984
O. Noguera et al. / Journal of Physics and Chemistry of Solids 65 (2004) 981–993
largely covalent Te-O bonds with length estimated at about
˚
.85 A. So, by definition, a quantity of those groups must
than atoms of oxygen, will necessarily possess two peculiar
features in the Raman spectrum [6]: (i) its high-frequency
part, occupied by the asymmetric stretching vibrations of the
X–O–X bridges, would have vanishing intensity; (ii)
the spectrum would be dominated by a strong band situated
the middle-frequency range and originating from the
symmetric stretching vibrations of those bridges. The classic
1
necessarily appear in the tellurite anion (right-hand side of
Eq. (3)), whereas they are absent in the a-TeO lattice (i.e.
2
on the left-hand side of Eq. (3)). Since the formation of the
TeO3 group corresponds to the saturation of the co-
ordination spheres around atoms of Te, the maximal value
of the ðnr þ 2mÞ=m ratio in Eq. (3) is equal to three. Such,
indeed, is the case if the modifier with mono-valence (i.e.
weak) cations A is taken in an equimolar proportion with
examples of such XO structures are the silica polymorphs.
2
They always have the strongest Raman scattering in the range
2
450–480 cm , whereas only very weak bands can be
1
2
observed higher than 800 cm [8].
1
TeO , so that Eq. (3) can be re-written as
2
Consequently, if the Raman spectrum of any oxide
structure containing the X–O covalent bonds has strong
bands in the highest-frequency range, whereas the middle-
frequency range is empty or contains only weak bands, it
can be thought that the X–O–X bridges are absent in the
structure, and those strong bands relate to the vibrations of
terminal X–O bonds. (The spectra of ortho-silicate lattices,
A O þ TeO ¼ A TeO ;
ð4Þ
This assures the formation of three Te–O bonds per atom
2
2
2
3
of Te. Consequently, the anion subsystem of the tellurite
lattice on the right-hand side of Eq. (4) would contain only
2
2
the ðTeO Þ ortho-groups.
3
The two following questions are important for our further
consideration: (i) what is the number of Te–O bonds per
one atom of Te on the left-hand side of Eq. (4)? (ii) what
fragment of the paratellurite lattice should be considered as
e.g. of ZrSiO
The spectrum of a-TeO
or of Mg SiO
, beautifully illustrate this).
(Fig. 1b) is dominated by the
4
2 4
2
band in the highest-frequency range, and only very weak
band is seen in the middle-frequency range. So, keeping in
mind the above-mentioned sentences, it can be concluded
that the Te–O bonds in the paratellurite lattice are mainly
terminal ones, and the Te –O –Te bridge polymerisation
its basic structural unit? Traditionally, the a-TeO structure
2
is regarded as a covalently bonded three-dimensional
framework (like the silica polymorphs) made of the TeO4
units called disphenoids. This implies that there are four
Te–O chemical bonds per one atom of Te (two equatorial
eq
ax
is practically absent. In line with this, the ab initio electron
structure calculations [9] of a cluster cut from the a-TeO
˚
bonds are short—1.87 A, and two axial ones are long—
2
˚
.12 A), and all those bonds form the Te–O–Te bridges.
2
lattice reveal that the order of the Te–O axial bonds is much
lower than that of the equatorial bonds (0.3 and 1.7,
respectively).
According to the basic principles of chemistry, the existence
of such bonds is an essential factor for the lattice energy
minimisation, and their number should not be lowered
during the reaction represented by Eq. (4). However, the
Note that the molecular description of a-TeO would
2
imply that the number of Te–O bonds per atom of Te
necessarily increases from two to three during the formation
of the tellurite lattice represented by Eq. (4). Taking into
account the above facts and speculations, we venture the
opinion that the latter description is more chemically
consistent.
framework description of the a-TeO lattice means that the
2
formation of the tellurite lattice, as presented by Eq. (4),
would necessarily lower the number of the Te–O bonds per
one atom of Te from four to three, and thus the adequacy of
such a description to ‘chemical reality’ seems, at the very
least, debatable [6].
Irrespective of the extent to which the a-TeO lattice can
2
There is another view which holds that the a-TeO lattice
2
be considered as a molecular crystal (its dualism is
mentioned in Ref. [6]), it is natural to think that these are
the A–O bonds of the modifier and the weak axial Te–O
can be regarded as a largely molecular structure built up
from the TeO molecules [6,7] which correspond to pairs of
2
the short equatorial bonds in the TeO4 disphenoids.
Consequently, the two long axial bonds of the disphenoids
are considered as (mainly electrostatic) contacts between
oppositely charged extremities of the neighbouring mol-
ecules. Thus, in contrast to the framework description, the
molecular description suggests that there are only two
covalent bonds per one atom of Te, and those bonds are
essentially terminal (non-bridging).
‘bonds’ of a-TeO which would be broken primarily when
2
the compounds indicated on the left-hand side of Eq. (3)
22
begin to melt. Theoretically, nr negative ions O and np
þ2r=p
positive ions A
dipole TeO
the melt during this process. To saturate the co-ordination
carried by the modifier, and m neutral
molecules carried by a-TeO would appear in
2
2
2
2
spheres around atoms of Te, the O anions would react
2
2
with the molecules, thus forming nr TeO pyramid-like
3
To judge which of those two descriptions is more
chemically consistent (and thus to answer the question: are
the Te–O bonds in the paratellurite lattice bridging or
terminal bonds?), we turn our attention to the Raman
dipole ortho-anions.
22
22
TeO þ O ¼ TeO3
ð5Þ
2
If the number of O 2 ions is sufficient to transform all the
2
spectrum of a-TeO (Fig. 1b). It is useful to recall, that any
2
homogeneously polymerized XO framework built up from
2
molecules, i.e. nr ¼ m; the melt would eventually consist of
2
r=pþ
and m ortho-anions TeO : Depending on
3
22
non-linear X–O–X bridges with atoms of X much harder
np cations A