Single-crystal x-ray diffraction from an icosahedral quasicrystal
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Recent transmission electron diffraction observations1'2 of icosahedral point symmetries in numerous rapidly quenched intermetallic compounds have understandably caused great excitement. The incompatibility of icosahedral symmetry and long-range positional order was resolved by introducing a new class of structures that have long-range bond orientational order and perfect quasiperiodic translational order.3 One theoretical approach has been to utilize the density wave description of this new class of material, which leads to phenomenological Landau theory for quasicrystals.45 Another elegant approach makes use of a quasiperiodic packing of two or more unit cells, known as three-dimensional Penrose tiles6 to describe a quasicrystal.4i7~9 A model10 based on orientationally ordered glasslike packing of icosahedra and three-dimensional Penrose tiling models both reproduce the electron diffraction patterns quite accurately, but little is known of the actual atomic positions that decorate the cells. This novel phase has been observed in micron-size grains and in a metastable form; therefore, most of the structural studies have been limited to transmission electron microscopy (TEM) and powder x-ray diffraction." A quantitative structural analysis is difficult with TEM because of multiple scattering, while powder x-ray diffraction cannot reveal the underlying microscopic symmetry. Very recently it has been demonstrated 12~15 that large icosahedral single crystals of an Al-Li-Cu alloy can be prepared in a stable form, and single-crystal x-ray paterns from some major axes have been reported.16 We have carried out quantitative x-ray diffraction measurements on a millimeter-size single icosahedral crystal of this alloy. The object of the present investigation is to verify the existence of the icosahedral point group symmetry and provide quantitative intensities to be used in structure determination. We prepared the bulk alloy Al(0.59)Cu(0.10)Li(0.31) in argon atmosphere, heated it at 700 °C for a day and then cooled it slowly in several hours. Metallographic study revealed three sep-
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J. Mater. Res. 2 (3), May/Jun 1987
http://journals.cambridge.org
arate phase formations in exact agreement with the previous study.15 Millimeter-size icosahedral grains were easily identified and isolated for detailed x-ray measurements. Single-crystal x-ray measurements were made with a 12 kW rotating anode x-ray generator equipped both with a triple axis, four circle single-crystal diffractometer, and a real-time Laue camera. Focusing a graphite monochromator in the nondispersive configuration yielded a resolution of 0.01 A ~ ' in the longitudinal and transverse directions and also 0.19 A " 1 in the vertical direction with the Cu Ka or Mo Ka radiations used. A real-time transmission Laue camera with a 0.5 mm beam collimator and two-circle goniometer were used to observe the diffraction patterns and measure the angles of the major symmetry axes as the sample was rotated in three dimensions. The major symmetry directions observed only exhi
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