Structure of Al–Co–Ni pentagonal quasicrystal studied by HAADF-STEM and ab initio calculations

Abstract

Using a combination of atomic-resolution high-angle annular dark-field (HAADF) Z-contrast imaging and ab initio calculations, atomic models of clusters 2 nm in diameter and 0.8 nm in height are proposed for the Al–Co–Ni pentagonal quasicrystal. This quasicrystal has 5-fold symmetry (the so-called 5f state) without superstructures, and is one of numerous modifications of the Al–Co–Ni decagonal quasicrystal. HAADF results reveal that the two-dimensional quasi-periodic lattice contains mainly Penrose pentagonal tiling. The centres within the decorated pentagonal tiles, i.e. the so-called pentagonal super-clusters, show structural characteristics having both a satellite-orbit shape and a pentagon-symmetry shape. The proposed atomic models, based directly on the HAADF images, are subjected to ab initio total energy calculations. After relaxation, the calculations demonstrate that the models with 5-fold symmetry are energetically more favourable than those with 10-fold symmetry.