28

Chapter Three

Characterization Techniques

The different characterization techniques used

in the work have been discussed in the present

chapter. Theory of X-ray diffraction and the

details of the structural analysis using XRD

technique have been presented. Fourier

Transform Infrared (FTIR) spectroscopy

technique for the confirmation of crystal

structure is outlined. Diffuse Ray spectroscopy

(DRS) technique for optical data measurement

is discussed. Details of the imaging technique

used (SEM) is also presented. Vibrating

Sample Magnetometry (VSM) for the magnetic

characterization of the samples has been

discussed. Dielectric characterization

technique has been briefly discussed.

3.1 Introduction

3.2 Powder X-ray Diffraction

Technique

3.3 Scanning Electron

Microscopic analyses

3.4 Fourier Transform

Infrared spectroscopy

3.5 Diffuse Ray Spectroscopy

(DRS) technique

3.6 Vibrating Sample

Magnetometer (VSM)

3.7 Electrical Properties

3.8 Dielectric Measurement

29

3.1 Introduction

Synthesis of materials and their proper and thorough characterization is an

inevitable part of material science research. The use of suitable preparation techniques

and proper analysis of properties using various characterization techniques can lead to

the design of nano-materials for different applications. Hence a detailed description of

the various experimental techniques employed for the analysis of the M-type

hexagonal ferrite samples are discussed in this section. The following characterization

techniques have been used for analyses of the samples in this research work.

3.2. Powder X-ray diffraction technique

Phase identification

Lattice parameters determination

X-ray and porosity calculation

3.3. Scanning electron microscopic analyses

Surface morphological and micro-structural studies

3.4. Fourier Transform Infrared spectroscopy

Confirmation of crystal structure

3.5. Diffuse Ray spectroscopy (DRS) technique

Optical properties measurement

3.6. Vibrating Sample Magnetometer (VSM)

Saturation magnetization determination

3.7. Electrical Properties

DC electrical resistivity

3.8. Dielectric measurements

Dielectric constant determination

Dielectric loss tangent determination

30

3.2 Powder X-ray Diffraction Technique

The powder X-ray diffraction technique was employed for the phase

identification of the synthesized material. Philips analytical diffractometer (Model

PW 3710) is used for the X-ray diffraction measurement. When a beam of fast

moving electrons, travelling in evacuated tube, strikes on the surface of a material

(target), X-rays are produced. These X-rays are considered as characteristics of that

material. Most of the X-ray diffractometer contain Cu as target material. The X-rays,

generated from Cu, strikes on the surface of the material under testing. A rich variety

of information can be extracted from X-ray Diffraction (XRD) measurements.

If „d‟ is the distance between the planes (considered as the characteristics of a

material) and „ ‟ is the wave length of X-rays then according to Bragg‟s law.

sind2n (3.1)

where, „ ‟ is the angle between the plane of the crystal and incident X-ray beam, d is

inter planer spacing.

Figure 3.1: Geometrical illustration of Bragg’s law

The intensity of powder diffraction peaks which depends on the crystal

structures including types of atoms and unit cell, thermal vibration of atoms, etc. In

addition to the primary structural factors, the intensity of diffraction is dependent on

other factors, which are not only relevant to sample effects such as its shape and size,

d

d

dsin

Incident x-ray Diffracted x-ray

31

particle size and particle size distribution etc., but also with the instruments including

source, monochromator and detector, etc. [65].

In most of the X-ray diffractometers, Cu source is usually used as X-ray

radiation source. The monochromator (Ni filter) is placed in the incident beam path

between the X-ray tube and the sample. When the incident X-ray radiation beam hits

the surface of powdered sample, the diffraction of that beam occurs in every possible

direction (angle) of 2 positions, as shown in Figure 3.2. The diffracted beam is

detected by detector, which sensitively detects the intensities of diffracted beams as

diffraction peaks. Computer software program then displays the diffracted pattern for

the sample, which plots the positions and intensities of the diffracted peaks.

Figure 3.2: Schematic diagram of a simple X-ray diffractometer

Using the data of the peaks, obtained from XRD patterns of polycrystalline

hexagonal structure, different structural parameters such as lattice constant (a & c),

crystallite size (D), cell volume (V) and X-ray density (ρx) can be calculated by using

the following formulae.

The lattice parameters (a & c) of hexagonal crystal structure can be calculated

by using the formula

Source (Cu)

Filter (Ni)

Incident beam

Diffracted beam

Diffractor (movable

Geiger Counter)

Source

32

2

2

2

22

2 c

l

a

khkh

3

4

d

1

(3.2)

where „h, k, l‟ are Miller indices and „d‟ is the interplaner spacing.

The crystallite size „D‟ is calculated by using Full Width at Half Maximum

(FWHM), obtained from the diffraction peaks in Scherrer‟s formula [65] given by

cos

9.0D

(3.3)

where „ ‟ is wave length, „ ‟ is FWHM and „ ‟ is the Bragg angle.

The volume of unit cell „V‟ can be calculated from formula

ca2

3V 2

(3.4)

X-ray density (theoretical density) „dx‟ is calculated by the formula

VN

M2d

A

x

(3.5)

where numeric factor denotes the number of formula units in a unit cell, „M‟ is the

molar mass, „NA‟ is the Avogadro‟s number and „V‟ is the unit cell volume.

3.3. Scanning Electron Microscopy

The scanning electron microscopy (SEM) is qualitative technique to provide

information about the morphology (texture) and microstructure of the sample. When

incident radiation beam of high-energy electrons strikes the surface of sample, it

generates variety of signals that may be recorded by the detector. The results of this

technique are usually a 2-dimensional image displaying the spatial variations in the

properties of the sample. The conventional SEM technique involves certain

specifications about the sample width as 1 cm to 5 microns that can be imaged,

magnification ranging from 20X to about 30,000X and resolution power ranging from

33

50 to 100 nm. The working principle for scanning electron microscope is shown in

Figure 3.3.

Figure 3.3: Working principle of scanning electron microscope (SEM)

An electron gun produces a beam of high-energy of electrons (of few hundred eV to

40 keV) at the surface of sample to be tested. Before reaching the surface of sample,

the electron beam passes through magnetic lens, pairs of scanning coils or deflecting

plates, which basically deflects the incident beam into x and y planes so that it can

scan through entire surface of the sample. When the incident beam finally strikes the

sample surface, energy is released from the sample in the form of electrons and X-ray

photons, which are then detected by the detector. The detector converts them to a

signal which is then used to make a final image of sample surface by a screen similar

to that of the television screen.

34

3.4 Infrared Spectroscopy

Infra-red spectroscopy is particularly applicable to the study of orientation in

ferrite materials. Infra-red absorbance is due to the interaction between the electric

field vector and the molecule dipole transition moments due to molecular vibrations.

The absorbance is at a maximum when the electric field vector and the transition

moment are parallel to each other, and zero when the orientation in perpendicular.

Different alignment of the molecules results in changes in the intensity of a

number of infra-red modes and therefore is an indicator of crystallinity. Because each

inter atomic bond may vibrate in several different modes (stretching or bending)

individual bond may absorb at more than one IR frequency. Stretching absorptions

usually produce stronger peaks than bending, however the weaker bending

absorptions can be useful in differentiating similar type of bonds (e.g. aromatic

substitution). It is also important to note that symmetrical vibration do no cause

absorption of IR radiation. In general, the most important factors determining where a

chemical bond will absorb or not are the bond order and type of atoms joined by the

bond. Conjugation and nearby atoms shift the frequency to a lesser degree. Therefore,

the same or similar functional group in different molecules will typically absorb

within the same and specific frequency range. Hooke's law states that the IR

frequency at which a chemical bond absorbs is inversely proportional to the square

root of the reduced mass of the bonded atoms [equation (3.6)]

μ

k

2π

1ν (3.6)

where = frequency in cm-1

, = reduced mass, ,)m+m()m(m 2121 m1 and m2 are the

atomic masses of two elements which make the bond, k= force constant (bond-order)

e.g. single, double or triple.

The complex lower region below 1000 cm-1

is known as the “finger print

region" because almost every organic compound produces a unique pattern in this

area, therefore identity can often be confirmed by comparison of this region to a

known spectrum.

35

The % transmission is simply

%T100IbeamreferenceofIntensity

IbeamsampleofIntensity

0

t

A more useful quantity for the quantitative work is the absorbance (A) or optical

density (O.D.)

t

O

I

IlogAAbsorbance

I

IlogA O

10

T

1logA 10

T%

100logA 10

T%log100logA 1010

T%log2A 10 (3.7)

The transmission data (%) is converted to absorbance data using equation (3.7).

The infrared spectra of all the samples of the present series were recorded at

room temperature in the range 400 cm-1

-4000 cm-1

on a Perkin Elemer spectrometer

(Model 783). To study the I.R. spectra of all the samples, about one gram of fine

powder of each sample was mixed with KBr in the ratio 1:250 by weight to ensure

uniform distribution in the KBr pellet. The mixed powder was then pressed in a

cylindrical die to obtain clean disc of approximately 1 mm thickness. The IR spectra

were used to locate the band position. The IR spectra were used to determine bond

length RA and RB, in a cubic crystal for tetrahedral (A) and octahedral [B] site using

formula given by Gorter [66]. Using the analysis of Waldron [67], the force constant

K0 and Kt were calculated.

36

3.5 Diffuse Ray Spectroscopy (DRS) Technique

Spectroscopy is the study of light (including the non-visible wavelengths)

emitted, reflected, or scattered from a sample. Light can be measured in units of

frequency or wavelength according to the equation

λν = c (3.8)

where λ is wavelength (m), ν is frequency (Hz, s-1

) and c is the speed of light,

2.998 108

m s-1

. With c as a constant, frequency can also be described as the

reciprocal of wavelength or wavenumber (ύ)

λ-1 = ύ (3.9)

This unit of measurement is analogous to wavelength and is used particularly in the

mid infrared region. Light travels in “packets” of energy, or photons, and each photon

carries a specific amount of energy related to the frequency or wavelength of the light

according to

E = hν (3.10)

where E is energy (J), h is Planck‟s constant (6.626 10-34

J · s). This equation

summarizes the qualitative impact of light – higher frequency results in higher energy

and thus a lower wavelength gives higher energy. This relationship can be viewed in

Figure 3.4, a diagram of the electromagnetic spectrum. The regions focused on here

will be the visible (Vis, 400-700 nm), the near infrared (NIR, 700-2500 nm) and the

mid infrared (MIR, 2500-25000 nm).

Figure 3.4: A diagram of Electromagnetic spectrum

37

Solid materials have five reactions to light which can be qualified and

quantified by spectroscopy: scattering, transmission, reflectance, diffraction and

absorption. Transmission spectroscopy is based upon the relationship known as

Beer‟s Law, a quantitative interpretation as to how photons are attenuated in relation

to an intervening medium (Clark, 1999). When used in transmission spectroscopy,

Beer‟s Law is stated as

I = Ioe-acl

(3.11)

where I is the output intensity at a specific wavelength, Io is the original intensity at

the same wavelength, a is the wavelength and material specific absorptivity, c is the

concentration of the analyte and l is the optical path length. This law only applies

when the analyte is diluted in a non-absorbing matrix such as KBr.

3.6 Vibrating Sample Magnetometer

A vibrating sample magnetometer or VSM is a scientific instrument that

measures magnetic properties invented in 1955 by Simon Foner at Lincoln Laboratory

MIT. The paper about his work was published shortly afterward in 1959 [68]. A

sample is placed inside a uniform magnetic field to magnetize the sample. The sample

is then physically vibrated sinusoidally, typically through the use of a piezoelectric

material. Commercial systems use linear actuators of some form and historically the

development of these systems was done using modified audio speakers, though this

approached was dropped due to the interference through the in-phase magnetic noise

produced, as the magnetic flux through a nearby pickup coil varies sinusoidally. The

induced voltage in the pickup coil is proportional to the sample's magnetic moment,

but does not depend on the strength of the applied magnetic field. In a typical setup,

the induced voltage is measured through the use of a lock-in amplifier using the

piezoelectric signal as its reference signal. By measuring in the field of an external

electromagnet, it is possible to obtain the hysteresis curve of a material.

A typical hysteresis curve of a spinel ferrite is also shown in Figure 3.5. A

great deal of information can be learned about the magnetic properties of a material

by studying its hysteresis loop. A hysteresis loop shows the relationship between the

38

induced magnetic flux density (B) and the magnetizing force (H). It is often referred

to as the B-H or M-H loop.

Figure 3.5: A typical hysteresis curve of a spinel ferrite

From the hysteresis loop, a number of primary magnetic properties of a

material can be determined such as magnetization (Ms), coercivity (HC), remanence

magnetization (Mr) etc.

3.7 Electrical Properties

Electrical resistivity is an important physical property of dielectric crystals,

required not only for practical applications but also for the interpretation of various

physical phenomenons. The first step in the understanding of electrical transport in

any solid is to know whether conductivity is ionic, electronic or mixed partially ionic

and electronic. There are several ways of determining the nature of conductivity. The

simplest way is to measure d.c. conductivity as a function of time using electrodes,

which blocks ionic conduction. In the case of pure ionic conduction d.c. conductivity

39

decreases with time and tends to become zero after sufficiently long time, whereas for

a pure electronic conductor it is essentially independent of time. For mixed

conduction it decreases with time but tends to stabilize at some finite constant value.

This is the electronic contribution.

The DC electrical conductivity of a material is an intrinsic property of the

materials. The conductivity of a solid dielectric depends on the mobility of charge

carriers and their concentration. The conduction however cannot occur unless the

charge carriers are made available for the process through activation by some external

agency. The variation of conductivity with temperature can be expressed by the

general exponential relation.

σ = σo exp (- E/kT) (3.12)

where, E is the activation energy, σ0 is the constant and k is the Boltzmann constant.

In terms of dc resistivity, it can be written as

ρ = ρo exp (-E/kT) (3.13)

Figure 3.6 The schematic diagram two probe methods

The electrical resistivity of oxides was extremely sensitive to the purity and

perfection of the crystal. In all cases the electrical resistivity is very high at low

40

temperatures and decreases rapidly as the temperature is raised, usually in an

exponential fashion. This type of variation can be due either to ionic conduction

(where ions themselves move under the influence of an applied electric field) or to

electronic semi-conduction that has been definitely shown as the primary mechanism

in oxides. In most experiments on electrical conductivity electrical semi-conduction

of a donor or acceptor type has been proven. The defects producing the donor or

acceptor states are usually either impurities or vacancies (or interstitials) caused by

non stoichiometry.

The measurements of DC resistivity of ferrite, ferroelectric and their

composites are carried out by conventional two probe method. The schematic diagram

of two probe method is shown in Figure 3.6. The samples were coated with thin layer

of silver paste for good Ohmic contact. The resistivity of the sample was calculated

using the relation

t

rRπρ

2

dc (3.14)

where, R is the ohmic resistance of the sample, r is the radius of the sample in meter

and t is the thickness of the pallet in meter. The resistivity measurements were made

in the temperature range from 300 K to 650 K in air. The plots of log ρ versus 1000/T

were plotted and the resultant activation energies for conduction were computed by

using relation 3.13.

3.8 Dielectric Properties

When an electric field is applied to the ferrite materials, there are a few

phenomenon occurred from atomic to the macroscopic level. At the atomic level,

through atomic polarization, the center of positive nuclei and negative electron clouds

are away from the original position with a small displacement. In ferrite, as an ionic

material, the ionic polarization occurs at the molecular level that will displace the

cation and anion sublattices. The ferrite crystal may polarize and become bipolar or

dipolar under an electric field. The ferrite materials are polycrystalline with grain

boundaries. The polarized charges or some free charges accumulated at the boundary,

41

and limit or restrict the movement of the charges moving inside the materials. All

these phenomena will contribute to the dielectric properties of the ferrite.

3.8.1 Dielectric constant

Dielectric Constant is used to determine the ability of an insulator to store

electrical energy. Various polarization mechanisms in solids such as atomic

polarization of the lattice, orientational polarization of dipoles, space charge

polarization etc. can be understood easily by studying the dielectric properties as a

function of frequency and temperature.

The dielectric constant is the ratio of the capacitance induced by two metallic

plates with an insulator between them to the capacitance of the same plates with air or

a vacuum between them. It measures the inefficiency of an insulating material [69]. If

the material is to be used for strictly insulating purpose, it would be better to have a

lower dielectric constant. The dielectric constant of solids can greatly vary in

magnitude with variations in their structural properties. Any mechanisms of

polarization can proceed in solid bodies.

A vacuum capacitor with an electric field E between its metallic plates has an

interfacial charge ,EQ 0O

where m/F10854.8C4

10 12

2

7

0 is the dielectric permittivity of free space. If the

field E varies with temperature, the charge Q0 follows exactly, there is no "inertia" in

the vacuum response. If the capacitor is filled with a material medium-gaseous, liquid

or solid, the charge induced is increased by the polarization P of the medium, so

EE1PQQ 0O (2.9)

where is the permittivity and the susceptibility of the dielectric medium. The

dielectric constant, of the sample was computed using the formula

42

,C

C

0

0 (2.10)

where C is the measured capacitance and ,t

AC 0O where, 0 is the permittivity of

free space, A is area of the electrode and t is thickness of the sample. The loss tangent

is the dissipation factor itself.

Carrier polarization covers a very wide range of mechanisms and materials,

the one common feature being that the charge carriers involved move by

discontinuous hopping jumps between localized sites, they may be electrons, polarons

or ions. Electrons or polarons normally hop between sites randomly distributed in

space and in energy but it is almost impossible to distinguish between them

experimentally. The d.c. conductivity is determined by hops in percolation paths

between the two electrodes, whereas the a.c. conductivity is thought to arise from

more limited displacements. In contrast, ions move typically over much smaller

nearest-neighbor distances and it is particularly interesting to note therefore that,

neither the magnitude of the a.c. conductivity and its activation energy nor its

frequency dependence can be taken as reliable guides to the nature of the dominant

carrier responsible for polarization.

3.8.2 Dissipation factor/tan

Dissipation factor is defined as the reciprocal of the ratio between the

insulating materials capacitive reactance to its resistance at a specified frequency [70].

The dielectric loss in an insulating material can be described by the power dissipated

per unit volume, called the specific loss, often, in evaluating the degree to which a

dielectric can dissipate the energy of the field; use is made of the angle dielectric loss

and also the tangent of this angle.

The dielectric loss angle is the complement of the dielectric phase angle to

90o. The angle is the angular difference in phase between the voltage and current in

43

the capacitive circuit, in the ideal case, the current phasor in such a circuit will lead

the voltage phasor by 90o, and the loss angle will be zero. As the thermal dissipation

of the electrical energy rises, the phase angle decreases, but the dielectric loss angle

grows and so does its function tan .