Raman studies of A2MWO6 tungstate double perovskites

Article abstract of DOI:10.1039/c4dt03789h

The Raman spectra of seven A₂MWO₆ tungstate double perovskites are analysed. Ba₂MgWO₆ is a cubic double perovskite with Fm3m symmetry and its Raman spectrum contain three modes that can be assigned in a straightforward manner. A fourth mode, the asymmetric stretch of the [WO₆]^6- octahedron, is too weak to be observed. The symmetry of Ba₂CaWO₆ is lowered to tetragonal I4/m due to octahedral tilting, but the distortion is sufficiently subtle that the extra bands predicted to appear in the Raman spectrum are not observed. The remaining five compounds have additional octahedral tilts that lower the symmetry to monoclinic P2₁/n. The further reduction of symmetry leads to the appearance of additional lattice modes involving translations of the A-site cations and librations of the octahedra. Comparing the Raman spectra of fourteen different A₂MWO₆ tungstate double perovskites shows that the frequency of the symmetric stretch (ν₁) of the [WO₆]^6- octahedron is relatively low for cubic perovskites with tolerance factors greater than one due to underbonding of the tungsten and/or M cation. The frequency of this mode increases rapidly as the tolerance factor drops below one, before decreasing gradually as the octahedral tilting gets larger. The frequency of the oxygen bending mode (ν₅) is shown to be dependent on the mass of the A-site cation due to coupling of the internal bending mode with external A-site cation translation modes.

Full text of DOI:10.1039/c4dt03789h

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Raman studies of A2MWO6 tungstate double
perovskites†
Cite this: DOI: 10.1039/c4dt03789h
R. L. Andrews, A. M. Heyns and P. M. Woodward*
The Raman spectra of seven A2MWO6 tungstate double perovskites are analysed. Ba2MgWO6 is a cubic
double perovskite with Fm3¯m symmetry and its Raman spectrum contain three modes that can be
assigned in a straightforward manner. A fourth mode, the asymmetric stretch of the [WO6]6− octahedron,
is too weak to be observed. The symmetry of Ba2CaWO6 is lowered to tetragonal I4/m due to octahedral
tilting, but the distortion is sufficiently subtle that the extra bands predicted to appear in the Raman spec-
trum are not observed. The remaining five compounds have additional octahedral tilts that lower the sym-
metry to monoclinic P21/n. The further reduction of symmetry leads to the appearance of additional
lattice modes involving translations of the A-site cations and librations of the octahedra. Comparing the
Raman spectra of fourteen different A2MWO6 tungstate double perovskites shows that the frequency of
the symmetric stretch (ν1) of the [WO6]6− octahedron is relatively low for cubic perovskites with tolerance
factors greater than one due to underbonding of the tungsten and/or M cation. The frequency of this
mode increases rapidly as the tolerance factor drops below one, before decreasing gradually as the octa-
hedral tilting gets larger. The frequency of the oxygen bending mode (ν5) is shown to be dependent on
the mass of the A-site cation due to coupling of the internal bending mode with external A-site cation
translation modes.
Received 10th December 2014,
Accepted 23rd January 2015
DOI: 10.1039/c4dt03789h
www.rsc.org/dalton
type of distortion in perovskites is octahedral tilting.2,3,8–10
When the tolerance factor is less than one, the size of the
Introduction
The perovskite family is one of the largest and most important A-site cation is too small for its cuboctahedral cavity and co-
in all of solid state chemistry. Perovskites have a stoichiometry operative tilts of essentially rigid octahedra are expected. Octa-
ˉ
of AMO3, and the aristotype structure possesses Pm3m space hedral tilting modifies the coordination environment of the
group symmetry. The M cation resides at the centre of an octa- A-site cation while maintaining the octahedral coordination
hedron, and the A cation occupies the cubooctahedral cavities environment of the M and M′ cations. At the same time it
that exist in the corner connected framework of MO6 octa- lowers the overall symmetry of the crystal structure.
hedra. Ordering of two unique octahedral cations on a three
There are many examples in the literature of incorrect struc-
dimensional checkerboard pattern (i.e. rock salt ordering) ture determinations that stem from an inability to correctly
leads to the A2MM′O6 double perovskite structure, where the identify the correct pattern of octahedral tilting. This is par-
unit cell is doubled along all three axes and the space group ticularly true for double perovskites because the diffraction
ˉ
symmetry becomes Fm3m. Double perovskites are a large peaks that arise from rock salt ordering of M and M′ ions are
group of compounds numbering more than 1000.1–3 They are the same as those that arise from out-of-phase tilting of the
prized for a variety of properties and are used as relaxor ferro- octahedra.11,12 In some instances neutron diffraction studies
electrics,4 microwave dielectrics,5 ionic conductors,6 and half- are needed to make definitive space group assignments, which
metallic conductors.7
Most perovskites do not adopt the aristotype cubic struc- ties is limited.
can be problematic because access to neutron scattering facili-
ture, but are distorted in some manner. The most common
Raman spectroscopy is an alternative technique for moni-
toring the reduction in symmetry that accompanies octahedral
tilting. In theory additional bands should appear as the sym-
metry is lowered, but in practice it is not always possible to see
all of the additional bands in spectra taken on polycrystalline
samples. In this paper Raman spectroscopy is used to probe
the local structure of seven A2M2+WO6 double perovskites. The
compounds studied were chosen to meet several criteria. By
Department of Chemistry and Biochemistry, The Ohio State University, 100 W. 18th
Avenue, Columbus, OH 43210-1106, USA. E-mail: woodward.55@osu.edu
†Electronic supplementary information (ESI) available: Lattice parameters deter-
mined from Rietveld refinements of X-ray powder diffraction data, values of ν1
and ν5 modes for A2MWO6 perovskites studied in the literature, and Raman
spectra of AWO4 scheelite phases. See DOI: 10.1039/c4dt03789h
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choosing perovskites whose tolerance factors range from 1.038
(Ba2MgWO6) to 0.867 (Ca2CaWO6) the group contains com-
pounds with various patterns of octahedral tilting. Because the
oxidation states of the M and M′ ions differ by four, the pres-
ence of antisite disorder, which can complicate interpretation
of Raman spectra, can be avoided. By systematically analysing
the Raman spectra of these compounds the links between
changes in crystallographic symmetry and the appearance of
new bands in the Raman spectra are revealed. By limiting the
study to a set of perovskites where the strongest bonding unit,
the [WO6]6− octahedron, remains constant we can study the
effect of changes in composition, bonding, and structure on
the frequencies and intensities of the internal vibrations of the
[WO6]6− octahedron.
Experimental
All samples were prepared using conventional solid state syn-
thesis methods. High purity (>99%) starting materials of
BaCO3, SrCO3, CdO, MgO, ZnO, CaCO3, and WO3 were used.
Stoichiometric amounts of the starting materials were ground
in an agate mortar and pestle before heating in ceramic cruci-
bles for 12–24 hours. Multiple heating cycles with intermittent
grinding were necessary for some materials. The annealing
temperature was 950 °C for Sr2CdWO6, 1000 °C for Sr2ZnWO6,
1200 °C for Ca2CaWO6, and 1300 °C for the remaining com-
pounds. X-ray powder diffraction patterns were collected with
a Bruker D8 Advance X-ray diffractometer (40 kV, 50 mA,
copper source λ = 1.5406 Å). Rietveld refinements of the X-ray
diffraction data were performed using Topas Academic soft-
ware.13 All Raman studies were performed using a Renishaw
Smith Raman IR microprobe with a 514 nm Argon ion laser.
In some samples a few percent of an AWO4 (A = Sr, Ba) sec-
ondary phase was detected by X-ray diffraction. To identify any
peaks in the Raman spectra that come from the scheelite
phases, phase pure samples of BaWO4, SrWO4 and CaWO4
were synthesized following the same conventional solid state
synthesis method with an annealing temperature of 1100 °C.
The Raman spectra of the scheelite tungstates are given in
the ESI.†
Fig. 1 The structure of a double perovskite with a0a0c− (upper), a0b−b−
(middle), and a−a−b+ (lower) tilting.
Table 1 The tolerance factors, tilt system at 300 K, and phase tran-
sitions that have been identified in the A2MWO6 perovskites under study
Tolerance
factor (t)
Composition
Octahedral tilting
17
Ba2MgWO6
1.038
0.976
0.972
0.930
0.926
0.917
0.867
a0a0a0 (at 300 K)
343 K
17
Sr2ZnWO6
Ba2CaWO6
Sr2CdWO6
aꢀaꢀcþ ꢀꢀꢀ! a0a0cꢀ
220 K
15,17
18,19
20
aꢀaꢀc0 ꢀꢀꢀ! a0a0cꢀ
Results
Crystal structures
1070 K
1230 K
aꢀaꢀcþ ꢀꢀꢀ! a0a0cꢀ ꢀꢀꢀ! a0a0a0
Ca2MgWO6
a−a−c+ (at 300 K)
Throughout this paper octahedral tilting will be described
1130 K
1250 K
19
Sr2CaWO6
Ca2CaWO6
aꢀaꢀcþ ꢀꢀꢀ! a0a0cꢀ ꢀꢀꢀ! a0a0a0
using the notation developed by Glazer.14 The a0a0a0
a−a−c+ (at 300 K)
17
ˉ
tilt system is the aristotype cubic structure with Fm3m
space group symmetry, while the other three tilt systems
encountered in tungstate double perovskites are illustrated
in Fig. 1.
The tilt systems reported in the literature, both at ambient
conditions and as a function of temperature, are summarized
in Table 1. There is some controversy regarding assignment of
tilt systems in Ba2CaWO6. Yamamura et al. assigned the 220 K
phase transition as being driven by a change from monoclinic
I2/m symmetry (a−a−c0 tilting) to tetragonal I4/m symmetry
(a0a0c− tilting),15 while Fu et al. claimed the transition was
0
0 0
ˉ
actually from I4/m symmetry to cubic Fm3m symmetry (a a a
tilting).16 Day et al. later investigated the room temperature
structure using both X-ray and neutron diffraction and
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Table 2 Refined atomic positions for Sr2CdWO6 as obtained from Riet-
veld refinement of powder diffraction data. The goodness of fit was χ2
=
1.148
a
Atom
Site
x
y
z
Beq.
Sr
Cd
W
O1
O2
O3
4e
2c
2d
4e
4e
4e
0.0074(4)
0.5
0
0.0700(9)
0.2604(9)
0.1812(5)
0.5371(9)
0.5
0
0.0142(5)
−0.1883(2)
0.2665(4)
0.2520(5)
0
0
−0.2312(5)
0.0300(2)
0.0444(0)
0.577(7)
0.402(9)
0.402(9)
1.003(0)
1.003(0)
1.003(0)
a The Beq. values for Cd and W were constrained to be the same, as
were the Beq. values of O1, O2, and O3.
Fig. 2 X-ray diffraction patterns of (a) Ba2CaWO6, (b) Ba2MgWO6, (c)
Sr2ZnWO6, (d) Sr2CdWO6, (e) Sr2CaWO6, (f) Ca2CaWO6 and (g)
Ca2MgWO6. The peak splitting that results from octahedral tilting can
clearly be seen in (c) through (g). The strongest peaks due to the sec-
ondary AWO4 scheelite phases are marked with an asterisk.
Fig. 3 Rietveld refinement of Sr2CdWO6. The upper (blue) and lower
(green) set of hash marks, denote the position of the Sr2CdWO6 and
SrWO4 reflection positions, respectively.
concluded that the symmetry at room temperature was tetra-
gonal I4/m.17 Therefore, the assignment originally put forward
by Yamamura et al. seems most credible and is given in
Table 1. However, there is a possibility that the symmetry of
this compound might be sample dependent.
mass, but Sr2MgWO6 and Sr2CdWO6 had approximately 3%
and 2% by mass, respectively. The presence of AWO4 crystal-
lites at such low levels is not likely to impact the crystallo-
graphy in any meaningful way. However, it is important to
identify these phases because as will be seen later, weak bands
associated with the scheelite phases are observed in many of
the Raman spectra.
To better understand how changes in structure impact the
Raman spectra that will be presented in the next section the
M–O–W bond angles, mean octahedral bond lengths, and dis-
tortion indices Δd are reported in Table 3. The distortion index
(Δd) measures the degree to which the M–O and W–O bond
distances are distorted from those found in a perfect octa-
hedron. The distortion index is calculated as follows:
The X-ray diffraction patterns illustrating the phase purity
and peak splitting characteristic associated with various types
of octahedral tilting are shown in Fig. 2. Rietveld refinements
yielded lattice parameters that are in good agreement with
those already reported in the literature, as shown in the ESI
(Table S1†).15,17–20 The atomic coordinates for six of the seven
compounds have previously been determined from neutron
powder diffraction data, thus the values obtained in our refine-
ments are not reported here. The lone exception is Sr2CdWO6,
where the high neutron absorption cross section of cadmium
makes neutron diffraction studies impractical. The refined
atomic positions for Sr2CdWO6 can be found in Table 2 and
the refined diffraction pattern is shown in Fig. 3. The mono-
clinic symmetry and atomic coordinates are in good agreement
with those reported by Gateshki et al.18
ꢀ
ꢁ
2
X
1
dnꢀ , d >
, d >
Δd ¼
6 n¼1ꢀ6
where dn is an individual M–O bond length and <d> is the
average M–O bond length. Octahedra with significant distor-
tions of the bond lengths (e.g. those containing Jahn Teller
During the synthesis of these particular tungsten based per-
ovskites, it was difficult to completely eliminate all traces of a
scheelite (A2+WO4) secondary phase, as can be seen by close
inspection of Fig. 2. Most samples contained less than 1% by
ions like Mn3+) have Δd values greater than 10−3 17,22
As can be
.
seen in Table 3 the values of Δd are generally quite small here,
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Table 3 Select bond distances, bond angles and octahedral distortion indices for the A2MWO6 perovskites under study. All parameters determined
from previous neutron powder diffraction studies, with the exception of Sr2CdWO6
Mean M–O
distance (Å)
M2+ distortion
index (×105)
Mean W–O
distance (Å)
W6+ distortion
index (×105)
M–O–W bond
angles (°)
Composition
17
Ba2MgWO6
Sr2ZnWO6
2.123
2.084
0
0.16
1.929
1.918
0
0.11
180
17
167.6
165.4
164.1
180
17
Ba2CaWO6
Sr2CdWO6
2.281
2.274
2.3
22
1.920
1.899
3.5
15
176.0
157.1
158.5
152.1
152.3
151.1
152.1
153.9
149.1
147.1
147.2
140.9
141.4
20
Ca2MgWO6
2.069
2.339
2.304
1.1
6.6
12
1.922
1.911
1.926
1.9
2.5
1.4
21
Sr2CaWO6
Ca2CaWO6
17
confirming the picture that these structures can be described The internal ν5 mode is due to an oxygen bending motion of the
by tilts of nearly rigid octahedra. The largest distortion occurs octahedron. The ν2 and ν5 modes are expected to occur in the
in Sr2CdWO6, but given the larger uncertainties associated ranges 470–610 cm−1 and 350–490 cm−1 respectively.23,24
with determining the structure using laboratory X-ray diffrac-
tion it’s quite possible that the values of Δd are overestimated modes (i.e. not associated with the internal vibration of an
in Sr2CdWO6. The next largest distortion occurs for the Ca-cen- octahedron).25 The external
modes found in the
Low energy lattice modes can be classified as external
T
tered octahedra in Ca2CaWO6 (Δd = 1.16 × 10−4). This distor- 100–300 cm−1 region arise from translations of the A cation,
tion is also present in the internal bond angles of the calcium and are referred to as translational lattice modes.23 The libra-
octahedron: O1–Ca–O3 = 94.83° and O2–Ca–O3 = 95.08°. tional modes, L, which are also considered lattice modes, can
According to Day et al., this can be attributed to the large octa- be described as rotations of rigid octahedra. When the crystal
ˉ
hedral tilting distortion and relatively ionic Ca–O bonds, con- has Fm3m symmetry, as Ba2MgWO6 does, the librational mode
ditions where the assumption of cooperative tilting of truly of F1g symmetry is silent and there is a single Raman active
rigid octahedra starts to break down.17
translational mode, T(F2g).
The average W–O distance is fairly constant for all seven
In the Raman spectrum of Ba2MgWO6 (see Fig. 4), the
compounds, as would be expected, with Sr2CdWO6 once again peaks at 126, 441, and 812 cm−1 are assigned to T(F2g), ν5(F2g),
showing up as somewhat of an outlier. The M–O–W bond and ν1(A1g) modes, respectively. The ν2 asymmetric stretching
angles, which are linear in the cubic perovskite structure, mode is too weak to be seen, but is calculated to occur at
become increasingly bent as the tolerance factor decreases and 540–550 cm−1 in normal coordinate calculations using a Urey-
the octahedral tilting becomes more pronounced. The fact that Bradley force field. Its intensity is likewise calculated to be
the Ca–O2–W bond in Ba2CaWO6 is nearly linear indicates approximately 8% of the ν1(A1g) mode. As we will see a very
that this compound is on the verge of a phase transition to the weak ν2 mode is not unusual for these ordered double perov-
ˉ
undistorted Fm3m structure.
skites. These values and assignments are in good agreement
with those reported by Liegeois-Duyckaerts and Tarte.23
When lowering the symmetry to I4/m, as is the case for
Raman spectra of Ba2MWO6 (M = Ca, Mg) double perovskites
Group theory analysis for a double perovskite with the aristotype Ba2CaWO6, additional Raman bands are allowed. The irreduci-
ˉ
cubic Fm3m structure shows that there are four Raman active ble representation, considering only Raman active vibrations,
bands expected, Γ = ν1(A1g) + ν2(Eg) + ν5(F2g) + T(F2g), where ν1, ν2, for a double perovskite with I4/m symmetry is Γ = ν1(Ag) + ν2(Ag
and ν5 are the internal vibration modes of an octahedron and T + Bg) + ν5(Bg + Eg) + T(Bg + Eg) + L(Ag + Eg), which corresponds
is a lattice mode. The ν1 mode is the symmetric oxygen stretch to nine Raman active modes. However, as shown in Fig. 4, only
vibration of the octahedra, during which all cations are at rest three bands are visible with the lowest energy band falling at
and the oxygen atoms are moving along the M–O–W axis.23 It the extreme low energy range that can be accessed with our
appears as a strong, relatively broad peak in the region of spectrometer. There are various reasons that could be respon-
750–850 cm−1 23,24
.
Just as there is an oxygen symmetric stretch, sible for the absence of extra bands predicted by group theory
ˉ
there is also an oxygen asymmetric stretching vibration, labelled on lowering the symmetry from Fm3m to I4/m: (1) bands may
as the ν2 mode. Again, during a ν2 vibration, all cations are at be so weak that they are not detected above the background,
rest while the oxygen atoms vibrate along the M–O–W axes.23 (2) bands may overlap to such an extent that we are not able to
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the degree of distortion from the cubic structure is quite small
in Ba2CaWO6, (see the bond angles and distances in Table 3).
The libration modes L and the additional T mode are either
too weak to see or fall outside of the spectral range of our
spectrometer. Liegeois-Duyckaerts and Tarte observed very
similar bands (838, 413, 105 cm−1) and from the presence of
just three Raman bands concluded that Ba2CaWO6 was
cubic.23 However, as discussed above careful diffraction
studies later showed that the true symmetry was tetragonal
I4/m.15,17 So in this case it appears that Raman spectroscopy is
no more sensitive, perhaps less so, than X-ray powder diffrac-
tion for detecting the subtle lowering in symmetry.
Raman spectra of monoclinic A2MWO6 double perovskites
The remaining five compounds have additional octahedral
tilting distortions (tilt system a−a−b+) that lower the symmetry
to the monoclinic space group P21/n. Considering only Raman
active modes, the irreducible representation for a P21/n perovs-
kite can be written as Γ = ν1(Ag + Bg) + ν2(2Ag + 2Bg) + ν5(3Ag +
3Bg) + T(3Ag + 3Bg) + L(3Ag + 3Bg). There are now a total of 24
bands predicted to be present in the Raman spectrum, however,
in the five compounds studied here only seven to thirteen
bands are experimentally observed (see Table 4). In these struc-
tures there are two A2MWO6 formula units per unit cell, and
this leads to the presence of Ag and Bg components for all of the
modes. It would not be unexpected if the Ag and Bg components
of the internal modes fell at a very similar frequencies, in which
case polarized Raman spectra of single crystals may be needed
to resolve them. If that is the case spectra collected on polycrys-
talline samples, as is the case here, should exhibit a single band
for the symmetric stretch ν1, a doublet for the asymmetric
stretch ν2, and a triplet for the bending mode ν5.
Fig. 4 Raman spectra of Ba2MgWO6 and Ba2CaWO6. The peaks marked
with an asterisk are due to the scheelite phase BaWO4.
resolve the splitting of the bands, or (3) new bands may fall at
energies lower than 100 cm−1
.
The bands appearing at approximately 834, 410, and
103 cm−1 can be assigned to ν1, ν5, and T modes respectively
for Ba2CaWO6, although there is some uncertainty in the fre-
quency of the band seen at 103 cm−1 because it falls at the
very edge of the accessible range of our spectrometer. As was
the case for Ba2MgWO6 the asymmetric stretch, ν2, is too weak
to be observed. Furthermore, the predicted splitting of the ν5
mode is too small to be resolved. This is presumably because
The Raman spectra of the monoclinic double perovskites
are shown in Fig. 5. An intense oxygen symmetric stretch
band, ν1, is seen in each spectrum at values ranging from
811 to 855 cm−1. Unlike Ba2CaWO6 and Ba2MgWO6, the
oxygen asymmetric stretching mode, ν2, can be seen in these
compounds, but it is so weak that it’s not possible to detect
splitting of this band without polarized Raman data. The peak
Table 4 Raman shifts (in cm−1) for the observed modes in the tungsten double perovskites with P21/n symmetry
Assignment
Sr2ZnWO6
Sr2CdWO6
Sr2CaWO6
Ca2MgWO6
Ca2CaWO6
T
T
T
T
T
T
L
L
137
152
170
—
—
—
—
—
—
—
129
151
172
190
—
—
246
—
—
390
411
440
465
554
824
110
126
134
150
173
195
—
149
165
176
192
212
—
249
304
330
406
424
472
—
132
144
193
207
218
—
247
256
301
—
416
453
465
594
811
—
—
—
L
ν5 or L
ν5 or L
ν5
395
415
441
465
583
818
922
—
436
445
573
855
921
ν5
ν2
584
836
908, 331
ν1
AWO4
921, 800, 371, 336
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assign as a libration mode L. Curiously this peak is too weak
to be observed in Sr2CaWO6. Additionally most of the com-
pounds have weak peaks between 390 and 420 cm−1 that
cannot be unambiguously assigned as being either an external
libration mode or an internal bending mode.
The translation lattice modes are expected at the lowest fre-
quencies. In a perovskite with P21/n symmetry, six translation
lattice modes are predicted, via a triplet splitting of the Ag and
Bg modes. Where the libration modes end and the translation
modes begin is not completely clear. Polarized Raman and
infrared spectra are needed to accurately differentiate libration
and translation lattice modes. In a study of A2CoM′O6 (A = Sr,
Ca; M′ = W, Te) Ayala et al. assigned the libration lattice modes
to frequencies in the range 190–310 cm−1, and translation
lattice modes to frequencies less than 190 cm−1 for P21/n
double perovskites,24 but as discussed below there is some evi-
dence that the translation lattice modes may extend as high as
220 cm−1 in these compounds.
Lentz previously reported the Raman spectra for Sr2ZnWO6
(t = 0.976), which showed weak bands at 78, 105, and 116 cm−1
,
the first of these is outside of the range of our spectrometer,
while the latter two are not observed in this study. Lentz also
observed modes at 140 and 153 cm−1, corresponding to the
translational lattice modes that are observed here.23 There is a
broad tailing that occurs on the high frequency side of the
doublet, centered approximately at 170 cm−1 and it is possible
that this broad feature may correspond to a third translational
mode. Looking back at Table 3, the Zn–O–W angles range from
164° to 168°, which are the least bent of all the P21/n perovskites
considered here. It could be argued that the relatively small
Fig. 5 Raman spectra of five tungsten-based perovskites with space
group P21/n. The peaks marked with an asterisk are due to the scheelite
secondary phase, either SrWO4 or CaWO4.
at approximately 918 cm−1 in the Sr2CdWO6 spectrum is magnitude of octahedral tilting leads to less splitting of the
assigned to SrWO4. Not only is this where the strongest band translational modes in this compound than the other P21/n per-
in the Raman spectrum of SrWO4 is observed (see ESI†), the ovskites. The close proximity to the P21/n→I4/m phase transition
presence of a peak from the secondary scheelite phase is not at 343 K (see Table 1) may also play a role in making the split-
unexpected given the presence of SrWO4 in the XRD pattern of ting of the translational modes too subtle to resolve.
Sr2CdWO6. Very weak AWO4 scheelite peaks can also be seen
in the spectra of several other compounds.
Sr2CdWO6 (t = 0.930) shows a definitive triplet splitting
with peaks at 129, 151, 172 cm−1, and a fourth very weak peak
The internal oxygen bending motion, ν5 that falls between at 190 cm−1. The lower tolerance factor leads to more distorted
400–500 cm−1 is the second strongest set of peaks in the Cd–O–W bonds, with angles that range from 152° to 159°.
spectra. If the Ag and Bg components cannot be resolved then Sr2CaWO6, which has the same A-site cation and a similar tol-
the ν5 mode is expected to split into a triplet. As shown in erance factor (t = 0.916), has four translational modes that fall
Fig. 5, the ν5 mode is clearly split into a doublet in Sr2ZnWO6 at nearly the same wavenumbers, as well as additional weak
and Ca2CaWO6. The splitting is more difficult to resolve in the peaks at 110 and 134 cm−1. These values are in good agree-
other three compounds. Why the splitting should be seen ment with those reported by Gateshki and Igartua.27
most easily in the compounds that have the largest and smal-
lest tolerance factors of the group, respectively, is not clear.
Coming to Ca2MgWO6 the tolerance factor lies in the same
range (t = 0.926) but the A-site cation is now Ca2+ instead of
Proceeding to lower wavenumbers, the libration lattice Sr2+. Since the translational modes involve motions of the A-
modes are the next peaks expected to appear. In a perovskite site cation the lighter mass of the Ca2+ ion (40.1 vs. 87.6 amu)
with P21/n symmetry, six libration lattice modes are predicted, should result in a shift of these modes to higher frequencies.
three Ag and three Bg modes. Sr2ZnWO6 does not appear to Based on that expectation five peaks between 149 and
have any librational modes that are strong enough to be seen 212 cm−1 are tentatively assigned as translational modes. If
above the background. Lentz reported peaks in this area of the this assignment is correct the modes shift to higher frequen-
spectrum in his study of Sr2ZnWO6, but they were extremely cies by 20 to 40 cm−1 when Sr2+ is replaced by Ca2+.
weak, thus explaining the absence of visible libration modes
Finally, Ca2CaWO6, which has the smallest tolerance factor
in our spectra.26 Sr2CdWO6, Ca2MgWO6 and Ca2CaWO6 all (t = 0.867) and more highly bent M–O–W bonds (141° to 147°),
have a peak of moderate intensity near 250 cm−1 that we also appears to have five translational modes that fall in a
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similar region of the spectrum, but the increased distortion of
the structure leads to clear differences in the intensities and
frequencies of these modes with respect to Ca2MgWO6.
Preliminary results obtained from force constant calcu-
lations show that considerable coupling occurs between the
lower-lying wavenumber bands of these solids. Unfortunately
because they are both weak and numerous unambiguous
assignments cannot be made without the availability of single
crystal Raman and infrared data.
Table 5 Tolerance factor, symmetric stretching frequency, and bond
valence sums for Ba2MWO6 double perovskites
Bond valence sums
Tolerance
factor
ν1
Compound
(cm−1
)
Ba
M2+
W
O
Ba2NiWO6
Ba2MgWO6
Ba2ZnWO6
Ba2MnWO6
Ba2CaWO6
1.048
1.038
1.035
1.014
0.972
816
812
822
810
834
2.58
2.49
2.45
2.27
1.87
1.81
1.88
1.87
2.11
2.57
5.70
5.87
5.88
5.90
6.02
2.11
2.12
2.11
2.09
2.06
compounds included in Fig. 6. Only in Ba2CaWO6 (t = 0.972)
does the bond valence sum of tungsten exceed its ideal value
of 6, and the Ca2+ ion is also overbonded in this compound.
Despite the tetragonal symmetry the bonds are still quite close
to linear in this compound (see Table 3). Given the fact that
both the M–O and W–O bonds are effectively compressed from
their ideal values, it should not come as a surprise that the
position of the symmetric stretch is 12–22 cm−1 higher than it
is in the other Ba2MWO6 compositions.
Discussion
The frequency of the symmetric stretch, ν1, is plotted as a
function of tolerance factor in Fig. 6 for the seven com-
pounds studied here, as well as an additional seven A2MWO6
double perovskites—Ba2NiWO6,23 Ba2ZnWO6 Ba2MnWO6,28
23
Sr2MgWO6,29 Sr2CoWO6,24 Sr2MnWO6,28 and Ca2CoWO6.24 The
tolerance factors and frequencies of the ν1 and ν5 bands for
these additional compounds are given in the ESI (Table S2†).
The frequency of the ν1 mode does not appear to be very sensi-
tive to the identity of the A cation, nor to the mass of the M
cation, as expected for an internal mode of the octahedron
that does not involve motion of the cations. However, it does
show a dependence on the tolerance factor.
Once octahedral tilting has set in a further decrease in the
tolerance factor leads to a decrease in the energy of the ν1 sym-
metric stretching mode. This trend can also be rationalized by
taking into account how the structure changes as the tolerance
factor continues to decrease. Because the W–O bonds are
easily the strongest bonds in these compounds the internal ν1
mode can be thought of as a vibration of the [WO6]6− octa-
hedra. When the W–O–M bonds are linear an expansion in the
W–O bond leads to an equivalent compression of the M–O
bonds, and vice versa. However, as the tolerance factor
decreases the M–O–W bonds become increasingly bent. Once
the W–O–M bonds are bent an expansion of the bonds in each
[WO6]6− octahedron does not lead to a pure compression of
the M–O bonds, but rather a mixture of compression and
bending. As a general rule bending modes are lower energy
than stretching modes, hence there is less resistance to changes
in the W–O bond lengths when the M–O–W bonds are bent.
Plotting the frequencies of the ν5 bending mode tells a
different story, as shown in Fig. 7. The frequencies for double
perovskites with A = Sr cluster into a narrow range of values
that fall between 439–450 cm−1. The frequency of the bending
mode shifts to higher values when A = Ca, and lower values
when A = Ba. The relative order ν5(A = Ba) < ν5(A = Sr) < ν5(A =
Ca) mirrors the relative masses of the three A-site cations, and
is a clear sign that a motion of the A-site cation must also be
involved in the oxygen bending mode. Returning to the group
theory discussed earlier we see that this coupling of internal
and external modes is allowed because the oxygen bending
mode and the A-site cation translation mode have one or more
common irreducible representations for all three space group
symmetries. Thus it is not completely accurate to describe this
mode as a pure internal vibration of the octahedron.
The cubic double perovskites with tolerance factors larger
than one have relatively low frequency symmetric stretches
(810–822 cm−1). Once the tolerance factor drops below one
and octahedral tilting distortions set in, the frequency of the
ν1 mode spikes. This result can be understood in the following
manner. In those A2MWO6 double perovskites where the toler-
ance factor is larger than one, the octahedra are stretched by
the oversized A-site cation. This effect weakens the M–O and/
or the W–O bonds, thereby lowering the energy of the oxygen
ion vibration along the M–O–W axis.
To support this hypothesis consider Table 5, which con-
tains the bond valence sums for each of the five Ba2MWO6
The frequency of the ν5 mode for the Ba-containing double
perovskites shows some dependence on tolerance factor. Once
again the bond valence sums shown in Table 5 are illustrative.
Because the oxygen bending mode leads to changes in the A–O
Fig. 6 Frequencies of the oxygen symmetric stretch ν1 as a function of
tolerance factor for A2MWO6 double perovskites.
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Dalton Transactions
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ˉ
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Acknowledgements
Financial support from the National Science Foundation
(Award number DMR-0907356) is acknowledged.
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Dalton Trans.
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