Twenty years of structure research on quasicrystals. Part 1. 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.