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The results of the first quantitative structure analysis of the Frank–Kasper decagonal Zn–Mg–Dy phase based on single-crystal X-ray diffraction data taken at different temperatures are reported.

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The crystal structure of the decagonal phase in the system Al–Ni–Rh (d-Al–Ni–Rh) was analyzed in the five-dimensional embedding approach based on single-crystal synchrotron X-ray diffraction data. The structure can be described as a quasiperiodic packing of partially overlapping decagonal and pentagonal columnar clusters with ∼ 21 Å diameter and ∼ 4 Å period along the tenfold axis.
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