Open AccessStructural transformations in quasicrystals induced by higher dimensional lattice transitions
Author(s) -
Giuliana Indelicato,
T. Keef,
Paolo Cermelli,
David Georges Salthouse,
Reidun Twarock,
Giovanni Zanzotto
Publication year - 2012
Publication title -
proceedings of the royal society a mathematical physical and engineering sciences
Language(s) - English
Resource type - Journals
eISSN - 1471-2946
pISSN - 1364-5021
DOI - 10.1098/rspa.2011.0680
Subject(s) - quasicrystal , aperiodic graph , substitution tiling , penrose tiling , icosahedral symmetry , lattice (music) , tile , planar , local symmetry , symmetry (geometry) , phason , transformation (genetics) , theoretical physics , physics , condensed matter physics , geometry , mathematics , materials science , combinatorics , computer science , quantum mechanics , chemistry , biochemistry , computer graphics (images) , acoustics , composite material , gene
We study the structural transformations induced, via the cut-and-project method, in quasicrystals and tilings by lattice transitions in higher dimensions, with a focus on transition paths preserving at least some symmetry in intermediate lattices. We discuss the effect of such transformations on planar aperiodic Penrose tilings, and on three-dimensional aperiodic Ammann tilings with icosahedral symmetry. We find that locally the transformations in the aperiodic structures occur through the mechanisms of tile splitting, tile flipping and tile merger, and we investigate the origin of these local transformation mechanisms within the projection framework
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