Personal reflections on the history of aperiodic crystals from early days to the state of the art

Abstract

Aperiodic crystals occur as modulated, intergrowth and quasicrystal structures. Their characterization in terms of symmetries possibly requires not only a higher-dimensional description, but also non-Euclidean transformations (like scaling). These crystallographic symmetries, observed in nature, have been investigated but only partially classified. Turning points in the structure determination of aperiodic crystals are presented in historical perspective up to the present time, together with methods and programs. The WEB allows us to get more information on all that, on additional tools and on databases. An attempt to present challenges towards lines of future research concludes the review.