CHAPTER 4
DIELECTRIC CONSTANT AND kc. CONDUCTIVITY STUDIES ON
Ca0-B20341203-Na20 AND CaO-B20+i1203-Fe203 GLASS SYSTEMS
CHAPTER 4
DIELECTRIC CONSTANT AND A.C CONDUCTIVITY STUDIES ON
CaO-B 0 -A1 0 -Na 0 AND CaO-B 0 -A1 0 -Fe 0 2 3 2 3 2 2 3 2 3 2 3
GLASS SYSTEMS
4.1. Introduction
Dielectric characteristics of glasses are of
increasing importance as the field of solid state
electronics continues to expand rapidly. The principal
applications of glassy dielectrics are as capacitance
elements in electronic circuits and as electrical
insulators. For these applications the properties of most
concern are the dielectric constant, dielectric loss
factor, and the dielectric strength. New devices and new
applications are continually increasing the frequency
range and the range of environmental conditions,
particularly temperature, that are of practical interest.
Numerous publications have been devoted to the study
of dielectric constant, a.c. conductivity and other
properties in the alternating fields in alkali oxide
containing oxide glasses[l-31, transition metal oxide
containing semiconducting glasses[4-71 and in a wide range
of superionic glasses[8-111. The study of dielectric
properties of glasses has attracted a great deal of
attention because of their promising utility in various
fields of interest to human beings. Due to their
application in solid high energy density batteries[l2,13]
and in some electrochemical devices[l4,15], the superionic
conducting glasses are extensively studied. The
frequency dependent conductivity and dielectric constant
provides important information on the ionic or electronic
transport mechanism in disordered materials. It can give
an insight into the structure of the materials since the
localised electronic states within the material are
created due to the presence of disorder in the atomic
configuration and/or the composition.
This chapter is divided into three parts. Part I
gives a brief review of the dielectric constant and a.c
conductivity studies in alkali oxide containing and
transition metal oxide containing oxide glasses. Part I1
gives a detailed account of the present studies conducted
by the author on the dielectric constant and a.c
conductivity of the quarternary glass system CaO-B 0 - 2 3
A1 0 -Na20. Part 111 is a detailed description of the 2 3
study of dielectric constant and a.c conductivity of the
quarternary glass system CaO-B 0 -A1203-Fe203. 2 3
PART I
REVIEW OF DIELECTRIC CONSTANT AND A.C CONDUCTIVITY STUDIES
ON OXIDE GLASSES CONTAINING ALKALI/TRANSITION METAL OXIDE
4.2. Review
A brief report of the dielectric constant, dielectric
loss and a.c. conductivity studies on inorganic oxide
glasses containing alkali oxide or transition metal oxide
is given in this section.
Study of a.c conductivity of several systems of
chalcogenide glasses and oxide glasses containing
transition metal oxide[5-81 have been reported. But
comparatively less work have been reported on inorganic
glasses containing alkali oxide. Bottger et a1.[9]
has reviewed the work up to 1976 on the hopping
conductivity in ordered and disordered solids.
It is observed that the dielectric constant,
dielectric loss, a.c electrical conductivity etc. always
depend on the frequency of the alternating field and the
temperature of the substance. In inorganic glasses
containing alkali oxide, the conduction and the dielectric
relaxation take place as a result of the local motion of
the trapped alkali ions around the non-bridging
oxygens[l0,ll]. However recent experimental and
theoretical advances[l2-151 suggested that the frequency
dependence of conductivity could also be due to the jump
diffusion of mobile ions as in the case of d.c
conductivity.
It is now well accepted that the general condition
for semiconducting behaviour in transition-metal oxide
glasses is that the transition-metal ion should be
capable of existing in more than one valence state, so
that the conduction can take place by the transfer of
electrons from low valence state to high valence state.
Possible oxides include those of Ti, V, Cr, Mn, Fe, Co,
Ni, Cu, Mo and W. The properties of these oxides are
much less fully understood than those of the classical
semiconductors such as silicon and germanium. The
vanadium system has been studied most thoroughly[l6-181
among the above said oxides.
It is not yet clear whether the electrical properties
are best described by an energy-band scheme as indicated
by Morin[l91 for some oxides or by hopping between
localized states as explained by Mott[ZO], and Austin and
Mott[21].
A review of the dielectric properties of glasses
investigated upto 1964 has been given by Mackenzie(221.
Reviews on the conduction processes are made by Mott[ZO],
Austin and Mott[21] and Owen[23]. The investigations on
the dielectric conductivity mechanism in ordered and
disordered solids were reviewed by Bottger et a1.[91 in
1976.
The frequency and temperature dependence of
conductivity, dielectric properties, infrared absorption
and EPR studies of semiconducting phosphate glasses were
reported by Sayer et a1.[8]. The examination of
conduction process in semiconducting phosphate glasses
suggests that a polaron model is applicable with some
evidence that hopping occurs in the adiabatic regime. It
was also found that the polaron interactions have to be
considered[81. Sayer et al. measured the a.c conductivity
and dielectric constant over a frequency range 0.1 -
100 KHz and a temperature range from 77 to 400 K and
observed that the conductivity increased with
temperature. These results were similar to the results
published in the case o f othersemiconducting
glasses[6,24]. At low temperature the frequency
dependence of the a.c conductivity was shown to be of the
f orm GaC O( as where S is about 0.85. This type of
behaviour is well-known in amorphous systems and has been
attributed to the relaxation times arising from local
order[6,24].
The frequency dependence of electrical conductivity
of semiconducting phosphate glasses containing tungsten
were studied by Mansingh et al.[25]. They observed that
the measured a.c conductivity depends strongly on the
frequency according to the relation c C w ] = A OS
where 0 < s < 1. The weak frequency dependence is due to
the contribution of d.c conductivity to the measured a.c
conductivity. Mansingh et a1.[25] also reported that the
conductivity increases with the concentration of the
tungsten oxide content.
a.c conductivity of binary V 0 -P 0 2 5 2 5 glasses
containing 40, 50, 50 and 70 mol% V205 was measured at
temperatures between 100 and 423 K and for frequencies up
to 100 MHz by Murawski et a1.[26]. The results were
interpreted in terms of the Long's polaron hopping model.
The polaron parameters calculated from the above model are
in good agreement with the values obtained by other
means[8].
Bogomolova et a1.[271 reported the a.c and d.c
electrical conductivity studies of some semiconducting
barium vanadate glasses doped with Fe 0 2 3'
The a.c electrical resistivity, dielectric constant,
and dielectric loss of calcium borate glass system
containing the transition-metal oxide (Fe203) was
investigated by Saleh et a1.[28] in order to determine the
conduction models of the system. Saleh et a1.[28]
prepared the glass system containing different iron
concentration of molar composition (70-x)B 0 -30CaO-xFe 0 2 3 2 3
with x upto 32 mol%. The electronic properties are
measured from 77 to 8 0 0 ~ ~ in the frequency range 20 Hz to
100 KHz. They observed that the glasses with Fe203
content less than 20 mol% were amorphous, while those
containing from 20 to 23 mol% were devitrified. It was
also observed that increasing the iron oxide content in
this glass system caused an increase in the d.c
conductivity, the a.c conductivity, the dielectric
constant, and the frequency of the dielectric loss peak.
Thermoelectric power measurements of the glass system
indicated that all glasses studied were n-type. The
experimental results of Saleh et a1.[28] on a.c and d.c
conductivity and its variation with frequency and
temperature support the idea of a hopping conduction
mechanism, for glasses less than 20 mol% Fe203 and a
diffusive conduction mechanism for calcium borate glasses
having Fe203 greater than 20 mo18.
Duran et a1.[29] reported some electrical properties
of phosphate glasses containing alkaline-earth oxide doped
with CuO. They observed a frequency and temperature
dependence on the dielectric constant, loss tangent and
a.c conductivity of the glass system. These properties
are also dependent on the concentration of CuO and hence
+ on the redox ratio Cu /Cutotal.
In 1987, Hassan et a1.[30] reported the a.c
conductivity, (cc), of copper phosphate semiconducting
glasses with different composition. They measured the
dielectric constant, a.c conductivity etc. in the
frequency range from lo2 to lo7 Hz and over the
temperature range from 300 to 513 K. Hassan et a1.[30]
observed a frequency and temperature dependence of
dielectric constant and a.c conductivity of this glass
system. The observed frequency dependence of conductivity
was expressed as G - C ~ ) ~ S where 0.7 < s < 1 up to 1 MHz.
At frequencies above 1 MHz the conductivity obeys an
equation of the form 6 ~ ~ ) d w S where s > 1. The
increase in conductivity at higher frequencies was
explained as follows: As the frequency increases the hops
will become shorter and shorter and in the limit of
interatomic distances, will no longer be randomly
distributed and will settle to a frequency dependence
2 which tends t o w [30].
Electrical conductivity studies (both d.c and a.c) on
semiconducting glasses of presodimium and calcium
containing copper phosphate glasses were reported by
Mohammed et a1.[311.
These glasses exhibit frequency dependence of a.c
conductivity and the main feature of a.c measurements was
that the observed frequency dependence in the measured
range could be expressed as 6 - - Gtotal -6d.c
= A@'. ac
The same type of behaviour was reported by Lynch and
Sayer[32] for vanadium phosphate glasses.
Dielectric properties and internal friction of
borate glass system containing mixed alkali was
investigated by Th. Van Gemert et a1.1331. They observed
that the dielectric properties of mixed alkali borate
glasses are completely analogous to the dielectric
properties of silicate and phosphate glasses. They also
reported a strong linear dependence of the dielectric
properties of the glass system on the concentration of
alkali oxide.
The electric and dielectric properties of ternary
inorganic glass containing alkali oxide (Na20-Mg0-Si02)
were studied by Abelard et a1.[34] over a frequency range
from 1 Hz to 100 K Hz and a temperature range from 350 - 600 K using the impedance spectroscopy. Similar types of
works on dielectric properties were also reported
earlier[35-371. Abelard et a1.[34] observed, a dependence
of dielectric relaxation on the concentration of the
+ . alkali ion (Na Ion). It has been proved that dispersion
+ arises from the motion of alkali (Na ) ions. Experimental
data were interpreted with the help of Continuous Time
Random Walk (CTRW), formalism developed by Sher and Lax
which assumes that all the alkali ions are mobile but with
different mobilities[34].
Kawamura et a1.[381 in 1987 reported some
measurements on a.c conductivity of borate glasses
containing mixed alkali oxides. The complex a.c
conductivity was measured in the range from 5 Hz to
500 KHz and for wide range of temperature. They observed
an increase in the conductivity with the frequency as well
as with temperature. Kawamura et a1.[38] concluded that
frequency dependence of a.c conductivity at lower
frequency region is due to the interfacial impedance or
space-charge polarisation[l2,39]. They also suggested
that the frequency dependence of conductivity in alkali
containing oxide glasses is a kind of dielectric
relaxation and may be due to the local motion of the
trapped alkali ions around the non-bridging oxygens.
Studies on the dielectric constant and conductivity
relaxation of Li20-B203-WO glasses weLr reported by 3
Huang et a1.1401. In ion containing glasses, the
dielectric properties mainly arise from the motion of
ions. The free energy barriers impeding the ionic
diffusion, however, can be expected to vary from site to
site, and hence there may be different ionic motions in
glasses. The first is the rotation of ions around their
negative sites. The second is the short-distance
transport, i.e., ions hop out of sites with low free-
energy barriers and tend to pile up at sites with high
free-energy barriers in the electric field direction in
d.c or low frequency electric field or oscillate between
the sites with high frequency barriers in an a.c electric
field. Huang et a1.[40] have indicated that both the first
and second motions make a contribution to the dielectric
constant of glasses.
The effect of sodium and molybdenum phosphate glasses
have been studied by d.c and a.c conductivity measurements
over a wide temperature range by Tarsikka et a1.[41] in
1990. The observed experimental results indicate that the
electronic contribution to d.c conductivity increases with
molybdenum concentration. It is difficult to seperate the
ionic conduction from electronic conduction. a.c
conductivity measurements reported by them showed a
dependence of a.c conductivity on frequency of the applied
electric field and the conductivity was found to obey the
relation caC = A a S , where s is a parameter. The value
of s evaluated from the relation c
= A m S is
comparable to those evaluated from the hopping over
barrier model[30]. The dielectric relaxation frequency
for these glasses has been observed to be 1.5 KHz in the
temperature range of 100-200 K.
PART I1
STUDY OF DIELECTRIC CONSTANT AND A.C CONDUCTIVITY IN
Ca0-B203-A1203-Na20 GLASS SYSTEM
4.3. Introduction
In this part the author reports a detailed study of
the dielectric constant and a.c conductivity in
quarternary glass system CaO-B 0 -A1203-Na20. 2 3 The
dependence of a.c conductivity and dielectric constant on
the concentrations of Na20, CaO and A1 0 and temperature 2 3
tias studied systematically.
4.4. Experimental Details
4.4.1. Glass composition and measurement of dielectric
constant and a.c conductivity
Three series of the glass system Ca0-B203-A1203-Na20
containing different concentrations of Na 0 , CaO and A1203 2
and of compositions as given below were prepared for the
present investigation:
Series (i) 10 CaO - 60 B203 - 15 A1203 - 15 Na20 ..SSl
10 CaO - 51 B203 - 15 A1203 - 24 Na20 ..SS4
Series (ii) 5 CaO - 65 B203 - 15 A1203 - 15 Na20 ..SCl
20 CaO - 50 B203 - 15 A1203 - 15 Na20 ..SC4
Series (iii) 10 CaO - 70 B203 - 5 A1203 - 15 Na20 ..SAl
10 CaO - 55 B203 - 20 AI2O3 - 15 Na20 ..SA4
Reagent grade chemicals (99% purity or better)
acquired from BDH were used for the preparation of the
glass samples. The glass samples were prepared by
following a procedure exactly similar to that described in
Section 3.6.2 of Chapter 3. Amorphous nature of the glass
samples was confirmed by the X-ray diffraction patterns.
Glass samples of uniform thickness about 1 mm and diameter
about lOmm were selected for the dielectric studies. Both
the faces of the glass samples were polished and coated
with a thin layer of silver paint to act as electrodes.
The electrical measurements of the glass samples were made
6 in the frequency range lo2 to 10 Hz. The dielectric
constant measurements were carried out by holding the
glass sample in a sample holder which could be heated to
different temperatures. The temperature of the sample
which could be maintained constant with an accuracy of
0 0.1 C was measured using a chromel-alumel thermocouple.
Dielectric constant and a.c conductivity measurements were
taken over a temperature range from 300 to 425 K.
Direct measurements of capacitance and dielectric
loss factor tand (D) in the glass samples were made by
a Hewlett-Packard impedance analyser (type 4192A LF)
having a frequency range of 5Hz to 13MHz. In these
measurements an a.c signal of 500 Vrms was applied across
the sample. Zero offset adjustments were made for
different frequency ranges to ensure the precision of the
measurements. Dielectric constant was derived from the
measured values of capacitance after eliminating the lead
and fringe capacitance.
4.5. Results and Discussion
(i) Dielectric constant
The real part of the dielectric constant ( ) of
the glass samples of the Ca0-B203-A1 0 -Na20 system was 2 3
determined for a wide range of composition using the
formula[421
where c, the capacitance of the glass sample in pico
farads t, the thickness of the sample in centimeters and
A, the area of cross-section of the electrodes in square
centimeters. The dielectric constant values obtained at
different temperatures and frequencies are tabulated in
table 4.1 to 4.6. Figures 4.1 to 4.6 represents the
variation of the real part of the dielectric constant
( E' ) with frequency of the glass samples at different
temperatures.
From the figures 4.1 to 4.6, it is clear that the
dielectric constant of all the series of glass systems
increases slightly with increase in temperature. The slow I
variation of the dielectric constant ( E ) with temperature
is the usual trend in ionic conducting materialsr431. The
temperature has a complicated influence on the dielectric
constant. Generally, increasing the temperature of the
material decreases the dielectric polarisation. The
increase of ionic distance due to the temperature
influences the ionic and the electronic polarisation.
Similarly the changes in the ionic polarisation are not
very large even assuming the presence of some dipoles and
their contribution to the dielectric constant[441. From
Debye's theory[44], it is known that the dielectric I
constant ( E ) is proportional to the temperature. Contrary
to this theory the ~eported results[471 indicate a slight
increase in the real part of the dielectric constant with
temperature. The present results are also in good
agreement with the reported results.
Table 4.1 Variation of dielectric constant with frequency for the sample SS1 at different temperatures
Frequency Dielectric constant KHz ..............................................
3231: 348K 373K 398K 423K
Table 4.2 Variation of dielectric constant with frequency for the sample SS4 at different temperatures
Frequency Dielectric constant KHz ..............................................
323K 348K 373K 398K 423i:
.5 13.31 13.61 14.10 14.78 15.39 1 12.91 13.01 13.24 13.45 13.96 10 12.62 12.72 12.91 12.96 12.98 3 0 12.51 12.62 12.86 12.92 12.94 5 0 12.35 12.45 12.79 12.80 12.89 7 0 12.00 12.31 12.59 12.65 12.69 100 12.22 12.47 12.50 12.58 12.40 300 12.13 12.35 12.40 12.45 12.15 500 12.06 12.27 12.35 12.40 12.07 700 12.01 12.23 12.33 12.38 12.01 1000 11.98 12.21 12.30 12.36 11.96 3000 11.97 12.21 12.27 12.35 11.89
Table 4.3 Variation of dielectric constant with frequency for the sample SC1 at different temperatures.
Frequency Dielectric constant KHz ..............................................
323R 348K 373K 398K 423K
Table 4.4 Variation of dielectric constant with frequency for the sample SC4 at different temperatures
Frequency Dielectric constant KHz ..............................................
323K 348K 373K 398K 423K
Table 4.5 Variation of dielectric constant with frequency for the sample SA1 at different temperatures
Frequency Dielectric constant KHz ..............................................
323;; 348K 373K 398K 423K
Table 4.6 Variation of dielectric constant with frequency for the sample SA4 at different temperatures
Frequency Dielectric constant KHz ..............................................
3231: 348K 373K 398K 423K
Log f
Figare.4.l Variation of dielectric constant with frequency for the sample SS1 at different temperatures.
Figure4.2 Variation of dielectric constant with frequency for the sample SS4 at different temperatures.
Log f
Figure4.3 Variation of dielectric constant with frequency for the sample SC1 at different temperatures.
Figure4.4 Variation of dielectric constant with frequency for the sample SC4 at different temperatures.
Figure4.5 Variation of dielectric constant with frequency for the sample S A ~ at different temperatures.
Figure4.6 Variation of dielectric constant with frequency for the sample SA4 at different temperatures.
As is seen from figures 4.1 to 4.6 value of &I
decreases monotonically with the increase of the frequency
of the applied electric field. Since the glass system
+ under the present study contains alkali ions (Na ions),
the dielectric properties mainly arise due to the movement
of these ions. The free energy barriers impeding the
ionic diffusion can be expected to vary from site to site,
so there are different types of ionic motions in
glasses[47]. The first is the rotation of ions around
their negative sites. The second is the short distance
transport, i.e., ions hop out of sites with low free
energy barriers or oscillate between the sites with high
free energy barriers in an a.c electric field. Both the
first and second type of motion make a contribution to
enhance the value of real part of dielectric constant of
the glass samples[44]. The decrease in dielectric
constant with frequency may also be due to the increase in
leakage current which is normally attributed to a
dielectric constant reduction[47]. The variation of€'
must be mainly due to the space - charge polarisation upto lo4 Hz and at higher frequencies it must be due to the
rontributions from ionic, dipolar and electronic
polarisation[46].
It is seen from figure 4.7 that the real part of the
dielectric constant &I increases with the concentration of
Na20 in the CaO-B203- A1 0 -Na20 glass system. When the 2 3
concentration of the alkali oxide is more, the number
+ density of the alkali ions (Na ions) increases and the
structure of the glass system gets modified so as to
benefit the ion motions, there by increasing the
polarisation. These factors lead to an increase in the
dielectric constant[47]. Since the concentrations of
A1203 and CaO are kept constant in the first series of the
glass system, their contribution for the enhancement of
remains almost constant in both the glass samples. Hence
the increase in & I , in the case of glass samples of the
+ . first series must be due to the increase in Na lons[47].
It is also observed from the figure 4.8 and 4.9 that the
value of &' increases slightly with the concentration of
CaO and A1203 respectively (for glass samples belonging to
series ii and iii respectively). This may also be due to
2 + the increased polarisation of Ca and ~ 1 ~ ' ions in the
corresponding glass systems[45,46]. It is inferred that
+ Na ions are much more effective in increasing the value
of than ca2+ or A13+ ions.
Ficpre4.7 Variation of dielectric constant with frequency for different concentrations of Na20.
Figure4.8 Variation of dielectric constant with frequency for different concentrations of CaO.
Figure4.9 Variation of dielectric constant with frequency for different concentrations of A1203.
1G
15.
1 4 .
E' 13.
12
2 3 4 5 G 7 8 Log t
'
Ter?p = 423 Y
& 5 3 4 SAl
.
(ii) a.c. conductivity
The a.c conductivity of the glass samples were
calculated using the formula Cac = d k o , whereo = 2TI f,
f is the frequency of the alternating field applied, 5" ,
the imaginary part of the dielectric constant and
Eo is the dielectric constant of the free space[8,57].
The measured a.c conductivity values of CaO-B 0 - 2 3
A 1 0 -Na 0 glass system containing two different 2 3 2
concentrations of Na20, A1203 and CaO at different
temperatures and frequencies are given in table 4.7 to
4.12. Figures 4.10 to 4.15 represent the variations of
a.c conductivity with frequency at different temperatures.
From figures 4.10 to 4.15 it is obvious that the a.c
conductivity increases with frequency of the applied
field and also with temperature. As the temperature
increases, more and more ions can dissociate and get over
high free-energy barriers to take part in the conduction
and hence the conductivity increases. The a.c
conductivity (6 ) is found to depend on the frequency (U) a c
of the applied a.c field according to the relation:
5 c = A ', where A is a constant, where s, is a
parameter and (a= Znf), the angular frequency. In glass
samples containing an alkali oxide variation in
Table 4.7 Variation of a.c conductivity with frequency for the sample S S 1 at different temperatures
Frequency a.c. conductivity KHz
323K 348K 373K 398K 423K
Table 4.8 Variation of a.c conductivity with frequency for the sample SS4 at different temperatures
Frequency a.c. conductivity KH 2
323K 348K 373K 398K 423K
Table 4.9 Variation of a.c conductivity with frequency for the sample SC1 at different temperatures
Frequency a.c. conductivity KHz
323K 348K 373K 398K 423K
Table 4.10 Variation of a.c conductivity with frequency for the sample SC4 at different temperatures
Frequency a.c. conductivity K H z
323K 348K 373K 398K 423K
Table 4 . 1 1 Variation of a.c conductivity with frequency for the sample SA1 at different temperatures
Frequency a.c. conductivity K H z
3 2 3 K 3 4 8 K 3 7 3 K 3 9 8 K 4 2 3 K
0 .5
Table 4 . 1 2 Variation of a.c conductivity with frequency for the sample SA4 at different temperatures
Frequency a . c . conductivity K H z
Figure.4.10 Variation of a.c conductivity with frequency for different temperatures.(sample SS1).
Figure4.11 Variation of a.c conductivity with frequency for different ternperatures.(sample 554).
-77 log l
Figure4.12 Variation of a.c conductivity with frequency for different temperatures.(sample SC1).
Figure4.13 Variation of a.c conductivity with frequency for different ternperatures.(sample S C 4 ) .
Ficpre4.14 Variation of a.c conductivity with frequency for different ternperatures.(sarnple S A l ) .
Figure4.15 Variation of a.c conductivity with frequency for different temperatures.(sample S A 4 ) .
conductivity with frequency may be attributed to a kind of +
dielectric relaxation of the local motion of the Na ions
around the non-bridging oxygens[lO,ll]. However, recent
experimental and theoretical studies[l2-151 suggest that
the frequency dependent conductivity can also be due to a
t . jump diffusion of the mobile alkali ions (Na Ions) as in
the case of d.c conductivity. Pike[50], ~pringlet[51] and
Elliot[52] have suggested that the frequency dependent
conductivity in alkali oxide containing glasses is due to
the hopping over inequivalent barriers of the charge
carriers in the glass system. At low frequency region the
enhancement of conductivity with frequency may be
attributed to the interfacial imped&?ce or space-charge
polarisation[l2,39]. At higher frequencies, the rate of
increase of conductivity of the glass system studied is
found to be slightly higher and this may be a continuation
of the low frequency process[481. As the frequency
increases the hopes will become shorter and in the limit
of interatomic distances, will no longer be randomly
distributed and the conductivity will settle to a
frequency dependence which tends to w S where s is
slightly greater than unity[8]. This type of behaviour is
well-known in amorphous systems and has been attributed to
the distribution of relaxation times arising from the
disorder[48,49].
Figure4.16 Variation of a.c conductivity with temperature for different concentrations of NaZO and frequency.
Figure4.17 Variation of a.c conductivity with temperature for different concentrations of CaO and frequency.
Figure4.18 Variation of a.c conductivity with temperature for different concentrations of A 1 2 0 3 and frequency.
- -rE -'-5 'S
b . 8'. J G
'
KHz
As it is seen from figure 4.16 that a.c conductivity
increases with concentration of Na20. This is
attributed to the increase in number of mobile carriers
taking part in the conductivity mechanism when the
concentration of Na 0 increases. From figure 4.17 and 2
4.18, it is obvious that a.c conductivity of the glass
system studied decreases with the concentration of CaO and
Al2O3, respectively. This may be attributed to the
blocking action of ca2+ ions in the case of the glass
samples belonging to the second series and due to the
electronegativity of the ~ 1 ~ ' ions for the third series.
4.6. Conclusion
CaO-B 0 -A1 0 -Na20 glasses containing different 2 3 2 3
concentrations of Fe203, CaO and A1203 were prepared.
The variation of dielectric constant and a.c conductivity
(6;;c) was studied over a temperature range from 300 to
425 K. The value of real part of the dielectric constant
and a.c conductivity was found to decrease with the
frequency and increases with temperature and to depend on
the concentration of the constituents.
PART 111
STUDY OF DIELECTRIC CONSTANT AND A.C CONDUCTIVITY IN
Ca0-B203-A1203-Fe203 GLASS SYSTEM
4.7. Introduction
It is now well accepted that the general condition
for semiconducting behaviour in transition metal oxide
containing oxide glasses is that the transition metal ion
should be capable of existing in more than one valence
state, so that conduction can take place by the transfer
of electrons from low to high valence state[52]. The
frequency dependence of electrical conductivity and
dielectric constant of these types of glasses have been
the subject of detailed theoretical and experimental
investigations[53,54]. a.c conductivity (6;;C) due to
hopping conduction has been reported to increase with
frequency) w according to the relation s cacd
where s is a parameter. Such a frequency dependence,
which has been attributed to a wide distribution of
relaxation times due to distribution of jump distanceL551
and barrier heights[50], has been observed in a wide range
of low mobility materials[56]. In this chapter, the author
presents the investigations carried out to study the
frequency and temperature dependence of dielectric
constant ( &' ) and a.c conductivity ( Cat) in CaO-B203- AL o -Fe 0
2 3 2 3 ' Effects of change in the concentration of
Fe203, CaO, and A 1 0 on the values of & and 6ac 2 3
have
been discussed on the basis of the existing theories.
4.8. Experimental Details
Three series of glass samples containing different
concentrations of Fe 0 CaO and A1203 and of different 2 3'
compositions as given below were prepared for the present
study.
Series (i) 20 CaO - 68 B203 - 10 A1203 - 2 Fe203 ..FFl
20 CaO - 62 B203 - 10 A1203 - 8 Fe203 ..FF4
Series (ii) 5 CaO - 80 B 0 2 3
- 10 A1203 - 5 Fe 0 ..FC1 2 3
20 CaO - 65 B203 - 10 A1203 - 5 Fe203 ..FC4
Series (iii) 20 CaO - 80 B203 - 5 A1203 - 5 Fe203 . . F A 1
20 CaO - 65 B203 - 20 A1203 - 5 Fe203 ..FA4
The details of the preparation of the glass samples
are described in Section 3.6.2 of Chapter 3. The
I experimental set up and the measurements of & and loss
factor tan 6 (D) are exactly similar to those given in
Section 4.4.1 of this chapter. The capacitance (c) and
loss factor tan 6 for different samples at different
temperatures were measured.
4.9. Results and Discussion
(i) Dielectric constant
The real part of the dielectric constant ( E' ) was
calculated with the help of the relation[42].
at different temperatures and for different concentration
of Fe203, CaO and A1203. The calculated values of the I
real part of the dielectric constant ( & ) are tabulated
in table 4.13 to 4.18. For a given composition of the
glass system, the value of &' were found to decrease with
temperature. The variation of &I with frequency
and temperature is schematically represented in figures
4.19 to 4.24.
As is seen from figures 4.19 to 4.24, the value of I
dielectric constant ( & ) decreases monotonically with
the frequency of the applied alternating field for all the
glass samples studied. The decrease in the value of
with the frequency may be due to an increase in the
leakage current with the increase in frequency which is I
normally attributed to a capacitance reduction[30]. Since&
is a measure of the capacitance, the value of &' should
decrease with the frequency of the alternating field
applied[ 301.
Table 4.13 Variation of dielectric constant with frequency for the sample FF1 at different temperatures
Frequency Dielectric constant
(KHz) 3231: 348K 373K 398K 423K
Table 4.14 Variation of dielectric constant with frequency for the sample FF4 at different temperatures
Frequency Dielectric constant ........................................... (KHz) 323K 348K 373K 398K 423K
Table 4.15 Variation of dielectric constant with frequency for the sample FC1 at different temperatures
Frequency ~ielectric constant ___________________------------------------ (KHz) 323K 348K 373K 398K 423K
.5 10.58 10.89 11.19 11.50 11.98 1 10.39 10.65 10.81 11.21 11.58 10 10.28 10.50 10.65 11.01 11.22 30 10.17 10.42 10.52 10.95 11.01 5 0 10.12 10.38 10.50 10.87 10.91 7 0 10.06 10.35 10.47 10.76 10.89 100 10.03 10.30 10.41 10.71 10.78 300 10.00 10.27 10.37 10.65 10.74 500 9.95 10.21 10.32 10.61 10.71 700 9.94 10.19 10.30 10.56 10.68 1000 9.92 10.17 10.28 10.53 10.65 3000 9.81 10.09 10.19 10.38 10.49
Table 4.16 Variation of dielectric constant with frequency for the sample FC4 at different temperatures
-- --
Frequency Dielectric constant ........................................... (KHz) 3231: 348K 373K 398K 423K
- .-
700 11.25 11.62 11.75 11.91 11.96 1 OOG 11.21 11.55 11.49 11.85 11.89 3000 11.07 11.14 11.25 11.34 11.38
Table 4.17 Variation of dielectric constant with frequency for the sample FA1 at different temperatures
Frequency Dielectric constant ..........................................
(KHz) 323K 348K 373K 398K 423K
Table 4.18 Variation of dielectric constant with frequency for the sample FA4 at different temperatures
Frequency Dielectric constant
(KHz) 3231: 348K 373K 398K 423K
15'
14
12
2 3 4 5 0 7
Log f
13
12
C'
11
10
Figure4.20 Variation of dielectric constant with frequency for the sample FF4 at different temperatures.
373K . 313K
1 3 I 5 6 7
Loq f
Figure4.19 Variation of dielectric constant with frequency for the sample FF1 at different temperatures.
Figure4.21 Variation of dielectric constant with frequency for thc sample FC1 at different temperatures.
Figure4.22 Variation of dielectric constant with frequency for the sample FC4 at different temperatures.
Figure4.23 Variation of dielectric constant with frequency for the sample FA1 at different temperatures.
14 '
1 3 '
373K
2 -
3 4 5 6 7 0
Log f
F i g ~ r ~ 4 . 2 4 Variation of dielectric constant with frequency for the sample FA4 at different temperatures.
Figures 4.19 to 4.24 represents the variation of
&I with frequency and temperature of the glass samples
belonging to the series (i). It is clear from the I
figures 4.25 that the value of & increases with the Fe203
concentration in the glass system. This may be due to
the increased number of electrons participating in the
polarization process. When concentration of Fe203
increases, the number of electrons involved in the I
polarization will also be more. Since & is a direct
measure of polarisation/unit volume, & should increase
with the concentration of Fe 0 2 3' The value of &' may
also depend on the concentration CaO and A1203. i.e., on
the polarization of ca2+ and ~ 1 ~ + ions in the glass
system. Since the concentration of CaO and A1203 were
kept constant in the glass samples of first series, their
contribution to & remains constant. Therefore, the
variation in 6' must be due to the Fe 0 content alone. 2 3 I
Similarly, it is observed that the value of increases
with the concentration of CaO and A1 0 of the 2nd and 3rd 2 3
series of glass system respectively (figures 4.26 and
4.27). This may also be due to the increased
polarization effect of ca 2+ and A1 3+ ions in the
corresponding systems[46]. In these series of glass
systems, since the concentration of Fe203 was kept I
constant the contribution to & remains almost same in
Fiqurc4.25 Variation of dielectric constant with frequency for different concentrations of ft 0 2 3
Fiqure4.26 Variation of dielectric constant with frequency for different concentrations of CaO.
~iqure4.27 Variation of dielectric constant with frequency for different concentrations of A 1 0
2 3 '
both the series. Similar results of increase in the value
of E with the concentration of transition metal oxide
were reported by many investigators[8,28,30].
(ii) a.c. Conductivity
a.c conductivity was calculated from the relation
given in Section 4.5 of this chapter, in the frequency
6 range lo2 to 10 Hz and over a temperature range 300 to
425 K for Fe203 containing glasses of different
composition. The a.c conductivity values calculated are
tabulated in tables 4.19 to 4.24. The graphical
representation of the conductivity with frequency and
temperatures are as shown in figures 4.28 to 4.33. It
was observed that in all samples CaC increases with
temperature as expected for normal semiconductors. As is
seen from the figures 4.28 to 4.33, conductivity increases
with the frequency of the applied field for all series of
Ca0-B203-A1 0 -Fe203 glass system. 2 3
The conduction in these type of glasses is mainly due
to the polaronic hopping and due to the motion of ions.
Since in the first series, the concentration of CaO and
A1203 were kept constant the ionic conductivity part
remains almost same in these series. Therefore the
Table 4. 19 Variation of a.c. conductivity with frequency for the sample FF1 at different temperatures
Frequency a.c. conductivity
(KHz) 323K 348K 373K 398K 423K
0 . 5
Table 4. 2 0 Variation of a.c. conductivity with frequency for the sample FF4 at different temperatures
Frequency a.c. conductivity ................................................
(KHz) 323K 348K 373K 398K 423K
Table 4. 21 Variation of a.c. conductivity with frequency for the sample FC1 at different temperatures
Frequency a.c. conductivity ................................................
(KHz ) 323K 348K 373K 398K 423K
Table 4. 22 Variation of a.c. conductivity with frequency for the sample FC4 at different temperatures
Frequency a.c. conductivity ................................................ (KHz) 323K 348K 373K 398K 423K
Table 4. 23 Variation of a.c. conductivity with frequency for the sample FA1 at different temperatures
Frequency a.c. conductivity ................................................ (KHz) 323:: 348X 373K 3 9 8 ~ 423K
Table 4. 24 Variation of a.c. conductivity with frequency for the sample FA4 at different temperatures
Frequency a.c. conductivity ................................................
(KHz) 323K 348K 373K 398K 423K
Figure4.28 Variation of a.c conductivity with frequency for different temperatures (sample FF1).
Figure4.29 Variation of a.c conductivity with frequency for different temperatures (sample FF4).
E'igure4.30 Variation of a.c corlductivity with frequency for different temperatures (sample FC1).
~igure4.31 Variation of a.c conductivity with frequency for
different temperatures (sample FC4).
Figure4.32 Variation of a.c conductivity with frequency for different temperatures (sample FA^).
Figure4.33 Variation of a.c conductivity with frequency for different temperatures (sample F A 4 ) .
variation in cat is due to the increase in concentration of Fe203. i-e., due to polaronic hopping. This conduction
mechanism can be discussed as follows. It is now well
accepted that in transition metal oxide containing
glasses, transition metal i'3n must be in more than one
valence state, so that conduction can take place by the
transfer of electron from the low to the high valence
states. In the present glass system containing Fe 0 the 2 3'
ions will be in different localised states and mainly in
Fe2+ state. In these glasses, the conduction may occur by
2 + electrons hopping directly between the occupied (Fe )
3 + and unoccupied (Fe ) sites according to the schematic
representation.
Since in the present work, the glass under study
contains low iron concentration, the above proposed
conduction mechanism may explain the thermally activated
conduction (because of the amorphous nature of the glass),
and in this case the likelihood that a large fraction of
the carrier will be trapped and the potentially high
density of localised states makes it necessary to consider
direct hopping for transport[23,24]. The carrier may be
imagined as spending its time trapped at a particular
localised state and making more or less transition to
neighbouring empty trapsL281.
~t low frequencies the variation of rac was found
to be slightly less compared with that at higher
frequencies. At higher frequencies the hops will become
shorter and, in the limit of interatomic distances, will
no longer be randomly distributed and will settle to a
frequency dependence to = A m s ; 5 > 1 where O = 271f; ac
f is the frequency of the applied alternating field. The
present experimental results on < in this glass system ac
support the idea of hopping of carriers between the iron
ions (Fe 2 + 3+ and Fe ) in the different valence states
following the band model suggested by Austin and Mott[21].
This type of behaviour is well known in amorphous systems
and has been attributed to the distribution of relaxation
times arising from the disorder[49].
From the figure 4.34, it is obvious that increasing
the iron oxide content in the glass system belongs to
series (i) caused an increase in the a.c conductivity.
This may be due to the increased number of electrons
hopping between the states of different valencies. This
type of results which support the idea of hopping
conduction mechanism is reported in oxide glasses
containing transition-metal oxides[28]. Since in this
series of glass samples, the concentration of CaO and
A1203 are kept constant, their contribution in enhancing
the conductivity remains almost same.
Figure4.34 Variation of a.c conductivity with temperature For different concentration of Fe2o3 and . - frequency.
Figure4.35 Variation of a.c conductivity with temperature for different concentration of CaO and frequency.
Figure4.36 Variation of a.c conductivity with ternperatvre for different concentration of A I Z O j 2nd frequency.
In the present study it is also observed from
figure 4.35 and 4.36 that a.c conductivity increases
with the concentration of CaO and A1203 in the 2nd and 3rd
series of glass system respectively. This may be due to
2+ . the increased ionic conductivity by the Ca Ions and the
non-bridging oxygens.
4.10. Conclusion
Ca0-B203-A1203-Fe 0 2 3
glasses containing different
concentration of Fe 0 CaO and A1203 were prepared. The 2 3'
variation of dielectric constant and a.c conductivity with
frequency, concentrations of Fe203, CaO and A1203 were
studied over a temperature range 300 to 425 K. The value
of real part of the dielectric constant was found to
decrease with the frequency and increases with
temperature. Also values of rac was found to be
dependent on the concentration of the constituents and the
frequency.
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