research paper

セラミックス基盤工学研究センター年報 (2006). Vol. 6, 19 - 22

欠陥パイロクロア型 Pb2Ru2O6.5 の構造
石澤伸夫 †・ドボーレイダグラス †・須田勝美 ‡・赤澤亜美 ¶・勝又哲裕 ¶・稲熊宜之 ¶† 名古屋工業大学セラミックス基盤工学研究センター‡ 東京工業大学応用セラミックス研究所¶ 学習院大学理学部化学科〒 507-0071 岐阜県多治見市旭ヶ丘 10-6-29〒 226-8503 神奈川県横浜市緑区長津田町 4259
〒 171-8588 東京都豊島区目白 1-5-1Structure of Defect Pyrochlore-Type Pb2Ru2O6.5
Nobuo Ishizawa†, Douglas du Boulay†, Katsumi Suda‡, Tugumi Akazawa¶, Tetsuhiro Katsumata¶,
and Yoshiyuki Inaguma¶† Ceramics Research Laboratory, Nagoya Institute of Technology, Asahigaoka, Tajimi 507-0071, Japan‡ Materials and Structures Laboratory, Tokyo Institute of Technology, 4259 Nagatsuta Midori, Yokohama 226-8503¶ Department of Chemistry, Faculty of Science, Gakushuin University, 1-5-1 Mejiro, Toshima-ku, Tokyo 171-8588

Temperature dependence of the defect pyrochlore-type structure of Pb2Ru2O6.5 has been investigated at 123, 193 and 293 K by the singlecrystal diffraction method. The oxide anion vacancies order preferentially on one of two inversion centre related sites, thereby breaking thesymmetry of the pyrochlore archetype. The Pb atoms are displaced by about 0.042 Å toward the oxide anion vacancy. The mean thermal
expansion coefficient of the unit cell dimension was 11.8 x 10-6 in the investigated temperature region. The excess electrons of 6 eÅ-3 at
the peak top are located about 0.8 Å along the principal axes from each Pb atom in the difference Fourier map, suggesting a disordereddistortion of the Pb electron cloud.
[Received February 8, 2007; Accepted March 9, 2007]

1. Introduction
The pyrochlore NaCa(Nb2O6)F adopts the spacegroup symmetry Fd3m, forming the archetype for a wide
range of substitutionally related pyrochlore-like compounds with the general formula A2B2O6O' 1). Thesematerials also host a wide variety of technologically important physical properties. In particular, the fractionally
populated Pb2Ru2O6.5 pyrochlore-like ceramics of interest here, demonstrate high electrical conductivities, i.e.,
2.3x10-4 Ω cm at 293 K 2) and find application as electrode materials and the conductive elements of thick film
resistors 3).
The structure of Pb2O'0.5・Ru2O6 was first reported by
the neutron powder diffraction 4). Hsu et al. 5) calculated
the band structure of Pb2Ru2O6.5 and suggested that themetallic behaviour of the compound is dominated by theadmixture of partially-filled t2g band of Ru 4d electrons
and the Pb 6p band via the framework O atoms. They
also pointed out that the Pb 6s band is about 10 eV deep
from the Fermi level and unlikely to contribute to themetallic conduction as previously believed 6). The present study was undertaken to investigate the temperaturedependence of the Pb2Ru2O6.5 structure.

2. Experimental
Crystals were grown from self-fluxing PbO and RuO2
starting powders. They were mixed in 9:1 molar ratio (i.
e., excess PbO) and placed in a platinum crucible. Thetemperature was raised from room temperature to 1523
K within 3 h, and maintained for 6 h before cooling at
the rate of 5 K/h. Metallic black coloured crystals weregrown to a maximum size of 9 x 7 x 4 mm3. The oxygen
content of the crystal was determined from the weightloss during the reduction of product at 773 K in a H2
atmosphere by thermogravimetric analyzer. The Pb/Ruratio was confirmed by the ICP analysis. The chemical composition of the crystals was Pb2Ru2O6+x wherex=0.50±0.02. The electric and magnetic properties of thegrown crystals have already been reported 2).
The sample has an irregular block in shape with— 19 —

石澤伸夫・ドボーレイダグラス・須田勝美・赤澤亜美・勝又哲裕・稲熊宜之+=Fig. 1. Interpenetrating sublattices of B2O6 (left) and the A2O' sublattice (centre) results in the A2B2O7 pyrochlore structure(right). The B2O6 sublattice is composed of corner-sharing BO6 octahedra. The O' atoms are further divided into O3 and Vo(vacancy presented as a point) to describe Pb2Ru2O6.5. The 293 K parameters are used for the illustration with thermal ellipsoids
drawn at the 99% probability level. The unit cell is given by the solid line.

100x120x133 μm3. X-ray diffraction data were measured
on a Rigaku RAPID imaging plate diffractometer 7) using
Mo Kα radiation with the Oxford cryosystems liquid nitrogen air stream at 123, 193 and 293 K. At Mo radiation
wavelengths, the dominant scatterer, Pb, displays verystrong anomalous dispersion. Satisfactory refinement results were only obtained after refining the absolute structure from separately averaged Friedel pairs. Presumably
because the Pb displacement was the dominant contributor of density to the inversion symmetry breaking, enantiomeric sensitivity of the absolute structure refinement
was enhanced. The extinction correction also played adominant role in the refinement 8). Attenuation factors ofaround 50% were observed for the strongest reflections,well outside the kinematic approximation and suggesting
the associated correction factors are highly questionable.
The Flack parameter provides quite convincing evidence
that the sample studied was monodomain. Crystal data at
123 K are given in Table 1.

3. Results and discussion
Results of refinements are given in Table 2. The structural parameters at 123, 193 and 293 K are given in Table

3. Selected interatomic distances and bond angles aregiven in Table 4. The ideal pyrochlore structure is easier
to discuss in terms of its two distinct, interpenetrating
sublattices represented as A2O'・B2O6 and shown more
succinctly in Fig. 1. Each B site is octahedrally coordinated to six O atoms and collectively they form a semi-infinite three-dimensional network of six-membered, cornersharing octahedral ring systems. On the other hand, theA2O' sublattice adopts the cuprite-like structure (Cu2O)
shown in Fig. 1 (middle), filling the voids and cavities
formed by the hexagonal rings of linked octahedra. Each
A site is linearly coordinated by two O' sites and each O'
site is tetrahedrally coordinated to four A sites.
When the A sites of the pyrochlore archetype arefilled with Tl+, Pb2+ or Bi3+, having polarizable 6s2 lonepair electrons, the population of the O' sites becomesvariable and the stoichiometry is better written as A2O'x.
B2O6, with x in the range between 0 and 1. In the case of
Pb2O'0.5.Ru2O6, our focus here, defect ordering destroys
the A site inversion centres of the Fd3m archetype, leading to the noncentrosymmetric subgroup F43m with twosymmetry distinct O' sites, i.e., O3 and Vo.
The linked Pb4Vo・Pb4O3 clusters are shown in Fig.
2. Because of the asymmetry of the O3−Pb−Vo vacancy
ordering in ideally defect-ordered Pb2Ru2O6.5, the Pb

Table 1. Crystal data at 123 K
CompoundCrystal system:
Space groupaVZ
DxMrRadiation

Pb2Ru2O6.5
CubicF43m
10.241 (2) Å1074.1 (6) Å388.912 Mg m-3
720.54
Mo K α radiation

Table 2. Results of refinements. N1: Number of measured reflections. N2:
Number of reflections used for refinements. Rint: Merge R factor for N1. R:
Final R factor for N2.
T(K)
a123
10.241 (2)193
10.253 (2)293
10.262 (2)— 20 —

N1
10286
11080
10663

Rint0.088
0.081
0.034

θ max

45.26
45.26
45.21

N2503
510
506

R
0.035
0.033
0.040

欠陥パイロクロア型 Pb2Ru2O6.5 の構造

Table 3. Fractional coordinates and atomic displacement parameters (Å2) at 123, 193 and 293 K.
Atom T(K) xyz
Uiso
U11
U22U33
Pb 123 .87738(10) .87738(10) .87738(10) .0047(3) .0047(3) .0047(3) .0047(3)193 .87756(6) .87756(6) .87756(6) .0078(3) .0078(3) .0078(3) .0078(3)293 .87733(6) .87733(6) .87733(6) .0117(2) .0117(2) .0117(2).0117(2)

U13-.00067(17)-.00144(15)-.00120(13)U23-.00067(17)-.00144(15)-.00120(13)Ru

123 .3752(2).3752(2).3752(2).0035(5)193 .37468(12) .37468(12) .37468(12) .0042(4)293 .37518(10) .37518(10) .37518(10) .0074(4).0035(5) .0035(5).0042(4) .0042(4).0074(4) .0074(4)O1

123 .3025(11)193 .3022(8)293 .3023(9)000000.006(2).006(2).012(2).010(4).008(3).014(3).0041(18) .0041(18) 0.0053(15) .0053(15) 0.0107(17) .0107(17) 0000.001(3)-.000(2)-.002(2)O2123 .4497(9)193 .4497(8)293 .4500(8)

0.25
0.25
0.25

0.25
0.25
0.25.004(2).007(2).010(2).005(3).004(3).010(3).0038(18) .0038(18) 0.0079(17) .0079(17) 0.0097(16) .0097(16) 0000-.003(3)-.001(2)-.002(2)O3

123 0.75
193 0.75
293 0.75

0.75
0.75
0.75

0.75
0.75
0.75.006(4).006(3).013(3).006(4).006(3).013(3).006(4).006(3).013(3)000000

inversion symmetry of the archetype is broken. Thatpermits the Pb−Pb contacts around the perimeter of thePb4Vo cluster to contract around the vacancy, reducing to3.561(1) Å in length while the Pb−Pb contacts defining
the Pb4O3 cluster expand to 3.696(1) Å. There is a concomitant increase in the Pb−O3 bond length to 2.2631(6)Å, whereas the Pb−Vo distance decreases to 2.1804(6)Å. The metallic Pb crystal with the 4.9496(3) Å fcc cell
leads to twelve metallic Pb--Pb bonds 3.50 Å in length 9),
which is close to the Pb--Pb distance of the Pb4Vo cluster.
There is a small but perceptible systematic increases
in the cubic cell dimensions with increasing temperature.
The mean thermal expansion coefficient of the cell dimension is 11.8 x 10-6 in the investigated temperature
region. Temperature dependent changes in the fractional
atomic coordinates were small.  
The vibrational motion of Ru is relatively small, inkeeping with its three short and strong octahedral bonds
to each of O1 and O2. Those bonds differ in length by
only 0.012(3) Å at 293 K so despite permissive symmetry, the Ru atom is scarcely displaced from the geometric

123K
2.2595(10)2.557(7)2.559(8)1.955(5)1.967(4)135.3(6)134.3(5)193K
2.2652(7)2.559(6)2.561(5)1.963(3)1.965(3)135.5(4)133.9(4).006(4).006(3).013(3)-.0002(3)-.0002(3)-.0002(3).0002(2).0002(2).0002(2)-.00049(19) -.00049(19) -.00049(19)000

centre of the RuO6 octahedron.
The isotropic atomic displacement parameters areplotted in Fig. 3 as a function of temperature. Taking intoconsideration their estimated standard uncertainties, theUiso values generally change almost proportional to tem-bcPbaFig. 2. Pb4O3 and Pb4V clusters at 193K with ellipsoids drawn
at the 99% probability level. The oxygen vacancy (Vo) is locatedat the origin of the unit cell.

Uiso (A2 )0.020

Table 4. Selected interatomic distances (Å) and angles (° ).
Pb—O3Pb—O2i
Pb—O1ii
Ru—O1iii
Ru—O2iv
Ruv—O1—Ruvi
Ruv—O2—Ru.0035(5).0042(4).0074(4)U12-.00067(17)-.00144(15)-.00120(13)293K
2.2631(6)2.560(6)2.563(6)1.960(3)1.972(3)135.1(5)134.2(4)

PbRu
O1
O2
O3

0.015

0.010

0.005

050

100

150

200

250

300

350

Temperature(K)Symmetry codes: (i) 1/2+ y, 1 － z, 3/2 － x; (ii) 1 + y, 1 － z, 1 －x; (iii) 1/2+ y, 1/2+ z, x; (iv) y, z, x; (v) x, 1/2 － y, 1/2 － z; (vi) x,
y － 1/2, z － 1/2— 21 —

Fig. 3. Changes of isotropic atomic displacement parameters withtemperature.

石澤伸夫・ドボーレイダグラス・須田勝美・赤澤亜美・勝又哲裕・稲熊宜之

perature except for O3. The odd behaviour of O3 may
suggest a possible structural change at low temperatures.
Because of the potential, and numerous, metal-metalbonds involved in this material, bond valence sums (BVSs)
derived and applicable only to fully ionic compounds,
are necessarily of dubious character. Charge neutrality ofthe Pb2Ru2O6.5 stoichiometry favours a mean valence of+4.5 for Ru in addition to the formal ionic charges of +2,-2 for Pb and O respectively. BVS values at 293 K were2.42 for Pb, 4.62 for Ru, -2.16 for O1, -2.10 for O2 and-2.64 for O3. Large deviations for Pb and O3 from theformal values may suggest a possible polarization of thePb electron cloud, which can be schematically modeled
as an electric dipole composed of Pb4+ and the 6s2 lonepair electrons with the former oriented toward O3. The
maximum difference electron density of about 6 eÅ-3 waslocated about 0.8 Å along the principal axes from each Pb
atom in the 123 K difference Fourier map. The height andlocation of the peak was almost the same at 193 and 293
K. The peak may evidence a disordered distortion of thePb electron cloud originating in the 6s2 electrons.
An excess electron density maximizing at 4 eÅ-3 wasfound at the Vo position at 123 K. The peak height decreased to 2 eÅ-3 at 193 K and disappeared at 293 K. Although the refinements assuming oxygen atom disorder
between O3 and Vo sites were undertaken at 123 K, nosignificant improvement of R factors were obtained. A
detailed study with more accurate data could reveal thepartial O atom disorder between O3 and Vo.

— 22 —

Acknowledgement
This study was supported by grants-in-aid for Scientific Research No. 18206071 and High-Technology Research Center Project from the Ministry of Education,Culture, Sports, Science and Technology, Japan.
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