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Modelling the transformation from quasicrystal to crystal

Authors
Publisher
North Holland
Publication Date
Keywords
  • Molecular Biophysics Unit
  • Physics

Abstract

The transformation from quasicrystal to crystal tilings using the projection formalism can be done in three ways. The first is the rational orientation of the window, the second is the continuous reorientation of the projection plane, and the third is the continuous evolution of the hyperlattice. Here the window as well as the projection plane are fixed in the same orientation and then the magnitude of basis vectors describing the hyperlattice are continuously changed. Such a transformation from a quasiperiodic tiling to a periodic one takes the phase through a series of intermediate rational approximate structures as well as other quasiperiodic ones which exhibit some micro-crystalline features. The final crystalline form does not contain overlapping vertices as obtained in the second alternative method. The intermediate tiling is made of two different squares and a parallelogram, and the periodic tiling has a superlattice. The Ammann lines are preserved and are continuous through the entire process.

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