Quantum diagrams, structural models and the prediction of new quasicrystals

A statistically-based diagrammatic scheme for classifying the full data base of crystal structures of binary, ternary and quaternary compounds and tendency to compound formation in binary and ternary alloy systems is used as the basis for the study of small sets of compounds of special interest. Application to quasicrystals results in the identification of diagrammatic regularities which facilitate the recognition of phenomenological trends and the identification of chemical factors which favor quasicrystal formation. This provides severe constraints on compositions at which quasicrystals or crystalline approximants are likely to form. A structural model is presented from which an additional quasicrystal condition is derived. Results of a computerized search which utilizes these conditions to identify compositions for experimental investigation are given.