Atomic structure of a decagonal Al-Co-Ni quasicrystal

A structure refinement of the decagonal quasicrystal ${\mathrm{Al}}_{70}$ ${\mathrm{Co}}_{20}$ ${\mathrm{Ni}}_{10}$ with the five-dimensional superspace group P10/mmm was made on the basis of single-crystal x-ray-diffraction data. The structure is a layer structure that consists of two kinds of layers stacked along the c (tenfold) axis with an interval of c/2 (c=4.08 Å). The structure has a local-atom arrangement similar to that of monoclinic ${\mathrm{Al}}_{13}$ ${\mathrm{Fe}}_4$, but includes stacking disorder of the layers. The model explains well the diffraction intensity, chemical composition, and density. There exists another model with P${10}_5$mc, which gives a diffraction intensity similar to that of the above model, except for the extinct reflections due to the extinction rule of the superspace group.