Are layered two-dimensional quasicrystals periodic in the third direction?
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“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 wordsQuasicrystals aperiodic tilings
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