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Structural transformations in quasicrystals induced by higher dimensional lattice transitions

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Publication details

JournalProceedings of the Royal Society of London. Series A, Mathematical and Physical Sciences
DateE-pub ahead of print - 8 Feb 2012
DatePublished (current) - 8 May 2012
Issue number2141
Number of pages20
Pages (from-to)1452-1471
Early online date8/02/12
Original languageEnglish


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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