Medium range real atomic structure of face centred icosahedral Ho9Mg26Zn65

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A new approach to solve quasicrystalline atomic structures in 3-dimensional (3D) real space is presented: The atomic pair distribution function (PDF) of face centred icosahedral Ho9Mg26Zn65 [a(6D) = 2x5.18(3)A was obtained from in-house X-ray diffraction data (MoKa1). Starting with rational approximant models, derived from 1/1- and 2/1-Al-Mg-Zn, its local and medium range structure was refined (r < 27A; R = 12.9%) using the PDF data. 85% of all atoms show Frank-Kasper (FK) type coordinations. Basic structural unit is the 3-shell, 104-atom Bergman cluster (d = 15A comprising a void at its center. The clusters are interconnected sharing common edges and hexagonal faces of the 3rd shells. The remaining space is filled by some glue atoms (9% of all atoms), yielding an almost tetrahedrally close packed structure. All Ho atoms are surrounded by 16 neighbours (FK-polyhedron "P"). Most of them (89%) are situated in the 2nd shell (pentagon dodecahedron), the other act as glue atoms. As a result and as can be expected for real matter, local atomic coordinations in quasicrystals are similar compared to common crystalline intermetallic compounds. From our results, the long range quasiperiodic structure of icosahedral Mg-Zn-RE (RE = Y and some rare earths) is anticipated to be a canonical cell tiling (CCT, after Henely) decorated with Bergman clusters.