Synchrotron-radiation study of the two-leg spin-ladder (VO)2P2O7 at 120 K

Article abstract of DOI:10.1107/S0108270101017553

The crystal structure of the ambient-pressure phase of vanadyl pyrophosphate, (VO)₂P₂O₇, has been precisely determined at 120 K from synchrotron X-ray diffraction data measured on a high-quality single crystal. The structu

Full text of DOI:10.1107/S0108270101017553

inorganic compounds
Acta Crystallographica Section C
Crystal Structure
exchange interactions give rise to a non-magnetic singlet
ground state accompanied by a singlet±triplet energy gap
Communications
(Barnes et al., 1993; Eccleston et al., 1994). From a crystal-
lographic point of view, (VO) P O has been widely con-
ISSN 0108-2701
2
2
7
1
sidered to be a prototype of a two-leg spin-ladder system. S = 2
spin ladders are of interest as an intermediate stage between
one-dimensional spin chains and two-dimensional spin lattices,
and it has been proposed that hole-doped spin ladders may
exhibit superconductivity (Dagotto et al., 1992; Dagotto &
Rice, 1996). The magnetism of (VO) P O has been inter-
Synchrotron-radiation study of the
two-leg spin-ladder (VO) P O at
2
2
7
1
20 K
2
2
7
pretated in a number of ways, which have been reviewed in
detail by Johnston et al. (2001). Initially, magnetic suscepti-
bility measurements and inelastic neutron scattering data were
discussed in terms of a two-leg spin-ladder model (Barnes &
Riera, 1994; Eccleston et al., 1994) and an alternating spin-
chain model (Johnston et al., 1987; Barnes & Riera, 1994).
Subsequent inelastic neutron scattering studies revealed that
the magnetic properties are dominated by alternating spin
chains, because the dispersion of magnetic excitations was
found to be inconsistent with a spin ladder (Garrett, Nagler,
Barnes & Sales, 1997; Garrett, Nagler, Tennant et al., 1997).
Recently, high-®eld magnetization measurements, and NMR
and Raman scattering studies proved the co-existence of two
magnetic subsystems associated with two different spin-gap
energies (Kikuchi et al., 1999; Yamauchi et al., 1999; Kuhlmann
et al., 2000).
a
a
a
Sandra Geupel, * Katrin Pilz, Sander van Smaalen, Frank
b
b
b
B uÈ llesfeld, Andrei Prokofiev and Wolf Assmus
a
Laboratory of Crystallography, University of Bayreuth, D-95440 Bayreuth,
b
Germany, and Institute of Physics, University of Frankfurt, D-60054 Frankfurt am
Main, Germany
Correspondence e-mail: sandra.geupel@uni-bayreuth.de
Received 8 October 2001
Accepted 16 October 2001
Online 14 December 2001
The crystal structure of the ambient-pressure phase of vanadyl
pyrophosphate, (VO) P O , has been precisely determined at
20 K from synchrotron X-ray diffraction data measured on a
high-quality single crystal. The structure re®nement unam-
2
2
7
1
biguously establishes the orthorhombic space group Pca2 as
1
Several studies of the crystal structure of (VO) P O at
2
2
7
the true crystallographic symmetry. Moreover, it improves the
accuracy of previously published atomic coordinates by one
order of magnitude, and provides reliable anisotropic
displacement parameters for all atoms. Along the a axis, the
structure consists of in®nite two-leg ladders of vanadyl cations,
room temperature have been published. Initial diffraction
experiments with X-rays and electrons suggested ortho-
rhombic symmetry with space group Pcam or Pca2 (Gorbu-
nova & Linde, 1979; Bordes & Courtine, 1979), but the ®nal R
values from the structure re®nement were unsatisfactory.
Subsequent single-crystal X-ray structure analyses gave
acceptable R values, but contradictory results, e.g. Ebner &
1
2
+
(
VO) , which are separated by pyrophosphate anions,
4�
(
P O ) . Parallel to the c axis, the unit cell comprises two
2
7
alternating crystallographically inequivalent chains of edge-
sharing VO5 square pyramids bridged by PO4 double
tetrahedra. No structural phase transition has been observed
in the temperature range between 300 and 120 K.
Thompson (1991) reported space group Pca2 with disorder
1
on the V sites, while Nguyen et al. (1995) found space group
P1121 with a pseudo-orthorhombic translation lattice, as
ꢀ
indicated by a monoclinic angle of 89.975 (3) . The P1121
structure model seems to be doubtful, since it presents
extremely distorted non-positive de®nite thermal vibration
ellipsoids for several V and P sites, but also unusually large
isotropic displacement parameters for two O sites that are
shared by opposing PO tetrahedra in the P O groups. Recent
Comment
Oxovanadium phosphates constitute a family of compounds
with a versatile crystallochemistry that results in an intricate
magnetochemistry. This diversity is due to the accessibility of
several oxidation states of vanadium, the ability of phosphate
and vanadium polyhedra to form a large variety of complex
network structures, and the involvement of phosphate groups
in the spin transfer between V ions. Vanadyl pyrophosphate,
4
2
7
diffraction studies with X-rays, neutrons and electrons on
(VO) P O powder samples showed systematic extinctions
which are consistent with space group Pca2 , and led to a
2
2
7
1
structure model with exceptionally large isotropic displace-
ment parameters for a number of O sites in the P O groups
also (Hiroi et al., 1999). Crystallographic disorder in
(
VO) P O , has been extensively studied by chemists, because
2 2 7
2
7
this compound is known to be a very ef®cient catalyst for
selective oxidation of n-butane to maleic anhydride (Centi et
al., 1988). This process is of considerable industrial impor-
tance, as it is presently the only (heterogeneously catalyzed)
alkane oxidation performed on a large scale. Recently,
(VO) P O was often detected in X-ray and electron-diffrac-
2
2
7
tion patterns as diffuse scattering (Bordes & Courtine, 1979;
Hiroi et al., 1999) and peak-broadening effects due to the
introduction of stacking faults (Nguyen et al., 1996). Several
studies revealed the ability of (VO) P O to accomodate
(
physicists due to its low-dimensional magnetic properties. It
VO) P O has attracted much attention by solid-state
2 2 7
2
2
7
various disordered or polytypic structures generated by
interlayer vacancies (Thompson et al., 1994) and O defect sites
(Gai & Kourtakis, 1995; Gai, 1997). On the other hand, the
4
represents a quantum magnetic spin system of V ions (3d
+
1
1
2
con®guration, spin S = ), whose antiferromagnetic super-
Acta Cryst. (2002). C58, i9±i13
DOI: 10.1107/S0108270101017553
# 2002 International Union of Crystallography i9

inorganic compounds
4
�
(P O ) . All V atoms show a (4+1) square-pyramidal coor-
2 7
structure of (VO) P O is capable of preserving mixed-
2
2
7
4
valence V /V pairs associated with interstitial O sites in the
+
5+
dination to ®ve O atoms, consisting of four equatorial VÐO
Ê
distances ranging from 1.940 (3) to 2.083 (4) A and one short
axial VÐO distance varying between 1.594 (3) and
Ê
1.612 (4) A. In the [100] direction and nearly opposite the
strong V O bond of the vanadyl group, the V atoms are also
weakly coordinated to the apical O atoms of neighbouring
VO5 pyramids, with long VÐO distances ranging from
P O sublattice (L o pez-Granados et al., 1993). Very recently, a
2
7
high-pressure phase treated at 2±3 GPa was found to crystal-
lize in the orthorhombic space group Pnab, with a unit cell of
half the size of that of the ambient-pressure phase (Azuma et
al., 1999; Saito et al., 2000).
Our investigations were motivated by the fact that none of
the previously published crystal structure data of the ambient-
pressure phase of (VO) P O provide accurate enough values
Ê
2.250 (4) to 2.341 (3) A. Along the c axis, the unit cell of
(VO) P O comprises two alternating crystallographically
2
2
7
2
2
7
for the spin-orbital interaction energies (Koo & Whangbo,
000). Knowledge of these spin-orbital interaction energies is
inequivalent chains built of pairs of edge-sharing VO square
5
2
pyramids. The chains are arranged in such a way that in every
VO pair the V O bonds are in trans positions, as each axial
indispensable to conclude unambiguously which of the alter-
nating spin chains has the larger energy gap, and which of the
bridged and edge-sharing spin dimers has the stronger spin
exchange interaction in the chains. The complications in
earlier studies may be attributed to sample preparation
conditions, poor crystal quality, and limited experimental
accuracy. The present structure determination from low-
temperature synchrotron X-ray data measured on a high-
quality single crystal con®rms the assignment of space group
5
O atom is located alternately above or below the basal plane.
The VO double pyramids in the V1±V2 chain are bridged by
5
tilted PO double tetrahedra involving P1 and P2 [with a
4
Ê
P1Á Á ÁP2 separation of 3.0112 (18) A], while those in the V3±
V4 chain are linked by untilted PO double tetrahedra
4
involving P3 and P4 [with a P3Á Á ÁP4 separation of
Ê
3.0873 (19) A]. Each equatorial O atom of the VO pairs
5
shares a corner with one PO group (Fig. 1). The PÐO
4
Ê
distances range from 1.487 (4) to 1.583 (3) A and the OÐPÐ
Pca2 . Moreover, the structure re®nement provides reliable
1
anisotropic displacement parameters for all atoms, and
improves the accuracy of the atomic coordinates, as given by
Hiroi et al. (1999) and Gorbunova & Linde (1979), by one
order of magnitude.
O bond angles within the PO tetrahedra vary between
4
ꢀ
104.1 (2) and 116.9 (2) . The P1ÐO6ÐP2 and P3ÐO5ÐP4
ꢀ
bridging angles are 144.50 (18) and 157.20 (17) , respectively.
Both values fall within the typical range found for P O7
2
The asymmetric unit of (VO) P O in Pca2 contains four V
2
groups. The shortest non-bonding VÁ Á ÁV distances in the [001]
2
7
1
sites, four P sites and 18 O sites. Along the a axis, the crystal
structure consists of in®nite two-leg ladders of vanadyl cations,
2
+
VO) , which are separated by pyrophosphate anions,
(
Figure 1
2 2 7
Polyhedral representation of the crystal structure of (VO) P O viewed
(
square pyramids are drawn in dark grey, the PO
a) along the [100] direction and (b) along the [010] direction. The VO
5
4
tetrahedra in light grey.
Large circles represent V atoms and medium circles represent P atoms.
Figure 2
View of (VO)
ellipsoids at 120 K are drawn at the 90% probability level.
2 2 7
P O with the atom-labelling scheme. Displacement
Small circles in (a) denote O atoms, which are not shown in (b).
ꢁ
i10 Sandra Geupel et al.
2
(VO) P
O
2 7
Acta Cryst. (2002). C58, i9±i13

inorganic compounds
direction (i.e. along the rungs of the ladder) are d(V3Á Á ÁV4) =
Crystal data
Ê
Ê
3
.2047 (12) A and d(V1Á Á ÁV2) = 3.2282 (12) A. Those in the
(VO) P O
7
Synchrotron radiation
Ê
2
2
M
r
= 307.82
Orthorhombic, Pca2
ꢁ = 0.70843 A
[
100] direction (i.e. along the legs of the ladder) are much
Ê
1
Cell parameters from 25
re¯ections
longer and approximately given as a/2 = 3.85 A. Bond-valence
calculations were carried out with the program VALENCE
Ê
a = 7.7004 (4) A
b = 9.5777 (5) AÊ
ꢀ
ꢂ = 16.1±22.5
Ê
c = 16.5825 (8) A
� 1
ꢃ = 3.55 mm
T = 120 (2) K
(
Brese & O'Keeffe (1991). The bond-valence sums agree very
Brown, 1996), using bond-valence parameters according to
Ê
V = 1222.99 (11) A
3
Z = 8
D = 3.344 Mg m
Rectangular prism, dark green
0.10 Â 0.04 Â 0.03 mm
4
+
well with the expected valence states V and P (Table 2),
5+
� 3
x
4
+
5+
and exclude the presence of mixed-valence V /V pairs for
the measured crystal. The equivalent isotropic displacement
parameters of the O atoms are found to be signi®cantly larger
than those of the V and P atoms, and the principal mean-
square atomic displacements of several O sites show a
pronounced anisotropy (Fig. 2). The thermal motion of these
O atoms could not be reasonably well described by a split-
atom model.
Data collection
Huber four-circle Kappa
diffractometer with a Siemens
SMART CCD area-detector and
an Oxford Cryosystems Cryo-
stream cooler
11 910 measured re¯ections
3149 independent re¯ections
2452 re¯ections with I > 2ꢄ(I)
R
int = 0.060
ꢀ
ꢂ
max = 30.4
!
and ' scans
Absorption correction: multi-scan
SADABS; Sheldrick, 1996)
min = 0.804, Tmax = 0.950
h = � 10 ! 9
k = � 13 ! 13
l = � 23 ! 23
(
T
At T = 300 K, the lattice parameters of (VO) P O have
2
2
7
Re®nement
been determined as a = 7.7285 (3), b = 9.5842 (4) and c =
Ê
2
Ê
� 3
Áꢅmax = 0.81 e A
1
6.5962 (6) A. Assuming a simple linear behaviour, the coef-
cients of linear thermal expansion in the temperature range
Re®nement on F
2
2
Ê
� 3
R[F > 2ꢄ(F )] = 0.031
wR(F ) = 0.068
Áꢅmin = � 0.67 e A
®
2
Extinction correction: SHELXL97
(Sheldrick, 1997)
�
5
� 1
between 300 and 120 K are estimated as ꢀ = 2.0 Â 10 K ,
a
S = 0.88
3149 re¯ections
�
6
� 1
� 6 � 1
ꢀ
= 3.8 Â 10
K
and ꢀ = 4.6 Â 10 K . This indicates a
Extinction coef®cient: 0.0165 (6)
Absolute structure: Flack (1983),
1303 Friedel pairs
b
c
2
37 parameters
2 2
strong anisotropic thermal expansion, taking place mainly in
the direction parallel to the legs of the ladder. The ꢀ value is
comparable with that obtained from Raman scattering
experiments (Kuhlmann et al., 2001).
2
) + (0.0302P) ]
w = 1/[ꢄ (F
o
2 2
c
where P = (F
(Á/ꢄ)max < 0.001
o
+ 2F
)/3
Flack parameter = 0.00 (13)
Table 1
Selected geometric parameters (A, ).
Ê
ꢀ
vii
Experimental
V1ÐO1
V1ÐO11
V1ÐO12
1.594 (3)
1.941 (3)
1.949 (3)
2.079 (4)
2.083 (4)
2.341 (3)
1.600 (5)
1.951 (4)
1.957 (4)
2.071 (4)
2.071 (4)
2.305 (5)
1.603 (6)
1.944 (4)
1.954 (4)
2.070 (4)
2.077 (4)
2.256 (6)
1.612 (4)
1.940 (3)
V4ÐO15
1.942 (3)
2.050 (4)
2.073 (4)
2.250 (4)
1.487 (4)
1.499 (4)
1.557 (4)
1.583 (3)
1.490 (3)
1.498 (4)
1.556 (3)
1.579 (3)
1.487 (4)
1.494 (3)
1.554 (3)
1.576 (3)
1.495 (4)
1.498 (4)
1.554 (3)
1.573 (3)
i
vii
V4ÐO9
V4ÐO10
V4ÐO4
P1ÐO11
2 2 7
In general, the single-crystal growth of (VO) P O is complicated by
i
V1ÐO7
V1ÐO8
V1ÐO1
two features. First, the phase stability and valence state of vanadium
are very sensitive to the oxygen content in the growth atmosphere
ii
vii
P1ÐO13
P1ÐO10
(
L o pez-Granados et al., 1993; Proko®ev et al., 2000). Secondly, the
V2ÐO2
V2ÐO14
V2ÐO13
iii
ix
melt exhibits a tendency towards glass formation during cooling due
to its high viscosity. Therefore, the single-crystal growth has to be
carried out with a very low growth rate and in a growth atmosphere
P1ÐO6
P2ÐO12
P2ÐO14
P2ÐO9
P2ÐO6
P3ÐO18
P3ÐO16
P3ÐO7
iv
V2ÐO8
V2ÐO7
V2ÐO2
V3ÐO3
v
with controlled oxygen content. (VO)
growth was prepared from the precursor vanadyl hydrogen phos-
phate hemihydrate, VOHPO O, via a topotactic dehydration
Á0.5H
Bordes et al., 1984; Torardi et al., 1995) in an argon ¯ow at 973 K. The
precursor was synthesized according to the procedure given by Centi
et al. (1985). Large single crystals of (VO) were grown using a
2 2 7
P O powder for the crystal
vi
vii
V3ÐO17
V3ÐO18
V3ÐO9
V3ÐO10
V3ÐO3
4
2
ix
(
P3ÐO5
viii
P4ÐO15
P4ÐO17
P4ÐO8
P4ÐO5
2
P
2
O
7
vi
V4ÐO4
V4ÐO16
combination of Czochralski and Kryopoulos methods, i.e. slow
cooling (4±8 K per day) of the melt with simultaneous pulling (2 mm
per day) of the dark-green crystals from the melt. Crystal growth was
carried out in a resistance furnace under a ¯ow of a gas mixture of
argon and oxygen (0.2 vol%), using a silica growth chamber and a
platinum crucible. Further details of the crystal-growth technique are
described by Proko®ev, B uÈ llesfeld & Assmus (1998). No impurity
phases were detected using electron microprobe analysis, scanning
electron microscopy, and X-ray powder diffraction. From thermo-
x
x
P4ÐO5ÐP3
157.20 (17)
P2ÐO6ÐP1
144.50 (18)
1
2
1
2
1
Symmetry codes: (i) � x; y � 1; ‡ z; (ii) ‡ x; � y; z; (iii) x; 1 ‡ y; z; (iv)
2
1
2
1
1
2
1
2
1
1
2
1
�
x; 1 ‡ y; z �
;
(v) ‡ x; 2 � y; z; (vi) x � ; 1 � y; z; (vii) � x; y; z � 2
; (viii)
2
1
2
1
2
1
� x; y; ‡ z; (ix) 1 � x; 1 � y; z � ; (x) 1 � x; 1 � y; ‡ z.
2
2
Table 2
Selected bond-valence sums.
gravimetric analysis studies based on the oxidation of (VO)
2
P
2
O
7
to
VPO , the oxidation state of the V ions was determined to be +4.05.
5
Atom
Bond-valence sum
Atom
Bond-valence sum
Furthermore, the single crystals were comprehensively investigated
using electron spin resonance and magnetic susceptibility measure-
ments (Proko®ev, B uÈ llesfeld, Assmus et al., 1998), as well as Raman
scattering and IR spectroscopy (Kuhlmann et al., 2000, 2001; Grove et
al., 2000).
V1
V2
V3
V4
4.08
4.07
4.11
4.13
P1
P2
P3
P4
4.89
4.90
4.94
4.91
ꢁ
Acta Cryst. (2002). C58, i9±i13
Sandra Geupel et al.
(VO)
2 2
P O
7
i11

inorganic compounds
Table 3
Bond-valence data.
meters and 1443 observed re¯ections), and unacceptably high
Ê
� 3
residuals (3.6 and � 6.4 e A ) lying close to the V atoms appear in
the difference Fourier map. Attempts to re®ne the data in Pcam
Atom 1
Valence
Atom 2
Valence
R
o
B
Ref.
(R
int = 0.063 for 1848 independent re¯ections) were also unsuccessful
(R = 0.121 for 151 parameters and 1466 observed re¯ections, highest
V
P
4
5
O
O
� 2
� 2
1.784
1.604
0.370
0.370
(a)
(a)
Ê
� 3
residuals 2.9 and � 5.3 e A ), although the statistical distribution of
normalized structure factors strongly prefers a centrosymmetric
2
Notes: (a) Brese & O'Keeffe (1991).
space group (the values of |E � 1| are 1.273 for 0kl, 1.040 for h0l,
1.076 for hk0, and 0.947 for all other re¯ections). Assuming mono-
clinic symmetry with space group P112
for 5581 independent re¯ections), the ®nal R values are, in com-
parison with those for Pca2 , only slightly higher (R = 0.0330, wR =
0.0758 for 471 parameters and 3882 observed re¯ections, highest
1
(inversion twin, Rint = 0.057
Single-crystal X-ray diffraction experiments with synchrotron
radiation were performed on beamline F1 of HASYLAB at DESY
Hamburg. A double-crystal Si(111) monochromator was used to
1
�
Ê
3
Ê
select a wavelength of ꢁ = 0.70843 A. Re¯ection groups h0l (h =
residuals 0.79 and � 0.77 e A ). However, the anisotropic displace-
ment parameters of ®ve unique O atoms in P112 possess a principal
axis Umax/Umin ratio of more than 15:1, and the anisotropic
2n + 1), 0kl (l = 2n + 1), h00 (h = 2n + 1) and 00l (l = 2n + 1) were
1
found to be systematically absent in the data collection carried out at
T = 120 K, with a measuring time of 5 s per frame and a crystal-to-
detector distance of 50 mm. Possible space groups consistent with the
displacement ellipsoids of three further O atoms even become non-
1
positive de®nite, while those of all the atoms in Pca2 display a
observed re¯ection conditions are only Pcam or Pca2
1
. Indications of
physically meaningful shape.
disorder, non-merohedral twinning or superstructure re¯ections were
not detected. SADABS (Sheldrick, 1996) was used for corrections of
variations in the primary beam intensity and for averaging symmetry-
equivalent re¯ections. Accurate lattice parameters at 120 and 300 K
were determined from laboratory four-circle diffractometer data,
because several systematic errors (e.g. the positions of the crystal and
detector) in the cell-re®nement procedure are not accounted for by
SAINT (Siemens, 1996). We checked the monoclinic cell constraints
Data collection: SMART (Siemens, 1996); cell re®nement: SET4 in
CAD-4 UNIX Software (Enraf±Nonius, 1998); data reduction:
SAINT (Siemens, 1996); program(s) used to solve structure:
SHELXS97 (Sheldrick, 1997); program(s) used to re®ne structure:
SHELXL97 (Sheldrick, 1997); molecular graphics: DIAMOND
(Brandenburg, 1999) and ORTEP-3 (Farrugia, 1997); software used
to prepare material for publication: SHELXL97.
ꢀ
also, but none of the unit-cell angles differed from 90 within one
standard deviation.
The authors thank H. Schmidt and H.-G. Krane for
experimental support on HASYLAB. Financial support from
the Deutsche Forschungsgemeinschaft (DFG) is gratefully
acknowledged.
The Flack (1983) parameter of an initial re®nement in space group
Pca2
without twinning yielded a Flack parameter of x = 0.27 (4), with R =
.0308 and wR = 0.0692. Transformation to the inverse structure
1
indicated that the crystal was twinned. The re®nement model
0
resulted in x = 0.54 (4), with R = 0.0316 and wR = 0.0716. Conse-
quently, an inversion twin was added to the structure model. The ®nal
re®nement gave a twin volume fraction of 34 (4)%. This value is in
good agreement with a ratio of 32% determined with the program
TWIN3.0 (Kahlenberg & Messner, 2000), using the procedure
proposed by Britton (1972). The deviation from the expected 1:1
distribution may be caused during the cutting of the crystals. Fixing
the twin fraction at 50% had no signi®cant in¯uence on the structure
parameters.
Supplementary data for this paper are available from the IUCr electronic
archives (Reference: BR1349). Services for accessing these data are
described at the back of the journal.
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y = and that such pairs of related atoms in Pca2
1
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2
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Ê
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1
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