Structural studies of monoclinic approximants of Al₁₃Fe₄ and τ²-inflated Al₁₃Co₄ by the high-angle annular dark-field method

We have taken high-angle annular dark-field (HAADF) images of two monoclinic approximants, Al₁₃Fe₄ with lattice parameters of a = 1.5489 nm, b = 0.80831 nm, c = 1.2476 nm and β = 107.72°(Black P J (1955), Acta Crystallogr. 8: 43-48) and its τ²-inflated Al₁₃Co₄ with lattice parameters of a = 3.984 nm, b = 0.8148 nm, c = 3.223 nm and β = 107.97°(Ma X L and Kuo K H (1994), Metallurgical Materials Transactions 25A: 47-56). The space group of the τ²-Al₁₃Co₄ approximant has been determined to be P2/m using the convergent-beam electron diffraction method. 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-Cu-Co, Al-Co and Al-Ni-Co by conventional high-resolution electron microscopy (HREM). A structural model of τ²-inflated Al₁₃Co₄ is constructed on the basis of the convergent-beam electron diffraction symmetry and HAADF images by referring to the structure of monoclinic Al₁₃Fe₄. The model is examined by the conventional HREM images and simulations. The 2 nm cluster of τ²-Al₁₃Co₄ is compared with the fivefold atom-cluster with a 2 nm diameter in decagonal quasicrystals of Al-Ni-Fe, Al-Cu-Co, Al-Co and Al-Ni-Co.