A new orthorhombic approximant of the Ga–Mn and Ga–Fe–Cu–Si decagonal quasicrystals consisting entirely of uniformly oriented ‘crown’ subunits

Abstract

Abstract By means of high resolution electron microscopy (HREM), the orthorhombic (2/1,1/1) approximant (a = 2.04 nm, b = 1.25 nm and c = 1.48 nm) of the decagonal quasicrystal in Ga–Mn and Ga–Fe–Cu–Si alloys was found to consist of a B-centred rectangular tessellation of the ‘crown’ or ‘concave octagon’ subunit, a binary tile composed of one thin and three fat Penrose rhombi with an edge length of 0.66 nm. Based on the atomic decoration of these Penrose rhombi, a structural model of the crown subunit and that of the Ga–Mn (2/1,1/1) approximant have been put forward. Simulated electron diffraction patterns and HREM images compared favourably with the experimental results. Various periodic tilings of the crown subunit, either alone or intermixed with other binary tiles (hexagon, 72° pentagonal star and/or decagon) were discussed and compared with a number of approximants found experimentally by HREM.