A common feature of stable quasicrystals, high-${\mathit{T}}_{\mathit{C}}$ ferroelectrics, and high-${\mathit{T}}_{\mathit{c}}$ superconductors is that their unusual physical properties are correlated with characteristic crystal stuctures that are often vicinal to structural instabilities. We describe a statistically based diagrammatic scheme, due to Villars, for classifying the full database of crystal structures of binary, ternary, and quaternary compounds and tendency to compound formation in binary- and ternary-alloy systems. Principles of an expert system using this global organization to study small sets of compounds of special interest are formulated. Application to quasicrystals, ferroelectrics, and superconductors results in the identification of diagrammatic regularities which enable us to recognize phenomenological trends and to develop computerized search strategies for the prediction of new materials.

• Received 1 November 1991

DOI:https://doi.org/10.1103/PhysRevB.45.7650