research paper

セラミックス基盤工学研究センター年報 (2007). Vol. 7, 7-16

Phase Transition of Gd3RuO7 f rom a Structural Point of View
H. Nakano†, K. Tateishi‡, and N. Ishizawa¶† Ryukoku University, Seta, Otsu 520-2194‡ Gifu Prefectural Ceramics Research Institute, Hoshigadai, Tajimi 507-0811¶ Ceramics Research Laboratory, Nagoya Institute of Technology, Asahigaoka, Tajimi 507-0071

構造的観点からみた Gd3RuO7 の相転移
中野裕美 †・立石賢司 ‡・石澤伸夫 ¶†龍谷大学 〒 520-2194 滋賀県大津市瀬田大江町横谷 1-5‡岐阜県セラミックス研究所〒 507-0811 多治見市星ヶ台 3-11
〒 507-0071 岐阜県多治見市旭ヶ丘 10-6-29¶ 名古屋工業大学セラミックス基盤工学研究センター

Gd3RuO7, the ordered oxygen-deﬁcient ﬂuorite-type compound, undergoes a structural phasetransition between the P21nb and Cmcm modiﬁcations at around 382 K. This paper describes
the phase transition from a structural point of view, based on the high–temperature single-crystal
X-ray and electron diﬀraction studies. The transition is almost reversible, and characterized byan additional tilt about the c axis that occurs in the low-temperature modiﬁcation for half of the
RuO6 octahedra in association with a reduction of apparent coordination number from 6+2 to 7
for one-third of Gd atoms. Dimerization of the Ru array along the [-RuO5-]∞ zigzagging chain
occurs below the transition temperature, which provides a folding eﬀect on the chain. The folding tendency of the chain explains geometrically an expansion of the b-length and a compressionof the c-length near 382 K on cooling and vice versa on heating. The transition is similar to thosegiven in the literature for Sm3RuO7, Eu3RuO7, Sm3OsO7, Eu3OsO7 and Gd3OsO7, except that
one of crystallographically independent Gd atoms in the high-temperature Cmcm modiﬁcationis statically or dynamically distributed between two positions located very close with each other.
The disordered distribution of the Gd atom in the high-temperature modiﬁcation is presumably
correlated with the octahedral tilts about the c axis, resulting in the experimental observation of
the extremely prolate atomic displacement ellipsoid for the O1 atom in the cis position along thechain. The P21nb-Cmcm phase transition contains two competing mechanisms characterized by
the order-disorder transition of the librating [-Gd-RuO6-Gd-RuO6-Gd-] linkage along the b axis,
and by the displacive-type dimerization of Ru atoms along the chain. The in situ electron diffraction experiments suggested a possible existence of intermediate phase between the high- andlow-temperature modiﬁcations.

1. Introduction
Compounds of the Ln3MO7 series are composed oftrivalent lanthanide (Ln) and pentavalent transition
PHWDOR[LGHVDQGFU\VWDOOL]HVLQWKHGHIHFWÀXRULWH
type structure (Allpress & Rossel, 1979). The
VWUXFWXUHZDV¿UVWGHWHUPLQHGIRU/D3NbO7 on thebasis of the Cmcm symmetry. Among the Ln3MO7
series, Ln3RuO7 and Ln3OsO7 contain the MO6 octahedral single-chains in the matrix composed of

Ln and O atoms. The unit-cell relationship between
WKH FXELF ÀXRULWHW\SH SDUHQW VWUXFWXUH I  DQG WKH
Gd3RuO7-type chain structure (c) is shown in
Fig. 1. The crystals show the polymorphism. The
phase transition between the space groups P21nb
and CmcmZDV¿UVWUHSRUWHGIRU6P3RuO7 at 190
K, and Eu3RuO7 at 280 K (Gemmill et al., 2004),
and then for Sm3OsO7 at 235 K, Eu3OsO7 at 330
K, and Gd3OsO7 at 430 K (Gemmill et al., 2005).

―7―

Phase Transition of Gd3RuO7 from a Structural Point of View

at room temperature was reexamined and found topossess the P21nb symmetry (Ishizawa et al., 2006).
The phase transition of Gd3RuO7 between P21nb andCmcm was then detailed by the in situ single-crystal
X-ray diffraction study (Ishizawa et al., 2007). The
SUHVHQWSDSHUDLPVDW¿OOLQJXSWKHXQUHSRUWHGWKLQJV
which were excluded from our past papers mainly
due to the space problems, and to discuss the natureof the phase transition of Gd3RuO7 from a structural
point of view. This paper also includes a latest¿QGLQJDERXWWKHSRVVLEOHSUHVHQFHRILQWHUPHGLDWH
phase near the phase transition obtained from theelectron microscopy study.
2. Crystal shape and its relation to the structure
Fig. 1. The unit-cell relationship between the cubicÀXRULWHW\SHSDUHQWVWUXFWXUH I DQGWKH*G3RuO7-type
chain structure (c). Metal and oxygen atoms are repreVHQWHGE\¿OOHGDQGXQ¿OOHGFLUFOHVUHVSHFWLYHO\The Cmcm structure is considered as archetypal,
possessing the highest symmetry among the
Ln3RuO7 polymorphs.
Bontchev et al. (2000) grew single crystals of
Gd3RuO7E\WKHÀX[PHWKRGDQGVXJJHVWHGWKDWWKH
crystal has localized carriers in one-dimension with
Mott variable range hopping along the octahedral
single chains. They also reported two phasetransitions at 14.5 and 8 K relevant to the orderingsof the Ru and Gd magnetic moments, respectively.
Harada & Hinatsu (2002) found another transition at
382 K for Gd3RuO7DQGUHSRUWHGIURPWKHVSHFL¿F
KHDW PHDVXUHPHQW WKDW WKH WUDQVLWLRQ LV RI WKH ¿UVW
order.
The room temperature structure of Gd3RuO7 was¿UVW DQDO\]HG DOVR DVVXPLQJ Cmcm, which madeRXUVHOYHVGLI¿FXOWWRSUHVXPHWKHV\PPHWU\RIWKH
KLJKWHPSHUDWXUH PRGL¿FDWLRQ RI *G3RuO7 above
382 K. Recently, the crystal structure of Gd3RuO7

Crystals were grown by cooling the SrCl2-RuO2Gd2O3 solution at the rate of 5 Kmin-1 from 1373
K. Experimental details are given in our previous
papers (Ishizawa et al, 2006, 2007). Metallic black
crystals had a prismatic shape surrounded by {120}side faces and capped by {101}. As shown in Fig.
2, these faces correspond to the planes extending
through the crystal so that they can avoid strong
bonds between the pentavalent Ru cation and thedivalent oxide anions. The RuO6 octahedral chainsare running along the c axis which corresponds
to the columnar direction of the as-grown crystal.
7KHUHIRUH LW LV QRW GLI¿FXOW WR GLVWLQJXLVK WKH
direction of the maximum electric conduction forthe crystals in columnar shape.
3. Choice of space group
Precession images were reconstructed from theframe data taken by the CCD single-crystal diffractometer (Smart Apex II, Bruker) at various
temperatures between 293 to 1223 K. The 0kl planes
at 423 K and 293 K are shown in Fig. 3. In the highWHPSHUDWXUHPRGL¿FDWLRQRQO\WKHUHÀHFWLRQVZLWKk=even were observed due to the lattice centering.

Fig. 2. Face indices of a typical as-grown crystal and their relation to structure.

―8―H. Nakano, K. Tateishi, and N. Ishizawa,Q WKH ORZWHPSHUDWXUH PRGL¿FDWLRQ RQ WKH RWKHUKDQG VDWHOOLWH UHÀHFWLRQV DW ERWK VLGHV RI SDUHQWUHÀHFWLRQV DSSHDU DORQJ WKH b axis. The satellites
are commensurate and can be indexed by doubling
the b-length. The lattice loses the centering andbecomes primitive.
Intensity data of the low-temperature
PRGL¿FDWLRQZHUHFROOHFWHGDW.XSWRd=0.40
Å resolution level (2ș IRU 0R .Į  E\ WKHCCD diffractometer. Those of the high-temperature
PRGL¿FDWLRQ ZHUH FROOHFWHG DW   DQG 
K. Crystal data are given in Table 1. Numericaldetails have been given by Ishizawa et al.,(2007). The agreement index for the intensities of
FU\VWDOORJUDSKLFDOO\ HTXLYDOHQW UHÀHFWLRQV Rmerge,
LQ WKH ORZWHPSHUDWXUH PRGL¿FDWLRQ VKRZHG QR
VLJQL¿FDQW LPSURYHPHQW E\ UHGXFLQJ WKH /DXH
symmetry from mmm to lower ones. The crystal was
thus assumed to have an orthorhombic symmetry.
)URPWKHV\VWHPDWLFDEVHQFHRIUHÀHFWLRQVSRVVLEOH
space groups were limited to P21nb and Pmnb. The
noncentrosymmetric P21nb was adopted because
the mirror planes perpendicular to the a axis in thecentrosymmetric Pmnb did not allow octahedral
tilts about the axes on the planes.
Figure 4 shows the temperature dependence ofthe mean |Fo|2RIHLJKWUHÀHFWLRQSDULW\JURXSVHRH
ooo, ooe, eoo, 0oo, 0oe, o0o and e0o, on the basis of
the P21nbODWWLFH7KHUHÀHFWLRQVLQWKHVHJURXSVFDQ
exist in P21nb and should disappear in Cmcm. The
data were collected upon heating. The temperaturedependence was essentially the same on cooling thespecimen, suggesting that the transition is almost
reversible. The mean |Fo|2RIWKH¿UVWVHYHQSDULW\groups, i.e., eoe, ooo, ooe, eoo, 0oo, 0oe and o0o,
decreased rapidly with increasing temperature and
GLVDSSHDUHG DERYH  . 7KH UHÀHFWLRQV RI WKHparity group e0o were slightly stronger and morediffuse than those of the other seven groups above
382K, although the |Fo|2 value of the strongest

Fig. 3. Precession images of the reciprocal 0kl plane at 423
K (Cmcm) and 293 K (P21nb), calculated from the CCD
frame data.

UHÀHFWLRQLQWKHJURXSHRGLGQRWH[FHHGWLPHV
its estimated standard uncertainty. They were thus
neglected for the space group determination.
Some of the Ln3MO7 crystals, e.g., Ln3MO7(M=Nb, Ta and Sb, Ln=Nd, Gd and Ho) (Allpress& Rossel, 1979), Y3TaO7 (Rossell, 1979), andDy3ReO7 (Hinatsu et al., 2004), have been reported
to crystallize in the space group C2221. The spacegroups of C2221 and Cmcm can be distinguishedfrom the h0lUHÀHFWLRQVi.e.WKHUHÀHFWLRQJURXSHR

Table 1. Crystallographic Data for Gd3RuO7
formula

Gd3RuO7

Gd3RuO7

Gd3RuO7

Gd3RuO7

fw (g/mol)

684.82684.82684.82684.82temperature (K)

293

423

773

1223

wavelength (Å)

0.71073

0.71073

0.71073

0.71073

crystal system

orthorhombic

orthorhombic

orthorhombic

orthorhombic

space group

P21nb

Cmcm

Cmcm

Cmcm

a㧔Å㧕

10.6399(2)10.6514(2)10.6847(2)10.7346(2)b㧔Å㧕

14.6769(2)7.3404(3)7.3694 (1)7.4112(2)c㧔Å㧕

7.3747 (1)7.3942 (1)7.4136 (1)7.4481(2)volume (Å3)

1151.64(3)578.12(3)583.75(2)592.54(3)

Z

8

4

4

4

unit cell dimensions―9―

Phase Transition of Gd3RuO7 from a Structural Point of View

monotonically and no anomaly was observed within
experimental errors.

Fig. 4. Temperature dependence of the mean |Fo|2 ofseven reflection parity groups, eoe, ooo, ooe, eoo,
0oo, 0oe, o0o and e0o, where o and e stands for
odd and even indices, respectively, on the basis of
the P21nb lattice. The data points are connectedby polylines in the high- and low-temperature
PRGL¿FDWLRQVIRUYLHZLQJSXUSRVH

are allowed for C2221 whereas not for Cmcm. The
possibility of C2221 was discarded for this crystal
by the aforementioned reason in the present study.
4. Changes in the cell dimensions
Temperature dependences of the cell dimensions
in the range between 293 K and 523 K are shownin Fig. 5. A small shrinkage of the b-length and an
expansion of the c-length were observed between
the 363 and 383 K data points upon heating andthe reverse took place upon cooling. Between thesedata points lies the phase transition temperature of.UHSRUWHGIURPWKHVSHFL¿FKHDWPHDVXUHPHQWThe changes in the cell dimensions suggest that thetransition is almost reversible. The a-length changed

5. Octahedral tilts and distortion
The structures of the high- and low-temperature
PRGL¿FDWLRQV DUH LOOXVWUDWHG LQ )LJ  7KHUH DUH
two crystallographically independent octahedra,
Ru1O6 and Ru2O6 in the low-temperature P21nb
PRGL¿FDWLRQ‫ޓ‬The two octahedra alternate along
the c axis by sharing the trans O3 atom (Ot) to forma zigzagging single chain of [-Ru1O5-Ru2O5-].
These single chains are embedded and separated
with each other in a matrix consisting of Gd and O
atoms. The Ru1O6 octahedron has practically one
tilt system about an axis parallel to the a axis. On
the other hand, the Ru2O6 octahedron has a second
tilt system about an axis parallel to the c axis in
DGGLWLRQWRWKH¿UVWWLOWDERXWWKHD[LVSDUDOOHOWRa.
The two independent Ru1O6 and Ru2O6
octahedra in the P21nb PRGL¿FDWLRQ EHFRPH
crystallographically identical in Cmcm. The Ru1O6
LQWKHKLJKWHPSHUDWXUHPRGL¿FDWLRQKDVDVLQJOHWLOW
system about a. The appearance and disappearanceof the tilt about c for every other RuO6 octahedra
is a structural feature that characterizes the P21nbCmcm phase transition.
Several important geometrical parameters
obtained from the least-squares procedure are listed
in Table 2. The RuO6 octahedra are elongated along
WKHFKDLQLQWKHKLJKWHPSHDWXUHPRGL¿FDWLRQDVVHHQ
from the ratio of <Ru-Ot>2 / <Ru-Oc>4, where Oc
stands for the O1 atom in the cis position of octahedrawith respect to Ot, and the angle brackets stand fortaking an average over the number of bonds given
as a subscript. The values of quadratic elongation
and angle distortion in Table 2 suggest that theshape of oxygen octahedra in the high-tempeature
PRGL¿FDWLRQ UHVROYHV LQWR PRUH GLVWRUWHG 5X26
and less distorted Ru2O6 in the low-temperature
PRGL¿FDWLRQ 5RELQVRQet al., 1971). The Ru-Ot-Ru
angle of 142.5 º at 423 K is slightly more obtuse

Fig. 5. Temperature dependence of the a-, b-, and c-lengths of Gd3RuO7'DWDSRLQWVRI¿OOHGEODFNPDUNVRQKHDWLQJDQG
open red ones on cooling are connected by polylines for viewing purpose. The b-length of the CmcmPRGL¿FDWLRQDERYH
.LVGRXEOHGLQWKH¿JXUHIRUFRPSDULVRQZLWKWKHORZWHPSHUDWXUHP21nbPRGL¿FDWLRQ7KHHVWLPDWHGVWDQGDUG
uncertainties of the cell lengths are less than the marker size.

― 10 ―

H. Nakano, K. Tateishi, and N. Ishizawa

Fig. 6. Comparison of the high- and low-temperature modifications at 423 K and 293 K with atomic
displacement parameter ellipsoids plotted at the 97% probability level.

Table 2. Selected interatomic distances (Å) and geometry parameters

a

293 K

423 K

773 K

1223 K<Ru1-O>6 (Å)<Ru1-Ot>2 (Å)<Ru1-Oc>4 (Å)<Ru1-Ot>2 / <Ru1-Oc>4
Octahedral volume (Å3)
Quadratic elongation
Angle variance1.947(8)1.945(8)1.948(6)0.9985
9.744
1.006
22.85

1.945(2)1.952(1)1.941(2)1.0057
9.738
1.005
16.94

1.953(4)1.959(2)1.950(4)1.0046
9.857
1.005
18.65

1.948(4)1.967(2)1.949(4)1.0092
9.897
1.005
16.78

<Ru2-O>6 (Å)<Ru2-Ot>2 (Å)<Ru2-Oc>4 (Å)<Ru1-Ot>2 / <Ru1-Oc>4
Octahedral volume (Å3)
Quadratic elongation
Angle variance1.949(7)1.953(6)1.947(8)1.0031
9.807
1.004
14.63

Ru1···Ru2 (Å)
Ru1-O1-Ru2 angle (º)
Ru1-O2-Ru2 angle (º)

3.683(4), 3.691(4)140.4(5)144.1(5)3.6971(1)142.5(2)3.7068(1)142.2(4)3.7241(1)142.4(4)Ru1···Ru1 (Å)
Ru-O3-Ru angle (º)

The interatomic distances (Å) in angle brackets are the average over the shortest n bonds with n given
as a subscript. The Ot represents trans O atoms connecting the RuO6 octahedra along the chain, and Oc
represents the other cis O atoms of RuO6 octahedra.

― 11 ―

Phase Transition of Gd3RuO7 from a Structural Point of View

WHPSHUDWXUHPRGL¿FDWLRQLVPXFKODUJHUWKDQWKHLU
PHDQ LQ WKH ORZWHPSHUDWXUH PRGL¿FDWLRQ 7KHelongation of octahedra, the unfolding tendency ofthe chain, and the increase of intermetallic Ru···Ru
distance accord geometrically with each other. They
also explain the shrinkage of the b-length and the
expansion of the c-length (Fig. 5) near the phasetransition point upon heating and vice versa uponcooling. The inequality of Ru···Ru intermetallic
distances along the chain in the low temperature
PRGL¿FDWLRQ )LJ LQGLFDWHVWKDWWKHGLPHUL]DWLRQ
of adjacent Ru atom pairs takes place in addition to
the general shortening of the Ru···Ru distances. Thissuggests a higher, and slightly different, electronic
correlation between the Ru atoms along the chain
LQWKHORZWHPSHUDWXUHPRGL¿FDWLRQFRPSDUHGZLWKthe high-temperature one. A detailed analysis of theband structure is necessary in order to understandthe phase transition as well as the conduction
properties.

Fig. 7. Changes in the intermetallic Ru···Ru distancealong the RuO 6 chain with temperature. The
estimated standard uncertainties are within themarker size. Two Ru···Ru distances in the P2 1nb
PRGL¿FDWLRQDW.OLHEHORZWKHGDVKHGTXDGUDWLF
polynomial line connecting the values in the Cmcm
PRGL¿FDWLRQDWKLJKWHPSHUDWXUHVthan the mean of the two Ru-Ot-Ru angles at 293K
LQWKHORZWHPSHDWXUHPRGL¿FDWLRQi. e., 140.4(5) ºfor Ru1-O1-Ru2 and 144.1(5) º for Ru1-O2-Ru2.
This indicates that the octahedral single chain tends
WRXQIROGLQWKHKLJKWHPSHUDWXUHPRGL¿FDWLRQ
6. Ru···Ru intermetallic distance
Along the chain, there is one kind of intermetallic
Ru···Ru distance in the high-temperature
PRGL¿FDWLRQ FRUUHVSRQGLQJ WR WKH KDOI RI WKH clength, whereas there are two kinds of Ru···Ru
GLVWDQFHVLQWKHORZWHPSHUDWXUHPRGL¿FDWLRQ7KH
temperature dependence of the Ru···Ru distance isshown in Fig. 7. The Ru···Ru distance in the high-Fig. 8. Shematic drawing of the RuO6 chain featuring
the relation between the dimerization of Ru
atoms and the changes of cell dimensions on thetransition.

7. Dynamic disorder in the high-temperature
PRGL¿FDWLRQThe RuO6 octahedral single chains are bridged witheach other along the b axis by the Gd1-O1 bonds, as
shown in Fig. 9. The bridging is symmetrical in the
KLJKWHPSHUDWXUHPRGL¿FDWLRQGXHWRWKHSUHVHQFH
of mirror planes perpendicular to the a axis. The
presence of mirrors prevents octahedral tilting aboutc. Below the transition temperature, each Gd1 atom
releases one bond to RuO6 octahedron, enabling atilt about c for every other RuO6 octahedra. This isessentially the same as those reported for the P21nbCmcm phase transitions in Sm3RuO7 and Eu3RuO7,
Sm3OsO7, Eu3OsO7 and Gd3OsO7 .
The Cmcm structures determined at 423, 773 and1223 K are shown in Fig. 10. The distance of the Gd
atom split pair was approximately 0.3 Å, and did
QRW VKRZ DQ\ VLJQL¿FDQW WHPSHUDWXUH GHSHQGHQFHThe atomic displacement parameters increased
almost linearly as a function of temperature. It isnotable that only the O1 atom in cis position has anextremely prolate atomic displacement parameter
ellipsoid, as the overlapped Gd1 split pair looks likein Fig. 9.
The coordination geometry around Gd1 can be
PRGL¿HGGHSHQGLQJRQWKHDFWXDO*GDWRPORFDWLRQ
in the spilt pair. Figure 11 illustrates four possible
JHRPHWULHV LQ WKH KLJKWHPSHUDWXUH PRGL¿FDWLRQ
The directions of Gd1 atom shifts are the same in(a) and (b), and are reversed in (c) and (d). The
Gd1 atom is coordinated by two Oc atoms of anoctahedron by occupying a closer position to theoctahedron. On the other hand, the shift provides
to the other adjacent octahedron one of the two
possible tilts (clockwise or counterclockwise) about
the axes close to c, by releasing one Gd1- Oc bond.
Depending on the directions of Gd1 atom shifts,― 12 ―

H. Nakano, K. Tateishi, and N. Ishizawa

Fig. 9. The [-Gd-RuO6-Gd-RuO6-Gd-] linkage in the Cmcm (a) and P21nb (b) strcutrues.

half number of octahedra accomodate tilts whereas
the remaining half remain untilted. The geometriesof (c) and (d) have the antiphase relation against (a)and (b) along the b axis, respectively.
The Cmcm structure can be considered asa superposition of four variants with different
geometries. Although each geometry has a doubled
periodicity of the Cmcm structure along the baxis, the superposition reduces it into the originalvalue. The Oc atoms are located at the cornersof clockwise-tilted, counterclockwise-tilted anduntilted octahedra. Superposing all the possible
geometries would then make the probability density
distribution of Oc rather complicatedly elongatedalong the arc connecting the octahedral corners.
Actually a simple superposition would give rise to
DSUREDELOLW\GHQVLW\GLVWULEXWLRQSUR¿OHFRPSRVHG

of three peaks weighted by 1:2:1 along the arc about
WKHWLOWD[LV6XFKGLVWULEXWLRQLVGLI¿FXOWWRDQDO\]H
on the basis of a simple split atom model for Oc.
It is also suggested that these four geometries exist
LQ WKH KLJKWHPSHUDWXUH PRGL¿FDWLRQ QRW VWDWLFDOO\
but dynamically because the phase transition at 482
K prescribes these geometries to get ordered in the
ORZWHPSHUDWXUH PRGL¿FDWLRQ ,Q WKLV UHJDUG WKH
P21nb-Cmcm phase transition can be considered as
an order-disorder transition of the librating [-GdRuO6-Gd-RuO6-Gd-] linkage along the b axis.
7KLV LV FRQVLVWHQW ZLWK WKH VWXG\ RI WKH VSHFL¿Fheat measurement (Harada & Hinatsu, 2002). The
present time-averaged X-ray analysis assumes
simple harmonic vibrations for constituent atoms.
The prolate feature of O1 ellipsoids thus obtained in
WKHKLJKWHPSHUDWXUHPRGL¿FDWLRQLPSO\VDSRVVLEOH

Fig. 10. Changes of the Cmcm structures projected along the c axis as a function of temperature.
The anisotropic displacement parameter ellipsoids are plotted at the 97% probability level.
The split atom pair of Gd1 (red) is partially overlapped and looks elongated along the b axis
LQWKH¿JXUH)RXUVKRUWHVW*G2ERQGVDUHFRORUHGLQOLJKWEOXHDQGWKHQH[WIRXULQUHG

― 13 ―

Phase Transition of Gd3RuO7 from a Structural Point of View

Fig. 12. Two alternative hypothetical structuresconnecting Gd atoms and Ru(Oc)4(Ot)2 octahedra
along the b axis in the high-temperature form. The
Gd1-O bonds are drawn by thick solid lines. The Gd1Oc distance indicated by double line is approximately
2.0 Å, which is the reason why this model has been
discarded. The original prolate atomic displacement
parameter ellipsoids of O1 atoms of the Cmcm
PRGL¿FDWLRQDUHVXSHULPSRVHGQHDU2c.

Fig. 11. Four alternative hypothetical structures connecting
Gd atoms and Ru(Oc)4(Ot)2 octahedra along the b axis
in the high-temperature form. The Gd1 atom is shownby a circle filled in red with an arrow indicating thedirection of its displacement vector from the centreof the split pair. The Gd1-O bonds are drawn by thicksolid lines. The original prolate atomic displacement
parameter ellipsoids of O1 atoms of the Cmcm
modification are superimposed near O c .Discarded
Cmcm model.

presence of complicated dynamical distribution of
Oc atoms. The vibrational mode analysis would
be a future subject for better understandings of the
GLVRUGHU LQ WKH KLJKWHPSHUDWXUH PRGL¿FDWLRQ DQGthe phase transition.
The variants with different displacement models
for Gd atoms are also taken into consideration in
the earlier stage of the study. Figure 12 illustrates
two possible and alternative geometries in the highWHPSHUDWXUH PRGL¿FDWLRQ LQ ZKLFK *G DWRPVshift in the same direction along b. The periodicityof the geometry is essentially the same as that of
the Cmcm PRGL¿FDWLRQ $OO WKH RFWDKHGUD KDYH
tilts about c with the same sign. The space group
becomes C1c1 if the direction of Gd1 atom shifts
reverses alternately along c. This model, however,
FRQWDLQVDÀDZLQWKDWLWLQFOXGHVWRRVKRUW*G2cdistance of around 2.0 Å, as shown by the double
OLQHLQWKH¿JXUH7KHOHDVWVTXDUHVUH¿QHPHQWVRI
the high-form based on the assumption of C1c1
were attempted to reproduce the octahedral tilts andthe shift mode of Gd1 atoms expected for the model,
but failed. The model has been thus discarded.
8. Mechanism of the phase transition

The libration of [-Gd-RuO6-Gd-RuO6-Gd-]linkage which takes place livelily in the highWHPSHUDWXUH PRGL¿FDWLRQ VKRXOG ORVH HQHUJ\XSRQ FRROLQJ DQG WHUPLQDWH ¿QDOO\ LQ WKH ORZWHPSHUDWXUHPRGL¿FDWLRQ7KHWHUPLQDWLRQFRXOGEH
triggered by the dimerization of Ru atoms along theoctahedral chain which work effectively to provide
an alternatively ordered arrangement of tilted anduntilted octahedra along the chain direction. The
stoppage of the libration of the [-Gd-RuO6-GdRuO6-Gd-] linkage indicates an order-disordernature for the transition whereas the dimerizationof Ru atoms adds a displacive nature to thetransition. These two mechanisms are considered ascompetitive. The decrease of temperature reduces
the libration energy whereas it urges the dimerizationof Ru atoms through the electronic interaction.
Below the transition temperature, the symmetry
becomes noncentrosymmetric, and has a primitive
cell with doubled volume compared with the
C-base centered centrosymmetric high-temperature
PRGL¿FDWLRQ7KLVPHDQVWKDWHLJKWSRVVLEOHYDULDQWV
can be brought in the low-temperature crystal, fourof which are the antiphase variants of the remainder.
6LQFH WKH KLJKWHPSHUDWXUH PRGL¿FDWLRQ FDQ EH
considered as a sort of dynamical mixture of fourgeometries as shown in Fig. 11, inclusion of various
YDULDQWV LQ WKH ORZWHPSHUDWXUH PRGL¿FDWLRQ PD\
be unavoidable.
Actually, a small fraction of Gd atoms wasevidenced at the Gd1B and Gd2B sites. The Gd
atoms occupy either positions Gd1A or Gd1B
with probabilities of approximately 92% and 8%,― 14 ―

H. Nakano, K. Tateishi, and N. Ishizawa

Fig. 13. Changes in the [001] zone axis electron diffration pattern as a function of temperature. The
UHÀHFWLRQLVSUREDEO\GXHWRPXOWLSHGLIIUDFWLRQ6DWHOOLWHUHÀHFWLRQVZHUHVFDUFHO\REVHUYHG
in this sample.

respectively. The Gd atoms also occupy either
positions Gd2A or Gd2B with probabilities ofapproximately 93% and 7 %, respectively. The highcorrelation between the probabilities of 92-93%
at the Gd1A and Gd2A sites suggests a possible
coexistence of major variants containing Gd atoms
at the A sites and minor variants containing Gd
atoms at the B sites in the crystal.
9. Electron diffraction
The in situ observation of the electron diffraction
pattern was carried out using JEM-2000EX and
EM-SHU2 specimen holder (JEOL). The [001]zone axis electron diffraction patterns at room
temperature, 358 and 378 K are shown in Fig.
13. Due to presence of the lattice centering in the
KLJKWHPSHUDWXUHPRGL¿FDWLRQWKHUHÀHFWLRQVZLWKh+k=odd should become extinct. Since the indicesin Fig. 13 are given based on the P21nb latticewith doubled b-length compared with the highWHPSHUDWXUH PRGL¿FDWLRQ WKH H[WLQFWLRQ UXOH LV

Fig. 14. The [001] zone axis electron diffration pattern
DW.6DWHOOLWHUHÀHFWLRQVZHUHFOHDUO\REVHUYHG
in many samples.

DSSDUHQWO\ PRGL¿HG DV h+k/2=odd. Actually, theUHÀHFWLRQV     HWF EHFRPH ZHHN
at 358 K and almost disappear at 378 K in Fig. 13.
This is consistent with the X-ray diffraction study.
On the other hand, many crystals showed aninteresting behavior when they are heated close to
the phase transition temperature. A typical [001]zone axis electron diffraction pattern is shown in
Fig. 14. The pattern taken at 358 K has diffuse split
pairs near the hklUHÀHFWLRQVZLWKh+k/2=odd. Thesesatellites align along the b axis at both sides of theUHÀHFWLRQV ZLWK h+k RGG 7KH FHQWHU UHÀHFWLRQV
with h+k/2=odd gradually lost their intensity
upon heating whereas the satellites became evenstronger. The satellites then disappeared suddenly
at the transition point and the the diffraction
pattern changed into that of the high-temperature
PRGL¿FDWLRQDVVKRZQLQWKHULJKWPRVWSKRWRJUDSKin Fig. 13. The reverse took place upon cooling.
The diffuse split satellites suggest a possible
existence of intermediate phase near the phasetransition temperature. As discussed in the sections
7 and 8, the transition assumes both properties ofthe order-disorder and displacive types. If there
is a difference in temperature between the two
events of termination/initiation of the libration of
the [-Gd-RuO6-Gd-RuO6-Gd-] linkage and thedimerization/dedimerization of the Ru atoms, then
DQLQKRPRJHQHRXVVWUHVV¿HOGVKRXOGDSSHDULQWKH
crystal between these events. This could trigger off
the intermediate phase.
10. Relation to the other Ln3RuO7 compounds
Gemmill et al.  UHSRUWHGWKDWWKHUH¿QHPHQW
of the CmcmPRGL¿FDWLRQVRI(X3RuO7 turned out a
SRRUHU¿WWLQJWKDQWKDWRI6P3RuO7. The anisotropic
atomic displacement parameters of Sm1 and Eu1
atoms in these compounds are approximately
4-times prolate along b, and the values for Eu1 areapproximately 50 % larger than those for Sm1. This
may indicate that the harmonic approximation of a

― 15 ―

Phase Transition of Gd3RuO7 from a Structural Point of View

non-split Ln1 atom model becomes less appropriate
for describing the Cmcm structure with decreasingionic radii in the sequence of Ln = Sm3+ (4f5), Eu3+
(4f6), and Gd3+ (4f7).
The P21nb PRGL¿FDWLRQV KDYH EHHQ IRXQG
recently for Ln3RuO7 (Ln=Tb3+ (4f8), Dy3+ (4f9))
They are also expected
at room temperature.
to undergo the P21nb-Cmcm phase transition athigh temperatures. If the known phase transition
temperatures are plotted against ionic radii of Ln
atoms, similar transitions are expected to occur
at roughly estimated temperatures of 440 K for
Tb3RuO7 and 510 K for Dy3RuO7. The disorder in
WKHKLJKWHPSHUDWXUHPRGL¿FDWLRQLVDOVRH[SHFWHG
for the Tb and Dy compounds, which are subjects offuture investigation.
11. Summary
Structural phase transition of trigadorinium
ruthenium heptaoxide, Gd3RuO7, has been
investigated by in situ high-temperature X-rayand electron diffraction. A small shrinkage of theb-length and an expansion of the c-length wereobserved between 363 and 383 K with increasing
WHPSHUDWXUH 1R VLJQL¿FDQW FKDQJH RFFXUUHG LQ
a-length within experimental errors. The changes
were essentially reversible against temperature.
6WUXFWXUHVRIWKHKLJKWHPSHUDWXUHPRGL¿FDWLRQKDYH
been determined at 423, 773, and 1223 K assuming
the orthorhombic Cmcm symmetry. The structure
RI WKH ORZWHPSHUDWXUH PRGL¿FDWLRQ KDV EHHQ
determined at 293 K, assuming the orthorhombic
P21nb symmetry with doubled unit cell along
the bD[LV RI WKH KLJKWHPSHUDWXUH PRGL¿FDWLRQ
The transition from high- to low-temperature
PRGL¿FDWLRQ FDQ EH VWUXFWXUDOO\ FKDUDFWHUL]HG E\tilts about axes close to the c-axis occurring on
half of the RuO6 octahedra. These octahedral tilts
couple with a reduction in coordination numberof the Gd atom bridging the adjacent RuO6 single
chains along the b-axis. Dimerization of the Ruarray along the chain occurs on the transition, which
provides a folding effect on the zigzagging chain
LQ WKH ORZWHPSHUDWXUH PRGL¿FDWLRQ 7KH SUHVHQW
study also revealed a presence of structural disorderin the Cmcm structure that had not been reported
for lanthanide ruthenates (Ln3RuO7) and osmates(Ln3OsO7) in the literature. The disorder includes
a dynamical or static distribution of h-third of Gd
atoms in the unit cell, which is presumably linked
to the libration of the octahedral tilts about the axes
close to c. The P21nb-Cmcm phase transition canbe considered as an order-disorder transition of thelibrating [-Gd-RuO6-Gd-RuO6-Gd-] linkage. Similarphase transitions are expected to occur in Ln3RuO7(Ln=Tb, Dy) with smaller Ln cation sizes at higher
temperatures than Gd3RuO7. The in situ electron
diffraction experiments on Gd3RuO7 revealed apossible existence of intermediate phase between
WKHKLJKDQGORZWHPSHUDWXUHPRGL¿FDWLRQV
Acknowledgements
This study was supported by Grants-in-Aid for
6FLHQWL¿F 5HVHDUFK 1R  +1  DQG 1R
18206071 (NI) from the Japan Society for the
Promotion of Science. One of the authors (KT) has
been involved in this study as a researcher of the
Project Laboratory based on the program of the
Ministry of Education, Culture, Sports, Scienceand Technology “Cooperation for Innovative
Technology and Advanced Research in Evolutional
Area, West Tounou, Gifu Prefecture”.
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― 16 ―