Vibrational analysis of the two non-equivalent, tetrahedral tungstate (WO4) units in Ce2(WO4)3 and La2(WO4)3

Article abstract of DOI:10.1016/s1386-1425(98)00036-5

The infrared and Raman spectra of Ce₂(WO₄)₃ and La₂(WO₄)₃, which are complicated by the superposition of bands from two non-equivalent WO₄ units, have been successfully assigned above 300 cm^-1 according to T_d point group symmetry. Individual assignment of the two types of tungstate units, W^IO₄ (C₂ site symmetry) and W^IIO₄ (C₁ site symmetry), relies on comparison with the spectra of tetrahedral reference tungstates of Na₂WO₄, CaWO₄, and MgWO₄, and on the differences between W^IO₄ and W^IIO₄ known from the crystal structure. Normal coordinate analysis indicates that the force constants for W^IO₄ and W^IIO₄ roughly correlate with the amount of deviation from ideal T_d point symmetry, W^IO₄ being similar to CaWO₄ (both mildly distorted tetrahedrons), while W^IIO₄ is closer to MgWO₄ (both highly distorted tetrahedrons). Non-ideality is also indicated by the calculated potential energy distribution (PED), which shows a substantial degree of vibrational interaction between bonds - especially in the less symmetric W^IIO₄ unit. Frequency differences between IR and Raman bands that originate from the same T_d point group modes are attributed mainly to factor group splitting (i.e. Raman active gerade and IR active ungerade factor group modes). However, the LO-TO polarization mixing and surface modes that generate the observed vibrational frequencies in powders may also contribute to these frequency differences, since the magnitude of these effects may not be the same in Raman as in IR. Finally, it is likely that other rare earth tungstates of stoichiometry Ln₂(WO₄)₃, where Ln = La ～ Dy, have similar vibrational spectra due to their similar structures.

Full text of DOI:10.1016/s1386-1425(98)00036-5

Spectrochimica Acta Part A 54 (1998) 1355–1368
Vibrational analysis of the two non-equivalent, tetrahedral
tungstate (WO4) units in Ce2(WO4)3 and La2(WO4)3
Loyd J. Burcham, Israel E. Wachs *
Department of Chemical Engineering and Zettlemoyer Center for Surface Studies, Lehigh Uni6ersity, Bethlehem, PA 18015, USA
Received 17 September 1997; received in revised form 31 January 1998; accepted 31 January 1998
Abstract
The infrared and Raman spectra of Ce2(WO4)3 and La2(WO4)3, which are complicated by the superposition of
bands from two non-equivalent WO4 units, have been successfully assigned above 300 cm−1 according to Td point
group symmetry. Individual assignment of the two types of tungstate units, WIO4 (C2 site symmetry) and WIIO4 (C1
site symmetry), relies on comparison with the spectra of tetrahedral reference tungstates of Na2WO4, CaWO4, and
MgWO4, and on the differences between WIO4 and WIIO4 known from the crystal structure. Normal coordinate
analysis indicates that the force constants for WIO4 and WIIO4 roughly correlate with the amount of deviation from
ideal Td point symmetry, WIO4 being similar to CaWO4 (both mildly distorted tetrahedrons), while WIIO4 is closer
to MgWO4 (both highly distorted tetrahedrons). Non-ideality is also indicated by the calculated potential energy
distribution (PED), which shows a substantial degree of vibrational interaction between bonds—especially in the less
symmetric WIIO4 unit. Frequency differences between IR and Raman bands that originate from the same Td point
group modes are attributed mainly to factor group splitting (i.e. Raman active gerade and IR active ungerade factor
group modes). However, the LO-TO polarization mixing and surface modes that generate the observed vibrational
frequencies in powders may also contribute to these frequency differences, since the magnitude of these effects may
not be the same in Raman as in IR. Finally, it is likely that other rare earth tungstates of stoichiometry Ln2(WO4)3,
where Ln=LaꢀDy, have similar vibrational spectra due to their similar structures. © 1998 Elsevier Science B.V. All
rights reserved.
Keywords: Infrared spectra; Raman spectra; Rare earth tungstates
1. Introduction
parison with the Raman bands measured in CeO2/
WO3/Al2O3 and La2O3/WO3/Al2O3 catalysts. An
extensive literature search revealed numerous vi-
brational studies on alkali rare earth tungstates
[2–5], rare earth ordered perovskites [6–8], rare
earth polytungstic acids [9,10], and rare earth
halotungstates [11,12]. A few vibrational studies
on pure rare earth tungstates were also found,
During recent catalytic studies [1], it became
necessary to determine the infrared and Raman
spectra of Ce2(WO4)3 and La2(WO4)3 for com-
* Corresponding author. Tel.: +1 610 7583600; fax: +1
610 7586555.
1386-1425/98/$19.00 © 1998 Elsevier Science B.V. All rights reserved.
PII S1386-1425(98)00036-5

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L. J. Burcham, I. E. Wachs / Spectrochimica Acta Part A 54 (1998) 1355–1368
including the measurement of the near-IR fluores-
cence spectra in La2(WO4)3 [13], determination of
periodic trends in the stretching modes of lan-
thanide tungstates [14], and the analysis of vibra-
tional spectra in h-Th(WO4)2 [15] and in Ln2WO6
(Ln=Sm, and rare earth-like Y and Bi) [16].
These studies, most of which concern tetrahedral
WO4 units [2–5,11,13–15], showed that the inter-
nal covalent vibrational modes in these WO4 units
can be successfully assigned based on tetrahedral,
Td, point group symmetry. However, very little
vibrational information is available for the tetra-
hedrally coordinated Ce2(WO4)3 and La2(WO4)3.
The objectives of this study, therefore, are firstly
to report the vibrational spectra of these
tungstates, and secondly to assign the internal
covalent vibrational modes according to Td point
group symmetry.
tungstate units meaningless. However, compari-
son of the IR and Raman spectra of Ce2(WO4)3
and La2(WO4)3 with the tetrahedral reference
tungstates of Na2WO4, CaWO4, and MgWO4, as
well as with the previously cited tetrahedral rare
earth tungstates [2–5,11,13–15], suggests that an
approximation of Td point group symmetry is not
only appropriate, but also desirable because of the
physical meaning which can be given to the inter-
nal Td vibrations observed in the spectra. There-
fore, the internal modes have been assigned by
assuming tetrahedral, Td, point group symmetry
as an approximation of the actual, non-ideal sym-
metry of the WO4 units.
2. Theoretical
Previous structural studies of Ce2(WO4)3 and
La2(WO4)3 indicate that they are isomorphous
with Eu2(WO4)3 [17–23], for which the scheelite-
like crystal structure was determined by Temple-
ton and Zalkin [24]. This crystal structure
determination showed that Eu2(WO4)3 has C26h
space group symmetry with four formula units per
crystallographic unit cell. Additionally, tungsten
resides on two different types of sites in which
each W atom is surrounded by four oxygen
atoms. One WO4 unit, WIO4, is close to being a
geometrically regular tetrahedron, with two bond
The representation for tetrahedral symmetry
is[25]:
GTd=A1(w1)+E(w2)+F2(w3)+F2(w4), in
which all four vibrational modes are Raman ac-
tive, but only the F2(w3, w4) modes are IR active.
The A1(w1) vibration is the symmetric stretch of
the WO4 unit, the F2(w3) vibrations are the anti-
symmetric stretches, and the E(w2) and F2(w4) vi-
brations are bending modes. Since the site and
factor groups of Ce2(WO4)3 and La2(WO4)3 are of
lower symmetry than Td, and the tetrahedral
point groups themselves are non-ideal, the dou-
bly-degenerate E(w2) and triply-degenerate
F2(w3, w4) vibrations split into non-degenerate
bands. For normal coordinate calculations the
arithmetic average of these non-degenerate bands
must be used, although in the past some investiga-
tors have used the theoretically less desirable in-
tensity-weighted average [26].
˚
˚
lengths of 1.70 A and two of 1.78 A (averaging
II
˚
1.74 A). The other unit, W O4, is a much more
distorted tetrahedron with two bond lengths of
˚
˚
˚
1.81 A, one of 1.72 A, and one of 1.77 A (averag-
˚
ing 1.78 A).
The assumption of tetrahedral, Td, point group
symmetry in the forthcoming internal mode anal-
ysis of the WO4 units in Ce2(WO4)3 and
La2(WO4)3 requires some justification. In their
description of the isomorphous Eu(WO4)3 struc-
ture, Templeton and Zalkin [24] consider the two
tungstate units (of C2 and C1 site symmetries,
respectively, for WIO4 and WIIO4) to be bridged
as an irregular trigonal bipyramid with roughly
D3h point group symmetry. However, the Bravais
cell does not contain an integer number of these
D3h point groups, making assignments based on
the internal modes of these bipyramidal molecular
Normal coordinate calculations were performed
to refine the assignments and to estimate force
constants (given in mdyn A−1). An algorithm was
˚
written in MATLAB© to allow calculations ac-
cording to the GF matrix method. The principle
of this method may be found in Nakamoto [25]
and elsewhere, and the technique requires finding
the solutions of the secular equation, ꢀGF−I¥ꢀ=
0, where u=4y2c2w2. The method of solution
follows that of [27,28], involving a least-squares
minimization of an eigenvalue-based variance.
Force fields used in the calculations include the

L. J. Burcham, I. E. Wachs / Spectrochimica Acta Part A 54 (1998) 1355–1368
1357
Table 1
three-constant
Urey–Bradley
Force
Field
Correlation table for WIO4 in Ce2(WO4)3 and La2(WO4)3
(UBFF), the three-constant Orbital Valence Force
Field (OVFF), and an approximated four-con-
stant Generalized Valence Force Field (GVFF).
For tetrahedral point group symmetry, the G and
F matrix elements corresponding to these force
fields, as well as a discussion of the physical
meaning of the force constants, can be found in
the excellent paper by Basile et al. [29]. In their
study, Basile et al. found that the UBFF was
generally superior for transition metal oxoanions
like (WO4)2−, but that in some cases the OVFF
was better (the GVFF has no degree of freedom
and always fits the four observed frequencies ex-
actly). Finally, in order to estimate the relative
contribution of the force constants to the various
normal modes, the potential energy distributions
(PED’s) were calculated as in [28], using the rela-
tionship PED=L−1(JZ)F, where L and F are
the diagonal matrices of eigenvalues and force
constants, respectively, and (JZ) is the Jacobian
matrix relating them.
Not surprisingly, the WO4 internal Td modes
are also significantly influenced by the site and
factor group symmetries of the cystal, so factor
group analysis must be incorporated into the as-
signment process, as well. The previously cited
crystal structure of Eu2(WO4)3, which is iso-
morphous with Ce2(WO4)3 and La2(WO4)3, was
used to perform the factor group analysis using
the correlation method described by Fateley et al.
for the Bravais cell [30]. For the C62h space group
with four formula units per crystallographic unit
cell there are only two formula units per Bravais
cell, and the factor group is C2h. The site sym-
metries of the atoms in the Bravais cell are as
follows: 2 WI (C2), 4 WII (C1), 4 Ce (C1), and
24 O (C1). The WO4 units were assumed to be
centered on tungsten sites, and there are two
WIO4 units and four WIIO4 units in the Bravais
cell. With this information the point group was
correlated to the site and factor groups, and the
results are summarized in Tables 1 and 2. After
subtraction of the acoustic modes, which are inac-
tive and have zero frequency (at wavevector k=
0) in the Raman and IR spectra, the total
representation for all vibrations, rotations, and
translations in the crystal becomes: Gtotal=25
Ag+24 Au+26 Bg+24 Bu. The 51 gerade modes
are Raman active in the factor group, while the 48
ungerade modes are IR active. However, by con-
sidering only the nine (3n-6) internal vibrations in
each type of WO4 unit, there are a maximum of
18 Raman and 18 IR internal bands to be as-
signed in the spectra of Ce2(WO4)3 and
La2(WO4)3—half originating from WIO4 and half
from WIIO4.
Table 2
Correlation table for WIIO4 in Ce2(WO4)3 and La2(WO4)3

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L. J. Burcham, I. E. Wachs / Spectrochimica Acta Part A 54 (1998) 1355–1368
3. Experimental
Raman spectra were recorded with a Triple-
mate spectrometer (Spex, Model 1877) coupled to
an optical multichannel analyzer (Princeton Ap-
plied Research, Model 1463) equipped with an
intensified photodiode array detector (cooled to
−35°C). Samples were physically mixed with KBr
and pressed into self-supporting wafers of ꢀ150
mg. The sample wafers were then mounted on a
sample rotator (Spex, Model 1445A), and the
514.5 nm line of an argon ion laser (Spectra
Physics) was focused onto the spinning sample.
Rotation of the sample reduces thermal broaden-
ing of the spectra from localized heating by the
laser exitation source (15–40 mW at the sample).
The ambient spectra were recorded as 25 signal
averaged scans of 30 s each, with a resolution of
The samples of Ce2(WO4)3 and La2(WO4)3 were
prepared by first mixing stoichiometric amounts
of ammonium metatungstate ((NH4)6H2W12O40;
Pfaltz and Bauer) with cerium(III) nitrate
(Ce(NO3)3 · 6H2O; Johnson Matthey) and lan-
thanum nitrate (La(NO3)3 · 6H2O; Aldrich), re-
spectively. The water soluble salt mixtures were
then dissolved with distilled water in a crucible,
and heated to a slow boil over a hotplate. The
solutions were stirred continuously with a glass
rod while the water was slowly evaporated. The
crucibles and paste-like residues were then placed
in a muffle furnace and heated to 900°C for 12 h.
This temperature ensures complete reaction of the
precursors to a single, homogeneous tungstate
phase (Nassau et al. [17] has reported that these
two tungstates form only a single, homogenous
phase below 970°C). Finally, the crucibles were
cooled to room temperature so that the samples
could be ground (in the crucibles) with an agate
pestle, followed by another 12 h of calcination at
900°C. The dissolution of the soluble precursors
in water and the subsequent evaporation of the
water are essential for producing a homogenous
final compound. Attempts at a solid state reaction
of well-mixed precursors in the solid phase re-
sulted in WO3 impurities in the final compounds,
as measured by Raman spectroscopy.
In addition, Na2WO4, CaWO4, and MgWO4
were also prepared as reference compounds using
ammonium metatungstate with stoichiometric
amounts of 50% w/w NaOH solution (Fisher),
calcium nitrate (Aldrich), and magnesium acetate
(Johnson Matthey), respectively. The identities of
the reference tungstates were confirmed by com-
parison of their measured Raman spectra with
spectra reported in the literature [26;31–35]. X-
ray diffraction was used to confirm the identities
of the Ce2(WO4)3 and La2(WO4)3 samples. For
the XRD experiments, a Philips APD 1700 Auto-
mated Powder Diffractometer was used with
CuꢀKh radiation of 45 kV and 30 mA. The
powdered samples were scanned over 2u from 10°
to 70° at a rate of 3° min−1. The resulting pat-
terns matched those reported in the literature for
both Ce2(WO4)3 [21] and La2(WO4)3 [17].
approximately 2 cm−1
.
Infrared spectra were recorded on a BioRad
FTS-40A FTIR spectrometer by averaging 250
scans with a resolution of 2 cm−1. All spectra
presented in the figures were taken in diffuse
reflectance mode (DRIFTS), although some trans-
mission spectra were also taken with samples
mixed in KBr wafers. The optics used for the
DRIFTS spectra were of the ‘Praying Mantis’
design (manf. by Graseby-Specac). Mid-IR spec-
tra (4000–400 cm−1; KBr beamsplitter) were ob-
tained by diluting the samples in FTIR grade KBr
powder (Alfa Aesar), while high density
polyethylene powder (Polysciences, 20 mm parti-
cles) was used as the scattering diluent for collec-
tion of far-IR spectra (500–100 cm−1; Mylar
beamsplitter). The spectra were combined in the
figures by scaling the data such that bands in the
overlapping region (500–400 cm−1) have the
same intensity in both the mid- and far-IR. Also,
some smoothing of the DRIFTS spectra was per-
formed in order to enhance the signal to noise
ratio.
4. Results
The Raman and IR spectra of Ce2(WO4)3 and
La2(WO4)3 are given in Figs. 1 and 2, respectively.
The Raman and IR spectra of reference
tungstates Na2WO4, CaWO4, and MgWO4 are
given in Figs. 3 and 4, respectively. The observed

L. J. Burcham, I. E. Wachs / Spectrochimica Acta Part A 54 (1998) 1355–1368
1359
pounds, although some important new bands
were also observed in addition to the bands at-
tributed to Ce2(WO4)3 and La2(WO4)3.
When Ce2(WO4)3 was prepared in excess cerium
precursor (2Ce2O3 · WO3) instead of the stoichio-
metric Ce2O3 · 3WO3, a new Raman band due to
CeO2 appeared at 467 cm−1 [36], new IR bands
appeared at 856 and 694 cm−1, and a slight
increase was observed in the IR band at 936
cm−1. The presence of CeO2 suggests that all of
the tungsten has been reacted. However, the ap-
pearance of new IR bands in conjunction with a
relative increase in the 936 cm−1 IR band sug-
gests that the new bands are due to a small
amount of a different tungstate phase (probably
2Ce2O3 · 9WO3 according to [21]). These same
new bands appeared in samples formed in excess
lanthanum (2La2O3 · WO3) and are also likely to
Fig. 1. Raman spectra of Ce2(WO4)3 and La2(WO4)3.
frequencies are also summarized in Tables 3 and
4. Note that there are bands in Ce2(WO4)3,
La2(WO4)3, and MgWO4 which are close to those
measured for WO3 (Alfa Aesar; Raman bands at
808, 714, 605, and 276 cm−1, IR bands at 1057,
899, 876, 800, 620, 383, 337, 290, and 218 cm−1
;
see also Ref. [36]). However, the presence of WO3
impurity can be ruled out in all of these samples
based on some additional information. Firstly, in
WO3 the Raman band at 605 cm−1 and the IR
bands at 1057 and 218 cm−1, while rather weak,
may be used as a fingerprint for the pure oxide
because they do not overlap with any of the
observed tungstate bands. These fingerprint bands
do not appear in any of the tungstate spectra.
Secondly, samples prepared with excess cerium
and lanthanum precursors, which should react
with all of the tungsten precursor, produced the
same tungstate bands in the same relative intensi-
ties as those observed in the stoichiometric com-
Fig. 2. Infrared spectra of Ce2(WO4)3 and La2(WO4)3. As is
typical for the DRIFTS technique, intensities are expressed in
Kubelka–Munk units to correct for diffuse reflectance distor-
tions that would otherwise appear in the absorption spectra
[37].

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L. J. Burcham, I. E. Wachs / Spectrochimica Acta Part A 54 (1998) 1355–1368
medium like KBr or polyethylene, the DRIFTS
spectra produced much sharper bands than the
spectra obtained in transmission mode. This is
most probably because scattering of the incident
radiation by the transmission wafer interferes with
the absorption signal in transmission mode, while
in DRIFTS mode the measured changes in scat-
tered radiation arise almost totally from sample
absorption—suffering very little broadening from
secondary effects. However, at high sample to
diluent ratios the diffuse reflectance technique
does suffer from the secondary effect of specular
reflection. In practice, this means that the sample
must be diluted and well-mixed in a scattering
medium [37]. The degree of dilution is somewhat
arbitrary, the requirement being that enough sam-
ple is present to generate a diffuse reflection spec-
trum but not so much as to cause specular
Fig. 3. Raman spectra of Na2WO4, CaWO4, and MgWO4.
be due to a new 2La2O3 · 9WO3 phase [22]. How-
ever, in addition to these new bands and bands
from the stoichiometric La2(WO4)3 phase, the ex-
cess lanthanum samples also exhibited very strong
bands (Raman bands at 878, 793, 759, 729, and
414 cm−1; IR bands at 907, 849, 797, 751, 686,
610, 588, and 494 cm−1) from a third phase that
is probably either La6WO12 or La6W2O15 accord-
ing to published phase diagrams [22,23]. Never-
theless, the only traces of these different tungstate
phases in the spectra of otherwise stoichiometric
samples of Ce2(WO4)3 and La2(WO4)3 are the
weak bands at 897 and 878 cm−1 in the Raman
spectra (Fig. 1), and the band at 936 cm−1 in the
IR spectra (Fig. 2). Thus, the spectra presented in
Figs. 1 and 2 are essentially due to pure
Ce2(WO4)3 and La2(WO4)3—in agreement with
the XRD data.
Fig. 4. Infrared spectra of Na2WO4, CaWO4, and MgWO4. As
is typical for the DRIFTS technique, intensities are expressed
in Kubelka–Munk units to correct for diffuse reflectance
distortions that would otherwise appear in the absorption
spectra [37].
Regarding the infrared results, it was observed
that when the sample was diluted in a scattering

L. J. Burcham, I. E. Wachs / Spectrochimica Acta Part A 54 (1998) 1355–1368
1361
Table 3
Band frequencies (cm−1) and assignments of reference tungstates
Td pt. grp. assignments
Na2WO4
R
CaWO4
R
MgWO4
R
IR
IR
—
IR
A1(w1)
923 (s)
919 (w)
908 (s)
914 (s)
899 (m)
F2(w3)
F2(w3)
F2(w3)
860 (s)
821 (s)
790 (m)
836 (w)
793 (m)
847 (s)
780 (m)
682 (w)
810 (m)
708 (m)
657 (s)
845 (s)
715 (s)
809 (m)
304 (m)
E(w2)
E(w2)
—
330 (m)
398 (w)
442 (m)
416 (m)
349 (m)
534 (m)
483 (m)
F2(w4)
F2(w4)
F2(w4)
334 (s)
296 (sh)
549 (m)
515 (w)
408 (sh)
382 (s)
338 (s)
370 (w)
311 (s)
External modes
232 (s)
170 (s)
273 (w)
210 (w)
116 (w)
233 (s)
148 (w)
313 (w)
293 (m)
277 (m)
268 (sh)
212 (w)
187 (w)
155 (w)
291 (m)
268 (s)
194 (m)
(see [33] for a review of the controversy), the
detailed study by Weinstock et al. [38] on this
issue demonstrated that E(w2) should always have
a greater relative Raman intensity than F2(w4).
Modeling of the tungstate units in MgWO4 with
roughly Td point group symmetry may seem
questionable since Keeling [39] found the tung-
sten to be formally octahedrally coordinated
based on the crystal structure. However, Blasse
[34] has shown that MgWO4 and other wol-
framite structures are better modeled as distorted
tungstate tetrahedrons for the purposes of inter-
nal (covalent) band assignments, since two of the
six WꢀO bonds are quite long and not likely to
be very covalent in nature. The reference
tungstates have been chosen so that splitting pat-
terns in the idealized, degenerate Td bands can be
monitored as the actual point and site sym-
metries become less tetrahedral—i.e. from
Na2WO4 (spinel with Td point and site symmetry
[26,31]) to CaWO4 (scheelite with D2d point and
S4 site symmetry [40]) to MgWO4 (wolframite
with less than D2d point symmetry and C2 site
symmetry [39]) in order to compare a wide range
of symmetries.
reflection. For all compounds studied in this in-
vestigation, mid- and far-IR DRIFTS spectra
were taken over a range of dilution levels. Specu-
lar reflection peaks were identified as those which
decreased relative to the other vibrational bands
as the dilution was increased. The spectra taken
for analysis were recorded at dilution levels in
which the identified specular reflection bands
were eliminated. Also, in the mid-IR it was possi-
ble to identify specular reflection bands by com-
paring the DRIFTS spectra to the corresponding
transmission spectra, which have no such bands.
Thus, the DRIFTS spectra presented in this pa-
per are free from specular reflection bands.
5. Discussion
5.1. Band assignments
The vibrational spectra of the reference
tungstates, summarized in Table 3, have been
assigned previously by many authors [26,31–35].
While the Raman assignments for E(w2) and
F2(w4) were quite controversial in previous years

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L. J. Burcham, I. E. Wachs / Spectrochimica Acta Part A 54 (1998) 1355–1368
either Ag and Au or into Bg and Bu factor group
Assignment of the internal vibrational modes of
modes, so that there is no splitting of non-degen-
erate bands within an individual Raman or IR
spectrum. However, the WIIO4 vibrations all split
into Ag, Au, Bg, and Bu factor group modes due to
the low symmetry C1 site group. Consequently,
factor group (correlation) splitting of non-degen-
erate modes is possible [25,30], in which, for ex-
ample, the A1 point group vibration is split into
two Raman bands (Ag and Bg) and two IR bands
(Au and Bu). It should also be acknowledged that
the measured spectral bands are most properly
assigned as Ag, Au, Bg, and Bu factor group
modes, and that the Td point group assignments
which will be given really refer to the types of
vibrations from which these factor group modes
Ce2(WO4)3 and La2(WO4)3 according to Td point
group symmetry requires consideration of the fact
that their crystal structures indicate two distinct
types of WO4 tetrahedrons within the Bravais cell.
Therefore, the spectra in Figs. 1 and 2 consist of
two different sets of internal Td vibrations super-
imposed onto one another, and these internal
modes are generally assumed to occur above ꢀ
300 cm−1 [2]. From the factor group correlation
tables, Tables 1 and 2, it is also apparent that
both types of WO4 tetrahedrons suffer a complete
loss of degeneracy due to the low site and factor
group symmetry of the crystal.
The factor group tables also indicate that, for
WIO4, all Td point group vibrations are split into
Table 4
Band frequencies (cm−1) and assignments of Ce2(WO4)3 and La2(WO4)3
Td pt. grp. assignments
Ce2(WO4)3
R
La2(WO4)3
R
IR
IR
A1(w1); WIO4
A1(w1); WIIO4
944 (s)
925 (vs)
949 (m)
929 (m)
945 (s)
927 (vs)
950 (m)
928 (m)
New phase
New phase
897 (m)
—
936 (m)
—
897 (m)
878 (w)
935 (m)
—
F2(n3); WIO4
F2(n3); WIIO4
F2(n3); WIO4
F2(n3); WIO4
F2(n3); WIIO4
F2(n3); WIIO4
840 (m)
818 (m)
800 (m)
784 (m)
728 (m)
707 (m)
870 (s)
825 (s)
810 (s)
756 (s)
738 (s)
656 (s)
841 (m)
818 (m)
800 (m)
783 (m)
727 (m)
703 (m)
871 (s)
823 (s)
804 (s)
760 (s)
738 (s)
655 (s)
E(w2); WIO4
E(w2); WIIO4
E(w2); WIIO4
387 (m)
352 (m)
336 (m)
472 (s)
451 (s)
—
383 (m)
349 (m)
335 (m)
470 (m)
447 (s)
—
F2(w4); WIO4
F2(w4); WIO4
F2(w4); WIO4
F2(w4); WIIO4
F2(w4); WIIO4
F2(w4); WIIO4
405 (vs)
375 (s)
—
344 (sh)
329 (vs)
300 (vs)
402 (vs)
373 (s)
—
345 (sh)
329 (vs)
301 (vs)
458 (w)
536 (w)
473 (w)
537 (w)
External modes
267 (m)
192 (w)
167 (w)
146 (w)
121 (w)
256 (m)
204 (m)
164 (vs)
263 (m)
237 (w)
224 (w)
191 (w)
166 (m)
148 (m)
121 (m)
254 (m)
203 (m)
160 (vs)

L. J. Burcham, I. E. Wachs / Spectrochimica Acta Part A 54 (1998) 1355–1368
1363
originate. Finally, while the discussion of band
assignments will use the frequencies from
Ce2(WO4)3, the exact same arguments hold for the
spectroscopically similar La2(WO4)3.
of point and site group symmetry in the reference
compounds splits the triply degenerate F2(w3) vi-
brations into two Raman and two IR bands in
CaWO4, and into three Raman and three IR
bands in MgWO4. More importantly, notice that
the high frequency w3 band in MgWO4 is 102
cm−1 higher than the other two w3 bands in the
Raman spectrum, and that it is 130 cm−1 higher
in the IR spectrum. The other two lower fre-
quency w3 bands are much closer together (sepa-
rated by only 26 and 58 cm−1 in the Raman and
IR spectra, respectively). The splitting of the
F2(w3) modes in Ce2(WO4)3 is expected to follow a
similar pattern. Therefore, the Raman bands at
840, 800, and 784 cm−1 (averaging 808 cm−1) are
assigned to the F2(w3) vibrations in WIO4, and the
Raman bands at 818, 728, and 707 cm−1 (averag-
ing 751 cm−1) are assigned to WIIO4. The corre-
sponding IR assignments are 870, 810, and 756
cm−1 (averaging 812 cm−1) for WIO4, and 825,
738, and 656 cm−1 (averaging 740 cm−1) for
WIIO4. This assignment is also consistent with the
fact that WIO4 is expected to be somewhat less
intense, and be at a higher average frequency,
than WIIO4.
The assignments for the E(w2) and F2(w4) bend-
ing modes are simplified by observing that a
frequency inversion relationship exists in the ref-
erence tungstates, in which w2(IR):w4(R) and
w4(IR):w2(R). This relationship, which is due to
factor group splitting, has been well known in
tetrahedral tungstates and molybdates for some
time [33]. In addition, E(w2) is more intense in the
Raman than F2(w4), whereas selection rules dictate
that the reverse is true in the IR. Therefore, the
Raman band at 387 cm−1 and the IR band at 472
cm−1 are assigned to E(w2) vibrations in WIO4,
while the Raman bands at 352 and 336 cm−1
(averaging 344 cm−1) and the IR band at 451
cm−1 are assigned to E(w2) vibrations in WIIO4.
Discrimination between the w2 bands of WIO4 and
WIIO4 is based on the higher frequencies and
lower intensities of WIO4 relative to WIIO4.
From the Ce2(WO4)3 Raman spectrum (Fig. 1),
it is clear by comparison with the reference
tungstates (Fig. 3) that the high frequency, intense
bands at 944 and 925 cm−1 are due to the sym-
metric A1(w1) vibrations of the two types of WO4
units. The band at 944 cm−1 is assigned to WIO4
because the crystal structure indicates that this
tetrahedron has the shortest average bond length
and is, therefore, expected to vibrate at the
highest frequency. Application of the bond
length-stretching frequency correlation, developed
by Hardcastle and Wachs [41], to this symmetric
stretching mode yields the same conclusion. Also,
the relative intensity of the WIO4 vibrations are
expected to be less than those of WIIO4 because
there are only two WIO4 units in the Bravais cell,
compared to four WIIO4 units. However, conclu-
sions based on relative Raman intensities must be
made with caution because reflection intensities
are generally non-linear with concentration and
dependent on frequency. Nevertheless, the IR
spectrum also shows that the 949 cm−1 band is
lower in intensity than the 929 cm−1 band, al-
though the difference is not as pronounced as in
the Raman spectrum. The IR intensities for the
A1(w1) modes are much weaker than the F2(w3, w4)
IR bands because w1 is IR inactive in pure Td
symmetry—the w1 modes appear in these spectra
only because the WO4 units are non-ideal in
Ce2(WO4)3. While factor group splitting cannot be
ruled out as a possible origin for the 936 cm−1 IR
band, the fact that the intensity of this band
increases relative to the other Ce2(WO4)3 bands in
samples prepared with excess cerium suggests that
this band is due to the secondary tungstate phase
discussed previously. The Raman band corre-
sponding to this minority phase appears at 897
cm−1
.
To assign the F2(w3) bands in Ce2(WO4)3, which
appear in the region from 840 cm−1 to 707 cm−1
in the Raman spectrum and from 870 to 656
cm−1 in the IR spectrum, the splitting patterns of
these bands in the reference tungstates must be
examined in more detail. For example, the decay
The assignment of the F2(w4) bands to specific
WIO4 or WIIO4 units is more complicated and
requires a closer examination of the splitting pat-
terns in the reference tungstates. The IR spectra
of the reference tungstates show that the F2(w4)

1364
L. J. Burcham, I. E. Wachs / Spectrochimica Acta Part A 54 (1998) 1355–1368
modes tend not to split as easily as the w3 vibra-
tions (a trend also noted in [42]). This ‘clumping’
effect on the split w4 bands means that, compared
to the w3 vibrations, there is more separation
between the w4 bands of WIO4 and the w4 bands of
WIIO4. As before, the higher average frequencies
and lower intensities of the IR bands at 405 and
375 cm−1 (averaging 390 cm−1) indicate that they
belong to the F2(w4) vibrations in WIO4, while the
IR bands at 344, 329, and 300 cm−1 (averaging
324 cm−1) belong to the F2(w4) vibrations in
WIIO4. Also notice that w4 is slightly more split in
WIIO4 because of the lower C1 site symmetry
(compared to the C2 site symmetry of WIO4) and
also because WIIO4 has a more distorted point
group symmetry than does the more ideally tetra-
hedral WIO4.
Finally, the Raman intensities for the F2(w4)
modes are too weak to display any observable
splitting behavior, but these bands may still be
assigned to WIO4 and WIIO4 based on symmetry
induced frequency shifts. In the reference
tungstates, the Raman frequency of the w4 mode is
higher than the w2 mode by only 66 and 68 cm−1
in Na2WO4 and CaWO4, respectively, but it is 160
cm−1 higher than w2 in less symmetric MgWO4.
This suggests that, in the Raman spectrum, the w4
vibration for the generally lower frequency WIIO4
is actually higher than the w4 vibration in WIO4
since WIIO4 has less point and site group symme-
try than WIO4. Indeed, the 536 cm−1 band in the
Raman spectrum of Ce2(WO4)3 is also more in-
tense than the band at 458 cm−1. Therefore,
assignment of the band at 536 cm−1 to WIIO4 is
consistent with the fact that there is a higher
population of WIIO4 units in the Bravais cell.
In summary, the assignments for all bands in
the infrared and Raman spectra of Ce2(WO4)3
and La2(WO4)3 are given in Table 4. Differences
between the Raman and IR frequencies of bands
originating from the same Td point group modes
are attributed primarily to factor group splitting
(Tables 1 and 2) of these point group modes into
Raman active gerade and IR active ungerade fac-
tor group modes (e.g. the frequency inversion of
the bending modes, and the A1(w1) mode of
MgWO4 vibrating at 914 cm−1 in Raman, but at
899 cm−1 in IR). However, for powders like those
used in the present study the observed vibrational
intensity maxima are actually generated by the
polarization mixing of longitudinal optic (LO)
and transverse optic (TO) vibrations, which are
often split in single crystals [43]. For example,
Tarte et al. [33] found that the IR absorption
maximum for the F2(w3) Td mode in CaWO4
powder was intermediate between the single crys-
tal LO and TO vibrations for this mode, although
the exact frequency of this polarization-mixed
mode varied by about 20 cm−1 depending on the
particle size of the powder. Also, surface modes in
the vicinity of the bulk polarization-mixed modes
can shift the frequencies of the apparent intensity
maxima of bands in vibrational spectra [43].
In the present study, the same particle size was
used for both the Raman and IR measurements,
so it is unlikely that particle size effects are re-
sponsible for the Raman and IR frequency differ-
ences of the same point group modes (also, the
measured frequencies of the reference tungstates
were very close to those reported in the literature
for powdered samples). However, even for the
same particle size it is possible that the surface
modes and LO-TO polarization mixing may not
behave identically in Raman as in IR. Hence,
these effects cannot be ruled out as possible con-
tributing sources to the Raman and IR frequency
differences observed for the same Td point group
modes. Nevertheless, the factor group splitting is
generally considered to be more significant [2,26].
Overall, the internal band assignments given in
Table 4 are similar to previous Td assignments for
single WO4 units in rare earth tungstates [2–
5,11,15], but with the important distinction that in
Ce2(WO4)3 and La2(WO4)3 there are two, non-
equivalent tungstate units which have been sepa-
rately assigned.
5.2. Normal coordinate analysis
Normal coordinate analysis provides additional
insight into the vibrational nature of these
tungstates, and has not appeared in the previous
vibrational studies of tetrahedral rare earth
tungstates [2–5,11,13–15]. The calculated fre-
quencies and force constants for the three force
fields used are shown in Table 5 for the reference

L. J. Burcham, I. E. Wachs / Spectrochimica Acta Part A 54 (1998) 1355–1368
1365
Table 5
modes which have been split by the lower sym-
metries of the crystal, and the Raman and IR
frequencies have also been averaged to estimate
the band positions of ‘effective’ Td point groups.
For the reference tungstates, it is important to
observe the trends in the force constants as the
point and site symmetries are lowered. For in-
stance, in highly symmetric Na2WO4 the magni-
tudes of the stretching force constants (K, K, and
fr in UBFF, OVFF, and GVFF, respectively) are
−1
Calculated frequencies (cm−1) and force constants (mdyn A
)
˚
of reference tungstatesa
Obs.
Calculated
UBFF
OVFF
GVFF
Na2WO4
A1(w1):
E(w2):
F2(w3):
F2(w4):
921
337b
817
341
—
921
342
817
336
921
336
817
342
921
337
817
341
4–6 mdyn A−1, whereas all of the other force
˚
Variance:
1.22×10−4 4.36×10−6 N/A
constants are less than 1 mdyn A−1. This indi-
˚
Force constants:
fr=6.21
cates that the stretching vibrations in highly sym-
metric WO4 units contain a significantly higher
amount of potential energy than do the other
modes. However, as the symmetry is lowered the
K=4.78
F=0.81
H=0.07
K=4.78
F=0.81
D=0.17
frr=0.60
fh=0.46
f
hh=0.05
CaWO4
A1(w1):
E(w2):
F2(w3):
F2(w4):
Variance:
908
907
379
815
366
914
364
810
376
908
386
815
357
stretching constants decrease. For the UBFF and
386
815
357
—
−1
˚
OVFF, K decreases from 4.8 mdyn A
Na2WO4 to 3.4 mdyn A
in
−1
˚
in MgWO4. The fr
3.02×10−4 0.0021
N/A
stretching constant in the GVFF also decreases
−1
Force constants
fr=6.13
frr=0.55
fh=0.50
˚
from ꢀ6 mdyn A
A
in Na2WO4 to ꢀ5 mdyn
K=4.85
F=0.73
H=0.18
K=4.69
F=0.80
D=0.037
−1
˚
in MgWO4. Conversely, the force constants
for bond angle deformation (H, D, and fh in
UBFF, OVFF, and GVFF, respectively) and
bond interactions (the F repulsion constant in
UBFF and OVFF; frr stretching and fhh bending
interaction constants in GVFF) are seen to in-
crease as the point and site symmetries are low-
ered. Thus, the WO4 units of lower symmetry are
experiencing a withdrawal of potential energy
away from the high energy stretching modes due
to an increased amount of vibrational interaction
between bonds.
f
hh=0.02
MgWO4
A1(w1):
E(w2):
F2(w3):
F2(w4):
Variance:
907
904
464
740
434
906
448
737
452
907
446
736
454
446
736
454
—
0.0017
1.93×10−5 N/A
Force constants:
fr=5.33
frr=0.81
fh=0.81
K=3.40
F=1.08
H=0.28
K=3.31
F=1.11
D=0.66
f
hh=0.09
a Arithmetic averages were used for w2, w3, and w4 when these
degenerate modes have been split into non-degenerate bands
by lower symmetries in the crystals. Also, Raman and IR
frequencies have been arithmetically averaged in order to
estimate the frequencies of an ‘effective’ Td point group.
b For Na2WO4, the IR inactive E(w2) mode was taken to be
370 cm−1 based on the relationship w2(IR):w4(R) [33]. Thus,
in Table 5: E(w2)=0.5 · {304 cm−1 (R)+370 cm−1 (IR)}=
For Ce2(WO4)3, Table 6 shows that the stretch-
ing force constants for WIO4 are similar to those
of CaWO4, whereas the force constants for WIIO4
are similar to those of MgWO4. For example, the
stretching force constants for WIO4 in Ce2(WO4)3
are 4.4 (K, UBFF and OVFF), and 6.2 ( fr,
337 cm−1
.
GVFF) mdyn A−1. The corresponding force con-
˚
−1
˚
stants for CaWO4 are ꢀ4.8 and 6.1 mdyn A
.
The same stretching force constants for WIIO4 in
compounds, and in Table 6 for Ce2(WO4)3. The
calculated values for La2(WO4)3 have been omit-
ted because of their similarity to those of
Ce2(WO4)3. The arithmetically averaged band po-
sitions were used to describe the degenerate Td
Ce2(WO4)3 are 3.5 and 5.5 mdyn A−1, compared
˚
−1
˚
to ꢀ3.4 and 5.3 mdyn A
in MgWO4. This
interesting correspondence is probably due to sim-
ilarities in the amount of deviation exhibited by

1366
L. J. Burcham, I. E. Wachs / Spectrochimica Acta Part A 54 (1998) 1355–1368
pulsion in these two force fields, indicating much
more interbond interaction due to the lower sym-
metry of this tetrahedron. The frr stretching inter-
action term in the GVFF also increases in the less
symmetric WIIO4 unit for the w1 mode. On the
other hand, the F2(w3) antisymmetric stretch ap-
pears to have greater stretching purity than w1 in
all three force fields. The bending modes, E(w2)
and F2(w4), are also quite pure in the GVFF, but
they have substantial replusion (F) in the UBFF
and OVFF. However, in all four modes and for
all three force fields, the interaction terms are
expectedly higher in the less symmetric WIIO4. In
general, the presence of significant vibrational in-
teraction in these tungstate units is consistent with
the fact that they are not perfect tetrahedrons—
both WIO4 and WIIO4 having varying degrees of
deviation from ideal Td point symmetry.
these WO4 units from ideal tetrahedral point sym-
metry: WIO4 and CaWO4 have only mild distor-
tion from Td point symmetry compared to the
much larger distortions in WIIO4 and MgWO4.
The bending and interaction constants are gener-
ally intermediate between those of CaWO4 and
MgWO4.
The potential energy distribution (PED) of
Ce2(WO4)3 is also presented in Table 7 for all
three force fields. The PED shows a high degree
of vibrational interaction between bonds, since
even in the more symmetric WIO4 tetrahedron the
A1(w1) symmetric stretch has 48% contribution
from the repulsion constant, F, in the UBFF and
OVFF. The WIIO4 symmetric stretch is 56% re-
Table 6
−1
Calculated frequencies (cm−1) and force constants (mdyn A
˚
)
of Ce2(WO4)a3
6. Conclusions
Ce2(WO4)3
Calculated
Obs. UBFF
In conclusion, the infrared and Raman spectra
of Ce2(WO4)3 and La2(WO4)3, which are compli-
cated by the superposition of bands from two,
non-equivalent WO4 units, have been successfully
assigned above 300 cm−1 according to Td point
group symmetry. Individual assignment of the
two types of tungstate units, WIO4 (C2 site sym-
metry) and WIIO4 (C1 site symmetry), has relied
heavily on comparison with the tetrahedral refer-
ence tungstates of Na2WO4, CaWO4, and
MgWO4. This was especially true for the degener-
ate Td bands, in which the reference tungstates
were used to observe trends in the splitting pat-
terns of these bands as the point and site sym-
metries became less tetrahedral. Assignment was
also aided by the fact that WIO4 is expected to be
somewhat less intense, and be at a higher average
frequency, than WIIO4 (there are only two WIO4
units in the Bravais cell, each with a relatively
short average bond length, compared to the four
WIIO4 units with a longer average bond length).
Normal coordinate analysis indicates that the
force constants for WIO4 and WIIO4 roughly cor-
relate with the amount of deviation from ideal
OVFF
GVFF
WIO4
A1(w1):
E(w2):
F2(w3):
F2(w4):
Variance:
947
430
810
424
—
947
436
810
417
950
421
807
431
947
430
810
424
2.21×10−4 3.31×10−4 N/A
Force constants:
fr=6.24
frr=0.74
fh=0.71
K=4.46
F=1.00
H=0.23
K=4.37
F=1.03
D=0.53
f
hh=0.06
WIIO4
A1(w1):
E(w2):
F2(w3):
F2(w4):
Variance:
927
398
746
430
—
923
425
753
401
920
416
753
416
927
398
746
430
N/A
0.0039
0.0015
Force constants:
fr=5.52
frr=0.86
fh=0.73
K=3.49
F=1.14
H=0.15
K=3.53
F=1.11
D=0.40
f
hh=0.12
a Arithmetic averages were used for w2, w3, and w4 when these
degenerate modes have been split into non-degenerate bands
by lower symmetries in the crystal. Also, Raman and IR
frequencies have been arithmetically averaged in order to
estimate the frequencies of an ‘effective’ Td point group.

L. J. Burcham, I. E. Wachs / Spectrochimica Acta Part A 54 (1998) 1355–1368
1367
Table 7
Potential energy distribution (PED) for Ce2(WO4)3a
Urey–Bradley force field
Orbital valence force field
Generalized valence force field
F
H
K
F
D
K
fr
frr
fh
fhh
WIO4
w1
0.47
0.62
0.22
0.57
0
0.53
0
0.78
0.08
0.49
0.68
0.23
0.54
0
0.51
0
0.77
0.08
0.74
0
1.12
0.01
0.26
0
−0.13
ꢀ0
0
0
w2
0.38
ꢀ0
0.34
0.32
ꢀ0
0.37
1.21
0.01
0.99
−0.22
0
0
w3
w4
WIIO4
w1
0.57
0.74
0.31
0.62
0
0.43
0
0.69
0.14
0.56
0.75
0.30
0.57
0
0.44
0
0.70
0.13
.68
0
1.16
0.02
0.32
0
−.18
ꢀ0
0
0
w2
0.26
ꢀ0
0.24
0.25
ꢀ0
0.30
1.46
0.02
0.98
−0.46
0
0
w3
w4
a
Table elements represent the fractional potential energy contribution of each force constant to each mode.
frequency differences in the stretching modes (e.g.
the A1(w1) mode of MgWO4 vibrating at 914
cm−1 in Raman, but at 899 cm−1 in IR). Finally,
it is likely that other rare earth tungstates of
stoichiometry Ln2(WO4)3, where Ln=LaꢀDy,
have similar vibrational spectra due to their simi-
lar structures [17].
tetrahedral point symmetry: the force constants of
WIO4 are similar to those of CaWO4 (both are
mildly distorted tetrahedrons), and WIIO4 is closer
to MgWO4 (highly distorted tetrahedrons). It is
possible that the site and factor groups may also
have some influence on the calculated force con-
stants due to the averaging procedure used to
estimate the frequencies of the ‘effective’ Td point
groups in these tungstates. Non-ideality is also
indicated by the calculated potential energy distri-
bution (PED), which shows a substantial degree
of vibrational interaction between bonds—espe-
cially in the less symmetric WIIO4 unit.
Lastly, the influence of the factor group ap-
pears mainly as frequency differences between IR
and Raman bands that have originated from the
same Td point group modes, since these point
group modes have been split by the factor group
into Raman active gerade and IR active ungerade
factor group modes. Some contribution to these
frequency shifts may also be due to the LO-TO
polarization mixing and surface modes that gener-
ate the observed vibrational frequencies in pow-
ders, since the magnitude of these effects may not
be the same in Raman as in IR. However, the
factor group is usually considered to have the
most significant splitting effect on the point group
modes [2,26]. This factor group effect is most
obvious for the bending modes, in which w2(IR):
w4(R) and w4(IR):w2(R), but it also accounts for
Acknowledgements
The authors gratefully acknowledge the United
States Department of Energy — Basic Energy
Sciences (DOE Grant cDEFG02-93ER14350)
for financial support of this work.
References
[1] (a) M.M. Ostromecki, L.J. Burcham, I.E. Wachs, N.
Ramani, and J.G. Ekerdt, J. Molec. Catal., in press
(1998), (b) M.M. Ostromecki, L.J. Burcham, and I.E.
Wachs, J. Molec. Catal., in press (1998).
[2] E.J. Baran, M.B. Vassallo, C. Cascales, P. Porcher, J.
Phys. Chem. Solids 54 (1993) 1005.
[3] J. Hanuza, Acta Phys. Pol. A70 (1986) 585.
[4] K. Byrappa, A. Jain, J. Mater. Res. 11 (1996) 2869.
[5] W.J. Schipper, G. Blasse, Z. Naturforsch. 29b (1974) 340.
[6] (a) A.F. Corsmit, H.E. Hoefdraad, G. Blasse, J. Inorg.
Nucl. Chem., 34 (1972) 3401, (b) G. Blasse and A.F.
Corsmit, J. Solid State Chem., 6 (1973) 513. c) K.C.
Bleijenberg and G. Blasse, J. Solid State Chem., 17 (1976)
71.

1368
L. J. Burcham, I. E. Wachs / Spectrochimica Acta Part A 54 (1998) 1355–1368
[7] A.N. Pandey, U.P. Verma, J.R. Chopra, Indian J. Pure
Appl. Phys. 18 (1980) 510.
[25] K. Nakamoto, Infrared and Raman Spectra of Inorganic
and Coordination Compounds, 4th edition, Wiley, New
York, 1986.
[26] R.H. Busey, O.L. Keller Jr., J. Chem. Phys. 41 (1964)
215.
[27] D.E. Mann, T. Shimanouchi, J.H. Meal, L. Fano, J.
Chem. Phys. 27 (1957) 43.
[28] J. Overend, J.R. Scherer, J. Chem. Phys. 32 (1960) 1289.
[29] L.J. Basile, J.R. Ferraro, P. LaBonville, M.C. Wall, Co-
ord. Chem. Rev. 11 (1973) 21.
[30] W.G. Fateley, F.R. Dollish, N.T. McDevitt, F.F. Bentley,
Infrared and Raman Selection Rules for Molecular and
Lattice Vibrations: The Correlation Method, Wiley, New
York, 1972.
[31] J.A. Horsley, I.E. Wachs, J.M. Brown, G.H. Via, F.D.
Hardcastle, J. Phys. Chem. 91 (1987) 4014.
[32] V.P. Mahadevan Pillai, T. Pradeep, M.J. Bushiri, R.S.
Jayasree, V.U. Nayar, Spectrochim. Acta 53A (1997) 867.
[33] (a) P. Tarte and M. Liegeois-Duyckaerts, Spectrochim.
Acta, Part A, 28A (1972) 2029. (b) M. Liegeois-Duyck-
aerts and P. Tarte, Spectrochim. Acta, Part A, 28A (1972)
2037.
[8] (a) H.J. Rother, A. Fadini, and S. Kemmler-Sack, Z.
Anorg. Allg. Chem., 463 (1980) 137, (b) H.J. Rother, S.
Kemmler-Sack, U. Treiber, and W.R. Cyris, Z. Anorg.
Allg. Chem., 466 (1980) 131, (c) M. Herrmann and S.
Kemmler-Sack, Z. Anorg. Allg. Chem., 476 (1981) 115.
[9] R. Shiozaki, E. Nishio, M. Morimoto, H. Kominami, M.
Maekawa, Y. Kera, Appl. Spectrosc. 50 (1996) 541.
[10] L. Chen, Y. Liu, Y. Chen, J. Solid State Chem. 68 (1987)
132.
[11] L.H. Brixner, H.Y. Chen, C.M. Foris, J. Solid State
Chem. 45 (1982) 80.
[12] L.H. Brixner, H.Y. Chen, C.M. Foris, J. Solid State
Chem. 44 (1982) 99.
[13] X. Qi, Z. Luo, Q. Huang, J. Liang, J. Chen, Y. Huang,
M. Qiu, H. Zhang, Phys. Status Solidi A 114 (1989) 127.
[14] Y.M. Golutvin, K.S. Bagdasarov, E.A. Fedorov, E.G.
Maslennikova, L.S. Strizhko, A.S. Popovich, L.G. Titov,
Sov. Phys. Crystallogr. 28 (1983) 425.
[15] M.S. Augsburger, J.C. Pedregosa, J. Phys. Chem. Solids
56 (1995) 1081.
[16] J.H.G. Bode, H.R. Kuijt, M.A. Lahey, G. Blasse, J. Solid
State Chem. 8 (1973) 114.
[17] K. Nassau, H.J. Levinstein, G.M. Loiacono, J. Phys.
Chem. Solids 26 (1965) 1805.
[18] J.B. Nelson, J.H. McKee, Nature 158 (1946) 753.
[19] L.H. Brixner, A.W. Sleight, Mater. Res. Bull. 8 (1973)
1269.
[34] G. Blasse, J. Inorg. Nucl. Chem. 37 (1975) 97.
[35] V.V. Fomichev, O.I. Kondratov, Spectrochim. Acta, Part
A 50A (1994) 1113.
[36] I.R. Beattie and T.R. Gilson, J. Chem. Soc. A, (1969)
2322.
[37] J.M. Olinger, P.R. Griffiths, Appl. Spectrosc. 47 (1993)
687.
[20] T. Gressling, H. Mu¨ller-Buschbaum, Z. Naturforsch. 50B
(1995) 1513.
[38] N. Weinstock, H. Schulze, A. Mu¨ller, J. Chem. Phys. 59
(1973) 5063.
[21] M. Yoshimura, F. Sibieude, A. Rouanet, M. Foex, J.
Solid State Chem. 16 (1976) 219.
[22] M. Yoshimura, A. Rouanet, Mater. Res. Bull. 11 (1976)
151.
[39] R.O. Keeling Jr., Acta Crystallogr. 10 (1957) 209.
[40] J.P. Russell, R. Loudon, Proc. Phys. Soc. 85 (1965) 1029.
[41] F.D. Hardcastle, I.E. Wachs, J. Raman Spectrosc. 26
(1995) 397.
[23] G.I. Tyushevskaya, N.S. Afonskii, V.I. Spitsyn, Dokl.
Akad. Nauk SSSR 170 (1966) 859.
[42] R.K. Khanna, E.R. Lippincott, Spectrochim. Acta, Part
A 24A (1968) 905.
[24] D.H. Templeton, A. Zalkin, Acta Crystallogr. 16 (1963)
762.
[43] P.M.A. Sherwood, Vibrational Spectroscopy of Solids,
Cambridge University Press, Cambridge, 1970.
.