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We have studied by NMR the electronic properties of the stable quasicrystalline phases AI57-Cuio.8Li32.2 and Al62Cu25.sFei2.5 and of two crystalline approximants, the bcc R phase AI56C1112L132 and the rhombohedral Al62.8Cu26Fen.2 phase. Low values of the density of states at the Fermi level are observed in the crystalline as well as in the quasicrystalline phases. The existence of a pseudogap at the Fermi level is therefore not a consequence of the quasiperiodicity. These results renew the debate on the stability of quasicrystals.PACS numbers: 61.42.+h, 76.60.Es Much work has been devoted to the electronic properties of newly discovered stable quasicrystalline (hereafter qc) phases with icosahedral symmetry, such as Al-Cu-Li [1], Al-Cu-Fe [2,3], or Al-Cu-Ru [4], to decide whether or not the quasiperiodicity induces specific properties. A well-established common feature of all these qc phases is a high room-temperature resistivity which moreover increases as the temperature decreases. Such effects have been ascribed to localization effects, and the proximity of a metal-insulator transition has been evoked [3]. Low values of the electronic density of states at the Fermi level, 7V(£>), deduced from specific-heat measurements, have been reported. The reduction of /V(£>) with respect to estimated free-electron values is about one-third in Al-Li-Cu [1] and Al-Cu-Fe [2,3]. It reaches one-tenth in Al-Cu- Ru [4]. This observation of a pseudogap at the Fermi level in qc materials is in agreement with theoretical predictions [5]. It has been suggested that this pseudogap could explain the thermodynamical stability of these qc phases, following a Hume-Rothery scheme [5-71.The qc phases are found in a very narrow composition range of complex ternary phase diagrams. Several different crystalline phases usually exist with close compositions. Among these, the so-called approximant phases are especially interesting. The qc and approximant phases have very similar local order and exhibit closely related diffraction spectra. Within a theoretical point of view, the existence of approximants is quite natural [8]. Whereas the 3D quasiperiodic lattice is obtained from a 6D hypercubic lattice by a cut and projection along irrational directions of the 6D space, periodic approximants are obtained by projection along rational close directions. The period of such an approximant, of course, increases when the rational directions get closer to the irrational ones. Although the existence of approximants should be quite general, their identification in real phase diagrams is not alway easy. The crystalline bcc phase AI56CU12L132 (the so-called R phase) has been recognized early as an approximant of the icosahedral qc AI57CU 10.8^32.2 phase [9]. The existence of an approximant in the Al-Cu-Fe system was suggested by the observation of a microcrystalline structure with a rhombohedral symmetry in small dodecahedral particles extracted from an ingot [10]. However, this approximant phase has been only very recently prepared in appreciable quantit...

Two stable phases of the Al-Li-Cu system exhibit interesting crystallographic features. The R-Al5CuLi3 compound has a Im3 point group with icosahedral and triacontahedral arrangements. The Al6CuLi3 compound has a quasi-crystalline like structure as confirmed by both X-ray and electron diffraction. This phase may be obtained either as large single quasi-crystals by conventional casting or as reversible precipitation by ageing of aluminium rich solid solutions

Using both powder and single crystal samples, neutron and x-ray diffraction data were obtained with quasicrystals of the AlLiCu system. lsotopic substitution on the Li and Cu atomic sites allowed amplitudes and phase shift of the partial StNCtUle factors to be determined, Using a high-dimensional crystallography approach results in the phases to be reconstructed and atomic densities were calculated. The six-dimensional periodic structure appeared as a primitive hypercubic lattice with mid-edge and vertex AI/Cu atomic surfaces plus a Li bodycentre site. The major drawbacks of the experimental approach are then bypassed by modelling details of the sixdimensional $tmcture, still in agreement with diffraction data. The related three-dimensional quasiperiodic structure can be described in terms of connected clusten or, alternatively. families of atomic planes. Comparison with the structure of the crystalline R-phase is of interest. 2 chemical from topological parameters. Such a procedure has been achieved to some extent with the AIMn quasicrystals [l, 21 thanks to contrast variation effects in neutron diffraction.Quasicrystals of the AlLiCu system are certainly an exciting subject within this scheme since contrast variations can be easily and rigorously produced by isotopic substitutions on Li(6Li, 'Li) and C U ( ~C U , %U) atoms [6]. Moreover, single grains of more than a millimetre across [7-101 can be grown and then single crystal x-ray and neutron diffraction studies are feasible [Il-141. The purpose of this paper is to derive the best possible structure of AlLiCu quasicrystals, directly from neutron and x-ray diffraction data. M de Boissieu et a1 Basic principles for quasicrystallographyThe relations between AD quasiperiodic and higher dimensional periodic structures are well understood [15][16][17]. Icosahedral quasicrystals have periodic structures in 6~ space which contains our 3D physical space, also called parallel space R3par and a complementary, or perpendicular, space R3,,,. In the cut method [18], an icosahedral quasiperiodic arrangement of atoms in 3D physical space R3,,, corresponds to a periodic arrangement of 3D hypersurfaces, or atomic shells A3,,, in 6 0 space R6. These atomic shells intersect the 3D real world hyperplane at the atom positions. For each type (or family) of atomic sites in three dimensions there is one A3,., shell whose relative volume is directly related to the corresponding relative atomic 3~ density. In an idealistic monoatomic icosahedral quasicrystal, with a single site at the origin of the 60 structure, and triacontahedral A3,,,, entirely contained in the R3,,,, space, the 3~ atomic density is a distribution of Dirac functions at the vertex positions of a 3D Penrose tiling ( 3 ~m ) . The volume of A3pc.p is equal to n3a6 in which ( I is th& 6D lattice parameter and n3 the 3~ atomic density.. Correspondence rules also exist between the reciprocal spaces R6*, R 3 g and R3&,. These reciprocal spaces contain the Fourier transforms (FT) of the densities. It is easy to demonstrate t...