Structural studies of decagonal quasicrystals and approximants using the high-angle annular dark-field method

High-angle annular dark-field (HAADF) images of an Al₇₂Ni₂₀Co₈ decagonal quasicrystal and monoclinic Al₁₃Fe₄ and τ²-inflated Al₁₃Co₄ approximants have been presented. We found that a 2 nm atom cluster of Al₇₂Ni₂₀Co₈, which have been believed to be tenfold so far, has no tenfold symmetry. A new structural model of Al₇₂Ni₂₀Co₈ has been constructed on the basis of the HAADF images and the structure of monoclinic Al₁₃Fe₄ approximant. We have found that the monoclinic Al₁₃Fe₄ and τ²-inflated Al₁₃Co₄ approximants are composed of the same basic structure of a pentagonal atom cluster with an edge length of 0.47 nm. We have also found that a fivefold atom-cluster with a 2 nm diameter exists in τ²-Al₁₃Co₄, which was observed in decagonal quasicrystals of Al-Ni-Fe, Al-Ni-Co, Al-Cu-Co and Al-Co by high-resolution electron microscopy. A structural model of τ²-inflated Al₁₃Co₄ is constructed on the basis of the convergent-beam electron diffraction symmetry, HAADF images and the structure of monoclinic Al₁₃Fe₄.