Modulated-Crystal Model for the Twelvefold Quasicrystal Ta62Te38

Why are quasicrystals quasiperiodic?

In the past two decades significant progress has been made in the search for stable quasicrystals, the determination of their structures and the understanding of their physical properties. Now, quasiperiodic ordering states are not only known for intermetallic compounds, but also for mesoscopic systems such as ABC-star terpolymers, liquid crystals or different kinds of colloids. However, in spite of all these achievements fundamental questions concerning quasicrystal formation, growth and stability are still not fully answered. This tutorial review introduces the research in these fields and addresses some of the open questions concerning the origin of quasiperiodicity.

Twenty years of structure research on quasicrystals. Part I. Pentagonal, octagonal, decagonal and dodecagonal quasicrystals

Is quasicrystal structure analysis a never-ending story? Why is still not a single quasicrystal structure known with the same precision and reliability as structures of regular periodic crystals? What is the state-of-the-art of structure analysis of axial quasicrystals? The present comprehensive review summarizes the results of almost twenty years of structure analysis of axial quasicrystals and tries to answer these questions as far as possible. More than 2000 references have been screened for the most reliable structural models of pentagonal, octagonal, decagonal and dodecagonal quasicrystals. These models, mainly based on diffraction data and/or on bulk and surface microscopic images are critically discussed together with the limits and potentialities of the respective methods employed.

Twelve-fold quasicrystal and its approximant of Ta62Te38 interpreted as modulated crystals

A transmission electron microscopy study reveals that the twelve-fold quasicrystal and its approximant in Ta62Te38 are crystals subjected to the structure modulation. It is composed of two modulated layers rotated by 30 degrees (or 90 degrees) to each other about their normal. Structures of the twelve-fold quasicrystal and its approximant can be related by modulation waves with the same directions but with slightly different wavelengths. The modulation is considered to be due to the rearrangement of atomic vacancies as a response to the occurrence of charge density waves.