Introduction to Higher Dimensional Description of Quasicrystal Structures
ISQCS, June 23-27, 2019, Sendai, Tohoku University Introduction to higher dimensional description of quasicrystal structures Hiroyuki Takakura Division of Applied Physics, Faculty of Engineering, Hokkaido University ISQCS, June 23-27, 2019, Sendai, Tohoku University Outline • Diffraction symmetries & Space groups of iQCs • Section method • Fibonacci structure • Icosahedral lattices • Simple models of iQCs • Real iQC structures • Cluster based model of iQCs • Summary ISQCS, June 23-27, 2019, Sendai, Tohoku University Crystal Amorphous Their diffraction patterns ISQCS, June 23-27, 2019, Sendai, Tohoku University Diffraction symmetries and space groups of iQCs ISQCS, June 23-27, 2019, Sendai, Tohoku University X-ray transmission Laue patterns of iQC 2-fold 3-fold 5-fold i-Zn-Mg-Ho F-type ISQCS, June 23-27, 2019, Sendai, Tohoku University Electron diffraction pattern of iQC i-AlMn 1 The arrangement of the diffraction spots is not periodic but quasi-periodic. D.Shechtman et al., Phys.Rev.Lett., 53,1951(1984). ISQCS, June 23-27, 2019, Sendai, Tohoku University Symmetry of iQC 2 Point group 31.72º 5 Order : 120 37.38º 2 5 3 20.90º 3 2 2 Asymmetric region: 6 +10 +15 + m + center ISQCS, June 23-27, 2019, Sendai, Tohoku University X-ray diffraction patterns of iQCs P-type i-Zn-Mg-Ho F-type i-Zn-Mg-Ho 2fy 2fy 5f 5f 3f 3f 2fx 2fx Liner plots ISQCS, June 23-27, 2019, Sendai, Tohoku University X-ray diffraction patterns of iQCs P-type i-Zn-Mg-Ho F-type i-Zn-Mg-Ho 2fy 2fy 5f 5f 3f 3f 2fx All even or all odd for 2fx No reflection condition Log plots ISQCS, June 23-27, 2019, Sendai, Tohoku University Vectors used for indexing 6 Any vectors can be used if all the reflections can be indexed correctly.
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