Local 3D real space atomic structure of the simple icosahedral Ho11Mg15Zn74 quasicrystal from PDF data

We present a new complementary strategy to quasicrystalline structure determination: The local atomic structure of simple icosahedral (si) Ho₁₁Mg₁₅Zn₇₄ [a(6D) = 5.144(3)Å in a sphere of up to r = 17Å was refined using the atomic pair distribution function (PDF) from in‐house X‐ray powder diffraction data (MoKα₁, Q_max = 13.5Å⁻¹; R = 20.4%). The basic building block is a 105‐atom Bergman‐Cluster {Ho₈Mg₁₂Zn₈₅}. Its center is occupied by a Zn atom – in contrast to a void in face centred icosahedral (fci) Ho₉Mg₂₆Zn₆₅. The center is then surrounded by another 12 Zn atoms, forming an icosahedron (1st shell). The 2nd shell is made up of 8 Ho atoms arranged on the vertices of a cube which in turn is completed to a pentagon dodecahedron by 12 Mg atoms, the dodecahedron then being capped by 12 Zn atoms. The 3rd shell is a distorted soccer ball of 60 Zn atoms, reflecting the higher Zn content of the si phase compared to the fci phase. In our model, 7% of all atoms are situated in between the clusters. The model corresponds to a hypothetical 1/1‐approximant of the icosahedral (i) phase. The local coordinations of the single atoms are of a much distorted Frank‐Kasper type and call to mind those present in 0/1‐Mg₂Zn₁₁. (© 2003 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)