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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