The four-layer superstructure of basic Co-rich decagonal ${\text{Al}}_{72.5}{\text{Co}}_{18.5}{\text{Ni}}_9$ was determined by single-crystal x-ray diffraction. Based on our previous work [A. Strutz, A. Yamamoto, and W. Steurer, Phys. Rev. B 80, 184102 (2009)], a superstructure model was derived with five-dimensional (5D) noncentrosymmetric space-group symmetry $P\overline{10}2c$ with some additional constraints resulting from normal-mode analysis. The 5D structure model was refined with 250 parameters, resulting in values of $wR=0.039$ and $R=0.186$ for 1222 unique reflections. Its close relationship with the structure of W-Al-Co-Ni, a $⟨3/2,2/1⟩$ approximant, proves the physical validity of our structure model and justifies the use of the W phase for the derivation of structural principles underlying the formation of Al-based decagonal quasicrystals.

• Received 25 May 2010

DOI:https://doi.org/10.1103/PhysRevB.82.064107