Approximants of Al–Cr–Fe–Si decagonal quasicrystals described by single structural block

The orthorhombic (3/2, 2/1) approximant with a = 3.06 nm, b = 1.23 nm, c = 2.24 nm, and the coexisting (2/1, 3/2) approximant of decagonal quasicrystals with a = 1.90 nm, c = 3.64 nm, and beta congruent to 90 degrees are found in Al-Cr-Fe-Si alloys by aberration-corrected transmission electron microscope. The structural relationships of these two approximants are analyzed and discussed based on the high-angle annular dark-field scanning transmission electron microscopy images at atomic resolution. We find that both of their structural tiling along the [010] direction can be described by one shield-like tile, with the superiority over the previous HBS tiling model due to the clarity. Combining the shield-like tile and HBS tiling model, the domains of approximants are clearly demonstrated. (C) 2015 Elsevier B.V. All rights reserved.