Structure determination of a pseudo-decagonal quasicrystal approximant by the strong-reflections approach and rotation electron diffraction

Abstract

The structure of a complicated pseudo-decagonal (PD) quasicrystal approximant in the Al–Co–Ni alloy system, denoted as PD1, was solved by the strong-reflections approach on three-dimensional rotation electron diffraction (RED) data, using the phases from the known PD2 structure. RED shows that the PD1 crystal is primitive and orthorhombic, witha= 37.3,b= 38.8,c= 8.2 Å. However, as with other approximants in the PD series, the superstructure reflections (corresponding toc= 8.2 Å) are much weaker than those of the main reflections (corresponding toc= 4.1 Å), so it was decided to solve the PD1 structure in the smaller primitive unit cell first,i.e.with unit-cell parametersa= 37.3,b= 38.8,c= 4.1 Å and space groupPnam. A density map of PD1 was calculated from only the 15 strongest unique reflections. It contained all 31 Co/Ni atoms and many weaker peaks corresponding to Al atoms. The structure obtained from the strong-reflections approach was confirmed by applying direct methods to the complete RED data set. Successive refinement using the RED data set resulted in 108 unique atoms (31 Co/Ni and 77 Al). This is one of the most complicated approximant structures ever solved by electron diffraction. As with other approximants in the PD series, PD1 is built of characteristic 2 nm wheel clusters with fivefold rotational symmetry, which agrees with results from high-resolution electron microscopy images. The simulated electron diffraction patterns for the structure model are in good agreement with the experimental electron diffraction patterns obtained by RED.