The crystal structure of the orthorhombic phase Al4(Cr,Fe) with a composition of Al80.6Cr10.7Fe8.7 has been determined by single-crystal x-ray diffraction (table 2). There are 11 crystallographically independent Cr/Fe sites, of which 10 are icosahedrally coordinated. Of the 28 crystallographically independent Al sites 5 are icosahedrally coordinated. However, owing to the presence of many partial occupancies, caused by split atoms, some of these coordinations are only pseudo-icosahedral with effective coordination numbers (section 4.3). The icosahedral and pseudo-icosahedral clusters are oriented with a two-fold axis parallel to [100]. They are linked either by vertex-, edge- or face-sharing or by mutual interpenetration, thus forming large clusters of icosahedra in the (100) layers with one of the five-fold axes in the [010] direction. Four of the 12 atoms defining the vertices of an icosahedral cluster lie in a mirror plane (F plane), while the other atoms are in puckered layers below and above the mirror plane. Thus, the icosahedral cluster consists of layers of three atoms thick. Two such layers stack within one lattice constant  nm. The interconnection of icosahedra in the layer block forms large triangular and hexagonal structural motifs, though they have only two-fold rotational symmetry. Similar geometrical motifs but displaying three- or six-fold symmetry do exist in the structure of the hexagonal μ-Al4Mn, κ-(AlCrNi), λ-Al4Mn and ν-Al12Cr2Fe phases.

Nu-Al(80.61)Cr(10.71)Fe(8.68), P6(3)/m (No. 176), a = 40.68 (7), c = 12.546 (1) A, V = 17,983 (8) A3, atoms/cell = 1184.56, Dx = 3.518 g cm(-3), lambda(Mo K alpha) = 0.71069 A, mu = 5.032 mm(-1), F(000) = 18,433, T = 293 K, final R = 0.075 for 3854 reflections with Fo > 4sigma(Fo). The [001] high-resolution electron-microscopic image of the nu-AlCrFe phase clearly shows similar local characteristics to those given by the complex icosahedral cluster found in somewhat smaller hexagonal approximant structures, such as kappa-Al76Cr18Ni6 [a = 17.674 (3), c = 12.516 (3) A; Sato et al. (1997). Acta Cryst. C53, 1531-1533; Marsh (1998). Acta Cryst. B54, 925-926] and lambda-Al(4.32)Mn [a = 28.382 (9), c = 12.389 (2) A; Kreiner & Franzen (1997). J. Alloys Compd. 261, 83-104]. Using the known atomic distribution of this icosahedral cluster in the kappa and lambda phases as the starting point, the structure of the nu phase, a hexagonal intermetallic compound with probably the largest a parameter, was solved by X-ray single-crystal diffraction using direct methods. As in kappa and lambda phases, almost all TM (transition metal) atoms in the complex icosahedral cluster are icosahedrally coordinated. However, contrary to the lambda structure in which about 98% of the TM atoms have icosahedral-coordination, the TM atoms in the v 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 v phase occurs together with a decagonal quasicrystal with a periodicity of about 12.5 A 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.

The three-dimensional (3D) structure of the huge quasicrystal approximant nu-AlFeCr (space group P6(3)/m, a = 40.687 and c = 12.546 A) was solved by electron crystallography. High-resolution transmission-electron-microscopy (HREM) images and selected-area electron diffraction patterns from 13 different zone axes were combined to give a 3D potential map. 124 out of 129 unique atoms were found in the 3D map. Procedures for ab initio structure determination by 3D reconstruction are given. It is demonstrated that 3D reconstruction from HREM images is very powerful for solving structures--even very complicated ones. There is no limit in terms of the number of unique atoms in a structure that can be solved by 3D reconstruction.

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