Aperiodic crystals and superspace concepts

Abstract

For several decades the lattice periodicity of crystals, as shown by Laue, was considered to be their essential property. In the early sixties of the last century compounds were found which for many reasons should be called crystals, but were not lattice periodic. This opened the field of aperiodic crystals. An overview of this development is given. Many materials of this kind were found, sometimes with very interesting properties. In the beginning the development was slow, but the number of structures of this type increased enormously. In the meantime hundreds of scientists have contributed to this field using a multi-disciplinary approach.