Icosahedral quasicrystals (i-QCs) are long-range ordered solids that show non-crystallographic symmetries such as five-fold rotations. Their detailed atomic structures are still far from completely understood, because most stable i-QCs form as ternary alloys suffering from chemical disorder. Here, we present the first detailed structure solution of i-YbCd 5.7 , one of the very few stable binary i-QCs, by means of X-ray structure determination. Three building units with unique atomic decorations arrange quasiperiodically and fill the space. These also serve as building units in the periodic approximant crystals. The structure is not only chemically feasible, but also provides a seamless structural understanding of the i-YbCd 5.7 phase and its series of related i-QCs and approximant crystals, revealing hierarchic features that are of considerable physical interest.Icosahedral quasicrystals (i-QCs) are the only class to show quasiperiodicity in three dimensions 1,2 . Obviously, structural knowledge is essential for understanding the physical properties, stability and tailoring applications of these exotic materials 3 . However, in contrast to other types of QCs that show periodic order in at least one direction, i-QCs cannot make effective use of two-dimensional (2D) imaging techniques such as high-resolution electron microscopy or high-angle annular dark-field scanning transmission electron microscopy for their structural characterization 4 . The i-QCs' structure determination is best achieved in the context of hyperspace crystallography 5,6 , where the structure can be described as a periodic crystal in higher dimensions. For i-QCs, the periodic space is 6D and decomposes into two orthogonal 3D subspaces: the parallel (physical) space and the perpendicular (complementary) space. The 6D unit cell is decorated by 3D objects known as 'occupation domains' (OD), the 3D QCs being obtained as a section of this decorated 6D lattice. This approach allows modelling and refinement of the structure against experimental diffraction data in a way similar to that achieved for 3D periodic crystals 6 . Although much progress has been achieved recently, for instance in the i-AlPdMn phase 7 , the models proposed so far are still being debated 8 . Indeed, the amount of observed diffraction data is in general rather limited, which precludes a detailed refinement of the chemical order in ternary QCs. Therefore, the atomic order in i-QCs remains a challenging and outstanding question. The recent discovery of the first stable binary icosahedral YbCd 5.7 QCs 9,10 has been a breakthrough and led to discoveries of a whole series of related ternary i-QCs 11 . This i-QC offers a unique opportunity for the structural analysis of i-QCs. Indeed, the i-YbCd 5.7 phase can be obtained as high-quality single grains. Furthermore, it is binary and exhibits very good X-ray contrast between Cd (Z = 48) and Yb (Z = 70) atoms.Finally, there is a series of periodic 'approximant crystals' (ACs) to the QC, having almost the same chemical composition and for...

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Quasicrystals are metallic alloys that possess long-range, aperiodic structures with diffraction symmetries forbidden to conventional crystals. Since the discovery of quasicrystals by Schechtman et al. in 1984, there has been considerable progress in resolving their geometric structure. For example, it is well known that the golden ratio of mathematics and art occurs over and over again in their crystal structure. However, the characteristic properties of the electronic states--whether they are extended as in periodic crystals or localized as in amorphous materials--are still unresolved. Here we report the first observation of quantum (T = 0) critical phenomena of the Au-Al-Yb quasicrystal--the magnetic susceptibility and the electronic specific heat coefficient arising from strongly correlated 4f electrons of the Yb atoms diverge as T→0. Furthermore, we observe that this quantum critical phenomenon is robust against hydrostatic pressure. By contrast, there is no such divergence in a crystalline approximant, a phase whose composition is close to that of the quasicrystal and whose unit cell has atomic decorations (that is, icosahedral clusters of atoms) that look like the quasicrystal. These results clearly indicate that the quantum criticality is associated with the unique electronic state of the quasicrystal, that is, a spatially confined critical state. Finally we discuss the possibility that there is a general law underlying the conventional crystals and the quasicrystals.

The structure of a decagonal Al72Ni20Co8 quasicrystal with space group P10(5)/mmc has been determined on the basis of a single-crystal X-ray data set using the five-dimensional description. The best-fit model structure based on a cluster model having lower symmetry than the decagonal symmetry with 103 parameters gives wR = 0.045 and R = 0.063 for 449 reflections. The structure is well described by the hexagon, boat and star tiling with an edge length of 6.36 A and is very consistent with recent high-resolution electron-microscopy images. The refined structure is compared with previously discussed model structures including cluster-based models having 20 A tenfold symmetric clusters.

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We present new evidence supporting the quasi-unit-cell description of the Al72Ni20Co8 decagonal quasicrystal which shows that the solid is composed of repeating, overlapping decagonal cluster columns with broken tenfold symmetry. We propose an atomic model which gives a significantly improved fit to electron microscopy experiments compared to a previous proposal by us and to alternative proposals with tenfold symmetric clusters.

Magnetic diffuse scattering in the Zn-Mg-Ho icosahedral quasicrystal has been studied by neutron scattering over a wide Q range using a single-quasicrystalline sample. It was found that the diffuse scattering obeys the icosahedral symmetry, and appears as satellite peaks of the intense nuclear Bragg reflections. The diffusescattering patterns were successfully accounted for by assuming short-range spin correlations in a sixdimensional hypercubic crystal with a magnetic modulation vector qϭ( 3 4 ,0,0,2 ) a* . A possible origin for the six-dimensional spin correlations is discussed.