chapter - ii experimental techniques 2.1....

CHAPTER - II

EXPERIMENTAL TECHNIQUES

2.1. Introduction

2.2. Preparation methods

2.2.1. Sol-gel process

2.2.1.1. Colloidal process

2.2.1.2. Chemical polymerization process

2.2.1.3. Advantages of the Sol gel process

2.2.2. Hydrothermal process

2.2.2.1. Advantages of Hydrothermal process

2.2.2.2. Disadvantages of Hydrothermal process

2.2.3. Co-precipitation process

2.2.3.1. Advantages of Co-precipitation process

2.2.3.2. Disadvantages of Co-precipitation process

2.2.4. Polyol process

2.2.4.1. Advantages of Polyol process

2.2.4.2. Disadvantages of Polyol process

2.2.5. Combustion Process

2.2.5.1. Combustion of Fuel – Oxidant

2.2.5.2. Polymeric Precursors process

2.2.5.3. Pechini Process

2.2.5.4. Advantages of Combustion process

2.2.5.5. Disadvantages of Combustion process

2.3. Preparation methods of polymer solid electrolytes

2.3.1. Solution-casting process

2.4. Characterization techniques

2.4.1. X-Ray Diffraction (XRD)

2.4.2. Fourier transforms infrared spectroscopy (FTIR).

2.4.3. Scanning Electron Microscopy (SEM)

2.4.4. Thermal Analysis

2.5. Principles of Impedance spectroscopy

2.5.1. Basic theory

2.5.2. Series combination of R and C

2.5.3. Parallel combination of R and C

2.5.4. Preparation of pellets for impedance measurement

References

CHAPTER - II

EXPERIMENTAL TECHNIQUES

2.1. Introduction

In recent times, a number of new lithium ion based polycrystalline,

polymer materials with high ionic conductivity have been synthesized and find

potential applications in various solid state ionic devices [1-10]. Recently,

further, enhancement of the electrical conductivity and mechanical properties

have been achieved by dispersing nanosized metal oxides in the polymer

solid electrolytes for better ionic device applications including lithium batteries.

This chapter briefly describes about the synthesis of rare earth based

lithium silicates by sol-gel process, nanocrystalline metal oxides by

combustion process and lithium ion conducting polymer solid electrolytes by

solution casting method and their characterization by different experimental

techniques like XRD, FTIR, TG/DTA, SEM-EDX and impedance.

2.2. Preparation methods

2.2.1. Sol-gel process

In recent years, the sol-gel method has become one of the most

popular and important techniques to synthesize various types of tailor made

new materials, including high ionic conductors with high homogeneity and

purity [11]. The versatility of the sol gel method is due to mixing of starting

chemicals (precursors) in the solution form at much lower temperature which

gives good control of various components at atomic level.[12] This technique

21

has been extensively used to prepare different types of new materials in the

bulk, powders, sheets, fibers, thin films, etc., for various advanced

technological applications. Thus, the sol gel route is more suitable for the

synthesis of glassy / amorphous and crystalline materials than conventional

methods. There are two essentially different routes in the sol gel process to

produce the various types

1. Colloidal process

2. Chemical polymerization process

2.2.1.1. Colloidal process

This process involves the dispersion of colloidal particles in a liquid to

form a sol and then destabilization of the sol to form a gel. This process is

represented in fig 2.1.a. In colloidal process, the aqueous solution of silicic

acid is used as the source of SiO2 network and also to form the sol. The

polymerization of monomer silicic acid leads to the formation of branched

chains in three dimensions, which result the gel and can be converted into

amorphous solids by one of the following ways.

Heat-treatment of the gel below the glass transition temperature

(Tg) to obtain glass through the polymerization.

Calcining the gel well above the Tg but within the melting point

range to form the polycrystalline sample.

22

(a) (b)

Fig.2.1. a and b. Flow chart representation for the preparation of SiO2 monolithic gel by sol-gel process a) colloidal route and b) chemical polymerization route.

Colloidal route

Metal salt SiCl4

Ultra pure particles

SiO2 Sol

Sio2 gel

Monolithic

pH adjustment

Chemical polymerization route

Organo metallic Si(OR)4

Acid catalyst

Polysilonane sol

Solid gel

Monolithic

pH adjustment

Hydrolysis and Polymerization

23

2.2.1.2. Chemical polymerization process

Alkoxide (like TEOS for preparing SiO2) is hydrolyzed with water in the

presence of corresponding alcohol to form the sol. Then the sol is casted to

form the gel and it heated to obtain the monolithic SiO2. The synthesis

procedure of SiO2 glass by chemical polymerization is shown in fig 2.1 (b) and

various steps involved in the sol gel process are briefly discussed.

The seven steps involved in the sol gel process are as follows

a. Mixing

The alkoxide precursor [Si(OR)4 (R=CH3, C2H5, C3H7 etc) is hydrolyzed

by mixing with water. The corresponding reaction mechanisms are as

follows.

Si OR

OR

OR

RO Si OH

OH

OH

HO4H2O 4ROH

Si OR

OR

OR

RO Si OH

OR

OR

ROH2O ROH

24

The hydrolyzed silica molecules can link together in the condensation

reaction by the removal of H2O and R-OH. This type of the reaction can

continue to build a larger and larger by the process of polymerization.

b. Casting

The prepared sol can be cast into mould to obtain the required shape.

The mould must be selected to avoid adhesion of the gel.

c. Gelation

As mentioned in the step I, with time, the condensation reaction can

build up larger and larger network by the process of polymerization to form

three-dimensional network, which leads to form the gel. The gelation time will

depend up on the temperature, solvent, pH condition and also removal of the

solvent.

d. Aging

Aging is the step maintaining the casted object for a period of time.

During the aging, the polycondensation continues and resulting the expulsion

of liquid from the pores. These increase the thickness of particle necks and

decrease the porosity. Thus, with aging, the strength of the gel increases.

Si OR

OR

OR

RO Si OR

OR

OR

HO Si O

OR

OR

RO Si

OR

OR

OR

ROH

25

e. Drying

Liquid existing in the interconnected pore network is removed during

the drying process. Thus, there is a decrease in the volume of the gel, which

is equal to the volume of the liquid lost by evaporation. Here after drying, the

pores of the gel substantially emptied.

f. Dehydration or chemical stabilization

The removal of the unwanted elements likes H and R respectively from

Si-OH (silanol) and Si-OR bonds to obtain the chemically stabile required

compound.

g. Densification

Densification is the last treatment process of gel. By heating the

porous gel at high temperatures, the pores can be eliminated and densified

poly crystalline can be obtained equivalent to the fused quartz or fused silica.

The densification temperature depends on the dimension of the pore network,

the conductivity of pores, surface area etc.

2.2.1.3. Advantages of the Sol gel process

1. Better homogeneity and purity

2. Low temperature preparation saving energy.

3. Minimize the evaporation losses.

4. Minimize air pollution.

5. No reaction with container.

26

6. Bypass phase separation.

7. New non-crystalline solids outside the range of normal glass

formation.

8. Better glass products from the special properties of the gel.

9. Special properties (e.g. fibers and films).

Hence, in the present investigation, lithium samarium silicate

(LiSmSiO4), Lithium lanthanum silicate (LiLaSiO4) and lithium dysprosium

silicate (LiDySiO4) are taken to synthesize by tailor made sol-gel process. The

synthesis procedures of the rare earth based lithiumsilicate by sol-gel process

are discussed in more detail in the chapter III.

2.2.2. Hydrothermal process

Water is an excellent solvent for many ionic compounds. It can even

dissolve non-ionic covalent compounds under high pressure and high

temperature. In hydrothermal synthesis, the above property of water has been

effectively exploited for the preparation of fine powders of metal oxides [13-

15]. Under these hydrothermal conditions, water plays two roles: 1) as

pressure transmitting medium and 2) as a solvent for reacting solids. Such

hydrothermal conditions effectively brings down the activation energy for the

formation of final phase, which can also speed up the reaction between the

solids which otherwise would occur only at very high temperatures [16-17]. An

autoclave is invariably employed to achieve hydrothermal conditions. The

pressures attained are in the range of 10 to 150 kilobar which depends on the

chosen temperature of water (>373 K). Powders are either crystalline or

27

amorphous depending on chosen hydrothermal temperature [18-22]. This

hydrothermal has certain advantages as well as some disadvantages, which

are listed below:

2.2.2.1. Advantages of Hydrothermal process

1. Powders are formed directly from the solution.

2. It is possible to control particle size and shapes by using

different starting materials and hydrothermal conditions.

3. Resulting powders are highly reactive which aid in low

temperature sintering.

2.2.2.2. Disadvantages of Hydrothermal process

1. Prior knowledge on solubility of starting materials is required.

2. Hydrothermal slurries are potentially corrosive.

3. Accidental explosion of the high pressure vessel cannot be ruled

out.

2.2.3. Co-precipitation process

In this method, the required metal cations from a common medium are

co-precipitated usually as hydroxides, carbonates, oxalates, formates or

citrates [23-25]. These precipitates are subsequently calcined at appropriate

temperatures to yield the final powder. For achieving high homogeneity, the

solubility products of the precipitate of metal cations must be closer [26]. Co-

precipitation results in atomic scale mixing and hence the calcining

28

temperature required for the formation of final product is low. This leads to

lower particle size in the resulting multi component oxide powders [27].

However, each synthesis requires its own special conditions, precursor

reactions, etc. Also, co precipitation route required to control the

concentration of the solution, pH, temperature, and stirring speed of the

mixture in order to obtain the final product with required properties [28-29].

2.2.3.1. Advantages of Co-precipitation process

1. Homogeneous mixing of the reactant precipitates reduces the

reaction temperature.

2. Simple direct route for the synthesis of fine metal oxide

powders, which are highly reactive in low temperature sintering.

2.2.3.2. Disadvantages of Co-precipitation process

1. This process is not suitable for the preparation of high purity,

accurate stoichiometric phase.

2. This method does not work well, if the reactants have very

different solubility as well as different precipitate rate.

3. It is not having universal experimental condition for the

synthesis of various types of metal oxides.

2.2.4. Polyol process

Ethylene glycol has been widely used in the polyol process for the

synthesis of metal (both pure and alloyed) nanoparticles due to its strong

29

reducing power and relatively high boiling point (~197 oC). Recently, it has

been widely used for the synthesis of nanocrystalline ceramic powders that

involved, complexation with ethylene glycol, followed by polymerization [30-

33]. In addition, ethylene glycol has been used to fabricate meso structures of

titania, tin dioxide, zirconia, and niobium oxide by forming glycolate

precursors because of its coordination ability with transition metal ions. This

route involves hydrolysis and inorganic polymerization carried out on the salts

dissolved in a polyol medium. The polyol acts as a solvent for the precursor

salts because of its high relative permittivity, and allows one to carry out

hydrolysis reactions under atmospheric pressure in a large temperature range

up to the boiling point of the polyol [34-35].

2.2.4.1. Advantages of Polyol process

1. Low temperature process which can able to control the

properties of the particles such as size, shape and uniformity,

etc.

2. It yields high pure organic free powders.

2.2.4.2. Disadvantages of Polyol process

1. Large amount of poly hydroxyl alcohol requirement.

2. Phase separation while synthesizing the multi-component

oxides.

3. Choosing the suitable poly hydroxyl alcohol for individual

processes.

30

4. Collecting and purifying the intermediate particles are

complicated.

2.2.5. Combustion Process

Combustion is a complex sequence of chemical reactions between a

fuel and an oxidant accompanied by the production of heat or both heat and

light in the form of either a glow or flames. The combustion concept that using

the art of rapid thermal degradation of precursor chemicals reaction with

oxygen has been effectively used for the synthesis of variety of metal oxides

in nanoscale. [36-40] Based on the fuels and their combinations with the

metal ions sources (commonly metal nitrates, acetates, hydroxides),

combustion process has classified into the following categories [41-42].

2.2.5.1. Combustion of Fuel – Oxidant

Fuel-oxidant combustion technique involves an exothermic

decomposition of a fuel – oxidant precursors such as urea- nitrate, glycine-

nitrate, DHF- nitrate, etc, relatively at lower temperatures [43-45]. Also, it

explores highly fast and self sustaining exothermic reaction between the

metal salts and organic fuels. The heat required for the phase formation is

supplied by the reaction itself and not by an external source. During this

ignition process, large volume of gases will evolve which prevent the

agglomeration and lead to the formation of fine powders with nano structures.

The release of heat during the combustion reaction depends on the fuel –

oxidant stoichiometry in the precursor composition. The fuel – oxidant

stoichiometry is used to calculate the required fuel, based on the thermo

31

dynamical concepts used in the field of propellants and explosives, for the

required nature of combustion process [46].

2.2.5.2. Polymeric Precursors process

The polymeric precursor route is known to be simple cost effective and

versatile low temperature combustion route for the synthesis of multi

component metal oxides relatively lower temperatures [47]. The general idea

of this process is to distribute the metal ions atomistically through the

polymeric structure and to inhibit their segregation and precipitation from the

solution [48]. Further heating of these polymeric intermediates at appropriate

temperatures, yields ultra fine nanocrystalline metal oxides. Generally

hydroxyl carboxylic acids such as citric acid, tartaric acid, etc., are used as a

polymerizing as well as chelating agents in this process [49]. The

physiochemical properties of the synthesized powders are critically depend on

the properties of polymeric intermediates, which influence on the combustion

parameters such as ignition temperature, heat evolution, combustion duration

etc [50]. Hence, wide ranges of polymeric precursors have been investigated

in order to control the structural properties of final products.

2.2.5.3. Pechini Process

Pechini process also one of the combustion process, is based on the

ability of certain weak acids (citric acid, tartaric acid, polyacrylic acid, etc.) to

chelates the various metal ions. These metal carboxylates can undergo

polyesterification when heated with polyhydroxyl alcohol (ethylene glycol,

glycerol, polyvinyl alcohol, etc.,) and lead to the formation of polymeric resin,

with three dimensional networks [31, 50-51]. The cations are uniformly

32

distributed throughout polymeric resin, which inhibits the precipitation.

Further, the calcinations of dried resin yield ultra fine oxide powders at very

low temperature.

2.2.5.4. Advantages of Combustion process

Gel combustion methods show advantages over the earlier mentioned

processes mainly due to the following important facts,

1. Low cost and low temperature process (compared to alkoxide

based sol gel methods).

2. Better control of stoichiometry.

3. Crystalline size of the final oxide products, produced by these

methods is invariably in the nanometer range.

4. Exothermic reaction makes product almost instantaneously.

5. Possibility of multicomponent oxides with single phase and high

surface area.

2.2.5.5. Disadvantages of Combustion process

1. Contamination due to carbonaceous residue, particle

agglomeration, no control on particle morphology.

2. Understanding of combustion behavior is needed to perform the

controlled combustion in order to get final products with desired

properties.

33

3. Possibility of violent combustion reaction, which needs special

production.

In the present investigation three different types of combustion

processes are employed for the synthesis of nanocrystalline metal oxides

TiO2, Dy2O3 and MgO. The details of the synthesis processes are discussed

in chapter IV.

2.3. Preparation methods of polymer solid electrolytes

The different methods are used to prepare various polymer solid

electrolytes. The various preparation methods are given below.

1. Solution-casting method

2. Thermal evaporation method

3. Flash evaporation method

4. Hot pressing method

5. Pyrolysis

6. Film blowing

7. Polymerization of monomer

8. Gaseous discharge

9. Sputtering

In the present investigation, the solution casting method is used to

prepare three different types of nano composite polymer solid electrolyte,

which is briefly discussed.

34

2.3.1. Solution-casting method

Polymer solid electrolyte films are generally obtained by solution

casting method. The required polymer and the inorganic salts are dissolved

in suitable solvents (e.g. THF, Acetonitrile, methanol, ethanol, acetone,

deionized water, etc.) and stirred & heat treated continuously till to get the

homogeneous viscous solution. The viscous solution casted on the glassy

substrates. It allows the solvent to evaporate and form the polymer solid

electrolyte film. The schematic representation of the preparation procedure of

polymer solid electrolyte film is shown in fig 2.2.

In the present investigation, three nanocrystalline metal oxides (TiO2,

Dy2O3 and MgO) are dispersed in three different polymer solid electrolytes

(PVdF-Li+, PVdF/PMMA - Li+, PVdF-HPF - Li+) and prepared three different

nanocomposite polymer solid electrolytes (PVdF-Li+ - (TiO2, Dy2O3 and MgO),

PVdF/PMMA - Li+ (TiO2, Dy2O3 and MgO), PVdF-HPF - Li+ (TiO2, Dy2O3 and

MgO)) using solution casting method. The detailed preparation procedures

for the three different nanocomposite polymer solid electrolytes using solution

casting method are discussed in Chapter V.

35

Fig 2.2. Flow chart representation for the preparation of nanocomposite polymer solid electrolyte (NCPSE) film using solution casting method.

Polymer dissolved in solvent

LiCl4 dissolved in solvent

Metal Oxide dispersed in solvent

Continuous stirred at 333K

EC:DMC (1:1)

Under the sonication

Casted on the glassy substratee

NCPSE film

36

2.4. Characterization techniques

2.4.1. X-Ray Diffraction (XRD)

X-ray diffraction method is one of the most important

characterization tool used in solid state chemistry and material science for

studying the atomic and molecular structure of crystalline substances.

Physical properties of the solids are in some way dependent on their crystal

structure and phase.

X-Ray Diffraction (XRD) measurements were carried out for all the

prepared samples using X-ray powder diffractometers (PHILIPHS make

X’Pert PRO PANalytical and Rigaku miniflex, Japan) with Cu-Kα radiation of

wavelength (λ) 1.5418 Å, with a scan rate of two degree per minute from 10 –

80o and also with an accelerating voltage of 40 kV and current 30 mA. Ni filter

was used to minimize CuKβ radiation. XRD patterns were recorded for all the

prepared powders and polymer samples. The crystalline phase identification

were compared with the JCPDS data

Crystallite size can be estimated from XRD patterns using the

Scherrer equation as follows. [52-55]

LB

0 9

12

.cos

Where, = Wavelength of the radiation used in

B= Bragg`s angle in degrees

1/2 = Full width at half maxima (FWHM) in radians

37

1/2 is calculated using the following expression:

2/122

2/1 )( SM

Where

M = measured width of the line of sample and

S = measured width of the Si standard.

Peak corresponds to the (111) plane of the Si standard was used to

derive the instrumental broadening. NBS silicon standard of known crystallite

size was used as external standard for estimation of the instrumental

broadening.

2.4.2. Fourier transform infrared (FTIR) spectroscopy

Each prepared sample (solid substance) is ground with potassium

bromide (KBr) (1:20) and made into thin transparent pellets using the micro

pelletizer. Also very thin transparent KBr pellet, as a reference, is made using

micro pelletizer. Fourier Transform Infrared (FTIR) Spectra are recorded for

all prepared thin transparent pellet samples using Schimadzu FTIR –

8300/8700 spectro photometer, 4 cm-1 resolution, auto gain, between the

frequency range of 4000 – 400 cm-1 for 32 scans. Schematic diagram,

showing the optical path in a FTIR spectrometer is shown in fig 2.3.

38

Fig. 2.3. Schematic diagramspectrometer.

2.4.3. Scanning Electron Microscopy

Small amount of each prepared

sonicated in few minutes. The dispersed sol was dropped on the conducting

carbon tape pasted over the aluminium stub. Further, thin layer of gold was

coated on each sample using the sputter coater for better conduction.

Microstructure of the each sample was recorded in the form of SEM images at

different magnification using scanning

3400N, Japan.

Photograph of the SEM

the present investigation is sh

Schematic diagram, showing the optical path in a FTIR

Scanning Electron Microscopy

amount of each prepared sample is dispersed in acetone and





different magnification using scanning electron microscopy,

Photograph of the SEM – setup (HITACHI S-3400N, Japan) used in

the present investigation is shown in fig 2.4.

showing the optical path in a FTIR

sample is dispersed in acetone and





opy, HITACHI S-

3400N, Japan) used in

39

Fig 2.4 Photograph of the SEM – setup (HITACHI S-3400N, Japan)

2.4.4. Thermal Analysis

TG/DTA curves are recorded for all the prepared dried gel samples

using TA instruments SDT Q600 V20.5 at the heating rate of 10 oC/min

between 30 - 900 oC under nitrogen atmosphere. Also DSC curves were

recorded for all the prepared polymer samples using TA instruments SDT

Q6000 at the heating rate of 10 oC/min between 30 - 250 oC under nitrogen

atmosphere

2.5. Principles of Impedance spectroscopy

Impedance is the opposition to flow of current, which is given by the

ratio of the applied voltage to the resultant current. Impedance spectroscopy

is a powerful technique used for electrical characterization of an electrolyte

material. It is a perturbation technique, which involves the measurement of

the current through a solid electrolyte when a sinusoidal voltage of low

amplitude is applied. This analysis has been widely used to investigate the

40

elementary process such as bulk conduction, grain boundary conduction, and

electrode-electrolyte interface process in the relevant frequency domain.

Study of conductivity as a function of parameters such as temperature,

chemical potential of the conducting species and sample dimension can yield

the activation energy and relaxation frequency for various conduction modes,

dielectric constant, diffusion coefficient, phase transition and microstructure

correlation [56].

2.5.1. Basic theory

A small amplitude of ac signal is used in impedance measurement to

perturb the system.

The applied potential E() is given by,

ܧ = (ݐ) expܧ

(2πf) is the angular frequency, t is time. The output current of the

system is also a sinusoidal and represented by,

ܫ = ݐ) expܫ + )

According to the Ohm’s law, impedance of the circuit (Z) at any angular

frequency can be represented by,

Z = E/I = ( Eo / Io )exp (-j)

= Zo exp (-j)

41

= Z cos - jZ sin

Z = Zr - jZi

Where j is the imaginary number having the value of -1, Zr and ZI are

respectively real and imaginary parts of the impedance. The phase angle is

represented by

= tan-1(ZI /Zr)

For pure resistor (R), capacitor (C) and inductor (L) impedance is given

by the following representations:

Z = R + 0 j

Z = 0 – j / C

Z = 0 + j L

From the above equations, it is seen that the impedance due to

capacitor and an inductor depend on the frequency of the input signal. The

plot of real and imaginary parts of impedance for a particular range of

frequency is known as impedance spectrum and it appears as semi circles or

straight lines depending on the combinations of resistance and capacitance. If

resistance and capacitance are connected in series or parallel, the impedance

of the circuits is given as follows.

2.5.2. Series combination of R and C

A circuit containing a resistance and a capacitance in series is shown

in fig 2.5.a. The total impedance (Z) of the circuit is given by

42

Z = R + ( 1 / j C) = R- (j / C)

The above equation contains real (Z’) and imaginary (Z”) terms as

indicated below:

Z’ = R and

Z” = 1/C

Fig 2.5. a also shows the complex impedance plot (Z” vs Z’) for the

circuit containing a resistance and a capacitance in series. From the Fig 2.5.

a, the complex impedance plot gives a vertical spike, because Z’ is of fixed

value and Z” decreases with increasing . The point at which the vertical

spike is touch in the real axis gives the resistance value of the circuit as

shown in fig.2.5.a

Fig. 2.5. a & b. Impedance plot for the series and parallel combinations of R and C.

2.5.3. Parallel combination of R and C

A circuit containing a resistance and a capacitance in parallel is shown

in fig 2.5.b. The total impedance (Z) is given by,

43

Z = (1 / R + jC)-1

= R/ (1 + jRC)

= {R / (1 + (RC)2)} – {RjRC / (1+(RC)2)}

Therefore,

Z` = R / (1 + (RC)2) and Z`` = RRC / (1+(RC)2)

Fig 2.5. b also shows the complex impedance plot (Z” vs Z’) for the

circuit containing a resistance and a capacitance in parallel. From Fig 2.5. b,

the complex impedance plot gives a semicircle. The point at which the

semicircle is touch in the real axis gives the resistance value of the circuit as

shown in fig.2.5.b

2.5.4. Preparation of pellets for impedance measurement

All the three prepared LiSmSiO4, LiLaSiO4 and LiDySiO4 samples were

grounded to fine powders with isopropanol as a binding solvent and made into

pellets using the pelletizer under a static pressure of 5 tons to form the pellet

of dimension 10 mm diameter and 2-3 mm thickness. All the three prepared

pellet samples were coated with silver paste as electrodes.

The prepared three nanocrystalline metal oxide samples were

grounded to fine powder and made into pellet using the pelletizer under a

static pressure of 8 tons to form the pellet dimension of 10mm diameter and

2-3mm thickness.All the prepared pellets were coated with silver paste as

electrodes.

44

The final pellet is of the following form for impedance measurements.

Silver electrode/metal oxide sample pellet/silver electrode

The real (Z) and imaginary (Z) parts of the impedance data were

measured on the pellets of metal oxide samples using a Nova control high

performance frequency analyzer in the frequency range 100mHz to 1MHz at

different temperatures. Bulk conductivity of the metal oxide samples were

calculated from the analyzed impedance data obtained at different

temperatures using the nova control winfit software.

45

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