Local atomic three-dimensional real-space structural analysis of icosahedral Mg–Zn–RE (RE = Y or Ho) alloys: strategy, method and models

Abstract

The local structure of any condensed matter is accessible via an atomic pair distribution function (PDF) analysis. Here, the local atomic structure of the well-ordered face-centred icosahedral (fci)-Mg₂₅Y₁₁Zn₆₄, fci-Ho₉Mg₂₆Zn₆₅ and simple icosahedral Ho₁₁Mg₁₅Zn₇₄ quasicrystals have been investigated by PDFs obtained from in-house X-ray and synchrotron powder data. Least-squares refinements using periodic 1/1 and 2/1 approximants as models for the local atomic structure have been performed. They reveal predominantly Frank–Kasper-type coordination polyhedra. The basic building block is a Bergman cluster of about 100 atoms of 14 Å diameter. RE₈ cubes of edge length 5.4 Å are part of the cluster occupying pentagon dodecahedral positions. The cluster connection scheme follows in general that of Henley's canonical cell tiling. However, according to our results, overlapping clusters are likely to be present in the quasicrystalline structure. Thus interpenetration seems to be a general feature for clusters in quasicrystals, which complicates the ongoing discussion on their nature.