structural and magnetic characterization of spinel
TRANSCRIPT
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
rch, 2
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
3.5.3 Saturation magnetization measurement 72
3.5.4 Magnetic moment calculation 74
3.6 Permeability Measurement 75
3.6.1 Alilent precision impedance analyzer (Alilent 4294A) 75
3.6.2 DC measurement 76
3.6.3 Initial and complex part of permeability 77
3.6.4 Curie temperature measurement with temperature dependence of
permeability
80
References 81
CHAPTER – IV : RESULTS AND DISCUSSION
82−119
4.1 Structural and Physical Characterization of A0.5B0.5Fe2O4
(where, A = Ni2+
, Mn2+
, Mg2+
, Cu2+
, Co2+
and B = Zn2+
)
82
4.1.1 Structural analysis 82
4.1.2 Experimental calculation of lattice parameter 85
4.1.3 Theoretical calculation of lattice Parameter 88
4.1.4 Physical properties of A0.5B0.5Fe2O4 90
VII
4.2 Magnetic Properties of A0.5Zn0.5Fe2O4 91
4.2.1 Magnetization measurement 92
4.2.2 Theoretical calculation of magnetic moment 96
4.3 Curie Temperature Measurement with Temperature Dependence of
Permeability
101
4.4 Complex permeability, Relative quality factor and Relative loss factor 107
References 118
CHAPTER - VI : CONCLUSIONS
120-122
5.1 Conclusions 120
5.2 Suggestion for Future Works 121
APENDEX
123-126
VIII
List of Figures
Fig. 2.1: The orbit of a spinning electron about the nucleus of an atom. 25
Fig. 2.2: Magnetic dipole of a bar magnet. 26
Fig. 2.3: Magnetic domain. 30
Fig. 2.4: Bloch wall. 31
Fig. 2.5: The magnetization changes from one direction to another one. 32
Fig. 2.6: Hysteresis loop. 35
Fig. 2.7: Periodic table showing different types of magnetic materials. 37
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.
38
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.
39
Fig. 2.10: Ferromagnetism. 40
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.
41
Fig. 2.12: Antiferromagnetism. 42
Fig. 2.13: Ferrimagnetism. 43
Fig. 2.14: Tetrahedral sites in FCC lattice. 45
Fig. 2.15: Octahedral sites in FCC lattice. 46
Fig. 2.16: Tetrahedral and Octahedral sites in FCC lattice. 46
Fig. 2.17: Normal ferrites. 48
Fig. 2.18: Inverse ferrites. 48
Fig. 2.19: Intermediate ferrites. 49
Fig. 2.20: Schemitic 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.
52
Fig. 3.1: Photographs of (a) Pellets (b) Toroids. 60
Fig. 3.2: Time versus temperature curves for (a) Pre-sintering and (b) sintering
process.
61
IX
Fig. 3.3: Flowchart of ferrite sample preparation. 63
Fig. 3.4: Bragg’s diffraction pattern. 66
Fig. 3.5: Block diagram of the PHILIPS (PW 3040) X’ Pert PRO XRD system. 66
Fig. 3.6: Photograph of PHILIPS X’ Pert PRO X-ray diffractometer. 67
Fig. 3.7: Photograph of VSM (Model EV7, System Micro sense,USA) 70
Fig. 3.8: Block diagram of a VSM 71
Fig. 3.9: Agilent 4294A Precision Impedance Analyzer (1 kHz to 120 MHz). 75
Fig. 3.10: Schematic diagram for DC measurement. 77
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.
83
Fig. 4.2: Field dependence magnetization (M−H curve) for (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.
93
Fig. 4.3: Variation of permeability with temperature for Ni0.5Zn0.5Fe2O4 at (a) 1325 °C/2 h and (b)1350 °C/2 h.
102
Fig. 4.4: Variation of permeability with temperature for Mn0.5Zn0.5Fe2O4 at (a) 1220 oC/3 h and (b)1240 oC/3 h .
103
Fig. 4.5: Variation of permeability with temperature for Mg0.5Zn0.5Fe2O4 at (a) 1300
°C/1 h and (b)1350 °C/1 h.
104
Fig. 4.6: Variation of permeability with temperature for Cu0.5Zn0.5Fe2O4 at (a) 1000
°C/1 h and (b)1050 °C/1 h.
105
Fig. 4.7: Variation of permeability with temperature for Co0.5Zn0.5Fe2O4 at (a) 1125
°C/2 h and (b)1175 °C/2 h.
105
Fig. 4.8: Frequency dependence (a) initial permeability ('), (b) imaginary
permeability (''), (c) relative quality factor and (d) relative loss factor of Ni0.5Zn0.5Fe2O4 for different sintering temperature.
109
Fig. 4.9: Frequency dependence (a) initial permeability ('), (b) imaginary
permeability (''), (c) relative quality factor (RQF) and (d) relative loss factor (RLF) of Mn0.5Zn0.5Fe2O4 for different sintering temperature.
112
Fig. 4.10: Frequency dependence (a) initial permeability ('), (b) imaginary
permeability (''), (c) relative quality factor (RQF) and (d) relative loss
factor (RLF) of Mg0.5Zn0.5Fe2O4 for different sintering temperature.
113
Fig. 4.11: Frequency dependence (a) initial permeability ('), (b) imaginary
permeability (''), (c) relative quality factor (RQF) and (d) relative loss
factor (RLF) of Cu0.5Zn0.5Fe2O4 for different sintering temperature.
115
Fig.
4.12: Frequency dependence (a) initial permeability ('), (b) imaginary
permeability (''), (c) relative quality factor (RQF) and (d) relative loss factor (RLF) of Ni0.5Zn0.5Fe2O4 for different sintering temperature.
116
X
List of Tables
Table 4.1: 2θ, dhkl and Miller indices value of A0.5Zn0.5Fe2O4 ferrite. 84
Table 4.2: Cation distribution (tetrahedral A-site and octahedral B-site), Ionic radii
(rAfor A-site and rB for B-site), Lattice parameters (ath for theoretical and
aexp for experimental value), X-ray density (dx), Bulk density (dB) and
Porosity (P) of A0.5Zn0.5Fe2O4 ferrites.
86
Table 4.3: Saturation magnetization (Ms), Molecular weight (M) and Magnetic
moment (µB) for A0.5Zn0.5Fe2O4.
95
Table 4.4: Theoretical calculation of magnetic moment of A0.5Zn0.5Fe2O4 ferrites. 98
Table 4.5: Curie temperature (Tc) of the A0.5Zn0.5Fe2O4 samples sintered at different
sintering temperatures (Ts) / time.
106
Table 4.6: The variation of complex permeability (µ' and ''), Resonance frequency
(fr), Relative quality factor (RQF), Relative loss factor (RLF) of the
A0.5Zn0.5Fe2O4 samples sintered at different temperature and time.
111
1
CHAPTER−I
GENERAL INTRODUCTION AND REVIEW WORKS
1.1 Introduction
Technological advances in a variety of areas have generated a growing demand for the soft
magnetic materials in devices. Among the soft magnetic materials, polycrystalline ferrites have
received special attention due to their good magnetic properties and high electrical resistivity
over a wide range of frequencies; starting from a few hundred hertz (Hz) to several gigahertz
(GHz). There are two basic types of magnetic materials, one is metallic and other is metallic
oxides. Metallic oxide materials are called ferrites. Spinel type ferrites are commonly used in
many electronic and magnetic devices due to their high magnetic permeability and low magnetic
losses [1, 2] and also used in electrode materials for high temperature applications because of
their high thermodynamic stability, electrical resistivity, electrolytic activity and resistance to
corrosion [3, 4]. Moreover, these low cost materials are easy to synthesize and offer the
advantages of greater shape formability than their metal and amorphous magnetic counterparts.
Almost every item of electronic equipment produced today contains some ferrimagnetic spinel
ferrite materials. Loudspeakers, motors, deflection yokes, electromagnetic interference
suppressors, radar absorbers, antenna rods, proximity sensors, humidity sensors, memory
devices, recording heads, broadband transformers, filters, inductors, etc are frequently based on
ferrites.
Ferrites are ferrimagnetic cubic spinels that possess the combined properties of magnetic
materials and insulators. They form a complex system composed of grains, grain boundaries and
pores. A ferrimagnetic material is defined as one which below a transition temperature exhibits a
spontaneous magnetization that arises from non parallel arrangement of the strongly coupled
magnetic moments. They have the magneto-dielectric property of material which is useful for
high frequency (2–30 MHz) antenna design. The usefulness of ferrites is influenced by the
physical and chemical properties of the materials and depends on many factors including the
Chapter-I Introduction
2
preparation conditions, such as, sintering temperature, sintering time, rate of heating, cooling and
grinding time. In the spinel structure, the magnetic ions are distributed among two different two
lattice sites, tetrahedral (A) and octahedral (B) sites. The electromagnetic properties of these
ferrites depend on the relative distribution of cations at the different sites as well as the
preparation condition. The magnetization of A site can be reduced by substitution of non
magnetic ions (i.e. Zn+2
) in the corresponding sites.
High saturation magnetization is a requirement in several applications where ferromagnetic
oxides are used. For those cases in which low coercive field (i.e. soft ferrite) are also a critical
parameter, spinel is the structure of choice because its maximum saturation magnetization (4πM)
is more than double than that of the magnetic garnet alternatives. In particular, all spinel ferrites
are important materials for high initial permeability applications and lithium-zinc (Li-Zn) and
new nickel-manganese-zinc (Ni-Mn-Zn) ferrites for devices requiring square hysteresis loops
[5]. Manganese-zinc (Mn-Zn) ferrites are used for lower frequency work. They have high
permeability, but their bulk resistivity is relatively low. On the other hand, nickel-zinc (Ni-Zn)
ferrite has a lower permeability on average, but it will be worked well at higher frequencies. This
material has much higher bulk resistivity.
Small amount of foreign ions in the ferrites can dramatically change the properties of ferrites.
Nonmagnetic Zn2+
ion is very promising and interesting substitution to handle the
electromagnetic properties of ferrites material. Therefore, substitution of Ni by Zn in
Ni1-xZnxFe2O4 is expected to increase the magnetic moment up to a certain limit, and then it
decreases for the canting of spins in B-sites. It is well known that the Zn concentration of x = 0.5
have high saturation magnetization [6, 7]. At higher sintering temperature (Ts = 1250 o
C), the
perfect crystal growth occurs, highly dense the material, the grain size is increased, finally the
permeability and the saturation magnetization is increased.
Manganese zinc (Mn-Zn) ferrites are very important soft magnetic material, in many high
frequency and magnetic application as a consequence of their magnetic permeability and
electrical resistivity. The concentration of Fe3+
and Fe2+
ions and their distribution between the
tetrahedral and octahedral sublattices, play a critical role in determining their magnetic and
electrical properties [8]. It is well known that manganese related ferrites are not exactly inverse
Chapter-I Introduction
3
or normal. They are mixed ferrites because 80% of Mn2+
ions occupy tetrahedral A-sites while
20% of Mn2+
occupy octahedral B-sites. However, Mn3+
ions occupy the octahedral B-sites
which depend on the presence of Fe2+
on this sites where the exchange interaction takes place [9].
Magnesium ferrite (MgFe2O4) is a pertinent magnetic material due to its high resistivity,
relatively high Curie temperature, low cost, high mechanical hardness and environmental
stability. Magnetic properties of ferrites strongly depend on their chemical compositions and
additives/substitutions. Nonmagnetic zinc ferrite is often added to increase saturation
magnetization (Ms) up to a certain critical concentration of zinc. Zinc ferrite (ZnFe2O4) possesses
a normal spinel structure, i.e. 2
4B
3
2A
2 O]Fe[)Zn( , where all Zn2+
ions reside on A-sites and Fe3+
ions on B-sites. Therefore, substitution of Mg by Zn in Mg1xZnxFe2O4 is expected to increase
the magnetic moment up to a certain limit, thereafter it decreases for the canting of spins in B-
sites. It is well known that diamagnetic substitution can result in spin canting, i.e. non-collinear
spin arrangements [10]. Yafet and Kittel [11] formulated a simple model, which could explain
the canting in these materials.
Copper ferrite (CuFe2O4) is an interesting material and has been widely used for various
applications, such as catalysts for environment and gas sensor [12, 13] and hydrogen production
[14]. Magnetic and electrical properties of Cu ferrites vary greatly with the change of chemical
composition and cation distribution. For instance, most of bulk CuFe2O4 has an inverse spinel
structure with 85% Cu2+
occupying B-sites, whereas ZnFe2O4 is usually assumed to be a
completely normal spinel and Zn2+
ions preferentially occupy A-sites while Fe3+
ions would be
displaced from A-sites for B-sites. Zn-substitution results in a change of cations in chemical
composition and a different distribution of cations between A-and B-sites. Consequently the
magnetic and electrical properties of spinel ferrites will change with changing cation.
Cobalt-zinc (Co-Zn) ferrites are quite important in the field of microwave industry, which is a
mixture of CoFe2O4 with long range ferromagnetic ordering with Tc 520 °C. Zinc is known to
play a decisive role in determining the ferrite properties [7]. Zn-ferrite is normal ferrite while Co-
ferrite is an inverse ferrite; therefore, Co-Zn ferrite is a mixed type with interesting properties.
When Co2+
is replaced by Zn2+
in Co1-xZnxFe2O4, Zn2+
ions preferentially occupies the
tetrahedral site and the Fe3+
ions are displaced to the octahedral sites. Thus, with increasing x, the
Chapter-I Introduction
4
FeA-O-FeB interaction becomes weak and Tc is expected to decrease. A spin-glass is a
magnetically disordered material exhibiting high magnetic frustration in which each electron
spin freezes in a random direction below the spin freezing temperature, Tf [15]. The most
important features characterizing the spin-glass include the existence of irreversibility between
field-cooled (FC) and zero-field-cooled (ZFC) magnetizations. Some works have been
performed on Co-Zn [16], Co-Ti-Zn [17], Co-Cd [18, 19] Co-Cr [20], Co-In [21] ferrites.
So, spinel ferrites of different compositions have been studied and used for a long time to get
useful products. Many researchers have worked on different types of ferrites in order to improve
their electrical and magnetic properties. There does not exist an ideal ferrite sample that meets
the requirements of low eddy current loss and usefulness at frequencies of the giga hertz. Each
one has its own advantages and disadvantages. Researchers have not yet been able to formulate a
rigid set of rules for ferrites about a single property. Scientists still continue their efforts to
achieve the optimum parameters of ferrites, like high saturation magnetization, high
permeability, high resistivity etc. Since the research on ferrites is so vast, it is difficult to collect
all of the experimental results and information about all types of ferrites in every aspect.
However, attempts have been made to present a systematic review of various experimental and
theoretical observed facts related to this study. The systematic research is still necessary for a
more comprehensive understanding and properties of such materials.
1.2 Historical Development of Ferrites
The first type of magnetic material known to man was in the form of lodestone, consisting of the
magnetite (Fe2O3). This is believed to have been discovered in ancient Greece around the time
period of 800 BC. Magnets found their first application in compasses, which were used in the
nineth century by the Vikings, or perhaps even earlier. A milestone in the history of magnetism
was work done by William Gilbert in 1600. His work “De Magnete, Magneticisque Corporibus,
et de Magno Tellure’’ described the magnetic properties of lodestone up to that point in time.
It was not until two hundred years later that major developments began to occur. These
developments included work done by Hans Christian Orsted, Andre Marie Ampere, Wilhelm
Eduard Weber, Michael Faraday, Pierre Curie, and James Clark Maxwell. Their work provided
Chapter-I Introduction
5
the basis of electromagnetic theory in general and for crystal structures. In 1947, J. L. Snoek
published the book, “New developments in ferromagnetic materials’’. Studies have done by
Snoek and others at Phillips Laboratories in the Netherlands led to magnetic ceramics with
strong magnetic properties, high electrical resistively and low relaxation losses.
At about the same time, in 1948, L. Neel announced his celebrated theoretical contribution on
ferrimagnetism. This dealt with the basic phenomenon of "spin-spin interaction" taking place in
the magnetic sublattices in ferrites. The stage was now set for the development of microwave
ferrite devices. In 1952, C. L. Hogan from Bell Labs made the first non-reciprocal microwave
device at 9 GHz that was based on the Faraday rotation effect. Research was conducted to
improve the properties of the spinel ferrite materials by various cation substitutions. This
modified the magnetic properties for different frequency ranges, power requirements and phase
shift applications.
In 1956, Neel, Bertaut, Forrat, and Pauthenet discovered the garnet ferrite class of materials. This
type of ferrite material has three sublattices and is also referred to as rare-earth iron garnets.
These materials, although having a magnetization lower than spinel ferrite, possess extremely
low ferromagnetic line width. Another class of ferrite material that was developed during this
time is the hexagonal ferrite. These materials have three basic sublattices combined in different
numbers in a hexagonal structure. The high anisotropy fields have been utilized in microwave
ferrite devices in the millimeter range. In 1959, J. Smit and H. P. J. Wijn [7] published a
comprehensive book on ferrite materials entitled “Ferrite’’.
Developments have been made on the magnetic characteristics of ferrite materials since the
1950s that have improved microwave device performances. These involve both compositional
and processing modifications. New application of ferrite materials continue to be realized, such
as in the cellular phone, medical, and automotive markets.
Spinel ferrites first commanded the attention first when S. Hilpert [22] focused on the usefulness
of ferrites at high frequency applications. The ferrites were developed into commercially
important materials, chiefly during the years 1933–1945 by Snoek [23] and his associates at the
Philips Research Laboratories in Holland. At the same time, Takai [24] in Japan was engaged in
the research work on the ferrite materials. In a classical paper published in 1948 by Neel [5]
Chapter-I Introduction
6
provided the theoretical key to an understanding of the ferrites. The subject has been covered at
length in books by Smit [7] and Standley [8] and reviewed by Smart [25], Wolf [26], and Gorter
[27]. Snoek had laid the foundation of the Physics and technology of practical ferrites by 1945
and now embrace a very wide diversity of compositions, properties and applications [28]. He
was particularly looking for high permeability materials of cubic structure. He found suitable
materials in the form of mixed spinels of the type (MZn) Fe2O4 where M stands for metals like
Ni, Mn, Mg, Cu, Co etc.
1.3 Application of Ferrites
Ferrites are very important magnetic materials because of their high electric resistivity; they have
wide applications in technology, particularly at high frequencies. Ferrites are used widely due to
their following properties:
i) Ferrites are primarily used as inductive components in a large variety of electronic
circuits such as low-noise amplifiers, filters, voltage-controlled oscillators,
impedance matching networks, for instance. The basic components to produce the
inductance are a very soft ferrite and a metallic coil.
ii) Almost every item of electronic equipment produced such as electromagnets, electric
motors, loudspeakers, deflection yokes, generators, radar absorbers, antenna rods,
proximity sensors, humidity sensors, memory devices, recording heads, broadband
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
REFERENCES
[1] T. Suzuki, T. Tanaka, and K. Ikemizu, “High density recording capability for advanced
particulate media” J. Magn. Magn. Mater., 235 (2001) 159.
[2] T. Giannakopoulou, L. Kompotiatis, A. Kontogeorgakos, and G. Kordas, “ Microwave
behavior of ferrites prepared via sol–gel method”, J. Magn. Magn. Mater. 246 (2002) 360.
[3] E. Olsen and J. Thonstad, “Nickel ferrite as inert anodes in aluminium electrolysis’’, J.
Appl. Electrochem., 29 (1999) 293311. [4] C. O. Augustin, D. Prabhakaran, and L. K. Srinivasan, “The use of the inverted-blister test to
measure the adhesion of an electrocoated paint layer adhering to a steel substrate”, J. Mater. Sci.
Lett., 12 (1993) 383.
[5] L. Neel, “Magnetique properties of ferrites: Ferrimagnetism and Antiferromagnetism”, Annales
de Phys., 3 (1948) 137–198.
[6] G. F. Dionne, “High magnetization limits of spinel ferrite”, J. Appl. Phys., 61(8) (1987) 3865.
[7] J. Smit and H. P. J. Wijn, “Ferrites”, John Wiley & Sons, New York (1959).
[8] K. J. Standley, “Oxide Magnetic Materials”, Oxford University Press, Oxford (1972) 204.
[9] H. J. Yoo and H. L. Tuller, J. Phys. Chem. Solids, 9 (1998) 761.
[10] C. Rath, S. Anand, R. P. Das, K. K. Sahu, S. D. Kulkarni, S. K. Date, and N. C. Mishra,“Dependence on cation distribution of particle size, lattice parameter, and magnetic
properties in nanosize Mn–Zn ferrite”, J. Appl. Phys., 91 (2002) 2211–2215.
[11] J. L. Dormann and M. Nogues, “Magnetic structures of substituted ferrites”, J. Phys.: Condens.
Matter., 2 (1990) 1223.
[12] J. L. Dormann, “Ordered and disordered states in magnetically diluted insulating system”,
Hyper. Interac., 68 (1991) 47.
[13] A. Balayachi, J. L. Dormann, and M. Nogues, “Critical analysis of magnetically semi-
disordered systems: critical exponents at various transitions”, J. Phys.: Condens. Matter., 10
(1998) 1599.
[14] S. C. Bhargav and N. Zeeman, “Mössbauer study of Ni0.25Zn0.75Fe2O4: Noncollinear spin structure”, Phys. Rev., B21 (1980) 1726.
[15] S. W. Tao, F. Gao, X. Q. Liu, and O. T. Sørensen. “Preparation and gas-sensing properties of CuFe2O4 at reduced temperature”, Mater. Sci. and Engg., B77 (2000) 172–176.
[16] M. A. Ahmed and M. H. Wasfy, “Effect of charge transfer behavior on the dielectric and AC conductivity of Co-Zn ferrite doped with rare earth element”, Indian J. Pure. Appl. Phys., 41
(2003) 713.
[17] T. M. Meaz, S. M. Attia, and A. M. Abo El Ata, “Effect of tetravalent ions substitution on the
dielectric properties of Co-Zn ferrites”, J. Magn. Magn. Mater., 257 (2003) 296.
[18] P. N. Vasambekar, C. B. Kolekar and A. S. Vaingankar, “Cation distribution and
susceptibility study of Cd-Co and Cr3+
substituted Cd-Co ferrites”, J. Magn. Magn. Mater., 186
(1998) 333.
[19] O. M. Hemeda and M. M. Barakat, “Effect of hopping rate and jump length of hopping electrons on the conductivity and dielectric properties of Co-Cd ferrite”, J. Magn. Magn. Mater.,
223 (2001)127.
[20] K. P. Chae, Y. B. Lee, J. G. Lee, and S. H. Lee, “Crystallographic and magnetic properties of
CoCrxFe2-xO4 ferrite powders”, J. Magn. Magn. Mater., 220 (2000) 59.
Chapter-I Introduction
22
[21] S. W. Lee, S. Y. An, and C. S. Kim, “Atomic migration in CoIn0.1Fe1.9O4”, J. Magn. Magn.
Mater., 226-230 (2001) 1403.
[22] S. Hilpert, Ber. Deutseh. Chem. Ges. Bd 2., 42 (1909) 2248.
[23] J. L. Snoek, “New Developments in Ferrimagnetism”, (1947) 139.
[24] T. Takai, “Introduction to magnetic ferrites and nanocomposites’’, J. Electr. Chems.
Jpn., 5 (1937) 411.
[25] J. S. Smart, “The Neel Theory of Ferromagnetism”, Amer. J. Phys., 23 (1955) 356.
[26] W. P. Wolf, “Ferrimagnetism,” Reports on Prog. in Phys., 24 (1961) 212.
[27] E. W. Gorter, “Some properties of ferrites in connection with their chemistry”, Proceedings of
the IRE, 43 (1955) 1945.
[28] G. Herzer, M. Vaznez, M. Knobel, A. Zhokov, T. Reininger, and H. A. Davies, “Present and
future applications of nanocrystalline magnetic materials”, J. Magn. Magn. Mater., 294 (2005)
252.
[29] X. Lu, G. Liang, Q. Sun, and C. Yang, “An interdisciplinary journaldevoted to rapid
communications on the science, applications, and processing of materials”, Matter. Lett., 65 (2011) 674–676.
[30] T. Jahanbin, M. Hashim, and K. A. Mantori, “Comparative studies on the structure and
electromagnetic properties of Ni−Zn ferrites prepared via co-precipitation and conventional
ceramic processing routes”, J. Magn. Magn. Mater., 322 (2010) 2684–2689.
[31] D. Guo, X. Fan, G. Chai, C. Jiang, X. Li, and D. Xue,“Structural and magnetic properties of Ni-
Zn ferrite films with high saturation magnetization deposited by magnetron sputtering”, Appl. Surf. Sci., 256 (2010) 2319–2332.
[32] A. M. El-Sayed, “Effect of chromium substitutions on some properties of NiZn
ferrites’’, Ceram. Internal., 28 (2002) 363–367. [33] T. B. Naughton and R. D. Clarke, “Lattice expansion and saturation magnetization of nickel–
zinc ferrite nanoparticles prepared by aqueous precipitation”, J. Am. Ceram. Soc., 90 (2007)
3541–3546.
[34] A. Verma, T. C. Goel, and R.G. Mendiratta, “Frequency variation of initial permeability of Ni-
Zn ferrites prepared by the citrate precursor method”, J. Magn. Magn. Mater., 210 (2000) 274–
278.
[35] A. M. Abdeen, “Dielectric behaviour in Ni–Zn ferrites”, J. Magn. Magn. Mater. 192 (1999)
121–129.
[36] A. Gonchar, V. Andreev, L. Letyuk, A. Shishhkanov, and V. Maiorov, “Problems of increasing
of thermostability of highly permeable Ni–Zn ferrites and relative materials for telecommunications”, J. Magn. Magn. Mater., 254 (2003) 544–546.
[37] J. G. Lopez, E. R. Senin, J. Y. Pastor, M. A. Paries, A. Martin, B. Levenfeld, and A. Varez,
“Microstructure, magnetic and mechanical properties of Ni-Znferrites prepared by powder
injection moulding”, Powder Technology, 210 (2011) 29–35.
[38] A. K. M. A. Hossain, K. K. Kabir, M. Seki, T. Kawai, and H. Tabata, “Structural, AC, and DC
magnetic properties of Zn1−xCoxFe2O4”, J. Phys. Chem. Sol., 68 (2007) 1933–1939.
[39] J. Hu, M. Yan, and W. Luo, “Preparation of high-permeability Ni-Zn ferrites at low sintering
temperatures”, Physica, B368 (2005) 251.
[40] E. J. W Verwey and E. L. Heilmann, “Physical properties and cation arrangement of oxides with
spinel structures I. Cation arrangement in spinels”, J. Chem. Phys., 15(4) (1947) 174–180.
Chapter-I Introduction
23
[41] C. G. Koops, “On the despersion of resistivity and dielectric constant of some semiconductors at
audio frequencies’’, Phy. Rev., 83(1) (1951) 121.
[42] S.A. El-Badry, “Influence of processing parameters on the magnetic properties of Mn-Zn ferrites’’, J. Mine. Mater. Char. Engi., 10 (2011) 397–407.
[43] P. Hu, H. Yang, D. Pan, H. Wang, J. Tian, S. Zhang, X. Wang, and A. A. Volinsky, “Heat
treatment effects on microstructure and magnetic properties of Mn–Zn ferrite powders”, J.
Magn. Magn. Mater., 322 (2010) 173‒177.
[44] M. J. N. Isfahani, M. Myndyk, D. Menzel, A. Feldhoff, J. Amighian, and V. Sepelak, “Magnetic
properties of nanostructured Mn-Zn ferrite’’, J. Magn. Magn. Mater., 321 (2009) 152–156.
[45] P. Mathur, A. Thakur, and M. Singh, “Effect of nanoparticles on the magnetic properties of Mn–
Zn soft ferrite”, J. Magn. Magn. Mater., 320 (2008) 1364–1369.
[46] D. Ravinder and K. Latha, “Electrical conductivity of Mn–Zn ferrites”, J. Appl. Phys., 75
(1994) 6118–6120.
[47] C. Venkataraju, G. Sathishkumar, and K. Sivakumar, “Effect of cation distribution on the
structural and magnetic properties of nickel substituted nanosized Mn-Zn ferrites prepared by
co-precipitation method”, J. Magn. Magn. Mater., 322 (2010) 230–233.
[48] M. A. El Hiti, “Dielectric behaviour in Mg-Zn ferrites”, J. Magn. Magn. Mater., 192 (1999) 305–313.
[49] L. B. Kong, Z. W. Li, G. Q. Lin, and Y. B. Gan, “Electrical and magnetic properties of magnesium ferrite ceramics doped with Bi2O3”, Acta Materialia, 55 (2007) 6561.
[50] S. S. Suryavanshi, R. S. Patil, S. A. Patil, and S.R. Sawant, “DC conductivity and dielectric behavior of Ti
4+ substituted Mg-Zn ferrites”, J. Less Com. Met., 168 (1991) 169.
[51] S. F. Mansour, “Frequency and composition dependence on the dielectric properties for Mg-Zn ferrite”, Egypt, J. Sol., 28(2) (2005) 263.
[52] M. A. Hakim, M. M. Haque, M. Huq, Sk. M. Hoque, and P. Nordblad, “Re entrant spin glass and spin glass behavior of diluted Mg-Zn ferrites”, CP 1003, Magnetic Materials, International
Conference on Magnetic Materials, (2007) AIP, 295.
[53] M. M. Haque, M. Huq and M. A. Hakim, “Effect of Zn2+
substitution on the magnetic properties
of Mg1-xZnxFe2O4 ferrites”, Phycica, B404 (2009) 3915.
[54] M. U. Rana, M. Islam, I. Ahmad, and Tahir Abbas, “Determination of magnetic properties and
Y–K angles in Cu–Zn–Fe–O system”, J. Magn. Magn. Mater., 187 (1998) 242.
[55] S. Akhter, D. Paul, M. Hakim, D. Saha, M. Al-Mamun, and A. Parveen, “Synthesis, structural
and physical properties of Cu1–xZnxFe2O4 ferrites”, Mater. Sci. Appl., 2(11) (2011)1675–1681.
[56] A. Muhammad and A. Maqsood: “Structural, electrical and magnetic properties of Cu1-
xZnxFe2O4 ferrites (0 ≤ x ≤ 1)”, J. Alloy. Compds., 460 (2008) 54–59.
[57] T. Abbas, M. U. Islam, and M. A. Choudhury, “Study of sintering behavior and electrical properties of Cu-Zn-Fe-O system”, Modern Phys. Lett., B9 (1995) 1419–1426.
[58] H. Dawoud and S. Shaat, “Magnetic properties of Zn substituted Cu ferrite”, An-Najah Univ. J. Res. (N. Sc.), 20 (2006) 87–100.
[59] P. N. Vasambekar, C. B. Kolekar, and A. S. Vaingankar, “Magnetic behavior of Cd2+
and Cr
3+substituted cobalt ferrites”, J. Mater. Chem. Phys, 60 (1999) 282.
[60] N. C. Pramanik, T. Fujii, M. Nakanishi, and J. Takada, “Development of Co1+xFe2−xO4 (x = 0–
0.5) thin films on SiO2 glass by the sol–gel method and the study of the effect of composition on
their magnetic properties”, Mater. Lett., 59 (2005) 88.
Chapter-I Introduction
24
[61] K. P. Chae, J. G. Lee, H. S. Kweon, and Y. B. Lee, “The crystallographic, magnetic properties
of Al, Ti doped CoFe2O4 powders grown by sol–gel method”, J. Magn. Magn. Mater., 283 (2004) 103.
[62] K. Haneda and A. H. Morrish, “Noncollinear magnetic-structure of CoFe2O4 small particles’’, J. Appl. Phys., 63 (1988) 4258.
[63] K. V. P. M. Shafi, A. Gedanken, R. Prozorov, and J. Balogh, “Sonochemical preparation and size-dependent properties of nanostructured CoFe2O4 particles”, Chem. Mater., 10 (1998)
3445−3450.
[64] M. Rajendran, R. C. Pullar, A. K. Bhattacharya, D. Das, S. N. Chintalapudi, and C. K.
Majumdar, “Magnetic properties of nanocrystalline CoFe2O4 powders prepared at room
temperature: variation with crystallite size”, J. Magn. Magn. Mater., 232 (2001) 71−83.
[65] A. Globus, H. Pascard, and V. Cagan, “Distance between magnetic ions fundamental properties in ferrites”, J. Physique (call), 38 (1977) C1-163.
[66] A. V. Ramana Reddy, G. Ranga Mohan, B. S. Boyanov, and D. Ravinder, Electrical transport properties of zinc substituted cobalt ferrites”, Mater. Lett., 39 (1999) 153.
[67] D. Ravinder and B. Ravi Kumar, “Electrical conductivity of cerium substituted Mn-Zn ferrites”, Mater. Lett., 57 (2003) 1738.
[68] M. A. Ahmed, “Electrical properties of Co-Zn ferrites”, Phys. Stat. Sol., 111 (1989) 567.
[69] P. B. Pandya, H. H. Joshi, and R. G. Kulkarni, “Bulk magnetic properties of Co-Zn ferrites
prepared by the Co-precipitation method”, J. Mater. Sci., 26 (1991) 5509.
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
presence of magnetic fields.
Fig. 2.2: Magnetic dipole of a bar magnet.
Chapter- II Theoretical Background
27
2.1.3 Magnetic field
A magnetic field (H) is a vector field which is created with moving charges or magnetic
materials. It is also be defined as a region in which the magnetic lines of force is present. The
magnetic field vector at a given point in space is specified by two properties:
(i) Its direction, which is along the orientation of a compass needle.
(ii) Its magnitude (also called strength), which is proportional to how strongly the compass
needle orients along that direction.
The magnetic field inside a toroid or long solenoid is
l
nIH
4.0 (2.1)
and zero outside it. The field H is here expressed in Oersted (Oe), the current I in amperes and
the length in cm, n is the number of turns [2]. In matter, atomic circular currents may occur.
Their strength is characterized by the magnetization M, which is the magnetic moment per cm3.
Then the matter provide the magnetic field is
H = 4πM (2.2)
The S.I. units for magnetic field strength H are Am-1
. The relation C.G.S and S.I. unit is
1Am-1
= 310
4Oe.
2.1.4 Magnetic moment of atoms
If a magnet is broken into small pieces, each part will be a magnet and it cannot get a separate
north or south pole. That means, dipole moment exists in each. Each of them is called a magnetic
dipole. Bar magnet, magnetic needle, current-carrying coil etc are considered as magnetic dipole.
The moment associated with a magnetic dipole is called magnetic dipole moment or simply
magnetic moment.
The magnetic moment or magnetic dipole moment is a measure of the strength of a magnetic
source. In the simplest case of a current loop, the magnetic moment is defined as:
dAIm (2.3)
Chapter- II Theoretical Background
28
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.
antiferromagnetic, ferrimagnetic, re-entrant spin-glass, spin-glass, cluster spin-glass properties
Chapter- II Theoretical Background
56
[10, 20]. Small amount of site disorder i.e. cations redistribution between A- and B-site is
sufficient to change the super-exchange interactions which are strongly dependent on thermal
history i.e. on sintering temperature, time and atmosphere as well as heating/cooling rates during
materials preparation. Microstructure and magnetic properties of ferrites are highly sensitive to
preparation method, sintering conditions, amount of constituent metal oxides, various additives
including dopants and impurities.
The factors affecting the cation distribution over A- and B-sites are as follows:
The size of the cations
The electronic configuration of cations
The electronic energy
The saturation magnetization of the lattice
Smaller cations (trivalent ions) prefer to occupy the A-sites. The cations have special preference
for A- and B-sites and the preference depends on the following factors:
Ionic radius
Size of interstices
Temperature
Orbital preference for the specific coordination
The preference of cations is according to Verway- Heilmar scheme [12, 21]:
Ions with strong preference for A-sites Zn2+
, Cd2+
, Ga2+
, In3+
, Ge4+
Ions with strong preference for B-sites Ni2+
, Cr3+
, Ti4+
, Sn4+
,Sm3+
, Gd3+
Indifferent ions are Mg2+
, Al3+
, Fe2+
, Co2+
, Mn2+
, Fe3+
, Cu2+
Moreover the electrostatic energy also affects the cation distribution in the spinel lattice.
Chapter- II Theoretical Background
57
REFERENCES
[1] N. Spaldin, “Magnetic materials: Fundamentals and device applications’’, Cambridge
University press (2003).
[2] B. D. Cullity and C. D. Graham, “Introduction to Magnetic Materials”, John Wiley & Sons,
New Jersey (1972).
[3] P. G. Hewitt. “Conceptual Physics”, 7th Ed. Harper Collins College Publishers, New York
(1993).
[4] Vowles, P. Hugh “Early Evolution of Power Engineering”. Isis University of Chicago Press,
17(2) (1932) 412.
[5] D. J. Griffiths, “Introduction to Electrodynamics’’, 2nd Ed. Prentice-Hall of India, Private Ltd,
New Delhi (1989).
[6] J. D. Jackson, “Classical Electrodynamics’’, 3rd Ed. John Wisley & Sons, New York (1998).
[7] D. Halliday, R. Resnick, and J. Walker, “Fundamentals of Physics’’, 6th Ed. John Wiley & Sons, New York (2002).
[8] M. S. Vijaya and G. Rangarajan, “Materials Science’’, McGraw-Hill Publ. Comp. Ltd., New Delhi (1999-2000) 447.
[9] C. Kittel, “Introduction to Solid State Physics’’, 7th Ed. John Wiley & Sons, New York (1996).
[10] M. A. Omar, “Elementary Solid State Physics (Principles & Applications)’’, Addison-Wesley Amsterdam (1962).
[11] A. H. Morish, “The Physical Principles of Magnetism’’, John Wiley & Sons (1965).
[12] J. R. Reitz, F. J. Milford, and R. W. Chrisly, “Foundations of Electromagnetic Theory’’, 3rd Ed. Addison-Wesley London (1979).
[13] J. Smit and H. P. J. Wijn, “Ferrites”, Jhon Wiley & Sons, New York (1959).
[14] K. J. Standley, “Oxide Magnetic Materials” 2nd ed., Oxford University Press, (1972).
[15] F. S. Li, L. Wang, J. B. Wang, Q. G. Zhou, X. Z. Zhou, H. P. Kunkel, and G. Williams, J.
Magn. Magn. Mater., 268 (2004) 332.
[16] L. Neel, “Magnetic properties of ferrites: Ferrimagnetism and Antiferromagnetism’’, Annales de
Phys.e, 3 (1948) 137–198.
[17] G. Mumcu, K. Sertel, J. L. Volakis, A. Figotin, and I. Vitebsky, “RF propagation in ferrite
thickness nonreciprocal magnetic photonic crystals’’, IEEE Antenna Propagant. Soc. Symp. 2
(2004) 1395.
[18] E. J. W. Verway and E. L Heilmann, J. Chem. Phys., 15(4) (1947) 174.
[19] F. C. Romeign, Philips Res. Rep., 8 (1953) 304.
[20] D. S. Parasnis, Harper and Brothers, “Magnetism: from lodestone to Polar Wandering”, New York (1961).
[21] P. W. Anderson, in “Magnetism’’, 1, Eds, G. T. Rado and H. Suhl (Academic Press, New York (1963).
58
CHAPTER−III
EXPERIMENTAL DETAILS
3.1 Compositions of Studied Ferrite Samples
In the present research, conventional ceramic method has been employed for high saturation
magnetization samples as Ni-Zn, Mn-Zn, Mg-Zn, Cu-Zn and Co-Zn ferrites [1]. The following
compositions were fabricated, characterized and investigated thoroughly.
Ni0.5Zn0.5Fe2O4
Mn0.5Zn0.5Fe2O4
Mg0.5Zn0.5Fe2O4
Cu0.5Zn0.5Fe2O4
Co0.5Zn0.5Fe2O4
3.2 Sample Preparation
Sample preparation technique is an important part for ferrites sample. Knowledge and control of
the chemical composition, homogeneity and microstructure are very crucial. The preparation of
polycrystalline ferrites with optimized properties has always demanded delicate handling and
cautious approach. The ferrite is not completely defined by its chemistry and crystal structure but
also requires knowledge and control of parameters of its microstructure such as grain size,
porosity, intra- and inter-granular distribution. There are many processing methods such as solid
state reaction method [2]; high energy ball milling [3]; sol-gel [4]; chemical co-precipitation
method [5]; microwave sintering method [6]; auto combustion method [7] etc for the preparation
of polycrystalline ferrite materials. The normal methods of preparation of ferrites comprise of the
conventional ceramic method i.e., solid state reaction method involving ball milling of reactions
following by sintering at elevated temperature range and non-conventional method, also called
wet method. Chemical co-precipitation method and sol-gel method etc. are examples of wet
method.
Chapter-III Experimental Details
59
3.1.1 Solid state reaction method
The samples were synthesized by solid state reaction method. The starting materials for the
preparation of the studied compositions were in the form of powder oxides (Fe2O3, NiO, ZnO,
MnO, MgO, CuO and CoO) of Inframat Advanced Materials, USA. The purity of our materials
is up to 99.99%. The reagent oxide powders were weighed precisely according to their molecular
weight. The weight percentage of the oxide to be mixed for various samples was calculated by
using formula:
Weight % of oxide =sampleainoxideeachofwtMolofSum
sampletheofweightrequiredoxideofwtMol
..
..
Intimate mixing of the materials was carried out using agate mortar (hand milled) for 4 hours for
fine homogeneous mixing and strong concentration. Then the material was ball milled in a
planetary ball mill in ethyl alcohol media for 4 hours with stainless steel balls of different sizes
in diameter. Then the mixed sample was pre-sintered at temperature between 850 to 900 °C for 5
hours at a heating rate of 3 °C/min in air to form ferrite through chemical reaction. The sample
was then cooled down to room temperature at the same rate as that of heating. The pre-sintered
material was ball milled for another 4 hours in distilled water to reduce it to small crystallites of
uniform size. The mixture was dried and a small amount of saturated solution of polyvinyl
alcohol was added as a binder. The resulting powders were pressed uniaxially under a pressure of
(15–20) KN.cm2
in a stainless steel die to make pellets and toroids Fig. 3.1, respectively. The
pressed pellet and toroid shaped samples were then finally sintered at different temperatures in
air and then cooled in the furnace.
3.2.2 Pre-sintering
After ball milled, the mixture was dried and again hand milled for 2 hours. Then the mixed
powder was transferred in a small ceramic pot for pre-sintering at temperature between 850 to
900 °C in the furnace named Gallen Kamp at Materials Science Division of Atomic Energy
Centre, Dhaka. The cooling and heating rates were 3 °C/min as shown in Fig. 3.2(a). The pre-
sintering is very crucial because in this step of sample preparation a ferrite is formed from its
component oxides. The solid-state reactions, leading to the formation of ferrites, actually
Chapter-III Experimental Details
60
Fig. 3.1: Photographs of (a) Pellets (b) Toroids
achieved by counter diffusion. This means that the diffusion involves two or more species of
ions, which move in opposite direction initially across the interface of two contacting particles of
different component oxides. During the pre-sintering stage, the reaction of Fe2O3 with metal
oxide (MO or M'2O3 where M is divalent and M' is the trivalent metal atom) takes place in the
solid state to form spinel according to the reactions [8]:
MO + Fe2O3 → MO. Fe2O3 (spinel)
2M'2O3 + 4Fe2O3 4M'Fe2O4 (spinel) + O2
For Ni-ferrite,
NiO + Fe2O3 NiFe2O4
For Ni-Zn ferrite,
(1-x) NiO + x ZnO + Fe2O3 Ni1-xZnxFe2O4 (x = 0.5)
For Mn-ferrite,
MnO + Fe2O3 MnFe2O4
For Mn-Zn ferrite,
(1-x) MnO + x ZnO + Fe2O3 Mn1-xZnxFe2O4 (x = 0.5)
For Mg-ferrite,
MgO + Fe2O3 MgFe2O4
For Mg-Zn ferrite,
(1-x) MgO + x ZnO + Fe2O3 Mg1-xZnxFe2O4 (x = 0.5)
For Cu-ferrite,
CuO + Fe2O3 CuFe2O4
For Cu-Zn ferrite,
(1-x) CuO + x ZnO + Fe2O3 Cu1-xZnxFe2O4 (x = 0.5)
For Co-ferrite,
CoO + Fe2O3 CoFe2O4
Chapter-III Experimental Details
61
For Co-Zn ferrite,
(1-x) CoO + x ZnO + Fe2O3 Co1-xZnxFe2O4 (x = 0.5)
The cation distribution of Ni-Zn ferrites can be presented as;
_2
4
3
5.1
2
5.0
3
5.0
2
5.0 )( OFeNiFeZnBA
The cation distribution of Mn-Zn ferrites can be presented as;
2
4
3
9.1
2
1.0
3
1.05.0
2
4.0 ][)( oFeMnFeZnMn BA
The cation distribution of Mg-Zn ferrites can be presented as;
2
4
3
55.1
2
45.0
3
45.05.0
2
05.0 ][)( oFeMgFeZnMg BA
The cation distribution of Cu-Zn ferrites can be presented as;
_2
4
3
5.1
2
5.0
3
5.0
2
5.0 )( OFeCuFeZnBA
The cation distribution of Co-Zn ferrites can be presented as;
_2
4
3
5.1
2
5.0
3
5.0
2
5.0 )( OFeCoFeZnBA
[
Fig.3.2: Time versus temperature curves for (a) Pre- sintering and (b) sintering process.
In order to produce chemically homogeneous, dense and magnetically better material of desired
shape and size, sintering at an elevated temperature is needed.
900
oC
5 h OFF
T °C 5 h
3 oC/min
Time
a. Pre-sintering program
1200 °C
4 h
T °C 5 h 2 h 5 min
700 °C
4 °C/min
Time
Chapter-III Experimental Details
62
3.2.3 Sintering
Sintering is a widely used but very complex phenomenon. The fundamental quantification of
change in pore fraction and geometry during sintering can be attempted by several techniques,
such as: dilatometry, buoyancy, gas absorption, porosimitry indirect methods (e.g. hardness) and
quantitative microscopy etc. The description of the sintering process has been derived from
model experiments (e.g. sintering of a few spheres) and by observing powdered compact
behavior at elevated temperatures.
Sintering is the final and a very critical step of preparing a ferrite with optimized properties. The
sintering time, temperature and the furnace atmosphere play very important role on the magnetic
property of final materials. Sintering commonly refers to processes involved in the heat treatment
by which a mass of compacted powder is transformed into a highly densified object by heating it
in a furnace below its melting point. Ceramic processing is based on the sintering of powder
compacts rather than melting/solidifications/cold working (characteristic for metal), because:
Ceramics melt at high temperatures.
As solidified microstructures cannot be modified through additional plastic
deformation and re-crystallization due to brittleness of ceramics.
The resulting coarse grains would act as fracture initiation sites.
Low thermal conductivities of ceramics (< 30–50 W/mK) in contract to high
thermal conductivity of metals (in the range 50–300 W/mK) cause large
temperature gradients, and thus thermal stress and shock in melting-solidification
of ceramics.
For the studied samples, these are sintered at temperature between 1000 to 1350 °C in the
furnace named Gallen Kamp at Materials Science Division of Atomic Energy Centre, Dhaka.
The cooling and heating rates were 4 °C/min as shown in Fig. 3.2(b). Sintering is the bonding
together of a porous aggregate of particles at high temperature. The thermodynamic driving force
is the reduction in the specific surface area of the particles. The sintering mechanism usually
involves atomic transport over particle surfaces, along grain boundaries and through the particle
interiors.
Chapter-III Experimental Details
63
Any un-reacted oxides form ferrite, inter diffusion occurs between adjacent particles so that they
adhere (sinter) together, and porosity is reduced by the diffusion of vacancies to the surface of
the part. Strict control of the furnace temperature and atmosphere is very important because these
variables have marked effects on the magnetic properties of the product. Sintering may result in
densification, depending on the predominant diffusion pathway. It is used in the fabrication of
metal and ceramic components, the agglomeration of ore fines for further metallurgical
processing and occurs during the formation of sandstones and glaciers. Sintering must fulfill
three requirements:
to bond the particles together so as to impart sufficient strength to the product,
to densify the grain compacts by eliminating the pores and
to complete the reactions left unfinished in the pre-sintering step [8].
The theory of heat treatment is based on the principle that when a material has been heated above
a certain temperature, it undergoes a structural adjustment or stabilization when cooled at room
temperature. The cooling rate plays an important role on which the structural modification is
mainly based.
3.2.4 Flowchart of sample preparation
The sample preparation process can be easily presented by the following flowchart:
Fig. 3.3: Flowchart of ferrite sample preparation.
FERRITES SAMPLE PREPARATION:
Oxides of raw materials as powder
Weighing by different mole percentage
Dry mixing by agate mortar (hand milling) for 4 h
Ball milling for 4 hours in distilled water
Dry and hand mixing for 2h
Wet mixing by ball milling in ethyl alcohol for 4 hours
Drying
Finished products
Again hand milling for 2 h and Pre-sintering
Sintering
Chapter-III Experimental Details
64
3.3 Experimental Measurements
The following measurements were done in the present work:
Phase analysis was done by using Phillips (PW3040) X′ Pert PRO X-ray diffractometer. The
lattice constant (a), X-ray density (dx) and Porosity (P) were measured from the XRD data. The
magnetic moment measurement from the VSM was performed. The Curie temperature was
determined from the temperature dependence of permeability measurements. Field dependence
of magnetization at room temperature was measured by using a vibrating sample magnetometer
(VSM 02, Hirstlab, England) at Materials Science Division, Atomic Energy Centre, Dhaka,
Bangladesh. The complex permeability of the toroid shaped samples at room temperature were
measured with the Agilent precision impedance analyzer (Agilent, 4294A) in the frequency
range 1 kHz to 120 MHz. The temperature dependence of initial permeability of the samples was
carried out by using Hewlett Packart impedance analyzer (HP 4291A) in conjunction with a
laboratory made furnace at Materials Science Division of Atomic Energy Centre, Dhaka.
3.4 X-ray Diffraction
To study the crystalline structure of solids, X-rays diffraction is a versatile and non-destructive
technique that provides detailed information about the materials. A crystal lattice is a regularly
arranged three-dimensional distribution (cubic, rhombic, etc.) of atoms in space. They are
fashioned in such a way that they form a series of parallel planes separated from one another by a
distance d (inter-planar or inter-atomic distance) which varies according to the nature of the
material. For a crystal, planes are found in a number of different orientations each with its own
specific d-spacing.
3.4.1 X-ray diffraction method
X-rays are the electromagnetic waves whose wavelength is in the neighborhood of 1Ǻ. The
wavelength of an X-ray is that the same order of magnitude as the lattice constant of crystals and
it is this which makes X-ray so useful in structural analysis of crystals. X-ray diffraction (XRD)
provides precise knowledge of the lattice parameter as well as the substantial information on the
crystal structure of the material under study. X-ray diffraction is a versatile nondestructive
Chapter-III Experimental Details
65
analytical technique for identification and quantitative determination of various crystalline
phases of powder or solid sample of any compound. When X-ray beam is incident on a material,
the photons primarily interact with the electrons in atoms and get scattered. Diffracted waves
from different atoms can interfere with each other and the resultant intensity distribution is
strongly modulated by this interaction. If the atoms are arranged in a periodic fashion, as in
crystals, the diffracted waves will consist of sharp interference maxima (peaks) with the same
symmetry as in the distribution of atoms. Measuring the diffraction pattern therefore allows us to
deduce the distribution of atoms in a material. It is to be noted here that, in diffraction
experiments, only X-rays diffracted via elastic scattering are measured. There are following three
methods used for the diffraction of X-ray.
Laue method
Rotating-crystal method
Powder method
The studied samples are in powder form; therefore we used only the powder method was used to
determine XRD.
3.4.2 Powder method of X-ray diffraction
X-ray powder diffraction (XRD) is a rapid analytical technique primarily used for phase
identification of a crystalline material and can provide information on unit cell dimensions. The
analyzed material is finely ground, homogenized, and average bulk composition is determined.
X-ray diffraction is based on constructive interference of monochromatic X-rays and a
crystalline sample. These X-rays are generated by a cathode ray tube, filtered to produce
monochromatic radiation, collimated to concentrate, and directed toward the sample. The
interaction of the incident rays with the sample produces constructive interference (and a
diffracted ray) when conditions satisfy Bragg's Law
Bragg’s law states that when a radiation falls on a series of parallel planes equally spaced at a
distance d. Then the path difference is 2dsinθ for the reflected rays, where θ is measured from
the plane. Let us consider an incident X-ray beam interacting with the atoms arranged in a
periodic manner as shown in two dimensions in Fig. 3.4. The atoms, represented as spheres in
the illustration, can be viewed as forming different sets of planes in the crystal.
Chapter-III Experimental Details
66
Fig. 3.4: Bragg’s diffraction pattern.
For a given set of lattice planes with an inter-plane distance of d, the condition for a diffraction
(peak) to occur can be simple written as
nnd sin2 (3.16)
This is known as Bragg’s law. In the equation, λ is the wavelength of the X-ray, θ is the
scattering angle, and n is an integer representing the order of the diffraction peak. The Bragg’s
Law is one of the most important laws used for interpreting X-ray diffraction data. From the law,
it is found that the diffraction is only possible when λ < 2d [9].
3.4.3 Phillips X Pert PRO X-ray diffractometer
Fig. 3.5: Block diagram of the PHILIPS (PW 3040) X’ Pert PRO XRD system.
Chapter-III Experimental Details
67
In this work, A PHILIPS (PW 3040) X’pert PRO X-ray diffractometer was used for taken XRD
patterns the lattice to study the crystalline phases of the prepared samples in the Materials
Science Division, Atomic Energy Centre, Dhaka. Fig. 3.5 shows the block diagram of X’ pert
XRD system.
X-ray diffraction (XRD) provides substantial information on the crystal structure. The
wavelength of an X-ray is of the same order of magnitude as the lattice constant of crystals and
this makes it so useful in structural analysis of crystals. The powder specimens were exposed to
CuK radiation with a primary beam of 40 kV and 30 mA with a sampling step of 0.02° and time
for each step data collection was 1.0 sec. A 2 scan was taken from 15° to 70° to get possible
fundamental peaks where Ni filter was used to reduce CuK radiation. All the data of the samples
were analyzed using computer software “X PERT HIGHSCORE”. X-ray diffraction patterns
were carried out to confirm the crystal structure. Instrumental broadening of the system was
determined from 2 scan of standard Si. At (311) reflection’s position of the peak, the value of
instrumental broadening was found to be 0.07°. This value of instrumental broadening was
subtracted from the pattern. After that, using the X-ray data, the lattice constant ‘a’ and hence the
X-ray densities were calculated.
Fig. 3.6: Photograph of PHILIPS X’ Pert PRO X-ray diffractometer.
Figure 3.6 shows the photographic view of the X’ pert PRO XRD system. A complex of
instruments of X-ray diffraction analysis has been established for both materials research and
specimen characterization. These include facilities for studying single crystal defects and a
variety of other materials problems.
Chapter-III Experimental Details
68
The PHILIPS X’ Pert PRO XRD system comprised of the following parts:
“Cu-Tube” with maximum input power of 60 kV and 55 mA,
“Ni- Filter” to remove Cu-Kα component,
“Solar Slit” to pass parallel beam only,
“Programmable Divergent Slits” (PDS) to reduce divergence of beam and control
irradiated beam area,
“Mask” to get desired beam area,
“Sample Holder” for powder sample,
“Anti Scatter Slit” (ASS) to reduce air scattering back ground,
“Programmable Receiving Slit” (PRS) to control the diffracted beam intensity and
“Solar Slit” to stop scattered beam and pass parallel diffracted beam only.
3.4.4 Lattice parameter
The XRD data consisting of θhkl and dhkl values corresponding to the different crystallographic
planes are used to determine the structural information of the samples like lattice parameter and
constituent phase. Normally, lattice parameter of an alloy composition is determined by the
Debye-Scherrer method after extrapolation of the curve. It is determined here the lattice spacing
(interplaner distance), d using these reflections from the equation which is known as Bragg’s
Law.
2dhkl Sinθ = λ
i.e., dhkl =
sin2 (3.17)
Where, λ is the wavelength of the X-ray, θ is the diffraction angle and n is an integer
representing the order of the diffraction.
The lattice parameter for each peak of each sample was calculated by using the formula [10]:
a = 222 lkhdhkl (3.18)
Where, h, k, l are the indices of the crystal planes. The get dhkl values from are found the
computer using software “X’ Pert HIGHSCORE”. So the number of ten ‘a’ values are obtained
Chapter-III Experimental Details
69
for ten reflection planes such as a a1, a2, a3 ….. etc. It is determined the exact lattice parameter
for each sample through the Nelson-Riley extrapolation method. The values of the lattice
parameter obtained from each reflected plane are plotted against Nelson-Riley function [11]. The
Nelson-Riley function, F (θ) can be written as
22 cos
sin
cos
2
1)(F (3.19)
Where, θ is the Bragg’s angle. Now drawing the graph of ‘a’ vs F(θ) and using linear fitting of
those points will give us the lattice parameter ‘a’. This value of ‘a’ at F(θ) = 0 or θ = 90°. These
‘a’ are calculated with an error estimated to be ± 0.0001 Ǻ.
3.4.5 X-ray density, bulk density and porosity
From the XRD data, the lattice parameter was determined by using Nelson-Riley function and
then X-ray density is determined from the lattice constant. X-ray density (dx) of the prepared
ceramic samples was calculated using the relation [12].
3Na
ZMd x (3.20)
Where, M is the molecular weight of the corresponding composition, N is Avogadro’s number, a
is the lattice parameter and Z is the number of molecules per unit cell, which is 8 for the spinel
cubic structure. The bulk density was calculated by considering the cylindrical shape of the
pellets and using the relation.
hr
m
V
md
2B
(3.21)
Where, m is the mass, r is the radius and h is the thickness of the pellet.
Porosity is a parameter which is inevitable during the process of sintering of oxide materials. It is
noteworthy that the physical and electromagnetic properties are strongly dependent on the
porosity of the studied samples. Therefore an accurate idea of percentage of pores in a prepared
sample is prerequisite for better understanding of the various properties of the studied samples to
correlate the microstructure property relationship of the samples under study. The porosity of a
material depends on the shape, size of grains and on the degree of their storing and packing. The
Chapter-III Experimental Details
70
difference between the bulk density dB and X-ray density dx gave us the measure of porosity.
Percentage of porosity has been calculated using the following relation [13].
00100)1(
x
B
d
dP (3.22)
3.5 Magnetization Measurement
The magnetic measurements such as magnetization versus magnetic field (M−H) loop, saturation
magnetization, magnetic moment etc were done by using a vibrating sample magnetometer
(VSM) model EV7 system in the Materials Science Division, Atomic Energy Centre, Dhaka.
3.5.1 Vibrating sample magnetometer of model EV7 System
Fig. 3.7: Photograph of VSM (Model EV7, System Micro sense, USA).
Vibrating sample magnetometer (VSM) is a versatile and sensitive method of measuring
magnetic properties developed by S. Foner [14] and is based on the flux change in a coil when
the sample is vibrated near it. The principle of VSM is the measurement of the electromotive
force induced by magnetic sample when it is vibrated at a constant frequency in the presence of a
static and uniform magnetic field. A small part of the pellet (10–50 mg) was weighed and made
to avoid movements inside the sample holder. Fig. 3.7 shows a vibrating sample magnetometer
(VSM) of model EV7 system. The magnetic properties measurement system model EV7 is a
sophisticated analytical instrument configured specially for the study of the magnetic properties
Chapter-III Experimental Details
71
of small samples over a broad range of temperature from 103 to 800 K and magnetic fields from
–20 to +20 kOe.
The VSM is designed to continuously measure the magnetic properties of materials as a function
of temperature and field. In this type of magnetometer, the sample is vibrated up and down in a
region surrounded by several pickup coils. The magnetic sample is thus acting as a time-
changing magnetic flux, varying inside a particular region of fixed area. From Maxwell’s law it
is known that a time varying magnetic flux is accompanied by an electric field and the field
induces a voltage in pickup coils. This alternating voltage signal is processed by a control unit
system, in order to increase the signal to noise ratio. The result is a measure of the magnetization
of the sample.
3.5.2 Working procedure of vibrating sample magnetometer
If a sample is placed in a uniform magnetic field, created between the poles of a electromagnet, a
dipole moment will be induced. If the sample vibrates with sinusoidal motion a sinusoidal
electrical signal can be induced in suitable placed pick-up coils. The signal has the same
frequency of vibration and its amplitude will be proportional to the magnetic moment, amplitude,
and relative position with respect to the pick-up coils system. Fig.3.8 shows the block diagram
of vibrating sample magnetometer.
Fig.3.8: Block diagram of a VSM.
Chapter-III Experimental Details
72
The sample is fixed to a sample holder located at the end of a sample rod mounted in a
electromechanical transducer. The transducer is driven by a power amplifier which itself is
driven by an oscillator at a frequency of 90 Hz. So, the sample vibrates along the Z axis
perpendicular to the magnetizing field. The latter induced a signal in the pick-up coil system that
is fed to a differential amplifier. The output of the differential amplifier is subsequently fed into a
tuned amplifier and an internal lock-in amplifier that receives a reference signal supplied by the
oscillator.
The output of this lock-in amplifier, or the output of the magnetometer itself, is a DC signal
proportional to the magnetic moment of the sample being studied. The electromechanical
transducer can move along X, Y and Z directions in order to find the saddle point. Calibration of
the vibrating sample magnetometer is done by measuring the signal of a pure Ni standard of
known saturation magnetic moment placed in the saddle point.
3.5.3 Saturation magnetization measurement
Saturation magnetization (Ms) can be measured by two ways. Experimentally, it is found from
VSM. When a magnetic material has an external magnetic field, the magnetization increases
with increasing magnetic field and attains its saturation value. For saturation magnetization, the
magnetic moments are in the same direction in a magnetic material. The saturation magnetization
are calculated theoretically for ferrites sample at 0 K and increases with increasing temperature.
The theoretical value of Ms for ferrite sample depends on (a) the moment of each ion, (b) the
distribution of the ions between A- and B-sites, (c) the exchange interaction between A- and B-
sites [15]. The net magnetization of collinear spin arrangement at any temperature (T) could be
expressed as,
Ms (T) = MB (T) – MA (T) (3.27)
Where, MA and MB are the magnetic moment of A and B sites.
In reality, A-B, A-A and B-B interactions all tend to be negative, but they cannot all be negative
simultaneously. A-B interactions are usually the strongest so that all the A moments are parallel
to one another but anti-parallel to B moments. Nickel ferrites have the inverse structure with all
the Ni2+
ions in B sites and the Fe3+
ions are evenly divided between A- and B-site. The moments
Chapter-III Experimental Details
73
of the Fe3+
ions in A- and B-sites cancel each other and the net moment is only due to the Ni2+
ions. Zinc ferrites have the normal structure with Zn2+
ions of zero magnetic moment in the A-
sites producing no A-B interaction. The weakest B-B interaction play the role and the Fe3+
ions
on B-sites have anti parallel moments providing no net moment. In case of Ni-Zn ferrites,
saturation magnetization increases with the increase in zinc concentration up to the certain value,
after which it decreases with the further increase in zinc concentration.
Increasing trend of saturation magnetization can be explained on the basis of Neel’s two sub-
lattice model [16] whereas the decreasing trend suggests that there are triangular type spin
arrangements on B-site which cannot be explained by Neel’s two sub-lattice model. The cation
distribution for nickel ferrites have inverse spinel structure that can be written as
2
4
323 )( OFeNiFe BA (3.28)
When non-magnetic divalent Zn2+
ions are substituted, they tend to occupy tetrahedral sites by
transferring Fe3+
ions to octahedral sites due to their favoritism by polarization effect. However,
site preference of cations also depends upon their electronic configurations. Zn2+
ions show
marked preference for tetrahedral sites where their free electrons respectively can form a
covalent bond with the free electrons of the oxygen ion. This forms four bonds oriented towards
the corners of a tetrahedron. Ni2+
ions have marked preference for an octahedral environment due
to the favorable fit of the charge distribution of these ions in the crystal field at an octahedral site
[17]. In view of the above considerations as an example the cation distribution of Ni0.5Zn0.5Fe2O4
ferrite sample can be written as,
Ni0.5Zn0.5Fe2O4 (Zn0.5Fe0.5)A[ Ni0.5Fe1.5]B O4 (3.29)
For A-site, MA = (0.5×0) + (0.5×5) and for B-site, MB = (0.5×2) + (1.5×5)
= 2.5 µB = 8.5 µB
Thus the net magnetization, Ms = (8.5 µB - 2.5 µB) = 6.0 µB
As zinc (non-magnetic) ions prefer to go into tetrahedral lattice and transfer some iron ions of
large magnetic moment to octahedral site resulting an increase in saturation magnetization. The
decreasing trend is due to the fact that after a certain amount of zinc concentration, there start
Chapter-III Experimental Details
74
fluctuations in the number of ratio of zinc and ferric ions on the tetrahedral sites surrounding
various octahedral sites i.e., fluctuations in the tetrahedral octahedral interactions. This shows the
weakening of A-B interaction whereas B-B interaction changes from ferromagnetic to
antiferromagnetic state. Satyamurthy et.al. and Yafet and Kittel have also observed similar kind
of weakening A-B interaction in two sub-lattices due to Zn substitution in mixed ferrites [17].
The remanence magnetization and magnetic moment also have similar trends.
3.5.4 Magnetic moment calculation
Using the values of saturation magnetization obtained from the M−H curve, the magneton
number or saturation magnetization per formula unit, nB (in Bohr magneton) has been calculated
by using the relation.
5585
s
B
s
B
MeightMolecularw
N
MMn
(3.30)
Where, Ms is the saturation magnetization in emu/g, M′ is the molecular weight in amu, N is the
Avogardro’s number ( 1231002.6 mole ) and µB is the magnetic moment in Bohr magneton
( 2010927.0 µB).
Magnetic moment may have different value from that of theoretical value. There are at least
three causes for the deviations of the magnetic moment from the theoretical values [17].
The ion distribution may not remain the same. For such ferrites, the saturation
magnetization is greater for quenching than after slow cooling.
In addition to spin moment, the ions may have an orbital moment which is not completely
quenched.
The angle between octahedral sub-lattices B1 and B2 is known as Yafet-Kittel angle may
occur.
An interesting case is that of mixed Ni-Zn ferrites in which the non-magnetic zinc ions prefer to
go to the tetrahedral with the increase in zinc concentration. For the small concentration of zinc,
the case remains true. For larger concentration of zinc, the deviations are found. The magnetic
moment of the few remaining Fe3+
ions on the A-site are no longer able to align all the moments
Chapter-III Experimental Details
75
of the B ions antiparallel to them as it is opposed by the negative B-B exchange interaction
which remains unaffected. At this stage, the B lattice will divide itself into two sub-lattices, the
magnetizations of which make an angle with each other varying from 0° to 180°. It is due to the
fact that the ions within one sub-lattice interact less strongly with each other than with those in
the other sub-lattices. The average magnetic moment of ions on the octahedral sites is twice as
large as that of ions on tetrahedral sites [17].
3.6 Permeability Measurement
Frequency and temperature dependence of permeability, Curie temperature, quality factor, loss
tangent etc were done by using a Agilent precision impedance analyzer, model Agilent 4294A, in
the Materials Science Division, Atomic Energy Centre, Dhaka.
3.6.1 Agilent precision impedance analyzer (Agilent 4294A)
Fig. 3.9: Agilent 4294A Precision Impedance Analyzer (1 kHz to 120 MHz).
The Agilent Technologies 4294A precision impedance analyzer greatly supports accurate
impedance measurement and analysis of a wide variety of electronic devices (components and
circuits) as well as electronic and non-electronic material. Moreover, the 4294A’s high
measurement performance and capable functionality delivers a powerful tool to circuit design
and development as well as materials research and development (both electronic and non-
electronic materials) environments. This system is suitable as:
Accurate measurement over wide impedance range and wide frequency range
Chapter-III Experimental Details
76
Powerful impedance analysis functions
Ease of use and versatile PC connectivity
The following are application examples:
Electronic devices
Passive components
Impedance measurement of two terminal components such as capacitors, inductors,
ferrite beads, resistors, transformers, crystal/ceramic resonators, multi-chip modules
or array/ network components.
Semiconductor components
C-V characteristic analysis of varactor diodes.
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.
Observed value for studied sample Miller
Indices
(hkl)
Standard value for base ferrite
(JCPDS)
Types of studied
ferrite
2θ
(deg.)
dhkl
(Å)
2θ
(deg.)
dhkl
(Å)
Types of base
ferrite
Ni0.5Zn0.5Fe2O4 29.99 2.9744 (220) 30.50 2.9486 NiFe2O4
35.41 2.4513 (311) 35.50 2.5146
37.01 2.4287 222 37.56 2.4076
37.01 2.1033 (400) 44.50 2.0850
53.34 1.7173 (422) 54.50 1.7024
56.90 1.6191 (511) 57.50 1.6050
62.38 1.4872 (440) 64.00 1.4743
Mn0.5Zn0.5Fe2O4 30.04 2.9905 (220) 30.50 3.0052 MnFe2O4
35.28 2.5502 (311) 35.50 2.5628
36.92 2.4416 222 36.98 2.4537
42.89 2.1145 (400) 41.50 2.1250
53.15 1.7265 (422) 46.00 1.7351
56.65 1.6277 (511) 57.20 1.6358
62.09 1.4952 (440) 64.30 1.5026
Mg0.5Zn0.5Fe2O4 30.13 2.9656 (220) 30.00 2.9557 MgFe2O4
35.32 2.5291 (311) 35.25 2.5206
36.97 2.4214 222 37.99 2.4133
43.08 2.0970 (400) 44.50 2.0900
44.70 1.7122 (422) 54.50 1.7065
53.39 1.6143 (511) 57.50 1.6089
56.89 1.4828 (440) 62.50 1.4778
Cu0.5Zn0.5Fe2O4 30.04 2.9680 (220) 30.12 2.9592 CuFe2O4
35.53 2.5312 (311) 35.50 2.5237
36.98 2.4234 222 37.10 2.4162
43.07 2.0988 (400) 44.40 2.0925
53.27 1.7136 (422) 51.50 1.7085
56.77 1.6156 (511) 56.50 1.6108
62.26 1.4835 (440) 63.50 1.4796
Co0.5Zn0.5Fe2O4 30.05 2.9656 (220) 30.14 2.9654 CoFe2O4
35.49 2.5291 (311) 35.62 2.5233
37.01 2.4214 222 37.50 2.4191
42.96 2.0970 (400) 43.12 2.0966
53.34 1.7123 (422) 53.81 1.7037
56.90 1.6143 (511) 57.03 1.6106
62.38 1.4828 (440) 62.71 1.4789
Chapter-IV Results and Discussion
85
4.1.2. Experimental calculation of lattice parameter
The lattice parameter or lattice constant refer to the distance between the atoms of the unit cell in
a crystal lattice which can be calculated from the diffraction patterns for all the samples by using
the formula [1]:
aexp = dhkl 222
lkh (4.1)
Where, h, k and l are the Miller indices of the crystal planes. The lattice constant (aexp) for all the
samples corresponding to the system A0.5Zn0.5Fe2O4 were calculated by indexing XRD pattern
of Fig. 4.1 using Eq. 4.1 and are tabulated in Table 4.2.
Figure 4.1(a) shows the XRD pattern of Ni-Zn ferrite. From the XRD pattern, the lattice
parameter (aexp) of Ni0.5Zn0.5Fe2O4 is calculated to be 8.413 Å, which is larger than the lattice
parameter of NiFe2O4 (8.34 Å) and smaller than that of ZnFe2O4 (8.44 Å) as tabulated [1] in
Table 4.2. The lattice parameter of Ni-Zn ferrite is increased with Zn substitution. It can be
explained on the basis of ionic radii. The ionic radius of Zn2+
(0.74 Å) is greater than that of Ni2+
(0.69 Å) [2], which enhance the lattice parameter of Ni-Zn ferrite. The experimental value of
studied samples are in good agreement with earlier works, with the composition
Ni0.65Zn0.35Fe2O4 and Ni0.55Zn0.45Fe2O4 having a = 8.4116 Å and a = 8.4142 Å, respectively
[3, 4]. When the larger Zn2+
ions are entered into the lattice, the unit cell expands while
preserving the overall cubic symmetry.
The lattice parameter of Mn-Zn ferrite is found to follow the opposite trend of Ni-Zn ferrite. Fig.
4.1 (b) shows the XRD pattern of Mn-Zn ferrite. From the XRD pattern, the lattice parameter
(aexp) of Mn0.5Zn0.5Fe2O4 is calculated to be 8.458 Å, which is smaller than MnFe2O4 (8.50 Å)
but greater than ZnFe2O4 (8.44 Å) as tabulated [1] in Table 4.2. The fundamental reason is the
difference of ionic radii of Mn2+
and Zn2+
ions. The lattice constant decreases because the ionic
radius of Zn2+
(0.74 Å) is smaller than that of Mn2+
(0.83 Å) [2]. Since the radius of the
substituted ions is smaller than that of the displaced ions, it is expected that the lattice should
shrink. The experimental values of lattice parameter of studied Mn0.5Zn0.5Fe2O4 have a good
match with the reported value of previous works Mn0.55Zn0.45Fe2O4, in which lattice parameter
was found to be 8.4645 Å [5].
Chapter-IV Results and Discussion
86
Table 4.2: Cation distribution (tetrahedral A-site and octahedral B-site), Ionic radii (rA for A-site
and rB for B-site), Lattice parameters (ath for theoretical and aexp for experimental value), X-ray
density (dx), Bulk density (dB) and Porosity (P) of A0.5Zn0.5Fe2O4 ferrites.
Sample
Cation Distribution
Ionic radii Lattice
parameter
X-ray
density
dX
(g/cm3)
Bulk
density
dB
(g/cm3)
Porosity
P
(%) A-site
B-site
rA
(Å)
rB
(Å)
ath
(Å)
aexp
(Å)
NiFe2O4 )(
3
1
Fe
2
4
3
1
2
1][ OFeNi
0.645 0.668 8.325 8.340* 5.38 9.40*
Ni0.5Zn0.5Fe2O4 )(3
5.0
2
5.0
FeZn
2
4
3
5.1
2
5.0][ OFeNi 0.692 0.656 8.369 8.413 5.39 4.95 8.16
MnFe2O4 )(3
1
Fe
2
4
3
1
2
1][ OFeMn 0.645 0.738 8.511 8.500
* 5.00
Mn0.5Zn0.5Fe2O4 )(
3
1.0
2
5.0
2
4.0
FeZnMn 2
4
3
9.1
2
1.0][ OFeMn
0.692 0.691 8.461 8.458 5.17 4.26 17.60
MgFe2O4 )(3
1
Fe
2
4
3
1
2
1][ OFeMg 0.645 0.683 8.365 8.360
* 4.52 18.35*
Mg0.5Zn0.5Fe2O4
)(3
45.0
2
5.0
2
05.0
FeZnMg
2
4
3
55.1
2
45.0][ OFeMg
0.692 0.663 8.388 8.415 4.96 4.68 5.64
CuFe2O4 )(3
1
Fe
2
4
3
1
2
1][ OFeCu
0.645 0.688 8.378 8.370* 5.35 32.80*
Cu0.5Zn0.5Fe2O4 )(
3
5.0
2
5.0
FeZn
2
4
3
5.1
2
5.0][ OFeCu
0.692 0.666 8.395 8.412 5.38 4.90 8.55
CoFe2o4 )(
3
1
Fe
2
4
3
1
2
1][ OFeCo
0.645 0.683 8.365 8.380* 5.29 21.60*
Co0.5Zn0.5Fe2O4 )(3
5.0
2
5.0
FeZn [
2
4
3
5.1
2
5.0]OFeCo 0.693 0.664 8.388 8.418 5.21 4.91 5.75
ZnFe2o4 )(2
Zn 2
4
3
1
3
1][ OFeFe 0.740 0.645 8.411 8.440
* 2.70*
Note: „*‟Marked values are taken from Smit & Wijn and Shannon [1, 2].
Figure 4.1(c) shows the XRD pattern of Mg-Zn ferrite. The lattice parameter of MgFe2O4 ferrite
is 8.36 Å [1]. It is seen from the XRD pattern and Table 4.2 that the lattice parameter (aexp) of the
studied sample Mg0.5Zn0.5Fe2O4 is found to be 8.415 Å, which is greater than MgFe2O4 ferrite
but smaller than ZnFe2O4 ferrite. Therefore it is concluded that the lattice parameter of Mg-Zn
Chapter-IV Results and Discussion
87
ferrite is increased with Zn substitution. It can be explained on the basis of ionic radii. The ionic
radii of Mg2+
and Zn2+
ions are 0.72 Å and 0.74 Å, respectively [2]. Since the radius of the
substituted ions (Zn2+
) is larger than that of the displaced ions (Mg2+
), it is expected that the
lattice should expand and increase the lattice constant with zinc substitution. The earlier
researcher reported that the lattice constant (aexp) of the composition Mg0.5Zn0.5Fe2O4 was 8.417
Å [6], which is well matched the same composition of studied sample.
Figure 4.1(d) shows the XRD pattern of Cu-Zn ferrite. From XRD pattern, it is obtained that the
lattice parameter (aexp) of studied sample Cu0.5Zn0.5Fe2O4 is 8.412 Å. But the lattice parameter of
CuFe2O4 ferrite is 8.370 Å [1]. The lattice parameter of studied Cu-Zn ferrite is smaller than that
of ZnFe2O4 ferrite but greater than CuFe2O4 ferrite. This is because of the ionic radii of these
materials. The ionic radius of Cu2+
(0.73 Å) is smaller than that of Zn2+
(0.74 Å) [2]. The earlier
researcher found that the lattice parameter of Cu0.5Zn0.5Fe2O4 was to be 8.416 Å [7]. The value (a
= 8.412 Å) of presently studied samples have a good matching with the reported value (a = 8.416
Å). When the larger Zn2+
ions enter into the lattice, the unit cell expands resulting in
enhancement of lattice parameter.
Figure 4.1(e) shows the XRD pattern of Co-Zn ferrite. It is observed that the lattice parameter of
studied Co0.5Zn0.5Fe2O4 ferrite is 8.418 Å as obtained from XRD pattern, whereas the lattice
parameter of CoFe2O4 ferrite is a = 8.38 Å [1]. The experimental value of Co-Zn ferrite is greater
than Co-ferrite and less than Zn-ferrite. The lattice constant is in between that of Co-ferrite and
Zn-ferrite, because the ionic radius of Zn2+
(0.74 Å) is greater than that of Co2+
(0.72 Å) [2].
Similar composition Co0.5Zn0.5Fe2O4, has been studied and found the lattice parameter to be a =
8.417 Å by S. Noor et al. [8], which is a good correlation with the experimental value (aexp =
8.418 Å). It is well known that the distribution of cations on the octahedral B-sites and
tetrahedral A-sites determines to a great change the physical and electromagnetic properties of
ferrites. There exists a correlation between the ionic radius and the lattice constant, the increase
of the lattice constant is proportional to the increase of the substituted ionic radius [9].
Chapter-IV Results and Discussion
88
4.1.3. Theoretical calculation of lattice parameter
Theoretical lattice parameters for all the studied samples (Ni0.5Zn0.5Fe2O4, Mn0.5Zn0.5Fe2O4,
Mg0.5Zn0.5Fe2O4, Cu0.5Zn0.5Fe2O4, and Co0.5Zn0.5Fe2O4) have been calculated to compare with the
experimental values. It is known that there is a correlation between the ionic radii of both A and
B sub-lattices and the lattice parameter. The lattice parameter can be calculated theoretically
using the following equation [1]:
00
3
33
8RrRra
BAth
Where, R0 is the radius of the oxygen ion (1.32 Å) [2], and rA and rB are the ionic radii of the
tetrahedral (A-site) and octahedral (B-site) sites, respectively. The values of rA and rB will depend
critically on the cation distribution of the system. The knowledge of cation distribution and spin
alignment is essential to understand the magnetic properties of spinel ferrite. The investigation of
cation distribution helps to develop materials with desired properties which are useful for many
devices from the applications point of view [10].
Theoretically the nickel ferrite (NiFe2O4) have inverse spinel structure in which half of the Fe3+
ions specially fill the tetrahedral sites and the rest occupy the octahedral sites with the Ni2+
ions.
Generally, an inverse spinel ferrite can be represented by the formula [Fe3+
] tet [A2+
, Fe3+
]octO42-
(A = Ni), where the "tet" and "oct" indices represent the tetrahedral and octahedral sites,
respectively. Likewise, these results specify that the synthesized zinc ferrite (ZnFe2O4) have a
normal spinel structure in which all Zn2+
ions fill tetrahedral sites, hence the Fe3+
ions are forced
to occupy all of the octahedral sites. Formation of the inverse spinel structure for nickel ferrites
and formation of normal spinel structure for zinc ferrites are the basis for the formation of mixed
spinel structure for Ni-Zn ferrite ( Ni0.5Zn0.5Fe2O4) when they are mixed together to form a solid
solution. Their cation distribution can be demonstrated below.
In order to calculate rA and rB of Nio.5Zn0.5Fe2O4 the following cation distribution is proposed:
2
4
3
5.1
2
5.0
3
5.0
2
5.0OFeNiFeZn
BA (4.3)
Where, the brackets ( ) and [ ] indicate the A site and B site, respectively. According to the cation
distribution of Ni-Zn ferrites, the ionic radius of the A site (rA) and B site (rB) can be
theoretically calculated using the following relations [11]:
(4.2)
Chapter-IV Results and Discussion
89
)()(
32
FerCZnrCr
eAFAZnA (4.4)
)]()([
2
1 32 FerCNirCr
BFeBNiB
(4.5)
Where, r(Zn2+
), r(Ni2+
), and r(Fe3+
) are ionic radii of Zn2+
(0.74 Å), Ni2+
(0.69 Å) and Fe3+
(0.645
Å) [2], respectively, while CAZn and eAF
C are the concentrations of Zn
2+ and Fe
3+ ions on A sites
and CBNi and CBFe are the concentrations of Ni2+
and Fe3+
ions on B sites. Using these formulae,
the ionic radius of the A-site (rA) and B-site (rB) were calculated and are tabulated in
Table 4.2. The theoretical lattice parameter (ath) of Ni-ferrite and Zn-ferrite were also calculated
on the basis of above relations, Eq. (4.2–4.5) and found to be 8.325 Å and 8.411 Å, respectively
which are exactly same as corresponding literature values [3]. The calculated theoretical lattice
parameter of the sample with composition Ni0.5Zn0.5Fe2O4 is 8.369 Å, which is larger than the
literature value of Ni-ferrite but smaller than Zn-ferrite. This increase in the lattice parameter can
be attributed to the ionic size differences between Ni2+
and Zn2+
resulting in expansion of unit
cell of the lattice [12]. Since the ionic radius of Zn2+
ions (0.74 Å) is larger than that of Ni2+
ions
(0.69 Å), the substitution is expected to increase the lattice parameter with the substitution of Ni
with Zn. This behavior has an effect on the magnetic properties such as Curie temperature (Tc)
and physical properties such as density and porosity. Since the Curie temperature (Tc) of
magnetic materials is dependent on the interatomic distance, the lattice expansion of
Ni0.5Zn0.5Fe2O4 ferrite is expected when Zn is substituted for Ni with concomitant decrease of
Curie temperature due to weakening of exchange interaction between A-B sublattice. Previous
researchers stated that for the composition Ni0.65Zn0.35Fe2O4 and Ni0.55Zn0.45Fe2O4, the theoretical
lattice parameter is 8.4116 Å and 8.4142 Å, respectively [3, 4]. The theoretical lattice parameter
values of the studied sample have a good correlation with the earlier works.
Similar way, the details of the lattice parameter including their rA and rB for all other studied
samples such as Mn-Zn, Mg-Zn, Cu-Zn and Co-Zn ferrites were calculated according to their
cation distribution and are presented in Table 4.2. It is noticed that the theoretically calculated
value of lattice parameter (ath) for A0.5Zn0.5Fe2O4 ferrites are larger than the literature values of
base ferrites (AFe2O4) and are smaller than that of ZnFe2O4 ferrite except for Mn-Zn ferrite. The
lattice parameter (ath) of Mn0.5Zn0.5Fe2O4 is smaller than the value of MnFe2O4 ferrite and is
larger than ZnFe2O4 ferrite. Similar behavior is also observed for the experimental lattice
Chapter-IV Results and Discussion
90
parameter (aexp) of the same composition due to the fact that ionic radius of Zn2+
(0.74 Å) are
smaller than that of Mn2+
ions (0.83 Å).
From the Table 4.2, it is observed that the similar trend of an expansion of lattice compared with
base ferrites (AFe2O4) due to Zn2+
substitution for all the studied ferrites in theoretical and
experimental investigation with the exceptional being Mn-Zn ferrite. The lattice parameter (aexp)
is always greater than that of (ath) except for Mn-Zn ferrite. The difference between (ath) and
(aexp) can be attributed to the deviation from the formula of cation distribution in Eq. (4.3) and
this deviation is related to the presence of divalent iron ions Fe2+
[7] and other crystal
imperfections. This small difference of lattice parameter of the theoretical values of the studied
sample and literature value may be related to lattice mismatch from the ideal condition and/or
due to different ionic radii measurement techniques.
4.1.4. Physical properties of A0.5B0.5Fe2O4
Density plays a vital role in controlling the properties of polycrystalline ferrites. The effect of Zn
substitution on the physical properties such as X-ray density, bulk density and porosity for all the
studied samples A0.5Zn0.5Fe2O4 (where A = Ni2+
, Mn2+
, Mg2+
, Cu2+
and Co2+
) were calculated
using Eq. (3.20−3.22). The bulk density, dB was measured by usual mass and dimensional
consideration whereas X-ray density, dX was calculated from the molecular weight and the
volume of the unit cell derived from the lattice for each sample. The calculated values of the bulk
density and theoretical or X-ray density of the studied ferrite system are presented in Table 4.2.
An increasing trend in X-ray density and decreasing trend in porosity has been observed with the
substitution of Zn for all the compositions. It is also observed that the bulk density is lower than
the corresponding X-ray density. This may be due to the existence of pores, which were formed
and developed during the sample preparation or sintering process [13]. This increase in X-ray
density is also due to the difference in ionic radii between A and Zn [14].
The X-ray density and bulk density increase slightly with the Zn substitution, which is due to the
atomic weight and density. The atomic weight and density of Zn are 65.37 amu and 7.14 g/cm3,
which is higher than that of Ni (58.69 amu and 8.91 g/cm3) [15]. Therefore there is a small
change of the X-ray density and porosity of Ni-Zn ferrite. Similarly, atomic weight and density
Chapter-IV Results and Discussion
91
of Mn are 54.94 amu and 7.43 g/cm3 [16], Mg are 24.32 amu and 1.74 g/cm
3 [15], Cu are 63.55
amu and 8.96 g/cm3 [7] and Co are 58.90 amu and 8.60 g/cm
3 [8]. It is found that all the studied
samples have slight change of density and porosity with substitution of Zn.
The percentage of porosity was also calculated using the Eq. (3.22). In literature, porosity value
of Ni-ferrite is 9.4% and Zn-ferrite is 2.7% [1]. The porosity of the present studied sample
Ni0.5Zn0.5Fe2O4 is found 8.16%. The porosity has decreased in Ni-Zn ferrite systems by Zn
substitution, which may be due to the creation of more oxygen vacancies with the substitution of
Zn ions in the samples and virtually less cation are created [14]. It was reported that the porosity
results from the formation of ZnO which favors the growth of inner pores and leads to the
increase of the porosity [17].
Similarly, porosity with Zn substitution for other studied ferrites were calculated and are
depicted in Table 4.2. It is seen that porosity decreases from 32.8% to 8.55% for Cu-ferrite,
21.6% to 5.75% for Co-ferrite, 18.35% to 5.64% for Mg-ferrite and 9.40% to 8.16% for Ni-
ferrite. The decrease of porosity may be due to the creation of more oxygen vacancies with the
substitution of Zn ions in the samples and virtually less cation is created. The porosity of the
Mn0.5Zn0.5Fe2O4 is 17.60% which is higher than that of other studied ferried.
It is also known that the porosity of ferrite samples results from two sources, intragranular
porosity (Pintra) and intergranular porosity (Pinter) [18]. Thus the total porosity (P %) could be
written as the sum of the two types i.e.,
P (%) = Pintra+Pinter (4.6)
Decrease of total porosity of the studied sample due to Zn substitution may be due to increased
number of oxygen vacancies as claimed by earlier work [19].
4.2. Magnetic Properties of A0.5Zn0.5Fe2O4
The effect of Zn substitution in base ferrites AFe2O4 has a significant influence on magnetic
properties such as magnetic moment, saturation magnetization, Curie temperature, permeability
etc. Saturation magnetization increases with the substitution of Zn. All studied samples shows
reasonably high initial permeability. The possible reason responsible for the change in magnetic
properties with the substitution of Zn have been described below.
Chapter-IV Results and Discussion
92
4.2.1. Magnetization measurement
The magnetic measurements of the A0.5Zn0.5Fe2O4 samples sintered at temperatures between
1000 to 1350 °C were measured using vibrating sample magnetometer (VSM) in the range of
magnetic field H = 0 to 20 kOe. Magnetic field was applied parallel with sample plane and
magnetization was taken at temperatures T = 100 and 300 K, which shows that samples exhibited
magnetic behavior. From the VSM measurements, magnetizations versus magnetic field (M−H)
curves are plotted for all samples as shown in Fig. 4.2. It is seen that magnetization is completely
saturated at lower field (< H = 50 Oe) and decreased with increasing temperature indicating
typically ferromagnetic as well as ferrimagnetic behavior, which is in good agreement with X-
ray diffraction data. The value of saturation magnetization was obtained from M−H curves.
The experimental values of the net magnetic moment in Bohr magneton is calculated from M–H
loops using magnetization value in emu/g. The saturation magnetization value of a sample has
been taken at high field where M is independent of magnetic field. The magnetic moment in
Bohr magneton is calculated from the measured saturation magnetization value per unit mass
using the formula.
nBexp =B
S
N
MM
(4.9)
Where, Ms is the saturation magnetization, N is the Avogadro‟s number, M′ is the molecular
weight and B is the magnetic moment in Bohr magneton. The values of the saturation
magnetization Ms, molecular weight M′ and magnetic moment nBexp at 100 and 300 K are
depicted in Table 4.3.
Figure 4.2(a) shows the field dependence magnetization measured at 100 and 300 K for sample
Ni0.5Zn0.5Fe2O4 sintered at Ts = 1350 °C with time 2 h. It is observed that the magnetization
increases sharply at very low field (H < 35 Oe) which corresponds to magnetic domain
reorientation and thereafter increases slowly up to saturation. The saturation magnetization is
defined as the maximum possible magnetization of a material. The saturation magnetization is
78.5 emu/g at 300 K and 107.5 emu/g at 100 K for Ni-Zn ferrite, which is in good agreement
with the reported value 75.6 emu/g for the composition of Ni0.65Zn0.35Fe2O4 and 77.3 emu/g for
Ni0.55Zn0.45Fe2O4 at room temperature [3, 4].
Chapter-IV Results and Discussion
93
Fig.4.2: Field dependence magnetization (M−H curve) for (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.
0 5 10 15 200
30
60
90
120
150Ni
0.5Zn
0.5Fe
2O
4(a)
Ms(e
mu
/g)
Applied field, H (kOe)
300 K, Ms = 78.5 (emu/g)
100 K, Ms = 107.5 (emu/g)
0 5 10 15 200
25
50
75
100
125
300 K, Ms = 90.1 (emu/g)
100 K, Ms = 118.2 (emu/g)
(b) Mn0.5
Zn0.5
Fe2O
4
Ms (
em
u/g
)
Applied field, H (kOe)
0 1 2 3 4 50
20
40
60
80
Ms (
em
u/g
)
Applied field, H (kOe)
(c) Mg0.5
Zn0.5
Fe2O
4
300 K, Ms = 53.3 (emu/g)
100 K, Ms = 59.1 (emu/g)
0 5 10 15 200
15
30
45
60
75(d)
Ms (
em
u/g
)
Applied field, H (kOe)
Cu0.5
Zn0.5
Fe2O
4
300 K, Ms = 38.4 (emu/g)
100 K, Ms = 56.3 (emu/g)
0 5 10 15 200
20
40
60
80
100
120Co
0.5Zn
0.5Fe
2O
4
Ms (
em
u/g
)
Applied field, H (kOe)
(e)
300 K, Ms = 91.4 (emu/g)
100 K, Ms = 101.5 (emu/g)
Chapter-IV Results and Discussion
94
As reported the saturation magnetization of Ni-ferrite is 56 emu/g and Zn-ferrite is 0 emu/g [1].
It is seen that the saturation magnetization of Ni-Zn ferrite is increased with the substitution of
Zn. Increasing trend of saturation magnetization can be explained on the basis of Neel‟s two sub-
lattice model [20, 21]. The increase of magnetization is due to the dilution of magnetic moment
of A-sublattice by substitution of nonmagnetic Zn ions. Since the resultant magnetization is the
difference between the B and A sublattice magnetization, it is obvious that increase of net
magnetization/magnetic moment is expected on dilution of the A-sublattice magnetization due to
occupation of A-site by nonmagnetic Zn as well as enhancement of B-sublattice magnetization
due to the introduction of Fe3+
ions having 5 µB.
Figure 4.2(b) shows the field dependence magnetization measured at 100 and 300 K for sample
Mn0.5Zn0.5Fe2O4 sintered at 1240 °C with time 3 h. The saturation magnetization is 90.1 emu/g at
300 K and 118.2 emu/g at 100 K for Mn-Zn ferrite. The saturation magnetization of Mn-ferrite
as reported is 112 emu/g [1]. It is observed that the magnetization of the sample increases
sharply with increasing applied magnetic field up to 50 Oe. Beyond this applied field
magnetization increases slowly. It is reported that the saturation magnetization was found 57.9
emu/g for Mn0.5Zn0.5Fe2O at 300 K [5]. But the value (90.1 emu/g) for the same composition of
studied sample is higher than reported work. It is well known fact that the magnetic characteristic
of Mn-Zn ferrites is controlled by the Fe-Fe interaction. Addition of suitable dopant and sintering
process can replace the iron cations which in turn causing the alternation of magnetic behavior of
the samples.
Field dependence magnetization of Mg0.5Zn0.5Fe2O4 sintered at Ts = 1350 °C with time 1 h are
shown in Fig. 4.2(c). It is observed that the saturation magnetization is 59.1 emu/g and 53.3
emu/g at 100 and 300 K, respectively. Magnetization increases sharply with the increase of
magnetic field up to 10 Oe. The saturation magnetization of Mg-ferrite as reported is 31 emu/g
[1] at room temperature. The saturation magnetization of Mg-Zn ferrite is increased with
substitution of Zn. The observed variation in saturation magnetization can be explained on the
basis of cation distribution and the exchange interactions between A- and B-sites. The
magnetization value depends on the distribution of Fe3+
ions among the two sites A and B, where
Mg2+
and Zn2+
ions are nonmagnetic.
Chapter-IV Results and Discussion
95
Table 4.3: Saturation magnetization (Ms), Molecular weight (M) and Magnetic moment (µB) for
A0.5Zn0.5Fe2O4 ferrites.
Sample
Saturation
magnetization
Molecular
weight
(g)
Experimental
magnetic moment
Theoretical
magnetic
moment
T = 0 K
(µB)
T = 300 K
(emu/g)
T = 100 K
(emu/g)
T = 300 K
(µB)
T = 100 K
(µB)
NiFe2O4 50*
Ni0.5Zn0.5Fe2O4 78.5 107.5 237.725 3.34 4.57 6
MnFe2O4 80*
Mn0.5Zn0.5Fe2O4 90.1 118.2 235.845 3.80 4.99 7.5
MgFe2O4 27*
Mg0.5Zn0.5Fe2O4 53.3 59.1 220.53 2.10 2.33 5.9
CuFe2O4 25*
Cu0.5Zn0.5Fe2O4 38.4 56.3 240.11 1.65 2.42 5.5
CoFe2o4 80*
Co0.5Zn0.5Fe2O4 91.4 101.5 237.805 3.89 4.32 6.5
ZnFe2o4 0* 10
Note: * Marked values are taken from Smit & Wijn where, T = 293 K [1].
The saturation magnetization of sample Cu0.5Zn0.5Fe2O4 sintered at Ts = 1050 °C with time 1 h
are 56.3 emu/g and 38.4 emu/g at 100 and 300 K, respectively as shown in Fig. 4.1(d).
Magnetization is completely saturated at lower field (H < 30 Oe). The saturation magnetization
of Cu-ferrite as reported is 30 emu/g [7] at 300 K. It is observed that magnetization increases
with nonmagnetic Zn substitution in Cu at 300 K. The increase in magnetization is due to the
dilution of magnetic moment of A-sublattice, which can be explained on the basis of Neel‟s
sublattice model [20]. Since the resultant magnetization is the difference between the B and A
sub-lattice magnetization, thus the increase of net magnetization/magnetic moment is expected
on dilution of the A-sublattice magnetization due to occupation of A-site by nonmagnetic Zn as
well as enhancement of B-sublattice magnetization due to the introduction of Fe3+
ions. The
magnetization value of studied sample is well matched with the results obtained earlier by other
workers [22].
Chapter-IV Results and Discussion
96
The field dependence magnetization of Co-Zn ferrite sintered at 1175 °C with time 2 h are shown
in Fig. 4.2(e). The saturation magnetization is found to be 101.5 emu/g and 91.4 emu/g at 100
and 300 K, respectively. Magnetization increases sharply but comparatively slower among the
other samples with the increase of applied field up to 80 Oe indicating semi-hard magnetic
ferrite. Beyond this applied field magnetization increases slowly. The saturation magnetization
of pure Co-ferrite as reported is 90 emu/g at 0 K [1]. It is observed that the saturation
magnetization is increased with Zn substitution. Magnetic moment of Co-Zn ferrites depends on
the distribution of Fe3+
ions between A and B sublattice. The Zn2+
substitution leads to increase
Fe3+
ions on B-sites. Zn is nonmagnetic having zero net magnetic moment and Fe3+
is 5 µB. So
the magnetization of the B-sites increases while that of A-sites decreases resulting in increases of
net magnetization i.e., M = MB – MA. The earlier studies reported that the magnetization of
composition Co0.5Zn0.5Fe2O4 was found to be 119 emu/g at 5 K [8]. This value is well matched
with the presently studied sample.
The saturation magnetization values observed in studied ferrites are higher than any other
reported value of nearby compositions. The observed higher value of saturation magnetization
can be explained on the basis of grain size and the exchange interaction among the adjacent
grains. The exchange interaction leads to inter-granular magnetic correlations in a material with
densely packed grains [23]. The correlation length depends on the size of the grain and more
significant when the grain size is smaller than the domain wall width present in ferrites. The
grain growth traps inter-granular pores with grains and hence increases the overall sample
properties. This inter-granular porosity leads to poor magnetic properties [24].
4.2.2. Theoretical calculation of magnetic moment
Increasing trends of saturation magnetization with the substitution of nonmagnetic Zn in base
ferrite (AFe2O4) can be explained on the basis of Neel‟s two sublattice model [20]. The magnetic
ordering in the simple spinel ferrites is based on the Neel‟s two sublattices (tetrahedral A-site
and octahedral B-site) model of ferri-magnetism in which the resultant magnetization or
saturation magnetization is the difference between B-site and A-site magnetization, provided that
they are collinear and anti-parallel to each other, i.e.,
M = MB – MA (4.7)
Chapter-IV Results and Discussion
97
In a ferrimagnetic material, the magnetic moments of tetrahedral A-sites and octahedral B-sites
are aligned anti-parallel, showing a ferrimagnetism with a net magnetization or magnetic
moment expressed in Bohr magnetons for collinear spin arrangement at any temperature T (T
Tc) could be written as,
nBth (T) = MB(T) – MA(T) (4.8)
Where, MA and MB are the magnetic moments of A- and B-sites. The substitution of Zn (on the
A-site) will lead to increase the Fe3+
ions on the B-site and consequently the magnetization of B-
site will increase. At the same time, the magnetization of A-site will decrease according to
decrease in the Fe3+
ion on A site resulting in increase of net magnetization of the sample.
Theoretical values of magnetic moment per formula unit for relevant ferrites and their cation
distribution were calculated using from Eq. (4.8) and are listed in Table 4.4. It is observed that
Zn substitution has increased magnetization of the pure ferrite system.
The cation distribution of Ni-ferrite and Ni-Zn ferrites can be presented as [1]:
2
4
323][)( OFeNiFe
BA
Where, MA = 5 1 = 5 µB and MB = 2 1 + 5 1 = 7 µB
2
4
3
5.1
2
5.0
3
5.0
2
5.0)( OFeNiFeZn
BA
Where, MA = 0 0.5 + 5 0.5 = 2.5 µB and MB = 2 0.5 + 5 1.5 = 8.5 µB
Using the cation distribution, the values of magnetic moment for example of Fe3+
, Zn2+
and Ni2+
are 5, 0 and 2 µB [1] respectively. The total magnetic moment per formula unit could be written
as, nBth = 8.5–2.5 = 6.0 µB, where µB is the Bohr magneton and this value is shown in Table 4.3
and 4.4. The calculated theoretical magnetic moment of the studied sample Ni0.5Zn0.5Fe2O4 is 6.0
µB and the literature value of theoretical magnetic moment of Ni-ferrite is 2 µB and Zn-ferrite is 0
µB [1]. It is observed that Ni-Zn ferrite magnetic moment value is higher than the literature
value. It is known that Zn ferrite is a normal spinel ferrite. It is also observe that, from the cation
distribution of ZnFe2O4, Zn2+
ion always remain in A-sites and Fe3+
in B-sites. But NiFe2O4,
MnFe2O4, MgFe2O4, CuFe2O4 and CoFe2O4 are inverse spinel ferrite, in which the divalent ions
are on B-sites and trivalent ions are equally divided between A- and B-sites.
When nonmagnetic divalent Zn2+
ions are substituted, they tend to occupy tetrahedral sites by
transferring Fe3+
ions to octahedral sites due to their favoritism by polarization effect. However,
Chapter-IV Results and Discussion
98
site preference of cations also depends upon their electronic configurations. Zn2+
ions show
markly preference for tetrahedral sites where their free electrons respectively can form a covalent
bond with free electrons of the oxygen ion. This forms four bonds oriented towards the corners
of a tetrahedron. Ni2+
ions have marked preference for an octahedral environment due to the
favorable fit of the charge distribution of these ions in the crystal field at an octahedral site [1].
In view of the above consideration the substitution of Zn (on A-site) will lead to increase the
Fe3+
ions on the B-site and consequently the magnetization of B-site will increase. At the same
time, the magnetization of A-site will decrease according to decrease in the Fe3+
ion on A-site.
Thus, the net magnetization will increase with Zn substitution.
Table 4.4: Postulated tetrahedral (A-site) and octahedral (B-site) ions and their theoretically
calculated of magnetic moment per molecule at 0 K of A0.5Zn0.5Fe2O4 ferrites.
Sample A-site ions & their
magnetic moments
(B )
B-site ions & their
magnetic moments
(B )
Magnetic moment
per molecule
(B )
NiFe2O4 Fe
5.0
Ni Fe
2.0 5.0
2.0
Ni0.5Zn0.5Fe2O4 Fe0.5 Zn0.5
2.5 0
Ni0.5 Fe1.5
1.0 7.5
6.0
Mn Fe2O4 Fe0.2 Mn0.8
1.0 4.0
Mn0.2 Fe1.8
1.0 9.0
5.0
Mn0.5Zn0.5 Fe2O4 Fe0.5 Zn0.5
2.5 0
Mn0.5 Fe1.5
0.5 9.5
7.5
Mg Fe2O4 Fe0.9 Mg0.1
4.5 0.0
Mg0.9 Fe1.1
0.0 5.5
1.0
Mg0.5Zn0.5 Fe2O4 Fe0.5 Zn0.5
2.3 0
Mg0.5 Fe1.5
0.45 7.75
5.9
Cu Fe2O4 Fe
5.0
Cu Fe
1.0 5.0
1.0
Cu0.5Zn0.5 Fe2O4 Fe0.5 Zn0.5
2.5 0
Cu0.5 Fe1.5
0.5 7.5
5.5
CoFe2O4 Fe
5.0
Co Fe
3.0 5.0
3.0
Co0.5Zn0.5 Fe2O4 Fe0.5 Zn0.5
2.5 0
Co0.5 Fe1.5
1.5 7.5
6.5
ZnFe2O4 Zn
0
Fe2
10
10
Cation Ni2+
[1]
Zn2+
[1] Fe3+
[1]
Mn2+
[1] Mg2+
[1 ] Cu2+
[1] Co2+
[ 1]
Magnetic
Moment (B )
2.0 0 5.0 5.0 1.0 1.0 3.0
Chapter-IV Results and Discussion
99
The cation distribution of Mn-ferrite and Mn-Zn ferrites can be presented as [1]:
2
4
323][)( OFeMnFe
BA
Where, MA = 5 µB and MB = 10 µB
( )3
1.0
2
5.0
2
4.0
FeZnMn A[
3
9.1
2
1.0FeMn ]B
2
4O
Where, MA = 2.5 µB and MB = 10 µB
The values of magnetic moment for Fe3+
, Zn2+
and Mn2+
are 5, 0 and 5 µB [1], respectively. Thus
the total magnetic moment per formula unit of Mn0.5Zn0.5 Fe2O4 is nBth = 10–2.5 = 7.5 µB and is
tabulated in Table 4.3 and 4.4. The theoretical magnetic moment of the Mn-ferrite was found to
be 5 µB [1]. It is observed that the magnetic moment is increased in the Mn-Zn ferrite with
substitution of Zn. The magnetic moment of Mn2+
is same as that of the Fe3+
(5 µB) by partial
substitution of Mn2+
(5µB) ions by A- and B-sites. But the non magnetic substitution of Zn2+
(0
µB) ion attains only A-site. According to the occupancy tendency of ions, 80% of Mn2+
ions have
strong site preference for A-site and 20% of Mn3+
ions for B-site [1]. With the substitution, the
magnetization of A-site will decrease according to decrease in the Fe3+
ion on A-site. Whereas,
the substitution of Zn2+
ions (on the A-site) will lead to increase the Fe3+
ions on the B-site and
consequently the magnetization of B-site will increase. So, the magnetic moment nB (µB) is
expected to increase as a result of Fe3+
displacement to B sites.
The cation distribution of Mg-ferrite and Mg-Zn ferrites can be presented as [1].
2
4
323][)( OFeMgFe
BA
Where, MA = 4.5 µB and MB = 5.5 µB
( 3
45.0
2
5.0
2
05.0FeZnMg )A[
3
55.1
2
45.0FeMg ]B
2
4O
Where, MA = 2.3 µB and MB = 8.2 µB
From the cation distribution, the values of magnetic moment of Fe3+
, Zn2+
and Mg2+
are 5, 0 and
1 µB, [1], respectively. The total magnetic moment per formula unit is nBth = 8.2–2.3 = 5.9 µB and
the calculated value is shown in Table 4.3 and 4.4. Mg-ferrite is a frequent component of mixed
ferrites. If its structure completely inverse, its net magnetic moment would be zero, because the
magnetic moment of the Mg2+
ions is zero. But, as noted earlier 10% of the Mg2+
ions are on A-
sites, displacing an equal number of Fe3+
ions and 90% of the Mg2+
ions are located on B-
sites[1]. The ionic magnetic moment of Mg2+
is zero (non-magnetic) and the magnetic moment
Chapter-IV Results and Discussion
100
of Fe3+
is 5 B. The substitution of Zn will lead to increase Fe3+
ions on the B-sites and
consequently the magnetization of the B-sites will increase. At the same time the magnetization
of A-site will decrease according to the decrease of the Fe3+
ions on A-site.
The cation distribution of Cu-ferrite and Cu-Zn ferrites can be presented as [1]:
2
4
323][)( OFeCuFe
BA
Where, MA = 5 µB and MB = 6 µB
2
4
3
5.1
2
5.0
3
5.0
2
5.0)( OFeCuFeZn
BA
Where, MA = 2.5 µB and MB = 8 µB
The values of magnetic moment of Fe3+
, Zn2+
and Cu2+
are 5, 0 and 1µB [1], respectively. The
total magnetic moment per formula unit is nBth = 8–2.5 = 5.5 µB and this calculated value is
tabulated in Table 4.3 and 4.4. The magnetic moment of the studied sample Cu0.5Zn0.5Fe2O4 is
5.5 B whereas the magnetic moment of CuFe2O4 is 1 B [1], in which magnetic moment
increases with Zn substitution. In the present system Zn2+
ions of magnetic moment 0 B
occupies tetrahedral A-site and push the Fe3+
(5 B ) to octahedral B-site. This migration of Fe3+
ions from A-site to B-site increases the net magnetic moment of B-site.
The cation distribution of Co-ferrite and Co-Zn ferrites can be presented as [1];
2
4
323][)( OFeCoFe
BA
Where, MA = 5 µB and MB = 8 µB
2
4
3
5.1
2
5.0
3
5.0
2
5.0)( OFeCoFeZn
BA
Where, MA = 2.5 µB and MB = 9 µB
The values of magnetic moment of Fe3+
, Zn2+
and Co2+
are 5, 0 and 3 µB [1], respectively and the
total magnetic moment per formula unit of Co0.5Zn0.5Fe2O4 is nBth = 9−2.5 = 6.5 µB and this
value is shown in Table 4.3 and 4.4. In literature the theoretical magnetic moment of CoFe2O4 is
3 B [1]. It is observed that the magnetic moment of Co0.5Zn0.5Fe2O4 is increased with the
substitution of Zn. Magnetic moment of any composition depends on the distribution of Fe3+
ions
between A and B sublattice. So the magnetization of the B-sites increases while that of A-sites
decreases resulting in increases of net magnetization i. e, M = MB ‒ MA.
Chapter-IV Results and Discussion
101
It is seen from Table 4.3, that experimental magnetic moment in Bohr magneton calculated from
magnetization value in emu/g at 100 and 300 K is lower than the theoretical calculated magnetic
moment. It is because the theoretical magnetic moment calculated from the cation distribution is
corresponding to the value of magnetization measured at absolute zero K, i.e., T = 0 K.
Therefore the Bohr magneton calculated from the magnetization data measured at T = 100 and
300 K should always be less than the theoretical value calculated from the cation distribution
since this lower value of magnetization, M is due to disordering effect of spin alignment by
thermal energy, kBT. The difference between the experimental values of the magnetic moments
and theoretical values may be attributed to the sintering conditions and canting effects. A. M.
Kumar et al. [25] explained that at higher sintering temperature the evaporation of zinc from the
surface of the samples results non-stoichiometry in the material, which reduces the
magnetization further.
4.3 Curie Temperature Measurement with Temperature Dependence of
Permeability
Curie temperature, Tc is a basic quantity in the study of magnetic materials. It corresponds to the
temperature at which a magnetically ordered material becomes magnetically disordered, i.e. a
ferromagnetic or a ferrimagnetic material becomes paramagnetic one. The temperature
dependence of magnetic permeability is a very simple way to determine Curie temperature. The
initial permeability was measured at a constant frequency (100 kHz) of a sinusoidal wave by
using Impedance Analyzer. It is directly related to the magnetization and to the ionic structure
and then the thermal spectra of permeability can be taken as a test of homogeneity of the
prepared samples.
The real (µ') and imaginary ('') part (magnetic loss component) of the complex permeability as
dependent on temperature were taken for all samples at two different sintering temperature of
each composition at 1000 to 1350 °C and are shown in Fig. 4.3 and 4.4. It is found that the initial
permeability, µ' increases with the increase of temperature, while it falls abruptly close to the
Curie temperature. The Curie temperature, Tc is determined by drawing a tangent for the curve
at the rapid decrease of µ'. The intersection of the tangent with the temperature axis determines
Tc. The vertical drop of the permeability at the Curie point indicates the degree of homogeneity
Chapter-IV Results and Discussion
102
of the sample composition [26]. At the Curie temperature, where complete spin disorder takes
place, corresponds to maximum of imaginary part of the permeability and sharp fall of the real
part of permeability towards zero. Therefore for accurate determination of Curie temperature, the
maxima of imaginary part and the corresponding sharp fall of the real part of the permeability
towards zero is very essential, simultaneously to determine Tc accurately. The Curie
temperatures for all the samples are determined by temperature dependent permeability
measurements and are presented in Fig. 4.3−4.7. These values and corresponding Tc for the base
ferrites taken from literature are listed in Table 4.5. In this respect Curie temperature, Tc to be the
temperature where rate of change of µ' is maximum (dµ'/dT = max.) as well as where '' attains
its maximum value. It is found that these two values of Tc are close to each other with in ± 2 °C.
But the difference between the Tc values of samples for the same composition sintered at
different temperatures is observed, which is ± 10 °C.
Fig. 4.3: Variation of permeability with temperature for Ni0.5Zn0.5Fe2O4 at (a) 1325 °C with time 2 h and
(b) 1350 °C with time 2 h.
Permeability versus temperature curve for the sample Ni0.5Zn0.5Fe2O4 sintered at Ts = 1325 and
1350 oC are shown in Fig. 4.3(a) and 4.3(b), respectively. It is observed that µ' increases with T
and demonstrates a sharp maximum generally known as Hopkinson peak before a rapid fall at T
= Tc. Similarly '' attains a maximum value at temperature at which steepest fall of permeability
is observed. This temperature is 271 °C ± 2 and has been taken as T = Tc for the sample sintered
at Ts = 1325 °C. But for the sample sintered at Ts = 1350 oC, Curie temperature Tc = 280 °C has
been observed. This difference value of Tc may be attributed to volatization of Zn at higher
0 100 200 300 4000
100
200
300
400
500
600
25
50
75
100
125
150(b)
Ts=1350
0C/2 h
Tc=280
0C
Im
ag
ina
ry
pa
rt
of
Perm
ea
bil
ity
Rea
l p
art
of
Perm
ea
bil
ity
Temperature(0c)
Ni0.5
Zn0.5
Fe2O
4
µ’ µ’
µ’’ µ’’
Chapter-IV Results and Discussion
103
temperature above 1300 °C. This sample also demonstrates a maximum of '' at Tc = 282 °C.
This small difference (2 °C) may be considered as experimental uncertainty. The values, Tc of
the present samples are very close to the reported value for composition Ni0.55Zn0.45Fe2O4 ferrite
of Tc = 320 o
C [4]. But the Tc of NiFe2O4 ferrite is 585 o
C [1], which is higher than that of
Ni0.5Zn0.5Fe2O4 ferrite. This may be attributed to the fact of the weakening of exchange
interaction according to Neel‟s model, thereby reducing the Tc with substitution of Zn.
The variation of µ' with temperature can be expressed as follows: The anisotropy constant (K1)
and saturation magnetization (Ms) usually decreases with increase in temperature. But decrease
of K1 with temperature is faster than that of Ms. When the anisotropy constant reaches to zero, µ'
attains its maximum value known as Hopkinson peak [27] and then drops off sharply to
minimum value near the Curie point. According to the equation
1
2
μK
DMs
[28], µ' must show a
maximum (infinity) at temperature at which K1 vanishes, where D is the diameter of the grain.
The above relation shows that initial permeability, µ' is directly related to saturation
magnetization Ms of the sample. The higher value of Ms is found to be higher the µ'. From this
equation it is clear that the initial permeability, µ' also depends on grain size D, i.e. µ' increases
with increase of D. It is generally expected that D increases with increase of sintering
temperature, Ts, provided the density also increases with Ts. If µ' decreases with increasing Ts,
then it must be assumed that the grain growth was heterogeneous with increasing Ts and the
density also have decreasing trend with increasing Ts.
Fig. 4.4: Variation of permeability with temperature for Mn0.5Zn0.5Fe2O4 at (a) 1220 oC with time 3 h and
(b) 1240 oC with time 3 h.
0 50 100 1500
100
200
300
400
0
25
50
75
100
125
150
Im
ag
ina
ry
pa
rt
of
Perm
ea
bil
ity
Rea
l p
art
of
Perm
ea
bil
ity
Temperature (0C)
(a)
Tc=86
0C
Ts=1220
0C/3h
Mn0.5
Zn0.5
Fe2O
4
0 50 100 1500
100
200
300
400
500
25
50
75
100
125
150
Im
ag
ina
ry
pa
rt
of
Perm
ea
bil
ity
Rea
l p
art
of
Perm
ea
bil
ity
Temperature (oC)
(b)
Tc=90
0C
Ts=1240
0C/3h
Mn0.5
Zn0.5
Fe2O
4
µ’ µ’
µ’’ µ’’
Chapter-IV Results and Discussion
104
Figure 4.4(a) and 4.4(b) show permeability versus temperature curves for composition
Mn0.5Zn0.5Fe2O4 at different sintering temperature. The Curie temperature, Tc is determined to be
86 and 90 °C sintered at Ts = 1220 and 1240 °C, respectively. This difference may be attributed
to the similar effect as mentioned above or experimental error. The Tc values of the present
samples are in good agreement with the reported value for composition Mn0.55Zn0.45Fe2O4 ferrite
of Tc = 90 oC [5]. The Tc value for the base ferrite MnFe2O4 is 300 °C [1]. It is well known fact
that the magnetic characteristics of Mn-Zn ferrites are controlled by the Fe-Fe interaction.
According to the occupancy tendency of ions, 80% of Mn2+
ions have strong site preference for
A-site and 20% of Mn2+
ions for B-site [1]. Whereas, Zn2+
ions prefer to A-site. Addition of Zn
dopant can replace the iron cations which in turn causing the alteration of magnetic behavior of
the samples and hence the Tc is lower than base ferrite.
Fig. 4.5: Variation of permeability with temperature for Mg0.5Zn0.5Fe2O4 at (a) 1300 °C with time 1 h and
(b) 1350 °C with time 1 h.
Figure 4.5(a) and 4.5(b) show the permeability versus temperature curves for composition
Mg0.5Zn0.5Fe2O4 sintered at 1300°C with time 1 h and 1350 °C with time 1 h. Curie temperature,
Tc = 152 and 150 °C are found respectively. Good correlations between both the samples are
observed. The Tc values of the samples are in well matched with the reported value for
composition Mg0.5Zn0.5Fe2O4 ferrite of Tc = 149 o
C [6]. Curie temperature of MgFe2O4 is 440 °C
[1]. It is found that Curie temperature goes on decreasing with substitution of Zn. In Mg-Zn
ferrites, most of Mg2+
ions are located on B-sites and small fraction migrates to A-sites [1]. The
presence of Mg2+
and Zn2+
ions either on A-site or on B-site will cause a decrease in A-B
magnetic interaction thereby lowering the Curie temperature.
100 150 200 2500
200
400
600
800
1000
0
100
200
300
400
Im
ag
ina
ry
pa
rt
of
Perm
ea
bil
ity
Rea
l p
art
of
Perm
ea
bil
ity
Temperature (oC)
(b)
Tc=150
0C
Ts=1350
0C/1h
Mg0.5
Zn0.5
Fe2O
4
µ’ µ’
µ’’ µ’’
Chapter-IV Results and Discussion
105
Fig. 4.6: Variation of permeability with temperature for Cu0.5Zn0.5Fe2O4 at (a) 1000 °C with time 1 h and
(b) 1050 °C with time 1 h.
Curie temperature, Tc for Cu0.5Zn0.5 Fe2O4 is 185 and 187 °C for samples sintered at T = 1000
and 1050 °C, respectively as shown in Fig. 4.6(a) and 4.6(b). The values are very close to each
other and are in good agreement with the reported value for same composition of Tc = 184 oC [7].
Curie temperature of corresponding base ferrites is 455 °C [1]. It is known that the Curie
temperature depends strongly on the strength of exchange interaction between A and B sublattice
(JAB) which in turn is related with inter-atomic distance, `a‟. The decrease of Tc with the
substitution of Zn, may be explained by a modification of the A-B exchange interaction strength
due to the change of the Fe3+
distribution between A- and B-sites.
Fig. 4.7: Variation of permeability with temperature for Co0.5Zn0.5Fe2O4 at (a) 1125 °C with time 2 h and
(b) 1175 °C with time 2 h.
100 200 30050
100
150
200
250
300
50
75
100
125
Im
ag
ina
ry
pa
rt
of
Perm
ea
bil
ity
Rea
l p
art
of
Perm
ea
bil
ity
Tc=185
0C
Cu0.5
Zn0.5
Fe2O
4
Temperature (oC)
(a)
Ts=1000
0C/1h
50 100 150 200 250 300 35050
100
150
200
250
300
50
75
100
125
Im
ag
ina
ry
pa
rt
of
Perm
ea
bil
ity
Rea
l p
art
of
Perm
ea
bil
ity
Temperature (oC)
(b)
Tc=187
0C
Ts=1050
0C/1h
Cu0.5
Zn0.5
Fe2O
4
0 50 100 150 200 2500
50
100
150
200
250
300
350
400
48
50
52
54
56
58
Im
ag
ina
ry
pa
rt
of
Perm
ea
bil
ity
Rea
l p
art
of
Perm
ea
bil
ity
Temperature (oC)
(a)
Tc=139
0C
Ts=1125
0C/2h
Co0.5
Zn0.5
Fe2O
4
0 50 100 150 200 2500
100
200
300
400
48
52
56
60
64
68
72
76
80
Im
ag
ina
ry
pa
rt
of
Perm
ea
bil
ity
Rea
l p
art
of
Perm
ea
bil
ity
Temperature (0C)
(b)
Tc=139
0C
Ts=1175
0C/2h
Co0.5
Zn0.5
Fe2O
4
µ’ µ’
µ’
µ’
µ’’
µ’
µ’’
µ’
µ’’ µ’’
Chapter-IV Results and Discussion
106
The Tc values of Co0.5Zn0.5 Fe2O4 are found to be 139 ± 1 °C for the both samples sintered at Ts =
1125 and 1175 °C, respectively as shown in Fig. 4.7(a) and 4.7(b). But the reported value of Tc
for same composition Co0.5Zn0.5Fe2O4 ferrite is 413 oC [8]. For the case of CoFe2O4, the Tc value
is larger i.e. 520 °C as compared with the determined values. As Fe3+
are gradually replaced by
Zn2+
ions, the number of strong magnetic ion begin to decrease at both the sites which weakening
the strength of A-B exchange interactions. Thus, the thermal energy required to offset the spin
alignment decreases, thereby decreasing the Curie temperature of the studied samples.
Table 4.5: Curie temperature (Tc) of the A0.5Zn0.5Fe2O4 samples sintered at different sintering
temperatures (Ts)/time.
Sample Ts (oC)/ time Tc (
oC)
NiFe2O4 585*
Ni0.5Zn0.5Fe2O4
1325/2 h 271
1350/2 h 280
MnFe2O4 300*
Mn0.5Zn0.5Fe2O4
1220/3 h 86
1240/3 h 90
MgFe2O4 440*
Mg0.5Zn0.5Fe2O4
1300/1 h 152
1350/1 h 150
CuFe2O4 455*
Cu0.5Zn0.5Fe2O4
1000/1 h 185
1050/1 h 187
CoFe2o4 520*
Co0.5Zn0.5Fe2O4
1125/2 h 139
1150/2 h 139
ZnFe2o4 TN = 9 K*
Note: * Marked values are taken from Smit & Wijn [1].
Chapter-IV Results and Discussion
107
In all cases it is observed that the Curie temperature, Tc values of the studied samples substituted
with Zn have been found to decrease substantially compared with their unsubstituted base
ferrites. This could be attributed to the increase in distance between the moments of A- and B-
sites, which is confirmed by the increase in the lattice parameter with Zn substitution. In ferrites,
there are three kinds of interactions between the tetrahedral A-sites and octahedral B-sites: A-A
interaction, B-B interaction and A-B interaction [20]. Among these three types of interactions A-
B interaction is strongest. 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-B sites antiferromagnetic interaction [21]. The substituted Zn2+
preferentially occupies the
tetrahedral A-site replacing an equal amount of Fe3+
to octahedral B-sites. In such a situation JAA
becomes weaker. Therefore, decrease of Tc is due to the weakening of A-B exchange interaction
and this weakening becomes more pronounced when more Zn2+
replaces more tetrahedral Fe3+
to
octahedral B-sites.
4.4 Complex Permeability, Relative Quality Factor and Relative Loss Factor
The permeability as dependent on frequency of a magnetic material is an important parameter
from the application consideration such as insulator. Therefore the study of initial
permeability/susceptibility has been a subject of great interest from the both the theoretical and
practical points of view. A detail study of complex permeability is essential to understand the
practical application range in AC field. The optimization of the dynamic properties such as
complex permeability in the high frequency range requires a precise knowledge of the
magnetization mechanisms involved. The magnetization mechanisms contributing to the
complex permeability is given by µ = µ'−i'', where, µ' is the real permeability that describes the
stored energy expressing the component of magnetic induction B in phase and '' is the
imaginary permeability that describes the dissipation of energy expressing the component of B
90o out of phase with the alternating magnetic field H.
The complex permeability (µ'and '') has been determined as a function of frequency in the
range 1 kHz to 120 MHz at room temperature for all the sample A0.5Zn0.5Fe2O4 ferrites by using
the conventional technique based on the determination of the complex impedance of a circuit
Chapter-IV Results and Discussion
108
loaded with toroid shaped sample. The results obtained from Fig. 4.8−4.12, it is revealed that the
real permeability, ' is fairly constant with frequency up to certain low frequencies, rises and
then falls rather rapidly to a very low value at higher frequencies. The imaginary component ''
first rises slowly and then increases quite abruptly making a peak at a certain frequency (called
resonance frequency, fr) where the real component ' is falling sharply. This phenomenon is
attributed to the natural resonance [29]. Resonance frequencies were determined from the
maximum of the imaginary permeability (peak position) of all the samples and are tabulated in
Table 4.6. The resonance frequency peaks are the results of the absorption of energy due to
matching of the oscillation frequency of the magnetic dipoles and the applied frequency.
The permeability would be resolved into two types of mechanisms such as contribution from
spin rotation and contribution from domain wall motion. But the contribution from spin rotation
was found to be smaller than domain wall motion and it is mainly due to irreversible motion of
domain walls in the presence of a weak magnetic field [30]. The imaginary part of permeability
corresponds to the loss component of the real permeability. For a device application, the
frequency range up to which the material can be used as an inductor is always much less than the
frequency at which '' attains its maximum value i.e. below the resonance frequency, fr of the
materials. Generally application range of frequency is best suited below the frequency from
where the '' starts rising sharply. At the resonance frequency, '' attains its maximum value and
generally become equal to µ', i.e. µ' = '' which means that tanδ = ''/ µ' = 1. According to the
Snoek‟s limit frµ' = constant [31]. This means that high frequency and high permeability cannot
go together or in other words if we want to use the ferrite inductor for high frequency
application, then the permeability of the device materials must be sacrificed. Again if a device
needs very high µ', then it must be used ferrite materials having lower resonance frequency i.e.,
the device is suitable for lower frequency range of application.
The variation of complex permeability (µ' and '') as a function of frequency range 1 kHz to
120 MHz for Ni0.5Zn0.5Fe2O4 ferrites sintered at 1325 °C with time from 0.5 to 4 h and at 1350
°C with time 2 h are presented in Fig. 4.8(a) and 4.8(b), respectively. It is seen that the
permeability value ' for the sample remains independent of frequency until resonance takes
place, above which it starts decreasing sharply with simultaneous increase of imaginary part of
the permeability. It is observed that permeability increases with sintering time up to 3 h and
Chapter-IV Results and Discussion
109
sintering temperature 1325 oC and then decreases with higher sintering time (4 h) and
temperature1350 oC. The initial increase of µ' may be attributed to the increase in density and
grain size simultaneously. According to Globus-Duplex relation [32]
1
2
μK
DMs
, i.e. µ' is directly
related to Ms and D, while it is inversely related to K1.
Fig. 4.8: Frequency dependence (a) initial permeability ('), (b) imaginary permeability (''), (c) relative
quality factor and (d) relative loss factor of Ni0.5Zn0.5Fe2O4 for different sintering temperature.
Therefore with increasing sintering time, it is expected that grain size D will increase resulting in
enhancement of µ' and it has been demonstrated that permeability increases with the increase of
density. Ferrites with higher density and larger average grain size posses a higher initial
permeability. The decrease of µ' for higher sintering time and temperature may be connected
with the evaporation of small amount of Zn from the sample that depleted with Zn content. This
103
104
105
106
107
1080
100
200
300
400
225
251
290
318
329
350
Rea
l p
art
of
Per
mea
bil
ity Ni
0.5Zn
0.5Fe
2O
4a)
Frequency,f(Hz)
Ts=1325OC/0.5h
Ts=1325OC/1h
Ts=1325OC/2h
Ts=1325OC/3h
Ts=1325OC/4h
Ts=1350OC/2h
105
106
107
1080
50
100
150
200
103
97
112
138
189Ni
0.5Zn
0.5Fe
2O
4b)
Frequency,f (Hz)
Im
ag
ina
ry p
art
of
Per
mea
bil
ity
Ts=1325oC/0.5h
Ts=1325oC/1h
Ts=1325oC/2h
Ts=1325oC/3h
Ts=1325oC/4h
Ts=1350oC/2h
104
105
106
107
0
2
4
6
8
645
48314941
5710
6477
Ts=1325oc/0.5h
1325oC/1h
1325oC/2h
1325oC/3h
1325oC/4h
1350oC/2h
c) Ni0.5
Zn0.5
Fe2O
4
RQFx10-3
Frequency, f(Hz)10
310
410
510
610
710
80
5
10
15
20
25
30
1.34E-41.56E-4
2.03E-4
1.56E-3
1.5
6E
-4
2.5
1E
-4
d)
Ts=13250C/0.5 h
Ts=13250C/1 h
Ts=13250C/2 h
Ts=13250C/3 h
Ts=13250C/4 h
Ts=13500C/2 h
Ni0.5
Zn0.5
Fe2O
4
RLFX104
Frequency, f(Hz)
Chapter-IV Results and Discussion
110
may have effect of creation of some vacancies resulting in impediment of domain wall
movement along with slight reduction of magnetization [33]. The vacancy, which is created due
to Zn evaporation may also enhance the anisotropy energy and thereby increase the value of K1.
As a result the µ' is expected to decrease. But the decreasing value of µ' for Ts = 1350 oC /2 h is
higher than the sample Ts = 1325 oC /4 h, which may be due to the higher activation energy of
the sample with Ts = 1325 oC /4 h, because the temperature has an exponential relation compared
with the linear dependence effect of activation energy. From Fig. 4.8(b) and Table 4.6, it is
observed that the resonance peak of the '' shift to lower frequency range as the permeability µ'
increases.
Figure 4.8(c) and 4.8(d) show the variation of relative quality factor (RQF) and relative loss
factor (RLF) with frequency. Both of these two quantities are shown here for a better
understanding for the merit of the prepared materials for an inductor device application.
Generally the very high value of RQF or extraordinary low value of RLF is essential requirement
for a soft magnetic material to be used as transformer core material in particular for inductor
material. A good inductor should have a value of RLF approximately ≈ 10-4
−10-5
.
The RQF increases with an increase of frequency, showing a peak and then decreases with
further increase in frequency as shown in Fig. 4.8(c). The highest RQF (6477) is found for the
sample sintered at 1325 oC with time 0.5 h. This is probably due to the growth of less
imperfection and defects compared to those of other sintering samples [34]. The peak associated
with the RQF decreases with increasing sintering time and temperature and is shifted to lower
frequencies. This phenomenon is associated with the Snoek‟s law [35], where an increase in
saturation magnetization leads to a decrease in the resonance frequency and vice versa. Whereas
RLF at low frequency region is found to decrease sharply with increasing frequency and is
minimum up to certain level and then it rises rapidly at higher frequencies as shown in Fig.
4.8(d). At the resonance, maximum energy transfer occurs from the applied field to the lattice
which results the rapid increases in loss factor. The loss is due to lag of domain wall motion with
the applied alternating magnetic field and is attributed to various domain wall effect, which
include non-uniform and non-respective domain wall motion, domain wall bowing, localized
variation of flux density, nucleation and annihilation of domain wall [36]. This happens at the
frequency where the permeability begins to drop.
Chapter-IV Results and Discussion
111
Table 4.6: The variation of initial permeability (µ'), Resonance frequency (fr), Relative quality
factor (RQF), Relative loss factor (RLF) of the A0.5Zn0.5Fe2O4 samples sintered at different
temperature and time.
Sample Sintering
temp.
(oC)
Sintering
time
(h)
µ' fr
(Hz)
RQF RLF
Ni0.5Zn0.5Fe2O4 1325 0.5 225 2.00 107 6477 1.34 10
-4
1325 1 290 9.96 106 5710 1.55 10
-4
1325 2 318 6.93 106 4941 1.56 10
-4
1325 3 350 7.36 106 645 1.56 10
-3
1325 4 329 6.95 106 4831 2.51 10
-4
1350 2 251 9.28 106 4830 2.03 10
-4
Mn0.5Zn0.5Fe2O4 1220 3 547 4.18 103 6389 1.63 10
-4
1240 3 457 4.13 103 7686 1.28 10
-4
Mg0.5Zn0.5Fe2O4 1300 1 306 9.96 106 8674 1.16 10
-4
1300 2 222 9.73 106 5861 1.86 10
-4
1300 4 229 9.76 106 5598 1.78 10
-4
1325 1 242 9.96 106 6076 1.64 10
-4
1350 1 297 9.76 106 7063 1.43 10
-4
Cu0.5Zn0.5Fe2O4 1000 1 126 4.96 107 3481 2.92 10
-4
1000 2 148 4.01 107 4565 2.15 10
-4
1000 3 183 3.00 107 3481 2.82 10
-4
1050 0.5 115 4.96 107 3853 2.54 10
-4
1050 1 192 5.01 107 5805 1.99 10
-4
Co0.5Zn0.5Fe2O4 1125 2 400 4.91 106 2598 3.97 10
-4
1175 2 472 4.94 106 3066 3.24 10
-4
It is observed from the figure that the maximum RQF and minimum RLF corresponds to the
sample Ni0.5Zn0.5Fe2O4 sintered at Ts = 1325 oC /0.5 h. The lowest permeability corresponds to
the sample Ts = 1325 oC /0.5 h has the highest RQF or lowest RLF. This sample is therefore the
most optimum for inductor material and also for high frequency application less than 20 106 Hz
(fr = 20 MHz). If RLF ≈1.56 10-3
, high permeability is essential for the device, then the sample
with Ts =1325 oC /3 h is a good choice, but in that case the frequency range up to which the
device can be used will be reduced to less than 6.93 106 Hz.
Chapter-IV Results and Discussion
112
Fig. 4.9: Frequency dependence (a) initial permeability ('), (b) imaginary permeability (''), (c) relative
quality factor and (d) relative loss factor of Mn0.5Zn0.5Fe2O4 for different sintering temperature.
Figure 4.9(a) and 4.9(b) show the frequency dependence of complex permeability of the sample
Mn0.5Zn0.5Fe2O4 sintered at Ts = 1220 and 1240 oC. It is observed that µ' is substantially high
leading to a value of 547 and 457 respectively. Increasing sintering temperature has effect of
increasing permeability possibly due to increased grain size and density. It is observed that the
real component of permeability ' is fairly constant with frequency up to certain low frequency,
rises slightly and then falls rather rapidly to a very low value at a high frequency. The imaginary
component '' first rises slowly and then increases quite abruptly making a peak at a certain
frequency (called resonance frequency, fr) where the real component ' starts falling sharply.
This phenomenon is attributed to the natural resonance. The resonance frequency peaks are the
results of the absorption of energy due to matching of the oscillation frequency of the magnetic
102
103
104
0
100
200
300
400
500
600
457
547
Rea
l p
art
of
Perm
ea
bil
ity
Frequency,f(Hz)
a) Mn0.5
Zn0.5
Fe2O
4
Ts=12200C
Ts=12400C
102
103
104
0
50
100
150
200
250
Frequency,f (Hz)
147
174
Im
ag
ina
ry p
art
of
Per
mea
bil
ity
Ts=12200C
Ts=12400C
b) Mn0.5
Zn0.5
Fe2O
4
101
102
103
104
0
2
4
6
8c)
Ts=12200C
Ts=12400C
6389
7686
Mn0.5
Zn0.5
Fe2O
4
RQ
FX
10
-3
Frequency,f (Hz)10
110
210
310
40.0
0.2
0.4
0.6
0.8d)
Ts=12200C
Ts=12400C
Mn0.5
Zn0.5
Fe2O
4
Frequency,f (Hz)
RL
FX
10
3
Chapter-IV Results and Discussion
113
dipoles and the applied frequency. The resonance frequency was determined from the maximum
of imaginary permeability of the ferrites. The resonance frequency of both the samples are
around 4 103 Hz, which means that they are more or less suitable for application at frequency
less than 1 106
Hz as can be seen from the maximum of RQF (7686) from Fig. 4.9(c) which is
around ≈ 0.3 103
Hz. This means that this material can be used in the frequency range 0.3 103
Hz. Fig. 4.9(d) shows the minimum RLF is around 0.3 103 Hz with a value of 1.28 10
-4 for the
sample with Ts = 1240 oC /3 h.
Fig. 4.10: Frequency dependence (a) initial permeability ('), (b) imaginary permeability (''), (c) relative
quality factor and (d) relative loss factor of Mg0.5Zn0.5Fe2O4 for different sintering temperature.
In Fig. 4.10(a) and 4.10(b), frequency dependence of complex permeability (' and '') are
shown for Mg0.5Zn0.5Fe2O4 ferrites sintered at 1300 o
C with time 1−4 h, 1325 oC and 1350
oC
with time 1 h. It is observed that the initial permeability ' is fairly constant with frequency up to
104
105
106
107
108
50
100
150
200
250
300
350
222
229
242
297
306a)
Rea
l p
art
of
Per
mea
bil
ity
Mg0.5
Zn0.5
Fe2O
4
Frequency,f (Hz)
Ts=1300oC/1 h
Ts=1300oC/2 h
Ts=1300oC/4 h
Ts=1325oC/1 h
Ts=1350oC/1 h
105
106
107
1080
30
60
90
120
73
75
80
106
113b)
Im
ag
ina
ry p
art
of
Per
mea
bil
ity
Mg0.5
Zn0.5
Fe2O
4
Ts=1300oC/1 h
Ts=1300oC/2 h
Ts=1300oC/4 h
Ts=1325oC/1 h
Ts=1350oC/1 h
Frequency,f (Hz)
104
105
106
107
0
20
40
60
80
100
55985861
6076
7063
8674
Ts=1300oC1h
Ts=1300oC2h
Ts=1300oC3h
Ts=1325oC1h
Ts=1350oC1h
c) Mg0.5
Zn0.5
Fe2O
4
Frequency,f (Hz)
RQ
FX
10
-2
104
105
106
107
0.0
0.2
0.4
0.6
1.16E-4
1.43E-4
1.64
E-4
1.78E-4
1.86E-4
d)
Ts=1300oc/1 h
Ts=1300oc/2 h
Ts=1300oc/4 h
Ts=1325oc/1 h
Ts=1350oc/1 h
Mg0.5
Zn0.5
Fe2O
4
Frequency,f (Hz)
RL
FX
10
3
Chapter-IV Results and Discussion
114
5 106
Hz, thereafter rises slightly and then falls rather rapidly to a very low value at higher
frequency. This phenomenon is known as dispersion of initial permeability. This is due to the
domain wall displacements or domain rotation or both of these contributions [37]. As decreasing
' at higher frequencies is due to the fact that at higher frequencies impurifies between grains and
intragranular pores act as pining points and increasingly hinder the motion of spin and domain
walls therby decreasing their contribution to permeability [38]. The imaginary component ''
first rises slowly and then suddenly rises with steep slope which passes through a maxima known
as resonance frequency before falling to lower value. The resonance frequency peaks are the
results of the absorption of energy due to matching of the oscillation frequency of the magnetic
dipoles and the applied frequency. The resonance frequency was determined from the maximum
of imaginary permeability of the ferrites.
Figure 4.10(c) and 4.10(d) show the frequency dependence of relative quality factor and relative loss
factor of sample Mg0.5Zn0.5Fe2O4 sintered at Ts = 1300, 1325 and 1350 oC with different sintering time (as
shown inside the graph). The variation of the RQF and RLF with frequency showed a similar trend for all
the samples. RQF increases with an increase of frequency, showing a peak and then decreases
with frequency. This happens at the frequency where the permeability begings to drop. This
phenomenon is associated with the ferromagnetic resonance within the domains [29] and at the
resonance, maximum energy is transferred from the applied magnetic field to the lattice resulting
in the rapid decrease in RQF.
Figure 4.11(a) and 4.11(b) show the frequency dependent permeability dispersion of Cu0.5Zn0.5Fe2O4
ferrites sintered at 1000 and 1050 °C with time 0.5−3 h. Initial permeability shows flat profile from 1 kHz
to 120 MHz indicating good low frequency stability for the sample and its dispersion occurs slightly
above 1 107
Hz frequency. This dispersion occurs because the domain wall motion plays a relatively
important role when the spin rotation reduces [39]. It is clearly seen from Fig. 4.11(a) that the
permeability is very much affected with sintering time. The permeability for the sample sintered
at Ts = 1050 °C with time 1 h shows maximum, whereas the permeability of the same sintering
temperature with lower sintering time (0.5 h) shows minimum. The permeability for the sample
sintered at 1000 oC increases with increasing sintering time. It is also seen from Fig. 4.11(b) that
the imaginary part associated with loss factor increases with increase in frequency beyond (5–10)
106
Hz. For all the samples, the imaginary part of permeability rises rapidly near the resonance
Chapter-IV Results and Discussion
115
frequency of around (1–5) 107
Hz. Resonance frequency of the prepared samples were found to
be between 2 107 and 6 10
7 Hz.
Fig. 4.11: Frequency dependence (a) initial permeability ('), (b) imaginary permeability (''), (c) relative
quality factor and (d) relative loss factor of Cu0.5Zn0.5Fe2O4 for different sintering temperature.
The relative quality factor and relative loss factor for the sample Cu0.5Zn0.5Fe2O4 sintered at Ts
= 1000 and 1050 °C with different time are shown in Fig. 4.11(c) and 4.11(d), respectively. It is
found that the maximum RQF (5805) value at Ts =1050 °C/1 h and the minimum value of RLF
1.99 10-4
at same sintering temperature and time. Low RQF (3481) is required for high
frequency magnetic applications. The loss is due to lag of domain wall motion with respect to the
applied alternating magnetic field and is attributed to various domain wall defects. This
improvement of RQF may be attributed to Zn substitution which is expected to increase the
saturation magnetization Ms and decrease of anisotropy constant K1.
104
105
106
107
108
0
50
100
150
200
250
Rea
l p
art
of
Per
mea
bil
ity
115
126
148
183
192
a) Cu0.5
Zn0.5
Fe2O
4
Frequency, f (Hz)
Ts= 1000
oc/1 h
Ts= 1000
oc/2 h
Ts= 1000
oc/3 h
Ts= 1050
oc/0.5 h
Ts= 1050
oc/1 h
105
106
107
108
0
25
50
75
100
Im
ag
ina
ry p
art
of
Per
mea
bil
ity
52
60
67
7982
Frequency, f (Hz)
b) Cu0.5
Zn0.5
Fe2O
4
Ts= 1000
oc/1 h
Ts= 1000
oc/2 h
Ts= 1000
oc/3 h
Ts= 1050
oc/0.5 h
Ts= 1050
oc/1 h
104
105
106
107
108
0
1
2
3
4
5
6
34813481
4565
3853
5805
Ts= 1000
oc/1 h
Ts= 1000
oc/2 h
Ts= 1000
oc/3 h
Ts= 1050
oc/0.5 h
Ts= 1050
oc/1 h
c) Cu0.5
Zn0.5
Fe2O
4
Frequency,f (Hz)
RQ
FX
10
-3
103
104
105
106
107
108
0.0
0.1
0.2
0.3
1.99E-4 2.15E-4
2.8
2E
-4
2.5
4E
-4
2.92E-4
c)
Ts= 1000
oc/1 h
Ts= 1000
oc/2 h
Ts= 1000
oc/3 h
Ts= 1050
oc/0.5 h
Ts= 1050
oc/1 h
Cu0.5
Zn0.5
Fe2O
4
Frequency,f (Hz)
RL
FX
10
2
Chapter-IV Results and Discussion
116
Fig. 4.12: Frequency dependence (a) initial permeability ('), (b) imaginary permeability (''), (c) relative
quality factor and (d) relative loss factor of Co0.5Zn0.5Fe2O4 for different sintering temperature.
Figure 4.12 (a) and 4.12(b) represents the results of the real part, µ' and imaginary part, µ'' of the
permeability as a function of frequency of Co0.5Zn0.5Fe2O4 ferrite samples sintered at 1125 and
1175 oC with time 2 h. It is observed that the real component of permeability, µ' is not constant
with frequency, but rather decreases very sluggishly up to high frequency of 13 106
Hz. The
resonance frequency for Co-Zn ferrite could not be determined precisely possible due to
experimental uncertainty. When ferrite specimens are subjected to an AC field, permeability
shows several dispersions: as the field frequency increases, the various magnetization
mechanisms become unable to follow the AC field. The dispersion frequency for each
mechanism is different, since they have different time constant. The low frequency dispersions
are associated with domain wall dynamics [40] and high frequency to spin rotation.
103
104
105
106
107
0
100
200
300
400
500
600
(412)
(487)
a)
Ts=11250C
Ts=11750C
Frequency,f(Hz)
Rea
l p
art
of
Perm
ea
bil
ity Co
0.5Zn
0.5Fe
2O
4
104
105
106
107
0
1
2
3
4
2985
3504
c)
RQ
Fx10
-3
Frequency,f (Hz)
Ts=11250C
Ts=11750C
Co0.5
Zn0.5
Fe2O
4
101
102
103
1040.0
0.2
0.4
0.6
0.8
1.0
1.2d)
3.24E-4
3.97E-4
Ts=1125oC/2 h
Ts=1175oC/2 h
Co0.5
Zn0.5
Fe2O
4
Frequency,f (Hz)
RL
FX
10
3
Chapter-IV Results and Discussion
117
Figure 4.12(c) and 4.12(d) show the relative quality factor and relative loss factor of the same
samples. Both of these two quantities are shown here for a better understanding for the merit of
the prepared materials for an inductor device application. Since cobalt ferrite is the only spinel
ferrite which is not soft, but semi hard magnetic materials, RLF values were found abrupt and the
values were 3.97 10-4
and 3.24 10-4
at Ts = 1125 and 1175 oC, respectively.
It is found that the initial permeability of all studied samples is reasonably high. The value
ranges between 547 and 115. Higher values are observed for Ni-Zn Mg-Zn and Mn-Zn ferrites.
A very high value of RQF or extraordinary low value of RLF is found. It is also observed that the
permeability increases with the increase of sintering temperature possibly due to increased grain
size and density. A drastic fall of permeability at T = Tc is noticed for all the studied samples,
implying that the samples are quite homogenous and single phase in line with XRD result. The
results show that ferrite with high magnetization and reasonably lower Curie temperature is
suitable for high permeability inductor materials. Ni-Zn and Mg-Zn ferrites have been found to
demonstrate reasonably good permeability at room temperature covering a wide range of
frequencies indicating the possibilities for applications as high frequency inductor and/or core
material, while Mn-Zn ferrite shows quite high permeability up to lower frequency range of less
than 1 MHz. This means that Mn-Zn ferrite materials are suitable for low frequency applications
with high permeability.
Chapter-IV Results and Discussion
118
REFERENCES
[1] J. Smit and H. P. J. Wijn, “Ferrites‟‟, John Wily & Sons, New York (1959).
[2] R. D. Shannon and C. T. Prewitt, “Effective ionic radii in oxides and fluorides‟‟, Acta
Crystallogr., 25 (1969) 925−946.
[3] R. Islam, M. A. Hakim, and M. O. Rahman. “Effect of sintering temperature on initial
permeability of Ni0.65Zn0.35Fe2O4 ferrites prepared by using nanoperticles‟‟, International
Conference on Recent Advance in Physics, University of Dhaka, Bangladesh, 27−29 March
(2010) 70.
[4] R. Islam, M. A. Hakim, and M. O. Rahman. “Effect of sintering temperature on initial
permeability of Ni0.55Zn0.45Fe2O4 ferrites prepared by using nanoperticles‟‟, Mater. Sci. Appl.,
03 (2012) 326−331.
[5] R. Islam, M. A. Hakim, and M. O. Rahman. “Study of Mn-Zn ferrites and effect of substitution
(Ni2+
,Gd3+
) ions on the eletromagnetic properties‟‟, Ph. D. Thesis, Department of Physics,
Jahangir Nagar University, ( 2012).
[6] M. M. Haque, M. K. Islam, and M. A. Hakim. “Structural, magnetic and electrical properties of
Mg-based soft Ferrite‟‟. Ph. D. Thesis, Department of Physics, BUET, (2008).
[7] K. H. Maria, S. Choudhury, and M. A. Hakim, “Structural phase transformation and hysteresis
behavior of Cu-Zn ferrites‟‟, Inter. Nano. Lett., 3:42 (2013) 1–10.
[8] S. Noor, R. Islam, S. S. Sikder, A. K. M. Hakim and M. Hoque. “Effect of Zn on the magnetic
ordering and Y-K angles of Co1-xZnxFe2O4 Ferrites‟‟. J. Mater. Sci. Engg., A01 (2011)
1000−1003.
[9] A. A. Sattar, H. M. El-Sayed, K. M. El-Shokrofy, and M. M. El-Tabey, “Improvement of
themagnetic properties of Mn-Ni-Zn ferrite by the nonmagnetic Al3+
ion substitution‟‟, J. Appl.
Sci., 5(1) (2005) 162.
[10] W. D. Kigery, H. K. Bowen, and B. R. Uhlamann, “Introduction of Ceramics‟‟ John Wiley &
Sons, New York 458.
[11] A. Globus, H. Pascard, and V. J. Cagan: “Distance between magnetic ions and fundamental
properties in ferrites‟‟, J. De Phys. Colloque C1(38) (1977) 163–168.
[12] M. A. Hakim, S. K. Nath, S. S. Sikder, and K. H. Maria, “Cation distribution and
electromagnetic properties of spinel type Ni-Cd ferrites‟‟. J. Phys. Chem. Solids, 74 (2013)
1316−1321.
[13] A. Muhammad and A. Maqsood, “Structural, electrical and magnetic properties of
Cu1xZnxFe2O4 (0 ≤ x ≤1)‟‟, J. Alloy compds., 460 (2008) 54−59.
[14] T. Abbas, M. U. Islam, and M. A. Choudhury, “Study of sintering behavior and electrical
properties of Cu-Zn-O system‟‟, Modern Phys. Lett., B9 (1995) 1419−1426.
[15] C. Kittle, “Introduction to Solid State Physics‟‟, John Wiley & Sons, New York (1976).
[16] A. K. M. A. Hossain , T. S. Biswas , S. T. Mahmud , T. Yanagida, and H. Tanaka,
“Investigation of structural and magnetic properties of polycrystalline Ni0.50Zn0.5MgxFe2O4
spinel ferrites‟‟. J. Magn. Magn. Mater., 321 (2009) 81−87.
[17] C. B. Kolekar, P. N. Kamble, and A. S. Vaingankar, “Structural and DC electrical resistivity
study of Nd3+
substituted Zn-Mg ferrites‟‟, J. Magn. Magn. Mater., 138 (1994) 211–215.
[18] A. A. Sattar, H. M. El-Sayed, K. M. El-Shokrofy, and M. M. El-Tabey, “Improvement of the
magnetic properties of Mn- Ni- Zn ferrite by the non magnetic Al3+
ion substitution‟‟, J. Appl.
Sci., 5(1) (2005) 162–168.
Chapter-IV Results and Discussion
119
[19] S. S. Bellad, S. C Watawe, A. M. Shaikh, and B. K Chougule, “Cadmium substituted high
permeability lithium ferrite‟‟, Bull. Mater. Sci., 23 (2000) 83–85.
[20] L. Neel, “Magnetic properties of ferrites: Ferrimagnetism and Antiferromagnetism‟‟, Ann.
Phys., 3 (1948) 137−198.
[21] G. Mumcu, K. Serlet, J. L. Volakis, A. Figotin, and I. Vitebsky, “RF propagation in ferrite
thickness nonreciprocal magnetic photonic crystals‟‟, IEEE Antenna Propagant. Soc. Symp,. 2
(2004) 1395–1398.
[22] B. P. Ladgaonkar, P. N. Vasambekar, and A. S. Vaingankar, “Effect of Zn2+
and Nd3+
substitution on magnetisation and AC susceptibility of Mg ferrite”, J. Magn. Magn. Mater.,
210 (2000) 289–294.
[23] B. D. Cullity, “Elements of X-ray diffraction”, Addison Wesley Pub., USA (1978).
[24] C. M. Srivastava, S. N. Shringi, R. G. Srivastava, and N. G. Nandikar, “Magnetic ordering and
domain-wall relaxation in zinc-ferrous ferrite”, Phys. Rev., B14 (1976) 2032.
[25] R. N. Bhowmik and R. Ranganathan, “Anomaly in cluster glass behavior of Co0.2Zn0.8Fe2O4
spinel oxide”, J. Magn. Magn. Mater., 248 (2002) 101.
[26] R. Valenzuela, “Magnetic Ceramic‟‟, Cambridge University press, Cambridge (1994).
[27] S. Chikazumi, “Physics of Magnetism”, John Wiley & Sons, New York (1966).
[28] G. C. Jain, B . K. Das, R. S. Khanduja, and S. C. Gupta, “Effect of intragranular porosity of
initial permeability and coercive force in a manganese zinc ferrite”, J. Mater. Sci, (1976) 1335.
[29] F. G. Brockman, P. H. Dowling, and W. G. Steneck, “Dimensional effects resulting from a high
dielectric constant found in a ferromagnetic ferrite‟‟, Phys. Rev., 77 (1950) 85−93.
[30] E. C. Snelling, “Soft Ferrites: Properties and Applications”, Iliffe Books Ltd., London (1969).
[31] J. L. Snoek, “Dispersion and absorption in magnetic ferrites at frequencies above one Mc/s‟‟,
Physica, XIV (1948) 207−217.
[32] A. Globus, P. Duplex, and M. Guyot, “Determination of initial magnetization curve from
crystallites size and effective anisotropy field‟‟, IEEE Trans. Magn., 7 (1971) 617−622.
[33] S. M. Patange, S. E. Shirsath, B. G. Toksha, S. S. Jadhav, S. J. Shukla, and K. M. Jadhab,
“Cation distribution by rietveld spectral and magnetic studies of chromium-substituted nickel
ferrites‟‟, J. Appl. Phys., A95 (2009) 429–434.
[34] A. K. M. A. Hossain and M. L. Rahman, “Enhancement of microstructure and initial
permeability due to Cu substitution in Ni0.50-xCuxZn0.5Fe2O4ferrites‟‟, J. Magn. Magn. Mater.,
323 (2011) 1954−1962.
[35] A .M. Abdeen, “Electric conduction in Ni-Zn ferrites”, J. Magn. Magn. Mater., 185 (1998) 199.
[36] K. J. Overshott, “The causes of the anomalous loss in amorphous ribbon materrials‟‟, IEEE
Trans. Magn., 17 (1981) 2698−2700.
[37] R. B. Pujar, S. S. Bellad, S. C. Watawe, and B. K. Chougule, “Magnetic properties and
microstructure of Zr4+
-substituted Mg-Zn ferrites”, Mater. Chem. Phys., 57 (1999) 264.
[38] S. H. Seo and. J. H. Oh, “Effect of MoO3 addition on sintering behaviors and magnetic
properties of NiCuZn ferrite for multilayer chip inductor”, IEEE Trans. Magn., 35(5) (1999)
3412.
[39] M. U. Islam, M. A. Chaudhry, T. Abbas, and M. Umar, “Temperature dependent electrical
resistivity of Co-Zn-Fe-O system”, J. Mater. Chem. and Phys., 48 (1997) 227.
[40] O. F. Caltun, L. Spinu, Al. Stancu, L. D. Thung, and W. Zhou, “Study of the microstructure and
of the permeability spectra of Ni-Zn-Cu ferrites‟‟, J. Magn. Magn. Mater., 242−245 (2002)
160−162.
120
CHAPTER−V
CONCLUSIONS
5.1 Conclusions
Ferrites as magnetic materials have enormous potential from the applications point of views
especially those with high magnetization and subsequently high permeability. This unique
combination is found in ferrite compositions substituted with non-magnetic Zn2+
. In such case
the magnetization increases to high value compared with their base compositional counterpart
due to their cation distribution in A and B sublattices. A detail structural and magnetic
characterization of spinel ferrites having general formula A0.5B0.5Fe2O4 (where, A = Ni2+
, Mn2+
,
Mg2+
, Cu2+
, Co2+
and B = Zn2+
) have been carried out to find out their possible potential
applications in inductor devices which requires high magnetization and high permeability. From
our study the following findings and conclusions can be summarized:
All the studied samples of composition A0.5B0.5Fe2O4 (where, A = Ni2+
, Mn2+
, Mg2+
,
Cu2+
, Co2+
and B = Zn2+
) were found signal phase cubic spinel structure as confirmed
by X-ray diffraction study.
Lattice parameter ‘a’of the samples were found to be larger than base ferrite (without
Zn substitution) due to larger ionic radii of Zn2+
. This enhancement of ‘a’ obviously
expands the lattice resulting in decrease of the strength of JAB interaction.
A substantial reduction of Curie temperature Tc was observed for all the samples
resulting from the weakening of A-B exchange interaction due to non-magnetic Zn2+
substitution which preferentially occupies tetrahedral A-site. Some samples display
Hopkinson peak with sharp rise of permeability just before the Tc, possibly due to
substantial decrease of anisotropy constant K1 as a result of Zn substitution and
appropriate sintering of the sample. The weakening of A-B exchange interaction is
attributed to the enhancement of lattice parameter due to Zn2+
substitution. A drastic
fall of permeability at T = Tc is noticed for all the studied samples, implying that the
samples are quite homogeneous and single phase in line with XRD result.
Chapter-V Conclusions
121
Theoretical density was found to be larger for all the Zn substituted samples
compared with the bulk density. The lower bulk density of the sintered samples may
be attributed to inevitable existence of pores during sample processing.
The bulk densities for the prepared samples were between 4.95 and 4.26 g/cm3. The
porosity calculated from the theoretical and bulk density was in the range of 5.64%
for Mg0.5Zn0.5Fe2O4 and 17.6% for Mn0.5Zn0.5Fe2O4 ferrites.
Magnetization (emu/g) was measured using a VSM for all the samples. A large
increase of magnetization value compared with their base counterpart has been
observed. This increase of magnetization was attributed to non-magnetic substitution
of Zn2+
as a result of their preferential A-site occupancy and modification of cation
distribution of Fe3+
. Magnetization values of the studied samples at T = 100 K is
found to be much higher than at T = 300 K (room temperature). But still these values
of magnetization converted into Bohr magneton when compared with that of the
theoretical magnetic moment (considered at T = 0 K) are much lower due to the effect
of thermal energy, kBT at the measured temperature of 100 K and 300 K. The values
of Ms for all the samples are really very high which is a good requirement for any
inductor material.
Initial permeability of all studied samples is reasonably high. The value ranges
between 547 and 115. Higher values were observed for Ni-Zn, Mg-Zn and Mn-Zn
ferrites. It was also observed that the permeability increased with the increase of
sintering temperature.
The results of magnetization and permeability for Ni-Zn, Mg-Zn and Mn-Zn ferrites
suggest that these materials are suitable for inductor applications.
5.2 Suggestion for Future Work
With the development and advancement of nanotechnology a tremendous growth in research on
miniaturization and high efficiency electronic devices is taking place. The studied ferrites are
suitable for these devices for future the advanced technology. Therefore future work on these
types of system may be carried out using nanoparticle and nanosysthesis techniques for the
development of efficient miniaturized device for advance technology.
Chapter-V Conclusions
122
Some studied on different aspects are possible for fundamental interest and also for potential
applications of the studied materials.
Neutron diffraction analysis may be performed for these compositions to determine the
distribution of substituted ions A- and B-sites. Mossbauer spectroscope can also be
studied.
AC and DC electrical properties may be studied.
SEM can be studied for better understand surface nature and domain wall motion.
123
APPENDIX
Stoichiometric calculation of the studied samples
The weight percentage of the oxide to be mixed for various samples was calculated by using
formula:
Weight % of oxide =sampleainoxideeachofwtMolofSum
sampletheofweightrequiredoxideofwtMol
..
..
Required each sample weight = 10 g
For Ni-Zn ferrite: (1-x) NiO + xZnO + Fe2O3 Ni1-xZnxFe2O4
Or, 0.5NiO + 0.5ZnO + Fe2O3= Ni0.5Zn0.5Fe2O4 (x = 0.5)
Or, 0.5(58.693+16) + 0.5(65.37+16) + (55.852+163) = (58.6930.5+65.37x0.5+562+164)
Or, 37.35 + 40.68 + 159.7 = 237.73
571110.173.237
1035.37
NiO g
711185.173.237
1068.40
ZnO g
717705.673.237
107.15932
OFe g
For Mn-Zn ferrite: (1-x) MnO + xZnO + Fe2O3 Mn1-xZnxFe2O4
Or, 0.5MnO + 0.5ZnO + Fe2O3 = Mn0.5Zn0.5Fe2O4 (x = 0.5)
Or, 0.5(54.94+16) + 0.5(65.37+16) + (55.852+163) = (54.940.5+65.370.5+55.852+164)
Or, 35.47 + 40.68 + 159.7 = 235.85
∴ 503922.185.235
1047.35
MnO g
For Mg-Zn ferrite: (1-x) MgO + xZnO + Fe2O3 Mg1-xZnxFe2O4
Or, 0.5MgO + 0.5ZnO + Fe2O3= Mg0.5Zn0.5Fe2O4 (x = 0.5)
Or, 0.5(24.31+16) + 0.5(65.37+16) + (55.852+163) = (24.310.5+65.370.5+55.852+164)
Or, 20.155+ 40.68 + 159.7 = 220.535
Appendix
124
913913.0535.220
10155.20
MgO g
For Cu-Zn ferrite: (1-x) CuO + xZnO + Fe2O3 Cu1-xZnxFe2O4
Or, 0.5CuO + 0.5ZnO + Fe2O3= Cu0.5Zn0.5Fe2O4 (x = 0.5)
Or, 0.5(63.54+16) + 0.5(65.37+16) + (55.852+163) = (63.540.5+65.370.5+55.852+164)
Or, 39.77 + 40.68 + 159.7 = 240.15
656048.115.240
1077.39
CuO g
For Co-Zn ferrite: (1-x) CoO + xZnO + Fe2O3 Co1-xZnxFe2O4
Or, 0.5CoO + 0.5ZnO + Fe2O3= Co0.5Zn0.5Fe2O4 (x = 0.5)
Or, 0.5(58.9+16) + 0.5(65.37+16) + (55.852+163) = (58.90.5+65.370.5+55.852+164)
Or, 37.45 + 40.68 + 159.7 = 237.83
574654.183.237
1045.37
CoO g
AO (g) ZnO (g) Fe2O3 (g)
Ni = 1.571110 1.711185 6.717705
Mn = 1.503922 1.724825 6.771253
Mg = 0.913914 1.844605 7.241481
Cu = 1.656048 1.693941 6.650011
Co = 1.574654 1.710455 6.714881
Theoretical calculation of lattice parameter
For Ni0.5Zn0.5Fe2O4 ferrite:
00 333
8RrRra BAth
)()( 32
FerCZnrCr eBFAZnA = 0.5 0.74+ 0.5 0.645 = 0.37+ 0.3225 = 0.6925
)]()([2
1 32 FerCNirCr BFeBNiB = ½[(0.50.69) + (1.5+0.645)] = 0.65625
)32.165625.0(3)32.16925.0(33
8 tha 5268885.30725.2
33
8 = 8.368 Å
Appendix
125
For Mn0.5Zn0.5Fe2O4 ferrite:
rA = 0.5 0.74+ 0.5 0.645 = 0.6925
rB = ½[(0.50.83) + (1.5+0.645)] = 0.69125
00 333
8RrRra BAth )32.169125.0(3)32.16925.0(
33
8 = 8.461 Å
For Mg0.5Zn0.5Fe2O4 ferrite:
rA = 0.5 0.74+ 0.5 0.645 = 0.6925
rB = ½[(0.50.72) + (1.5+0.645)] = 0.66375
00 333
8RrRra BAth )32.1666625.0(3)32.16925.0(
33
8 = 8.388 Å
For Cu0.5Zn0.5Fe2O4 ferrite:
rA = 0.5 0.74+ 0.5 0.645 = 0.6925
rB = ½[(0.50.73) + (1.5+0.645)] =0.66625
00 333
8RrRra BAth
)32.166625.0(3)32.16925.0(33
8 = 8.395 Å
For Co0.5Zn0.5Fe2O4 ferrite:
rA = 0.5 0.74+ 0.5 0.645 = 0.6925
rB = ½[(0.50.72) + (1.5+0.645)] =0.66375
00 333
8RrRra BAth )32.166375.0(3)32.16925.0(
33
8 = 8.388 Å
Calculation of X-ray density
For Ni0.5Zn0.5Fe2O4 ferrite:
3
311339.5
)369.8(1002.6
725.23788
gcm
Na
Md x
For Mn0.5Zn0.5Fe2O4 ferrite:
3
311317.5
)461.8(1002.6
845.23588
gcm
Na
Md x
Appendix
126
For Mg0.5Zn0.5Fe2O4 ferrite:
3
311396.4
)388.8(1002.6
53.22088
gcm
Na
Md x
For Cu0.5Zn0.5Fe2O4 ferrite:
3
311338.5
)395.8(1002.6
11.24088
gcm
Na
Md x
For Co0.5Zn0.5Fe2O4 ferrite:
3
311321.5
)388.8(1002.6
805.23788
gcm
Na
Md x
Calculation of porosity
For Ni0.5Zn0.5Fe2O4 ferrite:
%16.8%100)39.5
95.41(%100)1(
x
B
d
dP
For Mn0.5Zn0.5Fe2O4 ferrite:
%60.17%100)17.5
26.41(%100)1(
x
B
d
dP
For Mg0.5Zn0.5Fe2O4 ferrite:
%64.5%100)96.4
68.41(%100)1(
x
B
d
dP
For Cu0.5Zn0.5Fe2O4 ferrite:
%55.8%100)38.5
90.41(%100)1(
x
B
d
dP
For Co0.5Zn0.5Fe2O4 ferrite:
%75.5%100)21.5
91.41(%100)1(
x
B
d
dP