Crystal Structure of Superconducting 1/1 Cubic Au–Ge–Yb Approximant with Tsai-Type Cluster

Abstract

We report the synthesis of a single-phase sample of the superconducting crystalline approximant Au64.0Ge22.0Yb14.0 and present a structure model refined by Rietveld analysis for X-ray diffraction data.Quasicrystals (QCs) are metallic alloys that possess long-range, quasi-periodic structures with diffraction symmetries forbidden to conventional crystals, while approximant crystals (ACs) are alloys whose composition is close to that of QCs and whose unit cell has atomic decorations similar to those of the QCs. In this Short Note, we report a detailed structure analysis of the AGY(I) AC. For AGY(II), we are unable to provide a structure model owing to the lack of a single-phase sample.Polycrystalline samples of the optimally compositioncontrolled compound Au 64.0 Ge 22.0 Yb 14.0 were synthesized, and their structures were characterized by powder X-ray diffraction using Cu Kα-radiation. Details of the sample preparation and X-ray diffraction analysis experiments were described in Refs. 3 and 1, respectively. Figure 1 shows a powder X-ray diffraction pattern of AGY(I), indicating the body-centered cubic structure (space group Im3) with a lattice parameter a = 1.4724(2) nm. The Rietveld analysis successfully converged with R-factors, R wp = 5.41%, R I = 0.95%, and R F = 0.59% (for the structure parameters, see Table I), assuming that the cluster center is occupied by an orientationally disordered tetrahedron. 4 This suggests that the alloy has a similar structure to the Tsaitype 1/1 AAY AC. This structure model contains 9 crystallographic sites and includes 174.1 atoms in total in a unit cell, which corresponds to the chemical * E-mail: deguchi@edu3.phys.nagoya-u.ac.jp Figure 2 shows the structure model for the AGY(I) AC. As shown in Fig. 2(a), the cluster center (M7 site) is occupied by Au atoms with an occupancy of 26.9%. The complicated shape of the cluster center, in which 4 atoms in total are ideally included, indicates an average of variously oriented tetrahedrons. The second shell [ Fig. 2(b)] is a dodecahedron, in which there are Au/Ge mixed sites named M2 and M4 sites. The third shell [ Fig. 2(c)] is an icosahedron, in which Yb ions exclusively occupy the Yb1 site. The icosahedron is surrounded by an icosidodecahedron [ Fig. 2(d)] in which the M1 and M6 sites are almost occupied by Au atoms and the M8 site is occupied by Ge with an occupancy of 95%. These shells, i.e., the dodecahedron, icosahedron, and icosidodecahedron compose the so-called Tsai-type cluster. Finally, Tsaitype clusters are embedded in the cage composed of M3 and M5 [ Fig. 2(e)]. The periodic arrangement of this cage 1

Synthesis and Atomic Structure of the Yb–Ga–Au 1/1 Quasicrystal Approximant

“…In both cases, the atomic structures consist up of Tsai-type RTH clusters but with different central shells. In the Ge-poor phase, four atoms (a mixture of Au and Ga) are situated at the cluster center, while in the Ge-rich phase, a single Yb atom occupies the center. − This results in different compositions and lattice parameters {i.e., Yb 14.0 Ge 22.0 Au 64.0 [ a = 14.724(2) Å] and Yb 16.0 Ge 20.5 Au 63.5 [ a = 14.605(4) Å]}. These two 1/1 APs may also form in the Yb–Ga–Au system, and the increase in the lattice parameter with a decrease in Ga concentration may be explained by the occupation of four atoms (a mixture of Au and Ga) at the cluster center.…”

“…A Rietveld analysis of the Yb–Al–Au 1/1 AP has demonstrated positional disorder at the cluster centers and the presence of atomic mixing of Au and Al at specific sites in RTH clusters . Because these characteristics were also found in the isostructural Yb–Ge–Au 1/1 AP, − they appear to be peculiar to Au-based APs and iQCs. To verify this hypothesis, structural analysis of other Au-based APs is required, particularly the Yb–Ga–Au 1/1 AP and Yb–Sn–Au 2/1 AP, which correspond to the recently discovered Yb–(Ga, Sn)–Au iQCs. , …”

Superconductivity of Au–Ge–Yb Approximants with Tsai-Type Clusters

“…The Rietveld structure analysis of the former successfully converged and indicated that the sample with an optimal composition x = 64.0 is of single phase and its cluster-center tetrahedron is orientationally disordered. 10 For the latter, on the other hand, the predominant phase has an optimal composition of y = 63.5 and the sample contains a small amount of an unidentified phase. The inclusion of the secondary phase prevented the complete Rietveld refinement.…”

High Dimensional Approach to Antiferromagnetic Aperiodic Spin Systems

“…c n ). To save calculation time, therefore, the number of points in lattices of n = 5, 6, were restricted to 3 5 = 243 and 3 6 = 729, respectively. In the 2D case, 11 2 lattice points and spins were used.…”