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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.
Chapter 2 Materials Fabrication and Characterization Techniques
33
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.
Chapter 2 Materials Fabrication and Characterization Techniques
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.
Chapter 2 Materials Fabrication and Characterization Techniques
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
Chapter 2 Materials Fabrication and Characterization Techniques
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
Chapter 2 Materials Fabrication and Characterization Techniques
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
Chapter 2 Materials Fabrication and Characterization Techniques
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
Chapter 2 Materials Fabrication and Characterization Techniques
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.
Chapter 2 Materials Fabrication and Characterization Techniques
40
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
Chapter 2 Materials Fabrication and Characterization Techniques
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].
Chapter 2 Materials Fabrication and Characterization Techniques
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’
Chapter 2 Materials Fabrication and Characterization Techniques
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
Chapter 2 Materials Fabrication and Characterization Techniques
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
Chapter 2 Materials Fabrication and Characterization Techniques
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.
Chapter 2 Materials Fabrication and Characterization Techniques
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
Chapter 2 Materials Fabrication and Characterization Techniques
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
Chapter 2 Materials Fabrication and Characterization Techniques
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
Chapter 2 Materials Fabrication and Characterization Techniques
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.
Chapter 2 Materials Fabrication and Characterization Techniques
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
Chapter 2 Materials Fabrication and Characterization Techniques
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.
Chapter 2 Materials Fabrication and Characterization Techniques
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
Chapter 2 Materials Fabrication and Characterization Techniques
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).
Chapter 2 Materials Fabrication and Characterization Techniques
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.
Chapter 2 Materials Fabrication and Characterization Techniques
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
Chapter 2 Materials Fabrication and Characterization Techniques
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.
Chapter 2 Materials Fabrication and Characterization Techniques
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.
Chapter 2 Materials Fabrication and Characterization Techniques
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
Chapter 2 Materials Fabrication and Characterization Techniques
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.
***