Quasicrystal Approximants

AbstractThe concept of quasicrystal approximants is best pursued with reference to the quasicrystals themselves. This makes the classification of approximants into classes congruent to those for quasicrystals useful, that is, axial and icosahedral. As noted by several authors, work on approximants has come full circle; the initial interest in approximants grew out of a desire to understand particularly the enigmatic structure of the quasicrystals, but lately it has become increasingly clear that not only the structure but also many of the physical properties of quasicrystals may be more conveniently probed and understood through the study of their approximants. Although the uniqueness of quasicrystals lies in their structures, the approximants approximate this to such an extent that most questions about quasicrystals can be addressed through the proxy of the approximant phases. This treatise deals mainly with the structural properties of approximants.