Three surprising discoveries in the past fifteen years, quasicrystals, fullerenes and ceramic high-Tc superconductors are often quoted as milestones in the evolution of materials science. From a crystallographic point of view quasicrystals represent the most challenging class of these new materials. Perfect structural order in connection with non-crystallographic symmetry caused a change of paradigm in crystallography. Higher-dimensional crystallo-graphy, a fascinating rapidly developing field, has become an extremely valuable tool for the study of aperiodic crystals.
The development of quasicrystal research is reflected in the contributions to the international conferences on quasicrystals. The first meeting, ICQ-1, held 1986 in Les Houches, was marked by theoretical considerations on quasiperiodic order (tilings), first atomic structure modelling and speculations about some special physical properties of quasicrystals. Just a single stable quasicrystalline phase, icosahedral Al-Cu-Li, was known at that time. Last year, ICQ-6 took place in Tokyo. Eleven years and approximately 3000 publications later, the focus of interest has shifted towards the real structure of quasicrystals and their approximants, the theory and experimental study of their phase transformations, their physical properties and potential applications.
The stable quasicrystals known so far are mostly ternary intermetallic phases of composition A-TM(1)-TM(2) (A = Al, Ga, Ti; TM = transition metal), Mg-Zn-RE (RE = rare earth element) and binary Ta-Te. According to their diffraction symmetry, they are classified as icosahedral, decagonal or dodecagonal phases. Some quasicrystals can reach a degree of perfection equivalent to that of silicon. Nevertheless, it is still not clear, whether their structures are strictly quasiperiodic or only on average. Much more, even though several structure analyses of icosahedral and decagonal phases have been performed, not all the results are reliable. One reason is that the reproducible preparation of high-quality single crystals with equilibrium composition has not been ensured yet because the ternary phase diagrams around the stability regions of quasiperiodic phases are extremely complicated and still hardly known in most systems. Another reason is that inherent disorder has not been considered in structure analyses so far.
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