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Start date: 1988End date: 1988Subject: search.filters.subject.530Author: search.filters.author.Gähler, Franz

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    Quasicrystal structures from the crystallographic viewpoint
    (1988) Gähler, Franz; Fröhlich, J. (Prof. Dr.)
    Quasikristalle sind neuartige Phasen, die in schnell abgekühlten Metall-Legierungen vorkommen. Ihre wichtigste Eigenschaft ist, dass Ihre Fourier-Transformierte aus scharfen Bragg-Peaks besteht, deren Positionen und Intensitäten eine Punktsymmetrie haben, die mit einer dreidimensionalen periodischen Struktur nicht verträglich ist. Die Positionen der Bragg-Peaks eines Quasikristalls können jedoch alle als ganzzahlige Linearkombinationen von endlich vielen fundamentalen Wellenvektoren geschrieben werden; dies legt nahe, diese Strukturen als Schnitt durch eine höherdimensionale, periodische Struktur aufzufassen.
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    Quasiperiodic tilings : a generalized grid projection method
    (1988) Korepin, Vladimir E.; Gähler, Franz; Rhyner, Jakob
    We generalize the grid-projection method for the construction of quasiperiodic tilings. A rather general fundamental domain of the associated higher-dimensional lattice is used for the construction of the acceptance region. The arbitrariness of the fundamental domain allows for a choice which obeys all the symmetries of the lattice, which is important for the construction of tilings with a given non-trivial point-group symmetry in Fourier space. As an illustration, the construction of a two-dimensional quasiperiodic tiling with 12-fold orientational symmetry is described.
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    Crystallography of dodecagonal quasicrystals
    (1988) Gähler, Franz
    A detailed model structure of dodecagonal quasicrystals is proposed which applies to both dodecagonal Ni-Cr and V-Ni or V-Si-Ni. This model structure can be represented as the restriction of a 5d periodic structure to a 3d subspace, which is identified with physical space. The point group and the space group of the 5d periodic structure are determined. The latter is non-symmorphic, containing a set of glide "planes" and a screw axis. These space group elements lead to characteristic extinctions in the Fourier spectrum, which should be experimentally observable. A numeric calculation, which includes multiple scattering effects for electron diffraction, confirms the presence of the extinctions predicted by the space group analysis. The model structure proposed here serves as a very instructive example how crystallographic concepts, such as Bravais type, point group, or space group, can be applied to quasicrystals.