ν-Al80.61Cr10.71Fe8.68, P63/m (No. 176), a = 40.68 (7), c = 12.546 (1) Å, V = 17 983 (8) Å3, atoms/cell = 1184.56, D
x
= 3.518 g cm−3, λ(Mo Kα) = 0.71069 Å, μ = 5.032 mm−1, F(000) = 18 433, T = 293 K, final R = 0.075 for 3854 reflections with F
o
> 4σ(F
o
). The [001] high-resolution electron-microscopic image of the ν-AlCrFe phase clearly shows similar local characteristics to those given by the complex icosahedral cluster found in somewhat smaller hexagonal approximant structures, such as κ-Al76Cr18Ni6 [a = 17.674 (3), c = 12.516 (3) Å; Sato et al. (1997). Acta Cryst. C53, 1531–1533; Marsh (1998). Acta Cryst. B54, 925–926] and λ-Al4.32Mn [a = 28.382 (9), c = 12.389 (2) Å; Kreiner & Franzen (1997). J. Alloys Compd.
261, 83–104]. Using the known atomic distribution of this icosahedral cluster in the κ and λ phases as the starting point, the structure of the ν phase, a hexagonal intermetallic compound with probably the largest a parameter, was solved by X-ray single-crystal diffraction using direct methods. As in κ and λ phases, almost all TM (transition metal) atoms in the complex icosahedral cluster are icosahedrally coordinated. However, contrary to the λ structure in which about 98% of the TM atoms have icosahedral coordination, the TM atoms in the ν structure also form capped pentagonal prisms in the region between these complex icosahedral clusters, yielding an average icosahedral coordination of about 70% for TM atoms. After rapid solidification, the ν phase occurs together with a decagonal quasicrystal with a periodicity of about 12.5 Å along its tenfold axis and thus also consists of six layers, two flat ones each sandwiched between two puckered layers in mirror reflection, stacked along the c axis.
Full spin and spatial symmetry adapted technique for correlated electronic hamiltonians: Application to an icosahedral cluster
