Basic Co-rich decagonal Al-Co-Ni: Superstructure

The four-layer superstructure of basic Co-rich decagonal Al _72.5Co_18.5Ni₉ was determined by single-crystal x-ray diffraction. Based on our previous work, a superstructure model was derived with five-dimensional (5D) noncentrosymmetric space-group symmetry P 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.