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A complementary approach to solve quasi crystalline atomic structures in 3-dimensional (3D) real space is presented: The atomic pair distribution function (PDF) of face centred icosahedral Ho 9 Mg 26 Zn 65  [ a (6D) = 2 × 5.18(3) Å] has been obtained from in-house powder X-ray diffraction data (Mo K α   1 ). For the first time, full profile PDF refinements of a quasicrystal were performed: Starting with rational approximant models, derived from 1/1- and 2/1-Al—Mg—Zn, its local and medium range structure was refined ( r  &lt; 27 Å;  R  = 12.9%) using the PDF data. 85% of all atoms show Frank-Kasper (FK) type coordinations. The basic structural unit is the 3-shell, 104-atom Bergman cluster ( d  ≈ 15 Å) 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 and form a Ho 8  cube (edge length 5.4 Å); they are completed by 12 Mg atoms to a pentagon dodecahedron. Cubes in neighbouring clusters are tilted with respect to each other; their superposition generates diffraction symmetry 2/ m 3̅5̅. The remaining Ho atoms act as glue atoms. As a result and as can be expected for real matter, local atomic coordinations in quasicrystals are similar when 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.

Medium range real atomic structure of face-centred icosahedral Ho 9 Mg 26 Zn 65