materials fabrication and characterization...

CHAPTER - 2

Materials Fabrication and

Characterization Techniques

CHAPTER 2

Materials Fabrication and Characterization Techniques

2.1 Introduction

In this chapter, a general introduction, basic principle, working and applications of different

methods utilized in the present studies have been described in brief. The chapter is divided in

two main parts; the first part goes through the methods used for fabrication of the compounds

whereas the second part describes the methods used for characterization of the synthesized

compounds. So far as material synthesis is concerned, till date a lot of synthesis processes

such as; solid state reaction technique, sol-gel, citrate-gel, self combustion etc. were

developed. Each of the synthesis processes has its own advantages and disadvantages which

certainly perturbs the material properties.

2.2 General methods of samples preparation

There are several methods for fabrication and characterization of multiferroic ceramics of

desired shape, size and composition. Some of them are briefly described below.

(i) Mechanical method - Some of the mechanical methods are; (a) mixed oxide

process (MOP), (b) high-energy ball milling, (c) attrition milling, (d) vibratory milling, (e)

hammer milling, (f) roll crushing, (g) fluid energy milling and (h) turbo milling.

(ii) Chemical method:- There are several chemical methods such as (a) co-

precipitation method, (b) sol-gel process, (c) decomposition, (d) emulsion combustion

method, (e) non-aqueous liquid reaction, (f) spray pyrolysis method, (g) hydrothermal

techniques, (h) liquid phase and gas phase reaction, (i) cryo-chemical processing, (j) polymer

pyrolysis, (k) pechini and citrate gel methods, (l) aerosols and emulsions which are essentially

used to fabricate the materials.

2.2.1 High-energy ball milling process

Conventional ceramic powders prepared by a high-temperature solid-state reaction method

have a particle size of few microns. The particle size of the ceramics becomes larger on firing

Chapter 2 Materials Fabrication and Characterization Techniques

32

at high temperature. The growth of particle size, inhomogeneous distribution of particles and

variation in densification are some of the major problems to prepare conventional ceramics.

Chemical approach of processing requires several cautious steps, including refluxing,

distillation, drying and calcinations of powders at an elevated temperature to convert the

precursors into the desired phase. All these processes require high purity inorganic or

organometallic chemicals which are expensive as well as highly moisture sensitive. Therefore,

special precautions have to be taken during the synthesis process. The above difficulties can

be overcome by using mechanical method such as high energy ball milling process. The ball-

milling process is used to reduce the grain size of metal powders; the powders must be

consolidated in order to form macro scale structural materials. Powder consolidation to the

theoretical densities of a nanostructure-reinforced metal composite without significant grain

growth is necessary for many material properties such as mechanical behavior.

The high-energy ball milling (mechanical alloying (MA)) is a unique processing

method where solid-state reaction takes place between the fresh powder surfaces of the

reactant materials at room temperature. The final grain size is a function of the amount of

input energy during milling, the time and temperature during milling and the milling

atmosphere [155]. The advantage of this technique is that it is simple, requires low-cost

equipment, and many materials are capable of being processed. However, there can be

difficulties, such as agglomeration of the powder particles, broad particle size distributions,

and contamination from the process equipment itself.

The basic principle behind MA involves repeated cold welding, fracturing, and re-

welding of powder particles achieved by repeated collisions of powder particles between the

grinding medium in the milling container. During each collision the powder particles get

trapped between the colliding balls, between the ball, and the inner surface of the vial and

undergo severe plastic deformation. This results in the formation of cold welds and building

up of composite metal particles consisting of various combinations of the starting powder

mixture. A balance is achieved between the rate of welding that increases the average

composite particle size and the rate of fracturing that decreases the average composite particle

size. This leads to a steady-state particle size distribution of the composite metal particles

[156]. The continuous interaction between the fracture and welding events tends to refine the

grain structure and leads to a uniform distribution of the fine reinforcement.


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2.2.2 Planetary ball mill

The high-energy ball mill for MA is the planetary ball mill, the most popular being

manufactured by Fritsch GmbH in Germany. The sample container used in this mill is

attached to a support disk and rotate around a central axis; the sample container itself also

rotates about its own axis, in the opposite direction to the support disk. The centrifugal forces,

created by the rotation of the bowl around its own axis together with the rotation of the turn

disc, are applied to the powder mixture and milling balls in the bowl. The powder mixture is

fractured and cold welded under high energy impact. This causes the grinding media to run

down the inside of the vial, causing a friction/grinding effect on the powders, and when the

media reaches inboard location in the spinning vials, the centrifugal forces align and the

media is propelled into the opposite wall, causing an impact effect on the powders [157]. This

process is most easily visualized in Fig. 2.1(a). As the rotation directions of the bowl and turn

disc are opposite, the centrifugal forces are alternately synchronized. Thus friction resulted

from the hardened milling balls and the powder mixture being ground alternately rolling on

the inner wall of the bowl and striking the opposite wall. The impact energy of the milling

balls in the normal direction attains a value of up to 40 times higher than that due to

gravitational acceleration. Hence, the planetary ball mill can be used for high-speed milling.

In our case we have carried out the ball milling using Retsch Planetary Ball Mill model PM

100 (shown in Fig. 2.1(b))

Fig. 2.1: (a) Schematic illustration of the movement of working parts and balls in a

planetary mill and (b) Retsch Planetary Ball Mill PM 100.


34

The ball milling process is affected by several factors that play an important role in the

fabrication of homogeneous materials. Some of the important parameters that have an effect

on the final constituents of the powder are; (i) Milling Media and container, (ii) Milling

Speed/Energy, (iii) Milling Time, (iv) Milling Atmosphere, (v) Ball to Powder Weight Ratio,

and (vi) Process Control Agent (toluene).

Milling Medium and container

The material of the milling container (grinding vessel, vial, jar, and bowl) is important since

due to impact of the grinding medium on the inner wall of the container, some material will

be dislodged and get incorporated into the powder. The inner wall of the container should be

thick and high enough to allow the ball to create high impact force on the grinding material

[157]. If the material of the grinding vessel is different from that of the powder, then the

chance of contamination of the powder with the grinding vessel material arise. To avoid

contamination of samples caused by unwanted abrasion of grinding components, grinding

vials and balls are available of different materials such as stainless, hardened chromium,

tungsten carbide, zirconia, agate, alumina, silicon nitride, etc. In general, high-density and

larger balls give better results because of high impact forces on the powders. The balls should

be denser than the material to be milled. We have chosen the zirconium grinding jar of 250 ml

capacity with 10 mm zirconium balls for the preparation of the samples. As we know, the

milling media plays an important role to control the size of the particle. It is reported that wet

grinding synthesis process synthesizes fine particles more efficiently as compared to the dry

grinding. As the adsorption of the solvent on the newly formed particle surfaces lowers the

surface energy, which in turn, prevents the agglomeration [158].

Milling Time

According to many researchers, the milling time is the most important milling parameter. To

obtain desirable results, powder should be milled for an optimal time. If the powder is milled

longer than the required time, unwanted contamination and phase transformation might take

place. The required milling time for a particular sample can be found based on the parameters

such as type of mill, ball to powder ratio, temperature of milling and intensity of milling

[159]. The time has to be decided for each combination of the above parameters. In the

present study, the milling was carried out at room temperature for 30 h. The milling was

stopped for 15 minutes after every 1 h of milling to cool down the system.


35

Milling Speed

It is obvious that higher the speed higher is the rate of energy transfer to the powder and lower

is the milling time to achieve the desired homogeneity. The kinetic energy supplied to the

powder will be higher at higher velocities of the grinding medium. Milling was done in the

ball mill at a speed of 400 rpm for 30 h for synthesizing the samples. The milling speed can

have an important influence on particle size but it varies with the type of milling. Above a

certain critical speed, the balls will be pinned to the wall of the milling chamber, and not exert

any impact force on the powder. Below this critical speed, however, the higher is the milling

speed, the higher the milling intensity will be. At higher speeds, the temperature of the system

may increase and may accelerate the transformation process and result in the decomposition

of the solid solution or crystallization of the amorphous phases [160].

Milling Atmosphere

As the milling atmosphere influences the kinetics of alloying, transformation behavior and

nature of the product phase; the milling is frequently carried out in evacuated, argon, or

helium charged milling chambers [161]. Contamination can be avoided by milling the

powders with a milling media made up of the same material as that of the powders being

milled. Generally, the milling chamber is evacuated or filled with inert gas such as argon or

helium to avoid this contamination. Different atmosphere can be used in the milling media if

particular effects are desired [157]. Also the loading and unloading of powders into the vial is

carried out in the inert gas. The milling atmosphere is one of the factors responsible for

contaminating the milling powder.

Ball to Powder Weight Ratio

The ratio of the weight of the balls to the powder (BPR), also referred to as charge ratio (CR),

has a significant effect on the time required to achieve a particular phase in the powder being

milled. The preferred ratio of the weight of the balls to powder ratio is 10:1 [157]. The high

BPR implies higher weight proportion of balls and, in turn, higher number collisions per unit

time. In general, the BPR should be appropriately chosen according to the maximum capacity

of the vial. In most of the cases, the extent of filling the vial is about 50 % of its volume (i.e.

half of the vial space is left empty for optimum results).

Process Control Agent

The main purpose of the process control agent (PCA) is to minimize any unwarranted and

excessive cold welding of the powder particles onto the internal surfaces of the vial and to the

surface of the grinding medium during heavy plastic deformation. A process-control agent


36

(lubricant) is added to the powder mixture during milling to minimize the cold welding

between the powder particles, and thereby inhibits agglomeration. The particle size of the

powder tends to increase, if the weight proportion of PCA to powder is below a critical value.

It decreases above this value as the PCA lowers the surface tension of solid materials. Most

important PCAs include stearic acid, hexane, toluene, methanol and ethanol. The quantity of

PCA used will determine the amount of powder recovered from the process [162]. It should

be noted that excessive PCA beyond the critical amount will be detrimental resulting in

decomposition leading to formation of carbides. In the present case, milling was carried out in

toluene medium.

2.2.3 Steps for processing of material in this method

Selection of raw materials

The raw materials are selected on the basis of high purity and particle size, which are required

for attainment of chemical equilibrium, particularly for the formation of solid solution or

substitution at different atomic sites. Impurity can affect the reactivity as well as electrical

properties of the polycrystalline ceramics. When raw materials have volatile ingredients or

impurities, the ignition losses must be taken into account.

Weighing and mixing

The stoichiometry amount of the constituent materials for the required ceramics is one of the

most important parts of the ceramic technology. The required amount of different chemicals

(metallic oxides or carbonates) is needed for the synthesis of a given amount of ceramics with

the following calculation.

Let M be the molecular weight of the desired sample, m be the amount of prepared

material. Ma is the molecular weight of ath

metallic oxide used in the fabrication of ceramics

in which z fraction of the ‘a’ metallic ion is present. Then the weight required for ath

metallic

oxide is given by ma = Mamz/M

Samples Preparation

The compounds with a general formula Bi1-xAxFe1-x MnxO3 (A = Ba, Sr and Ca with x = 0.0,

0.05, 0.10, 0.15, 0.20) were synthesized by a high-energy ball milling technique. To prepare

samples of suitable stoichiometric proportions, high-purity (>99.9%) Bi2O3 (with 2 mol. %

extra), Fe2O3, SrCO3, CaCO3, BaCO3 and MnO2 (M/S Loba Chemie) were taken, and

thoroughly ball-milled in a zirconium grinding jar of 250 ml capacity and 10 mm diameter of

zirconium balls in a planetary ball mill (Retsch PM 100, Germany). Wet milling was carried


37

out for 30h with ball to powder weight ratio of 10:1 and 400 rpm in a toluene medium. After

milling, the mixture was dried at 100 ºC for 24h. The next step is mixing, eliminating

aggregates and/or reducing the particle size. The ceramics need to be intimately mixed so that

the neighboring particles can inter-diffuse, which is essential for compound formation during

calcination.

Calcination

Calcination means a thermal treatment of endothermic process in the absence or limited

supply of air or oxygen applied to ores and other solid materials to bring about a thermal

decomposition, phase transition, or removal of a volatile fraction. The calcination process

normally takes place at temperatures below the melting point of the product materials in a

high temperature programmable furnace. The decomposition and volatilization reactions have

been taken place at/above the thermal temperature. During this decomposition reaction the

particle size, its distribution, extent of agglomeration, porosity and morphology are usually

established. The thermal process (calcinations) is often the final step in the production of

high-purity ceramic powders. The calcination temperature can be defined as the temperature

at which the standard Gibbs free energy becomes equal to zero for that particular reaction.

The calcination temperature of high energy ball milled sample is usually less than that of

fixed firing (sintering) temperature. During high energy balling milling, defect density in the

samples increases which is, in turn, responsible for enhancing the infusibility of the

ingredients for phase formation. So, it is evidenced that mechanical activation process

decreases the synthesis or phase formation temperature of the prepared system [163]. The

calcinations are done in a furnace with 30 h milled materials taken in high-purity alumina

crucibles and the temperature is optimized for both the completion of reaction as well as the

prevention of volatile oxides.

Pelletization

The calcined powders were grinded by an agate mortar to avoid aglomarization of the

particles, and were used for the study of their phase formation as well as their reaction

mechanism. The intermediate grinding helps to mix the constituent materials for ceramic

preparation and also homogenize the mixture of the ingredient compounds. If the grinding is

coarser, the ceramics can have large inter-granular voids and lower density. If grinding is too

fine, the colloidal properties may interfere with subsequent forming operations. The calcined

powders are again ground to very fine powder and mixed with polyvinyl alcohol (PVA) used

as an organic binder to reduce brittleness of the pellets and then pressed into desired shapes

http://en.wikipedia.org/wiki/Ore

http://en.wikipedia.org/wiki/Thermal_decomposition



http://en.wikipedia.org/wiki/Phase_transition

http://en.wikipedia.org/wiki/Melting_point


38

and dimension. Mostly the conventional method of cold pressing is followed, where the

samples are used to be pressed by die-punch in a hydraulic press at a pressure of 4×106 Nm

-2.

The samples are usually circular or cylindrical in shape.

Sintering

Sintering is thermal treatment of fine-grained material at a temperature below the melting

point of the main constituent, for the purpose of increasing its grain size and strength by

bonding together the particles. Sintering is effective for reducing the porosity, and enhancing

the physical properties such as strength, translucency and thermal conductivity. The grain

growth occurs along with the formation of grain boundaries during the sintering process,

accompanied by the elimination of inter-granular voids (pores). Re-crystallization and grain

growth may follow, and the pores tend to become rounded and the total porosity, as a

percentage of the whole volume, tends to decrease. Thermodynamically, sintering is an

irreversible process in which a free energy decrease is brought about by a decrease in surface

area.

Electroding

To study the electrical properties, samples need electroding by high-purity air-drying

conducting (silver, gold, graphite etc) paste. Electroding materials can be applied after

considering the specific requirements, (i.e., (i) materials must be adhesive with the samples,

(ii) almost zero contact resistance is required and (iii) it should be pasted in the form of thin

layer). The electrode adherences are critical on the smooth ceramic pellet. There should not be

any gap between electrode and the flat faces of the pellet; otherwise, these gaps will affect the

electrical properties of the sample. Hence, the sintered pellets are polished with fine emery

paper to make both the faces flat and parallel.

2.3 Materials synthesized for present study

The polycrystalline samples of Bi1-xAxFe1-xMnxO3 (A = Ba, Sr and Ca with x = 0.0, 0.05,

0.10, 0.15, 0.20) were prepared by a high-energy ball milling reaction method using high-

purity oxides. The materials were first stoichiometrically weighed and mixed thoroughly

using agate mortar and pestle for 1 h, and then ball milled for 30h (as discussed earlier). The

homogeneous mixtures of the above compounds were calcined at optimized temperature 700o

C in alumina crucible for 2 h in air atmosphere. The calcined powders were pressed into small

disc of diameter=10 mm and thickness = 1-2 mm at a pressure of 4×106

N/m2 with a binder

(polyvinyl alcohol (PVA)). The pellets were then sintered at different temperature (780-850


39

˚C) for 4 h. The details of the calcination and sintering temperatures of the samples are given

in Table 2.1. The sintered pellets were polished with fine emery paper in order to make both

the faces flat and parallel. The flat polished surfaces of sintered pellets were then coated with

high-purity air-drying conducting silver paste. The pellets were dried at 150 ˚C for 4 h to

remove moisture (if any) before taking any electrical measurements.

Table 2.1: Calcination and sintering temperatures of the studied the materials.

Materials Composition

(x)

Calcinations

temperature (˚C)

Sintering

temperature (˚C)

BiFeO3 Pure 700 780

Bi1-xBaxFe1-x MnxO3

x = 0.05 700 850

x = 0.10 700 850

x = 0.15 700 850

x = 0.20 700 850

Bi1-xSrxFe1-x MnxO3

x = 0.05 700 850

x = 0.10 700 850

x = 0.15 700 850

x = 0.20 700 850

Bi1-xCaxFe1-x MnxO3

x = 0.05 700 85

x = 0.10 700 850

x = 0.15 700 850

x = 0.20 700 850

2.4 Brief description of characterization techniques used

Scientific disciplines have been identified and differentiated by the experiment and

measurement techniques. A single experimental technique is not sufficient to characterize the

materials. Different aspects of the materials like: structure, microstructure, electrical,

magnetic and magnetoelectric properties have been studied in details in order to understand

the physics and chemistry of the materials. The basic principles, preliminary descriptions and

uses of important experimental methods along with the scope of the present investigation are

furnished in the following sections.


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2.4.1 X-ray diffraction studies for phase and structure determination

X-ray diffraction (XRD) technique is capable of supplying a wide variety of information

about the fine scale structure of materials. As the physical properties of solids (e. g. electrical,

optical, magnetic, ferroelectric, etc.) depend on atomic arrangements of materials,

determination of the crystal structure is an essential part for the characterization of materials.

Therefore, to determine the crystal structure using well known diffraction theory, use of X-

rays as incident radiation becomes extremely useful. X-rays have high energy and short

wavelengths, λ, on the scale of the atomic spacing. The analysis of X-ray diffraction profile

helps in the accurate determination of inter-planar spacing, lattice parameters, lattice

expansion, bond lengths, etc [164].

The relationship between the wavelengths of the X-rays (λ), the incidence angle (θ)

and spacing between two crystal lattice planes (d), is shown in the Bragg's Law expressed as:

nλ = 2dsinθ, where n is an integer

The powder profile of a substance can be used for identification of materials. The

advantage of x-ray powder diffraction method is capable to develop quantitative and

qualitative analysis of a substance. The accurate determination of lattice parameters provides

an important basis in understanding various properties of the materials. The calculation of

lattice constants from the line positions or d spacing can be done from a general formula:

V2

[h2b

2c

2sin

2α+k

2c

2a

2sin

2β+l

2a

2b

2sin

2γ] (2.1)

Where V2= volume of the unit cell

= abc(1-cos2α-cos

2β- cos

2γ+cosαcosβcosγ)

1/2 (2.2)

where a, b, c, α, β and γ are lattice parameters and h, k, l are the Miller indices. Using the

above formula lattice parameters for all the compositions were found out and from the

measured position of a given powder diffraction line, Bragg angle θ can be determined. By

knowing the wavelength of X-ray beam used and the Bragg angle, the interplanar spacing of

the corresponding reflecting lattice planes can be calculated. The interpretation of powder

diffraction pattern/profile can be a simple or difficult task depending upon the number of

atoms present in the unit cell and the complexity of the phase composing the specimen. The

simplest way to interpret the experimental data is by comparing it with the standard pattern of

reference material. For a polycrystalline material consisting of sufficiently large and strain

free crystallites, the lines of powder pattern should be extremely sharp. Actually it is difficult


41

to expect such sharp diffraction profile due to the combined effects of instrumental errors and

other physical factors, which broadens the diffraction line profile.

Using the well known Scherrer’s equation, the X-ray diffraction data can also be used

to calculate the crystallite size from a particular reflection (hkl), as given by [165]:

cos2/1

khkl (2.3)

where β1/2 is the FWHM (full width at half maximum (in radians)) of the diffraction profile

corresponding to hkl plane, k is a constant approximately equal to unity and related to the

crystallite shape, is the angle at which the peak of the representative (hkl) profile is

observed. The best possible value of k was obtained as 0.89. The limitation to the Scherrer’s

equation is the presence of strain and instrumental response in the diffraction data. In order to

eliminate the instrumental error, the value of FWHM (β1/2) of the standard sample is

subtracted from the β1/2 value of the sample (i.e., β1/22

effective= β1/22

sample- β1/22 silicon).

Fig. 2.2: Schematic

diagram of X-ray

diffractometer [Pan

Analyticals X’pert PRO].


42

The instruments and strain in the material play a very vital role in determining the

width of the diffraction peaks which are used in the calculation of crystallite size. The easiest

way to serve this purpose is to analyze the diffraction peaks by Rietveld refinement technique.

X-ray diffraction combined with Rietveld analysis provides detailed information regarding

unit cell dimensions, bond-lengths, bond-angles and the site ordering of crystallites.

In the present case, calcined powders were characterized with respect to phase

identification, phase quantity measurement, crystallite size determination and lattice

parameter measurement, etc. using X-ray powder diffractometer (Pan Analyticals X’pert Pro

3050/60 (Fig. 2.2)) with Co-target. The calcined powder of the material was packed uniformly

into a slotted-glass slide in order to avoid preferred orientation and induced packing. The

glass slide having the powder specimen was placed at the center of the instrument. Ideally, the

powder was mounted in such a way that no foreign material was exposed to the X-ray beam.

The diffraction patterns were recorded in a wide range of 2θ (10 → 80˚) at a step size of

0.017˚, 2θ with 30 second/step.

2.4.2 Structural analysis using Rietveld method

The Rietveld refinement technique is a powerful tool for refining and extracting detailed

structure information of the materials from powder diffraction data. This was developed by

H.M. Rietveld in 1967 [166, 167]. In this technique, the things actually being refined are

parameters in models for the structure and the instrumental effects on the diffraction pattern.

The least-squares refinements are carried out until the best fit is obtained between the entire

observed powder diffraction patterns taken as a whole. The strength of the least-squares

method is that it is a method for solving over determined systems.

The powder diffraction pattern is recorded in digitized form, i.e., as a numerical

intensity value, yi, at each of several thousand equal increments (steps), i, in the pattern.

Depending on the method, the increments may be either in scattering angle, 2θ or some

energy parameters such as velocity (for time-of-flight neutron data) or wavelength (for X-ray

data collected with an energy dispersive detector and an incident beam of ‘white’ X-

radiation). For constant wavelength data, the increments are usually the steps in scattering

angle. The intensity yi at each step, i, in the pattern is measured either directly with a quantum

detector on a diffractometer or indirectly with step-scanning micro-densitometry of film (e.g.

Guinier) data. Typical step sizes range from 0.01 to 0.05o in 2θ for the fixed wavelength X-

ray data and a bit larger for the fixed wavelength neutron data. In all cases, the ‘best-fit’


43

sought is the best least-squares fit to all of the thousands of yi’s simultaneously. The quantity

minimized in the least-squares is the residual, Sy:

i

ciiiy yywS 2)( (2.4)

Where wi= 1/yi,

yi= observed (gross) intensity at the ith

step,

yci= calculated intensity at the ith

step and the sum is over all the data points.

Typically, many Bragg reflections contribute to the intensity, yi, observed at any arbitrarily

chosen point, i, in the pattern. The calculated intensities; yci, are determined from the [Fk]2

values, calculated using the structural model by summing the calculated contributions from

the neighbouring Bragg reflections plus the background:

bikkikkci yAPFLsy 222

(2.5)

Where s is the scale factor, Lk contains the Lorentz polarization, and multiplicity

factors, Fk is the structure factor for the Kth

Bragg reflection, is the reflection profile

function, Pk is the preferred orientation function, A is an absorption factor, K represents the

Miller indices, h, k, l, for a Bragg reflection, and ybi is the background intensity at the ith

step.

The effective absorption factor ‘A’ differs with instrument geometry, It is usually

taken to be a constant for the instrument geometry most used for X-ray diffractometers, that

of a flat specimen with its surface maintained normal to the diffraction vector by a θ-2θ

relationship between specimen rotation and detector rotation about the diffractometer axis. It

does depend on angle for other geometries.

The model allows the refinements of atomic positional coordinates, thermal and site-

occupancy parameters, background polynomial functional parameters, lattice, instrumental

geometrical-optical features, specimen aberrations (e.g. specimen displacement and

transparency), an amorphous component and specimen reflection-profile-broadening agents

such as crystallite size and micro strain, etc. In some cases, it is important to model extinction,

as well. Although it is in general a much less severe problem with powders than with single

crystals, extinction can be quite important in some powder specimens. Multiple phases may

be refined simultaneously and comparative analysis of the separate overall scale factors for


44

the phases offers what is probably the most reliable current method for doing quantitative

phase analysis.

The powder diffraction patterns are simulated providing all necessary structural

information and some starting values of micro-structural parameters of the individual phases

with the help of the Rietveld software, the MAUD l.99 [168]. Initially, the positions of the

peaks were corrected by successive refinements of zero-shift error. Considering the integrated

intensity of the peaks as a function of structural parameters only, the Marquardt least-squares

procedures were adopted for minimization of the difference between the observed and

simulated powder diffraction patterns, and the minimization was carried out by using the

reliability index parameter, Rw (weighted residual error), and Rb (Bragg factor) defined as:

(2.6)

(2.7)

(2.8)

where yi(obs) and yi(calc) are the observed and the calculated intensities, respectively, wi =

1/yi(obs), N are the weight and number of experimental observations and P is the number of

fitting parameters. The goodness of fit (GoF) is established by comparing Rw with the

expected error, Rexp. This leads to the value of goodness of fit [169]:

(2.9)

Refinement continues till convergence is reached with the value of the quality factor, GOF

very close to 1, which confirms the goodness of refinement.

2

1

2

)(

2

)()(

100

i

obsii

i

caliobsii

w

yw

yyw

R

i

obsi

i

caliobsi

b

y

yy

R

)(

)()(

100

21

2

)(

exp

i

obsii yw

PNR

expR

RGOF w


45

2.4.3 Scanning Electron Microscope

The scanning electron microscope (SEM) is an instrument that records the images of a

material by scanning the sample with a focused electron beam, under low or high vacuum.

The SEM provides topographical, morphological and compositional information which

provides valuable information about this material. SEM essentially offers a very high

magnification with very high-resolution capabilities and a large depth of focus. The signals

that derive from electron-sample interactions reveal information about the sample including

external morphology (texture), chemical composition, crystalline structure and orientation of

materials making up the sample. Mostly data are collected over a selected area of surface of

the sample and a 2-dimensional image is generated that displays the spatial variations in these

properties. A schematic diagram of scanning electron microscope is shown in Fig. 2.3.

Fig. 2.3: A simplified schematic diagram of a scanning electron microscope.


46

When a beam of highly energetic electrons strikes the sample, the secondary electrons, x-rays

and back-scattered electrons are ejected from the sample. These secondary electrons emitted

are collected and converted into a current that is amplified to produce a signal voltage. This

signal is passed to a cathode-ray tube (CRT) where it determines the potential of the

regulating or modulating electrode which controls the current in the cathode ray tube. As a

result, a point on the screen of the CRT is formed whose brightness is controlled by the

current reaching the collector. The essential components of a scanning electron microscope

are: (a) electron-optical columns together with appropriate electronics, (b) the vacuum system,

which includes the specimen chamber and stage and (c) signal detection and display system.

The electron column contains magnetic lenses whose function is to focus the electron beam.

Two sets of scanning coils are coupled with appropriate scan generator and cause the beam to

be deflected over the specimen surface in a raster like pattern. The specimen chamber is

designed in such a way that the various types of movements such as translation, rotation and

tilting of the specimen in desired direction can be done in the chamber. The normally attained

orientations in the specimen stages are translation, 360˚ rotation and provision for tilting the

specimen. The detection system used in SEM depends on the interaction of primary electron

beam with the specimen. The different effects like secondary electron emission, reflected or

back scattered electron current, x-ray production and cathode luminescence etc. are usually

observed. All of the signals can be detected, amplified and used to control the brightness of

the cathode ray tube (CRT). The deflection of the electron beam in the CRT is controlled by

the same scan generator, which determines the position of the electron beam on the sample.

Thus SEM is a powerful technique for point to point scanning of the small region such as

grain and grain boundaries. The interaction of high-energy electrons with specimen leads to

the excitation of variety of signals, which can be used in the characterization of microstructure

etc.

For microscopic study, a small piece of sintered pellet has been taken and then gold

was coated (thickness ~ 40Å) using a vacuum coating unit. The micrographs were recorded at

different magnifications using FEI QUANTA 250 system.

2.2.4 Energy Dispersive X-ray (EDX) Analysis

One of the useful technologies that come with SEM is energy dispersive X-ray (EDX)

analysis, which allows elemental analysis without destroying the sample. The EDX analysis

relies on the investigation of a sample through interactions between electromagnetic radiation

and matter, analyzing x-rays emitted by the matter in response to being hit with charged


47

particles. As the electron beam of the sample surface is scanned across the sample surface, it

generates X-ray fluorescence from the atoms in its path. The energy of each X-ray photon is

characteristic of the element which produces it. The EDX system collects the X-rays, sorts

and plots them by energy and automatically identifies and labels the elements responsible for

the peaks in the energy distribution. The EDX data are typically compared with either known

or computer generated standards to produce a full quantitative analysis showing the sample

composition. Data output plots the original spectrum showing the number of X-rays collected

at each energy and line scan over a given length.

Fig. 2.4: An inter-shell diagram of an atom and energy dispersion illustrating the

principle of EDX.

When a high-energy electron beam hits the atom at the point of contact, secondary and

backscattered electrons are emitted from the surface. At rest, an atom within each sample

contains ground state electrons in the discrete energy levels or electron shells bound to the

nucleus. The electron beam excites an electron, ejecting it from the shell while creating a

hole in the electron shell. An electron from the outer-higher energy-shell drop into the hole in

the inner shell, X-rays is generated as shown Fig. 2. 4. The energy of each photon is the

representative of the elements present in the sample. The energy dispersive spectrometer

collects the X-rays and plots them as counts versus energy curve. Since the X-rays generated

are formed by interaction of high-energy electron beams with sample surface, elemental


48

analysis is possible for very small areas of the sample. By calculating the area under the peaks

of each identified element and considering accelerating voltage of the beam, quantitative

analysis can be performed. The intensity of the EDX spectra represents the concentration of

the related element in the testing area. The EDX analysis in this thesis has been carried out by

using a scanning electron microscope (FEI Quanta, 250) integrated with EDAX GENESIS

PRIME Spectrum v6.33 from AMETEK.

2.2.5 Electrical Measurements

When an insulator is placed in an external electric field, electrons of the atoms are displaced

slightly with respect to the nuclei, so induced dipole moment results which cause the

electronic polarization. When the atoms of a molecule do not share their electrons

symmetrically, the electron-clouds are displaced eccentrically towards the stronger binding

one, and thus the ions acquire charges of opposite polarity. The net charges tend to change the

equilibrium positions of the ions themselves under the action of an external electric field. This

displacement of charged ions or groups of ions with respect to each other creates a second

type of induced dipole moment. It represents the ionic polarization of the unlike partners of

molecule giving rise, in addition, to permanent dipole moments, which exist even in the

absence of an external electric field. Such dipoles experience a torque in an electric field that

tends to orient them in the direction of the field. Consequently an orientation (or dipole)

polarization can arise. These three mechanisms of polarization are due to charges locally

bound in atoms, molecules or in the structure of solids. In addition to all these, there usually

exist charge carriers that can migrate for some distance through the dielectric. Generally

carriers are impeded in motion because of being trapped in the materials interfaces. Hence

they cannot freely discharge at the electrodes and space charges result. Such distortion

appears as an increase in the capacitance of the sample and may be distinguishable from a rise

of the dielectric constant. Thus a fourth polarization, called the space charge (or interfacial)

comes into play. For electronic and ionic polarizations, the frequency effect is negligible upto

about 1010 Hz. As the optical range of frequencies is reached, electronic contribution

becomes sole contributor. The effect of temperature on both electronic and ionic polarizations

is small. At higher temperatures, polarization increases due to ionic and crystal imperfection

mobility. The combined effect produces a sharp rise in the dielectric constant at low

frequency with increasing temperature corresponding to both dipole orientation effects and


49

space charge effects. The total polarization is a sum of these four polarizations (assuming that

they act independently) [170].

Dielectric characteristics of materials are of increasing importance due to their various

applications in the field of solid-state electronics and electrical engineering. The main

applications of ceramic dielectrics are as capacitive elements in electronic circuits, and as

electrical insulators. The dielectric constant, loss tangent and dielectric strength are the

important characteristics of dielectrics relevant to their suitability for application purpose.

When the dielectric is placed in an alternating field, a phase shift is occurred between the

driving field and the resulting polarization, and a loss current component appears giving rise

to the dielectric loss of the sample. Here the polarization (P) as well as the electric

displacement (D) varies periodically with time. In general, P and D may lag behind in phase

relative to electric field E, so that;

D = D0 cos (ωt - δ) = D1cosωt + D2sinωt (2.10)

where δ is the phase angle and slightly less than 900.

D1= D0cosδ and D2 = D0sinδ

The ratio of displacement vector to electric field (D0/E0) is generally frequency dependent. To

describe the situation one may thus introduce two-frequency dependent dielectric constant:

εr'(ω) = (D0/E0) cosδ , and εr"(ω) = (D0/E0) sinδ (2.11)

where εr' (ω) and εr"(ω) are real and imaginary pat of complex dielectric permittivity

respectively, such that εr = εr' - jεr". If a sinusoidal voltage V = V0ejωt

is applied to a capacitor

of capacitance C, then the total current is given by,

I = dQ/dt = d(CV)/dt = jωεrC0V (2.12)

where C0 is the capacitance in vacuum.

Therefore, I = jωC0V (εr'-jεr") = ωεr"C0V + jωC0Vεr' = I1 + IC (2.13)

The total current I through the capacitor can be resolved into two components, a charging

current (Il) in quadrature with voltage and conduction current IC in phase with the voltage.

The loss factor or tangent loss is given by

tan δ = I1/IC = ε r''/ ε r' (2.14)

The loss factor is the primary criterion for the usefulness of a dielectric as an insulator. So, for

some applications where high capacitance in the smallest physical space is required, materials

with high dielectric constant and low tangent loss (tan δ) must be used. The dielectric

properties of ferroelectrics depend on the field strength at which it is measured.


50

The total current I through the capacitor can be resolved into two components, a

charging current (Ic) in quadrature with voltage and conduction current I1 in phase with the

voltage. The vector resolution of current is shown in Fig. 2.5.

Fig. 2.5: The vector resolution of

ac current in a capacitor.

For a parallel plate capacitor with sinusoidal applied voltage, loss current density is given by

Jl = ω ε0 ε r'' V = ζ V (2.15)

Where ζ = ω ε r' ε0 tan δ is the dielectric conductivity.

The effective conductivity defined in this manner depends upon frequency and is always

greater than dc conductivity. The loss factor is the primary criterion for the usefulness of a

dielectric as an insulator. So for application purposes where high capacitance in the smallest

physical space in required, materials with high dielectric constant and low tangent loss (tan δ)

must be used. The dielectric properties of ferroelectrics depend on the field strength at which

they are measured. This is a consequence of non-linear relation between polarization and

electric field.

Complex Impedance spectroscopy

Complex impedance spectroscopy (CIS) enables us to evaluate and separate the contribution

to the overall electrical properties in frequency domain due to electrode reactions at the

electrode/material interface and the migration of charge carriers (ions) through the grains and

across the grain boundaries within the specimen sample [171, 172]. The results of the

complex impedance measurement of a sample as a function of the applied signal frequency


51

having both resistive (real part) and reactive (imaginary part) components can be displayed

conventionally in a complex plane in terms of any of the following representations.

Complex permittivity, ε* = ε΄-ε˝ (2.16)

Complex impedance, Z* (ω) = Z΄- jZ˝ = Rs-j/ωCs (2.17)

Complex modulus, M*(ω) = M΄+jM˝ (2.18)

Complex admittance, Y* = Y΄+jY˝ (2.19)

where ε', Z', M', and Y' are the real parts and ε", Z", M", and Y" are the imaginary parts and

C0 is the geometrical capacitance of the cell, ω is the angular frequency and j = √−1.

In impedance spectroscopy technique, a sinusoidal signal of low amplitude is applied across a

sample and the response at the output is compared with the input signal in order to determine

the impedance (Z) and phase shift (θ). Due to this directional characteristic, the impedance

data can be represented in terms of a vector diagram or in the form of real and imaginary

components of a complex number in the complex plane as shown in Fig. 2.6. The diagonal

distance represents the magnitude of impedance from center (origin) of the plane whereas the

angle subtended with the abscissa (real axis) corresponds to the phase angle between the input

voltage applied across the sample and the output current measured.

Fig. 2.6: Representation of cell impedance (Z) on a vector diagram/complex plane.

The impedance of the circuit Z(ω) at an applied frequency ω can be expressed in both polar

as well as Cartesian form.


52

Z* (ω) = ׀Z׀ exp (-jθ) = ׀Z׀cosθ - j׀Z׀sinθ = Z΄ - jZ˝ (2.20)

The magnitude of the complex impedance (Z)* = [(Z΄)2

- (Z˝)2]1/2

and θ = tan-1

(Z΄/Z˝). This

complex quantity is only real when θ=0 (current and voltage are in phase) and thus Z*(ω) =

Z΄(ω), (i.e., for purely resistive surface).

Fig. 2.7: Phase Sensitive Meter (PSM 1735): N4L impedance analyzer.

In the present investigation, the dielectric measurements have been carried out using PSM

1735: N4L (Fig. 2.7) impedance analyzer with indigenously developed two terminal sample

holder. The sample was heated or cooled, above or below room temperature with the help of a

laboratory-made furnace. The temperature was recorded by a thermocouple (chromel -

alumel) connected with a dc micro-voltmeter (RISH multi 15S) with an accuracy of 0.01 mV

(equivalent to accuracy in temperature ±0.25 K). Experimental data were recorded when the

sample attained the steady temperature. The temperature interval of the measurement was

about 5o

C. Measurement was carried out in the frequency range of 103-10

6 Hz at different

temperatures. The impedance analyzer is connected with a PC for data acquisition. The

sinusoidal ac frequencies were applied along the axis of the cylinder keeping the d.c. bias

voltage disabled. The capacitance and loss tangent of the materials were measured as a


53

function of ac frequency. The dielectric constant of the materials at different frequencies were

calculated using the relation εr= tCp/A ε0, where t is the thickness, A is the area of the

electrode, t is the thickness of the material, Cp is the capacitance measured in parallel mode

and ε0 is the permittivity of the free space which is 8.854x10-12

F/m. The ac conductivity of

the samples was calculated using capacitance and tan δ.

I~V measurement

An electrometer is an electrical instrument designed to measure very small voltage, current

and other parameters. The sensitivity of these instruments is about 0.01 volt. A much more

sensitive device is the vacuum-tube electrometer, a direct-current amplifier capable of

measuring currents as minute as 10-15 amperes (about 10,000 electrons per second).

Calculation of the resistance using Ohm’s law (R=V/I). The high resistance materials and

devices produce very small currents that are difficult to measure accurately; Keithley

electrometer (Fig. 2.8) and pico-ammeter are used for such measurements.

Fig. 2.8: Keithley Electrometer (Model 6517B).

The (J–E) characteristics of the samples were obtained as a function of voltage (1–100 V)

with an interval of 25 ˚C starting from room temperature (25 ˚C) up to 400

˚C using a

programmable electrometer (Keithley, model 6517B).


54

2.2.6 Polarization Study

The polarization (the electric dipole moment per unit volume) can be obtained from hysteresis

loop parameters (Valasek, 1921). In the present study, all the samples were first poled at an

optimized electric field for 12h using a dc electric field 2 kV/cm in a silicon oil bath at room

temperature using a DC poling unit (M/s Marine India, New Delhi) (Fig. 2.9). Poling is done

to align the randomly oriented electric dipoles in a specified direction. The process of polling

of ferroelectrics is to switch reverse domains below Curie temperature (Tc) with higher

electric fields than coercive field. For several materials the high coercivity allows poling in

this way only near Tc, but in most materials electrical poling may be achieved by cooling the

sample from the paraelectric phase to ferroelectric phase in an applied electric field parallel to

the polar crystallographic axis under a constant electric field.

Fig. 2.9: The DC Poling Unit. Fig. 2.10: The P~E loop tracer.

The hysteresis loops were obtained on the poled samples using a P-E loop tracer (M/s Marine

India, New Delhi) (Fig. 2.10). Ferroelectric crystals have polarization vectors which can be

oriented in two opposite directions. The displacement causes the reduction in the symmetry of

the crystal automatically. Thermodynamically stable, the states can be switched from one to

the other by applying an external electric field. Usually, ferroelectric crystal includes domains

(regions with many unit cells containing ions displaced in the same direction) that have

mixture of polarizations.


55

Fig. 2.11: Sawyer-Tower electric circuits for ferroelectric hysteresis loop measurement.

The classic electric circuit for FE hysteresis loop measurement is named as Sawyer-Tower (S-

T) electric circuit [173]. The S-T circuit is useful for the material, which has a low loss and

high polarization. Here the field applied across the sample is attenuated by a resistive divider,

and the current is integrated into charge by virtue of a large capacitor in series with the

sample. The circuit (Fig. 2.11) consists of two capacitors, one due to ferroelectric material

(C1) and other one is a linear-known-valued reference capacitor (C2). They are in series,

where C2 is chosen much greater than C1 so that voltage drop across C2 is much less than that

across C1 (sample). The voltage across C2, which gives polarization of the sample, is applied

to vertical plates of the oscilloscope and the drive voltage (Vd) after safe attenuation is applied

to horizontal plates of the oscilloscope to measure electric field across the sample.

The polarization (P) = (C2/A) Vy

Electric Field (E) = Vd / d, where‘d’ is thickness of the sample in cm.

2.2.7 Magnetic Measurements

The magnetic properties of a material can be obtained by studying its hysteresis loop (M ~ H).

From the hysteresis loop, a number of primary magnetic properties of a material, such as (a)

retentivity, (b) residual magnetism, (c) coercive field, (d) permeability, and (e) reluctance can

be obtained. For the measurements of these parameters various types of magnetometers have


56

been developed, and are now commercially available. They have been broadly classified into

two categories: (i) those employing direct techniques, such as measurement of the force

experienced by the specimen in a non-uniform field, and (ii) those based on indirect

techniques such as measurement of magnetic induction due to relative motion between the

sample and the detection coils system (vibrating sample, vibrating coil, SQUIDs) or use of

galvanomagnetic effects such as the Hall effect.

The experimental technique of vibrating sample magnetometer (VSM), originally

developed by Foner [174], has been the most successful technique for low-temperature and

high-magnetic field studies of correlated electron systems due to its (i) simplicity (ii) ease of

measurement and (iii) reasonably high sensitivity. Each of our samples was placed inside a

uniform magnetic field generated by the electromagnets. It was then vibrated sinusoidally at

certain amplitudes and frequencies—typically through the use of a piezoelectric material. The

vibration induced a magnetic flux change through the sample, which subsequently resulted in

a voltage in the pick-up coils. The induced voltage in the pickup coil was observed to be

proportional to the sample's magnetic moment, but was not dependent on the strength of the

applied magnetic field. In a typical VSM setup, the induced voltage is measured through the

use of a lock-in amplifier, with the piezoelectric signal serving as its reference signal.

Fig. 2.12: Schematics of the sample rod and puck setup in the dewar of the PPMS.


57

The magnetic moment measured by the VSM can be related to the magnetization of the

sample. In the present study, magnetic study of the proposed compounds was carried out

using a 14 tesla PPMS (Physical Property Measurement System)-VSM of Quantum Design

model-6000. The vibrating sample magnetometer has become a widely used instrument for

determining magnetic properties of a large variety of materials: diamagnet, paramagnets,

ferro-magnets, ferri-magnets and anti-ferromagnetics. The main objective of the VSM is to

determine magnetic properties according to the applied magnetic field and the temperature.

The VSM is based upon Faraday’slaw according to which an e.m.f. is induced in a conductor

by a time-varying magnetic flux. Use of the VSM involves measurement of the harmonic

oscillation of the sample in a uniform magnetic field.

2.2.8 Magnetoelectric coefficient measurement

Magnetoelectric materials possess simultaneously piezoelectric (PE) and piezomagnetic (PM)

properties: when magnetic field is applied on electrically and magnetically poled ME sample,

a local distortion in PE phase generates electric field across it. Basically three direct methods

are there to measure ME effect in ceramics, namely: static, quasi-static and dynamic method.

In the static method, the ME signal is measured as function of increasing magnetic field using

a high input impedance electrometer. For the quasi-static case, the ME signal is measured as a

function of time using a high input impedance electrometer, while the applied DC magnetic

field is varied with time [175]. In dynamic technique, measurement is carried out with a

variable dc magnetic field in the presence of biased ac magnetic field [176]. The ac field will

not allow the charges to move towards the electrode since a suitable signal with an

appropriate frequency is used. As the output signal is very weak, the appearance of noises

should be avoided. In our case magnetoelectric measurements were carried out following the

dynamic ME method as adopted by some research groups [177, 178].

The main devices required for the ME set up are (i) Electric poling unit, (ii) Magnetic

poling unit, (iii) Helmholtz coil with a desired frequency, (iv) DC power supply for producing

a stable dc magnetic field, (v) Lock-in amplifier, (vi) ME setup with Gauss meter and (vii)

Data recorder unit. At first the pellet sample was poled at an optimized electric field for 2 h

using a dc electric field 2kV/cm in a silicon oil bath at room temperature using a DC poling

unit (M/s Marine India, New Delhi) (details are described in section 2.2.6). Then the same

pellet was put into a sample holder, and placed between the poles of an electromagnet. The

experiment set-up is shown in Fig. 2.13.


58

Fig. 2.13: The magnetoelectric measurement setup.

The dc magnetic bias field up to 7 kOe is produced by the electromagnet and a Hall probe is

engaged to measure the dc field. The time-varying dc field is achieved by a programmable dc

power source (ME Setup, M/s Marine India, NewDelhi). Additionally, an ac magnetic field up

to 15.368 Oe with frequency 1 kHz and amplitude of 5V is superimposed onto the dc field.

The ac magnetic field was provided by a Helmholtz coil (HC) having 200 turns with a

diameter of 50 mm and it was fed with a frequency generator provided with a power supply

for producing the bias ac magnetic field at a desired frequency. The pellet is placed in the

magnetic field with its surface perpendicular to the field direction. The electric signal

produced by the sample was input to a lock-in-amplifier [Stanford research system SR-830].

At the same time, the signal generator sent a signal synchronized with the coil excitation

signal to the lock-in amplifier as reference. ME coefficients were determined for various

magnitudes of the dc static magnetic field (0 –5 kOe). Data acquisition was performed by a

computer using a ME setup interference program.

When a dc magnetic field is applied to a material, the ME output voltage (V) appears

and the expression for V is

V = f (H) = Const. + αH + βH2 + γH

3 + δH

4 + ….

= α + 2 βH + 3γH 2+ 4 δH

3 + ……………….. (2.15)

When a small AC field h = h0 sinωt superimposed onto a DC bias field H, the total field:

Htotal = H+h0 sinωt


59

h0 is the amplitude of the ac magnetic field, and d is the thickness of the sample.

Substituting the value of H in the above equation and solving it out, we can get the following

expression:

Vout = h0 (α + 2 βH + 3γH2+ 4 δH

3) (neglecting high order terms in (h0/H) when (h0/H) << 1)

= h0 (2.16)

The ME coefficient (αME) can be calculated using relation

αME = = = (2.17)

where d is the thickness of the pellet sample

2.5 Conclusion

A comprehensive description of the selected techniques used in the present work has been

presented here. The real time experimental conditions to record data on the samples under

study have also been described briefly.

***

materials fabrication and characterization...

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