Crystalline phases related to a decagonal quasicrystal. I. A single-crystal X-ray diffraction study of the orthorhombic Al₃Mn phase

Al3Mn (with the stoichiometric composition Al28.1Mn10.9), M(r) = 1356.5, orthorhombic, Pn2(1)a, a = 14.837 (4), b = 12.457 (2), c = 12.505 (2) angstrom, V = 2311.2 (8) angstrom3, atoms/cell = 4 x 39, D(x) = 3.90 g cm-3, lambda(Mo Kalpha) = 0.71069 angstrom, mu = 65.82 cm-1, F(000) = 2550.15, room temperature, R = 0.068 for 1289 reflections. About two-thirds of Mn atoms have icosahedral coordination. In a repeat unit b, there are four interpenetrated icosahedra with two Mn and two Al atoms at their centers. This phase has a layer structure consisting of an almost 'flat' layer F sandwiched between two puckered P and p layers in the sequence PFpP'F'p'..., where P'F'p' and PFp are related by the 2(1) axes parallel to [010]. A similar layer structure has also been found in the pi-AlMnM (M = Ni, Cu, Zn) phases. Both these two crystalline structures can be obtained from that of the Al-Mn decagonal quasicrystal by substituting a rational ratio of two consecutive Fibonacci numbers for the irrational tau = [1 + (5)1/2]/2 in the two quasiperiodic directions.