Crystal structure, Raman spectrum and lattice dynamics of a new metastable form of tellurium dioxide: γ-TeO2

Article abstract of DOI:10.1016/S0022-3697(00)00012-3

The crystal structure of a new metastable form of tellurium dioxide, γ-TeO₂ (orthorhombic, P2₁2₁2₁ (no. 18); a = 4.898 angstroms, b = 8.576 angstroms, c = 4.351 angstroms; Z = 4) was solved ab initio and refined to R_B = 0.0387 and R_p = 0.115, on the basis of a Rietveld analysis of its powder X-ray diffraction pattern. Each Te atom is coordinated to four oxygen atoms, and its coordination polyhedron has a view of distorted trigonal bipyramid (disphenoid) TeO₄E with one equatorial corner occupied by lone pair E. These units frame a three-dimensional network of the same type as the α-TeO₂ one. There exist two different kinds of Te-O-Te bridges in γ-TeO₂; one of them is nearly symmetric, and the other is highly asymmetric. The former bridges constitute polymeric chains along the Oz-axis. Such a characterization of the γ-TeO₂ structure is supported by the analysis of the Raman spectra using the lattice dynamical model treatment in which the lattice vibrations are considered jointly with the elastic properties. All the longwave frequencies and the elastic constants were thus estimated. Possible relations between the structure of the TeO₂ glass and the γ-phase are discussed.

Full text of DOI:10.1016/S0022-3697(00)00012-3

Journal of Physics and Chemistry of Solids 61 (2000) 1499–1507
www.elsevier.nl/locate/jpcs
Crystal structure, Raman spectrum and lattice dynamics of a new
metastable form of tellurium dioxide: g-TeO2
J.C. Champarnaud-Mesjard, S. Blanchandin, P. Thomas, A. Mirgorodsky,
*
´
T. Merle-Mejean , B. Frit
´
´
SPCTS, UMR-CNRS 6638, Universite de Limoges, Faculte des Sciences, 123 Avenue A. Thomas, 87060, Limoges, France
Received 8 October 1999; accepted 6 December 1999
Abstract
ꢀ
The crystal structure of a new metastable form of tellurium dioxide, g-TeO2 (orthorhombic, P212121 (no. 18); a ˆ 4:898 A;
ꢀ
ꢀ
b ˆ 8:576 A; c ˆ 4:351 A; Z ˆ 4) was solved ab initio and refined to RB ˆ 0:0387 and Rp ˆ 0:115; on the basis of a Rietveld
analysis of its powder X-ray diffraction pattern. Each Te atom is coordinated to four oxygen atoms, and its coordination
polyhedron has a view of distorted trigonal bipyramid (disphenoid) TeO4E with one equatorial corner occupied by lone pair E.
These units frame a three-dimensional network of the same type as the a-TeO2 one. There exist two different kinds of Te–O–Te
bridges in g-TeO2; one of them is nearly symmetric, and the other is highly asymmetric. The former bridges constitute
polymeric chains along the Oz-axis.
Such a characterization of the g-TeO2 structure is supported by the analysis of the Raman spectra using the lattice dynamical
model treatment in which the lattice vibrations are considered jointly with the elastic properties. All the longwave frequencies
and the elastic constants were thus estimated. Possible relations between the structure of the TeO2 glass and the g-phase are
discussed. ᭧ 2000 Elsevier Science Ltd. All rights reserved.
Keywords: A. Oxides; A. Glasses; D. Crystal structure; C. Raman spectroscopy; D. Phonons
1. Introduction
The crystals built up from such structural units therefore
contain cavities, tunnels or planes in which the lone pairs E
are located and interact. Their lattices, as a rule, are micro-
scopically labile, macroscopically compliant and predis-
posed to polymorphism. Many of them, like TeO2, and
almost all the TeIV containing compounds (including the
glasses), exhibit remarkable properties related to macro-
scopic polarization and polarisability (dielectric, piezoelec-
tric, optic, electro-acoustic) which are of great interest for
fundamental science and technology. The origin of such
properties, particularly for TeO2-based glasses, is not yet
clearly identified, but it can be thought that it is surely
related to the peculiarities of the electron distribution inside
the coordination polyhedra. Therefore the detailed knowl-
edge of the atomic arrangement in those polyhedra is of
prime importance.
Tellurium dioxide TeO2 belongs to the category of
compounds in which all the atoms are the so-called
p-elements, having non-bonding valence electron pairs
(lone pairs E). For such compounds, in their solid phases,
the stereochemical effect of the lone pairs results in a strong
asymmetry of the coordination polyhedra of the constitutive
p-elements. Actually those polyhedra can be regarded as
consisting of two demi-spheres of different radii. Demi-
sphere I contains active valence electrons which form
(relatively short) chemical bonds with the nearest neigh-
bours situated on the one side of the p-element. Demi-sphere
II, situated on the other side, contains the inert electron
cloud surrounded by more distant neighbours weakly inter-
acting with it.
In discussing the structure of TeO2-based glasses, which
are promising materials for use in optical fibre or in
non-linear optical devices [1], the two well-known
crystalline ambient-pressure polymorphs of tellurium
* Corresponding author. Tel.: ϩ 33-5545-7431; fax: ϩ 33-5545-
7270.
´
E-mail address: merle@unilim.fr (T. Merle-Mejean).
0022-3697/00/$ - see front matter ᭧ 2000 Elsevier Science Ltd. All rights reserved.
PII: S0022-3697(00)00012-3

1500
J.C. Champarnaud-Mesjard et al. / Journal of Physics and Chemistry of Solids 61 (2000) 1499–1507
Table 1
Conditions of data collection and profile refinement (esd’s are given
in parentheses)
˚
Lattice parameters (A)
a ˆ 4:898ꢀ3†; b ˆ 8:576ꢀ4†
c ˆ 4:351ꢀ2†
182.76(2)
5.80(5), 5.85
4
3
˚
Volume (A )
rexp (g cmϪ3), rcalc (g cmϪ3
)
Z
Space group
Wavelength (A)
P212121 (no. 18)
1.540598
˚
2u range (Њ)
20–100
Step range (Њ)
0.04
Counting time (s)
Zero shift (Њ)
75
Ϫ 0.017(1)
Number of reflections
Number of parameters
Scale
Refinement program
Profile function
Profile parameters
258
21
0.319(3) × 10Ϫ3
Fullprof [10]
Pseudo-Voigt
V ˆ 0:21ꢀ3†; V ˆ 0:06ꢀ2†
W ˆ 0:003ꢀ4†; h ˆ 0:77ꢀ1†
Rbragg ˆ 3:87; Rp ˆ 11:5;
Rwp ˆ 12:6
Fig. 1. The disphenoid as a basic structural unit of the a- and
b-TeO2 crystal structures (the arrows visualize the direction toward
which points the lone pair E of the Te atom).
Reliability factorsa (%)
P
P
P
P
a
Rbragg ˆ 100 ͉Ii Ϫ Ici͉= ͉Ii͉; Rp ˆ 100 ͉Yi Ϫ Yci͉= ͉Yi͉;
dioxide, a-TeO2 paratellurite [2,3], and b-TeO2 tellurite [4],
are usually referred to as the virtual parents. In both poly-
morphs, the oxygen environment of Te atoms corresponds to
a highly distorted TeO6 octahedron. Its demi-sphere I
contains four oxygen atoms forming two strong (largely
covalent) short equatorial bonds (Te–Oeq), and two much
weaker, and therefore longer, axial bonds (Te–Oax). Demi-
sphere II contains two Te···O non-bonding contacts and the
lone pair E.
P
P
Rwp ˆ 100‰ Wi=͉Yi Ϫ Yci͉2=‰ wi=͉Yi͉ Š
:
2
1=2
reinforced by the Raman spectrum behaviour during hydro-
static compression of a-TeO2 [6], which clearly indicates
(as previously shown by a powder diffraction study [2]) an
evolution of the crystal structure toward a framework.
Now, an interesting question arises: can polymerized
TeO2 lattice exist under ambient conditions? In this article
we present the detailed structural and spectroscopic (Raman
diffusion) data on a new crystalline form of tellurium dioxide
(that we have called g-TeO2) which, in our opinion, positively
answer this question. These data are analysed jointly with the
results of the lattice-dynamical model treatment, which
provides an interpretation of the crystal vibrations and clari-
fies their connection with the structural peculiarities.
Customarily, the TeO4 disphenoids corresponding to
demi-sphere I (Fig. 1) are considered as the basic structural
units which build up:
• either the three-dimensional network of a-TeO2, by shar-
ing the O corners (via simple Te–eqOax–Te bridges);
• or the two-dimensional framework of b-TeO2, by sharing
alternately the O corners and the O–O edges (double bridge
2. Experimental techniques
Consequently, the crystal chemistry of TeO2-rich crystalline
compounds or glasses are usually discussed within the frame
of this idea.
More or less well-crystallized g-TeO2 is obtainable when
pure TeO2 glass, or TeO2-rich glasses containing 5–10 mol%
of oxides like WO3 [7], Nb2O5 [8] or PbO [9], are recrystal-
lized at low temperatures. Well crystallized and practically
pure g-TeO2, (small amounts of a-TeO2 and of the residual
TeO2-rich glass were detected on the X-ray diffraction (XRD)
pattern) was prepared by slowly heating up to 440ЊC, and
then annealing for 60 h at the same temperature, a glassy
sample containing 5 mol% of Nb2O5.
The XRD pattern used for the ab initio crystal structure
determination was recorded on a D5000-Siemens diffract-
ometer (Bragg–Brentano configuration) equipped with a
back monochromator, under the conditions reported in
However, such an opinion is not unique. Some authors
consider TeO2 crystals as molecular structures (see Ref. [3]
and references therein). In our recent treatment of the vibra-
tional properties of a- and b-TeO2 [5], we have found spec-
trochemical arguments supporting this point of view. It
could be concluded that the electron cloud inside the asym-
metric Te–eqOax–Te bridges is so disbalanced that the
vibrating lattices behave rather as molecular structures
consisting of the isolated TeO2eq entities, than a framework
of polymerized Te–O–Te bridges. These arguments are

J.C. Champarnaud-Mesjard et al. / Journal of Physics and Chemistry of Solids 61 (2000) 1499–1507
1501
Fig. 2. Powder Raman spectra of the g-TeO2 crystallized from TeO2 glasses doped with oxides: (a) WO3; (b) Nb2O5; (c) PbO.
ꢀ
ꢀ
ꢀ
Table 1. Changing the way of dusting the holder with the
sample holder did not result in significant changes of the
relative intensities of the diffraction lines, so indicating that
no orientation effects were occurring.
The individual structure factors were extracted from the
pattern by a “pattern matching procedure” using the full-
prof Rietveld program [10]. Then the shelxs 90 and
shelxl 97 [11,12] programs were used for the structure
determination. The scattering factors were those of the Inter-
national Tables for X-ray Crystallography [13]. They were
corrected for anomalous diffusion effects.
meters: a ˆ 4:893ꢀ3† A; b ˆ 8:576ꢀ4† A; c ˆ 4:351ꢀ2† A)
with the help of the ITO automatic indexing program [14].
The density measured ꢀdexp ˆ 5:80ꢀ5† g cmϪ3† implies
Z ˆ 4 TeO2 per unit cell ꢀdcalc ˆ 5:85 g cmϪ3†: These
values are not contradictory with (but are more accurate
than) the previously published ones [7] which corre-
sponded to a less well-crystallized sample obtained
from a pure TeO2 glass. The coordinates of atomic posi-
tions are given in Table 3, and some characteristics of
the atomic arrangement in the g-TeO2 lattice are
presented in Table 4.
Raman spectra of all the samples were recorded in the
20–1200 cmϪ1 range using a Dilor spectrometer (XY
model) equipped with a CCD detector and an Arϩ laser
(514.5 nm exciting line) in a backscattering geometry. Fig.
2 exhibits the spectra of g-TeO2 synthesized from TeO2-rich
glasses containing different dopings, WO3 (5%), NbO2.5
(10%) and PbO (5%). The shapes of these spectra are
close, but that related to the lattice doped by PbO is more
refined. Therefore, it will be referred throughout this paper.
For comparison, the Raman spectra of a-, b- and g-TeO2 as
well as the spectrum of the glass, are jointly presented in
Fig.3.
The environment of tellurium atom is shown in Fig. 5.
Formally, it is coordinated to six oxygen atoms forming a
highly distorted octahedron involving four oxygen atoms
˚
separated from Te by an interval of about 1.85–2.20 A,
and two distant oxygen atoms, separated by 2.69 and
˚
3.16 A. If the latter atoms are excluded, the typical dis-
phenoid TeO4E becomes appropriate, in which the lone
pair constitutes the third equatorial vertex of the trigonal
bipyramid. It is worth noting that one of the two axial
1
˚
bonds (Te–O(1) ˆ 2.20 A) is much longer than the other
1
˚
one (Te–O(2) ˆ 2.02 A). By sharing O(1) and O(2)
corners, the TeO4E units frame the three-dimensional
network visualized in Fig. 6a. Such a network makes
room for wide rectangular tunnels containing the lone
pairs of tellurium atoms.
3. Structure
The shortest three bonds, namely, the two equatorial
ones, Te–O(1) and Te–O(2), and the shortest axial one,
Te–O(2)1, can be regarded as constituting the helical
The XRD pattern (Fig. 4) has been indexed (Table 2) in the
orthorhombic system (space group P212121; unit cell para-

1502
J.C. Champarnaud-Mesjard et al. / Journal of Physics and Chemistry of Solids 61 (2000) 1499–1507
Fig. 3. Raman spectra of various phases of TeO2: (a) a-TeO2; (b) b-TeO2; (c) g-TeO2; (d) glassy TeO2.
chains of corner-sharing TeO3 pyramids (TeO3E tetrahedra)
displayed in Fig. 6a. Two of those chains, developed around
the 21 screw axes along the Oz direction, are shown in
Fig. 7a.
A comparison of the structure of g-TeO2 with that of
paratellurite, a-TeO2 (space group P41212) [2,3], reveals a
general analogy (Figs. 6 and 7) in their constitutions. Actu-
ally, both structures are built up from similar basic units
interconnected in the same way, e.g. via the Te–eqOax–Te
simple bridges. However, a-TeO2 contains a single set of
such bridges which are essentially asymmetric (1.87–
˚
2.12 A) and which constitute a regular three-dimensional
network (Fig. 6b), whereas in g-TeO2, the TeO4E units are
˚
alternately linked by nearly symmetric (1.95–2.02 A) and
Fig. 4. Observed (···), calculated (—) and difference (below) X-ray powder patterns for g-TeO2. Vertical bars indicate the reflection positions
for g-TeO2 (upper bars) and for a-TeO2 (lower bars).

J.C. Champarnaud-Mesjard et al. / Journal of Physics and Chemistry of Solids 61 (2000) 1499–1507
1503
Table 2
X-ray powder data for g-TeO2
˚
˚
˚
˚
h,k,l
dobs (A)
dcalc (A)
I/Imax (%)
h,k,l
dobs (A)
dcalc (A)
I/Imax (%)
0 2 0
1 1 0
0 1 1
1 0 1
1 2 0
0 2 1
1 1 1
1 2 1
2 0 0
0 3 1
2 1 0
0 0 2
1 3 1
0 4 0
2 0 1
2 2 0
0 1 2
2 1 1
1 0 2
1 4 0
0 2 2
1 1 2
2 2 1
2 3 0
1 2 2
4.30
4.26
3.884
3.255
3.230
3.047
4.29
4.25
2
8
31
41
100
55
1 4 1
0 3 2
2 3 1
1 3 2
2 4 0
3 1 0
2 1 2
3 0 1
3 2 0
1 5 1
1 4 2
3 2 1
0 1 3
0 6 0
2 3 2
1 0 3
1 1 3
1 6 0
0 6 1
3 3 1
0 5 2
2 5 1
1 6 1
2 4 2
0 3 3
3 1 2
1.7925
1.7278
1.7122
1.6330
1.6147
1.5989
1.7902
1.7311
1.7102
1.6322
1.6132
1.6039
1.5979
1.5287
1.5259
1.5172
1.4578
1.4399
1.4299
1.4293
1.4136
1.3905
1.3726
1.3721
1.3579
1.3480
1.3469
1.3370
1.3086
1.2958
1.2933
1.2910
11
Ͻ 1
9
14
6
3.880
3.253
3.226
3.054
3.041
2.591
2.449
2.389
2.355
2.175
2.147
2.144
2.134
2.127
2.109
2.071
1.9881
1.9641
1.9399
1.9367
1.9106
1.8599
1.8036
9
2.597
2.451
2.392
2.355
2.177
2.149
3
8
10
3
2
7
1.5301
1.5262
1.5171
1.4548
1.4384
1.4328
1.4267
1.4119
1.3914
1.3726
3
2
7
Ͻ 1
Ͻ 1
1
2
1
2
5
2.130
2
2.110
2.073
1.9877
1.9651
1.9381
13
4
2
6
13
1.3588
1.3477
1
5
1.3380
1.3091
1.2948
1
2
2
1.9128
1.8622
1.8031
16
3
Ͻ 1
˚
highly asymmetric (1.86–2.20 A) bridges, thus forming a
lattice in which the above mentioned chains can be clearly
identified.
Table 3
Final atomic coordinates and isotropic thermal coefficients for
atoms in g-TeO2 (esd’s are in parentheses)
2
˚
Atom
Site
x
y
z
B (A )
4. Raman spectrum and lattice dynamics
Te
O(1)
O(2)
4a
4a
4a
0.9696(4)
0.759(3)
0.855(3)
0.1016(2)
0.281(2)
0.036(2)
0.1358(4)
0.173(4)
0.727(3)
0.17(3)
4.0(4)
4.3(4)
The primitive cell of g-TeO2 contains 12 atoms, and the
33 longwave lattice vibrations are distributed between the
Table 4
˚
Main interatomic distances (A), angles (Њ), symmetry operations and bond valences in g-TeO2 (esd’s are given in parentheses)
Te
O(1)
1.86(2)
91.9(5)
158.2(6)
99.2(4)
91.8(5)
88.3(5)
O(1)1
2.93(2)
2.20(2)
106.7(6)
76.1(4)
O(1)2
O(2)
2.90(2)
2.56(2)
3.89(2)
1.94(1)
77.6(5)
138.8(6)
O(2)1
O(2)2
nij
Symmetry
O(1)
4.94(2)
4.34(2)
3.16(2)
96.3(5)
76.7(4)
85.3(4)
2.79(2)
4.11(2)
3.34(2)
2.48(2)
2.02(2)
61.7(5)
3.23(2)
4.66(2)
3.38(2)
4.35(2)
2.48(2)
2.69(1)
1.38
0.54
0.04
1.09
0.88
0.14
4.07
O(1)1
O(1)2
O(2)
x, y, 1 ϩ z
x, Ϫy, 0.5 ϩ z
O(2)1
153.6(5)
144.5(6)
1 Ϫ x, 0.5 ϩ y, z
0.5 ϩ x, 0.5 Ϫ y, Ϫz
O(2)2
P
nij

1504
J.C. Champarnaud-Mesjard et al. / Journal of Physics and Chemistry of Solids 61 (2000) 1499–1507
is the region of the stretching modes of the TeO2 lattices [5].
Only four of those, near 611, 683, 752 and 819 cmϪ1 are
seen well in the experimental spectra, and a weak band near
645 cmϪ1 can be added to them (Fig. 2). The existence of
one high-frequency strong band dominating the stretching
region is typical for the Raman spectra of TeO2 polymorphs
[5]. The particular feature of the spectra in Fig. 2 is the very
high intensity of the band near 426 cmϪ1. Qualitatively, the
origin of these two intense bands has been already discussed
in Ref. [5].
To better clarify the relationships between the crystal
structure and the Raman spectrum under considerations,
the lattice-dynamical treatment of g-TeO2 was performed
by using the above structural data and the modified valence
force field model recently elaborated for a- and b-TeO2
lattices [5]. Within this model, the short-range Te–O and
ꢀ
O–O interactions up to distances L ˆ 3:5 A were taken into
account. They were characterized by two-body force
constants KTe–O and KO–O evaluated from the empirical
K
Te–O/LTe–O and KO–O/LO–O dependences empirically found
Fig. 5. Anionic coordination around the tellurium atoms. The arrow
indicates the direction toward which the lone pair E points.
in Ref. [5]. To these parameters, the three-body force
constants of the O–Te–O and Te–O–Te angles were
added jointly with the non-diagonal Te–O/Te–O para-
meters describing the interactions between two adjusted
Te–O bonds via Te and O atoms. The corresponding values
were transferred from Ref. [5].
symmetry species as follows:
9A1 ϩ 8A2 ϩ 8B1 ϩ 8B2
Among the calculated results, the main attention was paid
to the Raman active modes (frequencies and eigenvectors)
and to the elastic properties of the lattice. Some of these
results are presented in Table 5.
All of them are Raman active. The eight modes correspond-
ing to the vibrations of the eight shortest (equatorial) Te–O
bonds can be expected in the interval 500–850 cmϪ1 which
Fig. 6. Stereoview of the 3D network of corner-sharing TeO4E units in (a) g-TeO2 and (b) a-TeO2 for comparison (the symbols for O(1) and
O(2) atoms are the same as in Fig. 5). In (a), the broken lines visualize the longer Te–O(1) bonds which individualize the polymeric chains
parallel to Oz (shadowed zones).

J.C. Champarnaud-Mesjard et al. / Journal of Physics and Chemistry of Solids 61 (2000) 1499–1507
1505
Fig. 7. Spatial view of the two polymeric chains underlined (shadowed zones) in Fig. 6 in (a) g-TeO2 (real chains) and (b) a-TeO2 (virtual
chains).
5. Discussion
that the spatial arrangement of the molecules during
their condensation into a solid phase would be primarily
governed by electrostatic interactions. Actually, a nega-
tive (oxygen) anion of any molecule would approach a
positive (tellurium) cation of another molecule. It is highly
likely that the way going via tellurium perpendicularly to
the TeO2 plane is the most probable: along this line, the
electron screening of the Te(ϩϩ)–O(Ϫ) attraction is the
smallest. Two oxygen atoms can symmetrically approach
any Te atom along this line, thus forming the two (largely
ionic) Te–Oax bonds with the relevant O–Te–O angle close
to 180Њ.
The present analysis of the structure and the Raman
spectrum of g-TeO2 is mainly aimed at understanding
the peculiarities of the interatomic bonding in this
lattice, and their spectrochemical manifestations. To
compare our results with the properties of the known
TeO2 structures, it is necessary to take into account the
data on an isolated TeO2 molecule [15], as well as the
previous considerations of the lattice dynamics of a- and
b-TeO2 [5].
In gaseous state, TeO2 exists as three-atomic polar
molecules (C2v) in which the double TeyO bonds ꢀL ˆ
Thus, in solid TeO2, the four oxygen atoms are present in
the demi-sphere I of Te atom; jointly with the E pair, they
constitute the TeO4E disphenoid. However, the electron
distribution among the four relevant Te–O contacts is essen-
tially anisotropic in accordance with their nature. The two
shortest Te–Oeq ones evidently correspond to the initial
TeyO covalent bonds of the molecule; their lengths, as a
ꢀ
1:83 A† form an angle of 110Њ [15]. It can be thought
Table 5
Calculated frequencies (cmϪ1), elastic constants Cij (GPa) and the
bulk modulus B (GPa) of the g-TeO2 lattice. The frequencies in
brackets show the positions of the observed vibrations to which
the calculated ones are attributed
˚
rule, lie in interval 1.85–1.95 A, and they form an angle
O–eqTeeq–O of about 100Њ. The two Te–Oax contacts have
lengths in interval of about 2.05–2.20 A and form an angle
A1
A2
B1
B2
Elastic characteristics
˚
close to linear, thus manifesting their ionic nature. Demi-
sphere II includes two O atoms separated from Te by about
2.7–3.2 A and, in fact, it is a part of a spatial cavity serving
56 (66)
104 (77?) 108
119 (116) 127
156 (140) 177 (174) 193
241 (226) 264 231
311 (307) 309 (291) 341
419 (426) 438 430
622 (611) 614 (645) 701
C11 29.6
95 C22 39.8
83 (77?)
121
˚
131 C33 67.0
159 C12 21.7
223 C13 7.7
315 C23 2.3
442 C44 28.6
701 C55 11.6
as a storage of the E-pairs.
The recent quantum mechanical ab initio calculations of
the cluster-like fragments of the a-TeO2 lattice estimate the
˚
bond orders of the Te–O contacts as follows: 1.7 (1.87 A),
˚
˚
0.3 (2.12 A), and ϳ0 (2.9 A) [16]. This is in line with the
results of our lattice-dynamical study of a- and b-TeO2 [5].
In analysing the energetics of the atomic motions in these
702 (683) 752 (752) 806 (812) 758 C66 24.1
B 21.7

1506
J.C. Champarnaud-Mesjard et al. / Journal of Physics and Chemistry of Solids 61 (2000) 1499–1507
two lattices, it was found that: (i) The high-frequency vibra-
tions ꢀv Ͼ 500 cmϪ1† represent the intramolecular Te–Oeq
stretching motions; the number of those vibrations always
corresponds to the number of Te–Oeq bonds; (ii) Among the
Raman-active stretching vibrations, there is always one
with very high intensity which dominates all the spectra.
This is absolutely opposite to the view of the Raman
spectra of typical “homogeneous” framework-like XO2
structures built up from symmetric X–O–X bridges (see,
e.g. Raman spectra of silica [15]). In such structures, the
high-frequency region of the spectra consists of the stretch-
ing asymmetrical vibrations nasym of the X–O–X bridges.
Therefore, they would necessarily have low Raman-intensity,
which is dictated by asymmetrical bond length changes
(within the bridges) inherent for these vibrations; (iii) The
Te–Oax potentials (jointly with O–O ones) dominate the
frequency interval below 400 cmϪ1, thus describing the inter-
molecular forces.
and of nasym of the a-bridges, respectively, whereas the
vibration near 820 cm-1 (attributed to the B1 species) is
more delocalized.
The high intensity of the line near 683 cmϪ1 unambigu-
ously indicates that, from the point of view of crystal chem-
istry, its description as nasym of the a-bridges is not adequate
to “chemical reality”. Actually, this is due to the totally
symmetric pulsation of all the covalent Te–Oeq bonds
˚
(1.86 A), that the line in question has such a high intensity
(such a picture is characteristic for the strongest high-
frequency vibrations in the Raman spectra of a- and
b-TeO2). Formally, those are the asymmetric vibrations
nasym of the Te–eqOax–Te bridges, but in reality the Te–
Oeq bond contribution essentially predominates [5]. More-
over, the calculations show that no vibration can be speci-
fied as nsym of the a-bridge; so the term “a-bridge” has rather
geometrical than chemical sense. In fact, it must be con-
sidered as the strong (largely covalent) Te–Oeq bond
˚
The discussed properties manifest well a quasi-molecular
character of the a and b-TeO2 lattices [5], i.e. the essential
anisotropy of the electron distribution in their TeO4 group-
ings, or, in other words, the strong asymmetry of the chemi-
cal bonding in the Te–O–Te bridges.
(1.86 A) adjusted with the weak electrostatic Te–Oax
˚
contact (2.20 A) interconnecting the above mentioned
helical chains.
The two vibrations of the s-bridge demonstrate other
situation: the line near 426 cmϪ1 (nsym) is rather intense,
whereas that near 611 cmϪ1 (nasym) is much weaker. Thus
this resembles the properties of X–O–X bridge vibrations in
the Raman spectra of such typical (“homogeneous”) XO2
frameworks as various polymorphs of silica [18]. For exam-
ple, the A1-spectrum of a-quartz contains a very intense line
near 464 cmϪ1 and a weak line near 1080 cmϪ1. Those lines
are unambiguously attributable to nsym and to nasym of the
Si–O–Si bridge, respectively [19]. According to our present
treatment of the g-TeO2 spectrum, the two lines near 426
and 611 cmϪ1 are the homologues of the two above
mentioned lines of quartz, respectively.
Let us concentrate now on the data obtained for g-TeO2.
In the light of the issue made above, the central attention
must be paid to the point which differentiates this structure
from the a- and b-TeO2 ones. That is the existence of two
types of Te–O–Te bridges in g-TeO2, respectively, less
symmetric (we call it a-bridge) and much more symmetric
(s-bridge) than the bridges in a- and b-TeO2. In the a-bridge,
˚
the shortest Te–Oeq bond of 1.86 A (close to that in the TeO2
molecule), is alternated with a much longer Te···O axial
˚
contact (2.20 A). In contrast to this, the characteristics of
the s-bridge indicate much more isotropy in the Te–O bond-
ing. This bridge is shorter than any other Te–O–Te bridge
existing in the crystalline lattices of TeO2 and tellurates
Thus the spectrochemical properties indicate that a
Te–axOeq–Te polymerization occurs in the s-bridges,
and is practically absent in the a-bridges. At the same
time, in extrapolating the above mentioned quantum-
chemical estimates [16] of the orders of the different
tellurium–oxygen bonds, it can be thought that, in a-
˚
[17]. The bond lengths (1.95 and 2.02 A) are very close to
their average magnitude, i.e. the bridge is almost
“balanced”.
In contrast to the Raman spectrum of a-TeO2, which
manifests the quasi-molecular character of this lattice [5],
it is likely that the vibrational properties of g-TeO2 indicate
the occurrence of the intermolecular bonding (polymeriza-
tion) within the Te(1)–O(2)–Te(2)–O(2) chain (Fig. 7a).
Let us consider the Raman spectrum of g-TeO2 (Fig. 2)
and focus our attention on the six lines observable above
400 cmϪ1: 426, 611, 645, 683, 752 and 812 cmϪ1. The
assignment of these lines to the calculated vibrations is
given in Table 5. The analysis of their shapes (eigenvectors)
leads us to the following issue: the lines near 426 and
611 cmϪ1 correspond to the totally symmetric combinations
(A1 species) of the nsym and nasym stretching vibrations in the
s-bridges, respectively; the line near 683 cmϪ1 to the totally
symmetric combination (A1 species) of the nasym vibrations
of the a-bridge. The weak lines near 645 and 752 cmϪ1
correspond to A2-combinations of nasym of the s-bridges
˚
bridge, the order of the Te–O (1.86 A) bond is nearly 2,
˚
and that of the Te···O (2.20 A) contact is about ten
times lesser. At the same time, the orders of the
bonds in the s-bridge are much closer to their average
value of about 1. Consequently, the g-TeO2 lattice can
be considered as a chain structure with well-pronounced
covalent bonding along the z-axis, and with mainly
ionic inter-chain interactions. In this case, the lattice
can be compared with the chain structure of crystalline
SeO2 [20] (this latter compound is isovalent to TeO2, and,
in a gaseous phase, also exists as an isolated three atomic
molecule).
The calculated bulk modulus of g-TeO2 (Table 5), mainly
˚
determined by interactions of atoms separated by 2.5–3.3 A,
is found to be about two times lower as that of b-TeO2 and
three times lower than that of a-TeO2.

J.C. Champarnaud-Mesjard et al. / Journal of Physics and Chemistry of Solids 61 (2000) 1499–1507
1507
6. Concluding remarks
dynamical treatment thus interpreting the lines in the
spectrum. In analysing the results obtained, we find that
the g-TeO2 lattice can be considered as a chain system. In
discussing the Raman spectra of a-, b, g lattices jointly with
that of the TeO2 glass, we venture the opinion that chain
character of the structure is well pronounced in the glass.
From the crystal chemistry point of view, the main issue
of the present analysis of the new g-form of crystalline TeO2
is that this material can exist under ambient condition
as a system having a well-pronounced one-dimensional
(intermolecular) polymerization. In jointly considering the
properties of a-, b-, and g-TeO2, it can be concluded that the
electron cloud within the TeO4 grouping has a very variable
character providing the polymorphism of the TeO2 lattices.
Taking into account the high compressibilities of these
lattices, it is likely that the structure and the potential
function relief of any solid phase of TeO2 has to be very
sensitive to the increase of external pressure which would
provoke a homogenization of the electron distribution, i.e.
the Te–Oeq–Te–Oax bond polymerization. Any solid phase
of TeO2 at ambient conditions (including the glass) can be
regarded as an “incipient” framework which would develop
at increasing pressure, in continuously changing the picture
of the interatomic bonding and, most likely, the related
properties, as for example, optic characteristics.
References
[1] E.M. Vogel, M.J. Weber, D.M. Krol, Phys. Chem. Glasses 32
(1991) 231.
[2] T.G. Worlton, P.A. Beyerlain, Phys. Rev. B 12 (1975) 1899.
[3] P.A. Thomas, J. Phys. C, Solid State Phys. 21 (1988) 4611.
[4] V.H. Beyer, Z. Kristallogr. 124 (1967) 228.
´
[5] A.P. Mirgorodsky, T. Merle-Mejean, J.C. Champarnaud, P.
Thomas, B. Frit, J. Phys. Chem. Solids 61 (2000) 501.
[6] A. Jayaraman, G.A. Kourouklis, Pramans—J. Phys. 36 (2)
(1991) 133.
[7] S. Blanchandin, P. Marchet, P. Thomas, J.C. Champarnaud-
Mesjard, B. Frit, A. Chagraoui, J. Mater. Sci. 34 (1999) 4285.
[8] S. Blanchandin, P. Thomas, P. Marchet, J.C. Champarnaud-
Mesjard, B. Frit, J. Mater. Chem. 9 (1999) 1785.
In comparing the Raman spectra of the TeO2 glass with
those of a-, b-, and g-TeO2 crystals, it can be observed (see
Fig. 3), that the band centred near 430 cmϪ1 in the spectrum
of the glass is essentially stronger than the line near
400 cmϪ1 of a-TeO2, and then that at 440 cmϪ1 of
b-TeO2. Therefore, it can be thought that a considerable
contribution to this band comes from nsym vibrations of
symmetric Te–O–Te bridges resembling those present in
the chains of g-TeO2; thus it appears that such chains repre-
sent one of main structural features of the TeO2 glasses. If
so, in the TeO2-glass Raman spectrum, the intensity of the
band near 430 cmϪ1 would increase under hydrostatic
compression, whereas that of the band near 650 cmϪ1
would decrease. We believe that such an idea can be
checked by studying the pressure-induced evolution of the
relevant spectra, and hope that it can stimulate the experi-
mental activity in this direction.
[9] A. Oufkir, P. Marchet, P. Thomas, J.C. Champarnaud-
´
Mesjard, B. Frit, REMCES VIII, Tetouan (Maroc), October
1999.
[10] J. Rodriguez-Carvajal, program Fullprof (ILL), Grenoble,
1990.
[11] G.M. Sheldrick, Acta Crystallogr. A 46 (1990) 467.
[12] G.M. Sheldrick, shelxl-97, Program for the Refinement of
¨
Crystals Structures, University of Gottingen, Germany, 1997.
[13] International Tables for X-ray Crystallography, Vol. IV,
Kynoch Press, Birmingham, 1974.
[14] J.W. Visser, J. Appl. Crystallogr. 24 (1969) 987.
[15] D.W. Muenov, J.W. Hastie, R. Hauge, Trans. Faraday Soc. 65
(1969) 3210.
[16] D. Yakovlev, B. Schegolev, A.P. Mirgorodsky, to be
published.
`
´
[17] B. Jeansannetas, These de l’Universite de Limoges, France,
1998.
[18] K.J. Kingma, R.J. Hemley, Am. Mineralogist 79 (1994) 269.
[19] A.N. Lazarev, A.P. Mirgorodsky, Phys. Chem. Miner. 18
(1991) 231.
In summary, we present the detailed information on the
structure of the new g-phase of TeO2, complemented by its
Raman spectrum. By using these data, we carry out a lattice
[20] K. Stahl, J.P. Legros, J. Galy, Z. Kristallogr. 202 (1992) 99.