The aim of the present article is to give a review of the state-ofthe-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 Id, 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 techniques 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. 1. What is a quasicrystal?

The structure of quasicrystals

The aim of the present article is to give a review of the state-ofthe-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 Id, 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 techniques 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. 1. What is a quasicrystal?

The Structure of Quasicrystals

Quasicrystals uncovered in aluminium alloys are still a matter of intense research regarding their structure which does not obey the rules of classical crystallography. Today, they also offer a new challenge in relation with their specific electronic properties and surprising mechanical behaviour. These properties are summarized in this review in the light of some structural data. The technological relevance of these results is briefly advocated.

https://iopscience.iop.org/article/10.1088/0031-8949/1993/T49A/002/pdf

The applied physics of quasicrystals

Mn-Si (Manganese-Silicon)

Le processus de transition est decrit par simulations numeriques des cliches de diffraction. On presente la transition d'une quasi periodicite octagonale a une periodicite dans une structure de type Mn-β. La transition implique la nucleation des regions de periodicite translationnelle locale dans le quasicristal d'origine

/pdf/effect-of-phason-strain-on-the-transition-of-an-octagonal-m57yjibd6a.pdf

Effect of phason strain on the transition of an octagonal quasicrystal to a β-Mn-type structure

The microstructure of a rapidly solidified Mn4Si alloy is studied by electron diffraction and high resolution lattice imaging. A new two-dimensional octagonal quasicrystal is found together with 45° microdomains of s-Mn, similar to the case of CrNiSi and VNiSi reported earlier. In addition, an ordered Mn3Si and a metastable Mn12Si5 also occur and the close structural relationship between them is discussed.

A new octagonal quasicrystal and related crystalline phases in rapidly solidified mn4si

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A new octagonal quasicrystal and related crystalline phases in rapidly solidified mn4si