A new basis for the classification of quasicrystals

The traditional basis for the classification of quasicrystals has been the majority constituent element, and thus Al-, Ga-, Ti-, Zr-, Hf-, Zn-, Cd- and Cu-based quasicrystals have been analyzed in the literature. Occasionally, when two elements are present in comparable proportions, they have been termed as Ti-Zr-, Zn-Mg-, Cd-Mg- and Ag-In-based quasicrystals. We propose a new classification of quasicrystals on the basis of atomic size to recognize the dominant role of the large size atoms in forming the icosahedral phases. We propose a classification of quasicrystals as centered on Li-, Mg-, Al-, Ga-, Ca-, Sc-, Y-, Ti-, Zr-, Hf- and rare-earth elements, as they are the largest atoms in the constituent quasicrystals. The term centered is used to indicate the central importance of this element, even though compositionwise it may not be the majority constituent. The usefulness of Pettifor maps in this context will be illustrated and extended by treating several ternary and quaternary quasicrystals as pseudo-binaries.