Journal of Statistical Physics, Vol. 65, Nos. 1/2, 1991. p. 395-401.
"Two-dimensional" quasicrystals have generally been believed to be quasiperiodic in the XY plane and periodic in the Zdirection. 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 true d-peaks, while a more ordered Z-periodic quasicrystal shows less sharp, power-law-decaying peaks.