DIELECTRIC AND ELECTRICAL

PROPERTIES OF SOME

DOUBLE ALKALI

molYbdates/ TUNGSTATES

CHAPTER-6DIELECTRIC AND ELECTRICAL PROPERTIES OF SOME

DOUBLE ALKALI MOLYBDATES/TUNGSTATES

6.1 INTRODUCTION

Electric polarization and electrical conduction processes are explored extensively

using spectroscopic dispersion of dielectric permittivity and associated regions in the

frequency range 10'h Hz to 1011 Hz. The magnitude of the effects and the frequency of

I lie energy absorption associated with the processes depend markedly upon the chemical

and physical nature of the material and the external variables (temperature, pressure, etc.)

at w hich measurements are performed. Dielectric relaxation spectroscopic (DRS) analysis

is used as an important tool to study molecular motions of dipolar molecules in

condensed phases. Whereas, the variation of complex dielectric permittivity with

frequency provides information on the rotational diffusional motions of dipolar

molecules. Whereas, the variation of electrical conductivity with measuring frequency is

used to obtain information on the natural translational diffusional motions of ions in a

material. Thus, the frequency dependent electrical/dielectric properties of various types of

materials are related to molecular processes involving the rotational motions of dipolar

species and translational motions of charged species.

The double alkali molybdates (NaK.Mo04, NaLiMo04, and K.LiMo04) and

tungstates (NaKW04, NaLiW04. KLiW 04) show' different structural forms at room

temperature [1-4]. The recent quest for improved functional materials like high dielectric

permittivity and/or multiferroics has shown upsurge in research on complex oxides.

Among many oxides investigated the molybdates and tungstates of general formula

A 'A "B 0 4 (A '’A") are large and small size alkali cations and B = Mo. W) are hardily

investigated in terms of' their electrical / dielectric properties, except few preliminary

reports on structural phase transitions using dielectric measurements [5-7]. The materials

are very important for electrical measurements due to

(i) They exhibit sequence of phase transitions from high temperature cubic phase to

low temperature ferroelectric distorted orthorhombic and/or monoclinic phase

with intermediate modulated phase.

(ii) The crystal structure of this family is mainly based on a frame work of comer

sharing M0O4/WO4 tetrahedral, and the stability of the cubic phase is supported

either by a disordering of the oxygen atoms or a dynamical liberation of the

tetrahedral groups as a whole.

Detailed crystal structural studies of CsLiMo04/CsLiW04 reveal [7-8] that high

temperature phases are cristobalite whereas low temperature one is tridymite like. Thus,

possibility of different types of skeleton structures in these materials may facilitate fast

ion conduction in them. Therefore, these may be the potential proton conducting ceramics

with great technological importance, especially for their applications as sensors, fuel cells

and steam electrolysis cell. Further, in the rigid framework of (B04)n, the small alkali ion

may transport through open channels. Thus, these materials should show insulating

behavior with significant defect related conductivity. Further, due to highly mobile

character of alkali ions and weak interaction of A7A ”with B 042‘ tetrahedral units, these

cations may be partly or completely missing giving rise to defects. The types of defects

formulated will depend upon chemical composition, chemical bond between (B04)n,

units and alkali atoms and the difference in the ionic radii of A'/A”. Presence of

detects/vacancies makes fast ion conductors possible [9]. Further like many fast ion

conductors such as defects pyrochlores based on Mo/W, these materials also gets

hydrated on exposure to air [10]. Therefore, the electrical/ dielectric studies become

important to understand the charge transport in these materials. Considering the fact that

no systematic investigation is available in literature on the dielectric and related

properties of these ceramics and also the fact that observed dielectric anomaly in earlier

reports may have extrinsic nature and may not be associated with electric polarization

and/or ferroelectric state, we investigated the dielectric properties of some double alkali

molybdates and tungstates.

The characterization of dielectric behavior is very important not only to the

theory of the polarization mechanism but also from application point of view; where

knowledge of the temperature and the frequency dependence of dielectric constant along

with the frequency dependence of dielectric anomaly (if any) are very important. The

relative dielectric constant of the material determines its ability to store electrostatic

energy. The loss tangent indicates the ability of dielectrics to support the electrostatic

field, while dissipating minimal energy in the form of heat. The study of dielectric

properties of samples under investigation as a function of temperature and frequency may

help in identifying these potential applications [1 1].

The dielectric dispersion behavior offers an opportunity to gain vital insight into

the details of ionic conduction processes [12]. Particularly in solids that show dielectric

polarization along with significant electrical conductivity (conducting dielectrics) as it

reveals the interaction of migrating ions with other defects. For ferroelectrics. in general,

the study of electrical conductivity is otherwise important as associated properties such as

piezoelectricity, pyroelectricity are dependent on the order and nature of conductivity in

the materials [13]. Similarly, the electrical impedance formalism helps to understand the

relaxation of defect species and dielectric behavior [14, 15].

Transport and relaxation properties can be described at higher temperatures with

reference to inter-particle interaction [16]. The electrical conductivity studies indicate the

nature of dominant constituent or charge species involved in the conduction on

application ot external electric field. Impedance spectroscopy has been applied

successfully in the investigation of conducting dielectrics/ferroelectric [17]. The

dielectric constant obtained from ac data would be unambiguous and would have a better

physical significance than those obtained from capacitance measurement at chosen fixed

frequencies [ 18].

In the present study, we have undertaken the study of ac impedance data in terms

ol dielectric constant, impedance, electric modulus and conductivity simultaneously.

Electrical characterization is an important part of any material characterization to decide

the suitability of the material for electrochemical, electronic and electromechanical

devices [19]. Impedance spectroscopy (IS) is an appropriate experimental technique to

obtain information about the electrical characteristics of polycrystalline materials [20,

21], The ac electrical conductivity as a function of frequency and temperature for

better understanding of the conduction processes present in the materials [2 2].

6.2 EXPERIMENTAL

Polycrystalline samples of KLiMo04 (KLM), NaLiMo04 (NLM) and NaKMo04

(NKM),KLiW04 (KLW), NaLiW04 (NLW) and NaKW 04 (NKW) were prepared by

solid state reaction technique using high purity carbonates and oxides. The raw materials

used are Na2C 0 3/ K2C 0 3 /Li2C 0 3 (AR grade Loba Chem. 99.9%) and M o03 / W 0 3 (AR

made Sigma 99.9%), in required stoichiometry, as ingredients for the desired materials

were thoroughly mixed in agate mortar for 2 h and calcined in silica crucibles between

500 -550 °C for 6 h. The process of grinding and calcination was repeated twice. The fine

and homogeneous powders of the calcined materials repeated till the pure phase material

is obtained. The calcined powders were used to make cylindrical pellets of diameter 12

mm and thickness discs of 1-2 mm. The pressed discs were finally sintered at 600°C for 6

hours. Formation of pure phase was checked using x-ray diffraction (XRD) method in air

the details of structural analysis are presented. Sintered pellets were polished using fine

emery paper (as described in chapter-4) in order to make both their faces fiat and parallel.

The pellets were electroded with high purity air drying silver paste and used for all

electrical measurements, [by applying a pressure 5><106 pa using a hydraulic press.

Polyvinyl alcohol (PVA) was used as binder to reduce the brittleness of the pellets]. The

dielectric parameters (e, tan6) were calculated using Hioki LCR 3532 High- Tester as a

function of frequency (103-106 Hz) and temperature (3°-300°C) in a continuous scan

mode which was interfaced with a computer for automatic data capture. The temperature

was controlled with an accuracy of ±1°C using microprocessor controlled sample holder.

The ac conductivity was also measured also as a function of frequency and temperature.

All the samples were dried at 100°C for 12 h before each experiment.

6.3 RESULTS AND DISCUSSION

6.3.1 DIELECTRIC STUDY

The Figures 6.1-6.3 illustrate the temperature dependence of (a) real part of dielectric

constant (e‘) and (b) tangent loss in KLiMoO-t. NaLiMo04 and KNaMo04 respectively.

- e'1 kHz- 5 k H z e ' ■ 10ke '- e'50

e'100

100 150 200

Tem perature(°C)

250 300

(a)

2 -

■ tan* tan5k

tanlOk▼ tanlOOk

tandlOOO

8a*ju*.U I150 200 250

Temperature(°C)

300

(b)

l i ” ure 6. 1 : Temperature dependent (a) dielectric constant and (b) tangent loss in

K I J M 0O 4

- • — 1kHz * - f ikHz s 10kHz

- T — 50kHz 100kHz

* / ,

......

T e m p e r a l u r e ( C )

I'.O 200Temperature; C)

(a) (b)

Figure 6.2: Temperature dependent (a) dielectric constant and (h) tangent loss in

N a l . iM o O j

1kHz5kHz 1 0 k Hz

f) 0 k H / 10 0kHz

ta n5 k 1a n 1 Ok lan 1 00kt a n d 1 0 G G

T e m p e r a t u r e ( C )

(a)

T e m p e ra tu re ( C )

(b)

Figure 6.3: Temperature dependent (a) dielectric constant and (b) tangent loss in

KNaMoCXj

There are some reports related to structural phase transitions in these

materials based on the dielectric anomaly [23]. However, systematic dielectric and

impedance analysis of these compositions is not reported so for. Literature survey

indicated no previous report with regard to dielectric dispersion and electrical

conductivity mechanism. The dielectric response of three molybdates materials

investigated has similar behavior; high dielectric permittivities at low temperature

especially at high frequencies are observed. The dielectric constant becomes almost

temperature independent in the temperature range that varies for three samples; tangent

loss is also very high at room temperature and decreases as the temperature increase,

l oss tangent also increases sharply at higher temperatures and low frequencies. In KLM,

a sharp dielectric peak is observed without any corresponding peak in tangent loss. The

high value of loss at room temperature is directly correlated with the ionic radii

difference in two alkali cations in three materials. This indicates that the conduction

mechanism may be due to motion of smaller ion in the channel formed due to comer

sharing of tetrahedra.The increase in dielectric response with temperature may be due to

interfacial polarization dominating over dipolar polarization at higher temperatures. The

observed high values of e* thus may be attributed to the ionic conduction mechanism

being dominant at high temperatures.

Figure 6.4 (a)-(c) illustrates the temperature dependence of dielectric constants for

tungstate samples (a) KLiW04 (b) NaLiW04 and (c) NaKW04 at different frequencies

respectively. The same for tangent losses are depicted in figure 6.5 (a) - (c).

□ele

ctric

C

onst

ant

• 1kHz500 - 5kHz

10kHz450 - ♦ 50kHz

100kHz400 -

E 350; *B 300 '0 •p 250 -I 200 - : •

150 - * •♦ ? A •100 - ■* *.

50 - t*

150 200Termperature(°C)

(a)

1kHz5kHz10kHz50kHz100kHz

..... ******“ * ........................

150 200Term perature(°C)

(b)

i5 40

• 1kHz a 5kHz ■t 10kHz♦ 50kHz

100kHz

***

***** .......ttfij

50 100 150 200 250 300Termperature(DC)

(e)

Figure 6.4: Temperature dependent dielectric constant in (a) K L iW O .! (b) NaLi\VO.|

(c) K N a W 0 4

All the three materials have dielectric response similar to their molybdates

analogues; dielectric constant show strong frequency dispersion at room temperature in

NIAV and KLW, whereas a frequency dependent dielectric peak is observed in NKW at

around 80°C. The reason for high value of dielectric constant at room temperature may be

associated to electrode polarization or conducting ions. With further increasing the

temperature, dielectric constant increases and shows low frequency high temperature

dispersion.

Figure 6.5 (a)-(c) illustrates the temperature dependence of the dielectric loss for

tungstates (a) NaKW04 (b) KLiW 04 (c) NaLiW04at different frequencies. Value of tan5

increases at lower temperature (below 100°C) with decreasing frequency. When the

temperature increases about 100°C to 200°C, tanft is linear with respect to x-axis. But

above the higher temperature range (above 200°C) dielectric loss increases with

decreasing frequency. A small loss peak is observed in NKW. Interestingly, the observed

very high loss tangent values at low temperatures and high frequency in tungstates also

follow the correlation with alkali ionic radii difference. Losses are very high for K L iW 04

(ionic radii difference between K and Li, 6r = 0.62), moderate for NaLiW 04 (§r = 0.26)

and low for NaKW 04 (8r = 0.36). In case of NKM and NKW the low values of dielectric

loss may be understood, despite the higher ionic radii difference, as both ions have ionic

radii large enough to transport through channel without hopping. Thus the results predict

dc conduction mechanism to be dominating at low temperatures. The high values of

dielectric loss at room temperature may also be due to high water absoiption

characteristics of these materials. The kind of temperature dependence of the tan5 is

typically associated with losses by conduction.

1 k H z 5 k H z 10kHz

1 SO 200 2f*0

T em p era tu re (c,C )

(a)

U)M{/r>()kM/1 OOM iz

* • j * A*

ir>o 2oo

T e m p e r a tu r e ( C )

(b)

1 O k H z 5 0 k H z 1 0 0 k H z

(c)

Figure 6.5: Temperature dependent tan 6 in (a) KLi\V04 (b) NaLi\VO.i (c)

KNa\V04

In all the three materials, the rate of change of tan 6 with temperature is

very small (loss almost temperature independent) in the temperature range approximately

I()()"(' ' T 2: 175°C for all tungstates. At higher temperatures, loss increases sharply. The

sharp increase in tan 8 at higher temperatures may be due to scattering of thermally

activated charge carriers and some defects in the samples. At higher temperature the

conductivity begins to dominate, which in turn seems responsible for rise in tanfi.

The high temperature values of dielectric constant as well as that of tangent loss increase

with decreasing frequency. This increase in dielectric response with temperature may be

due to interfacial polarization dominating over dipolar polarization [24]. This also

indicates the onset of some additional relaxation mechanism in the material attributed to

the ac conduction mechanism being dominant at high temperature [25]. For all samples,

contribution of the reorientation of the off-centre ions coupling with the thermally

activated conduction electrons may appear due to ionization of the oxygen vacancies and

results into such response [26]. However, since the samples are sintered at relatively low

temperatures and the oxygen vacancies creation may be rules out.

figs. 6.6 and 6.7 shows frequency dependence of e' and c” for (a) NaLiMo04, (b)

KLiMoO^ (c) NaKMoC>4 at various temperatures respectively.

e '5 0 e'1 00 e'1 50 e ' 2 0 0 e '2 5 0 e ' 3 0 0 e ' 3 5 0 e ' 4 0 0

.. * * «<*«:***» -m

log (

(a)

e'50 e'1 00 e'1 50 e'200 e '250 e '300 e'350 e'400

log( .

(b)

■ e'50• e"IOOA, e '150▼ e'200

e'250« e'300

e'350m e'400

log( ' >)

(C)

■ e "5 0• e "1 0* e " 1 5

▼ e "2 0e "2 5

■« e " 3 0e "3 5

• e " 4 0

lo g (<> )

(a)

8 0 0 0 0 0 0 -

e "5 0 e "1 0 0 e"1 50 e "2 0 0 e "2 5 0 e "3 0 0 e "3 5 0 e "4 0 0

4 0 0 0 0 0 0 -

2000000 -

I o g (< ■)

(b)

■ e"50• e"100 «. e"150▼ e"200

e"250 + e"300

e"350• e"400

1 500000 -I •

1000000 -

3 000000 -

250 00 0 0 -

2000000 -

500000

0 ! ? * «* <r ■* ffWMS—----- ,--------------r-------------- ,-------------- 1-------------- >-------------- 1-------------- ------------

4 5 6

logO *)

(C)

The frequency dependence of dielectric permittiv ity (c') is shown in figure 6.8 and that of

tangent loss in figure 6.9 for three tungstate materials studied.

50 C

io o uc1 50lC

200"c?50UC

300"C

I ! : : :

A () 4 5 5 0 5 5 6 0 (» 5 / 0

l og( <, . )

(a)

50 ('■

1 5 o “ (:

200“(;2 50 °G:u )o “ c;

(b)

log(ro)

50c’C

100°C

,U )()350

400*

(c)

1600000 -

1400000 -

1200000 -

1000000 -800000 -

000000 400000 -

S .

log(ci)

(a)

■ 50 c

• 100 c

150 C

▼ 200 C

250 C

* :<oo 'c

50 C 100 C 150 C 200 C 250 C 300 C

■ 50 C• 1 0 0 C

150 C

▼ 200 C

250 C

■ 300 C

350 C

* 400 C

V - ¥ V Wvvv-

lo9((1) log((..)

(h) (c)

Figure 6.9: frequency dependent dielectric loss in (a) KI.i\V04 (b) NaF iW ()4

(c) NaK\V0 4

Both r.' and r." show strong dispersion at low frequency, especially at high temperatures.

I he dispersion in molybdates is more than in corresponding tungstates. The nature of

dielectric permittivity related to free dipoles oscillating in an alternating electric fields

may he described as follows: at very low frequencies, dipoles follow the field and the real

part of dielectric constant c‘ - t:s ( dielectric constant at quasistatic electric field). As the

frequency increases, dipoles begin to lag behind the field and the dielectric constant

decreases slightly. When frequency reaches the characteristic frequency, dielectric

constant drops. At very high frequencies, dipoles no longer are able to follow the field

and r,' - r., (high frequency value of e’). Qualitatively, this is the behavior observed in the

figures 6.6 and 6.8. The very high values of both the components of dielectric response at

low frequency (1 kHz) may be attributed to the space charge accumulation effect [19].

Such strong dispersions observed in both the components of complex dielectric constant

is a commonly observed features is disordered dielectrics with significant electrical

conductivity and studied in detail by Jonscher et al [27]. It may be noted that low

frequency dispersion in c' is more in NaLiMo04/ NaLiWQ4, whereas dispersion in e“ is

more in KLiMo04/ NaLiW04. This indicates that it is related to the disorder in

tetrahedral ions as seen from vibrational spectral results [28]. The low frequency

dispersion is observed and is interpreted as the conducting process is due to ion hopping.

The high values of e ' at lower frequencies, lower than 1 kHz, which increases in general,

with decreasing frequency and increasing temperature ( as shown in figure 6.8 and 6.9

may be attributed to free charge buildup at interfaces within the bulk of the sample

I interfacial Maxwell-Wagner (MW) polarization) [29]. The contribution of MW process

may be excluded by analyzing the nature of frequency dependent ac conductivity. The

plots of frequency dependent ac conductivity are shown in figures 6.10 and 6.11 for

molybdates and tungstates respectively. A plateau is observed in the plots that mean, the

region is observed where ojc is frequency independent. The plateau region extends to

higher frequencies with increasing temperature. It is the region where dc conductivity

dominates. This shows that MW polarization cannot be responsible the origin of high

value of r/ at low frequencies and higher temperatures as these appears in the region of

dc conductivity [30]. Moreover, atlc decreases with decreasing frequencies and high

temperatures, this drop correlating well with the increase in e’. The very high value of e"

dispersion in comparison to e’ dispersion implies that it may be influenced by dc

conductivity.

Recently, it has been stressed that complex oxides with multivalent ions having electric

polarization and significant electrical conductivity due to defects/vacancies may show

high dielectric permittivity that may not be associated with electric polarization rather

due to defect related conduction processes. In order to understand the contributions of

extrinsic defects (space charge) and/or the intrinsic electric polarization contribution to

the polarization and conduction mechanism, impedance spectroscopy has proved very

useful. We therefore analyzed the impedance equivalent graphs in various representations

to elucidate the contributions of various components to the impedance relaxation.

6.3.2 IMPEDANCE STUDIES

Impedance spectroscopy is used to study the electrical properties of variety of materials.

Polycrystalline materials have variety of frequency dependent effects associated with

heterogeneities. One of the advantages of frequency dependent measurements is that the

contributions of the bulk materials (grains), the grain boundaries and electrode effects can

easily be separated if the time constants (relaxation) involve with them are different

enough [3 1 ]. to allow separation.

I he frequency dependent properties of materials can be described via the complex

permittivity (c*). Complex impedance (Z*) and dielectric loss or dissipation factor (tan6).

Impedance spectroscopy may be a better tool to understand the relaxation process than

the dielectric analysis especially when the contribution of grains is separated from that of

grain boundaries [32]. The impedance data is generally compared or fitted to an

equivalent circuit, which is representative of physical processes taking place in the

system under investigation [33], A general equivalent circuit consists of ideal resistors,

capacitors inductance and various distributed circuit elements. In such a circuit, a

resistance represents the conductive path and given resistance might accounts for the bulk

conductivity of the material. Similarly, capacitance and inductance may be associated

with space charge polarization regions and with specific absorption and electro

crystallization processes at an electrode region [34]. Polycrystalline materials possess

both large grain boundary resistance and small crystallite resistance. The grain boundary

resistances dominate the ac response in the complex impedance plane and completely

mask the effect of grain resistance. In such a situation, complex electric modulus

representation may be used that reflects the response from those elements that have

smallest capacitance (grains). Thus, in this situation the grains effect are prominent and

grain boundary effect are masked. Thus, by comparing the results of two analyses, it may

be possible to separate out the contribution of grains and grains boundaries effectively

I-'H

In order to analyze and interpret experimental impedance data, it is pertinent to choose a

model equivalent circuit that provides a realistic representation of the electrical analog of

the ceramic under study. The choice is made on the basis of the criteria as discussed in

details [36].

A cco rd ing ly , grains/grain boundary each may be represented in terms of equivalent

circu it of parallel RC network connected in series and material with distributed relaxation

times RC' network gives rise to semicircular arc in complex impedance plane, Z* [37].

where Z* = Z ' - j Z "

R "R C/ --- antj / = --------1 i- (\\RC)2 \ + {wRC)2

The variation of real part of impedance (Z‘) as a function of frequency (Nyquist plot) is

plotted at different temperatures in Figs.6.10 for molybdates and in figure 6.11 for

tungstates ceramics respectively.

m Z ' 5 0» Z ' 1 0 0

Z '1 5 0▼ Z '2 0 0

Z '2 5 0Z ' 3 0 0Z ' 3 5 0

• Z '4 0 0

l o g ( ■■ )

(a)

Z '1 0 0 Z'1 50 Z '200 Z '2 5 0 Z '3 0 0 Z '3 2 5 Z '3 50 Z ’4 0 0

* # o »****+

(b)

Z'50 Z '100 Z ’ 1 50 Z ’ 200 Z '250 Z '300 Z'350 Z'400

<4 3 yySSSm

l o g ( , . )

(C)

50 C lOO C 1 50 C 200°C 250rC 300 'C

(a)

50 C1 00 c 1 50' c 200 C 250 t; 300* C

4 5 5 0

log (< .)

6.5 7 0

(b)

1 10 -I

1 00

90 -

80 -

70

GO

50

50' C 100 C 150‘ C 200 'C 250 C 300 C 350 C 400 C

*

4 3 Ss3S*3

log(< >)

(C)

1 he magnitude of Z' decreases with increase in frequency as well as temperature

indicating an increase in ac conductivity with rise in temperature and frequency. Typical

curves are observed in figures. The temperature affects strongly the magnitude of

resistance. At lower temperatures, Z' decreases monotonically with increasing frequency

up to some frequency and than becomes constant. At higher temperatures, Z' is almost

constant and for even higher frequencies decreases sharply. The higher value of Z' at

lower frequencies and low temperatures means the polarization is larger. The

temperatures where this change occurs vary in different materials. This may due to

release of space charge [38, 39J.

The variation of imaginary part of impedance (Z") as a function of frequency (Nyquist

plot) is plotted at different temperatures in Figs.6.12 for molybdates and in figure 6.13 for

tungstates ceramics respectively.

Z "3 0 0 2 3 2 5 Z "3 5 0 Z":u 5 Z "4 0 0

log(u)

(a)

(b)

2-200 Z"2 50

2'300

l ° g ( ,

(c)

Figure 6.12: Frequency dependent L " in (a) K L i M o 0 4 (b) N a L iM o 0 4 and (c)

N a K M o 0 4

200 C 250 C 300 C 325°C ] 350'CJ

log (<•>)

(a)

r>o c 100 c 1 so 't:

4 5 5 0

log(<->)

6 0 6 5 7 0

(b)

0 09

0 08

O 07

0 06

0 0'S ■

O 04

O 03 -

0 02 -

0 01 -

0 00 -

3 0 0 C 3 2 5 C 3f>0 C

______- * 0I * A A iW M A

(c)

At lower temperatures, Z" deerease monotonically (exeept in NKAV, which shows

relaxation peak even at 50°C) suggesting that the relaxation is absent. The temperature

ranee in which relaxation is seen is different for different samples [40]. This means that

relaxation species are immobile defects and the orientational effects may be associated.

As the temperature increases, the Z " peak starts appearing in all the materials. The peak

shifts towards higher frequency with increasing temperature showing that the resistance

of the bulk material is decreasing. Also the magnitude of Z" decreases with increasing

frequencv. As the temperature is increased, in addition to the expected decrease in

magnitude of Z‘\ there is a shift in the peak frequencies towards the high frequency side.

Also it is ev ident that with increasing temperature, there is a broadening of the peaks and

at higher temperatures, the curve appear almost flat. This behavior is apparently due to

the presence of space charges in the material [41].

The peak shifts towards higher frequencv with increasing temperature

indicating the spread of relaxation times and the existence of temperature dependent

electrical relaxation phenomena. Probably, high temperature triggers grain boundary

relaxation process as is also evident from the asymmetric broadening of the peaks [42].

fhe most probable relaxation time could be calculated using the loss peak in the Z" vs

Irequcncv plots using the relation, t = R|X b = From the Z" data, the i at various

temperatures is calculated and a graph between log ((om) vs. I T is shown in Figures 6.14

and 6.1 5 for molybdates and tungstates respectively.

1000frV 1000/fK1

(a) (b)

1000/T"K 1

(c)

^ if*ure 6.14: Temperature variation of relaxation time in (a) NaKMoO.) (b) KI.i.Mo().i(c) .\aLi.M0O 4

1000/T"K '

(a)

10OO/T K

(b)

io o o/t ' k '

(c)

Figure 6.15: Temperature variation of relaxation time in (a) KI.i\V()4 (b) N a L iW 0 4 and (e)

NaKW 0 4

I he c) value decreases with increasing temperature indicating that the behavior is typical

semiconductor one. The relation follows the Arrhenius law [43].

(o= WoExp (-Ea/kBT)

The nature of variation of relaxation time with temperature obeys the Arrhenius relation

for molybdates/ tungstates in the low temperature region. The activation energy

calculated from the linear fit is shown in figures. The value of t exhibits that the

relaxation time of the mobile charge carriers is again thermally activated [44]. In

polvcrystalline samples, grains are semi conducting while the grain boundaries are

insulating (45, 46]. The semi conducting nature of the grains is believed to be due to

oxygen vacancies/defects generally produced during high temperature sintering.

However, the low value of activation energies excludes the role of oxygen.

Estimated activation energy for the samples KLM NLM and NKM, are 0.30. 0.44 and

0.49 eV respectively, whereas for corresponding tungstates these are 0.56. 0.44 and

0.53eV respectively. It is observed that the value of Z"max (i.e., peak value) shifts

towards lower frequency side on increasing temperature, and shows the presence of

temperature dependent electric relaxation phenomena. The asymmetric peak is observed

with rise in temperature and suggests the existence of non-Debye type of relation

processes in the materials [47]. The relaxation process may be due to the presence of

immobile species at lower temperature and defects at higher at temperature. The

dispersion of the curves appears to be merged in the higher frequency region. This

behavior is again due to the presence of space charge polarization at lower frequencies,

which becomes insignificant at higher frequencies.

1 -inures 6.16 -6. IS show the Argand diagram (imaginary part of complex impedance vs.

real part) tor molybdates and in figures 6.19-6.21 the same are shown for tungstates

samples. Also shown in each figure is the fitting of the equivalent electric circuit model at

some representative temperatures. As seen in these figures, only an arc is observed at

low er temperatures which take the shape of semicircle at higher temperature. In general,

w hether a full, partial or no semi circle is observed depends upon the strength of the

relaxation and the experimentally available frequency range [4S]. The intercept of the

semicircular arc along Z' axis gives the value of resistance and it is observed that point of

intercept on the real axis shifts towards the origin of the complex impedance indicating

the increase in ac conductivity. At higher temperature, the arc could be fitted with two

semicircles (electrical phenomena modeled in terms of an equivalent circuit comprising

of a series combination of two parallel RC Circuits). The presence of two semi-circular

arcs mav be due to grain interior and grain boundary as per the brick layer model [49].

The absence of third arc (semi circle) suggests the negligible electrode-material interface

contributions. The lower frequency arc is attributed to grain boundary while the higher

frequency due to grains.

Z'

•JiJIJM.LL

- 'Jcl O b ' f i v e d

2 0D'l C f io-n rr c e

■ 2 Q“ l Ct se rved

1 - : : 1 T f ..I, fmrri fr. i Je

3 U”L L a 1 c u I a * e d f rom rr cde

N

1000000 -

(a)

■

Z'Q

(b)

Figure 6.16: (a) Cole-Cole explicit impedance plots in K L iM o ( ) 4at different temperatures; inset

shows the same at lower temperatures and. (h) NL1.S fitt ing with the equivalent

electrical circuit model at representative temperatures.

N

0.1 -

0.0

■ Z'200

' • Z’250* 'j

a Z'300 OUCH* j

-

, i ]

z

■■ \ ■

■H ^

■

0.0 0.1 0.2 0.3Z

(a)

0.4 0.5

N

%

$h H I -

\-j-- ,-- !-- ,-- (-- ,-- r

Til

(b)

■ifiiirc 6.17: (a) Kxplicit impedance plots in NaLi.M o04at different temperatures; inset shows the

same at lower temperatures and. (b) N L L S fitting with the equivalent electrical circuit

model at representative temperatures.

3.0

2.5

2.0

1.0

0.0

■ Z"50• Z"100* Z"150 ▼ Z"200

Z"250Z"300

0.0 0.5 1.0 1.5

Z*X10"£2

2.0 3.0

(a)

■i IjUOOOO-

1 jOC X'C

■

/

— ---- r

Z’ft

(b)

figure 6.18: (a) Explicit impedance plots in NaKMoO., at different temperatures; inset shows the

same at lower temperatures and. (b) M I S fitting with the equivalent electrical

circuit model at representative temperatures.

0 5

0 4

0.3 -

0 2

0 0

0 0 0 1

..................,

0 2 0 3 0 4

Z’X106u

■ 250 C• 300X* 325°C

V0 5 0 6

(a)

Z'Q

(b>

K i mi re 6.19: (a) Explicit impedance plots in K L i\ V 0 4 at different temperatures; inset shows the same

at lower temperatures and. (b) N L L S fitting with the equivalent electrical circuit model

at representative temperatures.

Z’x106U

(a)

— ?; ' 5 C Ubs.erv.-J; ' : s “ c C a l r u la t td fron 250 °C O b se r ve d

.........I 1 Sr jDil: C ale i j U] e d Iron

2 7 5 “ C 0 bse rv fd

2 75 C C ale ulat ed fr or-

-r-0 0000 -

M200000

, ■“100000 -

T il

(b)

figure 6.20: (a) Cole-Cole explicit impedance plots in N aL i\V 0 4 at different temperatures; inset

shows the same at lower temperatures and, (b) N L L S fitting with the equivalent

electrical circuit model at representative temperatures.

(irain and grain boundary resistances (Rg, Rgb) as well as grain and grain boundary

capacitances (Cg, Cgb) are obtained through non-linear least square fitting of the data.

Figure 6.22 and 6.23 gives the relation between impedance parameters and temperature

for prepared material NaKMo(>4 and NaKWCV

5x10

4x10 -

3x10 -

cr 2x10

CO c- 1x105

1 .8x1010

- 1 .6x10'10 o- 1.4x1 O’10 S- 1 .2x10’10 o

1.0x1 O'10 -S 11

8.0x10 6.0x1 0 11 “

- 4.0x10’11 g- 2.0x10"11 0.0

-2 .0x10'11

Temperature( C)

Figure 6.22: Temperature variations of the equivalent electrical circuit parameters

represent in the contribution of grain (up) and grains boundary

(down) in NaKM o 0 4.

Tempi e n lu n :(aE3

Figure 6.23: Temperature variations of the equivalent electrical circuit parameters

representing the contribution of electrode and grains in N aK \V ()4.

i. 4*1 nf i. 3m i a a I O i l o ' §■

+ .OB1C3' J"

Te m pe ra t i re ^ C )

Te m pe r a t i « (^C)

Figure 6.24: Temperature variation of the equivalent electrical circuit parameters

representing the Contribution of grain boundary (up) and grains (down) in

KLiM oO.,.

Orairi

Reset

ance

Bulk

Resis

tanc

e 3r

ain

Resi

stan

c

1 2% 1D

sc* in“

im icT aa

Tern pe rati re ^C )

ID"1!

SO 1CQ 150 2 DCI

T b 7i pe ra ti re <°C)!50 3DD 3 5 0

Figure 6.25: Temperature variation of the equivalent electrical circuit parameters

representing the contribution of grain boundary (up) and grains

(down) in K L iW O ^ .

J .QB id

■> a * 1 □1 □1 a

i P R r a t i r ? ( C )

Figure 6.26: Temperature variation of the equivalent electrical circuit parameters

representing the contribution of grain boundary (up) and grains

(dow n) in N aLiM oO j.

Grain

capacitanc

3 O i l □

2 5*1 OBi l i s b i cf 5_ 1 Oil cf U 5 X3b1 D* -

□ n - —I--- '—1S3 33 □

Tc <np erakjrr i*C)

- + r* 1 □,T 3£* 1 CTT o

• T Ua .» in x-- l m idT h>_ □£> 2

1 ,*«1 vf H l □' -d i a id 1S a a it f

e n i l cf^ + r* i cf

2 mi □’□ 13

■ C.

/ \

-V

~l— 5D

30 1 □

am in

1 X3l 1 C5,lti nET

►- on a

151 2DQ S O

remper«Lre('c)

Figure 6.27: Temperature variation of the equivalent electrical circuit parameters

representing the contribution of grain boundary (up) and grains

(do>vn) in N aL iW O j.

The value of Cg decreases slowly with increase in temperature whereas the Rg show

exponential increase at higher temperatures. The behavior could be associated with the

grain boundaries becoming conducting.

6.3.3 COM PLEX ELECTRIC MODULUS ANALYSIS

Complex modulus, electric modulus or inverse complex permittivity M* is defined by the

following.

M* =l/c* =l/(e‘-je” ) ={c7[(r/)2 +(f/*)2]} + !r/7[(r.')2 +(r/*)2]} = M'-jM"

The advantage of adopting complex electric modulus formalism is that it can discriminate

against electrode polarization and grain boundary conduction mechanism. It is also

suitable in detecting bulk phenomena properties as apparent conductivity relaxation time

[50. 51],The other advantage of the electric modulus is that the electrode effect can be

suppressed [52], Figures 6.28(a) NaKMo04. (b) KLiM o04. (c) NaLiMo04. shows the

v ariation of real part of dielectric modulus M' (oj) as a function of frequency at

temperatures respectively.

110000 1 0 0 0 0 0

90000 -

80000

70000 -

60000

50000 -

40000 -

30000 -

2 0 0 0 0

1 0000

0

M '50 M '1 00 M '1 50 M '200 M '250 M '300 M '350 M '400 S '

lo g (<■■)

(a)

lo g <..

(b)1 1 0 0 0 0 -

1 0 0 0 0 0 ■ M '50• M '1 00

9 0 0 0 0 A M '1 508 0 0 0 0 - ▼ M '2 0 0 # •

M '2507 0 0 0 0 - M '300 ▼

0 00 00 - M '350 ▼

• M '4 0 0 • x^ 0 0 0 0 - Tr

* ▼■1 0 0 0 0 - y

3 0 0 0 0 -•

* ▼ M-<

2 0 0 0 0 - • * ^• *** *

10 0 0 0 - m

0 - •m fcS ~4 +>

lo g ( ■ )

197

various

(c)

r,u c;1 oo' (:1 r,o c 200 ' C 2r>0°C 3 0 0 '( J

- » *

(a)

350000

300000

250000 -

200000 -

50 C 100 C 150 C 200 C 250 C 300 C

log(c>)

(b)

■ 50 C• 10 ore• 1 r>o’ cT 2 0 0 'C

2f>0,C < ,'400'C

3r>o'c:• 400"C

; ’9 I « « • mmtm « « « 4

logf, o

(C)

At low temperature the behavior is almost frequency independent. As the

temperature increases, electric modulus starts increasing with frequency and attains

saturation at higher temperature indicating that the electrode polarization makes a non-

negligible contribution to M' in same temperature range and the dispersion is mainly due

to conductivity relaxation [53]. The M ’ value is characterized in almost all materials by a

very low value (~ 0 ) in the low frequency region, except in temperature range 100-150

"('.The values of M ' at low frequencies indicate the removal of electrode polarization

[54|.Thus, accumulation of charges at electrode material interlace is high around 1()()°C

and may be the possible region of electric polarization and observed high dielectric

values up to this temperature. Thus the observed dielectric peaks may have the extrinsic

origin. A continuous dispersion in M ‘ values with increase in frequency have a tendency

to saturate at a maximum asymptotic value designated as M, in the high frequency region

in all samples. Such observations may possibly be related to lack ot restoring force

governing the mobility of charge carriers under the action ot an induced electric field

[55]. The behavior supports long range mobility of charge earners [56].

Figure 6.30and 6.31 show the frequency dispersion behavior of imaginary part of modulus

M" ((d) at different temperatures for molybdates and for tungstates.

1 1 u r t *■> '(• J r { 1 1 u « m \ dt |m rule n< f o f ( If < ( n c r r i 'x lu Iin !<«< t in i m > K I iM >4 < h » N j I ■ N1 •-.( », a n <1 < c

18000 -

16000

14000 -

12000 -

G 10000 “bx 8000 £

6000 -

4000

2000

0 -

200’C250'C300'Q

(a)

5U'Coo c

log(-

(b)

\

iog(' •)

(c)

I he variation of imaginary part of electric modulus M" is indicativ e of energv loss in the

sample under electrical field. In the assessable frequency range, the spectrum at each

temperature exhibited one relaxation peak with a symmetric maximum (M "nwx) at higher

temperatures. At lower temperature the peak is not observed and is probably beyond the

range ol frequency window. These peaks indicate the transition from short range to long

range mobility with decreasing frequency, where the low frequency side of the peak

represents the range of frequencies in which the ions are capable of moving long

distances i.e. performing successful hopping from one site to the neighboring site,

whereas, for the high frequency side, the ions are spatially confined to their potential

wells and can execute only localized motion [57].The position of the M "m;ix shifts to

higher frequencies as the temperature increases. This behavior suggests that the spectral

intensity of the dielectric relaxation is activated thermally in which hopping process of

charge carriers and small polarons dominate intrinsically. Both the electric modulus and

the impedance formalism produced peaks which are broader than predicted by Debye

relaxation processes (> 1.4 decades) [58]. The broadening of the peak indicates the

spread of relaxation time with different time constants, hence a non-Debye type of

relaxation. The frequency o)m corresponding to M "max gives the most probable relaxation

time rm from the condition d)mxin= 1. The relation between frequency corresponding to

most probable relaxation time and temperature is shown in Figs. 6.32(a)-(c) and Figs.

6.33(a)-(c) for molybdates and tungstates respectively. The nature of variation of

relaxation time with temperature obeys the Arrhenius relation for molybdates/ tungstates

in the low temperature region Figs.6.32 and 6.33. The activation energy calculated from

the linear fit is shown in figures. The value of x exhibits that the relaxation time of the

mobile charge carriers is again thermally activated. Figure 6.33 shows the temperature

variation of relaxation time in molybdates and figure 6.34 shows the same for tungstates

samples. The activation energy for the process is 0.11, 0.27 and 0.35 eV for KLM , NLM

and NKM, whereas it is 0.46, 0.23 and 0.27 eV for corresponding tungstates. Relatively

low values of activation energies show that grain conduction is associated with mobile

charge species most probably alkali cations.

2 0 2 2 2 4 2 6 2 B JO 3 2

1000/T"K ’

(a)

Fi gure 6.32Temperature variation of relaxation time in (b) K I J M 0 O 4 (c) NaLi.Mo0 4 K L M , N LM

and NK\i (a) NaKMoO^

(a)

-'t r,s

(b)

1

(C)

f igure 6.33Temperature variation of relaxation time in (a) N aKW 0 4 (b) K L iW 0 4

(e) N aL i\V 0 4

6.3.4 AC ELECTRICAL CONDUCTIVITY STUDY

The electrical conduction in dielectrics is due to ordered motion of weakly bound

charges under the influence of electric field. The conduction process is dominated by the

types of charge carriers like electron/ holes/ ions. The electrical conductivity of solids can

be divided into extrinsic and intrinsic conductivity regions. The extrinsic conductivity is

produced due to migration of vacancies, defects generated due to disorder and charge

compensation [59]. Extrinsic conduction may also be due to association of defects. The

degree of association depends on the temperature and also on the impurity concentration.

Flectrical conduction may be composed of electronic conduction and ionic conduction. In

these materials, electronic conduction in the grains is expected mainly from the defects

present in the lattice. Therefore the conductivity in these systems is expected to result

from the presence of defects, which introduce extrinsic levels allowing electrons/ defects

to be thermally activated. In addition, the high mobile alkali ions may contribute

significantly to the conduction. Further, the possibility of oxygen-alkali ion defects

associates is also expected [60].

The ac conductivity was calculated from the impedance data using the relation

<7;k. = c0 er tan5 and fitted through the expression a;)C = odc+ Ad)n, known as Jonsher's law

[52] where A is a thermally activated quantity and n is the frequency dependent exponent

that takes values <1. The exponent 'n‘ can have a range from 0 to 1. The exponent relates

to the degree of correlation between charge carriers. The power law dependence of ac

conductivity corresponds to short range hopping of charge carriers, through trap sites

separated by energy barriers with different heights [61]. The parameter *a’ is frequency

independent which may be temperature and material dependent. The data were fitted

using the above relation and the calculated values of A and n. Frequency dependent

AC' conductivity tor the samples molybdates and tungstates are shown in figure 6.34 and

6.35 respectively.

; -- • — C o n 100o o i - .... C o n . 1 5 0

C o n 2 5 0

l o y ( )

(a)

£ 1E-6-CX * XP*

50l,C100nC1 60 'C200UC250°C:300‘c

(a)

♦ t t *1r>o <; t do'ti r.ift 200 c 2r>o t :«>()

(b)

log(. .)

(C)

Frequency variation as depicted in the Figures indicates that the conductivity dispersion is

observed throughout the range of frequency under investigation. Also, it can be seen that

in low frequency region there is dispersion in the values of conductivity whereas in high

frequency region the curves approach each other. The conductivity spectra show a low

frequency dispersion followed by a high frequency plateau region. The plateau region at

high frequency and temperature may be related to a behavior independent of space

charge. It is reasonable because the space charge effect vanishes at higher temperature

and frequency. In some materials the plateau is not reached at low temperatures showing

that the space charges are present even at higher frequencies. Further that molybdates

samples have relatively higher conductivity (0.01 mho/cm) and the 05 order of variation

in it in the temperature range measured; behaves like potential fast ion conductor.

Curves also show a change of slope at a particular frequency known as hopping

frequency (o)n), this obeys the relation o) = o)o( I+okdh)11. The curves show dispersion,

which shift to higher frequency side with rise in temperature. At higher frequency the

conductivity becomes more or less temperature independent. From the nature of the

curves it can be concluded that although there are some differences in individual

behavior, the basic nature remains the same. The variation ot aac involves a power

exponent, which indicates the conduction process is a thermally activated process.

Figure 6.36 shows the Arrhenius ac conductivity plots for the molybdates samples and

figure 6.37 shows the same for the tungstates sample respectively.

1E-3

1E-5

♦ 50kHz 100kHz

2.0 2.5

1000/t V(a)

V '*

IE-6 •

• 1kHz* fikHz

10kHz♦ 50kHz

100kHz

2 5

1000/T K*

(b)

1000/T K'(c)

f igure 6.36 Plot of AC electrical conductivity vs. 1000/T in (a) N a K M o 0 4 (b) K l. iM o 0 4 (c) N a L iM o 0 4

!$ 1E~5

1000/T K

(a)

1 kHz5kH z10kHz50kH z100kHz

—I-- ■-- 1—2 0 2 2 2 4 2 6

1 0 0 0 / T °K 1

3 0 3 2

(b)

1000/T K

(c)

The variation of g;1c with temperature consists of different regions characterized by

different slopes indicating the presence of different conduction mechanisms associated

with their corresponding values of activation energy. It is observed that ac conductivity in

all ceramics at room temperature is very high and temperature independent. In this

temperature range, the materials show high values of dielectric response. Thus, the high

dielectric losses are due to extrinsic effect. Further increasing the temperature,

conductivity decreases indicating a PTCR behavior. Further increasing the temperature,

conductivity shows increasing behavior that continues up to high temperatures showing

NTCR effect like semiconductor and it is related to the bound carriers trapped in the

samples [62]. At higher temperatures, conductivity curves either become temperature

independent or starts merging except in NLM. Which may be due to release of space

charge effect? Goodman [63J observed that PTCR behavior is intimately connected with

the grain boundary. The origin of PTCR behavior is explained by Heywang model [64]

which assumes that the acceptor types states at grain boundaries create equivalent

potential barriers associated with resistive depletion layers near the grain boundaries. The

PTCR is the result of the dependence of barrier heights on dielectric constant of grains or

bulk; at higher temperature, increase of dielectric constant decreases the barrier height

and increase in conductivity. Thus higher conductivity at higher temperature is the result

of compensation of charges at grain boundaries in addition to the release of space

charges. In the higher temperature range a3C increases at faster rate possibly due to space

charge polarization.

The conductivity species in high temperature range may be defects created due to mobile

small alkali ions. This may give high conductivity due to large hopping possibility of

defects and ions through the available vacancies. Different slope changes are associated

with multiple activation processes. Thus contribution to the conductivity is due to several

processes especially at higher frequencies. Calculated Activation energy for molybdates

and tungstates at different temperatures are shown in Table 6.1(a) (b) (c) and 6.2(a) (b)

(c) respectively. In most of the materials the ac conductivity activation energy is smaller

at higher frequencies when compared with low frequencies. This is due to the fact that at

lower frequencies, the overall conductivity is due to mobility of charge earners or

transportation of charges over large distances. At high frequencies, carriers are confined

to their local potential wells and undergo localized motion. Since the energy required in

such motion is smaller than for transporting the charges, the effect is observed. From the

table, the low activation energies involve suggests the intrinsic conduction is due to large

number of space charge and charge earners. At higher temperatures vacancies and tan6

defect complexes may be generated giving higher values of activation energies. This

however, does not explain the higher activation energies in NLM and all tungstates. One

possible region may be presence of water at lower temperatures generating OF!' species

that may require higher activation energies. However, further studies are needed to prove

Table 6.1(a) Activation energy values at different frequencies calculated by linear

fitting of temperature dependence of AC conductivity of NaKMoQj

Frequency in (KHz) Activation Energy (eV)

50UC to 125(,C 125UC to 375UC

1 0.20 0.28

5 0.16 0.27

10 0.14 0.26

>0

100-

0.1 1

0.1 1

0.23

0.23

Table 6.1(b) Activation energy values at different frequencies calculated by linear

fitting of temperature dependence of AC conductivity of KIJM0O4

Frequencvin

(KHz)

Activation Energy (eV)

50°C to 100"C 100 C to 200 C

1 0.20 0.28

5 0.16 : 0.27

10 0.14 ! 0.26

50 0.1 1 0.23

100 0.11 0.23

fable 6.1 (c) Activation energy values at different frequencies calculated by linear

fitting of temperature dependence of AC conductivity of NaLiM oO .4

Frequency in Activation Energy (eV)

(KHz) 50 C to 100°C 100UC to 200UC 200(IC to 300(’C1 0.74 0.22 0.285 0.70 0.20 0.28

10 0.66 0.19 0.31

50 0.57 oTis 0.42100 0.54 0.16 0.44

Fable 6.2 (a) Activation energy values at different frequencies calculated by linear

fitting of temperature dependence of AC conductivity of NaKVV04

Frequency in (KHz) Activation Energy (eV)

(75UC - 200"C) (200°C - 400l,C)1 0.049 0.2735 0.038 0.28510 0.032 0.29850 0.030 0.327100 0.028 0.320

Table 6.2(b) Activation energy values at different frequencies calculated by linear

fitting of temperature dependence of AC conductivity for of KLi\V04

1 Frequency in

i (KHz)

Activation Energy (eV)

30()C - 100UC lOO'C-SOOV1 0.50 0.31

0.42 ' 0.29

; 10 0.39 0.2850 0.35 0.24100 0.35 0.23 ;

fable 6.2 (c) Activation energy values at different frequencies calculated bv linear

fitting of temperature dependence of AC conductivity of NaLiVV04

Frequency in

(KHz)Activation Energy (eV)

30UC to 60UC 60UC to 120l,C1 0.48 0.235 0.46 0.2410 0.45 0.25

50 0.42 0.57100 0.40 0.27

6.4 CONCLUSION

Double alkali molybdates KLiM o04 (KLM ), NaLiMo04 (NLM ), NaKMo04 (NKM),

and corresponding tungstates K L iW 0 4 (K LW ), N aL iW 0 4 (N LW ) and N aKW 0 4

(NKW ), are subjected to dielectric and electrical analysis using impedance spectroscopic

technique not studied so for with regard to dielectric dispersion and electrical

conductivity mechanism. Followings major inferences are drawn.

1. The increase in dielectric response with temperature is observed and attributed to

interfacial polarization dominating over dipolar polarization. This also indicates

the onset of some additional relaxation mechanism in the material attributed to the

ac conduction mechanism being dominant at high temperature.

2. All studied materials have similar dielectric response. In all materials, the rate of

change of tan5 with temperature is very small (loss almost temperature

independent) in the temperature range approximately 1 OO 'C < T < 175°C. At

higher temperatures, loss increases sharply. The sharp increase in tand at higher

temperature may be due to scattering of thermally activated charge carriers and

some detects in the samples. At higher temperature the conductivity begins to

dominate, which in turn seems responsible for rise in tan6.

Both e' and e" show strong dispersion at low frequency, especially at high

temperatures. The dispersion in molybdates is more than corresponding

tungstates. Such strong dispersions observed in both components of complex

dielectric constant is a commonly observed features in disordered dielectrics with

significant electrical conductivity.

The low frequency dispersion is observed and is understood that the conducting

process is due to ion hopping. The very high value of r." dispersion in comparison

to {:' dispersion is attributed to the processes being influenced by dc conductivity.

Impedance relaxation is observed and found to be temperature dependent with

distributed relaxation times confirming the existence of temperature dependent

electrical relaxation phenomena. High temperature triggers grain boundary

relaxation process

The nature of variation of relaxation time with temperature obeys the Arrhenius

relation for molybdates/tungstates in the low temperature region. The relaxation

time of the mobile charge earners is thermally activated. Estimated activation

energy for the samples KLM NLM and NKM, are 0.30, 0.44 and 0.49 eV

respectively, whereas for corresponding tungstates these are 0.56. 0.44 and

0.53eV respectively.

Nyquist plots are used to separate the grain and grain boundary contribution in

electrical processes and the equivalent circuit parameters for Grain resistance and

capacitance (Rg, Rgh) as well as grain and grain boundary capacitances ( C(J Cgh)

through non-linear least square fitting of the data.

S. Electric modulus approach is used to obtain the information about bulk behavior.

This behavior suggests that the spectral intensity of the dielectric relaxation is

activated thermally in which hopping process of charge carriers and small

polarons dominate intrinsically. Both the electric modulus and the impedance

formalism produced peaks which are broader than predicted by Debye relaxation

processes (> 1.4 decades). The broadening of the peak indicates the spread of

relaxation time with different time constants, hence a non-Debye type of

relaxation. The activation energy for the process is 0.1 1, 0.27 and 0.35 eV for

KLM , NLM and NKM, whereas it is 0.46, 0.23 and 0.27 eV for corresponding

tungstates.

{). AC conductivity shows PTCR behavior at low temperature and transforms into

NTC'R behavior at higher temperatures. The conductivity values approaches those

of ionic conductors at higher temperature. The conduction is due to both extrinsic

defects and migration of small alkali ions.

10. The electrical conductivity behavior of all studied materials is analyzed and

found to be of mixed ionic conduction type. The conductivity mechanism is

deduced and activation energies are obtained in different temperature ranges.

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