structure defects, or the number of unused, tetrahedral orbitals, is considered. A scheme has been developed which allows one to calculate the compositions of all theoretically possible normal and defect tetrahedral structures. Some 200 tetrahedral-structure compounds are known which all fit in the composition scheme. The system can be used as well to find the compositions of new tetrahedral-structure compounds or to test reported compositions of tetrahedralstructure minerals for their correctness. It was found that it is possible to present the composition scheme not only analytically but also graphically in a master composition diagram. A plot of a compound in a master composition diagram, regardless of the element combination, will show on first sight if the composition is right for a normal tetrahedral structure or a defect tetrahedral structure. In the latter case one can read from the diagram the number of structure defects. An average valence-electron concentration of four is a necessary but not sufficient condition for the formation of a tetrahedral structure. Other factors have to be considered, like the electronegativity difference Δx and the average principal quantum number of the valence shell of the participating atoms [unk]. The influence of those factors can be conveniently studied in a so-called “ Δx -versus-[unk]“ diagram, first introduced for normal valence compounds by M ooser and P earson . It is found that of all those compositions which have the correct average valence-electron concentration, only those which lie in a well defined region of the Δx -versus-[unk] diagram will crystallize with a tetrahedral structure.

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