STRUCTURAL AND MAGNETIC CHARACTERIZATION OF SPINEL FERRITES WITH HIGH MAGNETIZATION M. PHIL. THESIS MD. DULAL HOSSAIN Student No.: 102803-P Session: 2010-2011 DUET DEPARTMENT OF PHYSICS DHAKA UNIVERSITY OF ENGINEERING & TECHNOLOGY GAZIPUR, BANGLADESH MARCH, 2015
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STRUCTURAL AND MAGNETIC CHARACTERIZATION
OF SPINEL FERRITES WITH HIGH MAGNETIZATION
M. PHIL. THESIS
MD. DULAL HOSSAIN Student No.: 102803-P
Session: 2010-2011
DUET
DEPARTMENT OF PHYSICS
DHAKA UNIVERSITY OF ENGINEERING & TECHNOLOGY
GAZIPUR, BANGLADESH
MARCH, 2015
STRUCTURAL AND MAGNETIC CHARACTERIZATION
OF SPINEL FERRITES WITH HIGH MAGNETIZATION
A THESIS SUBMITTED TO THE DEPARTMENT OF PHYSICS, DHAKA
UNIVERSITY OF ENGINEERING AND TECHNOLOGY (DUET), GAZIPUR, IN
PARTIAL FULFILLMENT OF THE REQUIREMENT FOR THE DEGREE OF
MASTER OF PHILOSOPHY (M. PHIL.) IN PHYSICS
by
MD. DULAL HOSSAIN Student No.: 102803-P
Session: 2010-2011
DUET
DEPARTMENT OF PHYSICS
DHAKA UNIVERSITY OF ENGINEERING & TECHNOLOGY
GAZIPUR, BANGLADESH
MARCH, 2015
DHAKA UNIVERSITY OF ENGINEERING & TECHNOLOGY (DUET), GAZIPUR
DEPARTMENT OF PHYSICS
Certification of Thesis Work
The thesis titled “STRUCTURAL AND MAGNETIC CHARACTERIZATION OF
SPINEL FERRITES WITH HIGH MAGNETIZATION” submitted by MD.
DULAL HOSSAIN, Student No.: 102803-P, Session: 2010-2011, has been accepted as
satisfactory in partial fulfillment of the requirement for the degree of Master of Philosophy
(M. Phil.) in Physics on 08 March, 2015.
BOARD OF EXAMINERS
1. _______________________________
DR. ABU TALIB MD. KAOSAR JAMIL (Supervisor) Chairman
Professor, Department of Physics
DUET, Gazipur
2. _______________________________
DR. A.K.M. ABDUL HAKIM (Co-supervisor) Member
Consultant,Department of Glass and Ceramic
BUET, Dhaka
3. _______________________________
DR. SYED JAMAL AHMED (Ex-Officio) Member
Professor and Head, Department of Physics
DUET, Gazipur
4. _______________________________
DR. MD. KAMAL-AL-HASSAN Member
Professor, Department of Physics
DUET, Gazipur
5. _______________________________
DR. SHIBENDRA SHEKHER SIKDER Member (External)
Professor, Department of Physics
KUET, Khulna
DUET
CANDIDATE’S DECLARATION
It is hereby declared that this thesis or any part of it has not been submitted elsewhere
for the award of any degree or diploma.
___________________
(MD. DULAL HOSSAIN)
Student No.: 102803-P
Session: 2010-2011
Dedicated
To
My beloved parents
MD
. DU
LA
L H
OS
SA
IN
M. P
hil. T
hesis
Ma
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01
5
I
Acknowledgements
First of all I express my gratefulness to Almighty Allah, who gives me the strength and energy to
fulfill this research work.
I am deeply indebted to my reverend teacher Dr. Abu Talib Md. Kaosar Jamil, Professor,
Department of Physics, Dhaka University of Engineering & Technology (DUET), Gazipur for his
supervision, valuable suggestions and help that inspired me to complete this research work. He
guided me all the way with his characteristic wisdom and patience and bore all my limitations
with utmost affection. Indeed, without his unfathomable support this work would not have been
possible.
I feel a deep sense of gratitude to my co-supervisor Dr. A. K. M. Abdul Hakim, Consultant,
Department of Glass and Ceramic Engineering and Part time faculty, Dept. of Materials and
Metallurgical Engineering, Bangladesh University of Engineering and Technology (BUET)
Dhaka, a man known for his altruism and great insights in materials science and for introducing
the present topic and inspiring guidance and valuable suggestion throughout the research work.
It would have not been possible for me to bring out this thesis without his help and constant
encouragement.
I express special thanks to Prof. Dr. Syed Jamal Ahmed, Head, Department of Physics, DUET,
Gazipur, for providing necessary facilities to carry out this research work and valuable
suggestions regarding my thesis.
I am also grateful to Prof. Dr. Md. Kamal-Al-Hassan, Department of Physics, DUET, Gazipur,
for his constructive criticism, stimulating encouragement and various help.
I express my sincere thanks to Dr. Md. Nazrul Islam Khan, Senior Scientific Officer, Materials
Science Division, Atomic Energy Center, Dhaka, for his cordial help during this work. Over all
Materials Science Division, Atomic Energy Center, Dhaka, is highly acknowledged for preparing
the samples and some measurements.
II
I would like to thanks all the respected teachers of Department of Physics, DUET, Gazipur
including Mr. Md. Rezaul Karim, Mr. Md. Sahab Uddin, Mrs. Fatema, Mr. Md.
Rasaduzzaman and Ms. Farah Deeba.
I feel to thank all of my fellow graduate students: Kazi Asraful Islam, Mohammad Golam
Mawla and Mohammed Mozammel Hoque, working with them during these past years has truly
been delight.
I also offer my thanks to Junior Instructor of Mr. Md. Raihan Ali, and Mr. Md. Abdul Kayyum,
Department of Physics, DUET and all the staff members including Mr. Md. Borhan Uddin, Mr.
Md. Rezaul Islam, Mr. Md. Toffazzal Hossain and Mr. Md. Ansar Uddin for their sincere help.
I would like to extend my special thanks to Dilara Yasmin, Principal, Sher-e-Bangla Nagar
Adarsha Mohila Degree College, Dhaka for giving me opportunities to perform the works. Also
thanks to Mr. Akramuzzaman Khan, Chairman, Governing Body, Mr. Ali Ahsan Khan,
Assistant Professor & Teacher’s Representative and my colleagues of Sher-e-Bangla Nagar
Adarsha Mohila Degree College, Dhaka for their cooperation and kind help to my work from the
very beginning of this thesis work.
Finally I express my heartfelt gratitude to my parents and other family members for their
constant support and encouragement during this research work.
III
ABSTRACT
This thesis describes the theoretical and experimental investigation of structural and magnetic
properties of some spinel ferrites having high magnetization with the general formula
A0.5B0.5Fe2O4 (where, A = Ni2+
, Mn2+
, Mg2+
, Cu2+
, Co2+
and B = Zn2+
), synthesized through
conventional double sintering ceramic method. All the studied samples were found to be single
phase spinel structure by X –ray diffraction. An expansion of the lattice compared with base
ferrite AFe2O4 due to Zn2+
substitution has been observed both in theoretical and experimental
investigation with the exceptional being Mn-Zn ferrite. The enhancement of lattice parameter for
all the Zn substituted samples have been attributed to the large ionic radii of Zn2+
than the
substituted A2+
cations, while reduction in the case of Mn-Zn ferrite has been due smaller ionic
size of Zn2+
than that of Mn2+
. The Curie temperatures of all the samples compared with their
base ferrite have been found to decrease substantially due to weakening of JAB exchange
interaction resulting from the increase of lattice parameter which reduces the strength of
exchange interaction. A large increase of magnetization due to Zn2+
substitution has been
observed for all the studied sample both experimentally and theoretically due to increase of
B- site magnetization since Zn2+
occupies A-site and replaces an equal amount of Fe3+
to the B-
site. Theoretical density is found to increase with Zn2+
substitution except Co-Zn ferrite. The
results show that ferrite with high magnetization and reasonably lower Curie temperature is
suitable for high permeability inductor materials. Ni-Zn, Mg-Zn and Mn-Zn ferrites showed
reasonably good permeability at room temperature covering a wide range of frequencies
indicating possibilities for high frequency inductor and/or core material. Theoretical and
experimental results are well correlated and compatible with the theory based on ferrimagnetism.
IV
CONTENTS
Acknowledgements I
Abstract III
Contents IV
List of Figures VIII
List of Tables X
CHAPTER –I : INTRODUCTION
1−24
1.1 Introduction 1
1.2 Historical Development of Ferrites 4
1.3 Application of Ferrites 6
1.4 Review of the Earlier Research Work 8
1.4.1 Study of Ni-Zn ferrite 8
1.4.2 Study of Mn-Zn ferrite 11
1.4.3 Study of Mg-Zn ferrite 13
1.4.4 Study of Cu-Zn ferrite 15
1.4.5 Study of Co-Zn ferrite 16
1.5 Objectives of the Present Study 18
1.6 Outline of the Thesis 20
References 21
CHAPTER–II : THEORETICAL BACKGROUND
25−57
2.1 General Aspects of Magnetism 25
2.1.1 Origin of Magnetism 25
2.1.2 Magnetic dipole 26
2.1.3 Magnetic field 27
2.1.4 Magnetic moment of atoms 27
2.1.5 Magnetic moment of electrons 28
2.1.6 Magnetic Domain 30
2.1.7 Domain wall motion 31
V
2.1.8 Magnetic properties 33
2.1.9 Hysteresis 34
2.1.10 Saturation magnetization 36
2.2 Types of Magnetic Materials 36
2.2.1 Diamagnetism 38
2.2.2 Paramagnetism 39
2.2.3 Ferromagnetism 40
2.2.4 Antiferromagnetism 42
2.2.5 Ferrimagnetism 42
2.3 Introduction of Ferrites 43
2.4 Types of Ferrites 44
2.4.1 Spinel ferrites 45
2.4.2 Hexagonal ferrites 47
2.4.3 Garnets 47
2.5 Types of Spinel Ferrites 47
2.5.1 Normal spinel ferrites 48
2.5.2 Inverse spinel ferrites 48
2.5.3 Intermediate or mixed spinel ferrites 48
2.6 Types of Ferrites with respect to their Hardness 49
2.6.1 Soft ferrites 49
2.6.2 Hard ferrites 50
2.7 Super Exchange Interactions in Spinel Ferrites 50
2.8 Two Sublattices in Spinel Ferrites 51
2.8.1 Neel’s collinear model of ferrites 53
2.8.2 Non-collinear model 54
2.9 Cation Distribution in Spinel Ferrites 55
References 57
CHAPTER – III: EXPERIMENTAL DETAILS
58−82
3.1 Compositions of Studied Ferrite Samples 58
3.2 Sample Preparation 58
VI
3.2.1 Solid state reaction method 59
3.2.2 Pre-sintering 59
3.2.3 Sintering 62
3.2.4 Flowchart of sample preparation 63
3.3 Experimental Measurements 64
3.4 X-ray Diffraction Method 64
3.4.1 X-ray diffraction technique 64
3.4.2 Power method of X-ray diffraction 65
3.4.3 Phillips X Pert PRO X-ray diffractometer 66
3.4.4 Lattice parameter 68
3.4.5 X-ray density, bulk density and porosity 69
3.5 Magnetization Measurement 70
3.5.1 Vibrating Sample Magnetometer of model EV7 system 70
3.5.2 Working procedure of vibrating sample magnetometer 71
transformers, filters, inductors, etc are frequently based on ferrites.
iii) Ferrites are part of low power and high flux transformers which are used in television.
iv) Soft ferrites were used for the manufacture of inductor core in combination with
capacitor circuits in telephone system, but now a day, solid state devices have
replaced them. The soft Ni-Zn and Mn-Zn ferrites are used for core manufacture.
v) Small antennas are made by winding a coil on ferrite rod used in transistor radio
receiver.
vi) In computer, non volatile memories are made of ferrite materials. They store
information even if power supply fails. Non-volatile memories are made up of ferrite
materials as they are highly stable against severe shock and vibrations.
Chapter-I Introduction
7
vii) Ferrites are used in microwave devices like circulator, isolators, switches phase
shifters and in radar circuits.
viii) Ferrites are used in high frequency transformer core and computer memor ies i.e,
computer hard disk, floppy disks, credit cards, audio cassettes, video cassettes and
recorder heads.
ix) Ferrites used in magnetic tapes and disks are made of very small needle like particles
of Fe2O3 or CrO2 which are coated on polymeric disk. Each particle is a single
domain of size 10‒100 nm.
x) Ferrites are used to produce low frequency ultrasonic waves by magnetostriction.
xi) Iron-silicon alloys are used in electrical devices and magnetic cores of transformers
operating at low power line frequencies. Silicon steel is extensively used in high
frequency rotating machines and large alternators.
xii) Nickel alloys are used in high frequency equipments like high speed relays, wide
band transformers and inductors. They are used to manufacture transformers,
inductors, small motors, synchros and relays. They are used for precision voltage and
current transformers and inductive potentiometers.
xiii) They are used as electromagnetic wave absorbers at low dielectric values.
xiv) Ferro-fluids, as a cooling material, in speakers. They cool the coils with vibrations.
xv) Layered samples of ferrites with piezoelectric oxides can lead to a new generation of
magnetic field sensors. These sensors can provide a high sensitivity, miniature size,
virtually zero power consumption. Sensors for AC and DC magnetic fields, AC and
DC electric currents, can be fabricated.
xvi) Ferrite beads are found on all cable types including USB cables, serial port cables and
AC adapter power supply cables. They also are placed on coaxial cables to form so
called choke baluns. A choke balun can be used to reduce noise currents on the cable
and if placed at the point where the cable connects to a balanced antenna such as a
dipole, the beads transform the balanced antenna currents to unbalanced coaxial cable
currents.
Chapter-I Introduction
8
1.4 Review of the Earlier Research Work
Spinel ferrites are extremely important for academic and technological applications. The physical
properties such as structural, electrical and magnetic properties are governed by the type of
magnetic ions residing on the tetrahedral A-site and octahedral B-site of the spinel lattice and the
relative strength of the inter- and intra- sublattice interactions. In recent years, the design and
synthesis of non-magnetic particles have been the focus of fundamental and applied research
owing to their enhanced or unusual properties [28]. It is possible to manipulate the properties of
a spinel material to meet the demands of a specific application. A large number of scientists are
involved in research on the ferrites materials. Before discussing our research work, we shall see
the previous work done related to our work through literature survey.
1.4.1 Study of Ni-Zn ferrite
Magnetic properties of Ni-Zn ferrite nanoparticles have been studied by Xuegang Lu et al. [29].
They investigated the structure and high frequency magnetic properties of the ferrites. The
saturation magnetization was as high as about 60 emu/g and was comparable to the reported
value of high temperatures sintered Ni-Zn ferrite. The hysteresis loops have typical for a soft
magnetic material. The XRD patterns have confirmed the single phase spinel structure. The
imaginary part of permeability showed a broad peak, which indicates a notable magnetic loss in
high frequency range.
Tania Jahanbin et al. [30] have investigated the structure and electromagnetic properties of
Ni0.8Zn0.2Fe2O4 ferrites and compared results with samples prepared by co-precipitation and
conventional ceramic method. The toroidal and pellet form samples were sintered at various
temperatures such as 1100, 1200 and 1300 °C. The microstructure showed the grain size
increases and the porosity decreases with temperature in both methods. Dielectric constants
decreased with increase of frequency and increase with sintering temperature. The XRD pattern
and EDX have confirmed the ferrites phase.
The structural and magnetic properties of Ni-Zn ferrite films with high saturation magnetization
have been synthesized by Dangwei Guo et al. [31]. They observed the XRD patterns and confirm
Chapter-I Introduction
9
the samples were well crystallized and single phase. SEM images indicated that all the samples
consisted of particles nanocrystalline in nature. A large saturation magnetization (237.2
emu/cm3) and a minimum of coercivity (68 Oe) were obtained when the ferrite film was
deposited in the ratio 4:1. They have observed a large real part of permeability µ' of 18 and a
very high resonance frequency fr of 1.2 GHz.
A. M. El-Sayed [32] reported lattice constant, FTIRS, bulk density, X-ray density, apparent
porosity and diameter shrinkage of Ni1-yZnyFe2O4 ferrites for y = 0.1, 0.3, 0.5, 0.7 and 0.8
prepared by usual ceramic technology and sintered at 1250 °C in static air atmosphere. It was
noted that lattice constant and porosity increased whereas bulk density, X-ray density and
diameter shrinkage decreased with the increase in zinc concentration. The IR absorption spectra
at room temperature showed an ionic ordered state at B-sites in Ni1-yZnyFe2O4 with y ≥ 0.7.
Lattice parameter and saturation magnetization of Ni-Zn ferrites have been investigated by T.
Brian Naughton et al. [33]. The lower saturation magnetization was attributed to a combination
of the large lattice parameter, decreasing the per-exchange interactions between the Ni2+
and Fe3+
ions, and incomplete ordering of the cations between the octahedral and tetrahedral sites in the
spinel structure. The increase in saturation magnetization with increasing annealing temperature
above 600 oC as well as they observed that the magnetizations reach the bulk values at about the
same temperature at which grain growth begin.
A .Verma et al. [34] reported the temperature dependence electrical properties of Ni1-xZnxFe2O4
ferrites with (x = 0.2, 0.35, 0.5, 0.6), prepared by citrate precursor technique. The complex initial
permeability has been studied as a function of the composition and sintering temperature. They
showed that the permeability increase with increase in sintering temperature. Permeability loss
was higher at lower sintering temperature.
The dielectric properties have been studied as a function of temperature, frequency and
composition for a series of Ni1-xZnxFe204 ferrites by A. M. Abdeen [35]. He observed that
dielectric constant and dielectric loss factor decreases as the frequency of applied ac electric field
increases. Dielectric constant and dielectric loss factor increases while the activation energy ED
for dielectric decreases as Zn2+
ion substitution increases. The hopping mechanism of electron
between adjacent Fe2+
and Fe3+
ions and hopping of hole between Ni3+
and Ni2+
ions at B-sites
Chapter-I Introduction
10
are responsible for the dielectric polarization in the studied samples.
A. Gonchar et al. [36] have been reported the thermostability of highly permeable Ni-Zn ferrites
and relative materials for telecommunications. The researches have been allowed to obtain new
therrmostable and highly permeable Ni-Zn ferrites (initial permeability is 2000 and Curie
temperature is 140 °C), and relative Mg-Zn ferrites (initial permeability is 1500 and Curie
temperature is 130 °C). The obtained compositions have small surplus of Fe2O3 content from
stoichiometric composition and content of Cu ions.
J. Gutirrez. Lopez et al. [37] synthesized Ni-Zn ferrite by powder injection moulding (PIM) and
microstructure, magnetic and mechanical properties of these ferrites have been studied. They
have done a comparative study between PIM and uniaxial compacting manufacturing processes.
In both cases, the optimum sintering temperature was 1250 °C; at higher sintering temperatures
significant grain growth was observed. The microstructure study showed that grain size increases
with sintering temperature. In the case of uniaxial compaction heterogeneous grain growth were
observed and the present of significant porosity even at the highest temperature was detected.
A. K. M. A. Hossain et al. [38] have studied Ni1-xZnxFe2O4 (x = 0.2, 0.4) samples sintered at
different temperatures. They observed that the dc electrical resistivity decreases as the
temperature increases indicating that the samples have semiconductor like behaviour. As the Zn
content increases, the Curie temperature (Tc), resistivity and activation energy decrease while the
magnetization, initial permeability and the relative quality factor increases. A Hopkinson peak
was obtained near Tc in the real part of the initial permeability vs. temperature curves. The ferrite
with higher permeability has relatively lower frequency. The initial permeability and
magnetization of the samples has been found to correlate with density and average grain sizes.
J. Hu et al. [39] have considered the ways of reducing sintering temperature of high permeability
NiZn ferrites. It was found that optimum additions of CuO and V2O5 contributed to the grain
growth and the densification of matrix in the sintering process, leading to decrease in sintering
temperatures of Ni-Zn ferrites. The post-sintering density and the initial permeability were also
strongly affected by the average particle size of raw materials. The domain wall motion plays a
predominant role in the magnetizing process and loss mechanism at 100 kHz. Using raw
Chapter-I Introduction
11
materials of 0.8 m average particle size and adding 10 mol% CuO and 0.20 % V2O5, Ni-Zn
ferrite with initial permeability as high as 1618 and relative loss coefficient tan/ of as low as
8.6106
(100 kHz) were obtained for the sample sintered at 930 °C. The optimum additions of
CuO and V2O5 are 10 and 0.2 %, respectively.
E. J. W. Verwey et al. [40] found relations between electronic conductivity and arrangement of
cations in the crystal structure. It was found that in more complicated spinels, containing other
atoms as well as iron in both the divalent and trivalent state, the electronic interchange is more or
less inhibited by the foreign metal atoms. This phenomenon is now called hopping mechanism.
Koops [41] described the AC resistivity and dielectric dispersion in Ni-Zn ferrites by assuming
that the sintered ferrite is made up of grains separated at grain boundaries by thin layers of a
substance of relatively poor conductivity. The mechanism of dielectric polarization was found to
be similar to that of conduction. It was observed that the electron exchange between Fe2+
and
Fe3+
determines the polarization of ferrites.
1.4.2 Study of Mn-Zn ferrite
Influence of processing parameters on the magnetic properties of Mn-Zn ferrites have been
characterized by S. A. El-Badry et al. [42]. He observed that the density increased with increase
of sintering temperature. Also, it could be seen that the magnetic parameter of the samples milled
for 40 h and sintered at 1300 and 1400 °C respectively appeared to be closer to each other.
Therefore, it could be concluded that the best processing conditions were the milling for 40 h
followed by the sintering 1300 °C at for 2 h.
Ping Hu et al. [43] have been investigated the effect of heat treatment temperature on crystalline
phases formation, microstructure and magnetic properties of Mn-Zn ferrite by XRD, DTA, SEM
and VSM. Ferrites decomposed Fe2O4 and Mn2O3 after annealing at 550 °C in air, which have
poor magnetic properties. With continuously increased annealing temperature, Fe2O4 and Mn2O3
impurities were dissolved when the annealing temperature rose above 1100 °C. The sample
annealed at 1200 °C showed pure Mn-Zn ferrite phase, which had fine crystallinity, uniform
particle sizes and showed larger saturation magnetization (Ms = 48.15 emu/g) and the lower
coercivity (Hc = 51 Oe) than the auto-combusted ferrite powder (Ms = 44.32 emu/g, Hc = 70 Oe).
Chapter-I Introduction
12
M. J. N. Isfahani et al. [44] have been studied the magnetic properties of nanostructured
Mn0.5Zn0.5Fe2O4 ferrites. The M–H curve revealed the saturation magnetization of mechano-
synthesized Mn0.5Zn0.5Fe2O4 takes a value of Ms = 82.7 emu/g, which is about 41% lower than
the value reported for bulk ferrite. This reduced saturation magnetization can be attributed to the
prevailing effect of spin canting. The M–T curve of nanoscale ferrite gives evidence that the
mechano-synthesized material exhibits higher Neel temperature than the bulk sample. The
enhanced Neel temperature can be attributed to the effect of strengthening of the A-O-B super-
exchange interaction in the mechano-synthesized spinel phase.
Preeti Mathur et al. [45] have been synthesized the effect of nanostructure on the magnetic
properties like the specific saturation magnetization and coercivity for Mn-Zn ferrite. The
average size of the nanoparticles of Mn0.4Zn0.6Fe2O4 mixed ferrites ranging from 19.3 to 36.4 nm
could be controlled efficiently by modifying the sintering temperature from 500 to 900 °C. The
nanostructure was single domain up to a diameter of 25.8 nm, after they have an incipient
domain structure.
The electrical conductivity of Mn-Zn ferrites have been investigated by D. Ravinder et al. [46].
They observed the electrical conductivity in room temperature are vary from 5.23×10-9
Ω-1
cm-1
for MnFe2O4 to 1.79×10-5
Ω-1
cm-1
for Mn0.2Zn0.8Fe2O4. The activation energies in the
ferromagnetic and paramagnetic regions are calculated from ln(σT) versus 103/T and the
activation energies in the paramagnetic region is higher than that in the ferromagnetic region.
Plots of ln(σT) versus 103/T are almost linear and show a transition near the Curie temperature.
C. Venkataraju et al. [47] have been studied the effect of cation distribution on the structural and
magnetic properties of Ni substituted Mn-Zn ferrites. X-ray intensity calculation revealed that
there was a deviation in the normal cation distribution between A-sites and B-sites. The
magnetization of the nanoferrites was less than that of the bulk value and decreased with increase
in Ni concentration except for x = 0.3 where there was a rise. This is due to deviation in normal
cation distribution and significant amount of canting existing in B sublattice for lower Ni
concentration. The coercivity was very low for all samples.
Chapter-I Introduction
13
1.4.3 Study of Mg-Zn ferrite
Some physical and magnetic properties of Mg1-xZnxFe2O4 ferrites have been studied by M. A. El-
Hiti [48] for the MgxZn1-xFe2O4 ferrite samples prepared by ceramic technique. The experimental
results indicated that the dielectric loss (tan) and real dielectric constant () increases as the
temperature increases and as frequency decreases which is the normal dielectric behaviour in
magnetic semiconductor ferrites. This could be explained on the basis of Koops theory for the
double layers dielectric structure. Abnormal dielectric behaviour (peaks) were observed on tan
curves at relatively high temperatures and these relaxation peaks take place when the jumping
frequency of localized electrons between Fe2+
and Fe3+
ions equals to that of the applied ac
electric field. He found the real dielectric constant and loss tan to decrease with Mg2+
ion
concentrations. The relaxation frequency fD was found to be shifted to higher values as the
temperature increases. The hopping of localized electrons between Fe2+
and Fe3+
ions is
responsible for electric conduction and dielectric polarization in the studied MgxZn1-xFe2O4
ferrite.
L. B. Kong et al. [49] have prepared Bi2O3 doped MgFe1.98O4 ferrite by using the solid state
reaction process and studied the effect of Bi2O3 and sintering temperature on the dc resistivity,
complex relative permittivity and permeability. They found that the poor densification and slow
grain growth rate of MgFe1.98O4 can be greatly improved by the addition of Bi2O3, because liquid
phase sintering was facilitated by the formation of a liquid phase layer due to the low melting
point of Bi2O3. The average grain size has a maximum at a certain concentration, depending on
sintering temperature. Too high concentration of Bi2O3 prevents further grain growth owing to
the thickened liquid phase layer. The addition of Bi2O3 has a significant effect on the DC
resistivity and dielectric properties of the MgFe1.98O4 ceramics. The sample with 0.5% Bi2O3 has
a slightly lower resistivity than pure ones, which can be attributed to the ‘cleaning’ effect of the
liquid phase. With the increase of Bi2O3 concentration, an increase in DC resistivity is observed
due to the formation of a three-dimensional grain boundary network structure with high
resistivity. Low concentration of Bi2O3 increased the static permeability of the MgFe1.98O4
ferrites owing to the improved densification and grain growth, while too high concentration led
Chapter-I Introduction
14
to decrease permeability owing to the incorporation of the non-magnetic component (Bi2O3) and
retarded grain growth.
S. S. Suryavanshi et al. [50] studied the DC resistivity and dielectric behaviour of Ti4+
substituted Mg-Zn ferrites and they found that the linear increase of resistivity for higher Ti4+
concentration is attributed to an overall decrease of Fe3+
ions on Ti4+
substitution. Dispersion of
the dielectric constant is related to the Verwey conduction mechanism. Peaks have been
observed in the variation of dielectric loss tangent with the frequency. These peaks are shifted to
the low frequency side by increasing the Ti4+
content. The jump frequencies are found to be in
the range 70–120 kHz. All the samples exhibit space charge polarization due to an
inhomogeneous dielectric structure. It was concluded that the addition of Ti4+
obstructs the flow
of space charge.
S. F. Mansour et al. have observed [51] that the dielectric behaviour for Mg-Zn ferrites can be
explained qualitatively in terms of the supposition that the mechanism of the polarization process
is electronic polarization. He observed peaks at a certain frequency in the dielectric loss tangent
versus frequency curves in all the samples. He gave explanation of the occurrence of peaks in the
variation of loss tangent with frequency. The peak can be observed when the hopping frequency
is approximately equal to that of the externally applied electric field.
M. A. Hakim et al. [52] have synthesized Mg-ferrite nanoparticles by using a chemical co-
precipitation method in three different methods. Metal nitrates were used for preparing MgFe2O4
nanoparticles. In the first method, they used NH4OH as the precursor. In second method, KOH
was used as precipitating agent and in method three; MgFe2O4 was prepared by direct mixing of
salt solutions. They reported that first method is relatively good methods among the three.
Average size of the MgFe2O4 particles was found to be in the range of 1749 nm annealed at
temperatures of 500900 °C.
M. Manjurul Haque et al. [53] reported the effect of Zn2+
substitution on the magnetic properties
of Mg1-xZnxFe2O4 ferrites prepared by solid-state reaction method. They observed that the lattice
parameter increases linearly with the increase in Zn content. The Cure temperature decreases
with the increase in Zn content. The saturation magnetization (Ms) and magnetic moment are
Chapter-I Introduction
15
observed to increase up to x = 0.4 and thereafter decreases due to the spin canting in B-sites. The
initial permeability increases with the addition of Zn2+
ions but the resonance frequency shifts
towards the lower frequency.
1.4.4 Study of Cu-Zn ferrite
The effects of compositional variation on magnetic susceptibility, saturation magnetization,
Curie temperature and magnetic moments of Cu1-xZnxFe2O4 ferrites have been reported by M. U.
Rana et al. [54]. The Curie temperature and saturation magnetization increases from zinc content
0 to 0.75. The YK angles increases gradually with increasing Zn content and extrapolates to 90°
for ZnFe2O4. From the YK angles for Zn substituted ferrites, it was concluded that the mixed
zinc ferrites exhibit a non-co linearity of the YK type while CuFe2O4 shows a Neel type of
ordering.
Shahida Akhter et al. [55] were synthesized Cu1-xZnxFe2O4 ferrite (with x = 0.5) using the
standard solid-state reaction technique. X-ray diffraction was used to study the structure of the
above investigated samples. The theoretical and experimental lattice parameters were calculated
for each composition. A significant decrease in density and subsequent increase in porosity were
observed with increasing Zn content. Curie temperature, Tc has been determined from the
temperature dependence of permeability and found to decrease with increasing Zn content. The
anomaly observed in the temperature dependence of permeability was attributed to the existence
of two structural phases: cubic phase and tetragonal phase. Low-field hysteresis measurements
have been performed using a B–H loop trace from which hysteresis parameters have been
determined. Coercivity and hysteresis loss were estimated with different Zn contents.
The structural, electrical and magnetic properties of Cu1-xZnxFe2O4 ( 0 ≤ x ≤ 1) ferrites have been
reported by A. Muhammad et al. [56]. The variation of Zn substitution has a significant effect
on the structural, electrical and magnetic properties. Unit cell parameter increases linearly with
increase of Zn content. Saturation magnetization and magnetic moment both increased with the
increase in Zn content up to x = 0.2 and then decreased with the increase in Zn content.
Dielectric constant decreased with the increase in frequency.
Chapter-I Introduction
16
A study of sintering effect on structural and electrical properties of Cu1-xZnxFe2O4 ferrites with
(x = 0.1, 0.2 and 0.3), prepared by the solid state technique was done by T. Abbas et al. [57]. The
behavior of lattice constant, grain size, sintered density, X-ray density, porosity and resistivity
has been noted as a function of zinc concentration. Lattice parameter increased while density and
grain size decreased with increase of Zn content. Sintering temperature has a pronounced effect
on density and grain size in which density decreased and grain size increased with increasing of
sintering temperature.
The Cu-Zn ferrites samples having the general formula Cu1-sZnsFe2O4 (where 0.0 ≤ s ≤ 1.0) have
been investigated by Hussain Dawoud et al. [58]. In this communication, the samples are used to
measure the magnetization at room temperature. The magnetization increases with the increase
of zinc ions up to 60% and then it decreases with for the addition of zinc ions. The increase of
the magnetization is explained on the basis of Neel’s two sublattice model, while the decrease in
the magnetization beyond s = 0.6 was attributed to the presence of a triangular spin arrangement
on tetrahedral Oh sites and explained by the three-sublattice model suggested by Yafet-Kittle.
The Cu-Zn mixed ferrites viz. were synthesized by P. N. Vasambekar et al. [59]. Formation of
the cubic ferrite phase was confirmed by X-ray diffraction studies. Microstructure and
compositional features were studied by scanning electron microscope and energy dispersive X-
ray analysis technique. Magnetic properties were measured by B–H hysteresis loop tracer
technique. The variation of saturation magnetization; remanent magnetization and coercivity
were studied as a function of zinc content. The substitution of zinc ions plays decisive role in
changing structural and magnetic properties of copper ferrite.
[1.4.5 Study of Co-Zn ferrite
Co-ferrite is considered as a potential magnetic material due to its high electrical resistivity, high
Curie temperature, low cost and high mechanical hardness. CoFe2O4 is generally an almost
inverse ferrite in which Co2+
ions mainly occupies B-sites and Fe3+
ions are distributed almost
equally between A and B sites. It has been demonstrated that the inversion is not complete in
CoFe2O4 and the degree of inversion sensitively depends on the thermal treatment and method of
preparation condition [60]. Co-ferrite is known to have a large cubic magneto crystalline
Chapter-I Introduction
17
anisotropy (K1 = +2106 erg/cm
3) [61] due to the presence of Co
2+ ions on B-sites. It is well-
known that Co-ferrite is a hard magnetic material due to its high coercivity (5.40 kOe) and
moderate saturation magnetization (80 emu/g) as well as its remarkable chemical stability and
mechanical hardness [62]. It is therefore a good candidate for use in isotropic permanent
magnets, magnetic recording media and magnetic fluids. Co-ferrite crystallizes in partially
inverse spinel structure are represented as-2
4B
3
x1
2
x1A
3
x1
2
x O]Fe[Co)Fe(Co
, where x depends on
thermal history and preparation conditions [63, 64]. It is ferromagnetic with Curie temperature,
Tc around 520 °C [65] which suggests that the magnetic interaction in these ferrites is very strong
and show a relative large magnetic hysteresis which distinguishes it from the rest of spinel
ferrites.
Reddy et al. [66] have studied the electrical conductivity and thermoelectric power as a function
of temperature and compositions in CoxZn1-xFe2O4 (x = 0.2, 0.4, 0.5, 0.6, 0.8 and 1.0) ferrites.
The specimens with x = 0.6 and 1.0 show negative Seebeck coefficient indicating that they are n-
type semiconductors, whereas the specimens with x = 0.2, 0.4, 0.5 and 0.8 show positive
Seebeck coefficient indicating the p-type semiconductors. In the Co-Zn ferrite, the equilibrium
may exist during sintering as Fe3+
+ Co+2
Fe2+
+ Co3+
. Thus the conduction mechanism in the
n-type specimens is mainly due to the hopping of electrons between Fe2+
and Fe3+
ions, whereas
the conduction mechanism in the p-type specimen is due to the jumping of holes between Co3+
and Co2+
ions. From the log (T) vs. 103/T curves it was found that electrical conductivity of all
the ferrites increases with increasing temperature with a change of the slope at magnetic
transition. The change of the slope is attributed to the change in conductivity mechanism. The
conduction at lower temperature (below Curie point) is due to the hopping of electrons between
Fe2+
and Fe3+
ions, whereas at higher temperature (above Curie point) it is due to polaron
hopping. The activation energy in the ferromagnetic region is, in general, less than that in the
paramagnetic region. This suggests that in the paramagnetic region the conduction mechanism is
due to polaron hopping. Similar behaviour of the temperature dependence of conductivity is
observed in Mn-Zn ferrite [67].
Electrical properties of Co-Zn ferrites have been studied by M. A. Ahmed [68]. It was found that
the lattice parameter increases linearly with the increase of zinc content. The X-ray densities for
Chapter-I Introduction
18
all compositions of Co-Zn ferrites increase with the increase of zinc content. The X-ray densities
are higher than the bulk values. The addition of Zn, reduce the porosity thus increasing the
density of the sample. The conductivity increases due to the increase in mobility of charge
carriers.
P. B. Panday et al. [69] has synthesized Co-Zn ferrite by the co-precipitation method and studied
the structural and bulk magnetic properties. All the samples are single phase spinel showed the
X-ray diffraction pattern. The lattice constant gradually decreases on increasing Zn content,
shows a minimum at x ~ 0.5 and then increases on further dilution. The magneton number, i.e.,
saturation magnetization per formula unit in Bohr magneton (nB) at 298 K initially increases and
then decreases as x is increased up to x ≤ 0.3. The decrease in magnetization of these materials
after x = 0.3 is primarily associated with canting of the magnetic moments. Curie temperature
decreases with small addition of Zn.
From the above mentioned review works, it is observed that physical, magnetic, electrical
transport and microstructural properties are strongly dependent on additives/substitutions in a
very complicated way and there is no straight forward relationship between the nature and the
quantity of doping on the magnetic characteristics to be understood by any simple theory. These
are strongly dependent on several factors like sintering conditions, preparation methods,
compositions etc. In the present work, it is aimed at the theoretical and experimental
investigation of structural and magnetic properties of some spinel ferrites having high
magnetization with the general formula A0.5B0.5Fe2O4, where A = Ni2+
, Mn2+
, Mg2+
, Cu2+
, Co2+
and B = Zn2+
. Non-magnetic Zn2+
ion is very promising and interesting substitution to handle the
electromagnetic properties of ferrites materials.
1.5 Objectives of the Present Study
The magnetic properties of Zn-substituted ferrites have attracted considerable attention because
of the importance of these materials for high frequency applications. Zinc ferrite (ZnFe2O4)
possesses a normal spinel structure, i.e. (Zn2+
)A -2
4B
3
2 O][Fe
, where all Zn2+
ions reside on A sites
and Fe3+
ions on B sites. Therefore, substitution of A (i.e., Ni, Mn, Mg, Cu and Co) by Zn in A1-
Chapter-I Introduction
19
xZnxFe2O4 is expected to modify the magnetic properties. The magnetization behavior and
magnetic ordering of Zn-substituted Ni-ferrite [29-41], Mn-ferrite [42-47], Mg-ferrite [48-53],
Cu-ferrite [54-59] and Co-ferrite [60-69] have been studied by many authors. However, no detail
works have been found in the literature regarding structure, magnetic and electrical behavior of
mixed A1-xZnxFe2O4 ferrites. It is well known that the Zn concentration of x = 0.5 in different
ferrites have the high saturation magnetization. At higher sintering temperature, the perfect
crystal growth occurs, highly dense the permeability and the saturation magnetization is expected
to be increased. Therefore, the main objective of this research work is to synthesis of series of
spinel ferrite compositions of A1-xZnxFe2O4 with x = 0.5 by standard solid state reaction
technique and characterizing the prepared samples by magnetic measurements through
appropriate methodology. The ultimate goal is to find out an optimum composition and sintering
parameters such as temperature and time for high magnetization, high permeability with
minimum magnetic loss factor. The following investigations would be carried out and reported in
this thesis.
Ferrite samples would be prepared by conventional solid state technique with
composition A1-xZnxFe2O4 with x = 0.5, where A = Ni, Mn, Mg, Cu and Co.
Sintering of the samples would be carried out in microprocessor controlled furnaces.
Structural characterization of the prepared samples will be carried out by X-ray
diffractometer.
Magnetization measurement as a function of field and temperature will be performing
with vibrating sample magnetometer.
Permeability as a function of frequency and temperature would be measured by
impedance analyzer.
Curie temperature of the sample would be determined from the temperature dependence
of permeability µ (T).
Chapter-I Introduction
20
1.6 Outline of the Thesis
The thesis has been configured into five chapters which are as follows:
Chapter I: Introduction
In this chapter, a brief introduction of different type ferrites such as Ni-Zn, Mn-Zn, Mg-Zn, Cu-
Zn, Co-Zn and organization of thesis have been discussed. This chapter incorporates background
information to assist in understanding the aims and objectives of this investigation and also
reviews recent reports by other investigators with which these results can be compared.
Chapter II: Theoretical background
In this chapter, a briefly describes theories necessary to understand magnetic materials as well as
ferrites. Classification of ferrite, cation distribution, super exchange interaction, two sublattice
models etc have been discussed in details.
Chapter III: Experimental details
In this chapter, the experimental procedures are briefly explained along with description of the
sample preparation, raw materials. This chapter deals with mainly the design and construction of
experimental and preparation of ferrites samples. The fundamentals and working principles of
measurement setup are discussed.
Chapter IV: Results and discussion
In this chapter, results and discussion are thoroughly explained. The various experimental and
theoretical studies namely structural, magnetic and transport properties of A0.5Zn0.5Fe2O4 ferrites
are presented and discussed step by step.
Chapter V: Conclusions
In this chapter, the results obtained in this study are summarized. Suggestions for future work on
these studies are included.
References are added at the end of each chapter.
Chapter-I Introduction
21
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Chapter-I Introduction
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Chapter-I Introduction
24
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25
CHAPTER−II
THEORETICAL BCKGROUND
2.1 General Aspects of Magnetism
All mater is composed of atoms and atoms are composed of protons, neutrons and electrons. The
protons and neutrons are located in the atom’s neucleus and the electrons are in constant motion
around the neucleus. Electrons carry a negative electrical charge and produce a magnetic field as
they move through space. A magnetic field is produced whenever an electric charge is in motion.
The strength of this field is called the magnetic moment. Therefore, the general concept of
magnetism like origin of magnetism, magnetic moment, magnetic domain, domain wall motion,
magnetic properties, hysteresis, saturation magnetization etc. are described in details below.
2.1.1 Origin of magnetism
The origin of magnetism lies in the orbital and spin motions of electrons and how the electrons
interact with one another. The best way to introduce the different types of magnetism is to
describe how materials respond to magnetic fields. This may be surprising to some, but all matter
is magnetic. It is just that some materials are much more magnetic than others. The main
distinction is that in some materials there is no collective interaction of atomic magnetic
moments, whereas in other materials there is a very strong interaction between atomic moments.
A simple electromagnet can be produced by wrapping copper wire into the form of a coil and
connecting the wire to a battery. A magnetic field is created in the coil but it remains there only
while electricity flows through the wire. The field created by the magnet is associated with the
Fig. 2.1: The orbit of a spinning electron about the nucleus of an atom.
Chapter- II Theoretical Background
26
motions and interactions of its electrons, the minute charged particles which orbit the nucleus of
each atom. Electricity is the movement of electrons, whether in a wire or in an atom, so each
atom represents a tiny permanent magnet in its own right. The circulating electron produces its
own orbital magnetic moment, measured in Bohr magnetons (µB), and there is also a spin
magnetic moment associated with it due to the electron itself spinning. In most materials there is
resultant magnetic moment, due to the electrons being grouped in pairs causing the magnetic
moment to be cancelled by its neighbour.
In certain magnetic materials the magnetic moments of a large proportion of the electrons align,
producing a unified magnetic field. The field produced in the material (or by an electromagnet)
has a direction of flow and any magnet will experience a force trying to align it with an
externally applied field, just like a compass needle. These forces are used to drive electric
motors, produce sounds in a speaker system, control the voice coil in a CD player, etc.
2.1.2 Magnetic dipole
A dipole is a pair of electric charges or magnetic poles of equal magnitude but opposite polarity,
separated by a small distance. Dipoles can be characterized by their dipole moment, a vector
quantity with a magnitude equal to the product of the charge or magnetic strength of one of the
poles and the distance separating the two poles as in Fig. 2.2. The direction of the dipole moment
corresponds to the direction from the negative to the positive charge or from the south to the
north pole.
Dipoles are two types: one is electric dipole and another is magnetic dipole. A magnetic dipole is
a closed circulation of electric current. A simple example of this is a single loop of wire with
some constant current flowing through its [1]. Magnetic dipole experiences a torque in the
Where, A is the vector area of the current loop, and the current, I is constant. By convention, the
direction of the vector area is given by the right hand rule (moving one's right hand in the current
direction around the loop, when the palm of the hand is "touching" the loop's surface, and the
straight thumb indicate the direction). In the more complicated case of a spinning charged solid,
the magnetic moment can be found by the following equation:
dJrm
2
1
(2.4)
Where, d = r2sin dr d d, J
is the current density.
Magnetic moment can be explained by a bar magnet which has magnetic poles of equal
magnitude but opposite polarity. Each pole is the source of magnetic force which weakens with
distance. Since magnetic poles come in pairs, their forces interfere with each other because while
one pole pulls, the other repels. This interference is greatest when the poles are close to each
other i.e. when the bar magnet is short. The magnetic force produced by a bar magnet, at a given
point in space, therefore depends on two factors: on both the strength p of its poles and on the
distance d separating them. The force is proportional to the product, = pd, where, is the
"magnetic moment" or "dipole moment" of the magnet along a distance d and its direction as the
angle between d and the axis of the bar magnet. Magnetism can be created by electric current in
loops and coils so any current circulating in a planar loop produces a magnetic moment whose
magnitude is equal to the product of the current and the area of the loop. When any charged
particle is rotating, it behaves like a current loop with a magnetic moment.
The equation for magnetic moment in the current-carrying loop, carrying current I and of area
vector A
for which the magnitude is given by:
AIm
(2.5)
Where, m
is the magnetic moment, a vector measured in Am2, or equivalently joules per tesla, I
is the current, a scalar measured in amperes, and A
is the loop area vector.
2.1.5 Magnetic moment of electrons
The electron is a negatively charged particle with angular momentum. A rotating electrically
charged body in classical electrodynamics causes a magnetic dipole effect creating magnetic
Chapter- II Theoretical Background
29
poles of equal magnitude but opposite polarity like a bar magnet. For magnetic dipoles, the
dipole moment points from the magnetic south to the magnetic north pole. The electron exists in
a magnetic field which exerts a torque opposing its alignment creating a potential energy that
depends on its orientation with respect to the field. The magnetic energy of an electron is
approximately twice what it should be in classical mechanics. The factor of two multiplying the
electron spin angular momentum comes from the fact that it is twice as effective in producing
magnetic moment. This factor is called the electronic spin g-factor. The persistent early
spectroscopists, such as Alfred Lande, worked out a way to calculate the effect of the various
directions of angular momenta. The resulting geometric factor is called the Lande g-factor.
The intrinsic magnetic moment μ of a particle with charge q, mass m, and spin s, is
sm
qgm
2 (2.6)
Where, the dimensionless quantity g is called the g-factor. The g-factor is an essential value
related to the magnetic moment of the subatomic particles and corrects for the precession of the
angular momentum. One of the triumphs of the theory of quantum electrodynamics is its
accurate prediction of the electron g-factor, which has been experimentally determined to have
the value 2.002319. The value of 2 arises from the Dirac equation, a fundamental equation
connecting the electron's spin with its electromagnetic properties, and the correction of 0.002319,
called the anomalous magnetic dipole moment of the electron, arises from the electron's
interaction with virtual photons in quantum electrodynamics. Reduction of the Dirac equation for
an electron in a magnetic field to its non-relativistic limit yields the Schrödinger equation with a
correction term which takes account of the interaction of the electron's intrinsic magnetic
moment with the magnetic field giving the correct energy.
The total spin magnetic moment of the electron is
)( sg BSS (2.7)
Where, gs = 2 in Dirac mechanics, but is slightly larger due to Quantum Electrodynamics effects,
μB is the Bohr magneton and s is the electron spin. The z component of the electron magnetic
moment is
SBSZ mg (2.8)
Chapter- II Theoretical Background
30
Where, ms is the spin quantum number. The total magnetic dipole moment due to orbital angular
momentum is given by
)1(2
llLm
eB
e
L (2.9)
Where, μB is the Bohr magneton. The z-component of the orbital magnetic dipole moment for an
electron with a magnetic quantum number ml is given by
lBZ m (2.10)
2.1.6 Magnetic domain
A magnetic domain is an atom or group of atoms within a material that have some kind of
uniform electron motion. A fundamental property of any charged particle is that when it is in
motion, it creates a magnetic field around its path of travel. Electrons are negatively charged
particles, and they create electromagnetic fields about themselves as they move. It is known that
electrons orbit atomic nuclei, and they create magnetic fields while doing so. If one or more
atoms or groups of atoms are taken and align them so that they have some kind of uniform
electron motion, an overall magnetic field will be present in this region of the material. The
individual magnetic fields of some electrons will be added together. The uniform motion of the
electrons about atoms in this area creates a magnetic domainas shown in Fig. 2.3. In regular iron,
these magnetic domains are randomly arranged. But if it is aligned a large enough group of these
magnetic domains, it will have created a magnet.
In 1907 Weiss proposed that a magnetic material consists of physically distinct regions called
domains and each of which was magnetically saturated in different directions (the magnetic
moments are oriented in a fixed direction) as shown schematically in Fig. 2.3. Even each domain
is fully magnetized but the material as a whole may have zero magnetization. The external
Fig. 2.3: Magnetic domain.
Chapter- II Theoretical Background
31
applied field aligns the domains, so there is net moment. At low fields this alignment occurs
through the growth of some domains at the cost of less favorably oriented ones and the intensity
of the magnetization increases rapidly. Growth of domains stops as the saturation region is
approached and rotation of unfavorably aligned domain occurs. Domain rotation requires more
energy than domain growth. In a ferromagnetic domain, there is parallel alignment of the atomic
moments. In a ferrite domain, the net moments of the antiferromagnetic interactions are
spontaneously oriented parallel to each other. Domains typically contain from 1012
to 1015
atoms
and are separated by domain boundaries or walls called Bloch walls Fig. 2.4.
[
2.1.7 Domain wall motion
In magnetism, a domain wall is an interface separating magnetic domains. It is a transition
between different magnetic moments and usually undergoes an angular displacement of 90° or
180°. Although they actually look like a very sharp change in magnetic moment orientation,
when looked at in more detail there is actually a very gradual reorientation of individual
moments across a finite distance [3]. The energy of a domain wall is simply the difference
between the magnetic moments before and after the domain wall was created. This value is more
often than not expressed as energy per unit wall area. The width of the domain wall varies due to
Fig.2.4: Bloch wall.
Chapter- II Theoretical Background
32
the two opposing energies that create it: the magneto-crystalline anisotropy energy and the
exchange energy, both of which want to be as low as possible so as to be in a more favorable
energetic state. The anisotropy energy is lowest when the individual magnetic moments are
aligned with the crystal lattice axes thus reducing the width of the domain wall, whereas the
exchange energy is reduced when the magnetic moments are aligned parallel to each other and
thus makes the wall thicker, due to the repulsion between them (where anti-parallel alignment
would bring them closer working to reduce the wall thickness).
In the end equilibrium is reached between the two and the domain wall's width is set as such is
shown in Fig. 2.5. An ideal domain wall would be fully independent of position; however, they
are not ideal and so get stuck on inclusion sites within the medium, also known as
crystallographic defects. These include missing or different (foreign) atoms, oxides, and
insulators and even stresses within the crystal. In most bulk materials, it is found the Bloch wall:
the magnetization vector turns bit by bit like a screw out of the plane containing the
magnetization to one side of the Bloch wall. In thin layers (of the same material), however, Neél
walls will dominate. The reason is that Bloch walls would produce stray fields, while Neél walls
can contain the magnetic flux in the material [4].
Fig. 2.5: The magnetization changes from one direction to another one.
Chapter- II Theoretical Background
33
2.1.8 Magnetic properties
Every material is composed of atoms and molecules. There are protons and neutrons at the
nucleus of an atom and electrons are revolving around the nucleus in different orbits. Also,
electrons have rotation and spin motion are called respectively orbital motion moment and spin
motion moment. Due to the resultant action of these moments different magnetic characters and
properties of different materials.
Magnetic materials classified by their response to externally applied magnetic fields as
diamagnetic, paramagnetic and ferromagnetic. These magnetic responses differ greatly in
strength. Diamagnetism is property of all materials and opposes applied magnetic fields, but is
very weak paramagnetism, when present, is stronger than diamagnetism and produces
magnetization in the direction of the applied field and proportional to the applied field.
Ferromagnetic effects are very large; producing magnetizations sometimes orders of magnitude
greater than the applied field and as such as the much larger than either diamagnetic or
paramagnetic effects. The magnetization of a material is expressed in terms of density of net
magnetic dipole moments µ in the material. It is defined a vector quantity called the
magnetization M by
V
M total (2.11)
when the total magnetic field B in the material is given by
MBB 00
(2.12)
where, µ0 is the magnetic permeability of space and B0 is the externally applied magnetic field.
When magnetic fields inside of materials are calculated using Ampere’s law or the Biot-Savart
law, then the µ0 in those equations is typically replaced by just µ with the definition
0 r (2.13)
where, µr is called the relative permeability. If the material does not respond to the external
magnetic field by producing any magnetization then µr = 1. Another commonly used magnetic
quantity is the magnetic susceptibility
1 r (2.14)
Chapter- II Theoretical Background
34
For paramagnetic and diamagnetic materials the relative permeability is very close to 1 and the
magnetic susceptibility very close to zero. For ferromagnetic materials, these quantities may be
very large. Another way to deal with the magnetic fields which arise from magnetization of
materials is to introduce a quantity called magnetic field strength H. It can be defined by the
relationship
MH
BBH
00
0
(2.15)
And has the value of unambiguously designating the driving magnetic influence from external
currents in a material independent of the materials magnetic response. The relationship for B
above can be written in the equivalent form
)(0 MHB (2.16)
H and M will have the same units, amperes/meter
The magnetic susceptibility, χ is defined as the ratio of magnetization to magnetic field
H
M (2.17)
The permeability and susceptibility of a material is correlated with respect to each other by
)1(0
(2.18)
2.1.9 Hysteresis
The value of magnetic induction or flux density B depends on the magnetic field intensity H.
This is because that B is created due to H. If the value of magnetic field intensity H is changed in
cyclic order an unusual behavior is observed which is shown in Fig. 2.6. Scientist J. A. Ewing
invented this phenomenon after many experiments.
This graph of H versus B is called B−H graph or hysteresis loop. A piece of ferromagnetic
substance can be magnetized by placing it in a solenoid and passing current through it. If the
value of current increases gradually, the magnetic field intensity H also increases. As a result, the
magnetic induction B produced in the specimen also increases.
Chapter- II Theoretical Background
35
The ferromagnetic material that has never been previously magnetized or has been thoroughly
demagnetized will follow the dashed line as H is increased. As the line demonstrates, the greater
the amount of current applied, the stronger the magnetic field in the component. At point "a"
almost all of the magnetic domains are aligned and an additional increase in the magnetic field
intensity will produce very little increase in magnetic induction. The material has reached the
point of magnetic saturation. When H is reduced to zero, the curve will move from point "a" to
point "b." At this point, it can be seen that some magnetic induction remains in the material even
though the magnetic field intensity H is zero. This is referred to as the point of retentivity on the
graph and indicates the remanence or level of residual magnetism in the material. As the
magnetic field intensity is reversed, the curve moves to point "c", where the flux has been
reduced to zero. This is called the point of coercivity on the curve. The force required to remove
the residual magnetism from the material is called the coercive force or coercivity of the
material.
As the magnetic field intensity H is increased in the negative direction, the material will again
become magnetically saturated but in the opposite direction (point "d"). Reducing H to zero
brings the curve to point "e." It will have a level of residual magnetism equal to that achieved in
the other direction. Increasing H back in the positive direction will return B to zero. Notice that
Fig. 2.6: Hysteresis loop.
Chapter- II Theoretical Background
36
the curve did not return to the origin of the graph because some force is required to remove the
residual magnetism. The curve will take a different path from point "f" back to the saturation
point where it with complete the loop.
2.1.10 Saturation magnetization
Saturation magnetization is an intrinsic property independent of particle size by dependent on
temperature. Even through electronic exchange forces in ferromagnets are very large thermal
energy eventually overcomes the exchange energy and produces a randomizing effect. This
occurs at a particular temperature called the Curie temperature (Tc). Below the Curie temperature
the ferromagnetic is ordered and above it, disordered. The magnetization goes to zero at the
Curie temperature.
The saturation magnetization MS is a measure of the maximum amount of field that can be
generated by a material. It will depend on the strength of the dipole moments on the atoms that
make up the material and how densely they are packed together. The atomic dipole moment will
be affected by the nature of the atom and the overall electronic structure. The packing density of
the atomic moments will be determined by the crystal structure (i.e. the spacing of the moments)
and the presence of any non-magnetic elements within the structure. At finite temperatures, for
ferromagnetic materials, MS will depend on how well these moments are aligned, as thermal
vibration of the atoms causes misalignment of the moments and a reduction in MS. For
ferromagnetic materials, all moments are aligned parallel even at zero Kelvin and hence MS will
depend on the relative alignment of the moments as well as the temperature.
2.2 Types of Magnetic Materials
When a material is placed within a magnetic field, the magnetic forces of the material's electrons
will be affected. This effect is known as Faraday's Law of Magnetic Induction. However,
materials can react quite differently to the presence of an external magnetic field. This reaction
depends on a number of factors, such as the atomic and molecular structure of the material, and
the net magnetic field associated with the atoms. The magnetic moments associated with atoms
are the electron orbital motion, the change in orbital motion caused by an external magnetic
Chapter- II Theoretical Background
37
field, and the spin motion of the electron. Some materials acquire a magnetization parallel to B
(Paramagnets) and some opposite to B (Diamagnets) [5].
In most atoms, electrons occur in pairs. Electrons are in a pair, spin in opposite directions. When
electrons are paired together, their opposite spins cause their magnetic fields to cancel each
other. Therefore, no net magnetic field exists. Alternately, materials with some unpaired
electrons will have a net magnetic field and will react more to an external field. Most materials
can be classified as diamagnetic, paramagnetic or ferromagnetic.
Magnetic materials can also be classified in terms of their magnetic properties and uses. If a
material is easily magnetized and demagnetized then, it is referred to as a soft magnetic material,
whereas if it is difficult to demagnetize, then it is referred to as hard (permanent) magnetic
material. Materials in between hard and soft are almost exclusively used as recording media and
have no other general term to describe them. Other classifications for types of magnetic materials
are subset of soft or hard materials. Different types of magnetic materials are shown in periodic
table as in Fig. 2.7.
Fig. 2.7: Periodic table showing different types of magnetic materials.
Chapter- II Theoretical Background
38
2. 2.1 Diamagnetism
Diamagnetic substances consist of atoms or molecules with no net angular momentum. When an
external magnetic field is applied, there creates a circulating atomic current that produces a very
small bulk magnetization opposing the applied field [6]. Diamagnetism is exhibited by all
common materials but so feeble that it is covered if material also exhibits paramagnetism or
ferromagnetism [7]. When a material is placed in a magnetic field, electrons in the atomic
orbitals tend to oppose the external magnetic field by moving the induced magnetic moment in a
direction opposite to the external magnetic field. Due to this fact, the material is very weakly
repelled in the magnetic field. This is known as diamagnetism. The induced dipole moments
disappear when the external field is removed. The diamagnetic effect in a material can be
observed only if the paramagnetic effect or the ferromagnetic effect does not hide the weak
diamagnetic effect. Diamagnetism can be understood through Figs. 2.8 (a) and (b). In the
absence of the external magnetic field, the atoms have zero magnetic moment as shown in Fig.
2.8(a). But when an external magnetic field Ho is applied in the direction as shown in Fig. 2.8(b),
the atoms acquire an induced magnetic moment in the direction opposite to that of the field.
Diamagnetic materials have very small negative susceptibility. Due to this fact, a diamagnetic
material is weakly repelled in the magnetic field. When the field is removed, its magnetization
becomes zero. Examples of some diamagnetic materials are gold, silver, mercury, copper and
zinc [8].
Fig. 2.8: (a) Diamagnetic material: The atoms do not possess magnetic moment when H = 0; so M = 0.
(b) When a magnetic field Ho is applied, the atoms acquire induced magnetic moment in a direction opposite to the applied field that results a negative susceptibility.
Chapter- II Theoretical Background
39
2.2.2 Paramagnetism
In certain materials, each atom or molecule possess permanent magnetic moment individually
due to its orbital and spin magnetic moment. In the absence of an external magnetic field, the
individual atomic magnetic moments are randomly oriented. The net magnetic moment and the
magnetization of the material becomes zero. But when an external magnetic field is applied, the
individual atomic magnetic moments tend to align themselves in the direction of externally
applied magnetic field and results in to a nonzero weak magnetization as shown in Fig. 2.9 (a)
and (b). Such materials are paramagnetic materials and phenomenon is called paramagnetism [6].
Paramagnetism occurs in materials with permanent magnetic dipole moment, such as atomic or
molecular with an odd number of electrons, atoms or ions in unfilled orbitals. Paramagnetism is
found in atoms, molecules & lattice defects possessing an odd number of electrons as the total
spin of the system can’t be zero. Metals, free atoms & ions with partly filled inner shell,
transition elements and few compounds with an even number of electrons including oxygen also
show paramagnetism [9]. Paramagnetic materials are attracted when subjected to an applied
magnetic field. Paramagnetic materials also exhibit diamagnetism, but the latter effect is
typically very small. These materials show weak magnetism in the presence of an external
magnetic field but when the field is removed, thermal motion will quickly disrupt the magnetic
alignment. These materials have very weak and positive magnetic susceptibility to an external
magnetic field.
Fig. 2.9: (a) Paramagnetic material: Each atom possesses a permanent magnetic moment. When H = 0, all
magnetic moments are randomly oriented: so M = 0. (b) When a magnetic field Ho is applied, the atomic
magnetic moments tend to orient themselves in the direction of the field that results a net magnetization M = Mo and positive susceptibility.
Chapter- II Theoretical Background
40
The alignment of magnetic moments is disturbed by the thermal agitation with the rise in
temperature and greater fields are required to attain the same magnetization. As a result
paramagnetic susceptibility decreases with the rise in temperature. The paramagnetic
susceptibility is inversely proportional to the temperature. It can be described by the relation
T
C (19)
This is called the Curie Law of paramagnetism. Here χ is the paramagnetic susceptibility, T is the
absolute temperature and C is called the Curie constant. Examples of paramagnetic elements are
aluminum, calcium, magnesium and sodium [8].
2.2.3 Ferromagnetism
Ferromagnetism is a phenomenon of spontaneous magnetization. It has the alignment of an
appreciable fraction of molecular magnetic moments in some favorable direction in the crystal.
Ferromagnetism appears only below a certain temperature, known as Curie temperature. Above
Curie temperature, the moments are randomly oriented resultin the zero net magnetization [10].
Ferromagnetism is only possible when atoms are arranged in a lattice and the atomic magnetic
moment can interact to align parallel to each other Fig. 2.10. A ferromagnetic material has
spontaneous magnetization due to the alignment of its atomic magnetic moments even in the
absence of external magnetic field [8].
Fig. 2.10: Ferromagnetism.
Examples of ferromagnetic materials are transition metals Fe, Co and Ni, but other elements and
alloys involving transition or rare-earth elements are also ferromagnetic due to their unfilled 3d
Chapter- II Theoretical Background
41
and 4f shells. These materials have a large and positive magnetic susceptibility to an external
magnetic field. They exhibit a strong attraction to magnetic fields and are able to retain their
magnetic properties after the external field is removed. When ferromagnetic materials are heated,
then due to thermal agitation of atoms the degree of alignment of the atomic magnetic moment
decreases, eventually the thermal agitation becomes so great that the material becomes
paramagnetic. The temperature of this transition is the Curie temperature, Tc (Fe: Tc = 770 oC,
Co: Tc = 1131 oC and Ni: Tc = 358
oC). Above Tc the magnetic susceptibility varies according to
the Curie-Weiss law [8].
Ferromagnetic materials generally can acquire a large magnetization even in the absence of a
magnetic field, since all magnetic moments are easily aligned together. The susceptibility of a
ferromagnetic material does not follow the Curie law, but displayed a modified behavior defined
by Curie-Weiss law as shown in Fig. 2.11(b).
T
C (2.20)
Where, C is a constant and is called Weiss constant. For ferromagnetic materials, the Weiss
constant is almost identical to the Curie temperature (Tc). At temperature below Tc, the magnetic
moments are ordered whereas above Tc material losses magnetic ordering and show
paramagnetic character.
Fig.2.11. The inverse susceptibility varies with temperature T for (a) paramagnetic, (b) ferromagnetic, (c) ferrimagnetic, (d) antiferromagnetic materials. TN and Tc are Neel temperature and
Curie temperature, respectively.
Chapter- II Theoretical Background
42
2.2.4 Antiferromagnetism
Antiferromagnetic materials are those in which the dipoles have equal moments, but adjacent
dipoles point in opposite directions [10]. There are also materials with more than two sublattices
with triangular, canted or spiral spin arrangements. Due to these facts, antiferromagnetic
materials have small non-zero magnetic moment [11]. They have a weak positive magnetic
susceptibility of the order of paramagnetic material at all temperatures, but their susceptibilities
change in a peculiar manner with temperature. The theory of antiferromagnetism was developed
chiefly by Néel in 1932. Chromium is the only element exhibiting antiferromagnetism at room
temperature [2].
Fig. 2.12: Antiferromagnetism.
Antiferromagnetic materials are very similar to ferromagnetic materials but the exchange
interaction between neighboring atoms leads to the anti-parallel alignment of the atomic
magnetic moments Fig. 2.12. Therefore the magnetic field cancels out and the material appears
to behave in the same way as the paramagnetic material. The antiparallel arrangement of
magnetic dipoles in antiferromagnetic materials is the reason for small magnetic susceptibility of
antiferromagnetic materials. Like ferromagnetic materials, these materials become paramagnetic
above transition temperature, known as the Néel temperature, TN (Cr: TN = 37 oC).
2.2.5 Ferrimagnetism
Ferrimagnetic materials have spin structure of both spin-up and spin-down components but have
a net non-zero magnetic moment in one of these directions [12]. The magnetic moments of the
Chapter- II Theoretical Background
43
atoms on different adjacent sublattices are opposite to each other as in antiferromagnetism;
however, in ferrimagnetic materials the opposing moments are unequal Fig. 2.13. This magnetic
moment may also be due to more than two sublattices and triangular or spiral arrangements of
sublattices [11]. Ferrimagnetism is only observed in compounds, which have more complex
crystal structures than pure elements.
Fig. 2.13: Ferrimagnetism.
These materials, like ferromagnetic materials, have a spontaneous magnetization below a critical
temperature called the Curie temperature (Tc). The magnitude of magnetic susceptibility for
ferromagnetic and ferrimagnetic materials is similar, however the alignment of magnetic dipole
moments is drastically different.
2.3 Introduction of Ferrites
Ferrites are electrically non-conductive ferrimagnetic ceramic compound materials, consisting of
various mixtures of iron oxides such as Hematite (Fe2O3) or Magnetite (Fe3O4) and the oxides of
other metals like NiO, CuO, ZnO, MnO, CoO. The prime property of ferrites is that, in the
magnetized state, all the spin magnetic moments are not oriented in the same direction. Few of
them are in the opposite direction. But as the spin magnetic moments are of two types with
different values, the net magnetic moment will have some finite value. The molecular formula of
ferrites is M2+
O.Fe23+
O3, where M stands for the divalent metal such as Fe, Mn, Co, Ni, Cu, Mg,
Zn or Cd. There are 8 molecules per unit cell in a spinel structure. There are 32 oxygen (O2-
)
ions, 16 Fe3+
ions and 8 M2+
ions, per unit cell. Out of them, 8 Fe3+
ions and 8 M2+
ions occupy
the octahedral sites. Each ion is surrounded by 6 oxygen ions. The spin of all such ions are
Chapter- II Theoretical Background
44
parallel to each other. The rest 8 Fe3+
ions occupy the tetrahedral site which means that each ion
is surrounded by 4 oxygen ions. The spin of these 8 ions in the tetrahedral sites, are all oriented
antiparallel to the spin in the octahedral sites. The net spin magnetic moment of Fe3+
ions is zero
as the 8 spins in the tetrahedral sites cancel the 8 antiparallel spins in the octahedral sites. The
spin magnetic moment of the 8 M2+
ions contribute to the magnetization of ferrites [8].
Ferrites have been studied since 1936. They have an enormous impact over the applications of
magnetic materials. The resistivity of ferrites at room temperature can vary from 10-2 Ω-cm to
1011
Ω-cm, depending on their chemical composition [13]. They are considered superior to other
magnetic materials because they have low eddy current losses and high electrical resistivity.
Ferrites exhibit dielectric properties. Exhibiting dielectric properties means that even though
electromagnetic waves can pass through ferrites, they do not readily conduct electricity. This
also gives them an advantage over iron, nickel and other transition metals that have magnetic
properties in many applications because these metals conduct electricity. Another important
factor, which is of considerable importance in ferrites and is completely insignificant in metals is
the porosity. Such a consideration helps us to explain why ferrites have been used and studied for
several years. The properties of ferrites are being improved due to the increasing trends in
ferrites technology. It is believed that there is a bright future for ferrite technology.
2.4 Types of Ferrites
According to the crystallographic structures ferrites can be classified into three different types
[14].
(1) Spinel ferrites (Cubic ferrites)
(2) Hexagonal ferrites
(3) Garnets
The present research work is on spinel ferrites, therefore it has been discussed in detail the spinel
ferrites only.
Chapter- II Theoretical Background
45
2.4.1 Spinel ferrites
They are also called cubic ferrites. Spinel is the most widely used family of ferrites. High values
of electrical resistivity and low eddy current losses make them ideal for their use at microwave
frequencies. The spinel structure of ferrites as possessed by mineral spinel MgAl2O4 was first
determined by Bragg and Nishikawa in 1915 [14]. The chemical composition of a spinel ferrite
can be written in general as MFe2O4 where M is a divalent metal ion such as Co2+
, Zn2+
, Fe2+
,
Mg2+
, Ni2+
, Cd2+
or a combination of these ions such as ( 2
5.0
2
5.0 ZnNi or 2
5.0
2
5.0 ZnCu ) etc. The unit
cell of spinel ferrites is FCC with eight formula units per unit cell. The formula can be written as
M8Fe16O32. The anions are the greatest and they form an FCC lattice. Within these lattices two
types of interstitial positions occur and these are occupied by the metallic cations. There are 96
interstitial sites in the unit cell, 64 tetrahedral (A) and 32 octahedral (B) sites as shown in Fig.
2.14−2.15.
(I) Tetrahedral sites
Fig. 2.14: Tetrahedral sites in FCC lattice.
In tetrahedral (A) site, the interstitial is in the centre of a tetrahedron formed by four lattice
atoms. Three anions, touching each other, are in plane; the fourth anion sits in the symmetrical
position on the top at the center of the three anions. The cation is at the center of the void created
by these four anions. In the tetrahedral configuration, four anions are occupied at the four corners
of a cube and the cation occupying the body center of the cube. Here the anions at A, B, C are in
a plane, and the anion D is above the center of the triangle formed by the three anions. The
Chapter- II Theoretical Background
46
cation occupies the void created at the center of the cube. For charge neutrality of the system
only 8 tetrahedral (A) sites are occupied by cations out of 64 sites per unit cell in FCC crystal
structure. Fig. 2.14 shows the tetrahedral position in the FCC lattice.
(II) Octahedral Sites
In an octahedral (B) site, the interstitial is at the center of an octahedron formed by 6 lattice
anions. Four anions touching each other are in plane, the other two anions sites in the
symmetrical position above and below the center of the plane formed by four anions. Cation
occupies the void created by six anions forming an octahedral structure. The configuration Fig.
2.15 shows that six anions occupy the face centers of a cube and cation occupies the body center
of the cube.
Fig. 2.15: Octahedral sites in FCC lattice.
For charge neutrality, 16 octahedral (B) sites are occupied by cations out of 32 sites in a spinel
structure. In FCC there are 4 octahedral sites per unit cell. Fig. 2.16 shows the spin alignment of
tetrahedral and octahedral sites in an FCC lattice.
Fig. 2.16: Tetrahedral and Octahedral sites in FCC lattice.
Chapter- II Theoretical Background
47
2.4.2 Hexagonal ferrites
This was first identified by Went, Rathenau, Gorter & Van Oostershout in 1952 [14] and Jonker,
Wijn & Braunin 1956. Hexa ferrites are hexagonal or rhombohedral ferromagnetic oxides with
formula MFe12O19, where M is an element like Barium, Lead or Strontium. In these ferrites,
oxygen ions have closed packed hexagonal crystal structure. They are widely used as permanent
magnets and have high coercivity. They are used at very high frequency. Their hexagonal ferrite
lattice is similar to the spinel structure with closely packed oxygen ions, but there are also metal
ions at some layers with the same ionic radii as that of oxygen ions. Hexagonal ferrites have
larger ions than that of garnet ferrites and are formed by the replacement of oxygen ions. Most of
these larger ions are barium, strontium or lead.
2.4.3 Garnets
Yoder and Keith reported [14] in 1951 that substitutions can be made in ideal mineral garnet
Mn3Al2Si3O12. They produced the first silicon free garnet Y3Al5O12 by substituting Y111
+Al111
for
Mn11
+Si1v
. Bertaut and Forret prepared [14] Y3Fe5O12 in 1956 and measured their magnetic
properties. In 1957 Geller and Gilleo prepared and investigated Gd3Fe5O12 which is also a
ferromagnetic compound [13]. The general formula for the unit cell of a pure iron garnet have
eight formula units of M3Fe5O12, where M is the trivalent rare earth ions (Y, Gd, Dy). Their cell
shape is cubic and the edge length is about 12.5 Å. They have complex crystal structure. They
are important due to their applications in memory structure.
2.5 Types of Spinel Ferrites
The spinel ferrites have been classified into three categories due to the distribution of cations on
tetrahedral (A) and octahedral (B) sites.
(1) Normal spinel ferrites
(2) Inverse spinel ferrites
(3) Intermediate spinel ferrites
Chapter- II Theoretical Background
48
2.5.1 Normal spinel ferrites
If there is only one kind of cations on octahedral (B) sites, the spinel is normal. In these ferrites
the divalent cations occupy tetrahedral (A) sites while the trivalent cations are on octahedral (B)
sites. Square brackets are used to indicate the ionic distribution of the octahedral (B) sites.
Normal spinel have been represented by the formula .][)( 2
4
32 OMeM BA Where M represents
divalent ions and Me for trivalent ions. A typical example of normal spinel ferrite is bulk
ZnFe2O4.
Fig. 2.17: Normal ferrites
2.5.2 Inverse spinel ferrites
In this structure half of the trivalent ions occupy tetrahedral (A) sites and half octahedral (B)
sites, the remaining cations being randomly distributed among the octahedral (B) sites. These
ferrites are represented by the formula .][)( 2
4
323 OMeMM BA A typical example of inverse
spinel ferrite is Fe3O4 in which divalent cations of Fe occupy the octahedral (B) sites [15].
Fig. 2.18: Inverse ferrites
2.5.3 Intermediate or mixed spinel ferrites
Spinel with ionic distribution, intermediate between normal and inverse are known as mixed
spinel e.g.
2
4
3
1
2
1
3
1
2 ][)( OMeMMeM BA , where δ is called inversion parameter. Quantity δ
depends on the method of preparation and nature of the constituents of the ferrites. For complete
normal spinel ferrites δ = 1, for complete inverse spinel ferrites δ = 0, for mixed spinel ferrite, δ
ranges between these two extreme values. For completely mixed ferrites δ = 1/3. If there is
Chapter- II Theoretical Background
49
unequal number of each kind of cations on octahedral sites, the spinel is called mixed. Typical
example of mixed spinel ferrites are MgFe2O4 and MnFe2O4 [7].
Fig. 2.19: Intermediate ferrites
Neel suggested that magnetic moments in ferrites are sum of magnetic moments of individual
sublattices. In spinel structure, exchange interaction between electrons of ions in A- and B-sites
have different values. Usually interaction between magnetic ions of A and B-sites (A-B
interaction) is the strongest. The interaction between A-A is almost ten times weaker than that of
A-B interaction whereas the B-B interaction is the weakest. The dominant A-B-sites interaction
results into complete or partial (noncompensated) antiferromagnetism known as ferrimagnetism
[16]. The dominant A-B interaction having greatest exchange energy, produces antiparallel
arrangement of cations between the magnetic moments in the two types of sublattices and also
parallel arrangement of the cations within each sublattice, despite of A-A or B-
Bantiferrimagnetic interaction [17].
2.6 Types of Ferrites with respect to their Hardness
Due to the persistence of their magnetization, the ferrites are of two types i.e hard and soft. This
classification is based on their ability to be magnetized or demagnetized. Soft ferrites are easily
magnetized or demagnetized whereas hard ferrites are difficult to magnetize or demagnetize
[12].
2.6.1 Soft ferrites
Soft Ferrites are those that can be easily magnetized or demagnetized. This shows that soft
magnetic materials have low coercive field and high magnetization that is required in many
applications. The hysteresis loop for a soft ferrite should be thin and long, therefore the energy
loss is very low in soft magnetic material. Examples are nickel, iron, cobalt, manganese etc.
They are used in transformer cores, inductors, recording heads and microwave devices [8]. Soft
Chapter- II Theoretical Background
50
ferrites have certain advantages over other electromagnetic materials including high resistivity
and low eddy current losses over wide frequency ranges. They have high permeability and are
stable over a wide temperature range. These advantages make soft ferrites paramount over all
other magnetic materials.
2.6.2 Hard ferrites
Hard ferrites are difficult to magnetize or demagnetize. They are used as permanent magnets. A
hard magnetic material has high coercive field and a wide hysteresis loop. Examples are alnico,
rare earth metal alloys etc [8]. The development of permanent magnets began in 1950s with the
introduction of hard ferrites. These materials are ferrimagnetic and have quite a low remanence
(~400 mT). The coercivity of these magnets (~250 kAm-1
), however, is far in excess of other
materials. The maximum energy product is only ~40 kJm-3
. The magnets can also be used to
moderate demagnetizing fields and hence can be used for applications such as permanent magnet
motors. The hexagonal ferrite structure is found in both BaO.6Fe2O3 and SrO.6Fe2O3, but Sr
ferrites have superior magnetic properties.
2.7 Super Exchange Interactions in Spinel Ferrites
The difference of energy of two electrons in a system with anti-parallel and parallel spins is
called the exchange energy. The electron spin of the two atoms Si and Sj, are proportional to their
product .The exchange energy can be written as universally in terms of Heisenberg Hamiltonian
[7].
Eex = -∑Jij Si.Sj = -∑Jij SiSj cosφ, (2.21)
Where, Jij is the exchange integral represents the strength of the coupling between the spin
angular momentum i and j and φ is the angle between the spins. It is well known that the favored
situation is the one with the lowest energy and it turns out that there are two ways in which the
wave functions can combine i.e., there are two possibilities for lowering the energy by Eex.
These are:
(i) If Jij is positive and the spin configuration is parallel, then (cosφ = 1) the energy is
minimum. This situation leads to ferromagnetism.
Chapter- II Theoretical Background
51
(ii) If Jij is negative and the spins are antiparallel (cosφ = -1) then energy is minimum.
This situation leads to antiferromagnetism or ferrimagnetism.
Magnetic interactions in spinel ferrites as well as in some ionic compounds are different from the
one considered above because the cations are mutually separated by bigger anions (oxygen ions).
These anions obscure the direct overlapping of the cation charge distributions, sometimes
partially and sometimes completely making the direct exchange interaction very weak. Cations
are too far apart in most oxides for a direct cation-cation interaction. Instead, superexchange
interactions appear, i.e., indirect exchange via anion p-orbitals that may be strong enough to
order the magnetic moments. Apart from the electronic structure of cations this type of
interactions strongly depends on the geometry of arrangements of the two interacting cations and
the intervening anion. Both the distance and the angles are relevant. Usually only the interactions
with in first coordination sphere (when both the cations are in contact with the anion) are
important. In the Neel theory of ferrimagnetism the interactions taken as effective are inter- and
intera-sublattice interactions A-B, A-A and B-B. The type of magnetic order depends on their
relative strength.
2.8 Two Sublattices in Spinel Ferrites
In spinel ferrites the metal ions are separated by the oxygen ions and the exchange energy
between spins of neighboring metal ions is found to be negative, that is, antiferromagnetic. This
is explained in terms of superexchange interaction of the metal ions via the intermediate oxygen
ions [6]. There are a few points to line out about the interaction between two ions in tetrahedral
(A) sites:
(i) The distance between two A ions ( 3.5 Å) is very large compared with their ionic
radious (0.67 Å for Fe3+
),
(ii) The angle AO2A ( = 79
o38′) is unfavorable for superexchange interaction,
and
(iii) The distance from one A ion to O2
is not the same as the distance from the other
A ion to O2
as there is only one A nearest neighbour to an oxygen ion (in Fig.
2.20, M and M’ are A ions, r = 3.3 Å and q = 1.7 Å). As a result, two nearest A
ions are connected via two oxygen ions.
Chapter- II Theoretical Background
52
These considerations led us to the conclusion that super exchange interaction between A ions is
very unlikely. This conclusion together with the observation that direct exchange is also unlikely
in this case [8] support the assumption that JAA = 0 in the spinel ferrites. According to Neel’s
theory, the total magnetization of a ferrite divided into two sublattices A and B is,
MT(T) = MB(T) MA(T) (2.22)
Where, T is the temperature, MB (T) and MA (T) are A and B sublattice magnetizations. Both MB
(T) and MA (T) are given in terms of the Brillouin function BSi (xi);
MB (T) = MB (T = 0) BSB (xB) (2.23)
MA(T) = MA(T = 0) BSA(xA) (2.24)
with
ABB
B
AABA NM
Tk
Sgx
(2.25)
)( ABABBB
B
BBBB NMNM
Tk
Sgx
(2.26)
Fig.2.20. Schematic representation of ions M and M' and the O2-
ion through which the superexchange is
made. r and q are the centre to centre distances from M and M' respectively to O2- and is the angle
between them.
The molecular field coefficients, Nij, are related to the exchange constants Jij by the following
expression:
ij
ij
Bjij
ij Nz
ggnJ
2
2 (2.27)
M
M'
r
q
O2-
Chapter- II Theoretical Background
53
with nj the number of magnetic ions per mole in the jth sublattice, g the Lande factor, B is the
Bohr magneton and zij the number of nearest neighbors on the jth sublattice that interact with the
ith ion.
According to Neel’s theory and using JAA = 0, equating the inverse susceptibility 1/ = 0 at T =
Tc we obtain for the coefficients of the molecular field theory NAB and NBB of the following
expression:
c
ABA
B
cBB
T
NC
C
TN
2
(2.28)
Where, CA and CB are the Curie constants for each sublattice. Eq. (2.19) and (2.25) constitute a
set of equations with two unknown, NAB and NBB, provided that MA and MB are a known
function of T.
2.8.1 Neel’s collinear model of ferrites
Neel [18] assumed that a ferromagnetic crystal lattice could be split into two sublattices such as
A (tetrahedral) and B (octahedral) sites. He supposed the existence of only one type of magnetic
ions in the material of which a fraction λ appeared on A-sites and the rest fraction µ on B-sites.
Thus
λ + µ = 1 (2.29)
The remaining lattice sites were assumed to have ions of zero magnetic moment. A-ion as well
as B-ion have neighbours of both A and B types, there are several interactions between magnetic
ions as A-A, B-B, A-B, and B-A. It is supposed that A-B and B-A interactions are identical and
predominant over A-A or B-B interactions and favour the alignment of the magnetic moment of
each A-ion more [19].
Neel defined the interactions within the material from the Weiss molecular field viewpoint as
H = Ho + Hm (2.30)
Where Ho is the external applied field and Hm is the internal field arises due to the interaction of
other atoms or ions in the material. When the molecular field concept is applied to a
ferromagnetic material we have
Chapter- II Theoretical Background
54
HA = HAA + HAB (2. 31)
HB = HBB + HBA (2.32)
Here molecular field HA on A-site is equal to the sum of the molecular field HAA due to
neighboring A-ions and HAB due to neighboring B sites. The molecular field components can be
written as,
HAA = γAAMA, HAB = γABMB, (2. 33)
A similar definition holds for molecular field HB, acting on B-ions. Molecular field components
can also be written as
HBB = γBBMB, HBA = γBAMA, (2.34)
Here γ’s are molecular field coefficients and MA and MB are magnetic moments of A and B
sublattices. For unidentical sublattices
γAB = γBA, but γAA ≠ γBB (2.35)
In the presence of the applied magnetic field Ha, the total magnetic field on a sublattice a, can be
written as
Ha = Ho + HA (2.36)
= Ho+ γAAMA + γABMB (2.37)
And Hb = Ho + HB (2.38)
= Ho + γBBMB + γABMA (2.39)
2.8.2 Non-collinear model
In general, all the interactions are negative (antiferromagnetic) with JAB»JBB»JAA. In such
situation, collinear or Neel type of ordering is obtained. Yafet and Kittel theoretically considered
the stability of the ground state of magnetic ordering, taking all the three exchange interations
into account and concluded that beyond a certain value of JBB/JAB, the stable structure was a non-
collinear triangular configuration of moment wherein the B-site moments are oppositely canted
relative to the A-site moments. Later on Leyons et al. [13] extending these theoretical
considerations showed that for normal spinel the lowest energy correspond to conical spinal
structure for the value of 3JBBSB/2JABSA greater than unity. Initially one can understand why the
collinear Neel structure gets perturbed when JBB/JAB increases. Since all these three exchange
interations are negative (favoring antiferromagnetic alignment of moments) the inter- and intra-
Chapter- II Theoretical Background
55
sublattice exchange interaction compete with each other in aligning the moment direction in the
sublattice. This is one of the origins of topological frustration in the spinel lattice. By selective
magnetic directions of say A-sublattice one can effectively decrease the influence of JAB vis-à-vis
JBB and thus perturb the Neel ordering. The first neutron diffraction study of such system i.e.,
ZnxNi1-xFe2O4 was done at Trombay [18] and it was shown to have the Y-K type of magnetic
ordering followed by Neel ordering before passing on to the paramagnetic phase [19].
The discrepancy in the Neel’s theory was resolved by Yafet and Kittel [14] and they formulated
the non-collinear model of ferrimagnetism.
They concluded that the ground state at 0 K might have one of the following configurations:
have an antiparallel arrangement of the spins on two sites,
consists of triangular arrangements of the spins on the sublattices and
an antiferromagnetic in each of the sites separately.
2.9 Cation Distribution Effect in Spinel Ferrites
Ferrites posses the combined properties of magnetic materials and insulator. They from a
complex system composed of grains, grain boundaries and pores. Ferrites exhibit a substantial
spontaneous magnetization at room temperature, like the normal ferromagnetic. They have two
unequal sublattices called tetrahedral (A-site) and octahedral (B-site) and are ordered antiparallel
to each other. In ferrites, the cations occupy the tetrahedral A-site and octahedral B-site of the
cubic spinel lattice and experience competing nearest neighbor (JAB) and the next nearest
neighbor (JAA and JBB ) interactions with |JAB| >> | JBB| > |JAA|. The magnetic properties of ferrites
are dependent on the type of magnetic ions residing on the A- and B-sites and the relative
strengths of the inter (JAB) and intrasublattice (JBB, JAA) interactions. When the JAB is much
stronger than JBB and JAA interactions, the magnetic spins have a collinear structure in which the
magnetic moments on the A sublattice are antiparallel to the moments on the B sublattice. But
when JBB or JAA becomes comparable with JAB, it may lead to non-collinear spin structure [2].
When magnetic dilution of the sublattices is introduced by substituting nonmagnetic ions in the
lattice, frustration and/or disorder occurs leading to collapse of the collinear of the ferromagnetic
phase by local spin canting exhibiting a wide spectrum of magnetic ordering e.g.
Parasitic analysis of a diode, transistor, or IC package terminal/leads.
Amplifier input/output impedance measurement.
Other components
*Impedance evaluation of printed circuit boards, relays, switches, cables, batteries, etc.
Materials
Dielectric material
Permittivity and loss tangent evaluation of plastics, ceramics, printed circuit boards,
and other dielectric materials.
Magnetic material
Permeability and loss tangent evaluation of ferrite, amorphous, and other magnetic
materials.
Semiconductor material
Permittivity, conductivity, and C-V characterization of semiconductor materials.
3.6.2 DC measurement
For DC measurements, the variation of applied field H is very slow and the inducted voltage is
very small, and a numerical integration will give inaccurate results. The integration of the
inducted voltage is performed by the flux meter, which is more precise and can follow very well
the variation of B at such slow rate. After winding, the ring must be connected to the flux meter
Chapter-III Experimental Details
77
through the special cable for DC measurement as shown in Fig. 3.10. This cable is simply an
extension that takes signal from measuring connections to flux meter’s inputs. For devices with
two flux meters, use the B/J flux meter. This flux meter is then connected by the analog output
(in the back panel) to the PC board. A 4-poles connector permits the connection to auxiliary
optional devices. Connect the H turns to magnetization connectors and the B turns in the
connections in the DC cable. The sample put on the fan grid. In DC conditions, H and B are
always in phase, and the max value of H corresponds to the max value of B. The Hysteresis cycle
always has some sharp vertex.
Fig. 3.10: Schematic diagram for DC measurement.
3.6.3 Initial and imaginary part of complex permeability
For high frequency applications, the desirable property of a ferrite is the high initial permeability
with low loss. The present goal of the most of the recent ferrite researches is to fulfill this
requirement. The initial permeability i is defined as the derivative of induction B with respect to
the initial field H in the demagnetization state.
0,0, BHdH
dBi (3.1)
At microwave frequency, and also in low anisotropic amorphous materials, dB and dH may be in
different directions, the permeability thus a tensor character. In the case of amorphous materials
containing a large number of randomly oriented magnetic atoms the permeability will be scalar.
As we have
MHB 0 (3.2)
Chapter-III Experimental Details
78
and susceptibility,
11
00
H
B
dH
d
dH
dM (3.3)
The magnetic energy density
dBHE .1
0 (3.4)
For time dependent harmonic fields tHH sin0 , the dissipation can be described by a phase
difference between H and B. In the case of permeability, defined as the proportional constant
between the magnetic field induction B and applied intensity H;
B = H (3.5)
If a magnetic material is subjected to an ac magnetic field, we get
tieBB 0 (3.6)
Then it is observed that the magnetic flux density B experiences a delay. This is caused due to
the presence of various losses and is thus expressed as,
tieBB 0 , (3.7)
where is the phase angle and marks the delay of B with respect to H, the permeability is then
given by
H
B
ti
ti
eH
eB
0
0
0
0
H
eB i
sincos0
0
0
0
H
Bi
H
B
i (3.8)
where cos0
0
H
B (3.9)
and sin0
0
H
B (3.10)
The real part of complex permeability as expressed in the component of induction B,
which is in phase with H, so it corresponds to the normal permeability. If there are no losses, we
should have . the imaginary part corresponds to that part of B, which is delayed by
phase from H. The presence of such a component requires a supply of energy to maintain the
Chapter-III Experimental Details
79
alternation magnetization, regardless of the origin of delay. It is useful to introduce the loss
factor or loss tangent tan . The ratio of to as is evident from equation gives.
tan
cos
sin
0
0
0
0
H
B
H
B
(3.11)
This tan is called the loss factor. The Q-factor or quality factor is defined as the reciprocal of
this loss factor i.e.
tan
1Q (3.12)
And the relative quality factor (RQF) =
tan
. The behavior of and versus frequency is
called the complex permeability spectrum. The initial permeability of a ferromagnetic substance
is the combined effect of the grain wall permeability and rotational permeability mechanism. The
complex permeability of the toroid shaped samples at room temperature was measured with the
Agilent Precision Impedance Analyzer (Model-Agilent 4294A.) in the frequency range 1 kHz to
120 MHz. The permeability i was calculated by
0
iL
Lμ (3.13)
Where, L is the measured sample inductance and Lo is the inductance of the coil of same
geometric shape of vacuum. Lo is determined by using the relation,
dπ
SNμL
2o
o (3.14)
Here, o is the permeability of the vacuum, N is the number of turns (here N = 5), S is the cross
sectional area of the toroid shaped sample, S = (d×h), where, 2
~ 21 ddd and d is the average
diameter of the toroid sample given as
2
ddd 21
(3.15)
Where, d1 and d2 are the inner and outer diameter of the toroid samples. For these measurements
an applied voltage of 5 mV was used with a 5 turn low inductive coil.
Chapter-III Experimental Details
80
3.6.4 Curie temperature measurement with temperature dependence of
permeability
The temperature dependent permeability was measured by using induction method. The
specimen formed the core of the coil. The number of turns in each coil was 5. A constant
frequency (100 kHz) was used for a sinusoidal wave, ac signal of 100 mV Agilent 4294A
impedance analyzer with continuous heating rate of ≈ 5 K/min with very low applied ac field of
≈ 10-3
Oe. By varying temperature, inductance of the coil as a function of temperature was
measured. Dividing this value of Lo (inductance of the coil without core material), it is obtained
the permeability of the core i.e. the sample. When the magnetic state inside the ferrite sample
changes from ferromagnetic to paramagnetic, the permeability falls sharply. From this sharp fall
at specific temperature the Curie temperature was determined. For the measurement of Curie
temperature, the sample was kept inside a cylindrical oven with a thermocouple placed at the
middle of the sample. The thermocouple measures the temperature inside the oven and also of
the sample. The sample was kept just in the middle part of the cylindrical oven in order to
minimize the temperature gradient. The temperature of the oven was then raised slowly. If the
heating rate is very fast then the temperature of the sample may not follow the temperature inside
the oven and there can be misleading information on the temperature of the samples. The
thermocouple showing the temperature in that case will be erroneous. Due to the closed winding
of wires the sample may not receive the heat at once. So, a slow heating rate can eliminate this
problem. The cooling and heating rates are maintained as approximately 0.5 °C min-1
in order to
ensure a homogeneous sample temperature. Also a slow heating ensures accuracy in the
determination of Curie temperature.
For ferrimagnetic materials in particular, for ferrite it is customary to determine the Curie
temperature by measuring the permeability as a function of temperature. According to
Hopkinson effect [18] which arises mainly from the intrinsic anisotropy of the material has been
utilized to determine the Curie temperature of the samples. According to this phenomenon, the
permeability increases gradually with temperature and reaching to a maximum value just before
the Curie temperature.
Chapter-III Experimental Details
81
REFERENCES
[1] F. Gerald and Dionne, “Magnetic and dielectric properties of the spinel ferrite system
Ni0.65Zn0.35Fe2 − x Mn x O4 ’’, J. Appl. Phys., 61(8) (1987) 3868.
[2] L. B. Kong, Z. W. Li, G. Q. Lin, and Y. B. Gan, “Magneto-dielectric properties of Mg-Cu-Co
ferrite ceramics: II. Electrical, dielectric and magnetic properties’’, J. Am. Ceram. Soc., 90(7)
(2007) 2014.
[3] S. K. Sharma, R. Kumar, S. Kumar, M. Knobel, C. T. Meneses, V. V. S. Kumar, V. R. Reddy ,
M. Singh, and C. G. Lee, “Role of interpartical interactions on the magnetic behavior of Mg0.95Mn0.05Fe2O4 ferrite nanoparticals’’, J. Phys.: Conden. Matter., 20 (2008) 235214.
[4] S. Zahi, M. Hashim, and A. R. Daud, “Synthesis, magnetic and microstructure of Ni-Zn ferrite
by sol-gel technique’’, J. Magn. Magn. Mater., 308 (2007) 177.
[5] M. A. Hakim, D. K. Saha, and A. K. M. Fazle Kibria, “Synthesis and temperature dependent
structural study of nanocrystalline Mg-ferrite materials’’, Bang. J. Phys., 3 (2007) 57.
[6] A. Bhaskar, B. Rajini Kanth, and S. R. Murthy, “Electrical properties of Mn added Mg-Cu- Zn
ferrites prepared by microwave sintering method’’, J. Magn. Magn. Mater., 283 (2004) 109.
[7] Z. Yue, J. Zhou, L. Li, and Z. Gui, “Effects of MnO2 on the electro-magnetic properties of Ni-
Cu-Zn ferrites prepared by sol-gel auto combustion’’, J. Magn. Magn. Mater., 233 (2001) 224.
[8] P. Reijnen, 5th Int. Symp. React. In Solids (Elsevier, Amsterdam) (1965) 562.
[9] C. Kittel, “Introduction to Solid State Physics’’, 7th ed., John Wiley & Sons, Singapore (1996).
[10] B. D. Cullity and C. D. Graham, “Introduction to Magnetic Materials’’, John Wiley & Sons, New Jersey (1972) 186.
[11] E. C. Snelling, “Soft Ferrites: Properties and Applications’’, 2nd
ed., Butterworths, London (1988) 1.
[12] A. B. Gadkari, T. T. Shinde, and P. N. Vasambekar, “Structural and magnetic properties of
nanocrystalline Mg-Cd ferrites prepared by oxalate co-precipitation methods’’, J. Mater. Sci.
Mater. Electron, 21(1) (2010) 96–103.
[13] B. D. Cullity, “Elements of X-ray diffraction’’, Addision-Wisley Pub., USA (1959) 330.
[14] Simon Foner, “Versatile and sensitive Vibrating Sample Magnetometer”, Rev. Sci. Instr. 30
(1959) 548.
[15] K. J. Standley, “Oxide Magnetic Materials” 2nd ed., Oxford University Press, Oxford (1972).
[16] S. S. Bellad, R. B. Pujar, and B. K. Chougule. “Introduction to Solid State Physics’’, Mater.
Chem. Phys., 52 (1998)166.
[17] A. Withop, “Manganese-zinc ferrite processing, properties and recording performance”, IEEE
Trans. Magnetic Mag., 14 (1978) 439–441. [18] J. Smit and H. P. J Wijin, “Ferrites’’, John Wiley & Sons, New York (1959) 250.
82
CHAPTER−IV
RESULTS AND DISCUSSION
4.1. Structural and Physical Characterization of A0.5B0.5Fe2O4
The spinel ferrites having general formula A0.5B0.5Fe2O4 (where, A = Ni2+
, Mn2+
, Mg2+
, Cu2+
,
Co2+
and B = Zn2+
) have been prepared by the standard solid state reaction technique using
reagents of analytical grate. The substitution of nonmagnetic zinc in different base ferrites
AFe2O4 has a significant influence on the structural and physical properties such as lattice
constant, X-ray density, bulk density, porosity etc. XRD patterns reveal that the samples are of
signal phase cubic spinel structure. Lattice parameter „a‟ of the samples was found to be larger
than base ferrite. The porosity was calculated from the X-ray density and bulk density. The
possible experimental and theoretical reasons responsible for the change in substitution of the
above mentioned properties have been discussed below.
4.1.1 Structural analysis
Structural characterization and identification of phases are prior for the study of ferrite
properties. Optimum magnetic and transport properties of the ferrites necessitate having single
phase cubic spinel structure. X-ray diffraction patterns for the samples A0.5Zn0.5Fe2O4 sintered
between 1000 to 1350 °C for time 0.5–4 h are shown in Fig. 4.1. The XRD patterns for all the
samples were indexed for fcc spinel structure and the Bragg diffraction planes are shown in the
patterns. All the samples show good crystallization with well defined diffraction lines. It is
obvious that the characteristic peaks for spinel ferrites i.e., (220), (311), (222), (400), (422),
(511) and (440), which represent either all odd or all even indicating the samples are spinel cubic
phase. All the samples have been characterized as cubic spinel structure without any extra peaks
corresponding to any second phase.
Generally, for the spinel ferrites the peak intensity depends on the concentration of magnetic ions
in the lattice. The intensity of all the samples is found quite sharp that also demonstrates the good
crystallinity and homogeneity of the prepared samples. All diffraction peaks of the studied
Chapter-IV Results and Discussion
83
20 30 40 50 60
(b) Mn0.5
Zn0.5
Fe2O
4
(440)
(511)
(422)
(400)
(222)
(311)
(220)
Inte
ns
ity(a
.u)
Fig. 4.1: XRD patterns of (a) Ni0.5Zn0.5Fe2O4 sintered at 1325 °C, (b) Mn0.5Zn0.5Fe2O4 sintered at 1240
°C, (c) Mg0.5Zn0.5Fe2O4 sintered at 1350 °C, (d) Cu0.5Zn0.5Fe2O4 sintered at 1050 °C and (e)
Co0.5Zn0.5Fe2O4 sintered at 1175 °C.
samples are compared to the reported structure for relevant base ferrite, AFe2O4 in Joint
Committee on Powder Diffraction Standards (JCPDS) file and are tabulated in Table 4.1. A
20 30 40 50 60
(a) Ni0.5
Zn0.5
Fe2O
4
(42
2)
(44
0)
(51
1)
(40
0)
(22
2)(2
20)
(31
1)
Inte
ns
ity(a
.u)
20 30 40 50 60
(c) Mg0.5
Zn0.5
Fe2O
4(4
40)
(51
1)
(42
2)
(40
0)
(22
2)
(31
1)
(22
0)
Inte
ns
ity(a
.u)
20 30 40 50 60
(d) Cu0.5
Zn0.5
Fe2O
4
(44
0)
(51
1)
(42
2)
(40
0)
(22
2)
(31
1)
(22
0)
Inte
ns
ity(a
.u)
20 30 40 50 60
Co0.5
Zn0.5
Fe2O
4
(22
2)
(e)
(44
0)
(51
1)
(42
2)
(40
0)
(31
1)
(22
0)
Inte
ns
ity(
a.u
)
2θ (degree) 2θ (degree)
2θ (degree)
2θ (degree) 2θ (degree)
Chapter-IV Results and Discussion
84
small shift to lower angle of peaks position as compared with base ferrite is observed which
suggests the increase of the lattice parameter upon zinc substitution. This shift might be due to
larger ionic radius of Zn2+
than A ions. Some anomaly is found for Mn0.5Zn0.5Fe2O4 ferrite
because the ionic radii of substituted Zn2+
is lower than Mn2+
ion.
Table 4.1: 2θ, dhkl and Miller indices of A0.5Zn0.5Fe2O4 ferrites.