structural and magnetic characterization of spinel

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


DHAKA UNIVERSITY OF ENGINEERING & TECHNOLOGY

GAZIPUR, BANGLADESH

MARCH, 2015

DHAKA UNIVERSITY OF ENGINEERING & TECHNOLOGY (DUET), GAZIPUR


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


DUET, Gazipur

5. _______________________________

DR. SHIBENDRA SHEKHER SIKDER Member (External)


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


permeability (''), (c) relative quality factor (RQF) and (d) relative loss factor (RLF) of Mn0.5Zn0.5Fe2O4 for different sintering temperature.

112


permeability (''), (c) relative quality factor (RQF) and (d) relative loss

factor (RLF) of Mg0.5Zn0.5Fe2O4 for different sintering temperature.

113


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


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


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


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]


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.


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.


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 intrasublattice 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


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


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


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).


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.


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


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


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.


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


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


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-


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).


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.


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.


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.


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.


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.

http://www.wordiq.com/definition/Electric_charge

http://www.wordiq.com/definition/Magnetic_moment

http://www.wordiq.com/definition/South_pole

http://www.wordiq.com/definition/North_pole

http://images.search.yahoo.com/images/view;_ylt=A0PDoX5PqyZPXXMAfzuJzbkF;_ylu=X3oDMTA3cnMybzJvBHNsawNpbWc-?back=http://images.search.yahoo.com/search/images?_adv_prop=image&va=magnetic+dipole&fr=yfp-t-701&tab=organic&ri=12&w=200&h=150&imgurl=wikipremed.com/image_science_archive_th/010403_th/142100_Magnetic_dipole_moment_68.jpg&rurl=http://www.wikipremed.com/image_archive.php?code=010403&size=25.7+KB&name=Bar+magnet+dipole+moment.&p=magnetic+dipole&oid=b4c13c8a7f05597dc4fe8eddc5ac1842&fr2=&fr=yfp-t-701&tt=Bar+magnet+dipole+moment.&b=0&ni=84&no=12&tab=organic&ts=&sigr=11nq2jl75&sigb=13eubu8tq&sigi=12mgsic3v&.crumb=LsgHGBkw45x


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)

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

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


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


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)


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.


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.


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.


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)


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.


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.


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


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.


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.


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.


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


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.


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


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


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.


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


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.


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


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


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


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.


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.


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-


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


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-


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


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.


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).

http://en.wikipedia.org/wiki/Isis_(journal)

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


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


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


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.


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


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


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.

http://serc.carleton.edu/research_education/geochemsheets/BraggsLaw.html


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.


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.


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


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


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


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.


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


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


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


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


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


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)


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


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.


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.


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)


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


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].


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


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].


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)


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


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


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.


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].


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

)


0 1 2 3 4 50

20

40

60

80

Ms (

em

u/g

)


(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

)


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

)


(e)

300 K, Ms = 91.4 (emu/g)

100 K, Ms = 101.5 (emu/g)


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.


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].


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)


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,


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


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


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


2

4

3

5.1

2

5.0

3

5.0

2

5.0)( OFeCuFeZn

BA


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


2

4

3

5.1

2

5.0

3

5.0

2

5.0)( OFeCoFeZn

BA


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.


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


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’’


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’’


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


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’’


105

Fig. 4.6: Variation of permeability with temperature for Cu0.5Zn0.5Fe2O4 at (a) 1000 °C with time 1 h and


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


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’’


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].


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


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


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)


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.


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.


112


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


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.


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


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


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.


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


116


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


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.


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.


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


3

311339.5

)369.8(1002.6

725.23788

gcm

Na

Md x


3

311317.5

)461.8(1002.6

845.23588

gcm

Na

Md x

Appendix

126


3

311396.4

)388.8(1002.6

53.22088

gcm

Na

Md x


3

311338.5

)395.8(1002.6

11.24088

gcm

Na

Md x


3

311321.5

)388.8(1002.6

805.23788

gcm

Na

Md x

Calculation of porosity


%16.8%100)39.5

95.41(%100)1(

x

B

d

dP


%60.17%100)17.5

26.41(%100)1(

x

B

d

dP


%64.5%100)96.4

68.41(%100)1(

x

B

d

dP


%55.8%100)38.5

90.41(%100)1(

x

B

d

dP


%75.5%100)21.5

91.41(%100)1(

x

B

d

dP

structural and magnetic characterization of spinel

Documents