TeO2 Glass Structure and Properties

361Physics and Chemistry of Glasses Vol. 42 No. 6 December 2001
Phys. Chem. Glasses, 2001, 42 (6), 361–70
So far only a limited number of publications have been
concerned with the study of the mixed alkali effect in
glasses with the former TeO2. To our knowledge all were
focused on Li2O–Na2O–TeO2 glasses. The importance
of studying such a phenomenon in TeO2 glasses is due to
many industrial and technological applications concern-
ing this type. In the present work five different glass sam-
ples of the system (20-x)K2O.xNa2O.80TeO2 were
selected for the present study, here x=0, 5, 10, 15 and 20
mol%. Bulk density and infrared absorption spectros-
copy were measured at room temperature. Quantitative
evaluation of the infrared absorption spectra showed that
the molecular groups were affected by changing the type
of the nearest neighbour alkali species. AC and dc iso-
thermal electrical conductivity were measured in the tem-
perature range 300–600 K and in the frequency range
0–100 kHz. Electrical parameters such as dielectric con-
stant, loss factor and conductivity were extracted from
these experiments and show mixed alkali effect. The glass
transition temperature was obtained from DTA as well
as from the dc electrical conductivity with a minimum
at Tg=485 K for x=10 mol%. The present results were
discussed in the light of ionic diffusion and interchange
transport mechanism of conduction along with struc-
ture in TeO2 based glasses.
TeO2 based glasses possess excellent optical properties,
as they exhibit good light transmission in the visible
and infrared regions. For this reason tellurite glasses
are important for the construction of optical instru-
ments and thus have become the subject of many in-
vestigations.(1–4)
Also tellurite glasses are good
candidates for many technological applications and
have been widely studied due to their chemical stabil-
ity, high homogeneity, high electrical conductivity and
resistance to devitrification. These glasses also have a
relatively low melting point of about 430°C and hav-
ing a glass transformation temperature of about 220°C
depending on composition.(5)
They are not hygroscopic
with high thermal expansion coefficient and high den-
sity. In tellurite glasses the main glass former is tellu-
rium oxide (TeO2) which has been regarded as a con-
ditional glass former.
TeO2glassiscomposedmostlyof TeO4trigonalbipyra-
mids (tbp’s) in which one of the equatorial sites is occu-
pied by a lone pair of electrons and most of the tellurium
atoms are connected at vertices by Te–eqOax–Te linkage.(6)
The TeO2 glass has a unique structure as a consequence
of the structural unit and its connecting style differs from
conventional glass formers such as B2O3, SiO2, GeO2 and
P2O5. It is expected that TeO2 may have a structural role
differing from the conventional glass formers in binary
glasses which contain network modifiers.(6)
Generally, it was shown that the primary structural
unit of tellurite glasses having high TeO2 content is TeO6
polyhedron;(7–9)
however, this group is seldomly con-
sidered in most recent works.(6)
This together with a
distorted TeO4 tbp and that the fraction of TeO3 trigo-
nal pyramids (tp’s) increases with increasing mono- or
divalent cation content.(6,7)
It was also proposed that
the introduction of Na2O into TeO2 matrix results in a
change of the glass matrix from a three or two dimen-
sional network structure of a lower dimensional one.(10)
On the other hand on addition of Li2O to TeO2, the
strengths of Te–axObonds become weaker and the TeO4
tbp network breaks up accompanied by creation of
nonbridging oxygen atoms (NBOs) in both Te–eqO and
Te–axO bonds.(7,11)
A proposed mechanism for the
change of the coordination number of Te4 +
from 4
through 3+1 to 3 and from 4 to 3 in binary alkali
tellurite glasses was suggested.(6,12)
Although glasses containing TeO2 as the main
former has been extensively studied during the last two
decades, only few of these were concerned with their
mixed alkali effect ‘MAE’. To our knowledge all were
focused on the glass system containing Li2O–Na2O–
TeO2.(13–15)
However, single type alkaline metal intro-
duced into TeO2 glass has attracted much more
attention.(16–18)
When one alkali is progressively substituted for an-
other, the variation of physical properties with the
amount substituted is often nonlinear, giving rise to a
maximum or a minimum. Mixed alkali glass is con-
Mixed alkali effect in the K2O–Na2O–TeO2 glass system
A. A. Bahgat1
& Y. M. Abou-Zeid
Department of Physics, Faculty of Science, Al-Azhar University, Nasr City 11884,
Cairo, Egypt
Manuscript received 9 October 2000
Revision received 9 February 2001
Accepted 23 February 2001
1
Author to whom correspondence should be addressed. (e-mail:
alaabahgat@hotmail.com)

362 Physics and Chemistry of Glasses Vol. 42 No. 6 December 2001
sidered an important class of materials due to its sci-
entific as well as technological aspect.(19)
The most
prominent MAE for oxide glasses is the pronounced
nonlinear reduction in their dc conductivity and the
increase of activation energy as observed for systems
with two or more different types of alkali components.
Nonlinear changes in other properties such as dielec-
tric loss, relaxation and diffusivity are observed, as the
ratios of concentration of different alkalis are varied.(13–
15, 20–3)
For example, it was pointed out that dielectric
relaxation strengths of mixed alkali glasses were larger
than that of a single alkali glass which contain the same
total alkaline concentration.(23)
Recent analysis of elec-
trical relaxation in glasses and melts with large con-
centration of single type mobile ions were treated by
considering the dielectric modulus; M*=M¢+iM≤; and
applying Kohlrausch–Williams–Watts (KWW) distri-
butions of electric field relaxation times.(16–18,24,25)
How-
ever, in a very recent work it was pointed out that the
modulus representation is not a suitable tool for study-
ing transport properties in different ion conducting
materials.(26)
This is because a contribution of high fre-
quency permittivity, e¢(•), is unrelated to ion trans-
port processes and hence the dielectric modulus
formalism should be discouraged.(26)
In mixed alkali MA glasses of Na and K nonbridg-
ing oxygen NBO anionic sites are present. However, it
was postulated that during the cooling of the corre-
sponding melt, Na ions tend to create and exist in sites
of a particular volume with a particular NBO coordi-
nation, while K ions exist in larger sites having on the
average different coordination with respect to NBO.(20)
In the present work five glasses of the system
(20-x)K2O.xNa2O.80TeO2 were selected for the present
study with x=0, 5, 10, 15 and 20 mol%. Bulk density and
infrared absorption spectroscopy were measured. Iso-
thermal dc and ac electrical properties such as dielectric
permittivity and conductivity were also measured.
Experimental procedures
Samples used in the course of this study were prepared
from analytical reagent grade chemicals according to
the molar formula (20-x)K2O.xNa2O.80TeO2 where
x=0, 5, 10, 15 and 20 mol%. High purity 99·995% TeO2
was used while K2O and Na2O were added in the form
of their respective carbonates. The mixture was milled
in an agate mortar and then melted in porcelain cruci-
bles for half an hour to ensure complete homogeneity
and decomposition of the carbonates in a preheated
furnace at 440–460°C according to the composition. The
melt was quenched in air on a hot copper plate. The
materials produced are transparent to light and have
high reflectivity. Visual as well as optical microscopy
investigation indicated the homogeneity of the glasses
without any trace of precipitating crystallites.
Bulk densities were measured at room temperature
using the Archimedes method with carbon tetrachlo-
ride as the immersing liquid (1·593 g cm-3
). Infrared
spectra were measured for samples of equal weights in
the range 300–1400 cm-1
using computerised FTIR
spectrophotometer JASCO (FTIR-300). The infrared
study was performed in order to obtain information
about the main structural groups which form the glass
network and the incorporation of alkali cations within
this network.(4–6)
Differential thermal analyses, DTA,
were collected from room temperature up to 400°C with
a heating rate of 20°C/min.
The ac electrical conductivity, sac, dielectric constant,
e¢, and loss, tan(d), measurements were done using a
computer controlled CRL-bridge (Stanford Res. Model
SR-720) at four different frequencies ranging from 0·12
to 100 kHz. Sample temperature was varied in the range
300–600 K as measured using chromel/alumel type, K,
thermocouple placed near the sample. The disc shaped
samples were polished on both surfaces to be parallel,
then the disc was fixed to the double electrode of the
sample holder and silver paste was used as measuring
electrodes. The thickness of the samples and area of the
contacting electrodes were evaluated. Bulk dielectric re-
laxation processes of three different samples of the same
composition were analysed only if the values of the di-
electric parameters at any frequency and temperature
were independent of the thickness of a sample of fixed
area. This is necessary due to electrode polarisation or
Maxwell–Wagner effect.(27)
The dc electrical conductivity, sdc, was measured in
the temperature range 300–600 K using HP Model
425A electrometer at a fixed applied field.
Results
Bulk density, r, and molar volume for the glass sam-
ples according to the molar ratio Y, [Y=(20-x)/20,
where x =0, 5, 10, 15 and 20 mol%, i.e. Y=K/(K+Na)]
are shown in Figures 1 and 2, respectively. These prop-
erties changed linearly as a function of the glass com-
A. A. BAHGAT & Y. M. ABOU-ZEID: MIXED ALKALI EFFECT IN THE K2O–Na2O–TeO2 GLASS SYSTEM
Table 1. Physical parameters for the glass system
80TeO2.(20-x)K2O.xNa2O where x=0, 5, 10, 15 and 20
mol%, Ni is the ionic concentration. [Y=(20-x)/20]
Y r N Ni a Vmol Tg Tx
K/(Na+K) (g cm-3
) (1022
cm-3
) (1021
cm-3
) (nm) (cm3
/mol) (o
C) (o
C)
0·00 4·89 2·01 2·69 0·363 28·65 246 318, 376
0·25 4·80 2·04 2·73 0·366 29·52 243 340, 365
0·50 4·72 1·99 2·67 0·370 30·36 246 350
0·75 4·71 1·95 2·61 0·371 30·76 252 337, 371
1·00 4·61 1·89 2·53 0·375 31·77 255 389
Density(gcm3
)
4·9
4·8
4·7
4·6
0 0·2 0·4 0·6 0·8 1·0
K/K+Na
Figure 1. Bulk density of the glasses (20-x)K2O.xNa2O.80TeO2 where
x=0, 5, 10, 15 and 20 mol%. The x-axis label represents the fraction
Y according to the ratio (20-x)/20

position. On the other hand, Table 1 presents the cal-
culated ionic concentration, N and the average inter-
molecular separation a=(1/N)1/3.(28)
While molar volume
is given by; Vmol=M/r,where M is the molecular weight
of the glass. Similar behaviour was reported in MA
glasses containing SiO2 as the glass former.(22)
On the other hand five main absorption bands were
observed in the infrared spectra as shown in Figure 3.
The first band at 380 cm-1
is attributed to the original
crystalline TeO2 band at 338 cm-1
but shifted to this
higher frequency due to the probable shrink of the
Te–O bond as a result of increasing of the force con-
stant. A second band at 470 cm-1
is due to Te–O–Z
stretching vibration where Z=Na+1
or K+1
. The two
bands at 670 and 770 cm-1
correspond to the main
vibrations of the TeO4 structure units.(4–6)
These bands
together with an extra band at 610 cm-1
are strongly
superimposed with the band at 670 cm-1
.
Figures 4 and 5 show the dependence of the dielec-
tric constant, e ¢, as a function of frequency, tempera-
ture and composition. The dielectric constant is almost
constant as a function frequency and temperature and
is between 22 and 30 at 400 K and 0·12 kHz as shown
in Figure 6 and Table 2. However, e ¢, is increased con-
siderably as the glass transition temperature, Tg, is
reached, see next.
Figure 7 shows the variation of the loss tangent,
tan(d), as a function of composition at two different
temperatures. It is observed that tan(d) is insignificantly
dependent on composition even at temperatures of the
same order as Tg. This indicates that the value of the
real dielectric constant, e¢, is the controlling factor af-
fecting the ac conductivity sac data even below Tg where
generally
sac=wŒoe¢tan(d) (1)
Here Œo is the free space dielectric constant and w is
the applied frequency multiplied by 2p.
Figure 8 shows an example of electrical conductiv-
ity as a function of frequency and temperature for a
model glass with Y=0·5. It is observed that ln(sdcT)
against 1/T is linear up to the glass transition tem-
perature, Tg. The conductivity is usually applied for
e¢
60
50
40
30
20
300 350 400 450 500 550
Temperature (K)
Figure 4. Dielectric permittivity as a function of temperature and
frequency. Labels A–D correspond to applied frequencies 0·12, 1·0,
10·0 and 100 kHz, respectively
A
B
C
D
Y=0·5
e¢
50
40
30
20
350 400 450 500
Temperature (K)
K/(K+Na)
f=0·12 kHz
1·00
0·75
0·50
0·25
0·00
Figure 5. Dielectric constant as a function of composition and
temperature at a fixed applied frequency of 0·12 kHz
V(cm3
/mol) 32
31
30
29
28
0 0·2 0·4 0·6 0·8 1·0
K/K+Na
Figure 2. Molar volume in units of cm3
/mol as a function of Y for
glasses of the system (20-x)K2O.xNa2O.80TeO2 where x=0, 5, 10,
15 and 20 mol%
¨¨¨¨¨Absorption
A
B
C
D
E
14 13 12 11 10 9 8 7 6 5 4 3×100
Wavenumber (cm-1
)
770
380
670
610
470
Figure 3. Infrared absorption spectra of glasses of the system
(20-x)K2O.xNa2O.80TeO2. Labels A–E correspond to x=0, 5, 10,
15 and 20 mol%, respectively

ionic conducting glass by the relation(28)
sdcT=soe-Wdc/kT
(2)
where Wdc is the activation energy for conduction, T the
absolute temperature, k the Boltzmann and so the pre-
exponential factor having the dimension of (W m)-1
K.
The slope of the ln(sdcT) against 1/T plot produced
the value of the activation energy, Wdc, as shown in
Figure 9. It is observed that the activation energy is
slightly composition dependent up to about 460 K.
Similar observation was reported previously for the
glass system 30[(1-x)Li2O.xNa2O]:70TeO2.(15)
While it
shows a maximum at Y@0·5 at a temperatures near
and above Tg. On the other hand the glass transition
temperature, Tg, was evaluated by observing the change
from linearity of the, ln(sdcT) against 1/T curve which
is evaluated by differentiating the dc conductivity curve,
i.e. d[ln(sdcT)] /d[1/T] and finding the onset which rep-
resents the glass transition temperature. A representa-
tive example is given in Figure 10. All other glasses
show similar behaviour where the infliction point is
considered to indicate, Tg and changes as a function of composition. The glass transition temperature is one
of the fundamental properties related to the viscosity
of the glass and is not directly dependent upon the al-
kali ion mobility. Nevertheless, Tg is considerably af-
fected by MA as shown in Figure 11. The minimum in
Tg implies that the number of NBOs increases due to
formation of (TeO3) trigononal pyramids at the expense
of (TeO4), will in turn facilitate the interchange trans-
port process for the ion migration in the MA glasses.(15)
The present results could be compared with those
obtained by other workers on similar glasses and who
applied different techniques, differential scanning
calorimetery, DSC or DTA, e.g. 85TeO2+5K2O,(5,6)
80TeO2+20Na2O(6,14)
and 70TeO2+30Na2O(6,15)
see Fig-
ure 12. On the other hand as shown, Tg, obtained from
the present electrical conductivity measurements re-
sembling the same trend as obtained previously on the
mixed [Na/Li]:70TeO2 glass DTA measurements.(15)
However, from the present DTA results shown in Fig-
ure 11 the tabulated data, see Table 1, the glass transi-
tion temperature Tg and crystallisation temperatures
Permittivity(e¢)
30
28
26
24
22
0 0·2 0·4 0·6 0·8 1·0
K/K+Na
T=350 K
f=0·12 kHz
Figure 6. Variation of the dielectric constant at 350 K and constant
applied frequency of 0·12 Hz as a function of composition where the
molar fraction K/K+Na=(20-x)/20
tan(d)
0·20
0·15
0·10
0·05
0
0 0·2 0·4 0·6 0·8 1·0
K/K+Na
f=10 kHz
T=490 K
T=440 K
Figure 7. Variation of the loss tangent tan (d) as a function of glass
composition with molar fractions K/K+Na=(20-x)/20, at 440 and
490 K and at applied frequency 10·0 kHz
Figure 8. (a) Representative electrical conductivity as a function of
appliedfrequencyandtemperaturefortheglasssamplewithmolarfraction
Y=0·5. Labels (a)–(e )correspond to applied frequencies 0·0, 0·12, 1·0,
10·0 and 100 kHz, respectively. (b) ln–ln plot of the ac conductivity as a
function of frequency at a constant temperature of 400 K
ln(s(f))
- 4
- 8
-12
-16
1·8 2·0 2·2 2·4 2·6 2·8 3·0
Reciprocal of absolute temperature ×103
Y=0·5
e
d
c
b
a
-14
T=400 K
s=0·70
-16
-18
ln (sdc)
4 6 8 10 12
ln(f) (Hz)
ln(sT)(sm-1
deg)

Tx are given for comparison. As well as the system con-
taining mixed alkali [Na/Li]:80TeO2 glass(14)
both show
an almost independent behaviour on the MA concen-
tration. These results indicate that although Tg ob-
tained from different studies are within the same
temperature interval, the behaviour is dependent on
the technique of glass preparation and measurement
employed. On the other hand Figure 13 shows the vari-
ation of electrical conductivity as a function of com-
position, temperature and frequency. It is clearly
observed that the conductivity is weakly dependent on
composition. However, above or in the vicinity of Tg
the conductivity shows a slight minimum for Y=0·5.
Discussion
Bulk density
Bulk density results show that as the K+1
cations con-
centration increases the glass structure becomes more
open, allowing for the probable formation of increas-
ing number of nonbridging oxygen NBO or defects
within the glass network. This is presented next in more
detail from the infrared absorption results. A possible
cause of this extra molar volume increase may be in-
terpreted qualitatively as being due to the polarising
power strength, PPS, (ratio of valence charge of the
cation divided by the square of its ionic radius). As
the PPS of Na+1
cation is 1·84 times higher than that
of K+1
, this will cause the packing fraction to conse-
quently increase as due to stronger attracting force of
Na+1
cations to O-
anions. In the present glass system
the densities vary from 4·89 to 4·61 g cm-3
revealing a
linear relationship with obvious systematic trend as a
function of Y. This observation could be related to K2O
as replaced gradually by Na2O. The TeO4 tetrahedra is
transformed into a TeO3 triangle because both Na+1
and K+1
cations are introduced within the network of
the glass as a modifier and consequently change the
structural units into NBOs groups, and hence the struc-
tural units change into more open structure.(4)
Here
the composition dependence of the molar volume gives
W(eV)
1·6
1·2
0·8
0 0·2 0·4 0·6 0·8 1·0
K/K+Na
Figure 9. Activation energy as obtained from dc electrical conductivity
at two different temperatures as a function of glass composition
+ T=500 K 400 K
dln(sT)/d(1/T)(eV)
0
0·8
1·6
2·4
3·2
4·0
350 400 450 500 550
Temperature (K)
Tg
Figure 10. Representative variation of the activation energy
[d ln(sdcT)/d(1/T)] as a function of temperature for the glass sample
with molar fraction Y=1·0. The inflection point represents the glass
transition temperature Tg
ExoEndo
DT
Y=1·00
Y=0.75
Y=0.50
Y=0.25
Y=0
200 250 300 350 400
Temperature (°C)
Tg
Tx1
Tx2
Figure 11. DTA thermograms of the present glass system as obtained
with heating rate of 20°C/min
Tg(K)
560
540
520
500
480
0 0·2 0·4 0·6 0·8 1·0
K/(K+Na)
conductivity (present)
DTA (present)
DTA (ref. 5,6)
DTA (ref. 14)
Figure 12. Variation of the glass transition temperature Tg as a
function of glass composition. Several previous results of similar
glasses are also indicated for comparison
Present work 20[(1-x)K2O+xNa2O]:80TeO2
(dc conductivity)
(DTA) respectively
★ 20Na2O.80TeO2, 20K2O.80TeO2,
× 20Na2O.80TeO2

information about the coordination state of the indi-
vidual cations. The observed increase of the molar vol-
ume suggests that most Te cations have on average a
small coordination number because an increase of the
coordination number of tellurium atom would cause
a decrease of the molar volume.
Infrared spectral analysis
In the present infrared spectral analysis we assumed
that an absorption band observed in the spectrum of
a binary and the MA glass having the same
wavenumber as those of a binary crystal and in TeO2
glass is due to the same structure and vibrational
mode.(4–8)
Also both the two end member compositions,
i.e. Y=0 and 1·0, basically contain a high concentra-
tion of NBO.(5,6)
Where mixing the two alkali cations
would on average either increase or decrease the origi-
nal concentration according to the particular structure
group. Here the band at the frequency of 770 cm-1
corresponds to the vibration of the continuous net-
work composed of TeO4 tbps. In this case NBO has
little interaction from adjacent tellurium atoms, so the
corresponding decreasing relative intensity is a func-
tion of bridging oxygen, BO, decreasing concentration
with a minimum at Y=0·5 as shown in Figure 14. The
band at 670 cm-1
on the other hand is assigned to the
antisymmetric vibrations of Te–O–Te linkages con-
structed by two unequivalent Te–O bonds. Generally,
in binary tellurite crystals either or both tellurium at-
oms in this type of Te–O–Te linkage must form TeO4
tbp or TeO3+1 polyhedron.(6,13)
It was suggested recently
by Sekiya et al(6)
that this band indicates a continuous
network structure containing TeO4 tbps and TeO3+1
polyhedra. Therefore the intensity of this band will
probably reflect the fraction of TeO4 tbps and TeO3+1
polyhedra. Figure 14 shows that the relative intensity
of the 670 cm-1
band is almost constant as a function
of K+1
concentration, that is the substitution of Na by
K does not affect the overall concentration of those
structural groups.
The relative intensity of the band at 380 cm-1
shows
a positive deviation from linearity as a function of the
molar fraction, Y, with a maximum relative intensity
at Y=0·5. This particular band was considered as due
to starching vibration of TeO6 group(7–9)
while recently
it was assigned to symmetric bending vibration of the
d-TeO3 group with 3NBOs.(6,16–18)
The observed devia-
tion in the relative intensity is more than two times
(from (2·06±0·5)% minimum to (4·24±0·5)% maxi-
mum) in comparison to the end members' composi-
tions. This observation indicates that the concentration
of the corresponding structure group does change fol-
lowing the same trend, i.e. with a maximum concen-
tration at Y =0·5. It is also noticed that the relative
intensity shown in Figure 14 of the 380 cm-1
band is
acting opposite to that at 770 cm-1
. Consequently, we
can reach the conclusion that additional NBO in mixed
alkali 20[xNa2O.(1-x)K2O]:80TeO2 glasses favours
those oxygen cations sharing the TeO4 groups rather
than those corresponding to the 380 cm-1
group. This
observation will be supported more next.
s(S/m)
1E-5
1E-6
1E-7
0 0·2 0·4 0·6 0·8 1·0
K/K+Na
Figure 13. Variation of dc and ac electrical conductivity as a function
of glass composition and temperature
dc 440 K
dc 490 K
dc 525 K
100 kHz 490K
Figure 15. Variation of diffusion coefficient as obtained by applying
Equation(5) as a function of glass composition at 549 K
Equation (5)
logDs(cm2
s-1|
)
-10·7
-10·8
-10·9
0 0·2 0·4 0·6 0·8 1·0
K/(K+Na)
Absorption(%)
6
4
2
0
32
30
28
26
24
32
28
24
20
0 0·2 0·4 0·6 0·8 1·0
K/(K+Na)
470
380
670
610
770
Figure 14. Relative infrared absorption intensities as a function of glass
composition for the five absorption bands 380, 470, 610, 670 and 770
cm-1
, respectively. The curves are intended only as guides to the eyes

The weak band at about 470 cm-1
is assigned to the
symmetric stretching (and bending) vibrations of
Te–O— Z+
— O–Te linkages where Z+
stands for Na+
and/or K+
cations and were formed by vertex sharing
with TeO4 tbps, TeO3+1 polyhedra and TeO3 tps. It is
suggested that the existence of this band indicates a
continuous network consisting of TeOn (n=4, 3+1 or
3) polyhedra.(6)
The constancy of the 470 cm-1
band
intensity as shown in Figure 14 confirms the result ob-
tained above for the 670 cm-1
band, where substitut-
ing Na+
for K+
cations does not much change the
concentration of the corresponding structural units.
The band at 470 cm-1
however is basically the 380 cm-1
band but developed at this higher frequency due to the
formation of a smaller reduced mass group, where the
Te–O bonds are stretched as the 380 cm-1
units are
part of NBOs. This may be due to the strong field
strength, PPS, of the nearest alkaline atoms where part
of the oxygen anions surrounding the central Te cation
is coupled to an alkali cation instead.
One more observed important feature is the unclear
observation of the shoulder at 565 cm-1
, expected usu-
ally to Te–O vibrations when the O-
anions are con-
sidered as NBO.(4,5)
However, this observation in the
present work seems to be adequate to prove NBO for-
mation, where the band observed at 610 cm-1
is con-
sidered as a superposition of the original main band
at 670 cm-1
and that at 565 cm-1
band. The chemical
disorder, together with anisotropic molecular interac-
tions, results in strong local fluctuating energy barri-
ers acting against reorientational motions which in turn
leads to a broad distribution of absorption bands. The
main TeOn structural group corresponding to the ab-
sorption band at 670 cm-1
is shifted to the lower fre-
quency side as a result of the formation of Te–ONB—( )
link, a result of increasing the apparent reduce mass,
i.e. increasing the 565 cm-1
band width due to increas-
ing the NBO. This is due to the K2O content in the
glass composition being increased gradually. This trend
could be understood also on the basis of harmonic
approximation concepts where we have four main vi-
brational modes with frequencies decreasing in the
order, wTe–O—Te>wTe–O—Na>wTe–O—K>wTe–O—( ). On assum-
ing a fixed force constant, c, the vibrational frequency
is simply w=÷(c/µ)where µ is the reduced mass. The
band at 670 cm-1
shows almost constant intensity as a
function of mole fraction, Y, while the 610 cm-1
band
monotonically increases in intensity as a function of
K+1
cations increases on account of Na+1
cations as
shown in Figure 14.
In other words the infrared spectra collected in Fig-
ure 3 indicates that the structure of the present MA
tellurite glass consists of a continuous network that is
formed by TeO6, TeO4, TeO3+1 and TeO3 which is simi-
lar to other TeO2 based glasses. The probable exist-
ence of a TeO6 group may be considered here to
describe the 380 cm-1
band in order to make the present
results more consistent. The band at 610 cm-1
is con-
sidered as due to either Te–ONB—K or Te–ONB—Na
stretching vibrations mode. This particular observa-
tion supports the conclusion reached above that NBO
favours TeO4 groups rather than TeO6 ones as the K+
cations concentration increases up to Y=0·5.
As has been recognised in many previous works,
vertex sharing TeO4 trigonal bipyramids (tbp–TO3+1)
polyhedra and TeO3 trigonal pyramids (tp) that have
NBO are present and that these structural units com-
prise a continuous network in TeO2 based glass.(6)
Ac-
cording to the band at 610 cm-1
the NBO concentration
increases as the K2O content increases and conse-
quently the structural units change into more open
structure. This is also shown above as a molar volume
increase, Figure 2.
These observations could also be related to the PPS
where it is less for K+1
than for Na+1
as mentioned
above. Such smaller PPS results in easy breaking of
bonds between the K+1
cations and O-
anions to form
a more open structure and increasing amount of NBO,
according to Zachariasen random network.(28)
In conclusion we may say that the band at 770 cm-1
is a direct indication of the BO groups, while the band
at 610 cm-1
correspond to the concentration of the
NBO groups. No doubt both the infrared results and
bulk density as well as molar volume measurements
confirmed each other within the role of MA in the
glass structure. These results show that, as the K+
cation
concentration increases, the glass structure becomes
more open, i.e. less dense. This allows the formation
of an additional number of NBOs with a maximum
concentration at Y=0·5.
Dielectric permittivity
As shown in Figures 4 and 5 the dielectric permittivity
data are gradually increased as the temperature in-
creases. This variation occurs due to decreasing the
bond energies. That is, as the temperature rises two
effects on the dipolar polarisation may occur: (a) it
weakens the intermolecular forces and hence enhances
the orientation vibration; (b) it increases the thermal
agitation and hence strongly disturbs the orientation
vibrations.
The dielectric constant e¢ becomes large at lower fre-
quencies and higher temperatures which is not surpris-
ing in the MA oxide glass system of this kind and is
not an indication of spontaneous polarisation as in
the ferroelectric material.(29)
The correlation between dielectric constant e¢ and
the molar fraction, Y, at frequency f=0·12 kHz and at
T=350 K for all samples is shown in Figure 6. This
shows a negative deviation from the additivity with a
minimum at Y=0·5 and is almost the same as the val-
ues for other TeO2 based glasses.(12)
A similar result
was reached for the MA 20[(1-x)Li2O.xNa2O].80TeO2
glasses.(13)
In addition Figure 7 shows a slight decrease of tan(d)
(loss factor), as a function of the molar fraction at
constant frequency f =10 kHz at 440 and 490 K, re-
spectively. This variation may be interpreted, especially
at higher temperature, on the basis of decreasing the
mobility of Na+
and K+
due to mixing.(22)
The polari-
sation is greater in MA glasses than single alkali glasses,
this polarisation is caused by limited displacement or
stoppage of moving charge carriers (alkali ions). Ap-
parently, many alkali ions in MA glasses are being

stopped during their transport. On the other hand de-
creasing tan(d), may refer to increasing of NBO groups
causing a decrease in the mobility of ionic transport
and consequently decreasing the electrical conductiv-
ity as well be shown next. On the other hand, it is ob-
served that the present values of tan(d) are one order
of magnitude higher than those reported previously
by Komatsu et al(14)
for Li/Na mixed alkali TeO2 glasses.
This may be due to the strong influence of the method
of glass preparation procedure. However, it should be
pointed out that the MA tellurite glasses still hold the
characteristic properties of high dielectric constant and
small dielectric losses in comparison with glasses con-
taining transition metals.(23)
Electrical conductivity
AC conductivity
Obviously there are two distinctly different contribu-
tions to sac(w). One of them corresponds to hopping
motion of the mobile ions and is effective at relatively
low frequencies while the other is given as iwŒoe¢(•)
and is due to much faster polarisation processes, i.e.
vibrational or electronic, where e¢(•) corresponds to
the optical dielectric constant.(26,28)
Actually these two
contributions have an integral effect on the conductiv-
ity only at very high frequency in the infrared and op-
tical regions, i.e. f>106
Hz. The hopping part of the
conductivity may be given by a power law,
s(w)=sdc+Aws
, where the frequency exponent, s, is
usually a decreasing function of temperature, and
s£1·0.(28)
As can be seen from Figure 13 the ac conduc-
tivity is almost constant as a function of MA ratio
even in the vicinity of the glass transition temperature
while Figure 8(b) shows the variation of sac(f) as a
function of frequency, f, at a selected temperature of
400K. It is observed that the power law is applied and
the exponent is s=0·7.
DC conductivity
Generally, Equation (2) for ionic conductivity is given
according to Elliott(28)
as
2 2
i o
dc dcexp /
6
N e R
T W kT
k
(3)
where Ni is the number of mobile ions per unit volume
and Wdc the activation energy associated with ionic
hopping distance R and vibration frequency uo. It was
shown above that the distribution of either K or Na
ions are manifested by changes in the ion oscillation
frequencies in the near infrared. A model that places
special emphasis on the mobile ion oscillation fre-
quency is the free ion model introduced by Rice &
Roth(30)
to describe ionic conduction in crystalline
superionic conductors. According to this model an
energy gap, Wo, exists above which the mobile ion of
mass Mc can be thermally excited from its localised
ionic state to a free-ion like state. In the mth
excited
state the ion propagates with velocity nm and energy
Wm=(Mcn2
m)/2. Because of the interactions with the
rest of the solid the ion in the excited state loses energy
and turns eventually to its localised state. The excited
state on the other hand is characterised by a life time,
tm, during which the mobile ion travels a mean free
path lm given by lm=nmtm. For ion hopping one can
replace nm
2
by R2
uo
2
. Then the gap Wo is identified with
Wdc, the mean free path lo with R, and the inverse life
time 1/to with uo. Therefore the kinetic energy of the
mobile ion at the energy gap is, Wdc=McR2
uo
2
/2. We see
that this assumption ignores the effect of the potential
barrier due to the dielectric permittivity of the host.
Assuming that the ion (Na+1
and/or K+1
) should over-
come an electrostatic potential barrier due to the lo-
calised charges of the oxygen anions cage surmounting
of Coulomb type and gain a kinetic energy to diffused
to occupy new location. Accordingly, on the basis of
electrostatic principles(30,31)
Rice & Ross relation may be
modified to include a potential energy part such that
2 2 2
c 0
dc
o2 4
M R ne
W
r
(4)
where Œo is the free space dielectric permittivity, e¢ the
real dielectric constant and n the number of nearest
neighbors O-
anions (i.e. oxygen coordination number)
to the alkaline cations within an oxygen cage of an
average radius, <r+->, between cations and nearest
anions, Z+
–Z-
, including the molar volume effect. As-
suming that Na+
–O-
NB distance as 0·235 and 0·273 nm
for K+
–O-
NB distance respectively.(13,29)
Table 2 presents
calculated data from the electrical conductivity meas-
urements. Here uo was taken as the Debye frequency
and equals 1·14×1013
Hz and corresponds to an infra-
red absorption at 380 cm-1
. It is shown that the hop-
ping distance R as evaluated applying Equation (3) is
three times as large as the intermolecular separation,
a, and larger than the Z+
–Z-
distance. This observa-
tion indicates that there are accessible amount of va-
cant places for the alkaline ions to hop in.
Consequently, we may assume here that all the alka-
line ions are capable of electrical conduction. A rela-
tively simple relation of this kind between the infrared
absorption frequency uo and activation energy for ionic
conductivity is an attractive feature of free ion model.
A similar relation for the electrostatic potential bar-
rier was derived and applied for glasses.(32,33)
The jump-
ing distance, R, is obtained by assuming a homogenous
distribution of the ions and given in Table 2. Different
values of n were consequently evaluated for this par-
ticular band, see Table 2. Both the atomic mass of the
alkali atoms, Mc, and <r+ -> were obtained by assum-
ing linear variation with the fraction Y. While the di-
electric constant data were extracted from the present
results applying independent, ac measurements at 0·12
kHz. The present results correlate the infrared absorp-
tion to the electrical properties, both the ac and dc,
and can be used to explain quite well why the 380
cm-1
band relative intensity shows a deviation from
additivity as the K+1
concentration increases as ob-
served from the infrared spectra, see Figure 14. This
together with the results of free volume shown in Fig-
ure 2 indicate as explained above a more open struc-
ture with higher molar volume as K+
cations replaces
Na+
cations.

It is seen from Table 2 that the evaluated coordina-
tion number, n, shows a negative deviation from
additivity with a minimum at Y=0·5. This may be ex-
plained by noting that not all NBOs are directly cou-
pled to alkali cations, while creating oxygen anions with
dangling like bonds(20)
and utilising the nonbonding
lone pair electrons associated with TeO4 structural
group.(5)
Although the concentration of NBO shows a
maximum at Y=0·5, leaving space for alkali cations to
form oxygen clusters of smaller coordination number
in order to preserve the net charge neutrality.
Diffusion coefficient
Generally, the dc conduction in alkali containing
glasses is closely related to ionic diffusion. It is possi-
ble to obtain one quantity from the other using the
Nernst–Einstein relation(18,29)
sdc=Nie2
Ds/kT (5)
where Ds is the diffusion coefficient of alkali species,
Ni the alkali concentration (see Table 1), e the elec-
tronic charge, k Boltzmann constant and T the abso-
lute temperature. Equation (5) indicates that the unique
compositional dependence of dc conductivity of the
MA glasses is equivalent to the unique compositional
dependence of the diffusion coefficient and can be de-
rived from strictly kinetic consideration.(36)
Deviations
from this equation occur which can often be ascribed
to effects of structure or mechanism of transport. It
should be noted that the contribution to sdc from ions
that form part of the network (Te and oxygen) would
be negligibly small as their diffusion coefficients are
much smaller than those of the alkali ion.(35)
At a given
temperature e.g. 549 K as shown in Figure 15, the dif-
fusion coefficient shows a minimum at Y=0·5, a phe-
nomenon observed for several MA glasses.(37)
In the temperatures range 300 up to 490 K our ex-
perimental results are best described by a relation of
the form Ds=(3·54±0·4)×10-3
exp(-Wdc/kT) cm2
/s.
Uncertainty is within 10% depending on the glass com-
position. This relation shows that the pre-exponential
factor, Do, is about four to nine times higher for the
two end members compositions in comparison with
similar MA silicate glasses,(37)
while the activation en-
ergy, Wdc, is of the same order.(37–40)
Deviation in the
value of, Do, could be related to the low glass transi-
tion temperatures and melting points of the present
glass system. It is also noticed that the calculated val-
ues of the diffusion coefficients, Ds according to Equa-
tion (5) are of the same order of magnitude as those
mixed Na–K silicate glasses at about 400 K.(32)
The
analogy of the present diffusion coefficient as com-
pared with other types of MA glass indicates that the
conduction in the present system is mainly due to ionic
diffusion. The alkali diffusion in Te glasses is an inter-
esting point of research and needs further study ap-
plying the radioactive isotopes technique.
Conclusion
Electrical conductivity and dielectric properties were
examined in (20-x)K2O.xNa2O.80TeO2 was selected for
the present study. In all these properties the MA effect
was clearly observed. The concentration of nonbridg-
ing oxygen in a glass is an important contributory fac-
tor in the development of such an effect.(16)
It has been
possible, however, to determine whether the O-
ions
exert their influence by acting merely as relatively sta-
ble sites within the glass network for the closer congre-
gation of dissimilar alkali ions as they take a more
participatory role in the MA interaction. This is clearly
seen by evaluating the oxygen coordination number
shown in Table 2.
The deviations from additivity in the electrical con-
ductivity, activation energy and diffusion coefficient
were observed at high temperature. While strong MAE
is observed at low temperature for properties such as
dielectric constant and infrared absorption spectral
intensities. This indicates that the mobility of K+
and
Na+
cations in alkali tellurite glasses also reduces due
to mixing, similar to other types of oxide glasses but
not as strong. The mechanism of mixed alkali effect
and structural information reveals that the interchange
transport process operates in mixed alkali tellurite
glasses. The almost constant activation energy suggests
that the ions move through the interchange transport
process due to increasing the number of NBOs. Also
the present results showed a minimum in Tg implying
that the number of NBOs increases due to the forma-
tion of (TeO3) tripyramid in mixed alkali glasses.
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Y Wdc ln so R (nm) e¢ <r+ -> n
K/(K+Na) (eV) (W-1
m-1
deg) (Eqn.(3)) (at 120 Hz) (nm) Eqn.(4))
0·00 0·985 16·40 1·18 29·5 0·235 10·05
0·25 0·991 16·00 0·95 25·4 0·248 6·31
0·50 0·943 15·85 0·88 22·3 0·259 5·46
0·75 0·960 15·82 0·88 24·0 0·269 7·40
1·00 0·965 15·79 0·88 25·8 0·273 9·06

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