A new approach to solve quasicrystalline atomic structures in 3-dimensional (3D) real space is presented: The atomic pair distribution function (PDF) of face centred icosahedral Ho 9 Mg 26 Zn 65 [a(6D) = 2×5.18(3)Å] was obtained from in-house X-ray diffraction data (MoKα 1 ). Starting with rational approximant models, derived from 1/1and 2/1-Al-Mg-Zn, its local and medium range structure was refined (r < 27Å; R = 12.9%) using the PDF data. 85% of all atoms show Frank-Kasper (FK) type coordinations. Basic structural unit is the 3-shell, 104-atom Bergman cluster (d ≈ 15Å) comprising a void at its center. The clusters are interconnected sharing common edges and hexagonal faces of the 3rd shells. T he remaining space is filled by some glue atoms (9% of all atoms), yielding an almost tetrahedrally close packed structure. All Ho atoms are surrounded by 16 neighbours (FK-polyhedron "P"). Most of them (89%) are situated in the 2nd shell (pentagon dodecahedron), the other act as glue atoms. As a result and as can be expected for real matter, local atomic coordinations in quasicrystals are similar compared to common crystalline intermetallic compounds. From our results, the long range quasiperiodic structure of icosahedral Mg-Zn-RE (RE = Y and some rare earths) is anticipated to be a canonical cell tiling (CCT , after Henely) decorated with Bergman clusters.
Ultrasonic measurements were performed on a fci Zn-Mg-Y quasicrystal and on the related parent compound Zn2Mg. Absolute values of both the longitudinal and the transverse sound velocities as well as their temperature dependence were determined. The temperature dependence of the quasicrystal sound velocity in the millikelvin temperature range is very similar to the logarithmic behaviour observed for amorphous materials.Introduction. -Since the discovery of the first quasicrystalline structure by Shechtman et al. [1] in 1984 in the system Al-Mn, there is a great interest in these long-range ordered but not periodic structures. However, only a few systems exist which are thermodynamically stable, most of them in the Al-TM system (TM = transition metal) like Al-Li-Cu [2], Al-Cu-Fe [3] and Al-Pd-Mn [4]. In 1993 a stable icosahedral phase was discovered in the system Zn-Mg-RE by Luo et al. [5]. This icosahedral phase turned out to be identical with the Z-phase found in 1982 by Padezhnova et al. [6] with a composition of Zn 6 Mg 3 Y 1 , whose structure could not be determined at that time. A detailed investigation showed the stability of the i-phase for the RE elements Y, Gd, Tb, Dy, Ho and Er [7]. In contrast to most of the other known i-phases, this system is based on Zn -not Al-as the main constituent. Another interesting feature of this quasicrystalline alloy is the possibility of incorporating RE elements with 4f -electron carrying a localized magnetic moment (Tb, Ho, Gd) in the quasicrystalline lattice.Since the determination of the primary solidification area in 1997 by Langsdorf et al. [8], large face-centred icosahedral (fci) Zn-Mg-RE single grains can be grown from the melt by different techniques [9][10][11]. Since then, measurements on single grains could be performed. Recent results of neutron scattering experiments show that the fci Zn-Mg-RE quasicrystals do not develop long-range magnetic order [12], however, diffuse-scattering data can be interpreted as short-range spin correlations in a six-dimensional hypercubic crystal [13]. So far, no ultrasonic investigations have been done in this system.
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