Five-dimensional structure refinement of decagonal Al₆₅Cu₂₀Co₁₅

Abstract A single-crystal X-ray structure analysis of decagonal Al65 Cu20Co15 has been performed using the n-dimensional approach. The structure has been solved by Patterson analysis and subsequent least-squares refinement, both in the five-dimensional description. A final value of wR=0.097 for 259 independent reflections was achieved with I≥2σ(1) and 12 variables. There are three atoms in the asymmetric unit. The calculated density of the refined, structure model is ρc = 4.8 M gm −3. The three-dimensional decagonal structure consists of two planar quasiperiodic layers, related by the tenfold screw axis, stacked periodically one upon the other. Characteristic large elements of the crystalline Al13 Fe4 structure type can be found in new combinations in the quasiperiodic layers. It is remarkable that pentagonal channels appear which are empty or occupied statistically.