Indian Journal of Pure & Applied Physics Vol. 42. June 2004, pp. 445-451

Ac electrical properties of 60B20

3-(40-x) PbO-xMCI

2 and

50B20

3-(50-x)PbO-xMC1

2 (M=Pb, Cd) glasses

Shajo Sebastian & M Abdul Khadar*

School of Pure and Applied Physics. Mahatma Gandhi University. Priyadarshini Hill s P 0, Kottayam 686 560

*Department of Physics, Uni versi ty of Kerala, Kariavattom P 0, Thiruvananthapuram 695 581

Received 10 Seplelllber 2003; revised 7 Jalluary 2004; accepled 22 March 2004

The glasses 60B ~O,-(40-x) PbO-xMCl2

and 50BP,-(50-x)PbO-xMCI ~ (M = Pb, Cd) contai ning different concentrat ions of PbCl ) and CdCI ) were prepared. The ionic transference number of the glass samples was determined using dc polarization technique. The ionic transference number obtained is nearly I indicating th at the electrical conduction in the glass samples is purely ionic. The dependence of ac conductivity and dielectri c constant on temperature and freyuency was investigated and the electrical moduli were analyzed. The variation of dielectric constant and ac conducti vit y with increase in mole percentage of PbCI

1 or CdCl

1 has been investigated on the basis

of structural changes occ urring in the glass samples .

IPC Code: G 0 IN 33/38 [Keywords: Borate glass , Dielectric constant, Ac conduc ti vi ty, Modulus analysis I

1 Introduction The measurement of electrical conducti vity using

blocking electrode is a powerful method for determining both ionic and electronic conductivity of materi als l . By proper choice of electrodes, either ionic or electronic transport is suppressed in a mi xed conductor and the contribution to the conductivi ty by the non-suppressed transport can be determined. The current through an ionic conducting material in a constant dc field decreases with time2

, because in dc measurements a space charge region is often set up as a result of a parti al blocking of the ioni c current by the electrodes. Therefore, the electrica l characteristics of ionic conducting materials are studied by ac techniques to avoid the necess ity of develop ing the non-blocking ion-conducting electrodes for dc measurements}.

The majority of the research on fast ion conduction has dealt with cationic (lithium or sil ver) conducti vity. Research on ani onic conductors has been limited to on ly a few systems. Schultz and Mizzoni4 reported conducti vity studies in glasses of composition 48.S PbO-29.2 PbX

2-3S Si0

2 (X=F, CI , Br or J). The

results indicated that the conducti vity of these glasses increased when lead halide was subst ituted for lead oxi de. They also observed an increase in the

conducti vity with decreas ing radius of the halide ion. Studies on the tern ary PbO-PbCI

2-Si0

1 system have

been reported by several researchers).? These studies also showed an increase in conducti vity as PbF1 was substituted for PbO. Gressler and Shelbl~ in vest igated PbO-PbF,-B,O, glasses of different compos ition and

- - -' reported that these glasses are anionic conductors with F' ions as the conducting species. The conducti vity mec hani sm has been explained on the basis of direct substitution of flu orine ions for oxygen ions. EI­Damrawil() in vest igated the dc conductivity of xPbC1

2-

(40-x)PbO-60Bp } glasses and observed an increase in conductivity when PbCI

2 replaced PbO. The present

paper reports the study of dielectric constant, ac electrical conductivity and electric modulus of the glass systems 60Bp}-(40-x) PbO-xMCI2 and SOBP,­(S O-x )PbO- xMC I

2 (M = Pb ,Cd) of different

compos iti ons (x = 10, 12.S , I S, 17 .S and 20 mole percentage). The ionic transference number of the glass samples was determined using dc polarization technique. The variation of dielectric constant and ac electrica l conductivity of these glasses with composition over a wide range of frequencies from 100Hz to SMHz and over a temperature range from 300 to 4S0K were studied.

446 INDIAN J PURE & APPL PHYS, VOL 42, JUNE 2004

Table I-Glass composition, sample code and the value of the frequency dependent exponent s at different temperatures

Sample code Gl ass composition

BPPI 60B P ,-30PbO-1 OPbCl1

' BPP2 60BP, -27.5PbO-12.5PbCl1

BPP3 60BP, -25PbO-15PbCI1

BPP4 60BP, -22.5PbO-17.5PbCl1

BPP5 60BP, -20PbO-20PbCI1

BPP6 50BP, -40PbO-IOPbCl1

BPP7 50BP, -37.5PbO-12.5PbCl1

BPP!! 50BP, -35 PbO-15PbC11

BPPY 50BP, -32.5PbO-17.5PbCI1

BPPIO 50BP, -30PbO-20PbCI1

BPCI 60BP, -30PbO-lOCdCI1

BPC2 60BP, -27.5PbO-12.5CdCl1

BPC3 60B p , -25PbO-15CdC11

BPC4 60BP, -22.5PbO-17.5CdCl1

BPC6 50BP, -40PbO-IOCdCI1

BPC7 50BPJ -37.5PbO-12.5CdCI1

BPC8 50BP, -35P.bO-15CdCl1

BPC9 50BP, -32.5PbO-17.5CdCI1

BPCIO 50BP, -30PbO-2OCdCI1

2 Experimental Details 6OBP3-(40-x)PbO-xMCI2 (M=Cd, Pb) and 50BP3-

(50-x)PbO-xMCI2

(M=Cd,Pb) glasses of different compositions (x = 10,12.5,15,17.5 and 20) were prepared from appropriate amounts of analar grade H,BO,. PbO and PbCI2 or CdCI2. The composition of the glass samples along with sample codes is shown in Table I. The calculated quantities of the chemicals were mixed thoroughly in an agate mortar. While preparing glasses containing PbCI2 or CdCI 2•

considerable amount of vapour loss (chlorine) may occur during the melting process. To minimize such a loss, the melting of the charge was done first by heating it in an electric furnace for I hr at 500'C and then transferring the closed crucible containing the charge into another furnace kept at 850 to 950"C depending on the composition of the glasses. The melting process was continued for 15 minute. The mel.t was then poured into a brass mould and was pressed by another brass disc to quench the melt and to obtain

Value of's ' at different temperatures

300K 375K 450K

0.99 0.91 0.88

0.98 0.97 0.86

0.99 0.89 0.83

0.93 0.91 0.8

0.89 0.83 0.79

0.89 0.86 0.83

0.97 0.93 0.78

0.88 0.84 0.74

0.99 0.9 0.85

0.92 0.9 0.85

0.91 0.9 0.77

0.97 0.96 0.92

0.98 0.97 0.91

0.95 0.93 0.92

0.99 0.97 0.94

0.99 0.97 0.93

0.98 0.97 0.86

0.99 0.97 0.85

0.99 0.98 0.91

glass discs of diameter 2 cm and thickness approximately I mm. The samples were then annealed in a furnace pre-heated to 300"C for 3 h and then were allowed to cool to room temperature . The samples were then polished to obtain glass discs of thickness. about 0 .75mm.

A programmable KEITHELY 6 17 electrometer was used for transference number measurements. Both sides of the polished glass samples were coated with graphite electrodes. A constant voltage of 0 .5V was applied to the sample and the instantaneous current through the sample was recorded at intervals of I minute. The measurement was performed at room temperature (30 ± I" C) and at a pressure of 10.3 torr.

For ac conductivity measurements. both sides of the glass samples were coated with colloidal silvell electrodes. The conducting leads were attached to the electrodes and the samples were then encapsulated by non-conducting epoxy coating. The encapsulated samples were immersed in an oil bath (Julabo. GmbH, Germany)

SEBASTIAN & KHADAR : AC ELECTRICAL PROPERTI ES OF GLASSES 447

the temperature of which could be regulated with an accuracy of ± O.I ·'C over the range from - 50 to 200"C. The capacitance , phase angle and impedance were measured using a HIOKI 3532 Z HiTESTER. The die lec tri c constant and ac conductivity of the samples were determined knowing the dimension of the sample.

3 Results and Discussion 3.1 Ionic trallsference Ilumber

The block ing elec trode o r polarization method used fo r the measurement of transference number is o ri g in a ll y due to Wagner l

. The sample and the transference number of which is to be determined was sand wiched between two blocking e lectrodes and a dc vo ltage was applied across the e lectrodes. When the c ircu it is c losed, the instantaneous current U,) is a measure of the total conducti v ity (e lectronic and ionic) of the sample. The time variati on of the current through the sampl e g ives an idea about the polari zat ion at the electrode-electro lyte intelface. The final stabili zed current is the CUITent due to e lectronic conducti vity (i) a lone. T he variat ion of the dc current with time for

60BP.\-30PbO- 1 OPbCI ~ glass is shown in Fig.1 and fo r 60BP,-30PbO-1 OCdCI ~ g lass is shown as an in set to Fig. l . All the g lass samples in the present study showed the simil ar variat ion of current with time.

The io ni c transfe re nce numbe r (t i''') was determined using the relation II :

18

16

14

12

:? .s 10 ... C Q) ...

8 ... ::I U

6 Tirne(min)

4

2

0 0 50 100 150 200 250 300

Time (min)

Fig. 1- PIOl of de currenl ver~us lime for 60B,O,-30PbO­IOPhCl ~ glasses. Insel: Same plol for 60I3p ,-30PbO- IOCdCi ~

glasses

t = (i -i)/i 10 11 (e I

... ( I )

The least square fittin g of the experimenta l data points was performed and it was found that the current (I) through the sample foll ows the law

B C 1= A+-+ -

t I 2

. . . (2)

where A, Band C are constants, and the time I is expressed in minutes and current in nA . The constant A which is the limit of I when l~oc , represents the steady state e lectronic cun'ent (Ie)' g iven by the intercept of the asymptotic line on the current ax is. The value of the current at f = 0 was taken as the tota l current i, due to both the ionic and the e lectron ic contribution . The theoretical curve representing the vari ati on of CU ITent with time given by Eq. (2) is shown as the solid line

in the g raph (Fig. I ). For a ll the samples in the present stud y, the ionic

transference number was found to be g rate r than 0 .98 indicating that the samples were ionic conduc tors.

The real part of the die lect ri c (£') at diffe rent frequenc ies and temperatures were derived from the measured paralle l capacitance (CI') and knowing the geometrical dimensions of the g lass samples using the

ex press I on: , Cp / £=-- -

Eo A

where £0 is the permitivity of free space, I is the thi ck ness and A is the e lectrode area of the sample.

The vari ati on of real part of the die lectri c constant (£') with frequency o f typical g lass samples at different temperature is shown in Fig. 2. The va lues of £' for a ll the four samples are less th an 20 (Fig. 2). Thi s value o f £' agrees with tile va lues of £' reported for othe r borate and si I icate g lasses 12. The di e lectric

constants 11 of g lasses a re usua ll y low, gene ra ll y 4-11 at I MHz and at 20" C.

It can be seen from Fig .2 that the value of £'

decreases monotonicall y with increase in frequency of the applied e lectric fie ld . In silver based fas t ion conducting glass system (Agr-Ag20-Se01-V~O,) , Venkateswarulu el

o/. 14 observed a value of 9 for £' at a frequency 100 Hz

which decreased to 4 at I MH z. The low frequency dispersion in £' in thi s g lass system was attributed to the contribution of charge accumulation at the intelface . At higher frequenc ies, due to high periodical reversa l of the

448 IND IA J PU RE & APPL PHYS, VOL 42, J UNE 2004

24 -, ~~-

~ - . -- BPP1 at 325 K , 22 j -0 - BPP1 at 450 K

I . - BPP6 at 325 K

20 ~ o - BPP6 at 450 K

j -A BPC 1 at 325 K

"1 6 BPC 1 at 450 K

o~ '" - BPC6 at 325 K

16 <:1- BPC6 at 450 K

£' 14 .

12

to

A_~

8 A _

6 2 3 4 5 6 7

IOQ lOf Fig. 2- Variati on of real part or d ielec tric constant £' wit h

rreque ncy 1'0 1' 60Bp,-30PbO- IOMCI , and SOB,O,-40PbO-I OMCI ~ (M=Pb.Cd ) glasses -

field at the interface, the contri bution of charO'e carriers b

(ions) towards the dielectric constant decreased and hence E' dec reased wi th increase in frequencyl·'. The observed decrease in the va lue of E' of the glass samples in the present study can also be attributed to the charO'e b

accumu lati on at the interface at lower freq uencies. At hi gher freq uencies the charges cannot foll ow the fi eld and hence the contri bution of charge carriers towards the dielectri c constant was dec reased.

The effects of frequency and temperature on dielectric constant are not independent " . For all the glass samples in the present study the dielectric constant E'

increases slightly with increase in temperature (fi gure not shown). The slow vari at ion of the dielectric constant with temperature is the usual trend in ionic conducting materials Jf>.

The molecul es can not ori ent themse lves in solid dielectri cs. As temperature ri ses, the orientati on of dipo les is facilitated and the va lue of E' increases " . The ionic polari zation also increases as the temperature increases . The com bined effec t gives a ri se in the dielectric constant at low frequencies which increases wi th increase in tempe rature. Us in g Wag ne r 's po larizati on technique it was found that the charge carriers in the glass samples in the present study are ions. The dc conducti vity due to the hopping of mobile ions becomes important at hi gh temperatures. At lower freq uencies and high temperatures the dielectric constant

24

- . - BPP 1 ,Temp 300K,10KHz

22 - 0 - BPP1 ,Temp 450K, 10KHz

- . - BPP6 ,Ternp 300K,10KHz - 0 - BPP6, Temp 450K,10KHz

20 - . - BPC 1,Temp 300K,10KHz

- t:, - BPC 1 ,Temp 450K, 10KHz

18 - ,.. - BPC6, Temp 300K,10KHz

- \7- BPe6, Ternp 450K,10KHz

16

E' 14

12

10

8

I 6 -,--r , ----'---' 10 12 14 16 18 20

Mole percentage of PbCI or CdCI 2 2

Fig . 3- Vari ation o r rea l part or d ielec tric cu nstant £' with

mole pe rcentage or PbCl ~ o r CdCI ~ ror 60B~O)-30PbO-1 OMCI ~ and SOBp)-40PbO- IOMCl 1 (M= Pb,Cd) g lasses

increases , due to the increased concentration of charge carriers resulting fro m ion jump orientat ion effects and space charge effec ts.

The vari ati on of E' with mole percentaO'e of PbCl b ,

or CdC I ~ is shown in Fig, 3. The value of die lec tric constant initi a ll y increases with inc rease in the concentration of the PbClo or CdC lo and then it is decreased. The observed vall ati on of el i-electric constant (E') with increase in mole percen tage of PbCI, or CdC I

2 can be ex pla in ed on the bas is of d i~'ect

substituti on of PbCI, or CdC I, for PbO. For a given concentrati on of B,O" when PbCI, is substi tuteel ror PbO in B,O,-PbO-PbCI, glass sys t~m, a local chancre

_ .1 _ b

in the glass structure results"'. Substitution of PbCI, for PbO results in direct replacement of one 0 2- ion fOl: two Cl- ions. As more and more PbClo is substituted for PbO, the Cl- ion concentration in the net work increases . In additi on, the ionic rad ius of Cl- ions (0. 18 1 nm) is larger than that of 0 - ions (0 .132nm ). Hence, the g lass network becomes systematica ll y weakened and a more open network is formed as more PbCI

2 is substituted for PbO. For concentrations of

PbClo or CdC!, less than l.'i mole percent, the CI - ions could be accotll modated interstitially in the boron-oxygen

SEBASTI A & KH ADAR : AC ELECTR ICA L PROPERTIES OF GLASSES 449

network. The hopping of mobile CI- ions leads to an increase in the ion jump polarization and hence to an increase in the real palt of dielectric constant. When the concentration of PbCI2 or CdCI" is progressively increased, the CI- ions replaced bridging oxygen ions to f0l111 bridging chl ori ne ions. Hence the movements of CI- ions are res tricted th ereby decreas in g th e ion jump polarizat ion and hence the real part of dielectric constant.

The ac conductivity cr(w) of a material IS g iven by:

cr(w) = W Eo E' tan8

where w=2rrf and f is the frequency of the app lied alternating field , Eo the dielec tri c constant of free space, c' the real part of the dielec tric constant , tan8 is the loss fac tor l7.

The ac conducti vity (crJ of the glass sample in the present study showed frequency dependence, cr,," increases with increase in the frequency (Fig. 4). It has been reported that dispersion in the conducti vity is a direct ev idence for the hopping of charge carriers around the latti ce imperfect ions IX. The di spersion in conducti vity will occur when the carriers are not free to move through the sampl e.

-4

- - - BPPl at300K

- 0 BPP l at 450K

- . - BPP6 at 300K

-5 - 0 - BPP 6 at 450K

- £ - BPCl at 300K

- 6 BP Cl at 450K

- T- BPC6 at 300 K

E -6

u

E -7

-8

-9

2 3 4 5 6 7

Fig. 4-Vari at iun of log ", u " with frequ ency for 60B ~O l-30PhO- IOMCI l and SOBP,-40PbO-I OMCI! (M=Pb,Cd) glasses

The frequency dependence of conducti vity above kHz can be represented by the equation IIJ.

cr,,} w) = A w'

where w is angul ar frequency of the app lied fi eld, A and s are constants. The va lue of s is the slope or the log cr versus log w plot and is reported to be between 0.6 and I for ionic conducti ng material s . The experi­mental results reported by different researchers 20

.2:i

show a wide va ri ati on in the numeri cal va lues of .\' and its temperature dependence .

Two different models are available in the literature to interpret the frequency and temperature dependence of ac conducti vity in glasses . The first model is quantum mechanical tunneling2(1.2x model (QMT) which suggests that cr:) w,T) should increase linearl y with increase in temperature and the frequency exponent s

is given by the express ion s = 1- 4/In( l/w1: ), where 1:

is a characteri stic relaxat ion time which is independent of temperature. The second model is the correlated barrier hoppingN,i1l model (CBH). in which the height of the potential barrier is correlated with inter-s ite separation.

6kT According to thi s model .I' = 1- ------­

W", - kT In (1/ wr)

where Will is the effec ti ve barrier height , T the absolute temperature and k is the Bolt zmann 's constant. The quantum mechani ca l tunneling model g ives a va lue or 0.8 for s and does not predi ct a decrease in its val ue with increase in temperature. But the CBH mode l predicts a va lue of s closer to unity which decreases with increase in temperature . The va lue of s in the present study (Table I) was found to be approx imate ly equa l to I at roo m temperature and it decreased sli ghtl y with increase in temperatu re indicating that CB H model could be considered more appropri ate for ex plaining the ac conducti on in the glass sa mples of the present study.

Usua ll y as the temperature increases the nu mber or ions taking part in conduction mechani sm increases allli causes an increase in conduc ti vity. Bul for the glass sa mples in the present study ac conducti vity remains almost unchanged with temperature up to 450K.

For all the glass samples in the present st udy the <Ie conductivity is almost independent of the concentrati on of PbCI

2 or CdCI

2 (figure not shown ). The dc electrical

properties of lead f1uo roborate (BP,i-PbO-PbF]) glasses were reported by Gressler and Shelby XI} At high boric oxide concentration (greater than 50 mole percentage)

450 INDIA N J PURE & APPL PHYS, VOL 42. JUNE 2004

when PbF~ was substituted for PbO, these researchers observed no sign ificant change in the dc conductivity. Gress ler and ShelbyXY attributed the results on the basis of the direct subst itution of fluorine ions for oxygen ions. Substitution of PbF

2 for PbO resulted in the replacement

of some of bridging oxygen ions by flu orine ions. The replacement of bridging oxygen by bridging flu orine produced no effect on the dc conductivity because in crder to free the fluorine ions to migrate, the bond I:olding the bridging fluorine had to be broken.

In th e present study PbCI :> or CdCI2

was substituted for PbO in the glass systems 60BP3-(40-x) PbO-xMC I

2 and SOBP3-(SO-x)PbO-xMCI

2 (M=

Pb, Cd) similar to the substitution of PbF2

for PbO in B,O,-PbO-PbF, glassesx.9 As more and more PbCI, or

_ .' - -CdCI, was substituted for PbO, CI- ion concentrat ion in rhe network increased and the CI- ions replaced the bridging oxygen ions in the boron-oxygen network . The observed dependence of <J'I<' with increase in mole percentage of PbCI

2 or CdC I ~ may be attributed to the

direct substitut ion of bridging oxygen ions by bridging chlorine ions. Since to generate mobile CI- ions to mi grate through the network the bond holding the ions to the sites is to be broken , the number of mobile ions did not in crease considerabl y with increase in concentration of PbCI2 or CdCI:> and hence <J", was almost independent of the concentration of PbCI

2 or

CdCI ~ .

3.2 E Lectric moduLus anaLysis Electric modulus (M* = I IE*, where E* is the

dielec tric constant) fo rmali sm has become a common method of describing the features of the frequency dependence of ionic conduction in glasses32.35 . A major reason fo r selecting M* for descr ibing elec tri ca l relaxation in glasses is that electrode polari zation and other interfac ial effects which may interfere with the bulk behaviour of a spec imen are suppressed in thi s representat ion".' .

The variation of the imaginary part of the electrical modulus Mil as a function of log frequency for a typical sample is shown in Fig.5. It is seen from Fig.S that the peak hei ght is nearly equal irrespective of temperature, showing that the di stribution of re laxation time is .independent of temperature. The normalized plot of MIIM"lllax against log (jlf;n,,) is shown in Fig.6, where Mil is the value of (the imaginary part of) the

max

elec tric modulus at the peak max imum and !;nax is the corresponding frequency. The overlap of the curves for different temperatures i nd icates the temperature independence of relaxation. As the normalized modulus

peak does not show any sharp d iffe rence with temperature (Fig.6), it can be inferred that there is a single type of conduction mechan ism occurring in the sample throughout the temperature rangeJ

!>. The full width at half maximum (FWHM) for an ideal Debye peak in di sordered ,,7 materi a l (e .g. glasses and

0.030

0.025

0.020

Mil 0.015

0.010

0.005

0.000

"'" .. • ,.i ..

.~ \ 1 · • .. \ \

\ .6. • .. \ ' ,. . . l\ \ \

J. •• \ . \ \ \ . . '.

~.- 400Kl - . - 425K - "' - 450K

~ .. . . .. \ \ "" ..... ... ., ~

... • .• . .a., -----.- .-.. ' ..... ~ ····-·.::··I .. ~ ... ••• 2 3 4

109(f Hz)

l

5

Fig. 5- Typica l plot of variation of imagi nary part of electri c modu lus (M") with frequency for the 50Bp,· (50 .. x)PhO.

xPhCl ~ glass at diffe rent temperatures

M'/M".u

1.1

1.0

0 .9

0

0 .8 0 0

0 0 .7 0

0

0 .6 0

0

0.5

0.4

0 .3

.~Q.~ o f>

0

• 0

[ • 425K o 450K

o • o

• •

• c.

• •

0.2 -+-.-'--'~-r~--.~""-~ ~~~~, ~I~~~ ·0.6 ·0 .4 ·0.2 0 .0 0 .2 0.4 0 .6 0 .8 1.0

Fig. 6-Typica l normali zed plot of imaginary part of electric modulus (M") with normalized frequency for the 50Bp,·(50·

x)PbO-xPbCI1

glass at different temperatures

SEBASTIAN & KHADAR : AC ELECTRICAL PROPERTIES OF GLASSES 451

amorphous thin films) is 1.14, whereas for the present sys tem the FWHM of M* is found to be 1.3 indicating a non-Debye behaviour of the glass .

4 Conclusion

60BP3-(40-x) PbO-xMCI2

and 50BP3-(50-x) PbO-xMCI

2 (M = Pb, Cd) glasses containing different

concentrations of PbCI2

and CdCI2

were prepared . The ionic transference number of mobile ions in the glass samples was determined using dc polarization technique. The ionic transference number obtained is nearly I indicating that the sole charge carriers are ions. The variations of dielectric constant and ac conductivity with frequency, temperature and concentration of PbCI

2

and CdCI2

were studied . The value of dielectric constant was found to decrease with the frequency and increase with temperature. The ac conductivity was found to be strong ly dependent on frequency and slightly on temperature. Also, the ac conductivity was found to be varying only slightly with increase in the concentration of PbCI

2 and CdCl

2• The electric modulus analysis

shows that the dielectric relaxation process in the glasses is of non-Debye type and a single type of mechani sm exists over the temperature range of the study.

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