Quantum diagrams and the prediction of new materials

A statistically based diagrammatic scheme for classifying the full database of crystal structures of binary, ternary and quaternary compounds and the 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. Diagrammatic regularities are observed in stable quasi-crystals, high T_c ferroelectrics and high T_c superconductors, reflecting a correlation of these types of order with local structure and stability. Detailed application to quasi-crystals uses these diagrammatic regularities to facilitate the recognition of phenomenological trends and to identify chemical factors which favor quasi-crystal formation. This provides severe constraints on compositions at which quasi-crystals or crystalline approximants are likely to form. Several computerized search strategies which utilize the diagrammatic conditions to identify compositions for experimental investigation are outlined.