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

0.36 MB·English

by  Kazuhiko Deguchi

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.
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]
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:[e-mail]
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
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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
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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