Structure analysis of Zn–Mg–Ho icosahedral quasicrystal by modified Rietveld method using ellipsoid and sphere windows

A structure analysis of the Zn–Mg–Ho icosahedral quasicrystal was carried out by the powder X-ray diffraction method using synchrotron radiation (λ=0.73490 Å) at SPring-8. The intensity distribution was analyzed by the Rietveld method modified for an icosahedral quasicrystal, in which simplified models were assumed: ellipsoid and spherical windows were assumed at five crystallographic sites in a F-type hypercubic unit cell. The analysis revealed the presence of an almost perfect Penrose tiling with edge length 5.20 Å. The vertices are occupied alternatively by Zn and Mg, and almost all of the edge centers of the Penrose rhombohedra are occupied by 0.8Zn and 0.2Mg. Ho and Mg atoms tend to be present on the body diagonal of the prolate rhombohedra. Good agreement between the measured and calculated intensity distribution using the simplified model suggests the applicability and the limitation of the structure analysis using the powder X-ray diffraction method.