Journal of Statistical Physics

, Volume 65, Issue 1–2, pp 395–401 | Cite as

Are layered two-dimensional quasicrystals periodic in the third direction?

  • S. E. Burkov
Short Communications


“Two-dimensional” quasicrystals have generally been believed to be quasiperiodic in theXY plane and periodic in the Z direction. This is not necessarily the case. A layered material with equidistantly spaced layers and a “random tiling” two-dimensional quasicrystal in each layer is shown to exhibit delta-function diffraction spots even when the phason strain fields in different layers are completely uncorrelated. Surprisingly, such a Z-aperiodic quasicrystal shows trueδ-peaks, while a more ordered Z-periodic quasicrystal shows less sharp, power-law-decaying peaks.

Key words

Quasicrystals aperiodic tilings 


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Copyright information

© Plenum Publishing Corporation 1991

Authors and Affiliations

  • S. E. Burkov
    • 1
    • 2
  1. 1.Laboratory of Atomic and Solid State PhysicsCornell UniversityIthaca
  2. 2.Landau Institute for Theoretical PhysicsMoscowUSSR

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