The structure of quasicrystals

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Abstract
The aim of the present article is to give a review of the state-of-the-art on quasicrystal structure analysis. After a short discussion of the term “crystal” in chapter 1, the geometrical generation of quasilattices is touched in chapter 2. In the following the higher-dimensional description of 1d, 2d and 3d quasi-crystals is demonstrated in detail as well as the derivation of structure factor equations and symmetry relationships in the higher-dimensional space. Chapter 4 shows the experimental techniques and structure determination methods for the study of quasicrystals. The experimental results of structural studies performed with different tech-niques are critically reviewed in chapter 5. Some of the results of the literature research are that five years after the detection of the first quasicrystal not a single quantitative (in terms of a regular structure determination) analysis of its structure has been carried out, and that the famous Mackay-icosahedra do not play the important role as the basic structural building elements as one supposed before.