Local cluster symmetry of a highly ordered quasicrystalline Al58Cu26Ir16extracted through multivariate analysis of STEM images

The structure of a highly ordered Al58Cu26Ir16 decagonal quasicrystal (d-QC), which is constructed by a periodic stack of quasiperiodic atomic planes, was investigated using aberration-corrected scanning transmission electron microscopy. The entire quasiperiodic structure can be well described based on the pentagonal Penrose lattice decorated with a decagonal columnar cluster 2 nm across, and the individual clusters apparently showed up with localized atomic disorder to various degree that blurs the underlying cluster symmetry. Multivariate analysis of the cluster images with principal component analysis has successfully extracted two fundamental clusters, which are with definite mirror and 10-fold-rotation symmetries; this is the first solid example of the d-QC composed of multiple fundamental clusters with different symmetry. Consequently, it is found that all the observed variations can be reasonably interpreted by a linear combination between these two fundamental clusters of mirror and 10-fold symmetries, indicating that the possible atomic disorder is strongly restricted by these particular symmetries. Characteristic distributions of the mirror/10-fold clusters on the pentagonal Penrose lattice are also described.