JournalofthePhysicalSocietyofJapan Crystal Structure of Superconducting 1/1 Cubic Au-Ge-Yb Approximant with Tsai-type Cluster Kazuhiko Deguchi1∗, Mika Nakayama1, Shuya Matsukawa1, Keiichiro Imura1, Katsumasa Tanaka2, Tsutomu Ishimasa2, and Noriaki K. Sato1 5 1 1Department of Physics, Graduate School of Science, Nagoya University, Nagoya 464-8602, Japan 0 2Division of Applied Physics, Graduate School of Engineering, Hokkaido University, Sapporo 060-8628, 2 Japan n a We report the synthesis of a single-phase sample of the superconducting crystalline approximant J Au64.0Ge22.0Yb14.0 and present a structuremodel refined byRietveld analysis for X-raydiffraction data. 8 ] n co Quasicrystals (QCs) are metallic alloys that pos- 25x103 Au-Ge-Yb (I) r- sess long-range, quasi-periodic structures with diffrac- 20 p tionsymmetriesforbiddentoconventionalcrystals,while nt) u approximant crystals (ACs) are alloys whose composi- ou 15 c s tion is close to that of QCs and whose unit cell has y ( at. atomic decorations similar to those of the QCs. Re- ensit 10 m cently, new types of QC and AC have been discov- Int 5 - ered:1 The Au-Al-Yb (AAY) QC exhibits unconven- 0 d tional quantum critical behavior as T → 0 and the n AAY AC shows heavy Fermi liquid,2 and the Au-Ge- 10 20 30 40q 50 60 70 80 o Yb(AGY) ACsshow superconductivitybelow 1 K.3 For 2 (deg) c [ the latter system, there are two types of alloys with 1 different concentrations, Au64.0Ge22.0Yb14.0 [AGY(I)] Fig. 1. (Color online) Powder X-ray diffraction pattern of v and Au63.5Ge20.5Yb16.0 [AGY(II)], with superconduct- Au64.0Ge22.0Yb14.0 [AGY(I)].Fromtoptobottom:calculatedin- tensity, measured intensity, peak position, and difference between 2 ing transition temperatures of 0.68 and 0.36 K, respec- calculationandmeasurement. 2 tively. In this Short Note, we reporta detailed structure 7 analysis of the AGY(I) AC. For AGY(II), we are un- 1 able to provide a structure model owing to the lack of a 0 single-phase sample. 1. composition Au65.3Ge20.9Yb13.8. Note that this com- Polycrystalline samples of the optimally composition- 0 position is compatible with the nominal composition 5 controlled compound Au64.0Ge22.0Yb14.0 were synthe- Au64.0Ge22.0Yb14.0. 1 sized,andtheir structures werecharacterizedby powder Figure 2 shows the structure model for the AGY(I) : X-ray diffraction using Cu Kα-radiation. Details of the v AC.AsshowninFig.2(a),theclustercenter(M7site)is samplepreparationandX-raydiffractionanalysisexper- i occupiedby Au atoms withanoccupancy of26.9%.The X iments were described in Refs. 3 and 1, respectively. complicatedshapeoftheclustercenter,inwhich4atoms r Figure 1 shows a powder X-ray diffraction pattern a in total are ideally included, indicates anaverageof var- of AGY(I), indicating the body-centered cubic struc- iouslyorientedtetrahedrons.Thesecondshell[Fig.2(b)] ture (space group Im¯3) with a lattice parameter a = isadodecahedron,inwhichthereareAu/Gemixedsites 1.4724(2) nm. The Rietveld analysis successfully con- named M2 and M4 sites. The third shell [Fig. 2(c)] is verged with R-factors, R = 5.41%, R = 0.95%, wp I an icosahedron,in which Yb ions exclusively occupy the and R = 0.59% (for the structure parameters, see F Yb1 site. The icosahedron is surrounded by an icosido- Table I), assuming that the cluster center is occupied decahedron[Fig.2(d)]in whichthe M1 andM6sites are by an orientationally disorderedtetrahedron.4 This sug- almost occupied by Au atoms and the M8 site is occu- gests that the alloy has a similar structure to the Tsai- pied by Ge with an occupancy of 95%. These shells, i.e., type 1/1 AAY AC. This structure model contains 9 the dodecahedron, icosahedron, and icosidodecahedron crystallographic sites and includes 174.1 atoms in to- compose the so-called Tsai-type cluster. Finally, Tsai- tal in a unit cell, which corresponds to the chemical type clusters are embedded in the cage composed of M3 andM5[Fig.2(e)].Theperiodicarrangementofthiscage ∗E-mail:[email protected] 1 J.Phys. Soc. Jpn. Table I. ParametersinthestructuremodelofAGY(I)1/1cubicAC.OccupanciesofsitesM7andM8are26.9%and95%,respectively. NotethattheB-factorisproportionaltotheatomicdisplacementparameterUeq=B/(8π2). Site Set Atom x y z B (˚A2) M1 48h Au 0.33941(8) 0.2014(1) 0.10469(8) 0.39(3) M2 24g 0.414Au+0.586Ge 0 0.2381(3) 0.0850(2) 0.71(9) M3 24g Au 0 0.5986(2) 0.6431(1) 0.20(4) M4 16f 0.78Au+0.22Ge 0.1489(2) − − 1.4(1) M5 12e 0.070Au+0.930Ge 0.2012(4) 0 1/2 0.4(1) M6 12d Au 0.4042(2) 0 0 0.49(7) M7 24g 0.269Au 0 0.082(1) 0.076(1) 5.9(5) M8 8c 0.95Ge 1/4 1/4 1/4 3.0(4) Yb1 24g Yb 0 0.1867(2) 0.3046(2) 0.10(4) 1.6 Group 1 Group 2 Group 3a Group 3b Group 4 1.5 Group 5 ) m Au-Ge-Yb(+2) (n Au-Al-Yb(+3) Ag-Ga-Yb(+2) a Au-Al-Tm Au-Ga-Yb(+2) 1.4 0.14 0.15 0.16 r (nm) Fig. 3. (Coloronline)Linearrelationshipbetweenlatticeparam- eter a and average atomic radius r¯ of Tsai-type ACs. Group 1: Cu-Al-ScandCu-Ga-Sc.Group2:Zn-ScandZn-Cu-Sc.Group3a: Ag-In-R(R=rareearth)andAu-In-Ca,Group3b:Ag-In-R,Cd- Y, and Cd-R. Group 4: Cd-Ca and Cd-Yb. Group 5: Pd-Al-Sc, Zn-Yb,andAu-Ga-Ca.SeeRef.1andreferencestherein. Fig. 2. (Color online) Concentric shell structure of Tsai-type cluster in the AGY(I) AC. A square frame denotes a unit cell. (a)Orientationallydisorderedtetrahedron composedofAuatoms respectively, by assuming valences of Au: 1, Ge: 4, and at M7 site. (b) Second shell of dodecahedron composed of mixed Yb:2,wherethedivalentYbwasdeducedfromthe non- Au/Ge atoms at M2 and M4 sites. (c) Thirdshell of icosahedron magneticpropertiesoftheAGY(I)AC.3 Fromaresidual composed of Yb atom (Yb1 site). (d) Fourth shell of icosidodeca- resistivity ρ(0)=150 µΩcm, the mean free path is eval- hedron composed of Au atoms (M1 and M6 sites) and Ge atoms uated to be 0.59 nm. Note that this value is close to (M8site).(e)FifthshelloftriacontahedroncomposedofAuatoms (M3 site) and mainly of Ge atoms (M5 site). (f) Body-centered the intercluster distance.3 This suggests that the large cubic arrangement of Yb icosahedron in the projection along the residual resistivity, a common feature of Tsai-type QCs [001]direction. andACs,wouldmainlyoriginatefromanorientationally disordered tetrahedron because the M7 site has a large B-factorthatisproportionaltotheatomicdisplacement parameter, U =B/(8π2). eq formsabody-centeredcubic(bcc)structure,asshownin The e/a values of the isostructuralmaterials are sum- Fig.2(f).Acharacteristicfeatureofthismodelisachem- marizedinTableII.1,3,5 Typicale/avaluesfortheTsai- ical ordering of Au and Ge. These structural properties typeQCsandACsarebetween1.95to2.15.TheAGY(I) ofAGY(I)ACareverysimilartothoseofAu-Al-YbAC. AC may also be interpreted as belonging to the Hume- The valence electron concentratione/a and the Fermi Rothery phase, although the e/a value (≃ 1.80) of the wavevectorkF arecalculatedto be 1.80and1.17nm−1, presentsystemisslightlysmallerthanthoseofthe other 2 J.Phys. Soc. Jpn. Table II. Summary of Yb-based Tsai-type 1/1 cubic ACs. Yb Acknowledgments valence, valence electron concentration e/a, lattice parameter a, andaverageatomicradiusr¯. This work was partially supported by Grants-in-Aid Alloys Yb e/a a (nm) r¯(nm) for Scientific Research from JSPS, KAKENHI (Nos. Au Ge Yb +2 1.80 1.4724(2) 0.1496 64 22 14 24654102, 25610094, and 26610100). K.D. also thanks Ag Ga Yb +2 1.91 1.4687(1) 0.1506 47 38 15 the Yamada Science Foundation for financial support. Au Ga Yb +2 1.97 1.4527(1) 0.1504 44 41 15 Au Al Yb +3 1.98 1.4500(2) 0.1480 51 35 14 1) T. Ishimasa, Y. Tanaka, and S. Kashimoto: Philos. Mag. 91 (2011) 4218. 2) K. Deguchi, S. Matsukawa, N. K.Sato, T. Hattori, K. Ishida, ACs. H.Takakura,andT.Ishimasa:Nat.Mater.11(2012) 1013. 3) K. Deguchi, M. Nakayama, S. Matsukawa, K. Imura, The values of the lattice parameter a and average K. Tanaka, T. Ishimasa, and N. K. Sato: J. Phys. Soc. Jpn. atomic radius r¯ are also listed in Table II. Here, r¯ was 84(2015) 023705. calculated from the radii of divalent Yb (0.194 nm) and 4) Q.LinandJ.D.Corbett:Inorg.Chem.49(2010)4570. trivalentYb(0.174nm).6 InFig.3,r¯isplottedasafunc- 5) S. Matsukawa, K. Tanaka, M. Nakayama, K. Deguchi, tion of a for isostructural Tsai-type ACs. We observe a K.Imura,H.Takakura,S.Kashimoto,T.Ishimasa,andN.K. Sato: J.Phys.Soc.Jpn.83(2014)034705. linear relationship between them. This implies that the 6) W.B.Pearson:The Crystal Chemistry and Physics of Metals Yb valence (therefore, magnetism) is determined by the and Alloys(Wiley,NewYork,1972). relationship between r¯and a. 3