Crystallography of dodecagonal quasicrystals

Abstract

A detailed model structure of dodecagonal quasicrystals is proposed which applies to both dodecagonal Ni-Cr and V-Ni or V-Si-Ni. This model structure can be represented as the restriction of a 5d periodic structure to a 3d subspace, which is identified with physical space. The point group and the space group of the 5d periodic structure are determined. The latter is non-symmorphic, containing a set of glide "planes" and a screw axis. These space group elements lead to characteristic extinctions in the Fourier spectrum, which should be experimentally observable. A numeric calculation, which includes multiple scattering effects for electron diffraction, confirms the presence of the extinctions predicted by the space group analysis. The model structure proposed here serves as a very instructive example how crystallographic concepts, such as Bravais type, point group, or space group, can be applied to quasicrystals.