Periodically distributed objects with quasicrystalline diffraction pattern
Abstract
It is possible to construct fully periodically distributed objects with a diffraction pattern identical to the one obtained for quasicrystals. These objects are probability distributions of distances obtained in the statistical approach to aperiodic structures distributed periodically. The diffraction patterns have been derived by using a twomode Fourier transform—a very powerful method not used in classical crystallography. It is shown that if scaling is present in the structure, this twomode Fourier transform can be reduced to a regular Fourier transform with appropriately rescaled scattering vectors and added phases. Detailed case studies for model sets 1D Fibonacci chain and 2D Penrose tiling are discussed. Finally, it is shown that crystalline, quasicrystalline, and approximant structures can be treated in the same way.
 Authors:
 Faculty of Physics and Applied Computer Science, AGH University of Science and Technology, al. Mickiewicza 30, 30059 Krakow (Poland)
 (Switzerland)
 Publication Date:
 OSTI Identifier:
 22398811
 Resource Type:
 Journal Article
 Resource Relation:
 Journal Name: Applied Physics Letters; Journal Volume: 106; Journal Issue: 13; Other Information: (c) 2015 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA)
 Country of Publication:
 United States
 Language:
 English
 Subject:
 75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITY; CRYSTALLOGRAPHY; CRYSTALS; DIFFRACTION; DISTANCE; FOURIER TRANSFORMATION; PERIODICITY; PROBABILITY; VECTORS
Citation Formats
Wolny, Janusz, Email: wolny@fis.agh.edu.pl, Strzalka, Radoslaw, Kuczera, Pawel, and Laboratory of Crystallography, ETH Zurich, WolfgangPauliStrasse 10, CH8093 Zurich. Periodically distributed objects with quasicrystalline diffraction pattern. United States: N. p., 2015.
Web. doi:10.1063/1.4916830.
Wolny, Janusz, Email: wolny@fis.agh.edu.pl, Strzalka, Radoslaw, Kuczera, Pawel, & Laboratory of Crystallography, ETH Zurich, WolfgangPauliStrasse 10, CH8093 Zurich. Periodically distributed objects with quasicrystalline diffraction pattern. United States. doi:10.1063/1.4916830.
Wolny, Janusz, Email: wolny@fis.agh.edu.pl, Strzalka, Radoslaw, Kuczera, Pawel, and Laboratory of Crystallography, ETH Zurich, WolfgangPauliStrasse 10, CH8093 Zurich. 2015.
"Periodically distributed objects with quasicrystalline diffraction pattern". United States.
doi:10.1063/1.4916830.
@article{osti_22398811,
title = {Periodically distributed objects with quasicrystalline diffraction pattern},
author = {Wolny, Janusz, Email: wolny@fis.agh.edu.pl and Strzalka, Radoslaw and Kuczera, Pawel and Laboratory of Crystallography, ETH Zurich, WolfgangPauliStrasse 10, CH8093 Zurich},
abstractNote = {It is possible to construct fully periodically distributed objects with a diffraction pattern identical to the one obtained for quasicrystals. These objects are probability distributions of distances obtained in the statistical approach to aperiodic structures distributed periodically. The diffraction patterns have been derived by using a twomode Fourier transform—a very powerful method not used in classical crystallography. It is shown that if scaling is present in the structure, this twomode Fourier transform can be reduced to a regular Fourier transform with appropriately rescaled scattering vectors and added phases. Detailed case studies for model sets 1D Fibonacci chain and 2D Penrose tiling are discussed. Finally, it is shown that crystalline, quasicrystalline, and approximant structures can be treated in the same way.},
doi = {10.1063/1.4916830},
journal = {Applied Physics Letters},
number = 13,
volume = 106,
place = {United States},
year = 2015,
month = 3
}

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