FABRICATION AND CHARACTERIZATION

FABRICATION AND CHARACTERIZATION

OF TERBIUM SUBSTITUTED FERRITES

Ph.D. Thesis

Muhammad Azhar Khan

A Thesis Submitted in Fulfillment of the Requirement for the Degree of Doctor of Philosophy in Physics

DEPARTMENT OF PHYSICS

BAHAUDDIN ZAKARIYA UNIVERSITY

MULTAN – PAKISTAN

(2011)

DEDICATED

To

My Parents and Family

CERTIFICATE

This is to certify that Mr. Muhammad Azhar Khan has carried out the

experimental work in this dissertation under my supervision in the Department of

Physics, Bahauddin Zakariya, University, Multan, Pakistan and the Department of

Physics, University of Limerick, Ireland. This work is accepted in its present form

by the Department of Physics, Bahauddin Zakariya, University, Multan as

satisfying the dissertation requirement for the degree of Doctor of Philosophy in

Physics.

Submitted through: Supervisor:

Dr. Misbah-ul-Islam

Chairman, Department of Physics

Department of Physics Bahauddin ZakariyaUniversity

Bahauddin Zakariya University Multan, Pakistan.

Multan, Pakistan.

Declaration

I hereby declare that I have not submitted this research work titled “Fabrication and

Characterization of Terbium Substituted Ferrites” leading to the degree of Ph.D. in

Physics to other university with in the country or outside Pakistan. I also promise not to

submit the same thesis for the degree of Ph.D. to any other university in future if I am

awarded Doctorate in this regard. Research work on the same topic has never been

submitted before to the best of my knowledge. The responsibility of the contents solely

lies on me.

Muhammad Azhar Khan

ACKNOWLEDGEMENTS

All praise to omnipotent Allah, the most merciful, who enabled me to complete

this thesis. I offer my deepest gratitude to the Holy Prophet Muhammad (Peace be upon

him) whose life is forever guidance for the humanity.

I would like to express my sincere gratitude to my supervisor Dr. Misbah Ul Islam,

Associate Professor, Department of Physics, Bahauddin Zakariya University Multan,

whose continuous guidance, stimulating suggestions and encouragement helped me at

every step during my Ph.D. research work. Many thanks to him for suggesting me this

kind of research project and guided me the ways to approach a research problem and the

need to be persistent to accomplish any goal.

I am grateful to Higher Education Commission of Pakistan (HEC) for the

financial support for this project under HEC Indigenous and International Research

Support Initiative Program (IRSIP). My deepest appreciation to the Chairman

Department of Physics, B. Z. University Multan and all the faculty members in helping

me to broaden my view and knowledge. I am really grateful to Prof. Dr. Tahir Abbas for

his scientific guidance and support during the progress of my work. Many thanks to my

friends; Mr. Muhammad Ishaque, Muhammad Farooq Wsiq and Abdul hameed for their

supprt and co-operation.

I can’t help with out appreciating and thanking for the unconditional support of

Dr. I. Z. Rahman, Department of Physics, Material and Surface Science Institute,

University of Limerick, Ireland, for providing lab facilities and valuable suggestions

during my Ph.D. work. I also pay thanks to Prof. Dr. Stuart Hampshire and Dr. Annaik

Genson for valuable suggestions and providing facilities for FTIR Spectroscopy and

dielectric measurements. Many thanks to Professor Carl E Patton at the Department of

Physics, Colorado State University, Fort Collins, USA for providing facilities for FMR

measurements. Last, but not the least, I thank my family and my parents, for giving me

life in the first place, for educating me in sciences, for unconditional support and

encouragement to pursue my research work.

Muhammad Azhar Khan

ABSTRACT

This dissertation presents the effect of terbium substitution on the structural, magnetic, electrical

and dielectric properties of ferrites of nominal compositions Ni1−xTbxFe2O4 and Mg1-xTbxFe2O4

(where x = 0, 0.02, 0.04, 0.06, 0.08, 0.10, 0.12, 0.14, 0.16, 0.18 and 0.20). The samples were

initially sintered at 1000 °C and final sintering was performed at 1230 °C in order to prepare

homogeneous ferrites. The said ferrites were characterized by X-ray Diffractometry, Fourier

Transform Infrared Spectroscopy, Scanning Electron Microscopy, Energy Dispersive X-ray

Spectroscopy, Vibrating Sample Magnetometery and Ferromagnetic Resonance.

Phase analysis from XRD patterns reveals that the samples have a cubic spinel structure along

with a few traces of second phase recognized as orthorhombic phase (TbFeO3) and this phase

becomes more conspicuous as the terbium (Tb) is substituted in Ni1−xTbxFe2O4 and Mg1-

xTbxFe2O4 ferrites. The lattice parameter changes non-linearly as a function of Tb content in both

series that was attributed to the differences in ionic radii of the cations involved and the solubility

limit of terbium ions. A gradual increase in the bulk density was observed with the increase of

terbium concentration in both series. FTIR absorption spectra of Ni1−xTbxFe2O4 and Mg1-

xTbxFe2O4 ferrites exhibited two main absorption bands in the wave number range 370 cm-1 to

1500 cm-1, thereby confirming the spinel structure. The particle size measured from XRD analysis

found to decrease with the increase of Tb substitution. The morphology of the samples indicates

that samples are crack free along with a few agglomerates. The inclusion of Tb caused the

magnetization index to drop which is due to redistribution of cations on the tetrahedral and

octahedral sites. The coercivity is observed to decrease and this trend is deviated at higher

concentrations of terbium ions in Ni1−xTbxFe2O4 and Mg1-xTbxFe2O4 ferrites.

Ferromagnetic resonance linewidths are ≤ 1000 Oe for most of the samples. The nominal

composition Ni.94Tb.06Fe2O4 have minimum linewidth, ΔH = 593 Oe, which is minimum of the

reported linewidths for spinel ferrites. Hence these ferrites have potential in high frequency

applications. The relative initial permeability generally decreases for all the Tb-substituted

samples and these are attributed to the decrease in magnetization. The magnetic loss factor is

damped with respect to frequency and has very low values in the high frequency region. The

electrical resistivity increases and it is attributed to the hinderence in the hopping mechanism

caused by the presence of Tb-ions in these ferrites which enhance hopping length between the

cations involved in the conduction mechanism. The study on resistivity as a function of

temperature shows that all the samples obey semiconducting behaviour. The drift mobility drops

while the activation energy increases in a similar manner as that of resistivity. The samples

NiFe2O4 and MgFe2O4 have high dielectric constant as compared to the substituted samples.

Hence, introduction of Tb-ions in Ni1−xTbxFe2O4 and Mg1-xTbxFe2O4 decrease the dielectric

constant. All the substituted samples indicate small values of dielectric loss. These features make

these ferrites suitable for various applications.

Table of Contents

Contents Page No

CHAPTER 1

Introduction 1

1.1 Soft ferrites 1

1.2 Literature review 2

1.3 Aims and objectives 46

References 47

CHAPTER 2

Experimental details 54

2.1 Composition of ferrites 54

2.2 Preparation technique 54

2.3 Characterization techniques 56

2.3.1 X-ray diffraction 56

2.3.2 Fourier transform infrared spectroscopy 58

2.3.2.1 Principle of FTIR 59

2.3.2.2 Sample preparation for FTIR 59

2.3.3 Dielectric constant measurements 59

2.3.4 Electrical resistivity measurements 60

2.3.5 Bulk density measurements 62

2.3.6 Scanning electron microscopy 63

2.3.7 Vibrating sample magnetometer 63

2.3.8 The ferromagnetic resonance (FMR) 63

2.3.9 Relative initial permeability measurements 65

References 65

CHAPTER 3

Theoretical background 66

3.1 Soft magnetic materials 66

3.2 Structure of ferrites 66

3.3 Electrical properties 69

3.3.1 Electrical resistivity 69

3.3.2 Conduction mechanisms 70

3.3.3 Hopping model of electrons 71

3.3.4 Small polaron model 72

3.4 Frequency dependence of dielectric constant in ferrites 73

3.5 Magnetic properties 74

3.5.1 Diamagnetic materials 74

3.5.2 Paramagnetic materials 74

3.5.3 Ferromagnetic materials 75

3.5.4 Antiferromagnetic materials 75

3.5.5 Ferrimagnetic materials 76

3.6 Magnetization in ferrites 76

3.7 Neel’s theory of ferrimagnetism 77

3.8 Saturation moments 79

3.9 The magnetic interactions 80

3.10 Domains in ferrites 82

3.11 Magnetostatic energy 83

3.12 Magnetocrystalline anisotropy energy 84

3.13 Magnetostrictive energy 84

3.14 Domain Wall energy 85

3.15 Hysteresis loop 86

3.16 Permeability 87

3.17 Ferromagnetic resonance 96

3.18.1 Ferromagnetic relaxation 98

3.18.2 Gilbert damping model 98

3.18.3 Landau-lifshitz model 99

3.18.4 Other ferromagnetic damping models 99

References 100

CHAPTER 4

Results and discussion 102

Ni1-xTbxFe2O4 Series 102

4.1 Structural analysis 102

4.2 Fourier transform infrared spectroscopy (FTIR) 110

4.3 Scanning electron microscopy (SEM) 115

4.4 Compositional analysis 118

4.5 Static magnetic properties 121

4.5.1 Magnetization 121

4.5.2 Coercivity 122

4.6 Magnetodynamics of Ni-Tb-Fe-O system 130

4.7 Relative initial permeability 137

4.7.1 Frequency dependent loss factor 139

4.8 DC electrical resistivity 141

4.8.1 Temperature dependent electrical resistivity 142

4.9 Dielectric properties 148

Mg1-xTbxFe2O4 Series 155

4.10 Structural analysis 155

4.11 Fourier transform infrared spectroscopy (FTIR) 164

4.12 Scanning electron microscopy (SEM) 169

4.13 Compositional analysis 172

4.14 Static magnetic properties 175

4.14.1 Magnetization 175

4.14.2 Coercivity 176

4.15 Magnetodynamics of Mg-Tb-Fe-O system 184

4.16 Relative initial permeability 192

4.16.1 Frequency dependent loss factor 195

4.17 DC electrical resistivity 197

4.17.1 Temperature dependent electrical resistivity 198

4.18 Dielectric properties 204

Conclusions 212

References 215

Appendix A 221

Appendix B 222

Publications

Fig. No. List of Figures Page No

2.1 The line broadening of XRD pattern due to crystallite size 57

2.2 Two probe sample holder used in electrical measurements 61

2.3 The circuit diagram of electrical resistivity measurement apparatus 62

2.4 Ferromagnetic Resonance (FMR) Apparatus 64

3.1 The spinel structure 68

3.2 The tetrahedral cations, octahedral cations and O atoms 68

3.3 Magnetic structure of materials (a) ferromagnetic (b) antiferromagnetic

(c) ferromagnetic 76

3.4 Magnetic interactions 81

3.5 Magnetization in Domains. (a) single domain, (b) closure domains,

(c) closure Domains 83

3.6 Typical hysteresis loop along with initial magnetization curve

87

3.7 A circular coil carrying current I 88

3.8 A solenoid carrying current I 90

3.9 Equivalent circuit of a toroid 94

3.10 Ferromagnetic resonance line width ΔH 97

4.1 X-ray diffraction patterns for Ni1-xTbxFe2O4 ferrites

(x = 0.0, 0.02, 0.04, 0.06, 0.08) 103

4.2 X-ray diffraction patterns for Ni1-xTbxFe2O4 ferrites

(x = 0.10, 0.12, 0.14, 0.16, 0.18, 0.20) 104

4.3 FTIR Spectrum for NiFe2O4 ferrite 111

4.4 FTIR Spectrum for Ni.96Tb0.04Fe2O4 ferrite 111

4.5 FTIR Spectrum for Ni.92Tb.08Fe2O4 ferrite 112



4.8 FTIR Spectrum for Ni0.8Tb0.2 Fe2O4 ferrite 113

4.9 SEM micrographs of Ni 1-x Tb x Fe2O4 (x = 0.00) ferrite 116




4.13 EDX of the NiFe2O4 ferrite 119

4.14 EDX of the Ni0.92Tb0.08Fe2O4 ferrite 119



4.17 The MH-Loop for NiFe2O4 ferrite 124

4.18 The MH-Loop for Ni.98Tb.02Fe2O4 ferrite 124




4.22 The MH-Loop for Ni.9Tb.1 Fe2O4 ferrite 126





4.27 The MH-Loop for Ni.8Tb.2 Fe2O4 ferrite 129

4.28 The variation of saturation magnetization with the concentration

of terbium of the Ni1-xTbxFe2O4 (x = 0.0-0.2) ferrites 129

4.29 FMR profile of NiFe2O4 ferrite 131

4.30 FMR profile of Ni.98Tb.02Fe2O4 ferrite 131




4.34 FMR profile of Ni.9Tb.1 Fe2O4 ferrite 133





4.39 FMR profile of Ni.8Tb.2 Fe2O4 ferrite 136

4.40 Relative initial permeability as a function of frequency for

Ni 1-x Tb x Fe2O4, (0.0 ≤ x ≤ 0.10) ferrites 138


Ni 1-x Tb x Fe2O4, (0.12 ≤ x ≤ 0.2) ferrites 139

4.42 Loss factor as a function of frequency for Ni 1-x Tb x Fe2O4,

(0.0 ≤ x ≤ 0.10) ferrites 140

4.43 Loss factor as a function of frequency for Ni 1-x Tb x Fe2O4,

(0.12 ≤ x ≤ 0.20) ferrites 141

4.44 Plot of lo Room temperature resistivity (ρ) Vs terbium concentration

for Ni1-xTbxFe2O4 ferrites 142

4.45 Plot of logρ Vs 1000/T for Ni1-xTbxFe2O4 (x = 0.0-0.1) ferrites 143

4.46 Plot of logρ Vs 1000/T for Ni1-xTbxFe2O4 (x = 0.12-0.20) ferrites 143

4.47 The plot of drift mobility (μd) with temperature for Ni1-xTbxFe2O4

(x = 0.0-0.1) ferrites 145

4.48 The plot of drift mobility (μd) with temperature for Ni1-xTbxFe2O4

(x = 0.12-0.20) ferrites 145

4.49 Plot of activation energy Vs terbium concentration for Ni1-xTbxFe2O4

ferrites 147

4.50 Dielectric constant (ε') Vs frequency of Ni1-xTbxFe2O4 (x = 0.0- 0.10)

at room temperature 149

4.51 Dielectric constant (ε') Vs frequency of Ni1-xTbxFe2O4 (x = 0.12- 0.20)

at room Temperature 149

4.52 Dielectric loss (tanδ) Vs frequency of Ni1-xTbxFe2O4 (x = 0.0- 0.10)

at room Temperature 151

4.53 Dielectric loss (tanδ) Vs frequency of Ni1-xTbxFe2O4 (x = 0.12- 0.20)

at room temperature 152

4.54 The variation of ac conductivity with frequency for Ni1-xTbxFe2O4

(x = 0.0- 0.10) Ferrites 154

4.55 The variation of ac conductivity with frequency for Ni1-xTbxFe2O4

(x = 0.12- 0.20) ferrites 154

4.56 X-ray diffraction patterns for Mg1-xTbxFe2O4 ferrites

(x = 0.0, 0.02, 0.04, 0.06, 0.08) 156

4.57 X-ray diffraction patterns for Mg1-xTbxFe2O4 ferrites

(x = 0.10, 0.12, 0.14, 0.16, 0.18, 0.20) 158

4.58 Lattice parameter a (Å) Vs. Tb concentration for Mg1−xTbxFe2O4

Ferrites (0≤x≤0.2) 159

4.59 X-ray density (Dx) and bulk density (Db) Vs. Tb concentration for

Mg1−xTbxFe2O4 ferrites (0≤x≤0.2) 163

4.60 FTIR Spectrum for MgFe2O4 ferrite 165

4.61 FTIR Spectrum for Mg.96Tb0.04Fe2O4 ferrite 166

4.62 FTIR Spectrum for Mg.92Tb.08Fe2O4 ferrite 166



4.65 FTIR Spectrum for Mg0.8Tb0.2 Fe2O4 ferrite 168

4.66 SEM micrograph of Mg 1-x Tb x Fe2O4, (x = 0.00) ferrite 170




4.70 EDX of the MgFe2O4 ferrite 173

4.71 EDX of the Mg0.92Tb0.08Fe2O4 ferrite 173



4.74 The MH-Loop for MgFe2O4 ferrite 178

4.75 The MH-Loop for Mg0.98Tb0.02Fe2O4 ferrite 178










4.85 The saturation magnetization vs Tb-concentration for

Mg1-xTbxFe2O4 ferrites 183

4.86 FMR profile of MgFe2O4 ferrite 185

4.87 FMR profile of Mg0.98Tb0.02Fe2O4 ferrite 186











Mg 1-x Tb x Fe2O4, (0.0 ≤ x ≤ 0.10) ferrites 193


Mg 1-x Tb x Fe2O4, (0.12 ≤ x ≤ 0.2) ferrites 194

4.99 The variation of μi΄ with x for Mg 1-x Tb x Fe2O4 (0.0 ≤ x ≤ 0.20) ferrites 194

4.100 Loss factor as a function of frequency for Mg 1-x Tb x Fe2O4,

(0.0 ≤ x ≤ 0.10) ferrites 196

4.101 Loss factor as a function of frequency for Mg 1-x Tb x Fe2O4,

(0.12 ≤ x ≤ 0.20) ferrites 196

4.102 Plot of Room temperature resistivity (ρ) Vs terbium concentration

for Mg1-xTbxFe2O4 ferrites 197

4.103 Plot of logρ Vs 1000/T for Mg1-xTbxFe2O4 ferrites (0.00 ≤ x ≤ 0.10) 200

4.104 Plot of logρ Vs 1000/T for Mg1-xTbxFe2O4 ferrites (0.12 ≤ x ≤ 0.20) 201

4.105 The plot of drift mobility (μd) with temperature for Mg1-xTbxFe2O4

ferrites (0.00 ≤ x ≤ 0.10) 201

4.106 The plot of drift mobility (μd) with temperature for Mg1-xTbxFe2O4

ferrites (0.12 ≤ x ≤ 0.20) 202

4.107 Plot of activation energy Vs terbium concentration for

Mg1-xTbxFe2O4 ferrites 203

4.108 Dielectric constant (ε') Vs frequency of Mg1-xTbxFe2O4

(x = 0.0- 0.10) ferrites 205

4.109 Dielectric constant (ε') Vs frequency of Mg1-xTbxFe2O4

(x = 0.12- 0.20) ferrites 205

4.110 Dielectric loss (tanδ) Vs frequency of Mg1-xTbxFe2O4

(x = 0.0- 0.10) ferrites 207

4.111 Dielectric loss (tanδ) Vs frequency of Mg1-xTbxFe2O4

(x = 0.12- 0.20) ferrites 207

4.112 The variation of ac conductivity with frequency for Mg1-xTbxFe2O4

(x = 0.0- 0.10) ferrites 209

4.113 The variation of ac conductivity with frequency for Mg1-xTbxFe2O4

(x = 0.12- 0.20) ferrites 210

List of Tables

Table No Page No

2.1 XRD Measurement conditions 56

4.1 Phases, lattice constant, X-ray density, Bulk density and

Grain size of the Ni1-xTbxFe2O4 ferrites (0.0 ≤ x ≤ 0.2) 106

4.2 Miller indices (hkl) and interplaner spacing (d) for

Ni1-xTbxFe2O4 ferrites (0.0 ≤ x ≤ 0.1) 108

4.3 Miller indices (hkl) and interplaner spacing (d)

for Ni1-xTbxFe2O4 ferrites (0.12 ≤ x ≤ 0.2) 109

4.4 FTIR absorption bands for Ni 1-x Tb x Fe2O4 ferrite system 114

4.5 Nominal percentage of metal cations in Ni1-xTbxFe2O4 ferrites 118

4.6 The saturation magnetization (Ms) and Coercivity (Hc) of

Ni1-xTbxFe2O4 (x = 0.0-0.2) ferrites 123

4.7 FMR parameters of Ni1-xTbxFe2O4 ferrites measured

at X-band (9.5 GHz) 136

4.8 Phase, Lattice constant, X-ray density, Bulk Density, and

Grain size for Mg1-xTbxFe2O4 ferrites (0.0 ≤ x ≤ 0.2) 160

4.9 Miller indices (hkls) and interplaner spacing (d) for

Mg 1-xTbxFe2O4 ferrite (0.0 ≤ x ≤ 0.1) 161

4.10 Miller indices (hkls) and interplaner spacing (d) for

Mg 1-xTbxFe2O4 ferrite (0.12 ≤ x ≤ 0.2) 162

4.11 FTIR absorption bands for Mg1-xTbxFe2O4 ferrites 168

4.12 Nominal percentage of metal cations in Mg1-xTbxFe2O4 ferrites 172

4.13 The saturation magnetization (Ms) and Coercivity (Hc) of

Mg1-xTbxFe2O4 (x = 0.0-0.2) ferrites 177

4.14 FMR parameters of Mg1-xTbxFe2O4 ferrites measured at

X-band (9.5 GHz) 191

1 INTRODUCTION

1.1 Soft Ferrites

Soft ferrites have been under intense investigations for decades due to their useful

electromagnetic characteristics and number of applications. Ferrites are best materials as

they are less expensive, stable and have wide range technological applications, such as

radio wave circuits, high quality filters and operating devices. Soft ferrites are an integral

part of the modern industrial society. They are considered as an important class of

magnetic materials, which have many applications including use as humidity sensors, gas

sensors, green anode materials, stealth aircraft technology, T. V. image interference of

high rise buildings, microwave dark room and protection [1-3]. Ferrites become attractive

materials owing to their use as magnetic semi-conductors (ferrimagnetic) and electric

insulators [4]. Ferrites with high electrical resistivity and good magnetic properties are

used as core material for power transformers in electronics heads, antenna rods, loading

coils, microwave devices and telecommunication applications [5].

Soft magnetic materials are suitable for high frequency applications with low

magnetic coercivity, high electrical resistivity and low eddy current loss and are also key

materials for compact switched mode power supplies [6, 7]. Ferrites are also used as

electrode materials for high temperature applications because of their high

thermodynamic stability, electrical conductivity, electrocatalytic activity and resistance to

corrosion [8].

1.2 Literature Review

Ferrites have been studied since long in order to enhance the magnetic and

electrical properties. Ferrites are technologically important materials owing to their

structure, which can accommodate a variety of cations at different sites enabling a wide

variation in electrical and magnetic properties. In the recent years, the ferrites have been

demonstrated to be good materials for gas sensing applications and are suitable materials

for high frequency applications [2-4, 6]. The electrical properties can be enhanced either

by controlling the sintering temperature or by the addition of different types and amounts

of metal ion substitution.

Forestier prepared ferrites in1928. Japanese also studied magnetic oxides

materials between 1932 and 1935. Snoek started research on ferrites in 1936 and in the

period of about ten years, he laid the foundations of physics and technology of ferrites.

These materials are stable, relatively inexpensive and easily manufactured. The annual

production of ferrites is several tons in Europe and rest of the world. Up to now eight

international conferences on ferrites has been conducted in Japan. Beyond 1950

researchers made microwave devices. New applications in the field of microwave

engineering are expanding. The properties of these materials can be enhanced by the

substitution of various metal ions in these ferrites. Nowadays rare earth substituted spinel

ferrites are reported to be promising candidates for applications in high density magnetic

recording and enhanced memory storage. Rare earth ions having 4f unpaired electrons

can originate magnetic anisotropy due to their orbital shape. The substitution of rare earth

ions can improve their electrical and magnetic properties.

The magnetic structures of ZnxNi1-xFe2O4 (where x = 0, 0.25, 0.50 and 0.75)

ferrites were studied by neutron diffraction [9]. The analysis suggested the cation

distribution like (Znx2+

Fe1-x3+

) [Ni1-x2+

Fe1+x3+

] O4. All the samples under investigation

showed a noncollinear, Yafet-Kittel (Y-K) type of magnetic ordering. The YK-angles

were observed to increase with an increase in the zinc concentration. The angles

calculated in this way were consistent with three sub-lattice molecular field analysis of

the paramagnetic susceptibility data of Neel and Brochet. Mg1+xGexFe2-2xO4 (x = 0, 0.1,

0.2, 0.3, 0.4) ferrites prepared by ceramic method and their magnetic properties were

reported [10]. The results revealed that the lattice constant decreases with the

concentration of germanium and was attributed to the ionic radii of the cations. It was

observed that the Ge4+

ions prefer tetrahedral sites and this caused the redistribution of

Fe3+

and Mg2+

ions on both A- and B-sites.

The influence of Al3+

ions on the magnetic properties of Mg1Mn0.1Fe1.9-xAlxO4

ferrites prepared by ceramic method has been reported [11]. It was observed that the Al3+

ions preferred B-sites and its substitution resulted in the decrease of magnetization and

remanance. The structural and magnetic properties of CuLa2xFe2-2xO4 (x = 0. 0.2, 0.4, 0.6,

and 0.8) ferrites were investigated [12]. It was noticed that the samples exhibited spinel

phase up to x = 0.4 and for x > 0.4 pervoskite phase was identified. The magnetization

and magnetic moment revealed decreasing trend with the increase of La content. The

variation in magnetization was discussed on the basis of AB-interaction and migration of

Cu2+

and Fe2+

ions from B to A-sites. The results indicated that La ions occupied B-sites

only. The Y-K angles measured for NiFe2O4, Zn0.2Ni0.8Fe2O4, Ni0.8Cu0.2Fe2O4 and

Zn0.2Ni0.6Cu0.2Fe2O4 compositions revealed [13] Neel type of spin arrangement on

sublattices and all other compositions showed non-collinear type of spin arrangement.

Rare earth substituted Ni0.7Zn0.3Fe1.92R0.08O4 ferrites (where R is Yb, Er, Tb, Gd,

Dy, Sm and Ce) prepared by ceramic method, were reported [14]. It was observed that

the substitution of these ions had marked effect on the electrical and magnetic properties.

It was also noticed that Er-substituted samples show minimum Curie temperature (Tc).

This decrease in Tc was attributed to the influence of R-R and R-Fe interactions. On the

other hand highest specific magnetization was observed for Er and Gd substituted

samples and it was supposed that Er and Gd ions get ferromagnetically ordered while

others antiferromagnetically. Electrical transport properties of Cd0.5Ni0.5+xTixFe2-2xO4

ferrites have been investigated. The resistivity was observed to increase with Ti-contents

and this increase in resistivity was attributed to Ti-substitution in the spinel lattice with

large ionic radius. The activation energies in the para- and ferro-regions were calculated.

It was observed that the activation energies were larger in ferro-region than para-region.

Electrical conduction mechanism was explained on the basis of Verway-de-Boer

mechanism [15].

The effect of TiO2, GeO2 and R2O3 (R = Yb, Er, Dy, Tb, Gd, Sm, Ce) on the

properties of Ni0.7Zn0.3Fe2O4 ferrites was studied [16]. It was noticed that when

germanium was absent specific saturation magnetization (σs) exhibited smaller values

and by introducing germanium instead of titanium σs attains its highest values for

(GeO2)0.03(TiO2)0.01. It was observed that the substitution of R2O3 increase the dc

resistivity except for Ce2O3 and it was attributed to the formation of insulator

intergranular layers. The rare earth ions with large ionic radius and with stable valence of

3+ were found to be the best substituents for the improvement in the magnetic and

electrical properties. The Gd2O3 were preferred substituent in these ferrites.

The structural and electrical properties of CdxCu1-xFe2-yGdyO4 (x = 0.0, 0.2, 0.4,

0.6, 0.8 and 1; y = 0.0 and 0.1) ferrites synthesized by standard ceramic technique, were

investigated [17]. The X-ray study revealed that for x ≥ 0.2 the samples were cubic

spinels, while for x = 0 the samples were tetragonal. It was noticed that the variation of

the lattice constant with cadmium concentration obeyed the Vegard’s law. The infrared

absorption spectra indicated that Gd ions were occupied on octahedral sites.

The electrical and magnetic properties of Ni0.7Zn0.3Fe1.98R0.02O4 (R = Yb, Er, Dy,

Tb, Gd, Sm, Ce) ferrites prepared by ceramic method were reported [18]. The results

show that the substitution of rare-earth ions improved the temperature dependent initial

permeability and it does not depend on porosity. The electrical resistivity was found to

increase by the substitution of rare earth ions and it was attributed to the structural

heterogeneity generated by insulating intergranular layers. The highest magnetization

about 100-103 emu/g for Er and Gd substituted samples was observed while the lowest

magnetization for Cesium (Ce) substituted was indicated at 77 K.

Nickel ferrites were prepared by ball milling and their structural, electrical and

magnetic properties were studied [19]. It was noticed that NiFe2O4 spinel phase was

completed after 35 hrs of milling and the resistivity decreased by four orders of

magnitude with the increase of milling time. It was observed that the magnetization

increased as a function of milling time.

The electrical and magnetic properties of Cr3+

substituted Ni-Sn ferrites

synthesized by ceramic method were investigated [20]. The increase in dc resistivity was

observed when Cr-was substituted and it was explained on the basis of Verwey hopping

mechanism. The dielectric and magnetic loss tangent were decreased for Cr substitution.

It was noted that the saturation magnetization and the Curie temperature were decreased

with increased substitution of Cr and were explained on the basis of three sublattice

magnetizations and exchange interactions. The decrease in initial permeability was

attributed to the decrease in saturation magnetization.

The magnetization behaviour of Cr substituted Zn-Cu ferrites have been discussed

[21]. The observed higher values of Hc at low temperatures indicated the single domain

behaviour. The values of saturation magnetization and hysteresis loops at high magnetic

fields showed that the compounds were highly anisotropic ferrimagnets.

The properties of Ni-Zn ferrite powders prepared by chemical coprecipitation

were reported [22]. The results showed that the precipitate dried at 80 °C revealed cubic

structure and saturation magnetization Ms = 44 emu/g. When these precipitates were

calcined at 1200°C, the magnetization was observed to increase up to 67 emu/g. The

temperature dependence of magnetization indicated the Curie temperature Tc = 480°C.

Magnetic properties of Ni0.5Zn0.5BixFe2.0-xO4 (0 ≤ x ≤ 0.2) ferrites were investigated [23].

It was noticed that saturation magnetization decreases as the bismuth (Bi) concentration

increases. The decrease in saturation magnetization was explained on the basis of two

sublattices in the spinel structure, with Bi5+

ions replacing some of Fe2+

ions.

The ferromagnetic resonance (FMR) in polycrystalline MgFe2O4 ferrite spheres

have been analyzed by investigating the size of the sample [24]. The results indicated that

the values of signal intensity (SI), resonance field (Hres) and line width (ΔH) turned out to

increase with the increase of sample volume. Schlomann’s theories for Hres and ΔH

respectively, are satisfactory to explain the values of Hres (0) and ΔH (0) which do not

embody the shift of parameters due to the sample size. The volume dependence of SI

means the complete penetration of the rf field into the sample, and that of ΔH implies that

it may be closely related to the number of scattering sources like pores. It was concluded

that the effect of sample size on FMR should be considered when analyzing the physical

meaning of FMR parameters.

Rare earth substituted Ni-Zn ferrites (R= Yb, Er, Dy, Tb, Gd, Sm, and Se)

prepared by solid state reaction method have been reported [25]. The compositional

effect of these rare earth ions on lattice constant, bulk density, electrical resistivity,

activation energy, carrier concentration, mobility and vickers hardness was investigated.

It was concluded from XRD analysis that the substitutions of all rare-earth ions favour

the formation of a secondary phase. The electrical resistivity and bulk density were

observed to increase by rare earth ions substitution. The temperature dependent resistivity

measurements indicate two regions of different activation energies. These ferrites were

found to have high activation energies which were attributed to the carrier mobility at

higher temperatures.

The physical and initial permeability measurements on Cu-Mg-Zn ferrites

prepared by coprecipitation technique were reported [26]. It was noticed that as the

concentration of magnesium was increased the density increased while the lattice

parameter decreased and these were attributed to ionic sizes of Mg2+

and Cu2+

ions. The

Curie temperature was almost constant for all the compositions. The observed change in

the values of initial permeability was attributed to variations of magnetization (Ms) and

average particle diameter (D).

The properties of Mn-substituted Ni-Cu-Zn ferrites prepared by ceramic method

were investigated [27]. It was observed that the substitution of Mn for Fe revealed an

increase in initial permeability and bulk density of these ferrites. The results also showed

that the substituted samples have larger grain size. The resistivity was found to decrease

from 1010

to 107 Ω-cm with Mn content and was attributed to electron hopping

mechanism from Fe2+

to Fe3+

ions. The coercivity varies inversely to grain size.

The magnetic properties of the Mg1+xMnxFe2–2xO4 (0.1≤ x ≤ 0.9) spinels prepared

by double sintering ceramic method were investigated [28]. The cation distribution

revealed that Mn4+

ions occupy only octahedral sites replacing Fe3+

ions and Mg2+

ions

were substituted for Fe3+

ions on tetrahedral sites. The observed Mossbauer data

indicated the short range ordering in these samples. It was proposed that with increasing

Mn-concentration the frustration and disorder were increased in the system.

Electrical measurements were carried out on the compositions Co0.2Zn0.73Fe2O4,

Co0.30Zn0.60Fe2O4, Co0.37Zn0.51Fe2O4 and Co0.5Zn0.34Fe2O4 [29]. It was found that

resistivity initially decreases then increases as concentration of Co increases. It was

suggested that the decrease in resistivity was due to the shifting of Fe2+

ions to tetrahedral

sites and increase may be due to the unavailability of ferrous ions on octahedral sites. A

change of slope was observed in the Arhenius plots indicating the presence of two

regions of activation energy. The smallest value of activation energy for

Co0.30Zn0.60Fe2O4 was observed which was attributed to the creation of small number of

oxygen vacancies as Co was substituted into the spinel lattice.

The temperature dependent electrical and dielectric properties of Si-substituted

CoFe2O4 ferrites were studied [30]. The decrease in DC resistivity with increasing Si

concentration was observed and it was attributed to the hindrance in the Verwey

mechanism. It was observed that for various Si-concentrations in CoFe2O4 resistivity (ρAC

and ρDC) decreases with increasing temperature, whereas dielectric constant (ε/ and ε

// )

increases with increasing temperature suggesting that the dielectric constant is roughly

inversely proportional to both ac & dc resistivities.

A few properties of Li-Cd ferrites prepared by ceramic technique were studied

[31]. The single phase structure was confirmed by X-ray diffraction analysis. The lattice

parameter was observed to increase linearly with Cd concentration and was attributed to

ionic volume differences of the component cations involved. It was noticed that the

magnetic moment (nB) was found to increase with Cd content up to x = 0.3, and thereafter

it decreased. The increase in magnetization was explained on the basis of Neel’s two

sublattice model whereas decrease in magnetization was attributed to the presence of a

triangular type of spin arrangement on the B-site suggested by Yafet and Kittel.

The magnetic properties of the ferrites with compositions Co0.5Zn0.34Fe2O4,

Co0.37Zn0.51Fe2O4, Co0.3Zn0.6Fe2O4, Co0.2Zn0.74Fe2O4 were investigated [32]. The results

revealed that the coercivity and porosity exhibit almost similar behaviour, where as the

remanence was observed to decrease with increasing Zn content. The saturation

magnetisation and magnetic moments showed decreasing behaviour with increasing Zn-

content and was attributed to the strengthing of B-B interaction followed by the

weakening of A-B interaction. The Y-K angles increase with increasing Zn-concentration

and were explained on the basis of triangular-type spin arrangement on B sites.

The magnetization behaviour of Cu1-xZnxFe2O4 (x = 0, 0.25, 0.50, 0.75, 1) ferrites

measured by AC magnetic susceptibility using a mutual inductance technique was

reported [33]. It was noticed that with the increase of Zn-content from 0.0 to 0.75, the

Curie temperature and the saturation magnetization were found to increase and thereafter

decreasing trend was observed. This effect was partially related to the low magnetic

moments of Zn2+

ions. The Y-K angles increased gradually with increasing zinc content.

It was concluded that the values of Y-K angles indicated that mixed zinc ferrites exhibit

non-collinear type of ordering while CuFe2O4 showed Neel’s type of ordering.

Electrical properties of Mg-Zn ferrites prepared by solid state reaction method

have been reported [34]. The sintered density of these ferrites was found to increase from

2.01 to 4.3 g/cm3 with the substitution of Cu ions. The results indicated that the sintered

ferrites having electrical resistivity greater than 108 Ω-cm was obtained at relatively low

sintering temperature ~1050°C for x = 0.3.

Physical and electrical properties of gadolinium substituted NiFe2O4 ferrites

prepared by ceramic method have been reported [35]. The single phase spinel structure

was confirmed by x-ray diffraction. The effect of compositional variation on lattice

parameter, bulk density, theoretical density and porosity was reported. The room

temperature dc resistivity was discussed on the basis of Gd-substitution for Fe3+

ions on

octahedral sites (B-sites).

The superparamagnetic MgFe2O4 spinel ferrite nanoparticles with the particle size

from 6 to 18 nm were investigated [36]. It was observed that the blocking temperature

and coercivity unambiguously correlated with particle size. Such correlation was

consistent with the Stoner-Wohlfarh theory on single domain particles. The

superparamagnetic properties of these nanoparticles with relatively large size clearly

suggest great potentials of developing superparamagnetic nanoparticles from spinel

ferrites.

The physical properties of Al3+

substituted MgFe2O4 ferrites have been reported

[37]. X-ray diffraction analysis indicated the single-phase spinel structure. It was noticed

that the lattice constant decreases gradually obeying the Vegard’s law. The decrease in

lattice constant was attributed to the ionic radii of Al3+

and Fe3+

ions. It was observed that

the ionic radius of octahedral site decreases with the increase in Al3+

concentration and it

was attributed to the replacement of larger Fe3+

and Mg2+

ions by smaller Al3+

on B-sites.

The bulk density was observed to decrease and this was due to the difference in atomic

weight and density of Al3+

(27, 2.79 gm-3

) and Fe3+

(55.8, 7.87 gm-3

).

The formation of magnesium ferrite powders as a function of milling time and at

different sintering temperatures was investigated [38]. The powders after different

milling times were examined by X-ray diffractometry and optical microscopy. After a

milling the powder for 23 h, magnesium ferrite was formed. The milled and unmilled

powders were sintered for 2 h at temperatures of 800, 1000 and 1300°C. The unmilled

powder showed partial formation of magnesium ferrite sintered at 1300°C while

complete formation of magnesium ferrite was obtained for milled powder sintered at

1300°C.

The effect of substitution of rare earth ions (R= Yb, Er, Dy, Tb, Gd and Sm) on

the electrical and magnetic properties of Li-Zn ferrites synthesized by solid state reaction

was investigated [39]. It was noticed that the Li-Zn substituted ferrites may favour the

formation of second phase due to larger ionic radii and inhibited the grain growth and

hence increased the resistivity of these ferrites. Also the substitution of these rare earth

ions tend to flatten the initial permeability curves, shift the Curie point to lower

temperature and lowered the porosity from 8 % to 5 %.

The temperature dependent electrical transport properties of CoxZn1-xFe2O4

ferrites were studied [40]. It was found on the basis of the results of Seebeck coefficient

that these ferrites may be classified as n-type and p-type semiconductors. The electrical

conductivity of all the ferrites was observed to increase with increasing temperature

indicating semiconductor behaviour of these ferrites. It was noted that activation energy

in the ferromagnetic region was less than the paramagnetic region. The temperature

dependent mobility and electrical conductivity along with conduction mechanism in these

ferrites were discussed.

The electrical properties of Li-Mg ferrites synthesized by double sintering method

were studied [41]. The decrease in the ac resistivity was observed with increase in

frequency, which indicates that the samples exhibited normal ferrimagnetic behavior. The

inverse trends of compositional variation of resistivity and dielectric constant were

observed. The sample with x = 0.3 showed the lowest resistivity and the highest dielectric

constant. The dielectric loss tangent showed maxima at 3 kHz for x = 0.2. The variations

in all the parameters were explained on the basis of Fe2+

and Fe3+

ion concentrations and

electronic hopping frequency between these ions.

Electrical resistivity of Mg1.5-xZnxMn0.5Fe2O4 (where x = 0.0, 0.1, 0.2, 0.3, 0.4,

0.5, 0.6) ferrites prepared by double sintering ceramic method are reported [42]. X-ray

diffraction analysis confirmed the single-phase spinel structure. The lattice constant was

observed to decrease up to x = 0.3 and thereafter it was increased for further substitution.

The dc resistivity was decreased up to x = 0.2 and it increased there after. The observed

decrease in resistivity was attributed to the production of Fe2+

ions due to volatilization of

Zn at elevated firing temperature. The temperature dependent resistivity plots followed

Arrhenius relation.

Dielectric measurements on the ferrites with chemical composition NixZn1-xFe2O4

synthesized by double sintering ceramic technique are reported [43]. The dielectric

properties such as dielectric constant, dielectric loss tangent and complex dielectric

constant were investigated. It was noticed that the dielectric constant was inversely

proportional to the square root of the resistivity.

ZnxMg1-x-yZryFe2-2yO4 with x = 0.1, 0.2, 0.3, 0.4 0.5 and y = 0.01, 0.03, 0.05, 0.07

ferrites were synthesized by standard ceramic method and their structural properties were

studied [44]. It was reported that the X-ray diffraction analysis reveal single-phase spinel

structure and the observed increase in lattice constant with the increase of Zn and Zr-

concentrations obeyed the Vegard’s law. In the IR analysis the splitting of ν 2 band was

attributed to the presence of Zr4+

ions on the octahedral sites. It was concluded that the

addition of Zn lowered the Curie temperature and weakened the A-B interactions.

The magnetic properties of ZnxMg1-x+yZryFe2-2yO4 (x = 0.1, 0.2, 0.3, 0.4, 0.5 and

y = 0.01, 0.03, 0.05, 0.07) ferrites synthesized by ceramic method were investigated [45].

It was reported that magnetic moment and saturation magnetization of these ferrites obey

the Neel’s two sublattice model for x ≤ 0.3 and for x > 0.3 the Y-K model hold good. The

substitution of Zn caused to increase the Y-K angles above x =0.3 in these ferrites. The ac

susceptibility results revealed the presence of multidomain (MD) particles in these

ferrites. The single-phase structure was verified by the sudden drop of susceptibility

curves near the Curie temperature.

The spinel ferrites ZnxFe2O4 (where x = 0.3, 0.5, 0.7, and 0.9) prepared by double

sintering method and their temperature dependent electrical conductivity and

thermoelectric power was investigated [46]. The plots of temperature dependent electrical

conductivity were observed to increase with the increase of temperature and showed

transition near Curie temperature. It was noted that the activation energy in ferrimagnetic

region was less than that in the paramagnetic region.

The magnetic properties of Cu0.5Zn0.5Fe2-xRxO4 (R = La, Nd, Sm, Gd and Dy)

where x = 0.0 and 0.1 ferrites synthesized by ceramic method were reported [47]. The X-

ray diffraction analysis revealed single-phase spinel structure. The lattice parameter and

Curie temperature of these samples were found almost independent of the type of rare

earth ion substituted. The substitution of Dy ions revealed highest density and lowest

porosity as compare to other rare earth substituted ferrites. The relative permeability was

increased up to 60 % as compared to the unsubstituted samples.

The infrared spectra of LixMg0.4Zn0.6-2xFe2xO4 ferrites prepared by ceramic

method were investigated in the wave number range 200–800 cm-1

[48]. The X-ray

diffraction analysis confirmed the single-phase spinel structure. The spectra of these

ferrites showed two fundamental absorption bands ν1 and ν2 in the range 600–400 cm-1

,

corresponding tetrahedral and octahedral complexes, respectively. These bands were

found to shift gradually towards the lower frequency side with the increase of Zn content,

which was attributed to the increase in the lattice parameter and bond lengths (RA and

RB).

Structural and electrical properties of Nd3+

substituted Zn-Mg ferrites synthesized

by ceramic method were investigated [49]. Single-phase spinel structure was predicted by

XRD analysis and the lattice constant was increased linearly obeying Vagard’s law with

Zn- concentration. The lattice constant was observed to decrease slightly with the

substitution of Nd3+

for Fe3+

ions. This decrease in lattice constant was attributed to the

occupancy of Nd3+

ions on octahedral sites. It was proposed that Zn ions prefer A-sites

while Nd ions occupied B-sites. It was observed that Nd substituted samples have high

resistivity as compared to unsubstituted samples.

The electrical properties of Co substituted Li-Sb ferrites synthesized by double

sintering ceramic technique was reported [50]. XRD results revealed that the samples

were single-phase. The increase in lattice constant was noticed and it was attributed to

larger ionic radius of Co2+

as compare to other constituents. The decrease in temperature

dependent resistivity was reported and it was explained on the basis of cation distribution

and the presence of cobalt ions in the two valence states at the octahedral site. The

dielectric behaviour of all the samples were studied in the frequency range 100 Hz to 1

MHz and the possible mechanisms involved were discussed. The saturation

magnetization was explained on the basis of Neel’s model and the cation distribution.

It was noticed that the addition of Sb2O3, Na2O3, CaO and ZrO2 have marked

effect on the properties of Ni0.255Zn0.745Fe2O4 ferrites which have Curie point around 0°C

[51]. The results showed that Na2O3 and Sb2O3 addition increased the Curie temperature

while CaO addition lowered the Curie temperature. The change in Curie temperature was

attributed to the slight modification of the A-B exchange interaction strength. The Initial

permeability and electrical resistivity were improved by all these additives but CaO was

found to be the best one.

The magnetic properties of Ni0.65Zn0.35Cu0.2Fe1.8O4 particles synthesized by sol–

gel method were reported [52]. All the peaks of X-ray diffraction patterns were consistent

with the standard Ni-Zn ferrites. The magnetic behavior of these ferrite powders fired at

and above 623 K yielded a decrease of the coercivity and an increase of the saturation

magnetization was observed. The maximum coercivity and the saturation magnetization

of these ferrite powders were observed as Hc = 96 Oe and Ms = 68 emu/g respectively.

A systematic line broadening effect in the Mossbauer spectra was observed and was

explained on the basis of temperature dependence of the magnetic hyperfine fields at

various iron sites.

The dielectric properties of Li0.5-x/2CoxFe2.5-x/2O4 (where x = 0.1, 0.2, 0.3, 0.4, 0.5,

0.6, 0.7) ferrites have been reported [53]. It was noticed that the compositional variations

of DC resistivity and dielectric constant with concentration (x) shows inverse trend with

each other. The temperature dependent dielectric constant was observed to increase

slowly from 0 to 450 in the beginning and sharply after 200°C. The DC resistivity and

dielectric constant decreases with the increase in frequency for all the samples. The

variation of tanδ with frequency showed cusps for all the samples except for x = 0.5. All

these variations were explained on the basis of Koop’s theory and concentration of Fe2+

and Fe3+

ions.

The structural and infrared studies of MgCrxFe2-xO4 ferrites (where x = 0, 0.1, 0.3,

0.5, 0.7, 0.9 and 0.1) prepared by double sintering method were investigated [54]. The

lattice parameter, X-ray density and distance between magnetic ions in both octahedral

and tetrahedral sites were observed to decrease with increase in Cr- concentration. The

infrared spectra obtained in the range 200 to 800 cm-1

showed two absorption bands. The

force constants were obtained from the infrared absorption data and were discussed with

reference to the internuclear distances.

LixCu0.4Zn0.6-2xFe2+x (where x = 0.0, 0.05, 0.1, 0.15, 0.2, 0.25 and 0.3) ferrites

were studied [55]. It was noticed that the X-ray analysis revealed the single phase spinel

structure and the lattice parameter found to increase linearly with Zn content, which was

attributed to ionic size differences of the cations involved. The bond lengths RA and RB

were found to increase with increase in Zn concentration and were attributed to the

increase in lattice parameter. The magnetic moment found to increase with increase in

zinc content up to x =0.3 and thereafter decreased. The decrease in magnetic moment was

attributed to the triangular type of spin arrangement on B-sites suggested by Yafet and

Kittel.

The effect of small substitution of iron with rare-earth ions on the properties of

Ni0.50Zn0.51Fe1.96R0.040O4 (R = Pr, Nd, Eu, Ho, Tm, Lu) ferrites was investigated [56]. The

results revealed that depending on the type of precursor used, narrow particle size

distributions and a very homogeneous distribution of the rare-earth cations in the mixed

metal oxide were achieved. The sintering process indicated that all rare earth additions

form various secondary phases. The observed differences in the electrical and magnetic

properties of the doped samples were interpreted on the basis of phase composition and

microstructure.

The magnetic interactions in Zn-substituted CuFe2O4 ferrites were studied [57]. It

was noticed that the dominant interaction in all ferrite samples is A–B interaction which

is due to the negative values of paramagnetic Curie temperature θ (K) and the distribution

of cations among A and B sites showing that the magnetic ordering is antiferromagnetic.

The Curie temperature (Tc) was observed to rise up to x = 0.75 which may be due to

increase in exchange interaction and magnetic moments. For x > 0.75 , Tc decreased due

to cation distribution on A and B-sites resulting in the weakening of A–B interaction due

to the presence of triangular spin arrangement of the Y–K type on B-sublattice.

ZnxMg1−xFe2−yNdyO4 (x = 0.00, 0.20, 0.40, 0.60, 0.80 and 1.00; y = 0.00, 0.05 and

0.10) ferrites prepared by ceramic method were studied [58]. It was noticed that the

magnetization show increase in saturation magnetization with Zn2+

concentration up to x

= 0.40 and decreases thereafter, suggesting the existence of the canted spin structure. The

saturation magnetization was observed to decrease by the substitution of small amount of

Nd3+

ions. For the compositions, x ≥ 0.80 exhibited paramagnetic behaviour at and above

room temperature. The frequency dependence of the initial permeability spectrum was

observed to show dispersion in permeability against frequency. The dispersion frequency

was found to be lower for high permeability compositions than those of lower

permeability. The substitution of Nd3+

resulted into reduction in the initial permeability.

The effect of In3+

, Al3+

and Cr3+

ions on the electrical and magnetic properties of Mg–Mn

ferrites has been investigated [59].

The results revealed that the substitution of In3+

ions in place of Fe3+

ions

increases the lattice parameter, due to the larger size of the substituted ions, whereas

lattice parameter was observed to decrease by the substitution of Al3+

and Cr3+

ions in

place of the Fe3+

ions, owing to the smaller sizes of these substituted ions. The

improvement in the d.c. resistivity has been observed at the expense of deterioration in

the magnetic properties of Al3+

and Cr3+

substituted Mg–Mn ferrites. The saturation

magnetization and initial permeability were found to increase with the increase of In3+

ions and was attributed to the incorporation of indium ions into the A sublattice. A

marked increase in the value of initial permeability was found for the composition

Mg0.9Mn0.1In0.5Fe1.5O4.

The magnetic and dielectric properties of Mg1+xTixFe2-2xO4 (0.1 ≤ x ≤ 0.9) ferrites

were studied [60]. The analysis of X-ray diffraction showed that the unit cell parameter

increases with Ti concentration and ascribed to the predicted variation of the cation

distribution. It was noted that the variation of the dielectric properties depends mainly on

the valence exchange between the different metal ions in the same site or in different

sites. The parameters such as dielectric constant, dielectric loss and molar magnetic

susceptibility showed a decrease in magnitude with increasing Ti and Mg concentration.

It was found that the composition with x = 0.7 exhibit no significant behavior in the

dielectric constant and shows a typical paramagnetic behaviour without a spinel structure

as in the X-ray diffraction pattern which is compatible with the Monte-Carlo simulation

of Scholl and Binder.

The spectral and transport phenomena in NiGdxFe2-2xO4 (x = 0, 0.1, 0.3, 0.5 and

0.7) ferrites were studied [61]. The X-ray analysis exhibited that the sample have spinel

phase structure for x ≤ 0.1 and thereafter the samples have second phase besides the

spinel phase. The bands observed at 579 cm-1

(ν1) and 397cm-1

(ν2) in FTIR profile were

assigned to tetrahedral and octahedral group complexes, respectively. The results

indicated that the presence of the bands at 307 cm-1

and 455 cm-1

was the evidence of the

entry of Gd3+

ions instead of Fe3+

ions at B-site and these bands appeared due to (Gd3+

-

O2-

) stretching vibration. The second intergranual insulating phase increases the

resistivity of the samples. The activation energy of conductivity and that for mobility

showed a good agreement which is an evidence for the presence of hopping conduction in

the ferrimagnetic region.

Electrical transport properties of erbium substituted Ni–Zn ferrites of various

compositions have been investigated [62]. The plots of log (ρ) versus 103 /T indicated

linear behaviour. The results indicated that the activation energy in the ferrimagnetic

region was less than that in the paramagnetic region. It was observed that the resistivity

for gadolinium substituted ferrites was higher than the erbium substituted ferrites. The

higher resistivity was attributed to the increase in the lattice strain because of the higher

ionic radius of the gadolinium compared to that of erbium. Amongst all the samples

studied, the specimen Ni0.7Zn0.3Er0.2Fe1.8O4 exhibited the lowest value of charge carrier

mobility.

The rare earth (Dy, Ho and Er) substituted Co0.2Zn0.8Fe2-xRExO4 ferrites (x = 0.05,

0.1) were studied thoroughly [63]. It was observed that in these ferrites frustration and

exchange couplings between 3d and 4f electrons spin play a major role in magnetic

ordering. It was suggested that the substitution of Dy, Ho and Er in Co0.2Zn0.8Fe2-xRExO4

ferrites is possible up to x = 0.05 beyond which an impurity phase of ortho ferrite

appears. It was observerd that due to strong dilution on A-sites & B-sites moments form

finite clusters of Fe3+

ions with free moment 5 μB. The small finite clusters were freezed

at low temperature due to frustration and short range antiferromagnetic interaction,

showing spin glass like phase.

The ferrite samples with chemical composition Cu0.7 (Zn0.3-xMgx) Al0.3Fe1.7O4

(x=0.05, 0.1, 0.15 and 0.2) prepared by ceramic technique at 1000°C, were found to have

cubic spinel structure [64]. The lattice parameter was observed to decrease with

increasing Mg content and may be attributed to the small ionic radius of Mg relative to

that of Zn. It was observed that the increase of Mg content forced the structure of these

compounds to be a normal spinel. This is evident from parameters obtained during the

refinement of the structures. The bond length of the tetrahedral site was observed to

increase and the bond length of the octahedral site was decreased which was due to

relative fraction of magnesium to zinc occupied in the tetrahedral sites.

The changes in crystal structure of magnesium (MgFe2O) ferrite caused by

mechanically treated high-energy milling were investigated [65]. Mechanical treatment of

MgFe2O4 exhibited the formation of the nanoscale structure with the crystallite size of

about 10 nm. It was noticed that the metastable nanostructural state of the milled

MgFe2O4 was characterized by a reduced concentration of iron cations on (A) sites. The

range of the thermal stability of the mechanically induced defects in the structure of

milled MgFe2O4 was extended up to 600 K. Beyond this, a gradual recrystallisation of the

nanoscale MgFe2O4 powders were taken place and the mechanically induced cation

distribution was relaxed toward its equilibrium configuration.

A detailed investigations on CdxCu1-xFe2-yGdyO4 (X=0.00, 0.20, 0.40, 0.60, 0.80

and 1.00; y=0.00, 0.10 and 0.30) ferrites prepared by ceramic method were carried out

[66]. It was observed that X-ray diffraction indicate the formation of single phase cubic

spinel ferrite for the compositions with x ≥ 0.20 and tetragonal structure for the

compositions x = 0.00; and for all values of Gd3+

(y = 0.00, 0.10 and 0.30) concentration.

The saturation magnetization and magnetic moments were found to increase with

cadmium concentration up to x = 0.40 ; and for all values of Gd3+

content, obeying Neel’s

two sublattice model and for x > 0.4, the saturation magnetization decreased. This

decrease in Ms was due to occupancy of Gd3+

ions on octahedral sites, resulting into

dilution in the magnetization of B sublattices. It was observed that Curie temperature (Tc)

for all compositions decreases with the substitution of Cd2+

. The decrease in Tc was

attributed to the occupancy of cadmium on tetrahedral (A)-sites causing dilution in the

inter site magnetic interaction.

The preparation and characterization of LixMg0.4Zn0.6-2xFe2+xO4 (where x = 0,

0.05, 0.10, 0.15, 0.2, 0.25 and 0.3) ferrites have been reported [67]. X-ray diffraction

analysis indicated the single phase formation of these ferrites. It was noticed that the

lattice constant increases linearly obeying Vegard’s law. The observed increase in bond

lengths and site radii was attributed to the increase of lattice constant. FTIR spectra

revealed the absence of double band near 600 cm-1

which indicate the non-availability of

Fe2+

ions in these ferrites. The Curie temperature was found to decrease with Zn content.

Rare earth substituted (R = La, Nd, Sm, Gd and Dy) Mn–Zn ferrites have been

investigated [68]. The single spinel phase formation of these ferrites was exhibited by the

X-ray diffraction analysis. The substitution of rare earth ions in Mn-Zn revealed that the

porosity increases while the grain size is observed to decrease. Also the substitution of

these ions resulted in decrease of the initial permeability and Curie temperature. The

electrical resistivity was found to increase for all substituted samples, except for R = Sm.

The increase in resistivity was due to the presence of these ions inside the grains which

hinder the motion of electrons between Fe2+

and Fe3+

.

The magnetic properties of Mn-substituted MgCuZn ferrites were reported [69]. It

was noted that all the samples were sintered at low temperature (930 °C). The

substitution of Mn was reported to increases initial permeability and decreases the grain

size. The increase in the initial permeability of MgCuZn ferrites was attributed to the

decrease of magnetostriction constant. It was found that all the samples have fine grains

and the grain size was less than 2 μm.

The ferrites with nominal compositions Mg1+xTixRyFe2-2x-yO4 (where 0 ≤ x ≤ 0.9;

0 ≤ y ≤0.5; R = La, Nd and Gd) were fabricated for IR spectroscopic analysis [70]. The

presence of Fe3+

ions on both tetrahedral and octahedral sites was indicated by the

formation of absorption bands at ≈ 585 and ≈ 442 cm-1

. The existence of vibrational

bands at ~ 363 cm-1

revealed the presence of Fe2+

and Mg2+

ions on B-sites and enhances

the predominance of Verwey mechanism. It was observed that the rare earth type causes

a small shift in the vibrational bands. This shift was attributed to the variation of ionic

radii, which gives rise to the change in lattice constant.

Mg0.9Mn0.1InxFe2-xO4 and Mg0.9Mn0.1CryFe2-yO4 ferrites have been investigated

for magnetic properties [71]. It was observed from the results that the saturation

magnetization (Ms) values initially increase with the addition of In3+

ions and show a

rapid decrease at higher concentrations while in the case of Cr-samples saturation

magnetization decreases. The Curie temperature was observed to decrease with

increasing concentrations of both indium and chromium. The observed variations in

Curie temperature and Ms values were attributed to the exchange interactions. It was

found that In3+

ions play more significant role as compared to Cr3+

ions, in enhancing the

initial permeability. The results indicated that the magnetic loss factor values lie in the

range of 0.15–0.75 within the frequency range of 10 kHz–10 MHz.

The effect of Zn substitution on magnetic properties of Cu1-xZnxFe2O4 (where x =

0.0, 0.25, 0.50, 0.75, 1.00) ferrites have been reported [72]. The microstructure analysis

revealed that both porosity (P) and coercivity (Hc) were observed to decrease with the

substitution of Zn. The coercivity was inversely proportional to grain size while the Curie

temperature (Tc) was found to increase from 538 to 560 K. The decrease in Hc with grain

size was correlated fairly well with Neels’ two sublattice model.

The ferrite system MgxAl2x Li0.5(1-x)Fe2.5(1-x)O4 (x = 0.0, 0.1, 0.2, 0.3, 0.4 and 0.5)

have been investigated by means of X-ray diffraction, magnetization and a.c.

susceptibility measurements [73]. It was found that the cation distribution determined

through X-ray data is consistent with the magnetization and susceptibility measurements.

The results revealed that Li 1+

and Al3+

have strong preference for octahedral site as

compared to Mg2+

. The collinear type of magnetic ordering in the system was observed

and the variation of magnetization was explained on the basis of Neel’s collinear model.

The variation of the complex permeability with frequency of Ni1-xZnxFe2O4 (x = 0.5, 0.6

and 0.7) ferrites has been measured over a wide range of frequency ~ 1.8 GHz [74]. The

results exhibited that the substitution of Zn content improves permeability but moves the

onset of resonance to lower frequencies. The effect of the substitution of small amounts

of Ruthenium, Yttrium and rare-earth cations into the Ni0.5Zn0.5MxFe2-xO4 ferrite (x = 0.5,

0.6 and 0.7) has been also investigated. The samples substituted with Ru and Gd

improves microwave behavior compared to non-substituted samples.

The electrical and structural properties of Mg1+xTixRyFe2-2x-yO4 (x = 0.5, y = 0,

0.025 and R = Nd, Gd and La) have been reported [75]. It was observed that the samples

were crystallized in the spinel phase. The experimental results showed that the rare earth

ions initiate new sites called dodecahedral (C-sites) and increase the valence exchange

between the different metal ions existing in the different sites. This behavior was

observed at certain concentrations of the rare earth ions. The low rare earth concentration

and high sintering times (100h) leads to an inflection in the electrical properties. The

Verwey conduction mechanism and hopping were used to interpret the conductivity of

the samples. The activation energies were lower in low temperature range as compared to

high temperature range due to the presence of more than one conduction mechanism.

The ferrites system Mg1-xZnxFe2O4 (where x = 0, 0.1, 0.2, 0.3, 0.4, 0.5 and 0.6)

have been reported [76]. The lattice parameter was observed to increase with increasing

the zinc concentration and it was attributed to the ionic radii of the cations. The

magnetization results indicated that for x ≤ 0.3, the ratio Br/Bs (squareness ratio)

increased by 66% and Hc increased by 14 %. But for x ≥ 0.3 Br/Bs decreased by 27 %

and Hc decreased by 43 %. The behaviour of μi with temperature exhibited that the

samples for x ≤ 0.3 shows multi domain and thereafter the samples were found as single

domain.

The dielectric properties of Cu0.5Zn0.5Fe2–xRxO4 (R = La, Nd, Sm and Gd; x = 0

and 0.1) ferrites were reported [77]. The results revealed that ε′ and tan δ decrease with

increasing the frequency while σac is observed to increase. Also ε′, σac and tan δ were

found to increase with temperature. No relaxation was detected in tan δ(f) in the

investigated frequency range, while tan δ(T) showed two maxima. The composition

dependence of the dielectric parameters was discussed and the results were explained

using Koops’s model.

Electrical transport properties were investigated on Ni1-xCdxFe2O4 (x = 0.2, 0.4,

0.6 and 0.8) ferrites [78]. The results indicated that the electrical conductivity varies from

3.96x10-8

to 1x10-4

Ω-1

cm-1

and were observed to decrease with increase in the cadmium

concentration. It was noticed that the composition Ni0.2Cd0.8Fe2O4 exhibited the highest

value of electrical resistivity (ρ = 2.53 x 107 Ω cm). The Seebeck coefficient was found to

be negative for all the ferrites, indicating that these ferrites behave as n-type

semiconductors. These results suggested explanation for the conduction mechanism in

these ferrites.

The cation distribution in the ferrites having general formula Ni1+xPbxFe2-2xO4

(where x = 0.0, 0.1, 0.2, 0.3, 0.4 and 0.5) prepared by ceramic method were reported [79].

The single phase formation of the samples was observed by X-ray analysis. The linear

increase of lattice parameter with composition (x) was observed and was attributed to

ionic size difference of cations involved. X-ray intensity ratio calculations revealed that

Pb4+

occupies both A and B sites, which replace Fe3+

ions and added Ni2+

ions for B-sites

iron ions. The IR bands exhibited shift towards the lower frequency side with the addition

of Pb4+

for x = 0.0–0.2, which can be attributed to increase in lattice parameter.

The dielectric properties of mixed Ni-Zn-Er ferrites have been investigated in the

frequency range 1-13 MHz using impedance analyzer [80]. It was observed that the

dielectric constant, dielectric loss tangent and complex dielectric constant of these ferrites

increases by increasing the Er content. It was noticed that the composition

Ni0.7Zn0.3Er1.0Fe1.0O4 has the maximum divalent ion concentration. The dielectric

constant was observed to decrease continuously with increasing frequency. The

maximum dielectric dispersion was observed for the composition Ni0.7Zn0.3Er1.0Fe1.0O4

and it was attributed to the available ferrous ions on the octahedral sites. The values of

dielectric transition temperature Td and Curie temperature Tc indicated that the change in

dielectric constant with temperature may be due to magnetic transition.

The magnetic properties of CoMxFe2-xO4 (where M = Gd, Pr and x = 0, 0.1, 0.2)

were studied using vibrating sample magnetometer [81]. Thermogravimetric (TG)

indicated the formation of spinel ferrite at 220 °C and single phase nature was confirmed

by the XRD analysis. It was observed that the saturation magnetization of these ferrites

decreases with the reduction of size. It was attributed to the presence of

superparamagnetic fractions in the materials and spin canting at the surface of nano-

particles. The inclusion of rare-earth atoms inhibited the grain growth of the material.

The coercivity was observed to improve and was attributed to the contribution from the

single ion anisotropy of the rare earth ions present in the crystal lattice.

The properties of calcium substituted magnesium ferrite system were studied by

means of X-ray diffraction, magnetization, ac susceptibility and dc resistivity

measurements [82]. The XRD patterns revealed a single fcc spinel phase structure for x =

0.2. The XRD intensity analysis confirms the substitution limit and the percentage

formation of fcc phase. It was observed that about 23% of Ca2+

can be substituted for

Mg2+

for the composition x =0.25 and for x ≥0.25 an orthorhombic phase other than fcc

phase was observed. The additional orthorhombic phase appears to grow in intensity with

increase in Ca-concentration (x). The Neel’s two sub-lattice model was used to explain

the variation of Bohr magneton number. The Neel temperature determined through ac

susceptibility and dc resistivity measurements agree with those calculated using cation

distribution. The values of dc electrical resistivity were found to vary with the Ca-

content.

NiFe2O4 ferrites were synthesized by the solgel process [83]. The formation of

phase and the microstructure of these ferrites were studied by means of DTA/TG, XRD

and SEM techniques. It was noticed that the gel after combustion was transformed into

nanocrystalline ferrite powders. The combustion process is an oxidation-reduction

process. The results revealed that Fe/Ni = 2 ratio and calcination at 1000 °C, single phase

NiFe2O4 ferrites were formed. SEM micrograph indicated the particle size less than 100

nm. The dielectric measurements were carried out for the ferrite compositions Co1-

xZnxLayFe2-yO4 0.1 ≤ x ≤ 1.0, y = 0.25 fabricated by ceramic method [84].

The dielectric constant ε' and dielectric loss factor ε" of these ferrites were

measured at different frequencies (100 kHz to 5 MHz) and at different temperatures

(300–850 K). It was observed that Maxwell Wagner polarization was dominant in the

dielectric process in the high temperature region. The electrical conductivity

measurement showed that there were more than one conduction mechanisms participating

in conductivity. It was suggested that the hopping mechanism played main role in the

conduction process. The increase in conductivity was attributed to the thermally activated

mobility and not to thermal creation of additional mobile charge carriers. The

replacement of Fe3+

by La ions on octahedral sites and the presence of Co2+

as well as

Zn2+

ions on the tetrahedral sites played a significant role in the electrical and magnetic

properties of these ferrites. The values of the activation energy obtained in this study

indicate the semi-conducting behavior of the investigated samples.

Microwave-assisted flash combustion technique was used to synthesize

Ni0.8Zn0.2Fe2O4 ferrites [85]. The pressed samples were sintered at various sintering

temperatures such as 1150, 1250 and 1350 °C. The physical properties of these ferrites

such as bulk density and porosity were studied. The dielectric properties such as

dielectric constant, dielectric loss factor and tanδ were also measured. All these results of

the samples were compared with the properties of ferrites prepared by conventionally

heated flash combustion technique in normal heating.

The samples of Ni-Zn ferrites were fabricated by solid state reaction method [86].

In these ferrites the influence of Zn concentration on the magnetic properties was

investigated in a wide frequency range (1M–1.8 GHz). The results indicated that with the

increase of Zn concentration, the initial permeability and the relative loss factor were

found to increase while the cut-off frequency decreased. The influence of rare earth ions

(RE=Y, Eu or Gd) on the properties of these ferrites was also investigated. The

measurements showed that the partial substitution of rare earth ions with Fe3+

ions

increase the electrical resistivity and relative loss factor, whereas the Curie temperature

was slightly reduced. It was concluded that Y and Eu substitution tend to decrease the

initial permeability while Gd has no effect on it.

The effect of co-substitution of non magnetic ions, Mg+2

and Ti+4

in the nickel

ferrites fabricated by ceramic method was reported [87]. The XRD analysis confirmed

the single-phase formation of the materials. The effective modifications in the exchange

interactions were observed from structural, magnetic and Mössbauer studies. The

substitution of these ions (Mg2+

and Ti4+

) at Fe site resulted in the reduction of the

saturation magnetization, Neel temperature (TN) and initial permeability (μi). The

variations in different properties were discussed on the basis of the site occupancy of the

metal ions in the crystal structure. The reduction in magnetic moment on substitution was

also evident by the 57

Fe Mossbauer studies. At higher substitution level (x ≥ 0.4) the

relaxation was also observed from Mössbauer studies. The doublet with the two sextet

was observed in the Mossbauer spectra. This doublet was found to increase with the

increase of substituents and was explained on the basis of domain wall oscillation and

displacement model.

Standard ceramic technique was used to fabricate the following two series of

copper ferrites, Cu1+xGexFe2−2xO4 and Cu1+xTixFe2−2xO4 with x = 0, 0.1, 0.2, 0.3 and 0.4

[88]. The analysis of X-ray diffraction patterns indicated that the samples were formed in

a single spinel phase except the sample with x = 0.4 for both series. The Curie

temperature (TC) was observed to decrease from 714 to 542K for the first series while for

the second series it decreased from 714 to 570K. The ferrite composition CuFe2O4

showed lowest value of magnetization in both series. The observed decrease in

magnetization and Curie temperature was attributed to the decrease in A–B interaction

according to Neel’s molecular field theory. The cation distribution for both series was

also proposed. It was noticed that the relative permeability show two regions for first

series and three regions for the second series.

The microwave-assisted hydrothermal reactions were carried out in a microwave

accelerated reaction system to synthesize nanosized magnesium ferrite, MgFe2O4 under

mild conditions [89]. The results of X-ray diffraction and transmission electron

microscopy revealed the average particle size of the ferrite obtained was ~ 3 nm with a

narrow size distribution. The blocking temperature ~ 38 K was measured through

magnetic measurements. It was observed that the MgFe2O4 ferrite particles show typical

magnetic hysteresis behavior below the blocking temperature and it exhibit

superparamagnetic behavior above this temperature.

The X-ray diffraction, magnetization and AC susceptibility measurements were

carried out to study the structural and magnetic properties of ZnxMg1.5-xMn0.5FeO4 with x

= 0.0–0.6 ferrites fabricated by ceramic method [90]. The cation distribution was deduced

from the X-ray diffraction intensity analysis and the linear variation of lattice constant

with Zn concentration was explained using the proposed cation distribution. The

magnetization behaviour was explained by using three sublattice model based on the

uniform and localized spin canting approach with Zn-concentration. The AC

susceptibility measurements revealed that Neel temperature decreased with the increase

of Zn-concentration.

Aluminum substituted cobalt ferrites were prepared by ceramic method and their

AC conductivity and dielectric properties as a function of frequency and temperature

were investigated [91]. The quantum mechanical tunneling and small polaron tunneling

models were used to explain AC conductivity. The dielectric dispersion was found to be

discussed with the help of Koops model and hopping conduction mechanism. The

dielectric relaxation peaks were observed in dielectric loss tangent tan δ curves which

were due to the coincidence of the hopping frequency of the charge carriers with that of

the external fields. The increase in the dielectric parameters with the increase of

temperature was attributed to the increase of hopping frequency, while the decrease with

increasing Al ion concentration was due to the iron deficient available for the conduction

process at the octahedral sites.

Magnesium-nickel ferrites were fabricated by the solid state route at high

temperature [92]. The single-phase formation of these ferrites was confirmed by the X-

ray diffraction (XRD) analysis. It was noticed that the plot of lattice parameter versus

composition of these ferrites indicated an abrupt deviation of lattice parameter from

linearity near MgFeO4. The deviation was attributed to the distribution of Mg2+

in the

octahedral and tetrahedral sites of the oxygen lattice. In XPS spectra, a broadening of the

Mg1s peak in Ni rich Mg–Ni ferrites from that observed in pure MgFe2O4, was explained

by due to the distribution of Mg ion in tetrahedral and octahedral sites. A depth

distribution of Mg in Ni0.5Mg0.5Fe2O4 ferrites showed an enrichment of Mg on surface.

Structural and physical properties of MnxZn1−xFe2O4, ferrites with x = 0.66, 0.77, 0.88,

0.99 synthesized by conventional double-sintering method, in which 0.5 wt.% of Si was

added as an impurity [93].

The formation of the ferrite structure and chemical phase analysis was carried out

by X-ray powder diffraction (XRD) method. The results indicated that lattice constant

found to increase proportional to the Mn concentration. The mass density of the ferrites

was observed to increase while X-ray density depend on the lattice constant and

molecular weight of the samples and it showed decreasing behaviour with increasing Mn

content (x). It was noticed that the porosity, calculated using both densities, also show a

decreasing behaviour with increase in manganese content.

The ferrites, Mg1+xMnxFe2−2xO4 where x = 0.0, 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8

and 0.9 fabricated by ceramic technique and were investigated by means of X-ray

diffraction, a.c. susceptibility and dielectric constant measurements [94]. The single-

phase formation of these ferrites was confirmed by the analysis of XRD patterns. It was

observed that lattice parameter found to increase up to x = 0.3 and for further substitution

it decreased. The cation distribution was studied by X-ray analysis and magnetization

measurements. A collinear ferrimagnetic structure was observed for x ≤ 0.3 and for x >

0.3 non-collinear structure was suggested by magnetization results. The Curie

temperature (TC) deduced from a.c. susceptibility measurements found to decrease with

the increase of concentration. The dielectric constant ε' and loss tangent (tan δ) show

strong frequency dependence.

Standard ceramic technique was used to fabricate NixZn1−xFe2O4 ferrites, for x =

0.66, 0.77, 0.88 and 0.99, with the addition of few wt % of Si in order to improve the

resistivity of these ferrites [95]. The dc electrical resistivity was measured and then used

to calculate activation energy and drift mobility of these ferrites. The results indicated

that the resistivity was enhanced by the addition of Ni content. The temperature

dependent dc resistivity was also measured and found to decrease with increase of

temperature from 30 to 180 °C. The mobility showed increasing behaviour with

temperature and it decreased with the increase of resistivity. It was noticed that the

samples having higher values of resistivity also have higher values of activation energies

and vice versa.

Magnesium–manganese ferrites, Mg0.9Mn0.1InxFe2−xO4 and Mg0.9Mn0.1CryFe2−yO4

were prepared by the conventional ceramic process [96]. The effects of In3+

and Cr3+

ions

on the dc resistivity, dielectric constant and dielectric loss factor were investigated. The

resistivity was observed to increase with the addition of In3+

and Cr3+

ions in these

ferrites. The Verwey’s hopping mechanism was used to explain the variations in

resistivity. The activation energy, deduced from the temperature variation of resistivity,

was found to increase with increasing concentrations of In3+

and Cr3+

ions. The room

temperature dielectric constant at 100 kHz decrease with successive addition of these

ions. The variations in dielectric constant were explained on the basis of space charge

polarization. The dielectric loss tangent (tan δ) values measured at 100 kHz and 13MHz

were found to be very low for the samples with a higher concentration. The low values of

the loss factor at a high frequency indicated that the investigated samples may have great

potential for use in microwave devices.

Zinc substituted Li–Mg ferrites having the general formula

LixMg0.4Zn0.6−2xFe2+xO4 where x = 0, 0.05, 0.1, 0.15, 0.2, 0.25 and 0.3 were prepared by

double sintering ceramic method [97]. The thermoelectric power and electrical resistivity

measurements were carried out of these ferrites. The variation of log ρ with reciprocal of

temperature showed a discontinuity at Curie temperature. It was observed that the

activation energy in the ferrimagnetic region was lower than that in paramagnetic region.

The conduction mechanism was explained on the basis of hopping of electrons. The plots

of resistivity with composition indicated that resistivity initially decrease with Zn content

up to 0.3 and thereafter it increased for further increase in Zn content. The Curie

temperature found to decrease linearly with addition of Zn concentration. The variation

of Seebeck coefficient with temperature indicated that all the samples show n-type

conductivity.

The structural and electrical properties of Sn4+

substituted NiFe2O4 with general

formula Ni1−xSnxFe2O4 (x = 0.0, 0.2, 0.4, 0.6, and 0.8) fabricated by the combustion

synthetic method were studied [98]. The samples were sintered at 1000 ◦C. The analysis

of XRD patterns revealed that synthesized compounds were nanocrystalline size with

cubic structure. An intermediate NiSnO3 phase was also identified from this study during

substitution. The Fourier transform infrared (FT-IR) spectra showed the characteristic

features of the synthesized ferrite compounds. The stretching and bending vibrational

modes of the Ni2+

, Sn4+

, and Fe3+

were observed from FT-IR, which lead to the inference

of NiFe2O4 and substituted compound as an inverse spinel. It was observed that the band

gap values computed from both UV and electrical measurements indicated that the

synthesized materials were semiconductors. The dc electrical conductivity of the

compounds found to increase with increasing measuring temperature. A maximum dc

electrical conductivity of 6.0Scm−1

was obtained at a measuring temperature of 1000 ◦C

in the composition of x = 0.8, for which the activation energy found to be minimum.

The magnetic and microstructure studies of copper substituted Ni-Zn ferrites were

investigated [99]. The XRD patterns of powder samples showed the cubic spinel phase up

to x = 0.25 and a second phase of composition CuO above x > 0.25. The crystallite sizes

of as-dried samples when calcined at high temperatures changed from ~ 10 to 50nm at

1000 °C. The substitution of Cu2+

ions influenced the magnetic parameters due to

modification by cation distribution.

CuFe2O4 ferrites were prepared by the thermal decomposition of the acetate

precursors [100]. These ferrites were isothermally reduced in H2 flow at 400-600 °C. The

isothermal reduction profiles obtained in this study show that a topochemical mode of

reduction was done by which the reduction process proceeds. The nano-wire metallic

phase of iron (106nm) and copper (56nm), produced from the complete reduction of

CuFe2O4, were subjected to the direct reoxidation in CO2 flow at 400-600 °C. The

reoxidation process was found to be controlled by both the reduction and reoxidation

temperatures. It was observed that CO2 decompose to carbon nano-tubes during the

reoxidation of the freshly reduced CuFe2O4. The prepared samples were investigated by

X-ray diffraction, Scanning electron microscopy and transmission electron microscopy. It

was also noticed that at the initial stages the reaction was controlled by the interfacial

chemical reaction mechanism with some contribution to the gaseous diffusion

mechanism.

Copper ferrites of the nominal composition CuxFe3-xO4+δ where x = 0.2, 0.4, 0.6,

0.8, and 1 were prepared by standard ceramic technique [101]. The substitutional effect

of Cu ions on AC electrical conductivity and dielectric properties at different frequencies

(50Hz-5MHz) were studied. The conductivity results were discussed in terms of the

electron hopping model. The Koop’s theory and Rezlescu model were used to explain the

dispersion of dielectric constant. The dielectric loss tangent, tanδ plots exhibited

dielectric relaxation peaks which were attributed to the coincidence of the hopping

frequency of the charge carriers with that of the external fields. The frequency exponent

factor was estimated and found to vary between 0.4 for x = 1 and 0.83 for x = 0.2.

The polycrystalline ferrites with general formula CdxMg1-xFe2-yCryO4 (x = 0, 0.2,

0.4, 0.6, 0.8, 1.0; y = 0, 0.05 and 0.10) were prepared by ceramic method and their

permeability and magnetization measurements were carried out [102]. The XRD analysis

confirmed the fcc spinel structure. The saturation magnetization revealed that the Neel’s

two-sublattice model exists up to x = 0.4 for y = 0, 0.05 and 0.1 and a three-sublattice

model found predominant for x > 0.4 and y = 0, 0.05 and 0.10. The saturation

magnetization and magnetic moment were found to decrease with the increase in Cr3+

contents, which was attributed to the dilution of B–B site interaction. The variation of

initial permeability with temperature exhibited the long-range ferromagnetic ordering in

the compounds with x = 0.4. It was noticed that sample with x ≤ 0.4 and y = 0, 0.05 and

0.10 showed peaking behavior near Curie temperature, which was due to the decrease of

anisotropy constant K1 to zero. The low-frequency dispersion of initial permeability

suggested domain wall displacement. The Curie temperature was observed to decrease

sharply with the increase of Cd2+

ions. Also, the addition of Cr3+

ions resulted in the

decrease initial permeability.

The magnetic properties of the chromium substituted Li–Sb ferrite prepared by

the double sintering ceramic technique were studied [103]. The microstructure of the

samples showed that the grain size was larger and more uniform for pure Li–Sb ferrites.

The results revealed that the initial permeability was observed to decrease with the

increase of chromium concentration. The variation of permeability indicated that for all

samples resonance peak at a frequency above 15 MHz was observed and it was attributed

to domain wall oscillations. The hysteresis loop parameters were observed to decrease

with higher level of substitution. Hysteresis loops of the samples indicated that

squareness ratio found to decrease with the increase of chromium content.

The effects of rare-earth ions (La, Nd, Gd) synthesized by the emulsion method

on the magnetic properties of Ni–Mn ferrite were investigated [104]. X-ray diffraction

analysis ensured the presence of cubic structure of spinel ferrite for all samples. The

values of saturation magnetization and coercivity of the samples were reported to

increase with decreasing temperature and were explained by low temperature spin-wave

theory. It was noticed that the un-doped sample has the maximum value of saturation

magnetization (Ms), while the La3+

doped sample has the maximum value of coercivity

(Hc) at 2K. The values of Ms and Hc were observed to decrease with increasing of

testing temperatures for all samples. Mossbauer spectra tested at 273K revealed that the

samples were almost superparamagnetic and single domain particles. The magnetic

measurements exhibited that rare-earth ions can influence significantly the low

temperature magnetic properties of soft magnetic materials.

The structural and magnetization measurements of Mg0.7Zn0.3SmxFe2-xO4 ferrites

prepared by the solid-state reaction method were carried out [105]. The analysis of XRD

patterns indicated the single spinel phase with Sm3+

contents in the range 0.00 ≤ x ≤ 0.03.

The lattice parameter was found to increase at x = 0.01 and then decreases up to x = 0.03,

this may indicate distortion in the spinel lattice due to the relatively large ionic radius of

Sm3+

. The decrease in saturation magnetization was observed with the increase in x up to

0.04 and was attributed to the replacement of the Fe3+

ions by the Sm3+

ions in the

octahedral sites.

The effect of Al substitution on the structural and magnetic properties of NiFe2O4

ferrites prepared by standard ceramic method was investigated [106]. The single phase

spinel structure was confirmed from X-ray powder data analysis. The lattice parameter

was observed to decrease and it was attributed to the ionic radii of the cations involved.

The magnetic moment found to decrease which may be due to the reduction of Fe3+

ions.

The band position of the samples under investigation was studied using IR spectra. The

results indicated that net magnetization decreased and domain state changed from single

domain to multi-domain.

Ferrite nanoparticles, Ni0.65 Zn0.375 Inx Ti0.025 Fe1.95-xO4 of the size about 6 nm

were prepared by using high-energy ball mill [107]. To study the structural and magnetic

properties of the samples, XRD, VSM and FMR techniques were used. The XRD patterns

exhibited cubic spinel structure and the average particle size was estimated to be around 6

nm. The FMR spectra showed slight asymmetry and the deduced parameters such as

resonance field, line width and relaxation time for all the samples were found in

accordance with magnetic data obtained from hysteresis loops. The magnetic

characteristics of indium-doped samples were compared with those for bulk samples. It

was suggested that ball milling of ferrites could be a method to produce nanoparticle

powders.

The AC electrical conductivity and initial magnetic permeability were

investigated for some rare-earth substituted spinel ferrites prepared by double sintering

process [108]. The ferrites like Li0.5-0.5xCoxFe2.4-0.5xR0.1O4 where x = 0.0; 0.5, and 1; R =

Y, Yb, Eu, Ho and Gd were prepared by ceramic technique. The results of AC electrical

conductivity showed dispersion with frequency at low temperatures. The dispersion was

found to obey the universal power law. The frequency exponent of the power law

decreased with both Co ion content and temperature. This ensured the classical barrier

hopping mechanism to be predominant one in these samples. The temperature dependent

initial magnetic permeability exhibited multi domain structure only for x = 0.0; and

single domain for all other samples.

The spinel ferrites, MgxNi1-xSm0.02Fe1.98O4 (x = 0.1, 0.3, 0.5, 0.7 and 0.9)

prepared by the solid-state reaction method were characterized by X-ray diffraction and

magnetization measurements [109]. The single spinel phase ensured by the analysis of

XRD patterns. The lattice parameter was observed to increase and the X-ray density

decrease as the Ni2+

ions were replaced by the Mg2+

ions on the octahedral sites. The

coercivity measurements indicated a decrease of internal strains for enhanced Mg2+

content (x > 0.5) in the samples.

The samples, CuCr2O4 and NiCr2O4 were synthesized by the precursor method

[110]. These samples were crystallized at room temperature in a tetragonal distorted

spinel structure. The distortion was attributed to the Jahn–Teller ions Cu2+

and Ni2+

which flatten or elongate their surrounding oxygen tetrahedron. It was noticed that

CuCr2O4 and NiCr2O4 form a complete solid solution series Cu1-xNixCr2O4 where for

0.825 < x < 0.875 members with orthorhombic symmetry were found. On cooling, all

samples showed a temperature dependent crystallographic phase transition from cubic to

tetragonal symmetry between 865K (CuCr2O4) and 310K (NiCr2O4). Also, it was

remarkable that the phase Cu0.15Ni0.85Cr2O4 undergo a second crystallographic transition

to orthorhombic symmetry, at T = 300 K. At low temperatures all compounds showed

anti-ferromagnetic ordering. The Neel’s temperature was found to decrease and the

magnetization increased with increasing Ni content. This was due to the fact that Ni2+

has

two unpaired electrons whereas Cu2+

has only one. The observed two-step mechanism

may have its origin in different ordering temperature of the ion’s sub lattices.

The X-ray diffraction, magnetic and Mossbauer spectral studies were carried out

to study the cation distribution of chromium substituted nickel ferrites synthesized by

aerosol route [111]. The cation distribution revealed that the chromium atom occupy

octahedral site up to x = 0.8, and then also enter into tetrahedral site. The saturation

magnetization was observed to decrease linearly with the increase of chromium

concentration due to the diamagnetic nature of the Cr3+

ions. Initially the coercivity

increase slowly with the increase of chromium concentration but when x > 0.8 very large

increase was observed. It was attributed to the specific cation distribution of Cr3+

which

result an unquenched orbital angular momentum and a large anisotropy. The Mossbauer

spectra of the samples exhibited a broad doublet resolved into two doublets

corresponding to the surface and internal region atoms. The samples annealed at 1200 °C

show broad sextets, which were fitted with different sextets, indicating different local

environment of both tetrahedral and octahedral coordinated iron cations.

The ferrites with general formula Mn0.5Zn0.5RyFe2O4; where R = Dy, Gd, Sm, Ce,

and La were prepared by standard ceramic technique and sintered at 1200 °C with a

heating rate 4 °C/min [112]. The structural and dielectric properties like, dielectric

constant, AC conductivity, and seebeck coefficient were measured. X-ray diffractograms

confirmed that all samples have the spinel structure with the appearance of small peaks of

secondary phases. The decrease in porosity was observed after Sm-doped samples due to

the presence of the secondary phases, which limit the grain growth. The results showed

that the addition of rare earth ions to the system act as a sintering catalyst that help in the

development of the solid solution at lower temperatures. The seebeck measurements

indicated that manganese–zinc ferrites doped with the rare earth ions classified as P-type

semiconductors. The increase in the electrical resistivity was found by the addition of

small quantity of Dy3+

ions substitutions and it was attributed to the structural

heterogeneity generated by the insulating intergranular layers.

Zinc substituted nickel ferrites were fabricated by solid state reaction technique

and were sintered at various temperatures [113]. The electrical and magnetic properties of

these ferrites Ni1-xZnxFe2O4 (x = 0.2, 0.4) were investigated. The bulk density of the

Ni0.8Zn0.2Fe2O4 ferrites samples was found to increase as temperature increase from 1200

to 1300 °C and above 1300 °C the bulk density was decreased. The temperature

dependent electrical resistivity results revealed that the samples were semiconductor in

nature. The Curie temperature, resistivity and the activation energy decrease with the

addition of Zn content, while the magnetization, initial permeability, and the relative

quality factor (Q) increased. The permeability dropped off at fr because of the occurrence

of ferrimagnetic resonance. This factor limit the frequency at which a magnetic material

can be useful. A Hopkinson peak was obtained near Tc in the real part of the initial

permeability vs. temperature curves. The ferrite with higher permeability had relatively

lower resonance frequency. It was found that the choice of the basic composition

represented a compromise, since both resonance frequency and permeability were related

to crystalline anisotropy.

The ferrites of the general formula, Mg1+xTixRyFe2-2x-yO4; R = Ce and Er, y =

0.025 and 0 ≤ x ≤ 0.5), were synthesized by standard double sintering ceramic technique

at 1200 °C using heating rate of 4 °C/min [114]. The analysis of X-ray diffraction

patterns exhibited the single phase spinel cubic structure for all samples and also the peak

intensity was found to depend upon the magnetic ions present in the lattice. It was

observed that he values of dielectric constant for x = 0.1 was found much higher than

those of x = 0.5 (order of 103 times) and it was attributed to the effect of Ti and rare earth

addition. The activation energy was increased as the Ti concentration increased. The

variation of electrical resistivity in the ferromagnetic region was attributed to the ionic

radii of the substituted ions. The addition of Ti4+

ions resulted in the decrease of

magnetization. The Seebeck voltage coefficient was carried out for all samples to identify

the type of charge carriers. The magnetic susceptibility was measured by the Faraday’s

method. The effect of rare-earth (RE) ions was explained by the partial diffusion in the

spinel lattice.

The NiZn and NiCuZn ferrites were fabricated by the conventional ceramic

processing [115]. The magnetic and physical properties of these ferrites were

investigated. The results revealed that the lowest power loss could be obtained with the

equimolar composition for both NiZn and NiCuZn ferrites, which could be due to the

lowest porosity. A slight decrease or excess of Fe2O3 content had no remarkable effect on

saturation magnetic flux density (Bs). A slight excess of Fe2O3 was effective to improve

the initial permeability, which could be attributed to the decrease of the

magnetocrystalline anisotropy. The initial permeability and power loss of these ferrites

had different development trends with the increase of sintering temperature, which could

be explained by the different variation trend of the grain size and porosity. The power

losses of the NiCuZn ferrite samples were lower than that of the NiZn ferrites at any

sintering temperature. It was noticed that the NiCuZn ferrites had a better performance

than the NiZn ferrites in power field use.

The solid state reaction technique was used to prepare Zn substituted nickel

ferrites [116]. The AC conductivity and magnetic properties of these ferrites were

reported. The spinel structure of the samples was ensured by X-ray powder diffraction

analysis. The AC conductivity, lattice parameters sintered density and grain size were

increased where as the X-ray density and porosity were decreased with the increase of

zinc concentration. It was noticed that all the samples follow the Maxwell-Wagner

polarization. The saturation magnetization varied from 196.459 emu/g to 0.330 emu/g

while the coercivity decreased from 72 to 11.730 Oe with the increase in zinc

concentration. This was attributed to the non-magnetic behavior of zinc. The value of

Yafet–Kittel angles increased from zero to 89.975° with the increase in Zn concentration

this was due to the canted behavior of ions in octahedral site.

The co-precipitation technique was used to synthesize CoZn ferrite [117]

composites having the general formula (1−x)Co0.5Zn0.5Fe2O4 + xSiO2 with x = 0.0–0.8. It

was deduced from the X-ray diffraction analysis that the samples were bi-phasic in

nature. The resistivity was increased from 105 to 10

9 (Ωcm) for x = 0.0–0.8. This increase

in resistivity was attributed to the presence of pores and the segregation of Si at grain

boundaries. The temperature dependent resistivity plots indicated the semi conducting

behavior of the samples. Arrhenius plots exhibited change of slope at particular

temperature (except for x = 0.8) that may be attributed to their Curie temperature. It was

observed that the activation energies were small in Para-region as compared to Ferri-

region and this indicate hopping conduction mechanism in these samples. The

thermopower results revealed that the samples were degenerate type semiconductors. The

values of activation energies calculated from logμd vs. 1000/T were slightly lower than

the values of activation energies obtained from Arrhenius plots. This suggested polaron

hopping conduction phenomenon in these samples.

The composite ferrites with chemical formula (1-x)[Mn0.5Zn0.5Fe2O4].x[SiO2] (x =

0.0, 0.20, 0.30, 0.40, 0.50) were fabricated by the co-precipitation technique [118]. The

prepared samples were finnally sintered at 1150 °C followed by air quenching. The

phases precipitated out were identified from X-ray diffraction analysis in the samples.

AC magnetic susceptibility was measured using the low field mutual inductance

technique over the temperature range 298 K to 550 K at a frequency of 250 Hz. The

magnetic parameters like Lande splitting factor, g, Curie constant, C, effective magnetic

moment, Peff, Curie temperature, Tc, exchange integral, J/kB, and characteristic

temperature, θ(K) were calculated. The susceptibility measurements indicated that the

samples follow Curie Weiss behaviour above the Curie temperature. Below the Curie

temperature, all the samples exhibited the ferrimagnetic behaviour. The results revealed

that the magnetic properties were enhanced by the addition of Si in the lattice.

Spinel ferrite of the nominal composition Ni0.64Zn0.36Fe2O4 was prepared by the

solid state reaction technique [119]. The influence of vanadium oxide on the magnetic

and micro structural properties of this ferrite was investigated. The ferrite was doped with

V2O5, ranging from 0 to 3.2wt.% in steps of 0.4wt.%. The results indicated that with the

increase of this oxide up to a certain percentage (1.6wt.%), the permeability, relative

density and grain size initially increases and then decreases. The dc resistivity of the

samples was observed to increase with the increase of V2O5. The saturation

magnetization and Curie temperature indicated peak values at 1.2wt.% and 0.8wt.% of

V2O5 respectively.

The nanocrystalline samarium substituted cobalt ferrite powders were synthesized

by the citrate precursor method [120]. The effects of substitution of Sm3+

ions and

thermally treated temperature (400-600 °C) on the structure and the magnetic properties

of CoFe2O4 nanocrystalline powders were investigated. The results revealed that the

crystallite size of the produced powders decreased by increasing the Sm content and

increased with increasing the calcination temperature from 400 to 1000 °C. The analysis

of X-ray diffraction patterns exhibited the single phase spinel structure of CoFe2O4 ferrite

powders with out Sm3+

addition at different thermally treated temperatures. It was

noticed that with the increase of Sm3+

ions mole ratio to 0.2–0.4 led to the formation of

SmFeO3 and Sm2CoO4 phases with cobalt ferrite phase. The average crystallite sizes of

the samples were sensitive to the synthetic conditions and they were within the average

range of 8 - 86 nm. The saturation magnetization and coercive field were found strongly

dependent on the calcination temperature and structure of the formed powders. The

saturation magnetization was decreased by increasing the Sm content and increased by

increasing the calcination temperatures from 400 to 800 ◦C. The maximum saturation

magnetization was attained (62.86emu/g) for CoFe2O4 ferrite produced at 800 ◦C.

1.3 Aims and Objectives

The substitution of Tb in NiFe2O4 and MgFe2O4 ferrites has not been reported

extensively in the literature to the best of my knowledge. In the light of lack of

investigations of Tb Substituted Nickel and Magnesium ferrites, the present study aims at

structural, electrical, dielectric and static & dynamic magnetic properties of

Ni1-xTbxFe2O4 and Mg1-xTbxFe2O4 ferrites. The main objectives of the present work are;

To prepare ferrites with good crystal structure and high density.

To improve electrical and dielectric properties.

To control the magnetic properties for their use in switching and microwave

devices.

To reduce the FMR linewidth of these ferrites.

References

1. Mansour Al-Haj, J. Magn. Magn Mater. 299 (2006) 435-439.

2. N. Iftimie, E. Rezlescu, P. D. Popa, N. Rezlescu, J.Optoelectron. Adv. Mater. 7 (2005)

911-914.

3. S. B. Cho, D. H. Kang, J. H. Oh, J. Mater. Sc. 32 (1996) 4719-4722.

4. A. R. Shitre, V. B. Kawade, G. K. Bichili, K. M. Jadhav, Mater. Lett. 56 (2002) 188-

193.

5. A. C. F. M. Costa, E. Tortella, M. R. Morelli, R. H. G. A. Kiminami, J. Magn. Magn

Mater. 256 (2003) 174-182.

6. Ge-Liang Sun, Jian-Bao Li, Jing-Jing Sun, Xiao-Zhan yang, J. Magn. Magn Mater.

281 (2004) 173-177.

7. M. A. Ahmad, E. Ateia, S. I. El-dek, Mater. Lett. 57 (2003) 4256-4266.

8. L. John Berchmans, R. Kalai Selvan, P. N. Selva Kumar, C. O. Augustin, J. Magn.

Magn Mater. 279 (2004) 103-110.

9. N. S. Satya Murthy, M. G. Natera, S. I. Youssef, R. J. Begum, C. M. Srivastava, Phys.

Rev. 181 (1969) 969-977.

10. D R Sagar, Chandra Prakash and Pran Kishan, Solid State Commun. 68 (1988) 193-

195.

11. N. Sparvieri and Cattarin, Mater. Chem. Phys. 25 (1990) 167-75.

12. S.A.Patil, S.M.Otari, V. C. Mahajan, M.G. Patil, A. B. Patil, M. K. Soudagar, B. L.

Patil and S. R. Sawant, Solid State Commun. 78 (1991) 39-42.

13. G. K. Joshi, A. Y. Khot and S. R. Sawant, Solid State Commun. 65 (1991) 1593-

1595.

14. N. Rezlescu and E. Rezlescu, Solid State Commun. 88, 2, (1993) 139-141.

15. M. G. Patil, V. C. Mahajan, S. D. Lotke, B. V. Bhise and S. A. Patil, Solid State

Commun. 91, 8, (1994) 667-670.

16. N. Rezlescu, E. Rezlescu, C. Pasnicu, M. L. Craus, J. Magn. Magn. Mater. 136

(1994) 319-326.

17. C.B. Kolekar, P.N. Kamble, A.S. Vaingankar, J. Magn. Magn. Mater. 138 (1994)

211-215.

18. N. Rezlescu, E. Rezlescu, C. Pasnicu and M. L. Craus, J. Phys. Condens Matter, 6

(1994) 5707-5716.

19. C. Jovalekic, M. Zdujic, A. Radakovic, M. Mitric, Mater. Lett, 24 (1995) 365-

368.

20. V. K. Babbar and J. S. Chandel, J. Appl. Phys. 78 (1995) 2585-2589

21. V. M. Nanoti, C. S. Prakash, D. K. Kulkarni, Mater. Lett. 24 (1995) 167-169.

22. P.S. Anil Kumar, J. J. Shrotri, S.D. Kulkarni, C. E. Deshpande, S. K. Date, Mater.

Lett. 27 (1996) 293-296.

23. M. Pal, P. Brahma, D. Chakravorty, J. Magn. Magn. Mater. 152 (1996) 370-374.

24. Kee Tae Han, Phys. Stat. Sol. (a), 155 (1996) 215-222.

25. E. Rezlescu, N. Rezlescu, P. D. Popa, L. Rezlescu, and C. Pasnicu, Phys. Stat. Sol.

(a), 162 (1997) 673-678.

26. D.N. Bhosale, N.D. Choudhari, S.R. Sawant, P.P. Bakare, J. Magn. Magn. Mater. 173

(1997) 51-58.

27. J. H. Nam, W. G. Hur, and J. H. Oh, J. Appl. Phys. 81 (1997) 4794-4796.

28. N.N. Jani, Bimal S. Trivedi, H.H. Joshi and R.G. Kulkarni, Hyperfine Interact. 110

(1997) 227–237.

29. Misbah-ul-Islam, M. Ashraf Chaudhry, T. Abbas, M. Umar, Mater. Chem. Phys. 48

(1997) 227-229.

30. S. S. Shinde, K. M. Jadhav, Mater. Lett. 37 (1998) 63-67.

31. S. S. Bellad, R. B. Pujar, B. K. Chougule, Mater. Chem. Phys. 52 (1998) 166-169.

32. Misbah Ul Islam, Mazhar Uddin Rana, Tahir Abbas, Mater. Chem. Phys. 57 (1998)

190-193.

33. Mazhar U. Rana, Misbah Ul-Islam, Ishtiaq Ahmad, Tahir Abbas, J. Magn. Magn.

Mater. 187 (1998) 242-246.

34. N. Rezlescu, E. Rezlescu, P.D. Popa, M.L. Craus, L. Rezlescu, J. Magn. Magn.

Mater. 182 (1998) 199-206.

35. M. Z. Said, Mater. Lett. 34 (1998) 305-307.

36. Qi Chen and Z. John Zhang, J. Appl. Phys. 73 (1998) 3156-3158.

37. Kunal B. Modi, H. H. Joshi, J. Mater. Sci. Lett. 17 (1998) 741-743.

38. S. F. Moustafa, M. B. Morsi, Mater. Lett. 34 (1998) 241-247.

39. N. Rezlescu, E. Rezlescu, P.D. Popa, L. Rezlescu, J. Alloys Compd. 275– 277 (1998)

657–659.

40. A.V. Ramana Reddy, G. Ranga Mohan, B.S. Boyanov, D. Ravinder, Mater. Lett. 39

(1999) 153–165.

41. S. S. Bellad, S. C. Watawe, and B.K Chougule, Mater. Res. Bull. 34 (1999) 1099-

1106.

42. K. P. Thummer, H. H. Joshi, R. G. Kulkarni, J. Mater. Sci. Lett. 18 (1999) 1529 –

1532.

43. G. Ranga Mohan, D. Ravinder, A.V. Ramana Reddy, B.S. Boyanov, Mater. Lett. 40

(1999) 39–45.

44. R. B. Pujar, S. S. Bellad, B. K. Chougule, J. Mater. Sci. Lett. 18 (1999) 1083 –

1086.

45. R.B. Pujar, S.S. Bellad, S.C. Watawe, B.K. Chougule, Mater. Chem. Phys. 57 (1999)

264-267.

46. D. Ravinder, A.V. Ramana Reddy, Mater. Lett. 38 (1999) 265–269.

47. A. A. Sattar, A. H. Wafik, K. M. El-Shokrofy and M. M. El-Tabby, Phys. Stat. Sol.

(a), 171 (1999) 563-569.

48. M. Shaikh, S.A. Jadhav, S.C. Watawe, B.K. Chougule, Mater. Lett. 44 (2000)

192–196.

49. B. P. Ladgaonkar, P. N. Vasambekar, A. S. Vaingankar, J. Mater. Sci. Lett. 19

(2000) 1375 – 1377.

50. Laishram Radhapiyari, Sumitra Phanjoubam, H. N. K. Sarma, Chandra Prakash,

Mater. Lett. 44 (2000) 65–69.

51. N. Rezlescu, L. Rezlescu, P.D. Popa, E. Rezlescu. J. Magn. Magn. Mater. 215-216

(2000) 194-196.

52. Woo Chul Kim, Seung Iel Park, Sam Jin Kim, Seung Wha Lee and Chul Sung Kim,

J. Appl. Phys. 87 (2000) 6241-6243.

53. S. C. Watawe, B. D. Sarwade, S. S. Bellad, B.D. Sutar, B. K. Chougule, J. Magn.

Magn. Mater. 214 (2000) 55-60.

54. V. B. Kawade, G. K. Bichile, K. M. Jadhav, Mater. Lett. 42 (2000) 33–37.

55. S. A. Jadhav, Mater. Chem. Phys. 65 (2000) 120–123.

56. Rainer Hochschild and Hartmut Fuess, J. Mater. Chem., 10 (2000) 539-542

57. Mazhar U. Rana, Misbah-ul Islam, Tahir Abbas, Mater. Chem. Phys. 65 (2000) 345-

349.

58. B.P. Ladgaonkar, P. P. Bakare, S.R. Sainkar, A. S. Vaingankar, Mater. Chem. Phys.

69 (2001) 19–24.

59. M. Singh, S. P. Sud, Mater. Sci. Eng. B, 83 (2001) 180–184.

60. M. A. Ahmed, G. Abd-Ellatif, M. Rashad, J. Magn. Magn. Mater. 232 (2001) 194–

204.

61. O. M. Hemeda, M. Z. Said, M. M. Barakat, J. Magn. Magn. Mater. 224 (2001) 132–

142.

62. K. Vijaya Kumar, D. Ravinder, Int. J. Inorg. Mater. 3 (2001) 661–666.

63. R. N. Bhowmik, R. Ranganathan, J. Alloys Compd. 326 (2001) 128–131.

64. I. S. Ahmed Farag, M. A. Ahmed, S. M. Hammad, A. M. Moustafa, Cryst. Res.

Technol. 36 (2001) 85-92.

65. V. Sepelak, D. Schultze, F. Krumeich, U. Steinike, K.D. Becker, Solid State Ionics,

141–142 (2001) 677–682.

66. C.B. Kolekar, A.Y. Lipare, B.P. Ladgaonkar, P.N. Vasambekar, A. S. Vaingankar, J.

Magn. Magn. Mater. 247 (2002) 142–146.

67. A. M. Shaikh, S. c. Watawe, S. A. Jadhav, B. K. Chougule, Mater. Res. Bull. 37

(2002) 2547-2555.

68. A. A. Sattar, A. M. Samy, R. S. El-Ezza, and A. E. Eatah, Phys. Stat. Sol. (a), 193

(2002) 86–93.

69. Xiwei Qi, Ji Zhou, Zhenxing Yue, Zhilun Gui, Longtu Li, Magn. Magn. Mater. 251

(2002) 316–322.

70. M. A. Ahmed, E. Ateia, S. I. El-Dek, Vibrational spectroscopy, 30 (2002) 69-75.

71. Lakshman, K.H. Rao, R.G. Mendiratta, J. Magn. Magn. Mater. 250 (2002) 92–97.

72. Mazhar U. Rana, Tahir Abbas, J. Magn. Magn. Mater. 246 (2002) 110-114.

73. G. J. Baldha, K. G. Saija, K. B. Modi, H. H. Joshi, R. G. Kulkarni, Mater. Lett. 53

(2002) 233– 237.

74. S. E. Jacobo, W. G. Fano, A. C. Razzitte, Physica B, 320 (2002) 261–263.

75. M. A. Ahmed, E. Ateia, S. I. El-Dek, Mater. Lett. 57 (2003) 4256–4266.

76. S. A. Mazen, S. F. Mansour, and H. M. Zaki, Cryst. Res. Technol. 38 (2003) 471 –

478.

77. A. A. Sattar and Samy A. Rahman, Phys. Stat. Sol. (a), 200 (2003) 415–422.

78. D. Ravinder, S. Srinivasa Rao, P. Shalini, Mater. Lett. 57 (2003) 4040–4042.

79. B.K. Labde, Madan C. Sable, N.R. Shamkuwar, Mater. Lett. 57 (2003) 1651– 1655.

80. K. Vijaya Kumar, A. Chandra Shekhar Reddy, D. Ravinder, J. Magn. Magn. Mater.

263, (2003) 121-126.

81. R. N. Panda, J. C. Shih, T. S. Chin, J. Magn. Magn. Mater. 257, (2003) 79-76.

82. S.D. Chhaya, M.P. Pandya, M.C. Chhantbar, K.B. Modi, G.J. Baldha, H.H. Joshi,

J. Alloys Compd 377 (2004) 155–161.

83. J. Azadmanjiri and S. A. Seyyed Ebrahimi, Phys. Stat. Sol. (c) 1, 12 (2004) 3414–

3417.

84. M.A. Ahmed, N. Okasha, M. Gabal, Mater. Chem. Phys. 83 (2004) 107– 113.

85. R.V. Mangalaraja, S. Ananthakumar, P. Manohar, F.D. Gnanam, M. Awano,

Mater. Lett. 58 (2004) 1593– 1596.

86. Ge-Liang Sun, Jian-Bao Li, Jing-Jing Sun, Xiao-Zhan Yang, J. Magn. Magn Mater.

281 (2004) 173–177.

87. Anjana Dogra, Ravi Kumar, N. Kumar, P. Sen, M. Singh, Mater. Sci. Eng. B 110

(2004) 243–250.

88. H.M. Zaki, S.F. Mansour, Mater. Chem. Phys. 88 (2004) 326–332.

89. Seema Verma, P.A. Joy, Y.B. Khollam, H.S. Potdar, S.B. Deshpande, Mater. Lett. 58

(2004) 1092– 1095.

90. K.P. Thummer, M.C. Chhantbar, K.B. Modi, G.J. Baldha, H.H. Joshi, J. Mag. Magn.

Mater. 280 (2004) 23–30.

91. A.M. Abo El Ata, S.M. Attia, T.M. Meaz, Solid State Sci. 6 (2004) 61–69.

92. V.K. Mittal, Santanu Bera, R. Nithya, M.P. Srinivasan , S. Velmurugan, S.V.

Narasimhan, J. Nucl. Mater 335 (2004) 302–310.

93. Uzma Ghazanfar, S.A. Siddiqi, G. Abbas, Mater. Sci. Eng. B 118 (2005) 84–86.

94. A. A. Pandit, A. R. Shitre, D. R. Shengule, K. M. Jadhav, J. Mater. Sci.40 (2005)

423– 428.

95. Uzma Ghazanfar, S.A. Siddiqi, G. Abbas, Mater. Sci. Eng. B 118 (2005) 132–134.

96. A Lakshman, P. S. V. Subba Rao, B Parvatheeswara Rao and K H Rao, J. Phys. D:

Appl. Phys. 38 (2005) 673–678.

97. A.M. Shaikh, C.M. Kanamadi, B.K. Chougule, Mater. Chem. Phys. 93 (2005) 548–

551.

98. S. Balaji, R. Kalai Selvan, L. John Berchmans, S. Angappan, K. Subramanian, C.O.

Augustin, Mater. Sci. Eng. B 119 (2005) 119–124.

99. I. Z. Rahman and T. T. Ahmad, J. Magn. Magn. Mater. 290-291 (2005) 1576.

100. M. H. Khedr and A. A. Farghali, Appl. catalysis B: Environmental 61 (2005) 219.

101. H. M. Zaki, Physica B, 363 (2005) 232.

102. S.A. Masti, A.K. Sharma, P.N. Vasambekar, A.S. Vaingankar, J. Mag. Magn. Mater.

305 (2006) 436–439.

103. Radhapiyari Laishram, Chandra Prakash, J. Magn. Magn. Mater. 305 (2006) 35–39.

104. Lijun Zhao, Hua Yang, Lianxiang Yu, Yuming Cui, Xuepping Zhao, Shouhua Feng,

J. Magn. Magn. Mater. 305 (2006) 91–94.

105. Mansour Al-Haj, J. Mag. Mag. Mater. 299 (2006) 435–439.

106. A.G. Bhosale, B.K. Chougule, Mater. Chem. Phys. 97 (2006) 273–276.

107. B. Parvatheeswara Rao, Ovidiu Caltun, Ioan Dumitru, Leonard Spinu, J. Magn.

Magn. Mater. 304 (2006) e752–e754.

108. A.M. Abo El Ata, M.K. El Nimr, S.M. Attia, D. El Kony, A.H. Al-Hammadi, J.

Magn. Magn. Mater. 297 (2006) 33–43.

109. Mansour Al-Haj, Phys. Stat. Sol. (a) No. 2, 203 (2006) 343–348.

110. M. Tovar, R. Torabi, C. Welker, F. Fleischer, Physica B 385–386 (2006) 196–198.

111. Sonal Singhal, Kailash Chandra, J. Solid State Chem. 180 (2007) 296 – 300.

112. E. Ateia, M.A. Ahmed, A.K. El-Aziz, J. Magn. Magn. Mater. 311 (2007) 545–554.

113. A.K.M. Akther Hossaina, S.T. Mahmud, M. Seki, T. Kawai, H. Tabata, J. Magn.

Magn. Mater. 312 (2007) 210–219.

114. M.M. El Sayed, Ceram. Int. 33 (2007) 413–418.

115. Hua Su, Huaiwu Zhang, Xiaoli Tang, Yulan Jing, Yingli Liu, J. Magn. Magn. Mater.

310 (2007) 17–21.

116. Muhammad Ajmal, Asghari Maqsood, Mater. Lett. 62 (2008) 2077–2080.

117. M.U. Islam, Faiza Aena, Shahida B. Niazi, M. Azhar Khan, M. Ishaque, T. Abbas,

M.U. Rana, Mater. Chem. Phys. 109 (2008) 482–487.

118. M. U. Islam, M. Azhar Khan, Zulfiqar Ali, Shahida B. Niazi, M. Ishaque and T.

Abbas, Int. J. Modern Phys. B 15, 21 (2007) 2669-2677.

119. O. Mirzaee, M.A. Golozar, A. Shafyei, Mater. Charact. 59 (2008) 638 – 641.

120. M.M. Rashad, R.M. Mohamed, H. El-Shall, J. Mater. Proc. Technol.198 (2008)

139–146.

2 EXPERIMENTAL DETAILS

2.1 Composition of Ferrites

Two series of spinel ferrites of various compositions were prepared by ceramic

technique. The constituents for the ferrites were carefully selected keeping in view of

their valances (for charge balancing) and ionic radii. The effect of terbium substitution in

NiFe2O4 and MgFe2O4 spinel ferrites was studied. The following compositions were

prepared;

Ni1-xTbxFe2O4 for x = 0.00, 0.02, 0.04, 0.06, 0.08, 0.10, 0.12, 0.14, 0.16, 0.18, 0.20.

Mg1-xTbxFe2O4 for x = 0.00, 0.02, 0.04, 0.06, 0.08, 0.10, 0.12, 0.14, 0.16, 0.18, 0.20.

2.2 Preparation Technique

The ferrites of various compositions mentioned in section 2.1 were prepared by

ceramic technique. The starting materials were analytical reagent grade powders of NiO,

MgO, Tb4O7, and Fe2O3 (99.99 % pure), supplied by Aldrich. The weight percentage of

each oxide was calculated according to the stoichiometry. Samples were prepared by

standard ceramic technique. The oxides were weighed according to the required

stoichiometric calculations and were intimately mixed together. The mixture of the

oxides of each sample was ground for 3 h, using an agate mortar and pestle to a fine

powder. Before and after grinding, the mortar and pestle were rinsed with acetone to

avoid any contamination. The ground powder was then cold pressed into pellets using a

hydraulic pressing machine (Paul-Otto-Weber). The pressure of 30kN/mm2

was applied

for 1 to 1.5 minutes on each pellet. The pellets were initially sintered at 1000 °C for 48

hours in air atmosphere using box furnace. Then final sintering of the samples was

performed for six hours at 1230 °C in order to produce a homogeneous product. Finally

the samples were air quenched in order to obtain homogeneous distribution of cations on

the sublattices. Both sides of the pellets were cleaned with SiC paper of micron grade,

after quenching.

The toroid shape samples were prepared for both series for permeability

measurements. The powder mixtures were mixed with 5 wt % solution of polyvinyl

alcohol (PVA) as a binder. A die with outer diameter 22mm and inner diameter 10mm

and thickness of 5 mm was used to make toroid samples. The flow chart shows the steps

involved in the preparation of samples.

Powder

Firing

Mixing

Grinding

Pressing

Shaped powder

form

Dense

polycrystalline

product

2.3 Characterization Techniques

2.3.1 X-ray Diffraction

The XRD measurements were made on the sintered pellets using a Philips X pert

MPD X-ray diffractometer with X’pert High Score software. Each sample was scanned in

the 2θ range of 20-70°.The X-ray patterns were obtained using Cu-source with Cu-Kα

radiation (λ=1.540562 Ǻ). The XRD patterns of all the compositions were recorded at

room temperature. The measurement conditions were kept constant for all the

compositions and are tabulated in Table 2.1.

Table 2.1 XRD Measurement conditions

Tube voltage 40KV

Tube current 35mA

Target Cu

Filter Ni

Scan speed 0.0080°/s

Scanning range (2θ) 20-70°

Total scan time 29 minutes

The diffraction occurs due to the presence of certain phase relations between two

or more waves [1]. The differences in path length of various rays arise naturally when it

is assumed how a crystal diffracts X-rays. It is considered that a beam of perfectly

parallel, perfectly monochromatic X-rays K radiations are incident on the crystal at an

angle θ called the Bragg angle. A diffracted beam may be defined as a beam composed of

large number of scattered rays mutually reinforcing each other. This diffracted beam is

illustrated mathematically by Bragg’s law;

2dhkl Sinθhkl = n λ (2.1)

where d is the interplanar spacing of the (hkl) planes and n is called the order of

diffraction.

For phase identification of crystalline materials the d spacing of various peaks is

obtained and matched them with those of some standard reference cards from ICDD

“International Centre for Diffraction Data” or JCPDS “ Joint Committee on Powder

Diffraction Standard”. The average crystallite size of the crystalline materials can be

estimated from the analysis of XRD patterns using Scherrer’s formula [1]:

BB

Kt

cos (2.2)

where t is the average size of the crystallites, B is the Braggs angle for the actual peak

and K is a constant (=0.94). This relationship has been confirmed by number of

researchers. The width B is measured at an intensity equal to half the maximum intensity

(B is an angular width and not a linear width measured in radians) as shown in Fig. 2.1

Fig. 2.1. The line broadening of XRD pattern due to crystallite size [1].

2

1Imax

Imax

Inte

nsi

ty

2θ2 2 θ B 2 θ1

B

The Scherrer’s equation mentioned above is only valid for stress free materials.

The average value of lattice constant ‘ a ’ for all compositions can be calculated using the

Nelson-Riley function [2];

22

2

1 Cos

Sin

CosF (2.3)

where is the Bragg angle. The more precise value of lattice parameter can be obtained

from the extrapolation of the line to F ( ) = 0 or = 90°.

The actual density (X-ray density) was calculated from the values of lattice

parameter using the following relation [3];

3

8

Na

MDx (2.4)

where 8 represent the number of molecules in a unit cell of the spinel lattice, M is the

molecular weight of the sample, ‘ a ’is the lattice constant and N is Avogadro’s number.

2.3.2 Fourier Transform Infrared Spectroscopy (FTIR)

In spinel ferrites, the ceramic network has a certain number of characteristic

vibrations determined by the structure. These vibrations involve modifications of the

electric dipole moment that cause the absorption of electromagnetic radiations in the

range of 10000-100 cm-1

, the domain of the IR spectroscopy. Fourier transform infrared

spectroscopy or FTIR technique provide useful information about the nature and structure

of ferrites. Infrared spectroscopy deals with the interaction of infrared radiation with

matter. A fourier transform is a mathematical operation used to translate a complex curve

into its component curves. In a fourier transform infrared instrument, the complex curve

is an interferogram, or the sum of the constructive and destructive interferences generated

by overlapping light waves, and the component curves are the infrared spectrum.

2.3.2.1 Principle of FTIR

FTIR relies on the fact that the most molecules of sample absorb light in the

infrared region of the electromagnetic spectrum. These absorption peaks corresponds

specifically to the bonds present in the molecule. The sample is irradiated by a broad

spectrum of infrared light and the level of absorbance at a particular frequency is plotted

after fourier transforming the data. The resulting spectrum is characteristic of the bonds

present in the sample.

2.3.2.2 Sample Preparation for FTIR

Ferrites materials are IR active just like other ceramic materials. The present

ferrite materials were diluted with the help of potassium bromide (KBr) powder in order

to not saturate the signal. KBr is a compound known to be IR transparent. One percent of

sample mixed with KBr allow a good final resolution of the IR spectrum. The finally

sintered pellets were grounded carefully in an agate mortar and pestle. Then the powder

was kept in an oven at 105 °C for 72 hrs. The powder was dried in order to avoid water

interferences [4]. The mixed powder was then pressed in a cylindrical die to obtain discs

of approximately 1 mm thickness. These discs were again kept in an oven at 105 °C for

24 hrs to avoid moisture. Then these discs were used to study the FTIR spectra. The FTIR

spectra were measured using a Perkin Elmer FTIR spectrum-2000 spectrometer at room

temperature over the wave number range 370-1500 cm-1

.

2.3.3 Dielectric Constant Measurements

An impedance/gain-phase analyzer (Solatran analytical) along with a specifically

tuned cell was used to study dielectric properties for NiTbFe2O4 & MgTbFe2O4 ferrites.

The real and imaginary parts of the dielectric constant (ε' and ε'') were measured in the

frequency range from 10 Hz to 10 MHz. The dielectric constant for the samples was

calculated by using the formula [5];

A

Cd

0 (2.5)

where C is the capacitance in F, d is the thickness of pellet in meters, A is the cross

sectional area of the flat surface of the pellet and 0 is the permittivity of free space. The

dielectric constant at angular frequency ω is related to the capacitance C and

conductance G as follows [5];

i* (2.6)

* is the complex dielectric constant, is the real part of dielectric constant, and is

the imaginary part of the dielectric constant; where

A

dC

4 (2.7)

A

dG4 (2.8)

where d is the thickness of the sample, A is the cross sectional area of the electrode, and

f 2 (2.9)

where f is the frequency of the applied field.

The ac electrical conductivity of all the samples was calculated using the relation

[6];

σ ac = 2πftanδέε0 (2.10)

where tanδ is the dissipation factor.

2.3.4. Electrical Resistivity Measurements

The dc resistivity of the samples under investigation was measured by two probe

method. A sample holder used for the measurements is shown in Fig. 2.2. In this method

a sample holder with pressure contacts was used. The contacts were made up of copper

having effective area = 0.125 cm2. A dc power supply and sensitive electrometer model

610-C Keithley were connected in series with sample holder. By varying the voltage one

can measure the corresponding current on the electrometer. The circuit diagram is shown

in Fig.2.3. By plotting the I V-curve the resistance was calculated by using the following

relation [7];

t

RA (2.11)

where R is Resistance of the sample (Slope of I V-curve), A is effective area of the

electrode and t is thickness of the sample.

The effective area of the circular electrodes was calculated by using the relation

[7];

2rA (2.12)

where r is radius of the electrode.

Fig 2.2. Two probe sample holder used in electrical measurements

Fig 2.3. The circuit diagram of electrical resistivity measurement apparatus.

2.3.5 Bulk Density Measurements

The bulk density Db (g/cm3) of the sintered ferrites was measured using a

Sartorius density determination kit based on Archimedean principle using toluene as a

liquid. The sample has been immersed in liquid (toluene) and is exposed to the force of

buoyancy. The value of this force is the same as that of the weight of the liquid displaced

by the volume of the sample. With a hydrostatic balance that enables sample to be

weighed in air as well as in liquid. Therefore, it is possible to determine the density of

solid if the density of the liquid causing the buoyancy is known.

The bulk density of all sintered samples was determined by using the following

equation [8];

ta

ta

bWW

WD

. (2.13)

where, Db= bulk density

aW = weight of the sample in air

tW = weight of sample in toluene

t = density of toluene at the measurement temperature

The percentage of porosity (P) for all the compositions is calculated using the

following relation [8] ;

1001

x

b

D

DP (2.14)

where Dx is the X-ray density.

2.3.6 Scanning Electron Microscopy

The microstructure of the samples was observed using a scanning electron

microscope (SEM) model JEOL JSM-840. The average grain size was estimated from

SEM micrographs using the line intercept method.

2.3.7 Vibrating Sample Magnetometer

The M-H loops were plotted on the samples at room temperature. The computer

controlled vibrating sample magnetometer (VSM) LakeShore model 7300 was used in

which the sample was vibrated vertically between the pickup coils in a constant magnetic

field. The vibrating sample magnetometer was calibrated with Ni-standard having

magnetization of 3.475 emu at 5000 G. The field was swept in the range 60-10000 Oe.

2.3.8 The Ferromagnetic Resonance

The ferromagnetic resonance (FMR) measurements were performed on spherical

shaped samples using a standard FMR spectrometer at X-band (9.5GHz) and TE102

reflection cavity. The measurements were made under identical conditions on all the

samples. In FMR measurements, the sample was always saturated due to static magnetic field

required for resonance at microwave frequency. Field swept linewidth was measured by sweeping the field

from 60 Oe to 10 kOe.

Fig. 2.4. Ferromagnetic Resonance (FMR) Apparatus (Courtesy of Colorado State

University, USA).

For FMR the samples were converted into sphere form of dia ≈ 2mm. FMR

profiles of the samples were taken by scanning the field and the frequency was kept

constant at 9.5 GHz. The standard FMR spectrometer is shown in Fig.2.4. The

microwaves of frequency 9.5 GHz were produced from water cooled klystron tube. The

microwave was then allowed to fall on the sample placed at the centre of TE102 X-band

reflection cavity. The reflected microwave is detected by the crystal detector. The

reflected signal is fed into the lock-in amplifier. The lock-in is connected to the

modulation coils. The FMR profile is recorded on the computer using LabView software.

The scan field of the magnets is independently controlled by the LabView coupled with

Gausmeter.

2.3.9 Relative Initial Permeability Measurements

Solatron 1260 impedance analyzer (Solatron analytical) was used to measure the

high frequency impedance. The ferrite samples fabricated in the form of toroid has been

used which are wound with Cu wire to serve as inductor coil. The two ends of the wire

are connected to the analyzer. The two-probe method has been employed to measure the

high frequency impedance. The impedance analyzer is connected to a computer with

GPIB interface. The whole operation of the analyzer is controlled by Solatron materials

research and test, version 1.2 software. This analyzer has the capability to save the

measured data as real, imaginary and magnitude of impedance in ohms.

References

[1] B. D. Cullity, Elements of X-ray Diffraction 2nd

ed.: Addison-Wesley

Publishing Company, Inc. 1978.

[2] Briggs D. and C. J. Riviere, Practical Surface Analysis Vol.1: Auger and X-ray

photoelectron spectroscopy 2nd

ed.: John Wiley & Sons, Chichester, 1990.

[3] J. Smit, H. P. J. Wijn, Ferrites, John Wiley, New York, 1959, 233.

[4] William Kemp, Organic spectroscopy 3rd

ed.; Mac Millan press Ltd. 1991.

[5] E. C. Snelling, Soft Ferrites; Properties and applications, Butterworth, London, 1990.

[6] A. M. M. Farea, Shalendra Kumar, Khalid Mujasam Batoo, Ali Yousef, Chan Gyu

Lee, Alimuddin, J. Alloys Comp. 469 (2009) 451-457.

[7] Muhammad Javed Iqbal, Mah Rukh Siddiquah, J Magn. Magn. Mater. 320 (2008)

845-850.

[8] Noboru Ichinose, Introduction to Fine Ceramics, Ohmsha Ltd., Japan, 1987.

3

THEORETICAL BACKGROUND

3.1 Soft Magnetic Materials

Soft magnets or soft ferrites are those which can be easily magnetized and

demagnetized. The distinguish characteristic of these materials is that they have high

magnetic permeability which make them suitable for use in many electromagnetic

devices. Soft magnetic materials are used in a variety of high-frequency applications.

Examples are flux guidance in permanent magnet and other systems, transformer cores,

microwave applications, and recording heads. A feature of soft magnetic materials is their

low coercivity, which are often several orders of magnitude smaller than those of hard-

and semi-hard materials. Another figure of merit is the initial permeability, which

exceeds 1000 in soft magnets. High-frequency applications require small hysteresis

losses, so that the small coercivities are often more important than a high permeability [1,

2].

3.2 Structure of Ferrites

Soft ferrites have cubic spinel structure. The spinel structure is derived from the

mineral spinel, (MgAl2O4) whose structure was elucidated by Bragg [3] and it crystallizes

in the cubic system. Magnetic spinels have the general formula MOFe2O3 or MFe2O4

where M is one of the divalent metal ions of the transition metal elements such as Mn,

Fe, Co, Ni, Cu and Cd. A combination of these ions is also possible. Trivalent ions

in MFe2O4 can also be replaced partly or completely. All the ferrites contain iron oxide as

the major component. In addition other metal ions like Ni2+

, Co2+

and Mn2+

can be used

to provide the unpaired electron spins. Other divalent ions such as Mg2+

or Zn2+

or

monovalent Li are not paramagnetic but are used in order to disturb the concentration of

Fe3+

ions on the crystal lattice sites to provide or increase the magnetic moment.

The smallest cell of the spinel lattice consists of eight formula units (8

×MFe2O4). The 32 relatively large oxygen ions form a face centered cubic (fcc) lattice in

which two kinds of interstitial sites occur, namely, 64 tetrahedral sites, surrounded by 4

oxygen ions (A-sites) and 32 octahedral sites which are surrounded by 6 oxygen ions (B-

sites). In the cubic spinel discussed above 8 out of 64 tetrahedral sites and 16 out of 32

octahedral sites are occupied by metal ions to maintain the charge balance. In order to

describe the crystal structure more clearly, the unit cell is divided into eight octants with

edge 2

1a (a is the edge of unit cell) as shown in Fig. 3.1. The oxygen ions (anions) are

arranged in the same way in all the octants. Each octant contains four oxygen ions on the

body diagonals and they form the corners of a tetrahedron shown in Fig.3.2. Each octant

contains four tetrahedral metal ions. These metal ions are also arranged in the same

fashion as oxygen ions, from the other ends of the body diagonal. The octahedral metal

ions form four interpenetrating fcc lattices, with edge a, which are displaced with respect

to each other over a distance 24

1a in the direction of the face diagonals of the cube [4].

Fig. 3.1. The spinel structure.

If the tetrahedral sites are occupied by eight divalent metal ions and octahedral

sites are occupied sixteen trivalent metal ions then this kind of structure is called normal

spinel. e.g. ZnFe2O4. If the octahedral sites are occupied by eight divalent and eight

trivalent metal ions, this type of structure is called inverse spinel. Most of the

commercially available ferrites have inverse spinel structure.

Fig. 3.2. The tetrahedral cations (dark circles), octahedral cations

(small circles) and O atoms (large circles)

The oxygen atoms in the spinel structure are not generally located at the exact

positions of the fcc sublattice. Their detailed positions are determined by u parameter

(distance between oxygen ion and a face of a cube). It reflects the adjustment of the

structure to accommodate the differences in the radius ratio of the cations in the

tetrahedral and octahedral sites. The u parameter has a value of 0.375 for an ideal close-

packed arrangement of oxygen atoms. The ideal situation is almost never realized; hence

the value of u parameter of the majority of known spinels is in the range 0.375-0.385.

The u value increases because the anions in tetrahedral sites are forced to move in [111]

direction to give space to the A cations, which are always larger than the ideal space

allowed by the close packed oxygen [5].

3.3 Electrical Properties

3.3.1 Electrical Resistivity

The ferrites have resistivity in the range 10-2

-1011

ohm-cm depending upon their

chemical composition. It was observed that the resistivity was caused by the

simultaneous presence of ferrous and ferric ions on octahedral sites [6]. A lot of research

work has been carried out [7-9] on improving the electrical resistivity of ferrites. A small

amount of foreign ions, about 1 % can be incorporated in an oxide and if these ions have

different valency to those already present (e.g. titinum ions in Fe2O3), then these ions

may force some ions into different valency sites. In order to have high resistivity, the

number of ferrous ions in stoichiometric ferrites should be less. The temperature

dependent resistivity of ferrites obeys the following relation [10];

kTEaexp0 (3.1)

where ρ is the resistivity, k is Boltzman constant and Ea is the activation energy which

can be illustrated as the energy needed to release an electron from the ion for a jump to

the neighboring ion. The value of activation energy lies between 0.1 and 0.5 eV. It has

been noticed that the high activation energy usually goes hand in hand with the high

resistivity of ferrite at room temperature.

3.3.2 Conduction Mechanisms

Ferrites are key materials and exhibit interesting properties owing to which these

are useful in electronic devices. Ferrites which are ferrimagnetic semiconductor led to the

synthesis of new ferrites to achieve optimum resistivity. The substitution of different

cations like manganese or cobalt can also alter the resistivity of ferrites. To produce low

loss ferrites, an extensive research work has been done to study mechanism of electrical

transport properties and the influence of various substitutions on these properties. The

conduction mechanism in ferrites is entirely different from the semiconductors. In

semiconductors charge carriers occupy states in wide energy band. In ferrites charge

carriers are localized at the magnetic atoms. The conductivity is affected by the

temperature dependent mobility while carrier concentration remains unchanged by the

variation of temperature. The cations are surrounded by the close-packed oxygen anions

and the first order approximation can be regarded as an isolated from each other.

There will be a small overlap of the anions charge clouds or orbital. The electrons

related to a particular ion will usually remain isolated and hence localized electron model

is more applicable in ferrites rather than collective electron model (band model). The

conduction in ferrite is due to the exchange of 3d electrons, localized at the metal ions,

from Fe3+

to Fe2+

[11]. Suppose all the Fe2+

ions reside on B-sites to take part in hopping

transport, the number of charge carriers found to be 1022

/cm3. The mobility is low as the

conductivity is low even the number of charge carriers (n) is large. Some of the models

are depicted which explain the conduction mechanism in ferrites.

3.3.3 Hopping Model of Electrons

This model was suggested by Jonker [9]. In ferrites the charge carriers are not free

to move through the crystal lattice but these jump from ion to ion. These materials have

the capability of changing the valency of considerable fraction of metal ions specially

iron ions. In an equilibrium lattice, there is little overlap between the wave functions of

ions on adjacent octahedral sites, ensuing that the electrons/holes are not free to move

through the crystal but are mixed at the metal ions. The occurrence of lattice vibrations

causes the ions to come close together rarely for transfer and it happens with high degree

of probability. Hence the conduction is induced only by the lattice vibrations and the

carrier mobility shows temperature dependence as characterized by activation energy. In

the process of jumping the mobilities of electrons and holes are given by the following

relations

kT

kTqed )/exp( 11

2

1

(3.2)

kT

kTqed )/exp( 22

2

2

(3.3)

where the subscripts 1 and 2 represent the parameter for electrons and holes, d indicate

the jumping length, γ1 and γ2 lattice frequencies active in the jumping process, q1 and q2

activation energies involved in the lattice deformation.

The activation energy does not belong to the energy picture of electrons but to the

crystal lattice around the site of electrons. The expression for the total conductivity in this

case where we have two types of charge carriers is given by

2211 enen (3.4)

The temperature dependent conductivity occurs only due to mobility and not only

due to the number of charge carriers in the sample. The following are the outcomes of

this model. The low value of mobility less than the limiting value (0.1cm2

Vs) taken as

the minimum [12] for band conduction. The independence of seebeck coefficient on

temperature is due to the fact that in this model the number of charge carriers is fixed.

Thermally activated process with activation energy Ea called the hoping activation

energy. The occurrence of n-p transition with changes in the Fe2+

of oxygen concentration

in the system.

3.3.4 Small Polaron Model

A small polaron is a defect created when an electronic carrier is trapped at a given

site as the result of the displacement of adjacent atoms or ions. The whole defect (carrier

and distortion) then migrates by an activated hopping mechanism. The formation of small

polaron can also take place in those materials whose conduction electrons belong to

incomplete inner (d or f) shells which due to small electron overlap, tends to form

extremely narrow bands. The migrations of small polaron [13] require the hopping of

both electron and the polarized atomic configuration from one site to the nearest one. For

an fcc lattice the drift mobility is given by

kTeac /2)1( (3.5)

where c is the fraction of sites which contain an electron (c = n/N), n is number of

electrons, N is the number of available sites/unit volume, e is the electronic charge and a

is the lattice parameter. The symbol г indicates the jump rate of polaron from one site to

the neighboring site. This model explains the low value of mobility, temperature

independent Seebeck coefficient and thermally activated hopping. The hopping electrons

become localized by virtue of its interaction with phonons. In this way the small polaron

is formed and the electrical conduction is due to hopping motion of small polarons.

3.4 Frequency Dependence of Dielectric Constant in Ferrites

It has been known that the ferrites have high dielectric constant and that this

strongly depends on frequency. The loss factor tan δ is generally very high at low

frequency falling by several orders of magnitude as the frequency rises. Koops [8] found

that the dielectric constant of Ni-Zn ferrite Ni0.4Zn0.6Fe2O4 followed much the same

course with changing frequency as the electrical resistance i.e. it fell with rising

frequency down to a very small value. A comparison of the curves with the plotted

measured points shows that there is excellent agreement with the hypothesis. Koops was

able to show that the same dispersion law held for very differently annealed ferrites with

greater or less FeO content.

Fairweather and Frost investigated [14] the temperature dependence of the

dielectric constants of magnesium ferrites and Mg-Al ferrites. They found that the

dielectric constant rose with temperature at low and high frequencies. The maximum of

the tan δ curve shifted toward higher frequencies with rising temperature. The Cu-Zn

ferrites, Mn-Zn ferrites, Cu-Cd ferrites and Ni-Zn ferrites have a maximum dielectric

constant, ε, of 104-10

5. The high dielectric constants of the ferrites at room temperature

and at low frequencies, as discussed above, suggests that they would make excellent

dielectrics for capacitors.

3.5 Magnetic Properties

The magnetization of magnetic materials in general depends on the magnetic field

acting on it. For many materials magnetization, M is proportional to magnetic field, H

and we may write

M = χ H (3.6)

where χ is the magnetic susceptibility which is the property of the material. As both M

and H have same dimensions, χ is dimensionless. The magnetic materials on the basis of

magnetic susceptibility can be classified into subgroups.

3.5.1 Diamagnetic Materials

These materials have negative susceptibilities of the order of 10-6

and for practical

purposes are independent of temperature [15]. They have no intrinsic magnetic moments.

A perfect diamagnetic is a magnetic insulator in the sense that it bars the passage of

magnetic flux, just as an electrical insulator bars the passage of electric charge. Most of

the organic compounds, inert gases, many metals like Hg, Bi and non-metallic elements

like Boron and Sulfur are the examples of diamagnetic substances.

3.5.2 Paramagnetic Materials

These materials have positive susceptibilities lying between 10-3

to 10-6

. Most of

the gases, many salts in the iron group, the alkali metals, and also ferromagnetic and

ferrimagnetic materials at temperatures above the Curie temperatures are the examples of

paramagnetic substances. These substances possess intrinsic magnetic moments. When a

field is applied, it tends to align them but thermal agitation promotes randomization.

These contain atoms with permanent magnetic dipole moments. A subdivision of

paramagnetism is the phenomenon called the super paramagnetism. Super paramagnetism

is met in ferromagnetic and ferrimagnetic materials which are very finely divided as,

when they appear as colloids or precipitates in non-magnetisable matrices. Disappearance

of hysteresis and the collapse of the magnetizing curves of an anisotropic substance,

when plotted against H/T, are typical effects, among others, of super paramagnetism.

3.5.3 Ferromagnetic Materials

In these materials, all atomic spins are aligned more or less parallel. In these

materials susceptibility depends on the field strength. The relation between magnetization

and the field strength is not single valued (characterized by hysteresis). In these materials

below the Curie temperature there exist elementary regions of magnetization, known as

the Weiss domains. The metals iron, cobalt and nickel, many of their alloys, some rare

earths erbium, dysprosium and several of their alloys are ferromagnetic substances.

3.5.4 Antiferromagnetic Materials

These materials, like the ferromagnetic materials, are particular subgroup of

paramagnetic substances. These have susceptibilities of the order of 10-3

but they increase

with heating, up to critical temperature, and then fall off again. The temperature at which

the phenomenon of antiferromagnetism disappears is called Neel temperature.

Manganese monoxide (MnO), iron oxide (FeO), nickel oxide (NiO), iron chloride (FeCl2)

and manganese selenide (MnSe) are the examples of antiferromagnetic substances.

3.5.5 Ferrimagnetic Materials

In these materials, the moments on the two sites are not equal. Thus complete

cancellation did not occur and a net moment resulted which was the difference in the

moments on the two sites. The compounds of the general formula MFe2O4 where M

represents a divalent metal ion and mixed oxides of iron with other elements are

examples of ferrimagnets. These oxides usually have spinel type crystal lattice.

(a) (b) (c)

Fig. 3.3. Magnetic structure of materials (a) ferromagnetic (b) antiferromagnetic

(c) ferrimagnetic

3.6 Magnetization in Ferrites

The ferrites [16] are ionic compounds and their magnetic properties are due to the

magnetic ions they contain. Practically only the magnetism of ferromagnetic and

ferrimagnetic substances is of functionally important. The magnetism of magnetic oxide

materials, ferrimagnetism, is a crystal phenomenon. It occurs for crystal of spinel

structure. The lattice of this structure comprises sublattices A and B. The two sublattices

are magnetically antiparallel and show markedly different magnetic moments. Each

sublattice could be treated as possessing its own magnetization, and the resulting ferrite

would be the superposition of the two magnetizations.

The spontaneous magnetization in spinel ferrites can be estimated on the basis of

their composition, cation distribution and the relative strength of the possible interactions.

Since cation-cation distances are generally large, hence direct interaction is negligible.

The strongest interaction is expected to occur between octahedral and tetrahedral cations.

The next interaction is between octahedral and octahedral cations. The octahedral and

tetrahedral interaction is dominant interaction usually in inverse spinel and it leads to a

saturation magnetization at 0 K which depends only on the magnetic moment of the

divalent cation. Antiparallel order cancels Fe3+

moments in octahedral and tetrahedral

sites and the divalent cation moment on octahedral sites accounts for the net

magnetization. The temperature dependent magnetization in ferrimagnetic materials is the

difference in sublattice magnetizations. Since each sublattice has its own temperature

dependence, hence a wide variety of magnetization curves can be obtained in these

materials.

3.7 Neel’s Theory of Ferrimagnetism

L. Neel [17] suggested that a ferrimagnetic crystal could be divided into two

sublattices, namely A-sublattice (tetrahedral-sites) and B-sublattice (octahedral-sites) in a

spinel structure. He assumed the existence in the material of one magnetic ion only,

whose fraction λ appeared on A-site and fraction μ on B-site here λ + μ = 1 (note that λ =

μ = ½). The remaining lattice sites were assumed to house only ions of zero magnetic

moment. Consider a simple ferrite of the form MFe2O4 which satisfies Neel’s

assumptions, the magnetic ions are trivalent ferric Fe3+

, M is non-magnetic and the

formula might be written Fe2λ M (1-2λ) [Fe (2-2λ) M 2λ] O4. Where the bracketed ions are

those on the octahedral sites. There are several interactions between magnetic ions to be

considered and these may be termed as A-A, B-B, A-B and B-A interactions. Where A-A

refers to the interaction on A-site.

In the Neel’s theory it is assumed that the A-B and B-A interactions are identical

and predominate over A-A and B-B interactions, and are such as to favour the alignment

of the magnetic moment of each A-ion more or less antiparallel with the moment of each

B-ion. From the Weiss molecular field theory Neel described the interaction with in the

material. The magnetic field acting upon an atom or ion may be written as

H = H0 +Hm (3.7)

where H0 is the external applied field and Hm is the molecular field which arises due to

interactions with other atoms or ions within material. When the molecular field concept is

applied to ferrimagnetic material we have

H A = H AA + H AB (3.8)

H B = H BB + H BA (3.9)

Here the molecular field H A acting on an ion A-site is represented as the sum of the

molecular field HAA due to neighbouring A-ions, and HAB due to its neighbouring on B-

sites. A similar definition holds for the molecular field HB acting on B-ion. The molecular

field components may be written as γAA

HA = γAAMA HAB = γABMB HBB = γBBMB HBA = γBAMA

where γ’s are the molecular field coefficients and MA and MB are the magnetizations of A

and B sublattices respectively. It may be shown that

γAB = γBA but γAA ≠ γBB

unless the two sublattices are identical. Neel showed that γAB < 0, favouring antiparallel

arrangements of MA and MB gives rise to ferrimagnetism.

In the presence of an applied field H0, the total magnetic fields acting on each sublattices

may be written

Ha = H0 +Ha = H0 + γAA MA + γABMB (3.10)

Hb = H0 +Hb = H0 + γBB MB + γABMA (3.11)

3.8 Saturation Moments

The saturation magnetization of ferrite can be calculated at 0 °K by knowing the

moment of each ion, the distribution of ions on A and B sites and the interaction between

the two sites is negative [18]. In Ni ferrite, all Ni2+

ions reside on B-sites and Fe3+

ions are

randomly distributed on both A and B-sites. The moments of Fe3+

ions cancel and the net

moment is that of the Ni2+

ion, which is 2μB. Thus it can be generalized that the saturation

magnetization of any inverse ferrite is simply the moment of the divalent ion. The Zn

ferrite has normal structure. The Zn2+

ions are of zero moments occupies A sites. Hence

there can be no AB interaction. The negative BB interaction then occurs, Fe3+

ions on B

sites tend to have antiparallel moments and there is no net moment.

Magnesium ferrite is a well known mixed ferrite. If its structure were completely

inverse, its net moment would be zero, because the moment of Mg2+

ion is zero. It was

noted earlier that 0.1 of the Mg2+

ions are on A-sites and these displaces an equal number

of Fe3+

ions to B-sites. Hence Mg ferrite giving an expected net moment of 1.0 μB. This is

very close to the experimental value of 1.1 μB. In mixed ferrites containing zinc, it is

remarkable that the addition of nonmagnetic zinc increases the saturation magnetization.

Suppose a mixed ferrite containing 10 molecular percent Zn ferrite in Ni ferrite. The Zn2+

ions are of zero moments go to A sites in pure Zn ferrite and Fe3+

ions of Zn ferrite have

parallel moments in B-sites because of the strong AB interaction. The expected net

moment increases from 2.0 μB, for pure Ni ferrite to 2.8 μB for the mixed ferrite. If this

increase of 0.8 μB per 10 molecular percent of Zn ferrite continued with further additions,

we would expect pure Zn ferrite to have moment of 10 μB. This does not happens because

the A moments will soon become too weak to affect the B moments and the net moment

begin to decrease. The discrepancies between the theoretical and experimental moments

may be ascribed to the following;

Orbital moments may not be completely quenched

The structure may not be completely inverse.

The degree of inversion can sometimes be changed by heat treatment. Hence the

saturation becomes a temperature sensitive property.

3.9 The Magnetic Interactions

In ferrimagnets, the metal ions occupy the two crystallographic sites, namely A-

sites and B-sites. Three kinds of magnetic interactions between the metal ions are

possible through O2-

ions. These are A-A interactions, B-B interactions and A-B

interactions. It has been experimentally noted that the energies of these interactions are

negative and thus induce an antiparallel orientation. The magnitude of interaction energy

between the magnetic ions depends upon the distances from these ions to the oxygen ion

through which the interaction occurs and the angle between these two magnetic ions.

An angle of 180° will give rise to the greatest exchange energy and the energy

decreases very rapidly with increasing distance. The various possible configurations of

the ions pairs in spinel ferrites with favourable distances and angles for an effective

magnetic interaction [19] are shown in Figure 3.4. On the basis of the values of the

distance and the angle φ, it may be concluded that of the three possible interactions, the

A-B interaction has the greatest magnitude. From the Figure 3.4 it is evident that the two

configurations for the A-B interaction have small distances and the values of the angle φ

are fairly high. In the B-B interaction the first configuration will be effective since in the

second configuration the distance is too large for effective interaction.

Fig. 3.4. Magnetic interactions (Adapted from Gorter [19])

The A-A interaction is the weakest as the distance is large and the angle φ is ~

80°. Thus with only A-B interaction predominating, the spins of the A and B-site ions, in

ferrimagnets will be oppositely magnetized sublattices, with a resultant magnetic moment

equal to the difference between those of A and B site ions.

3.10 Domains in Ferrites

The magnetic materials are subdidvided into domains. Domains contain 1012

to

1015

atoms and their dimensions [20] are of the order of microns. In general, the magnetic

orientations are distributed at random, depending upon the microstructure of its crystals.

In each domain the magnetic moments of the atoms are mutually parallel. With in each

domain, the magnetization is uniform and is equal to saturation magnetization. But

different domains are magnetized in different directions. Domains are formed basically to

reduce the magnetostatic energy which is the magnetic potential energy contained in the

Φ = 125° 9¹ 154° 24¹ 90° 125° 2¹ 79° 38¹

field lines, connecting north and south poles outside of the material. In Figure3.5 the

arrows indicate the direction of the magnetization and consequently the direction of spin

alignment in the domain. We can substantially reduce the length of the flux path through

the unfavorable air space by splitting that domain into two or more smaller domains.

This splitting process continues to lower the energy of the system until the point

that more energy is required to form the domain boundary than is decreased by the

magnetostatic energy change. When a large domain is split into n domains, the energy of

the new structure is about l/nth of the single domain structure. In Fig. 3.5, the moments in

adjacent domains are oriented at an angle of 180° to each other. Other configurations may

occur which lead to lowering of the energy of the system. The triangular domains are

called closure domains. In this configuration, the magnetic flux path never leaves the

boundary of the material. Therefore, the magnetostatic energy is reduced. This type of

structure may also be found at the outer surfaces of a material. The size and shape of a

domain may be determined by the minimization of several types of energies.

Fig. 3.5. Magnetization in Domains. (a) single domain, (b) closure domains, (c)

closure domains.

3.11 Magnetostatic Energy

The magnetostatic energy is the work needed to put magnetic poles in special

geometric configurations. It is also the energy of demagnetization. It can be calculated for

simple geometric shapes. Neel (1944) and Kittel (1946) have calculated the magnetostatic

energy of flat strips of thickness, d, magnetized to intensity, M, alternately across the

thickness of the planes. The equation is;

Ep= 0.85 dM2 (3.12)

The general formula for the calculations of other shapes is

Ep= constant x dM2 (3.13)

Therefore the magnetostatic energy is decreased as the width of the domain

decreases. This mathematically confirms the assumption that splitting of domains into

smaller widths decreases the energy from the magnetostatic view.

3.12 Magnetocrystalline Anisotropy Energy

In most magnetic materials, the domain magnetization tends to align itself along

one of the main crystal directions. This direction is called the easy direction of

magnetization. Sometimes it is an edge of the cube and at other times, it may be a body

diagonal. The difference in energy of a state where the magnetization is aligned along an

easy direction and one where it is aligned along a hard direction is called the

magnetocrystalline anisotropy energy. This magnetocrystalline anisotropy energy is also

that needed to rotate the moment from the easy direction to another direction. The energy

of the domain can be lowered by this amount by having the spins or moments align

themselves along these directions of easy magnetization. Magnetocrystalline anisotropy

is due to the fact that there is not complete quenching of the orbital angular momentum.

3.13 Magnetostrictive Energy

When a magnetic material is magnetized, a small change in the dimensions

occurs. The relative change is on the order of several parts per million and is called

magnetostriction. The converse is also true. That is, when a magnetic material is stressed,

the direction of magnetization will be aligned parallel to the direction of stress in some

materials and at right angles to it in others. The energy of magnetostriction depends on

the amount of stress and on a constant characteristic of the material called the

magnetostriction constant

E = 3/2λσ (3.14)

where λ is magnetostriction constant and σ is applied stress.

If the magnetostriction is positive, the magnetization is increased by tension and

also the material expands when the magnetization is increased. On the other hand, if the

magnetostriction is negative, the magnetization is decreased by tension and the material

contracts when it is magnetized. Stresses can be introduced in ferrites which can affect

the directions of the moments.

3.14 Domain Wall Energy

Bloch (1932) was the first to present the idea of magnetic domains, with domain

wall boundaries separating them. In the domain structure of bulk materials, the domain

wall is the region where the magnetization direction in one domain is gradually changed

to the direction of the neighboring domain. If δ is the thickness of the domain wall which

is proportional to the number of atomic layers through which the magnetization is to

change from the initial direction to the final direction, the exchange energy stored in the

transition layer due to the spin interaction is;

Ee= kTc/a (3.15)

where kTc is thermal energy at the Curie point and ‘a’ is the distance between atoms.

Therefore the exchange energy is reduced by an increase in the width of the wall or with

the number of atomic layers in that wall. However, in the presence of an anisotropy

energy or preferred direction, rotation of the magnetization from an easy direction

increases the energy so the wall energy due to the anisotropy is;

Ek= kλ (3.16)

In this case, the energy is increased as the domain width or number of atomic layers is

increased. The two effects oppose each other and the minimum energy of the wall per

unit area of wall occurs according to the following equation;

Ew = 2(KaTc/a)1/2

(3.17)

where Ka is the Anisotropy constant

If magnetostriction is a consideration, the equation is modified to;

Ew= 2(kaTc/a)1/2

(Ka+3 λsσ/2)1/2

(3.18)

where λs is magnetostriction constant. Typical values of domain wall energies are on the

order of 1-2 ergs/cm2.

3.15 Hysteresis Loop

In soft magnetic materials, we want a high induction for a low field. In this case,

H is very small compared to 4πM and B is essentially equal to 4πM. If we start with a

demagnetized specimen and increase the magnetic field, the induction increases as shown

in Figure 3.6. At high fields, the induction flattens out at a value called the saturation

induction, Bs. If, after the material is saturated, the field is reduced to zero and then

reversed in the opposite direction, the original magnetization curve is not reproduced but

a loop commonly called a hysteresis loop is obtained. Figure 3.6 shows such a hysteresis

loop with the initial magnetization curve included. The arrows show the direction of

travel. We notice that there is a lag in the induction with respect to the field. This lag is

called hysteresis. As a result, the induction at a given field strength has two values and

cannot be specified without a knowledge of the previous magnetic history of the sample.

The area included in the hysteresis loop is a measure of the magnetic losses incurred in

the cyclic magnetization process. The hysteresis losses can also be correlated with the

irreversible domain dynamics. The value of the induction after saturation when the field

is reduced to zero is called the remanent induction or remanence, (Br). The values of the

reverse field needed after saturation to reduce the induction to zero is called the coercive

force or coercivity, (Hc). Most polycrystalline sintered samples of ferrites with spinel

structure have a relatively low coercive force.

Fig. 3.6. Typical hysteresis loop along with initial magnetization curve

3.16 Permeability

Ψ

Ψ

π2 - Ψ

dl

In ferromagnetics and ferrimagnetics we are concerned with the total flux density,

B, and it is more convenient to define a very important parameter, ‘μ’ the magnetic

permeability which is the ratio of induction, B to magnetizing field, H. However, this

parameter can be measured under different sets of conditions. For example, if the

magnetizing field is very low, approaching zero, the ratio will be called the initial

permeability μ0. It is defined as follows;

μ0 = limit (B/H) (3.19)

B 0

This parameter will be important in telecommunications applications where very

low drive levels are involved. On the other hand, when the magnetizing field is sufficient

to bring the B level up to the point of inflection, the highest permeability occurs. This can

be seen by visualizing the permeability as the slope of the line from the origin to the end

point of the excursion. Since the magnetization curve flattens out after the point, the μ

will decrease. It is important to know the position of the maximum permeability and the

course of μ versus B.

The permeability was calculated by using the following derivation.

The Biot and Savart law could be used [21] to define the magnetic flux density B

due to a circular coil carrying a current I. In Fig. 3.7, ‘a’ is the radius of the circular coil.

Let us calculate the magnetic flux density at the point P at a distance z 0 from point ‘O’ on

the axis of the coil.

r

Fig. 3.7. A circular coil carrying current I [22].

The element dl of the current carrying loop at the top of the coil points

perpendicularly out of the page. The point P and the current element ‘Idl’ of the coil are

separated by a distance ‘r’. The magnetic field produced by the element dl is dB, which is

normal to dl and ‘r’. This will act in the direction shown in the figure. On integrating

round the coil, the sum of the components of dB, normal to the axis, is zero. The

magnitude of the component parallel to the axis is given by [22]:

cos

4 2

0

r

IdldB (3.20)

where ψ is the angle between the axis and magnetic field dB.

Integrating equation 3.20, the magnetic flux density is given by:

r

a

r

Ia

r

Idl

r

IB

2

0

2

0

2

0

22

4

coscos

4

(3.21)

23

22

2

0

2 za

IaB

(3.22)

a Z0

d P I

The above derivation could be used to calculate the field on the axis of a solenoid having

N number of turns. In Fig. 3.8, the point P the axis of the solenoid is at a distance z0 from

O.

Fig. 3.8. A solenoid carrying current I

If the turns are equally spaced and closely wound, we may consider the current is

flowing uniformly round the cylinder. That is, if we consider the length to be divided into

elements dz, as shown at a distance z from O, the current in this section of the coil

is dzIl

N,

23

22

0

2

0

2

1

azz

dza

l

NIdB

(3.23)

Integrating the equation 3.23, the magnetic flux density is given by:

1

0

22

0

2

0

1

02

327

0

2

2

1

2

1

azz

dza

l

NI

azz

dza

l

NIB O

22

0

0

22

0

00

2

1

azl

zl

az

z

l

NI

coscos2

1 0 l

NI (3.24)

For infinite solenoid α = β = 0

Hence the equation 3.24, can be simplified as

l

NIB 0 (3.25)

The total flux produced by the coil is given by

BA (3.26)

where A denote the cross-sectional area of the solenoid.

When ac current will flow through the coil, the magnetic flux through the coil will

change as a function of time and an electromotive force, e will be produced. According to

Faradays law, Lenz’s law induced emf, e is directly proportional to the rate of change of

flux dt

d,

dt

dNe

(3.27)

where N is the number of turns in the winding which senses.

The negative sign indicates that the emf induced opposes the changes in flux.

Since, the magnetic flux is proportional to the current one can write:

dt

dIL

dt

d

(3.28)

where L is the self inductance. For an inductor the inductance can further be defined as:

IL

(3.29)

where, is the total linkage of the one turn inductor and ‘I’ is the current through the

inductor. An inductor having N-turn, the inductance can be defined as:

l

AN

I

BAN

I

NL

2

0 (3.30)

Any magnetic material as a core inside the solenoid having magnetic permeability,

will change the self inductance. Mathematically,

l

ANL r

2

0 (3.31)

Or, l

ANL a

2 (3.32)

Or, AN

Ll2

(3.33)

where, L is the self-inductance of the solenoid with magnetic core, r is the relative

magnetic permeability and = 0 r is the magnetic permeability in the presence of a dc

magnetic excitation.

In a coil with varying magnetic field, the magnetic permeability is measured as

the ratio of the mean induction across the specimen cross-section to the applied field. For

ac excitation, the magnetic field strength (H) and induction (B) are two sinusoidally

varying functions of the same frequency but not of the same phase in the presence of

losses. It is well known that the magnetic permeability is the result of macroscopic

atomic currents, which produce magnetic moments within the ferromagnetic materials.

As an ac current flows through the core material, a circular magnetic field is produced

around it. This induces the atomic magnetic dipole moments with in the core. The

induced magnetic moment is proportional to the external applied field. In the absence of

an external applied field these magnetic moments are randomly oriented. An applied field

tends to orient these moments along the field direction. Each magnetic dipole moment

makes an average angle with the field direction. An equivalent solenoid current

surrounding the specimen can replace this magnetic effect of the material. This current is

called the amperian surface current.

Now, during ac excitation, the net magnetic moment of the material rotates

according to the magnitude and the polarity of the induced field. The average angle of the

dipole moment direction with the field direction changes in each cycle, which changes

the magnetic induction. Finally, the magnetic induction becomes periodic due to the

periodic magnetic field strength. In this situation the observed magnetic permeability

can no longer be expressed by only real quantities. Magnetic permeability then can be

referred to as “Apparent Permeability, a ” This quantity consists of a real and an

imaginary part. The part of magnetic induction that is in phase with the applied field can

be attributed to the real part whereas, the out of phase part can be considered as the

imaginary part. Mathematically, the apparent permeability can be expressed as a complex

number:

aaa j (3.34)

where is real part of apparent permeability and imaginary part of apparent

permeability.

The real part of the permeability is a measure of how much energy is stored in a

material. The imaginary part of the permeability is a measure of how much energy is lost

in materials. So, the apparent permeability is the net change in energy, i.e. the difference

between the real and imaginary parts of the permeability [23].

Fig. 3.9. Equivalent circuit of a toroid.

For the toroidal specimen used in this work, wound with at least 25 equally

spaced turns (Fig. 3.9), the equivalent series circuit representing the magnetic core of the

coil is a self-inductance Lm in series with an intrinsic resistance Rm related to the complex

apparent permeability.

The permeability is a complex quantity expressing the loss of energy which

occurs as the magnetization alternates, so that the impedance of the winding is not purely

reactive but has also resistive component [24]. The total impedance of this series circuit

could be expressed as:

LjLjRZ mm (3.35)

Or, LjRLj m (3.36)

Or, mm LjjRLj 22 (3.37)

Or, mm LjRL (3.38)

Or,

m

m

RjLL (3.39)

Comparing equation 3.25 and 3.33 the apparent permeability could be related to the

impedance as follows:

AN

lRjL m

ma 2

(3.40)

Or, AN

lRj

AN

lL mm

a 22 (3.41)

From equation 3.39 the real and imaginary part of relative permeability can be expressed

as follows:

AN

lLm

a 2 (3.42)

real part of relative permeability,

0

a

r

(3.43)

AN

lRm

a 2 (3.44)

complex part of relative permeability

0

a

r

(3.45)

the imaginary part of the complex permeability, henceforth, is referred to as permeability

loss . Some times it can be divided by and formed as loss factor tanδ.

Loss Factor, r

rtan

(3.46)

3.17 Ferromagnetic Resonance

At very high frequencies, domains walls [16] are unable to follow the field and

the only remaining magnetization mechanism is spin rotation within domains. This

mechanism eventually also shows a dispersion, which always takes the form of a

resonance. Spins are subjected to the anisotropy field which represent spin-lattice

coupling and when an external field is applied, the spins experience a torque. The

response of spins is not instantaneous and spins precess around the field direction for a

certain time (the relaxation time τ) before adopting the new orientation. The frequency of

this precession is given by the Larmour frequency:

ωL = γμ0HT (3.47)

where HT is the total field acting on the spin,

HT = HK +H + Hd + …., (3.48)

where HK, H, and Hd are the anisotropy and the external and demagnetization fields,

respectively. If an ac field of angular frequency ωL is applied to the sample, a resonant

absorption (ferromagnetic resonance) occurs.

Ferromagnetic resonance experiments are usually performed by saturating the

sample with a strong dc field and applying a small perpendicular ac field at a constant

frequency. The dc field is then slowly varied to achieve resonance conditions. This is the

best arrangement for resonance experiments, because all the spins are oriented in a given

direction in the saturated sample and the ac field exerts a torque on their perpendicular

component. Experimentally, it is easier to use an ac field of high, constant frequency and

slowly vary a strong dc field to achieve resonance conditions. Resonance is plotted as

power absorption as a function of dc field, for a given constant frequency as shown in

Fig.3.10.

Fig. 3.10. Ferromagnetic resonance, ΔH is the resonance line width

The line width of resonance peaks (width measured at half the height of resonance

peak), ΔH, depends on variety of factors. Anisotropy field effects can be expressed in

terms of a damping constant leading to a contribution to ΔH. If the dc field is not strong

enough to saturate the sample, the total field in each domain is different and ΔH

increases. In polycrystalline samples, this effect is more dominant, because interactions

between grains result in larger variations in the total field. The surface roughness can also

produce significant contributions to ΔH.

ΔH

Applied magnetic field (H)

Ab

sorp

tion

3.18.1 Ferromagnetic relaxation

The power absorbed by the sample is limited due to microwave losses. This

process is called ferromagnetic relaxation. The magnetization time evolution equation

including losses can be written as;

dampingeff TtrHtrMdt

trMd ),(),(||

),(

(3.49)

It may be difficult to explicitly include all the causes of damping in eq. 3.49 as a

sum of various loss terms. However, they can be explained with the help of following

phenomenological models. Using these models some experimental parameters can be

determined which could be meant for the losses.

3.18.2 Gilbert Damping Model

This model of ferromagnetic relaxation has been presented by Gilbert [25]. If

there are driving force and damping in the physical system, the damping force will

interact with driving force. In this model the damping force is proportional to the rate of

change of the magnetization which is macroscopic dynamical variable in the magnetic

system. This is similar to mechanical damping in a viscous medium, which depends upon

velocity. This is taken into account by a damping field that reduces the actual magnetic

field to a field

dt

trMd

MtrH

S

G

eff

),(

||),(

or

dt

trMdtrM

MtrHtrM

dt

trMd

S

G

eff

),(),(),(),(||

),(

(3.50)

G is the Gilbert damping parameter, which is a material-dependent constant.

This model describes the intrinsic damping that is mainly caused due to magnon-electron

scattering, but also due to eddy currents and magnon-phonon scattering.

3.18.3 Landau-Lifshitz Model

Landau and Lifshitz presented another model of ferromagnetic relaxation.

According to this model the loss term in eq. 3.49 is proportional to the component of the

magnetic field that is perpendicular to the magnetization [25].

),(),(),(||),(),(||),( 2

trHtrMtrMM

trHtrMdt

trMdeff

S

LL

eff

(3.51)

LL2 is usually a very small number, hence it can be ignored.

3.18.4 Other Ferromagnetic Damping Models

Bloembergen and Wang [26] presented a model of ferromagnetic relaxation.

According to this model relaxation of the transverse components of the magnetization are

independent from the one of the longitudinal component. These elaxations are

characterized by the relaxation times T1 and T2 respectively. According to this model the

magnetization is described by the Bloch equations. That is why it is called the Bloch-

Bloembergen model.

2

)(

)(

)( ),(),(),(||

),(

T

trMtrHtrM

dt

trdM yx

yxeff

yx

(3.52)

1

),(),(||),(

T

MMtrHtrM

dt

trdM SZ

ZeffZ

(3.53)

The length of the magnetization vector ),( trM

is not conserved in this model.

If the condition

),().,(

),().,(),(

1

2

trHtrM

trHtrMtrHM

T

T

eff

effeffS

(3.54)

is fulfilled, the length of the magnetization vector will stay constant (Silva, Constrained

Codrington, Olds and Torrey model [27]).

),().,(

),(),(),(1),(),(||

),(

2 trHtrM

trHtrMtrM

TtrHtrM

dt

trMd

eff

eff

eff

(3.55)

Which is equivalent to the landau-Lifshitz model with a field dependent .

References

[1] R. A. McCurrie, "Ferromagnetic Materials Structure and Properties", Academic

Press, London, 1994.

[2] J. E. Evetts (Ed.), "Concise Encyclopedia of Magnetic and Superconducting

Materials", Pergamon Press, Oxford 1992.

[3] W. H. Bragg, Nature, 95 (1915) 561-561.

[4] J. Smit , H. P. J. Wijn, “Ferrites”, John Wiley, New York, 1959.

[5] R. J. Hill, J. R. Craig and G. V. Gibbs, Physical Chemistry of Minerals, 4, (1979)

317-339.

[6] E. J. W. Verwey and J. H. de Boer, Rec. Trav. Chim. Pays Bass, 55 (1936) 531-

540.

[7] L. G. Van Uitert, J. Chem. Phys. 23 (1955) 1883-1887.

[8] C. G. Koops, Phys. Rev. 83 (1951) 121-124.

[9] G. H. Jonker, J. Phys. Chem. Solids, 9 (1959) 165-175.

[10] J. Smit , H. P. J. Wijn, Ferrites, John Wiley, New York, 1959.

[11] A. J. Bosmann and C. C. Creve, Phys. Rev. 144 (1966) 763-770.

[12] J. H. Van Santen and G. H. Jonker, Physica, 19 (1953) 120-130.

[13] C. A. Bates and P. Steggels, J. Phys. C 8 (1975) 2283-2299.

[14] A. Fairweather and E. J. Frost, Proc. IEE (IIa) 100 (1953) 15-22.

[15] Dr-Ing. Carl Heck, “Magnetic Materials and their Applications,” Butterworth &

Co. Ltd. 1974.

[16] Raul Valenzuela, “Magnetic Ceramics”, Cambridge university press, New York,

1994.

[17] K. J. Standley, “Oxide Magnetic Materials”, 2nd

edition, Clarendon Press,

Oxford 1972.

[18] B. D. Cullity, “Introduction to Magnetic Materials”, Addison-Wesley Publishing

Company, Notre Dame, 1972.

[19] E. W. Gorter, Philips Res. Report 9 (1954) 295, 321, 403..

[20] Alex Goldman, Modern Ferrite Technology”, Van Nostrand Reinhold, New

York, 1990.

[21] M. Kamruzzaman, Study of Magneto-Impedance Effect in Cobalt and Iron based

Metallic Glass Ribbons, Ph. D. Thesis, 2003. Department of Physics, University

of Limerick, Limerick, Ireland.

[22] B. B. Laud, “Electromagnetics”, Wiley Eastern, 1983.

[23] A. Berkowitz, and E. Kneller, Magnetism and Metallurgy. Vol. 1: Academic

Press, New York. 230.

[24] E. C. Snelling and A. D. Giles, “Ferrites for Inductors and Transformers”, John

Willey & Sons, 1983.

[25] T. L. Gilbert, IEEE Trans. Magn. 40 (2004) 3443-3449.

[26] N. Bloembergen and S. Wang, Phys. Rev. 93 (1953) 72-83.

[27] S. Kalarickal, Ferromagnetic Relaxation in (1) Metallic Thin Films and (2) Bulk

Ferrites and Composite Materials for Information Storage Device and

Microwave Applications, Ph. D. Thesis, 2006. Department of Physics, Colorado

State University, Fort Collins, U. S. A.

4 RESULTS AND DISCUSSION

Ni1-xTbxFe2O4 Series

4.1 Structural Analysis

Figs. 4.1 and 4.2 show the X-ray diffraction patterns of the Ni1-xTbxFe2O4 ferrites

(x = 0 ≤ x ≤ 0.08 and 0.1 ≤ x ≤ 0.2 respectively). Table 4.1 shows the phases precipitated

out, lattice constant, X-ray density, bulk density and grain size of the Ni1-xTbxFe2O4

ferrites. For 0 ≤ x ≤ 0.08, all the samples are monophase cubic spinel structure while for

0.1 ≤ x ≤ 0.2 the samples are biphasic. A small reflection peak of a second phase that is

identified as an orthorhombic phase appeared at 2θ = 33.42˚ for 0.1 ≤ x ≤ 0.2. This

reflection peak can be identified as the (3 2 2) reflection of TbFeO3 phase (ICDD# 88-

0144). Strong diffraction peaks corresponding to the planes 220, 311, 222, 400, 422, 511

and 440 were observed. The d-spacings and the hkl values are given in Tables 4.2 and 4.3

respectively. The average value of lattice constant ‘ a ’ for all compositions was

calculated using the Nelson-Riley function [1];

22 cos

sin

cos

2

1F (4.1)

where θ is the Bragg angle. The precise value of lattice parameter was obtained from the

extrapolation of the line to F (θ) = 0 or θ = 90°. The concentration dependence of lattice

constant ‘ a ’ was determined from XRD data for x = 0.0-0.2 as given Table 4.1.

Fig.4.1.X-ray diffraction patterns for Ni1-xTbxFe2O4 ferrites (x = 0.0, 0.02, 0.04, 0.06,

0.08).

2θ (degrees)

Inte

nsi

ty (

Arb

itra

ry U

nit

s)

Fig. 4.2. X-ray diffraction patterns for Ni1-xTbxFe2O4 ferrites (x = 0.10, 0.12, 0.14,

0.16, 0.18, 0.20)

2θ (degrees)

Inte

nsi

ty (

Arb

itra

ry U

nit

s)

The lattice constant gradually increases up to x = 0.08 and it decreases for higher

terbium concentration. A slight increase in the lattice parameter with the increase of Tb-

concentration (x) can be explained on the basis of relative ionic radii of Tb3+

and Ni2+

ions. Since the Tb3+

ion has a larger ionic radius (0.93Å) than that of the Ni2+

(0.69Å) ion,

a partial replacement of the Ni2+

by Tb3+

causes an expansion of the spinel lattice, thereby

increasing the lattice constant. Ni2+

ions prefer B-sites [2] and it is expected that most of

the replacement of Ni+2

ions may occur on the octahedral sites. A possible explanation for

decrease in ‘ a ’ for 0.1 ≤ x ≤ 0.2 is that some Ni atoms may also change their site

preferences to tetrahedral sites because of the influence of terbium.

The decrease in ‘ a ’ may also suggest the existence of a solubility limit for

terbium ions at x = 0.08 to 0.1. Once the solubility limit is reached, the terbium ions no

longer dissolve in the spinel lattice and diffuse to the grain boundaries combining with Fe

to form TbFeO3 and forming an ultra thin layer around grains [3]. A non-linear behavior

of ‘ a ’ with Tb-concentration in other rare earth substituted ferrite systems has also been

reported by other researchers [4]. A notable feature in the X-ray patterns is the intensity

of the diffraction peaks which is weaker for the terbium substituted ferrites than for the

nickel ferrite without terbium. This may also indicates the more diffuse distribution of the

different cations on the A- and B- sites within the spinel structure which increases with

the concentration of terbium ions. The average grain size was measured by Scherrer’s

formula [1]. These values of grain size are comparable with the values calculated from

XRD as shown in Table 4.1.

Table 4.1 Phases, lattice constant, X-ray density, Bulk density and Grain size of the

Ni1-xTbxFe2O4 ferrites (0.0 ≤ x ≤ 0.2).

Serial

No.

Composition Secondary

phase

Lattice

constant (a)

(Å)

X-ray

density (Dx)

(g/cm3)

Bulk

density (Db)

(g/cm3)

Grain

size

(µm)

1 NiFe2O4 - 8.3234 5.4 5.1277 3.63

2 Ni.98Tb.02Fe2O4 - 8.3263 5.44 5.1845 3.41

3 Ni.96Tb.04Fe2O4 - 8.3274 5.48 5.2814 3.24

4 Ni.94Tb.06Fe2O4 - 8.3286 5.53 5.3428 3.05

5 Ni.92Tb.08Fe2O4 - 8.3295 5.57 5.3867 2.93

6 Ni.9Tb.1 Fe2O4 TbFeO3 8.3292 5.62 5.4387 2.58

7 Ni.88Tb.12Fe2O4 TbFeO3 8.3284 5.67 5.4876 2.35

8 Ni.86Tb.14Fe2O4 TbFeO3 8.3282 5.71 5.5278 2.09

9 Ni.84Tb.16Fe2O4 TbFeO3 8.3275 5.76 5.5789 1.96

10 Ni.82Tb.18Fe2O4 TbFeO3 8.3268 5.81 5.6334 1.42

11 Ni.8Tb.2 Fe2O4 TbFeO3 8.3259 5.86 5.6864 1.18

The actual densities (X-ray) of the samples under investigation were calculated

using the equation [5];

3

8

Na

MDx (4.2)

where M is the molecular weight of the sample, ‘ a ’ is the lattice constant and N is

Avogadro’s number. X-ray density increases linearly as a function of terbium content as

it mainly depends upon the molecular weight of the compositions.

The bulk density increases from 5.13 g/cm3 to 5.69 g/cm

3 with the increase of

terbium concentration from x = 0 to x = 0.2 while the X-ray density also increases from

5.4 g/cm3 to 5.86 g/cm

3 as terbium is incorporated into NiFe2O4 ferrite with the highest

density value obtained for a terbium concentration at x = 0.2. This is due to the atomic

weight of Tb (158 amu) which is higher than that of Ni (28 amu) [6]. The bulk density

increases almost linearly as a function of terbium concentration. Thus, a decrease in

porosity can be expected with increase of terbium concentration (x). This is consistent

with previous work reported for Tb-substitution in Li-Zn ferrites [7].

Table 4.2 Miller indices (hkl) and interplaner spacing (d) for Ni1-xTbxFe2O4 ferrites

(0.0 ≤ x ≤ 0.1).

T b-contents

Sr. No.

Miller Indices

hkl

x = 0 . 0

d (Å)

x = 0 . 0 2

d (Å)

x = 0 . 0 4

d (Å)

x =0.06

d (Å)

x = 0 . 0 8

d (Å)

x = 0 . 1

d (Å)

1 2 2 0 2.9219 2.8996 2.9200 2.9015 2.9304 2.904

2 3 1 1 2.4960 2.4802 2.4958 2.4816 2.5025 2.4832

3 2 2 2 2.3918 2.3757 2.3900 2.3765 2.3975 2.3789

4 4 0 0 2.0712 2.0607 2.0710 2.0620 2.0772 2.0634

5 4 2 2 1.6938 1.6874 1.6936 1.6879 1.6969 1.6893

6 5 1 1 1.5972 1.5920 1.5973 1.5926 1.5999 1.5931

7 4 4 0 1.4680 1.4638 1.4680 1.4643 1.4699 1.4648

Table 4.3 Miller indices (hkl) and interplaner spacing (d) for Ni1-xTbxFe2O4 ferrites

(0.12 ≤ x ≤ 0.2).

Tb-contents Miller Indices x = 0 . 1 2 x = 0 . 1 4 x = 0 . 1 6 x = 0 . 1 8 x = 0 . 2

Sr. No.

hkl

d (Å)

d (Å)

d (Å)

d (Å)

d (Å)

1 2 2 0 2.9309 2.9229 2.9002 2.9193 2.9067

2 3 1 1 2.5020 2.4975 2.4800 2.4939 2.4859

3 2 2 2 2.3974 2.3918 2.3750 2.3888 2.3804

4 4 0 0 2.0774 2.0748 1.0610 2.0724 1.0661

5 4 2 2 1.6965 1.6941 1.6874 1.6940 1.6896

6 5 1 1 1.5996 1.5979 1.5921 1.5974 1.5940

7 4 4 0 1.4698 1.4685 1.4638 1.4681 1.4654

4.2 Fourier Transform Infrared Spectroscopy (FTIR)

Figs. 4.3-4.8 show the FTIR spectra for Ni1-xTbxFe2O4 (x = 0.0- 0.2) ferrites

indicating the two absorption peaks in the wave number range 370-1500 cm-1

. The

position of bands obtained from FTIR spectra for Ni1-xTbxFe2O4 ferrites is given in Table

4.4. It has been reported [8] that the occurrence of ν1 (≈ 600 cm-1

) and ν2 (≈ 400 cm-1

)

bands are attributed to the intrinsic vibrations of tetrahedral and octahedral groups

respectively. These bands are mainly dependent on Fe-O distances and the nature of the

cations involved. In this study the band frequency ν2 slightly decreases with increasing

Tb concentration while ν1 remains almost constant. This decrease in ν2 may be attributed

to the terbium substitution for nickel on octahedral sites.

The absorption bands obtained in this study are found to be in the range reported

for nickel ferrites [9-10] but there is also a more diffuse region between them when

terbium is present compared with pure nickel ferrite (NiFe2O4). This diffuse region may

be attributed to the anomalous distributions of Iron and Nickel cations on the tetrahedral

and octahedral sites. A broadening of the spectral bands is observed for higher

concentrations of terbium. This broadening is due to the statistical distribution of Fe3+

on

A- and B-sites. The broadening of the spectral bands is a well known feature of inverse

spinel ferrites.

x = 0.00

0

20

40

60

80

100

37057077097011701370

Wave number(cm-1)

Tra

nsm

itta

nce (

%)

Fig. 4.3. FTIR Spectrum for NiFe2O4 ferrite.

x = 0.04

0

20

40

60

80

100

37057077097011701370

Wave number (cm-1)

Tra

nsm

itta

nce (

%)

Fig. 4.4. FTIR Spectrum for Ni.96Tb0.04Fe2O4 ferrite.

x = 0.08

0

20

40

60

80

100

37057077097011701370

Wave number (cm-1)

Tra

nsm

itta

nce (

%)

Fig. 4.5. FTIR Spectrum for Ni.92Tb.08Fe2O4 ferrite.

x = 0.12

0

20

40

60

80

100

37057077097011701370

Wave number (cm-1)

Tra

nsm

itta

nce (

%)


x = 0.16

0

20

40

60

80

100

37057077097011701370

Wave number (cm-1)

Tra

nsm

itta

nce (

%)


x = 0.20

0

20

40

60

80

100

37057077097011701370

Wave number (cm-1)

Tra

nsm

itta

nce (

%)

Fig. 4.8. FTIR Spectrum for Ni0.8Tb0.2 Fe2O4 ferrite.

Table 4.4 FTIR absorption bands for Ni 1-x Tb x Fe2O4 ferrite system.

Sr.No Composition ν1 (cm-1

) ν2 (cm-1

)

1 NiFe2O4 602 411

2 Ni.96Tb.04Fe2O4 602 409

3 Ni.92Tb.08Fe2O4 602 407

4 Ni.88Tb.12Fe2O4 602 405

5 Ni.84Tb.16Fe2O4 599 404

6 Ni.8Tb.2 Fe2O4 599 401

4.3 Scanning Electron Microscopy (SEM)

A few representative electron microscope images of the Ni1-xTbxFe2O4 ferrites

were taken as shown in Figs. 4.9-4.12. The investigated micrographs show the

inhomogeneous grain size distribution. The micrograph images revealed that the samples

are well packed and are almost crack free. Few agglomerates in the compositions x =

0.00, x = 0.08 and x = 0.2 were found which could not be individually resolved by SEM

technique. The agglomerates may form during the course of sintering due to chemical

reaction and can retain their identity under quite aggressive forces.

These agglomerates are formed by the particles which are bonded together by

surface forces. The agglomerates are held together by relatively weak bonds of magnetic

or van der walls force [11]. The average grain size was measured from SEM micrographs

by the line-intercept method. It can be observed that the grain size decreases with

increasing terbium content. The grain size measured from SEM was in the range from 5

to 2 μm. This may be due to the substitution of terbium that impedes the grain growth

[12].

Fig. 4.9. SEM micrographs of Ni 1-x Tb x Fe2O4 (x = 0.00) ferrite.




4.4 Compositional Analysis

The compositional analysis of few representative samples of Ni1-xTbxFe2O4

system has been performed by EDX (Energy Dispersive X-ray). EDX analysis shows the

elemental percentage of each element which is expected to be present in the finally

sintered samples. The peaks in the EDX analysis represent the proportion of each element

in the compound. The change in the size of the peaks of nickel and terbium can be

observed from the graphs. As the concentration of terbium is increased, the graphs show

an increase in the height of the peak of terbium as expected. As the terbium is substituted

for nickel in this study, the amount of nickel decreases and this decrease in nickel is

observed in the peak height of Ni as shown in Figs. 4.13 to 4.16. The detail of

composition of various metals in the samples is listed in Table 4.5. The observed % age

of metals is consistent with the stoichiometricy of the prepared samples by ceramic

method.

Table 4.5

Nominal percentage of metal cations in Ni1-xTbxFe2O4 ferrites

Terbium

Concentration

Ni weight % Tb weight % Fe weight % Total

0.00 30.69 - 69.31 100

0.08 30.5 1.37 68.13 100

0.14 28.17 1.88 69.95 100

0.20 27.66 2.43 69.91 100

Fig. 4.13. EDX of the NiFe2O4 ferrite.

Fig. 4.14. EDX of the Ni0.92Tb0.08Fe2O4 ferrite.



4.5 Static Magnetic Properties

4.5.1 Magnetization

The MH- loop of each sample was taken on a vibrating sample magnetometer

(VSM). The MH loops of Ni1-xTbxFe2O4 ferrites scanned up to 8000 (Oe) were recorded

at room temperature for all the samples as shown in Figs. 4.17-4.27. All the samples were

reasonably saturated at ~ 6000 (Oe). The narrow magnetic hysteresis loops of the samples

indicate that the samples are magnetically soft, with low coercivity. The shape and the

width of the hysteresis loops depend on factors such as chemical composition of the

material, porosity and crystallite size etc. The variation in saturation magnetization (Ms)

and coercivity (Hc) values with the substituent concentration of terbium are listed in

Table 4.6. The decrease in saturation magnetization has been observed with the

substitution of terbium (Tb). This decrease may be attributed to the weakening of AB-

interactions.

Since there are three types of exchange interactions [13] between the unpaired

electrons of two ions lying in A- and B- sites. The A-B interaction heavily predominates

over A-A and B-B interactions. The A-B interaction is negative that is it aligns all the

magnetic spins at A-sites in one direction and those at B-sites in the opposite direction.

The net magnetic moment of the whole lattice is therefore the difference between the

moments of the B and A sublattices. i.e M= |MB-MA|, where MA and MB are the

magnetic moments of the A and B sites respectively. It is an established fact that NiFe2O4

ferrite adopts the inverse spinel structure. In nickel ferrite, most of the Ni2+

ions occupy

octahedral sites (B-sites) and the Fe3+

ions are distributed on both octahedral and

tetrahedral sites (A-sites) [14-15].

The magnetic moment of each composition depends on the magnetic moments of

the constituent ions involved. The magnetic moments of Fe3+

and Ni2+

are 5 μB and 2 μB

while terbium is paramagnetic. The substitution of Tb with Ni ions takes place on

octahedral sites due to larger ionic radius and the possibility of occupying tetrahedral

sites is very rare as concluded in our previous work [16]. Hence, it is expected that the

number of magnetic moments on the octahedral sites will decrease. Thus the magnetic

moment of B-sublattice decreases and consequently the magnetization also decreases.

Hence, net magnetization of the samples decreases. In the present samples the decrease of

magnetization with Tb contents are consistent with results reported in references [3, 12,

17]. The dependence of saturation magnetization Ms on the terbium concentration is

depicted in Fig. 4.28. A slight increase in saturation magnetization for x = 0.02 may be

due to the migration of few Fe3+

ions on the B-sites from A-sites.

4.5.2 Coercivity

The observed values of coercivity (Hc) for all the samples of Ni1-xTbxFe2O4

ferrites are listed in Table 4.6. Due to small values of coercivity these materials can be

used in the switching devices. The coercivity is observed to decrease as the concentration

of terbium (Tb) increases up to x = 0.14 after which the coercivity increases. The

coercivity varies linearly with porosity [18] for 0.00 ≤ x ≤ 0.14 but for higher Tb

concentration it deviates. The porosity affects the magnetization process because pores

work as the generator of the demagnetizing field. All the samples have low coercivity as

compared to the unsubstituted sample. This shows that all the samples maintain their soft

ferrite nature with the terbium substitution. For higher concentration x ≥ 0.16 the

coercivity increases due to the unquenched orbital angular momentum of Tb3+

and

microstrains in the materials [19]. Since the grain size of the samples under investigation

decreases and hence the density of grain boundaries increases. At the grain boundaries,

the domain wall pinning takes place that also enhances the coercivity.

Table 4.6 The saturation magnetization (Ms) and Coercivity (Hc) of Ni1-xTbxFe2O4

(x = 0.0-0.2) ferrites.

S.No. Composition Ms(emu/gram) Hc(Oe)

1 NiFe2O4 34.05 40.00

2 Ni0.98Tb0.02Fe2O4 34.16 35.00

3 Ni0.96Tb0.04Fe2O4 32.70 30.00

4 Ni0.94Tb0.06Fe2O4 30.82 29.50

5 Ni0.92Tb0.08Fe2O4 30.72 29.00

6 Ni0.90Tb0.10Fe2O4 30.20 27.50

7 Ni0.88Tb0.12Fe2O4 30.76 24.00

8 Ni0.86Tb0.14Fe2O4 29.80 23.50

9 Ni0.84Tb0.16Fe2O4 32.88 25.00

10 Ni0.82Tb0.18Fe2O4 30.28 28.00

11 Ni0.80Tb0.20Fe2O4 27.26 35.00

-40

-30

-20

-10

0

10

20

30

40

-8000 -6000 -4000 -2000 0 2000 4000 6000 8000

H (Oe)

M (

em

u/g

)

x = 0.0

Fig. 4.17. The MH-Loop for NiFe2O4 ferrite.

-40

-30

-20

-10

0

10

20

30

40

-8000 -6000 -4000 -2000 0 2000 4000 6000 8000

H (Oe)

M (

em

u/g

)

x = 0.02

Fig. 4.18. The MH-Loop for Ni.98Tb.02Fe2O4 ferrite.

-40

-30

-20

-10

0

10

20

30

40

-8000 -6000 -4000 -2000 0 2000 4000 6000 8000

H (Oe)

M (

em

u/g

)

x = 0.04


-40

-30

-20

-10

0

10

20

30

40

-8000 -6000 -4000 -2000 0 2000 4000 6000 8000

H (Oe)

M (

em

u/g

)

x = 0.06


-40

-30

-20

-10

0

10

20

30

40

-8000 -6000 -4000 -2000 0 2000 4000 6000 8000

H (Oe)

M (

em

u/g

)

x = 0.08


-40

-30

-20

-10

0

10

20

30

-8000 -6000 -4000 -2000 0 2000 4000 6000 8000

H (Oe)

M (

em

u/g

) x = 0.10

Fig. 4.22. The MH-Loop for Ni.9Tb.1 Fe2O4 ferrite.

-40

-30

-20

-10

0

10

20

30

40

-8000 -6000 -4000 -2000 0 2000 4000 6000 8000

H (Oe)

M (

em

u/g

)

x = 0.12


-40

-30

-20

-10

0

10

20

30

40

-8000 -6000 -4000 -2000 0 2000 4000 6000 8000

H (Oe)

M (

em

u/g

)

x = 0.14


-40

-30

-20

-10

0

10

20

30

40

-8000 -6000 -4000 -2000 0 2000 4000 6000 8000

H (Oe)

M (

em

u/g

)

x = 0.16


-40

-30

-20

-10

0

10

20

30

40

-8000 -6000 -4000 -2000 0 2000 4000 6000 8000

H (Oe)

M (

em

u/g

)

x = 0.18


-40

-30

-20

-10

0

10

20

30

-8000 -6000 -4000 -2000 0 2000 4000 6000 8000

H (Oe)

M (

em

u/g

)

x = 0.20

Fig. 4.27. The MH-Loop for Ni.8Tb.2 Fe2O4 ferrite.

25

26

27

28

29

30

31

32

33

34

35

0 0.04 0.08 0.12 0.16 0.2

Tb Concentration (x)

Ms (

em

u/g

m)

Fig. 4.28. The variation of saturation magnetization with the concentration of terbium

of the Ni1-xTbxFe2O4 (x = 0.0-0.2) ferrites.

4.6 Magnetodynamics of Ni-Tb-Fe-O System

Ferromagnetic resonance (FMR) profiles of all the Ni1-xTbxFe2O4 ferrites taken at

X-band (9.5 GHz) are shown in Figs. 4.29-4.39. All the samples under investigation

showed single resonance peak and all the profiles are more or less slightly asymmetric as

shown in Figs. 4.29-4.39. The FMR linewidths and FMR position obtained from the

spectra are listed in Table 4.7. The line broadening observed in the FMR profiles may be

due to the decrease in magnetization, defects, inhomogenities and reduction of number of

Ni2+

ions in the samples. The asymmetry may be attributed to the contribution of non-

uniform resonance modes apart from the main mode (uniform mode k = 0) of resonance

[20, 21]. As the samples are saturated in the resonance field hence, the moments of the

magnetic ions within each particle are assumed to be linearly oriented in main mode. The

values of linewidths (751-2841 Oe) obtained for these ferrites fall in the usual range for

polycrystalline materials as compared to monocrystals. The largest linewidth observed

for the composition Ni0.8Tb0.2 Fe2O4 may be attributed to the increased number of

inhomogenities in this composition.

The minimum relaxation time calculated from linewidth for these ferrites is ~10-10

s. The variation in FMR intensities of the profiles depends on the gyromagnetic ratio (γ)

and g-values of the different cations. The gyromagnetic ratio (γ) has different values for

nickel, ferric and terbium ions because of the differences in the spectroscopic splitting g-

factors. The g- values for Ni2+

lie in the range 2.15 to 2.35 and for Fe3+

g = 2. The g-

value for terbium ions is ~1.95 [22]. The above mentioned differences in the g- values of

the cations involved are responsible for the observed variations in the intensity of the

FMR peaks. As terbium is substituted for nickel and nickel resides on the octahedral sites

and g-values for Ni and Fe have in fact the effective value for ferrimagnets that obey the

Tsuya-Wangsness [23] formula.

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0 2000 4000 6000 8000

H (Oe)

de

riva

tive

of

the

FM

R a

bso

rptio

n

curv

e

x = 0.00

Fig. 4.29. FMR profile of NiFe2O4 ferrite.

-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

0 1000 2000 3000 4000 5000 6000 7000 8000

H (Oe)

derivativ

e o

f th

e F

MR

absorp

tion

curv

e

x = 0.02

Fig. 4.30. FMR profile of Ni.98Tb.02Fe2O4 ferrite.

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0 2000 4000 6000 8000 10000

H (Oe)

derivative o

f th

e F

MR

absorp

tion

curv

e

x = 0.04


-0.6

-0.5

-0.4

-0.3

-0.2

-0.1

0

0.1

0.2

0.3

0.4

0 2000 4000 6000 8000

H (Oe)

deri

vati

ve o

f th

e F

MR

ab

so

rpti

on

cu

rve

x = 0.06


-1.5

-1

-0.5

0

0.5

1

1.5

0 1000 2000 3000 4000 5000 6000 7000 8000

H (Oe)

deri

vati

ve o

f th

e F

MR

ab

so

rpti

on

cu

rve

X = 0.08


-0.6

-0.5

-0.4

-0.3

-0.2

-0.1

0

0.1

0.2

0.3

0.4

0 1000 2000 3000 4000 5000 6000 7000 8000

H (Oe)

deri

vati

v o

f th

e F

MR

ab

so

rpti

on

cu

rve

x = 0.10

Fig. 4.34. FMR profile of Ni.9Tb.1 Fe2O4 ferrite.

-0.6

-0.5

-0.4

-0.3

-0.2

-0.1

0

0.1

0.2

0.3

0.4

0.5

0 2000 4000 6000 8000

H (Oe)

deri

vati

ve o

f th

e F

MR

ab

so

rpti

on

cu

rve

X = 0.12


-0.6

-0.5

-0.4

-0.3

-0.2

-0.1

0

0.1

0.2

0.3

0.4

0 1000 2000 3000 4000 5000 6000 7000 8000

H (Oe)

deri

vati

ve o

f th

e F

MR

ab

so

rpti

on

cu

rve

X = 0.14


-0.2

-0.15

-0.1

-0.05

0

0.05

0.1

0.15

0 1000 2000 3000 4000 5000 6000 7000 8000

H (Oe)

deri

vati

ve o

f th

e F

MR

ab

so

rpti

on

cu

rve

X = 0.16


-0.5

-0.4

-0.3

-0.2

-0.1

0

0.1

0.2

0.3

0 1000 2000 3000 4000 5000 6000 7000 8000

H (Oe)

deri

vati

ve o

f th

e F

MR

ab

so

rpti

on

cu

rve

X = 0.18


-0.2

-0.15

-0.1

-0.05

0

0.05

0.1

0.15

0.2

0.25

0 2000 4000 6000 8000 10000

H (Oe)

deri

vati

ve o

f th

e F

MR

ab

so

rpti

on

cu

rve X = 0.20

Fig. 4.39. FMR profile of Ni.8Tb.2 Fe2O4 ferrite.

Table. 4.7 FMR parameters of Ni1-xTbxFe2O4 ferrites measured at X-band (9.5 GHz)

Serial

No.

Composition FMR linewidth ΔHFWHM

(Oe)

FMR Position

(Oe)

1 NiFe2O4 1180 4491

2 Ni.98Tb.02Fe2O4 827 4497

3 Ni.96Tb.04Fe2O4 898 4324

4 Ni.94Tb.06Fe2O4 593 4556

5 Ni.92Tb.08Fe2O4 818 4979

6 Ni.9Tb.1 Fe2O4 751 4416

7 Ni.88Tb.12Fe2O4 925 4337

8 Ni.86Tb.14Fe2O4 992 4385

9 Ni.84Tb.16Fe2O4 949 4352

10 Ni.82Tb.18Fe2O4 1145 4381

11 Ni.8Tb.2 Fe2O4 2841 4559

4.7 Relative Initial Permeability

The relative initial permeability, μi΄, of Ni 1-x Tb x Fe2O4, ferrites has been

measured in the frequency range 1 KHz to 10 MHz and is depicted in Figs. 4.40 and 4.41

respectively. From the figures, it is observed that with the increase of terbium contents

relative initial permeability (μi΄) decreases with increase in frequency. It is known that

[24] the magnetization process of polycrystalline ferrites can be investigated as

superposition of domain wall motion and spin rotation. It was reported that [25] the

permeability was found to be almost proportional to the grain size when grain size lies in

the range 1-10 μm and the domain walls are assumed to be dominant. The permeability in

this range can be interpreted by the displacement of domain walls [26-27]. The domain

wall-motion is affected by both the composition and microstructures [24].

Normally, the walls remain pinned at the grain boundary and deviate when

subject to the small magnetic field [28]. The domain walls will gradually disappear if the

grain size is close to critical value i.e 0.2 μm. It is noticed that if grain size is less than 0.2

μm then spin rotation is dominant. A linear relationship between the grain size and

frequency dependent μi΄ has been observed in references [26, 29] and deviations from the

linearity have also been reported [30]. The Globus model [31] can be used to explain

magnetization process in the present study.

1

2 / KDM Si (4.3)

Ms is the saturation magnetization, D is the average grain size and K1 is anisotropy

constant. The relative initial permeability has linear relation to 2

SM and D while K1 is not

playing a significant role.

The saturation magnetization values are decreased with the substitution of terbium

ions. A remarkable decrease in the magnitude of relative initial permeability is observed

with the increasing concentration of terbium at low frequencies and it drops to a very low

value in high frequency region. The observed variations in the relative initial

permeability can also be explained by the following considerations. In the ferromagnetic

materials it depends on factors like reversible displacement of domain wall, bulging of

domain-walls. All the samples show a similar decreasing trend of μ΄ except for x = 0.20

in the present investigations. It shows a very small peak in MHz region and this may be

attributed to the abnormal behaviour of domain wall displacements [32]. The

substitutions of terbium ions decrease the value of Ms due to weakening of the A-B

interaction, hence the μ΄ is a complex phenomenon of magnetization, anisotropy constant

and microstructure.

0

500

1000

1500

2000

1000 10000 100000 1000000 10000000

Frequency (Hz)

Rel.

in

itia

l p

erm

eab

ilit

y,

μ΄i

x = 0.00

x = 0.02

x = 0.04

x = 0.06

x = 0.08

x = 0.10

Fig. 4.40. Relative initial permeability as a function of frequency for Ni 1-x Tb x Fe2O4,

(0.0 ≤ x ≤ 0.10) ferrites.

0

500

1000

1500

2000

1000 10000 100000 1000000 10000000

Frequency (Hz)

Rel.

in

itia

l p

erm

eab

ilit

y,

μ΄i

x = o.12

x = 0.14

x = 0.16

x =0.18

x = 0.20

Fig. 4.41. Relative initial permeability as a function of frequency for Ni 1-x Tb x Fe2O4,

(0.12 ≤ x ≤ 0.2) ferrites.

4.7.1 Frequency Dependent Loss Factor

The magnetic loss factor measured at room temperature for the given frequency

range for Ni 1-x Tb x Fe2O4, (0.0 ≤ x ≤ 0.2) ferrites is shown in Figs. 4.42-4.43. The loss

factors are found initially to decrease with increase in frequency for all the compositions.

The magnetic loss factor indicates a peak around 6000 Hz and it shifts towards the high

frequency region as the concentration of terbium is increased for 0.00≤ x ≤0.10. A

maximum loss peak is observed in the un-substituted sample as shown in Fig. 4.42.

Minimum values of the loss factor are attained in the range 50 KHz-10MHz. The samples

for the concentration of terbium x = 0.14- 0.18 exhibit two peaks in the loss factor. The

composition Ni 0.88 Tb 0.12 Fe2O4 shows no rise in the loss factor and it decreases gradually

to a minimum value. The values of magnetic loss factor are known to depend on different

parameters such as stoichiometry, Fe2+

contents, sintering temperature and composition

[33]. Main contribution to the magnetic losses in ferri magnetic materials is due to

hysteresis losses, which is associated with irreversible wall displacement and spin

rotations. However, the hysteresis losses are less important in the high frequency range

because the domain wall displacement is mainly damped and the hysteresis losses will be

due to spin rotation [34].

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

5

1000 10000 100000 1000000

Frequency (Hz)

Lo

ss f

acto

r

x = 0.00

x = 0.02

x = 0.04

x = 0.06

x = 0.08

x = 0.10

Fig. 4.42. Loss factor as a function of frequency for Ni 1-x Tb x Fe2O4,

(0.0 ≤ x ≤ 0.10) ferrites.

0

2

4

6

8

10

12

14

16

1000 10000 100000 1000000

Frequency (Hz)

Lo

ss f

acto

r

x = 0.12

x = 0.14

x = 0.16

x = 0.18

x = 0.20

Fig. 4.43. Loss factor as a function of frequency for Ni 1-x Tb x Fe2O4,

(0.12 ≤ x ≤ 0.20) ferrites.

4.8 DC Electrical Resistivity

Room temperature dc resistivity of Ni1-xTbxFe2O4 ferrites was measured by two

probe method. The variation of room temperature dc resistivity for the present samples as

a function of terbium (Tb) concentration is shown in Fig. 4.44. It has been noticed that

the resistivity increases linearly from 1.7 x 105

Ω-cm to 3.9 x105

Ω-cm as the

concentration of terbium (Tb) increases from 0.0 to 0.2 in steps of 0.02. This increase in

resistivity may be due to the fact that terbium has greater value of resistivity (111μΩ-cm)

as compared to that of Ni (7μΩ-cm) [35]. The increase in resistivity can be attributed to

the larger ionic radius of Tb3+

(0.93Å) as compared to the Ni2+

(0.69Å) which could

causes strain in the spinel lattice and impede the conduction process in the these ferrites.

Previous reported results also show an increase in resistivity Vs Tb concentration in Li-

Zn and NiZn ferrites [36, 37]. The increase in resistivity may also be related to 4f-3d

coupling between transition metal nickel and rare earth terbium ions.

0.E+00

1.E+05

2.E+05

3.E+05

4.E+05

5.E+05

0 0.04 0.08 0.12 0.16 0.2

Tb concentration (x)

Resis

tivit

y (

Ω-c

m)

Fig. 4.44. Plot of lo Room temperature resistivity (ρ) vs terbium concentration

for Ni1-xTbxFe2O4 ferrites.

4.8.1 Temperature Dependent Electrical Resistivity

Temperature dependent electrical resistivity measurements were also carried out

as a function of temperature in the temperature range 30-200ºC. The temperature

dependence of dc electrical resistivity of the Ni1-xTbxFe2O4 system is shown in Figs.4.45-

4.46. It is observed that as the temperature increases the resistivity decreases following

the Arrhenius equation [22];

ρ = ρ0 exp (Ea/kBT) (4.4)

where ρ0 is a constant, Ea is the activation energy and kB is Boltzmann’s constant and T is

the absolute temperature. The resistivity decreases as temperature increases that indicates

the semiconducting behavior of these samples. Such kind of behaviour of resistivity has

4

4.4

4.8

5.2

2 2.2 2.4 2.6 2.8 3 3.2 3.4

1000/T (K-1)

Lo

g ρ

, (Ω

cm

)

x = 0.00

x = 0.02

x = 0.04

x = 0.06

x = 0.08

x = 0.10

Fig. 4.45. Plot of logρ vs 1000/T for Ni1-xTbxFe2O4 (x = 0.0-0.1) ferrites.

4

4.4

4.8

5.2

5.6

6

2 2.5 3 3.5

1000/T (K-1)

Lo

g ρ

, (Ω

cm

)

x = 0.12

x = 0.14

x = 0.16

x = 0.18

x = 0.20

Fig. 4.46. Plot of logρ vs 1000/T for Ni1-xTbxFe2O4 (x = 0.12-0.20) ferrites.

been reported by many researchers [38-39]. The drift mobility is calculated from the

electrical resistivity data by using the following equation [40-41];

ned

1 (4.5)

where e is the charge of electron, ρ is the electrical resistivity and n is the concentration

of charge carriers and can be calculated from the following relation;

M

CNn bFeA (4.6)

where NA is the Avogadro’s number, CFe is the number of iron atoms in the chemical

formula of the samples, ρb the bulk density and M is the molar mass of the samples.

The variation of drift mobility with temperature is shown in Figs.4.47-4.48. As

the temperature increases the drift mobility is observed to increase. It is due to the reason

that the charge carriers start hopping amongst the sites with the increase of temperature.

The drift mobility at room temperature decreases from 1.4 x 10-9

to 5.97 x 10-10

cm2V

-1S

-1

by increasing the terbium concentration from 0.00 to 0.2 in steps of 0.02. The conduction

mechanism can be proposed as the ions of the same parent atom but in different valence

states are to be found in crystallographically similar positions in the lattice. Thus the

extra electron on a ferrous ion requires little energy to move on similarly situated

adjacent ferric ion. Hence the valence states of the two ions are interchanged. Under the

influence of an electric field, these extra electrons can be considered to constitute the

current from one iron ion to the next. The conduction mechanism [9] in nickel ferrites is

due to both n-and p-type charge carriers. The n-type charge carriers are due to electron

hopping of iron ions and p-type carriers are due to hole hopping between the nickel ions

at the octahedral sites.

0.E+00

1.E-09

2.E-09

3.E-09

4.E-09

5.E-09

6.E-09

7.E-09

8.E-09

9.E-09

1.E-08

300 320 340 360 380 400 420 440 460 480 500

T (K)

μd (

cm

2.v

-1.S

-1)

x = 0.00

x = 0.02

x = 0.04

x = 0.06

x = 0.08

x = 0.10

Fig. 4.47. The plot of drift mobility (μd) with temperature for Ni1-xTbxFe2O4

(x = 0.0-0.1) ferrites.

0.E+00

2.E-09

4.E-09

6.E-09

8.E-09

1.E-08

1.E-08

300 320 340 360 380 400 420 440 460 480 500

T (K)

μd(c

m2.v

-1.S

-1)

x = 0.12

x = 0.14

x = 0.16

x = 0.18

x = 0.20

Fig. 4.48. The plot of drift mobility (μd) with temperature for Ni1-xTbxFe2O4

(x = 0.12-0.20) ferrites.

Hence the following conduction mechanism in these ferrites can be possible,

Fe2+

↔ Fe3+

+ e-

(4.7)

Ni3+

+ e- ↔ Ni

2+ (4.8)

Combining these two relations;

Fe3+

+ Ni2+

↔ Fe

2+ + Ni

3+ (4.9)

When terbium is substituted for Ni ions it is expected to occupy on the octahedral sites

because nickel ferrite is an inverse spinel [42] in which nickel ions occupy on the

octahedral sites. The number of Ni2+

and Ni3+

ions on the octahedral sites will decrease.

The resistivity of the samples depends on the hopping probability of both type of charge

carriers. Hence the incorporation of terbium ions at the cost of nickel ions causes the

increase in resistivity. The presence of terbium ions on the octahedral sites and on the

grain boundaries (second phase) obstructs the degree of easy conduction between the

nickel and iron ions on the octahedral sites, thereby increasing the resistivity of the

samples under investigation. The increase in resistivity has been reported [43] when

gadolinium was substituted in nickel ferrites.

0.1

0.14

0.18

0.22

0 0.04 0.08 0.12 0.16 0.2Tb concentration (x)

Acti

vati

on

en

erg

y

(eV

)

Fig. 4.49. Plot of activation energy vs terbium concentration

for Ni1-xTbxFe2O4 ferrites.

The activation energy of the samples under investigation has been derived from

the slope of temperature dependent resisitivity plots. It has been noticed that the

activation energy varies with the terbium concentration in a similar manner to that of the

room temperature resistivity vs Tb concentration (x). It shows that the samples which

have high resistivity have high activation energy and vice versa. The activation enegy

values for the present system ranges from 0.14 to 0.20 eV and are in accordance with

Verwey hopping conduction mechanism. The dependence of activation energy for

various Tb concentrations is shown in Fig. 4.49.

4.9 Dielectric Properties

The dielectric properties of ferrites are dependent upon several factors, including

chemical composition, the method of preparation and grain size. This may be explained

by the fact that electronic exchange between Fe2+

and Fe3+

ions cannot follow the

frequency of externally applied alternating field beyond a critical frequency. The

frequency and composition dependent dielectric constant, ε', for Ni-Tb ferrites was

measured in the frequency range from10 Hz to 10MHz. The variation of dielectric

constant (ε') with frequency at room temperature for all the samples under investigation

has been shown in Figs.4.50 & 4.51. The figures revealed that the dielectric constant

decreases continuously with increase in frequency for all the samples and at a very high

frequency; the dielectric constant is almost frequency independent. This indicates that the

dispersion is due to Maxwell– Wagner type interfacial polarization which is in good

agreement with Koop’s phenomenological theory. According to these models, the

dielectric structure consists of two layers. The first layer, which is composed of ferrite

grains, is well conducting material and it is separated by a thin layer of poorly conducting

material called grain boundaries [44-46].

The frequency independent phenomenon occurs for the reason that electric

dipoles are unable to follow the fast variation of the alternating applied electric field at

very high frequencies. Also the polarization of ferrites in the high frequency region

occurs owing to electric and ionic polarization and both of these exhibit a frequency

independent behaviour [47].

0.E+00

5.E+03

1.E+04

2.E+04

2.E+04

3.E+04

3.E+04

4.E+04

4.E+04

5.E+04

5.E+04

00010 00100 01000 10000 100000 1000000 10000000

Frequency (Hz)

Die

lectr

ic c

on

sta

nt

(ε')

x = 0.0

x = 0.02

x = 0.04

x = 0.06

x = 0.08

x = 0.10

Fig. 4.50. Dielectric constant (ε') vs frequency of Ni1-xTbxFe2O4 (x = 0.0- 0.10) at room

temperature.

0.00E+00

5.00E+03

1.00E+04

1.50E+04

2.00E+04

2.50E+04

10 100 1000 10000 100000 1000000 10000000

Frequency (Hz)

Die

lectr

ic c

on

sta

nt

(ε')

x = 0.12

x = 0.14

x = 0.16

x = 0.18

x = 0.20

Fig. 4.51. Dielectric constant (ε') vs frequency of Ni1-xTbxFe2O4 (x = 0.12- 0.20) at room

temperature.

It has been found that the dielectric constant decreases with the substitution of

terbium. The decrease in the values of dielectric constant with composition may be

attributed to the decrease in internal viscosity of the system which provides more degrees

of freedom to the dipoles of the system contributing polarization. Thus disordering

increase in the system and hence the dielectric constant decrease. The hoping of electrons

from Fe3+

to Fe2+

ions and hole hopping between Ni 3+

and Ni2+

ions at B-sites are

responsible for the polarization. The hopping between A- sites is rare as there are only

Fe3+

ions present on A-sites and Fe2+

ions which are formed in the course of processing

occupy only B-sites [48, 49]. As a result of the substitution of terbium for the Ni ions, the

Ni as well as Fe ions on B-sites may decrease (Fe3+

+ Ni2+

↔ Fe

2+ + Ni

3+). Therefore the

dielectric polarization in the externally applied field decreases while in the opposite

direction increases. This explains the reason of the decrease of the dielectric constant for

the terbium substitution.

It has been noticed that there is no dispersion in the dielectric constant (ε') of all

the samples in the studied range. All samples show high dielectric constant of the order of

103-10

4 at very low frequencies. The higher values of dielectric constant in the lower

frequency region are explained on the basis of space charge polarization. This type of

polarization is attributed to the heterogeneity of the samples and to the fact that

ferroelectric regions are surrounded by non-ferroelectric regions similar to the case of

relaxor ferroelectric materials [50].

Figs. 4.52 & 4.53 show the variation of dielectric loss (tanδ) with frequency at

room temperature for Ni1-xTbxFe2O4 (x = 0.0- 0.20 in steps of 0.02) ferrites. The relations

of tanδ with frequency in the MHz range show a relaxation spectrum with a loss peak. It

has been reported [51] that the occurrence of loss peak in the tanδ versus frequency curve

may be attributed to the strong correlation between the hopping conduction mechanism

and dielectric behavior of ferrites (i.e the cation-cation correlation at the octahedral site).

The appearance of loss peak in tanδ is known as abnormal dielectric loss behaviour and it

has been observed for all the samples which could be related to the resonance effect.

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

1.1

10 100 1000 10000 100000 1000000 10000000

Frequency (Hz)

Die

lectr

ic l

oss (

tan

δ)

x = 0.0

x =0.02

x = 0.04

x = 0.06

x = 0.08

x =0.10

Fig. 4.52. Dielectric loss (tanδ) vs frequency of Ni1-xTbxFe2O4 (x = 0.0- 0.10) at room

temperature.

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

1.1

10 100 1000 10000 100000 1000000 10000000

Frequency (Hz)

Die

lectr

ic l

oss (

tan

δ)

x =0.12

x = 0.14

x = 0.16

x = 0.18

x = 0.20

Fig. 4.53. Dielectric loss (tanδ) vs frequency of Ni1-xTbxFe2O4 (x = 0.12- 0.20) at room

temperature.

The dielectric loss in ferrites is the result of lag of polarization ions with respect

to the applied alternating electric field. This abnormal behaviour may also be attributed to

the presence of both types of charge carriers [47]. In Ni ferrites the conduction

mechanism is p-type due to the hole exchange between Ni3+

and Ni2+

. The electrons

initiated from the hopping process between Fe2+

↔ Fe3+

+ e‾ capture some of Ni3+

ions

and it results in the formation of Ni2+

ions. With the substitution of terbium (Tb), in place

of Ni, the loss peaks become broader. It is worth noticing that the dielectric loss increases

with the increase of Tb contents up to x = 0.10 and for further substitution of Tb, the

dielectric loss has been observed to decrease. The increase in the dielectric loss could be

attributed to the cluster formation and this act as the trapping centers for different depths.

The composition x = 0.14 exhibit the minimum value of loss peak of all the samples

under investigation. The sample x = 0.2 exhibit a most broad peak as compared to all

other samples. Similar kinds of abnormal dielectric loss behaviour have been reported for

Mn-Zn, Ni-Mg, and Ni-Zn ferrites [47, 10, 52]. It has been observed that the values of the

dielectric loss are less than 1 even in the MHz frequency range and these values are

significantly lower compared to the ferrites synthesized by conventional method [48, 53].

The Figs. 4.54 and 4.55 show the variation of ac conductivity with frequency for

Ni1-xTbxFe2O4 ferrites at room temperature. The total ac conductivity of ferrites is given

by the following relation:

σ tot = σ 1 (T) +σ 2 (ω, T) (4.10)

The first term σ 1 indicates the DC conductivity which is frequency independent function.

The second term is the frequency dependent and it purely exhibit ac conductivity due to

electron hopping amongst the sites.

In all the samples it has been observed that the ac conductivity gradually increases

as the frequency of the applied external field increases. Since an increase in frequency

promotes the electron hopping frequency of the charge carriers, hence the conductivity

increases. The electron hopping and liberated charge together provide the basis for the

conduction mechanism in ferrites. The ac conductivity generally decreases by the Tb-

substitution. This may be due to the inclusion of Tb- ions in the spinel lattice which

affects the conduction mechanism. The sample x = 0.04 exhibit high conductivity in the

high frequency region as compared to the neighbouring compositions and it anomaly in

this behaviour. A decrease in the as conductivity of all the samples is noted beyond

8MHz and can be attributed to the occurrence of loss peaks appeared in the dielectric

loss.

0

0.002

0.004

0.006

0.008

0.01

0.012

0.014

0.016

0.018

0.E+00 2.E+06 4.E+06 6.E+06 8.E+06 1.E+07

Frequency (Hz)

σac (

oh

m-1

cm

-1)

x = 0.00

x = 0.02

x = 0.04

x = 0.06

x = 0.08

x = 0.10

Fig. 4.54. The variation of ac conductivity with frequency for Ni1-xTbxFe2O4

(x = 0.0- 0.10) ferrites.

0

0.004

0.008

0.012

0.016

0.02

0.E+00 2.E+06 4.E+06 6.E+06 8.E+06 1.E+07

Frequency (Hz)

σac (

oh

m-1

cm

-1)

x = 0.12

x = 0.14

x = 0.16

x = 0.18

x = 0.20

Fig. 4.55. The variation of ac conductivity with frequency for Ni1-xTbxFe2O4

(x = 0.12- 0.20) ferrites.

Mg1-xTbxFe2O4 Series

4.10 Structural Analysis

X-ray diffractograms of Mg 1-xTbxFe2O4 (0.0 ≤ x ≤ 0.2) ferrites sintered at 1230

oC

are shown in Figs. 4.56 and 4.57 respectively. The diffraction patterns were indexed on

the basis of fcc lattice and the phases precipitated out are listed in Table 4.8. Analysis of

XRD patterns revealed that all the samples with 0≤ x ≤ 0.04 have a single phase cubic

spinel structure. A small peak of second phase appeared at 2θ = 33.24° for x = 0.06 and

becomes more conspicuous for x > 0.06 as indicated in Figs. 4.56 and 457. The second

phase was not detected at x = 0.08 due to weak intensity of X-rays at the particular angle.

This peak was identified as the (1 1 2) reflection of the TbFeO3 (ortho ferrite) phase

(ICDD PDF # 47-0068). The formation of second phase has also been reported when rare

earth metal cations are substituted in Mn-Zn and bismuth ferrites [54, 55].

The diffraction peaks of spinel structure corresponding to the planes (220), (311),

(400), (422), (511 / 333) and (440) were observed. All the mentioned peaks of the fcc

lattice in the patterns matched well with the characteristic reflections of Mg-ferrite

reported earlier [56, 57]. The d-spacing and the hkls values are listed in Tables 4.9 and

4.10. The variation of lattice constants ‘ a ’ with Tb-concentration (x) for 0.0 ≤ x ≤ 0.2 are

listed in Table 4.8. The lattice constant increases up to x = 0.04 and then decreases. The

small increase in the lattice parameter with the increase of terbium contents (x) can be

explained on the basis of the differences of the ionic radii of Tb3+

and Mg2+

ions.

Since Tb3+

ion has larger ionic radius (0.93Å) as compared to Mg2+

(0.66Å), the

partial replacement of Mg2+

by Tb3+

leads to the expansion of the spinel lattice; thereby

increasing the lattice constant. It is therefore suggested that most of the replacement of

Mg2+

ions by Tb3+

ions takes place on the octahedral sites. A similar behavior was

observed when rare earth gadolinium (Gd) was substituted in Ni-ferrites [43].

Fig. 4.56. X-ray diffraction patterns for Mg1-xTbxFe2O4 ferrites

(x = 0.0, 0.02, 0.04, 0.06, 0.08).

A slight decrease in the lattice constant ‘ a ’ for x > 0.04 may be attributed to the

migration of Mg2+

ions to tetrahedral sites due to the presence of terbium ions on the

octahedral sites. This decrease also suggest the solubility limit for the terbium ions at x =

0.04. When the solubility limit is achieved no further terbium is dissolved in the spinel

lattice and terbium ions accumulate to the grain boundaries combining with Fe to produce

TbFeO3 and form thin insulating layer around the grains. The appearance of secondary

phase on the grain boundaries may suppress the grain growth by limiting the grain

boundary mobility [36].

A non- linear behaviour (positive curvature) of ‘ a ’ Vs Tb contents has been

observed as shown Fig. 58. Similar non-linear change of lattice constant ‘ a ’ with

concentration in spinel ferrites have been reported [58, 4, 59] by many researchers. It is

expected that the Tb3+

ions may reside on B-sites as Tb3+

ions have larger ionic radius

(0.93Å) as compare to that of Fe3+

(0.64Å) ions. The probability that terbium ions occupy

the tetrahedral sites (A- sites) may be very remote. This is due to the fact that the

tetrahedral sites are too small to be occupied by the large terbium ions. The internal

stresses may also occur on B-sites where terbium ions occupy these sites due to their

larger ionic radii. This result is in agreement with those already reported results by other

researchers [60].

Fig. 4.57. X-ray diffraction patterns for Mg1-xTbxFe2O4 ferrites

(x = 0.10, 0.12, 0.14, 0.16, 0.18, 0.20)

It has been reported that the site preference of Mg2+

ions in Mg-ferrite can be

inferred from the intensities of the (220) and (440) planes [10]. A remarkable feature in

the x-ray patterns of the samples under investigation are the relative intensities of the

(220) and (440) planes. The relative intensities of these two planes are observed to

increase with the increasing concentration of terbium compared to unsubstituted sample

(MgFe2O4). Since MgFe2O4 ferrite is reported to be partially inverse [61] in which most

of the Mg2+

ions occupy on B-sites i.e it is a mixed ferrite. The relative intensity of (220)

plane increases and it indicates that a fraction of Mg2+

ions migrate towards the A-sites

when terbium is substituted in these ferrites. On the other hand increase in the relative

intensity of (440) plane exhibits that the Mg2+

ions occupying on B-sites are substituted

by the terbium ions. Hence Tb-substituted Mg-ferrites are predicted to be intermediate

ferrites.

8.36

8.361

8.362

8.363

8.364

8.365

8.366

8.367

8.368

0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2


a

(Ǻ

)

Fig. 4.58. Lattice parameter a (Å) vs. Tb concentration for Mg1−xTbxFe2O4 ferrites

(0≤x≤0.2).

Table 4.8

Phase, Lattice constant, X-ray density, Bulk Density, and Grain size for Mg1-xTbxFe2O4

ferrites (0.0 ≤ x ≤ 0.2).

Sr.

No.

Composition Secondary

phase

Lattice

constant(Å)

X-ray

density(Dx)

(g/cm3)

Bulk

density(Db)

(g/cm3)

Grain

size

(µm)

1 MgFe2O4 - 8.361 4.55 3.5539 3.46

2 Mg.98Tb.02Fe2O4 - 8.3657 4.6 3.7155 3.27

3 Mg.96Tb.04Fe2O4 - 8.3669 4.66 3.8999 3.18

4 Mg.94Tb.06Fe2O4 TbFeO3 8.3664 4.72 3.9296 3.12

5 Mg.92Tb.08Fe2O4 - 8.3662 4.78 4.1257 3.05

6 Mg.9Tb.1 Fe2O4 TbFeO3 8.366 4.84 4.2909 2.87

7 Mg.88Tb.12Fe2O4 TbFeO3 8.3653 4.91 4.3133 2.79

8 Mg.86Tb.14Fe2O4 TbFeO3 8.3637 4.97 4.4676 2.81

9 Mg.84Tb.16Fe2O4 TbFeO3 8.3641 5.03 4.4845 2.62

10 Mg.82Tb.18Fe2O4 TbFeO3 8.3634 5.09 4.5605 2.37

11 Mg.8Tb.2 Fe2O4 TbFeO3 8.3605 5.16 4.6063 2.03

Table 4.9

Miller indices (hkls) and interplaner spacing (d) for Mg 1-xTbxFe2O4 ferrite (0.0 ≤ x ≤0.1)

Sr.

No.

hkl X = 0 . 0

d (Å)

X = 0 . 0 2

d (Å)

X = 0 . 0 4

d (Å)

X = 0 . 0 6

d (Å)

X = 0 . 0 8

d (Å)

X = 0 . 1

d (Å)

1 220 2.9419 2.9418 2.9415 2.942 2.9393 2.9352

2 311 2.5124 2.5124 2.5104 2.5112 2.5091 2.5069

3 400 2.085 2.0839 2.0844 2.0851 2.0837 2.0802

4 422 1.7026 1.7037 1.7023 1.7025 1.7023 1.7021

5 511 1.6061 1.6062 1.6063 1.6067 1.606 1.6048

6 440 1.4759 1.476 1.4761 1.4763 1.4757 1.4748

Table 4.10

Miller indices (hkls) and interplaner spacing (d) for Mg 1-xTbxFe2O4 ferrite (0.12 ≤ x ≤

0.2)

Sr.

No.

hkl X = 0 . 1 2

d (Å)

X = 0 . 1 4

d (Å)

X = 0 . 1 6

d (Å)

X = 0 . 1 8

d (Å)

X = 0 . 2

d (Å)

1 220 2.9374 2.9388 2.9426 2.9354 2.938

2 311 2.5078 2.5093 2.5117 2.5057 2.5089

3 400 2.0825 2.0824 2.0837 2.0805 2.0814

4 422 1.7025 1.7022 1.7038 1.7017 1.7013

5 511 1.6052 1.6057 1.6065 1.6045 1.6052

6 440 1.4751 1.4753 1.476 1.4744 1.475

The bulk density of these ferrites was observed to increase with the increase of

terbium concentration (x). The values of bulk density are listed in Table 4.8. The increase

in bulk density may be attributed to the higher atomic weights of Tb (158.92 amu) and its

higher specific gravity (8.23g/cm3) compared to the atomic weights of Mg (24.3 amu)

and the specific gravity of Mg (1.74g/cm3) atoms. The values of x-ray densities are larger

in magnitude as compared to bulk densities as listed in Table 4.8 and the difference in the

magnitude of these densities may be attributed to the existence of pores [62]. The

variations of both the densities with Tb concentration are depicted in Fig. 4.59.

It is observed that both the densities increase linearly with Tb concentration. The

substitution of terbium ions in magnesium ferrite causes an appreciable decrease in

porosity ~ 21 % to 10 %. This decrease in porosity may be related to the relative ratio of

densities of the samples. Hence densified and sintered samples have been obtained.

Fig. 4.59. X-ray density (Dx) and bulk density (Db) vs. Tb concentration for

Mg1−xTbxFe2O4 ferrites (0≤x≤0.2).

4.11 Fourier Transform Infrared Spectroscopy (FTIR)

Figures 4.60-4.65 show the room temperature FTIR spectra for Mg1-xTbxFe2O4

ferrites. It can be seen from the figures that FTIR spectra of the terbium (Tb) substituted

magnesium (Mg) ferrites are found to exhibit two absorption bands in the wave number

range 370-1500 cm-1

.The high frequency band ν 1 around around 600 cm-1

and the low

frequency band ν 2 around 400 cm-1

have been observed. These bands are the

characteristic features of the spinel ferrites as reported earlier [63-65]. It has been

reported that the occurrence of ν 1 and ν 2 bands are attributed to the intrinsic vibrations of

the tetrahedral and octahedral group complexes [65] respectively. In the present study,

the tetrahedral (ν 1) and octahedral (ν 2) bands occur in the range 571-567 cm-1

and 429-

418 cm-1

respectively. The difference in the band position is expected because of the

difference in Fe3+

-O2-

distance for the octahedral and tetrahedral compounds.

The band positions for the investigated Mg1-xTbxFe2O4 ferrites are given in Table

4.11. The range of absorption bands obtained in the present study is consistent with the

reported literature [66, 67]. It is noticed from the spectra that ν 2 band is shifted towards

lower frequencies with an increasing Tb concentration. It is reported that [61] in Mg-

ferrite most of the Mg2+

ions are located on the B-sites and small fraction on A-sites.

Thus the replacement of Mg2+

with Tb3+

ions (having larger ionic radius and higher

atomic weight than Mg2+

and Fe3+

) at octahedral sites in the ferrite lattice affects the Fe3+

-

O2-

stretching vibrations. This could be the reason for the observed decrease in ν 2 band

positions. The octahedral band ν2 seems to be continuously widened with Tb-

concentration this may be due to the statistical distribution of the Fe3+

ions on A- and B-

sites [68].

The change in ν 1 band may be attributed to the drifting of Fe3+

ions towards

oxygen ion on occupation of tetrahedral sites by few Mg2+

ions [10]. The change in the

peak intensity of the spectra has been noticed with increasing Tb contents. It is well

known that the intensity ratio is a function of the change of dipole moment with the inter-

nuclear distance [69]. This ratio represents the contribution of the ionic bond Fe-O in the

lattice. Hence the observed decrease in the peak intensity may be due to the perturbation

occurring in Fe-O bonds by the substitution of terbium ions.

0

20

40

60

80

100

37057077097011701370

wave number (cm-1)

Tra

nsm

itta

nce (

%)

x = 0.00

Fig. 4.60. FTIR Spectrum for MgFe2O4 ferrite.

x = 0.04

0

20

40

60

80

100

37057077097011701370

Wave number (cm-1)

Tra

nsm

itta

nce (

%)

Fig. 4.61. FTIR Spectrum for Mg.96Tb0.04Fe2O4 ferrite.

x = 0.08

0

20

40

60

80

100

37057077097011701370

Wave number (cm-1)

Tra

nsm

itta

nce (

%)

Fig. 4.62. FTIR Spectrum for Mg.92Tb.08Fe2O4 ferrite.

x = 0.12

0

20

40

60

80

100

37057077097011701370

wave number (cm-1)

Tra

nsm

itta

nce (

%)


0

20

40

60

80

100

37057077097011701370

wave number(cm-1)

Tra

nsm

itta

nce(%

)

x = 0.16


x = 0.20

0

20

40

60

80

100

37057077097011701370

wave number (cm-1)

Tra

nsm

itta

nce (

%)

Fig. 4.65. FTIR Spectrum for Mg0.8Tb0.2 Fe2O4 ferrite.

Table 4.11

FTIR absorption bands for Mg1-xTbxFe2O4 ferrites (x = 0, 0.04, 0.08, 0.12, 0.16, 0.2).

Sr. No Composition ν1 (cm-1

) ν2 (cm-1

)

1 MgFe2O4 571 429

2 Mg0.96Tb.04Fe2O4 567 428

3 Mg0.92Tb.08Fe2O4 571 427

4 Mg0.88Tb.12Fe2O4 566 425

5 Mg0.84Tb.16Fe2O4 566 419

6 Mg0.8Tb.2Fe2O4 567 418

4.12 Scanning Electron Microscopy (SEM)

Figs. 4.66-4.69 show representative SEM micrographs of the Mg1-xTbxFe2O4

ferrites. All the micrographs exhibit inhomogeneous grain size distribution. The

micrographs of Figs. 4.66 – 4.67 show monophasic microstructure along with few

agglomerates. The micrographs shown in Figs.4.68 – 4.69 depict biphasic microstructure.

From the Figs. 4.68 & 4.69, it can be observed that the second phase occurs in the form

of precipitates located among the matrix of dark grains. These precipitates in the ferrite

matrix were formed by either segregation to, or precipitating at the grain boundaries.

From these micrographs the grain size was calculated using line intercept method.

With the increase of terbium concentration from x = 0.0 to 0.2, the grain size

found to be decreasing and lies in the range from 7 to 4 µm. The decrease in the grain

size can be explained on the basis of ionic radii of the terbium ions. It is assumed that

some of the terbium ions may reside on the grain boundaries; these can hinder the growth

[70] and also exert stress on the grain which causes the reduction of grain size. It was

observed that the substitution of terbium inhibited the grain growth by approximately 53

%.

Fig. 4.66. SEM micrograph of Mg 1-x Tb x Fe2O4, (x = 0.00) ferrite.




4.13 Compositional Analysis

EDX has been performed on a few representative samples of Mg1-xTbxFe2O4

ferrites in order to study the compositional analysis. EDX analysis exhibit the elemental

percentage of each element expected to be present in the ferrite sample. The heights of

the peaks in the EDX graphs represent the proportion of each element in the finally

sintered ferrite sample. A change has been observed in the size and height of the peaks of

all the Tb-substituted samples. With the increase of Tb concentration, the graphs exhibit

an increase in the height of the Tb peaks.

In the present study, the terbium is substituted for magnesium. Hence, the amount

of magnesium decreases and this decrease in magnesium is observed in the peak height of

Mg as shown in Figs. 4.70 – 4.73. The detail compositions of various metals estimated

from EDX graphs present in the samples are listed in Table 4.12. The observed %age of

metals of each composition is consistent with the stoichiometricy of the prepared

samples.

Table 4.12

Nominal percentage of metal cations in Mg1-xTbxFe2O4 ferrites

Terbium

Concentration

Mg weight % Tb weight % Fe weight % Total

0.00 13.67 - 86.33 100

0.08 12.02 1.85 86.13 100

0.14 10.94 2.61 86.45 100

0.20 10.33 3.36 86.31 100

Fig. 4.70. EDX of the MgFe2O4 ferrite.

Fig. 4.71. EDX of the Mg0.92Tb0.08Fe2O4 ferrite.



4.14 Static Magnetic Properties

4.14.1 Magnetization

The MH- loops of Mg1-xTbxFe2O4 ferrites recorded on a VSM at room

temperature are shown in Figs. 4.74-4.84. All the samples are well saturated at ~ 6000

(Oe). The variation in saturation magnetization (Ms) and coercivity (Hc) with the

substituent concentration of terbium are listed in Table 4.13. The low coercivity values

and narrow s-type magnetic loops of the samples predict the soft magnetic nature of these

ferrites. When ferrite composition is modified with magnetic/diamagnetic ions, the

number of the magnetic ions on the A- and B-sublattices and the resulting magnetization

of the ferrite are affected. It is an established fact that the magnetic properties of the

spinel type ferrites (AB2O4) with fcc crystal structure depend on the distribution of the

cations on A- and B-sites.

The saturation magnetization is observed to increase for x = 0.02 and it decreases

thereafter up to x = 0.2 as shown in Fig. 4.85. The radius of Tb3+

ion (0.93Å) is larger

than that of Mg2+

(0.66Å) and Fe3+

ions (0.64Å) and the radius of tetrahedral site is small

as compared to the octahedral site, hence the Tb3+

ions will prefer to occupy the

octahedral sites. The possible explanation of the increase in saturation magnetization for

x = 0.02 may be explained on the basis of redistribution of cations on A-and B-

sublattices. In MgFe2O4 ferrite most of the Mg2+

ions reside on B-sites and small fraction

of these ions goes to the A-sites [71]. When terbium (Tb) ions are introduced into the

octahedral sites few of the Mg2+

ions are migrated to the tetrahedral sites. These Mg2+

ions force equal amount Fe3+

ions to the octahedral sites [72], this increase the

magnetization of the B-sublattice and hence the saturation magnetization of this

composition increases.

The decrease in saturation magnetization for further substitution x ≥ 0.04 of Tb3+

ions may be attributed to the magnetic disorder on B-sites. It has been quoted that [73]

the spin canting is caused by the substitution of rare earth ions, since Tb is a rare earth

metal ion and it causes the transformation of collinear ferrimagnetic order into non-

collinear arranagement of spins on B-sites. Hence the occupancy of Tb3+

ions on

octahedral sites stemmed the collinear arrangement and reduces the saturation

magnetization. Also, it is expected that no more Fe3+

ions are transferred to the

octahedral sites which lead to the decrease of saturation magnetization. The decrease of

saturation magnetization by the addition of rare earth ions in different ferrites has also

been reported [17, 74, 75].

The site occupancy of Mg2+

and Fe3+

ions in Mg-Tb ferrites is complicated;

however, the decrease of saturation magnetization for higher concentration of Tb3+

ions

may be attributed to the secondary orthoferrite phase (TbFeO3), which has a low value of

magnetization. The decrease in the saturation magnetization with the evaluation of

secondary phase has also been reported when Tb was substituted in Ni-Zn and Li-Zn

ferrites [3, 12].

4.14.2 Coercivity

The coercivity (Hc) values of all the samples of Mg1-xTbxFe2O4 ferrites are listed

in Table 4.13. The coercivity is found to decrease when Tb contents are increased up to x

= 0.06 after which the coercivity increases. The coercivity has a linear relationship with

porosity [18] for 0.00 ≤ x ≤ 0.06 but for higher Tb concentration it deviates. The

coercivity is the measure of magnetic field strength required for overcoming the

magnetocrystalline anisotropy to flip the magnetic moments. For Tb-concentration

0.08 ≤ x ≤ 0.12 the increase in coercivity may be attributed to the dominant role of L-S

coupling caused by the anisotropic terbium ions [76]. The increase in coercivity may also

be due to the appearance of second phase on or near the grain boundaries which impede

the motion of domain walls. The coercivity is decreased for higher concentration of Tb

that is for x ≥ 0.14; it could be due to the largest decrease in porosity which provides the

easiness to the domain wall movement.

Table 4.13

The saturation magnetization (Ms) and Coercivity (Hc) of Mg1-xTbxFe2O4

(x = 0.0-0.2) ferrites.

S.No. Composition Ms(emu/gram) Hc(Oe)

1 MgFe2O4 30.50 47.5

2 Mg0.98Tb0.02Fe2O4 32.00 44.0

3 Mg0.96Tb0.04Fe2O4 30.40 43.0

4 Mg0.94Tb0.06Fe2O4 30.30 41.0

5 Mg0.92Tb0.08Fe2O4 30.10 57.0

6 Mg0.90Tb0.10Fe2O4 29.00 61.0

7 Mg0.88Tb0.12Fe2O4 28.90 63.0

8 Mg0.86Tb0.14Fe2O4 28.40 58.0

9 Mg0.84Tb0.16Fe2O4 27.20 43.0

10 Mg0.82Tb0.18Fe2O4 26.10 37.0

11 Mg0.80Tb0.20Fe2O4 26.00 34.0

-40

-30

-20

-10

0

10

20

30

40

-8000 -6000 -4000 -2000 0 2000 4000 6000 8000

H (Oe)

M (

em

u/g

) x = 0.00

Fig. 4.74. The MH-Loop for MgFe2O4 ferrite.

-40

-30

-20

-10

0

10

20

30

40

-8000 -6000 -4000 -2000 0 2000 4000 6000 8000

H (Oe)

M (

em

u/g

) x = 0.02

Fig. 4.75. The MH-Loop for Mg0.98Tb0.02Fe2O4 ferrite.

-40

-30

-20

-10

0

10

20

30

40

-8000 -6000 -4000 -2000 0 2000 4000 6000 8000

H (Oe)

M (

em

u/g

)

x = 0.04


-40

-30

-20

-10

0

10

20

30

40

-8000 -6000 -4000 -2000 0 2000 4000 6000 8000

H (Oe)

M (

em

u/g

)

x = 0.06


-40

-30

-20

-10

0

10

20

30

40

-8000 -6000 -4000 -2000 0 2000 4000 6000 8000

H (Oe)

M (

em

u/g

)

x = 0.08


-40

-30

-20

-10

0

10

20

30

40

-8000 -6000 -4000 -2000 0 2000 4000 6000 8000

H (Oe)

M (

em

u/g

)

x = 0.10


-40

-30

-20

-10

0

10

20

30

40

-8000 -6000 -4000 -2000 0 2000 4000 6000 8000

H (Oe)

M (

em

u/g

) x = 0.12


-40

-30

-20

-10

0

10

20

30

40

-8000 -6000 -4000 -2000 0 2000 4000 6000 8000

H (Oe)

M (

em

u/g

)

x = 0.14


-30

-20

-10

0

10

20

30

-8000 -6000 -4000 -2000 0 2000 4000 6000 8000

H (Oe)

M (

em

u/g

)

x = 0.16


-30

-20

-10

0

10

20

30

-8000 -6000 -4000 -2000 0 2000 4000 6000 8000

H (Oe)

M (

em

u/g

)

x = 0.18


-30

-20

-10

0

10

20

30

-8000 -6000 -4000 -2000 0 2000 4000 6000 8000

H (Oe)

M (

em

u/g

)

x = 0.20


25

26

27

28

29

30

31

32

33

0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2


Satu

rati

on

Mag

neti

zati

on

(em

u/g

)

Fig. 4.85. The saturation magnetization vs Tb-concentration for Mg1-xTbxFe2O4 ferrites.

4.15 Magnetodynamics of Mg-Tb-Fe-O System

Room temperature ferromagnetic resonance (FMR) spectra of all the

Mg1-xTbxFe2O4 ferrites, taken at X-band (9.5 GHz) are shown in Figs. 4.86-4.96. A single

resonance peak has been observed in the samples and all the profiles are slightly

asymmetric as depicted in Figs. 4.86-4.96. The spectra have been used to obtain the

linewidths (ΔH) and FMR position and these are listed in Table 4.14. It can be observed

that linewidth vary distinctly from sample to sample, this may be due to considerable

inhomogeneities present in the samples. The valence exchange or charge-transfer

relaxation mechanism, which is important in spinel ferrites, is possible source of

linewidth in spinel ferrites.

In the charge transfer mechanism, the energy is directly transferred to the lattice

without going through either the degenerate or the thermal magnons. The line widths of

all the samples varies in the range (746-1015 Oe) except for x = 0.16, which has the

highest linewidth (1146 Oe) as compared to rest of compositions. The composition

Mg.98Tb.02Fe2O4 (x = 0.02) has the minimum linewidth (746 Oe) and highest saturation

magnetization (32 emu/gm). This composition is more suitable for device engineering.

The linewidths obtained in the present investigation are much lower than the reported

literature [77, 78]. The increase in linewidth has been correlated [79] to the two magnon

scattering process.

In the present studies, the increase in ΔH may also be attributed to the two

magnon scattering process. A second phase (TbFeO3) appears for x ≥ 0.06, other than the

fcc spinel phase. A comparatively high linewidth has been reported [79] due to the

presence of second phase. This second phase has the same effect as the surface pits in

polycrystalline ferrites. In the present samples the linewidth increases for ≥ 0.06 due to

the occurrence of second phase (TbFeO3). By using the linewidth, the minimum

relaxation time calculated for these ferrites lies in the range ~ 10-10

s. A remarkable

feature is the intensity of the FMR profiles. The substitution of terbium ions in these

ferrites has marked effect on the intensities of the FMR profiles. The intensities strongly

depend on the gyromagnetic ratio (γ) and g-values of the cations present in each

composition.

All the cations involved like magnesium, ferric and terbium have different values

of gyromagnetic ratio (γ) because of the differences in the spectroscopic splitting g-

factors. The FMR profiles of all the substituted samples have lower intensities as

compared to the unsubstituted sample (MgFe2O4) as depicted in the Figs. 4.86-4.96. The

differences in the g- values of the cations involved are responsible for the observed

variations in the intensity of the FMR peaks.

-1.5

-1

-0.5

0

0.5

1

1.5

0 1000 2000 3000 4000 5000 6000 7000 8000 9000

H (Oe)

deri

vati

ve o

f th

e F

MR

ab

so

rpti

on

cu

rve

x = 0.00

Fig. 4.86. FMR profile of MgFe2O4 ferrite.

-1.5

-1

-0.5

0

0.5

1

1.5

0 1000 2000 3000 4000 5000 6000 7000 8000 9000

H (Oe)

deri

vati

ve o

f th

e F

MR

ab

so

rpti

on

cu

rve

x = 0.02

Fig. 4.87. FMR profile of Mg0.98Tb0.02Fe2O4 ferrite.

-1.5

-1

-0.5

0

0.5

1

1.5

0 1000 2000 3000 4000 5000 6000 7000 8000 9000

H (Oe)

deri

vati

ve o

f th

e F

MR

ab

so

rpti

on

cu

rve

x = 0.04


-1

-0.5

0

0.5

1

1.5

0 1000 2000 3000 4000 5000 6000 7000 8000 9000

H (Oe)

deri

vati

ve o

f th

e F

MR

ab

so

rpti

on

cu

rve

x = 0.06


-1.5

-1

-0.5

0

0.5

1

1.5

0 1000 2000 3000 4000 5000 6000 7000 8000 9000

H (Oe)

deri

vati

ve o

f th

e F

MR

ab

so

rpti

on

cu

rve

x = 0.08


-1

-0.5

0

0.5

1

0 1000 2000 3000 4000 5000 6000 7000 8000 9000

H (Oe)

de

riv

ati

ve

of

the

FM

R a

bs

orp

tio

n

cu

rve

x = 0.10


-1.5

-1

-0.5

0

0.5

1

1.5

0 1000 2000 3000 4000 5000 6000 7000 8000 9000

H (Oe)

deri

vati

ve o

f th

e F

MR

ab

so

rpti

on

cu

rve

x = 0.12


-1.5

-1

-0.5

0

0.5

1

1.5

0 1000 2000 3000 4000 5000 6000 7000 8000 9000

H (Oe)

deri

vati

ve o

f th

e F

MR

ab

so

rpti

on

cu

rve

x = 0.14


-1

-0.5

0

0.5

1

0 1000 2000 3000 4000 5000 6000 7000 8000 9000

H (Oe)

deri

vati

ve o

f th

e F

MR

ab

so

rpti

on

cu

rve

x = 0.16


-1

-0.5

0

0.5

1

0 1000 2000 3000 4000 5000 6000 7000 8000 9000

H (Oe)

deri

vati

ve o

f th

e F

MR

ab

so

rpti

on

cu

rve

x = 0.18


-1

-0.5

0

0.5

1

0 1000 2000 3000 4000 5000 6000 7000 8000 9000

H (Oe)

de

riv

ati

ve

of

the

FM

R a

bs

orp

tio

n

cu

rve

x = 0.20


Table. 4.14 FMR parameters of Mg1-xTbxFe2O4 ferrites measured at X-band (9.5 GHz)

Serial

No.

Composition FMR linewidth ΔHFWHM

(Oe)

FMR Position

(Oe)

1 MgFe2O4 752 4399

2 Mg.98Tb.02Fe2O4 746 4390

3 Mg.96Tb.04Fe2O4 799 4436

4 Mg.94Tb.06Fe2O4 954 4375

5 Mg.92Tb.08Fe2O4 790 4372

6 Mg.9Tb.1 Fe2O4 1015 4203

7 Mg.88Tb.12Fe2O4 813 4365

8 Mg.86Tb.14Fe2O4 762 4420

9 Mg.84Tb.16Fe2O4 1146 4406

10 Mg.82Tb.18Fe2O4 991 4503

11 Mg.8Tb.2 Fe2O4 1001 4438

4.16 Relative Initial Permeability

The relative initial permeability, μi΄, of Mg1-xTbx Fe2O4 (0.00 ≤ x ≤ 0.2), ferrites is

measured in the frequency range from 1 KHz to 10 MHz and the plots of μi΄ vs

frequency are shown in Figs. 4.97 and 4.98 respectively. The Figs. indicate that the

relative initial permeability is observed to decrease generally with the increasing

concentration of terbium ions. It is well known that [80] the magnetization process is

considered as the superposition of domain wall motion and spin rotation. The domain

wall-motions are affected by both the composition and microstructures. The

microstructure mechanism of μi΄ of ferrites is mainly attributed to the motion of domain

walls and magnetic domains [24].

It has been found [81] that in the low frequency region, the major contribution to

the μi΄ is due to the movement of domain walls and this has also been observed in the

present samples as shown in Figs. 4.97 and 4.98. In the high frequency region (MHz)

spin rotations are assumed to be dominant over the domain wall displacements [82]. Our

observations are also in well agreement with the Globus model. The high μi΄ is observed

for the samples and it decreases with the increasing Tb-concentration as shown in Fig.

4.99. The decrease in μi΄ with the increasing concentration of terbium can be explained

on the basis of following relation [28]

1

2

K

DM m

Si (4.11)

where Dm is the average grain diameter, K1 is the magneto-crystalline anisotropy constant

and Ms is the saturation magnetization.

Since the saturation magnetization of the samples under investigation decreases

with the increasing concentration of terbium ions, so a reasonable decrease in μi΄ is

consistent with saturation magnetization results. The average grain size decreases of all

the substituted samples. Hence the decrease in of μi΄ is expected. The observed fall in μi΄

suggests that K1 is not playing a dominant role. A linear relationship of μi΄ vs grain size

has been reported [26, 29] and in some cases it may deviates [30]. All the samples have

almost similar decreasing trend of μi΄ except the samples having the terbium

concentration, x = 0.12 and x = 0.16. These exhibit a drastic decrease in the values of μi΄

in the low frequency region. From the Figs. 4.97 and 4.98, it is evident that very small

values μi΄ have been observed in the high frequency region.

0

500

1000

1500

1000 10000 100000 1000000 10000000

Frequency (Hz)

Rela

tive i

nit

ial

perm

eab

ilit

y

x= 0.00

x = 0.02

x = 0.04

x = 0.06

x = 0.08

x = 0.10

Fig. 4.97. Relative initial permeability as a function of frequency for Mg 1-x Tb x Fe2O4,

(0.0 ≤ x ≤ 0.10) ferrites.

0

500

1000

1000 10000 100000 1000000 10000000

Frequency (Hz)

Re

lati

ve

in

itia

l p

erm

ea

bil

ity

x = 0.12

x = 0.14

x = 0.16

x = 0.18

x = 0.20

Fig. 4.98. Relative initial permeability as a function of frequency for Mg 1-x Tb x Fe2O4,

(0.12 ≤ x ≤ 0.2) ferrites.

0

200

400

600

800

1000

1200

1400

1600

0 0.04 0.08 0.12 0.16 0.2

Tb-concentration (x)

μi΄

Fig. 4.99. The variation of μi΄ with x for Mg 1-x Tb x Fe2O4 (0.0 ≤ x ≤ 0.20) ferrites.

4.16.1 Frequency Dependent Loss Factor

The loss factor was measured at room temperature for the investigated samples in

the given frequency range for Mg 1-x Tb x Fe2O4, (0.0≤ x ≤ 0.2) ferrites and is shown in

Figs. 4.100-4.101 respectively. The loss factors of all the samples decreased with the

increase in frequency. The samples 0.00 ≤ x ≤ 0.10 indicate very small peaks in the low

frequency region and beyond10 KHz a drastic decrease in the loss factors of these

samples has been found. The sample x = 0.08 exhibit three loss peaks in the low

frequency region and its value drops more rapidly as compared to neighboring

compositions. The sample for the terbium concentration x = 0.06 also exhibit a small loss

peak in the high frequency region. The Fig. 4.101 indicates that the magnetic loss factor

of the samples having terbium concentrations 0.12 ≤ x ≤ 0.20, decrease more rapidly as

compared to the compositions mentioned in Fig. 4.100.

All the Tb substituted samples exhibit low values of loss factor as compared to the

unsubstituted sample in the low frequency region. In the high frequency range the loss

factor becomes frequency independent and indicates very small values. The minimum

loss factor has been observed for the compositions Mg 0.86 Tb 0.14 Fe2O4 and Mg 0.82 Tb

0.18Fe2O4 as compared to all other compositions. The previously reported results indicate

that [83] the partial substitution of rare earth ions (Eu, Ru and Gd) in Ni-Zn ferrites

significantly lowers the relative loss factor over a wide frequency range. All the samples

of terbium substituted Mg ferrites show small values of the loss factor over a large

frequency range. For ferrites to be useful as inductor and transformer materials, the

magnetic losses should be as low as possible over a wide frequency range. These

materials are suitable in this regard.

0

0.2

0.4

0.6

0.8

1

1000 10000 100000 1000000 10000000

Frequency (Hz)

Lo

ss f

acto

r

x = 0.00

x = 0.02

x = 0.04

x = 0.06

x = 0.08

x = 0.10

Fig. 4.100. Loss factor as a function of frequency for Mg 1-x Tb x Fe2O4,

(0.0 ≤ x ≤ 0.10) ferrites.

0

0.2

0.4

0.6

0.8

1

1000 10000 100000 1000000 10000000

Frequency (Hz)

Lo

ss f

acto

r

x = 0.12

x = 0.14

x = 0.16

x = 0.18

x = 0.20

Fig. 4.101. Loss factor as a function of frequency for Mg 1-x Tb x Fe2O4,

(0.12 ≤ x ≤ 0.20) ferrites.

4.17 DC Electrical Resistivity

The d.c. electrical resistivity of Mg1-xTbxFe2O4 (0.00 ≤ x ≤ 0.2) ferrites measured

at room temperature with the increasing Tb concentration is shown in Fig. 4.102. The

resistivity increases gradually from 2.33 x 106 Ω-cm to 5.71 x10

7 Ω-cm as the terbium

concentration is increased from 0.02 to 0.2. The increase in resistivity (decrease in

conductivity) of the Tb substituted samples may be attributed to the larger resistivity

value of Tb (111μΩ-cm) as compared to Mg (4.3μΩ-cm) [35]. The increase in resistivity

may be possibly due to the larger ionic radius of Tb3+

(0.93Å) ions in comparison to Mg2+

(0.66Å) ions which may increase the separation between the ferrous and ferric ions on the

octahedral sites and impede the conduction phenomenon between these two ions as

reported in [3, 84, 85].

0.00E+00

1.00E+07

2.00E+07

3.00E+07

4.00E+07

5.00E+07

6.00E+07

0 0.04 0.08 0.12 0.16 0.2

Terbium contents (x)

Resis

ivit

y (

Ω-c

m)

Fig. 4.102. Plot of Room temperature resistivity (ρ) vs terbium concentration

for Mg1-xTbxFe2O4 ferrites.

4.17.1 Temperature Dependent Electrical Resistivity

Temperature dependent electrical resistivity has been measured in the temperature

range 30- 200 ºC and is depicted in Figs. 4.103 and 4.104 respectively. The temperature

dependent resistivity data indicates a linear relationship suggesting that it obeys the well

known Arrhenius relation [39, 86]:

ρ = ρ0 exp (Ea/kBT) (4.12)

where ρ is the resistivity, ρ0 is constant, Ea is the energy of activation and kB is the

Boltzmann’s constant and T is the absolute temperature.

The temperature dependent resistivity plots are used to calculate activation energy

of hopping [87]. All these plots show that the resistivity decreases as the temperature

increases, hence it can be inferred that all the samples exhibit semi-conducting behaviour.

Since all the samples show temperature dependence in the entire temperature range,

therefore they may be called as degenerate type semiconductors. The band theory which

explains the conduction mechanism in semiconductors is not suited for ferrites [88].

Hence conduction mechanism in ferrites can be explained on the basis of hopping

mechanism. The drift mobility of all the compositions of Mg1-xTbxFe2O4 ferrites have

been calculated from the following relation [5, 62]:

ned

1 (4.13)

where ‘e’ is the charge on electron, ρ is the resistivity and ‘n’ is the concentration of

charge carriers calculated from the following equation:

M

PNn aa (4.14)

where Na is the Avogadro’s number, ρa is the bulk density of the sample, P is the number

of iron atoms in the chemical formula of the sample and M is the molecular weight of the

sample.

The graphs of drift mobility vs temperature are shown in Figs.4.105-4.106. It can

be seen that the drift mobility increases with increasing temperature. It is assumed that

the increase in drift mobility represents enhanced mobility of the charge carriers due to

thermal activation. It may be due to the fact that as the temperature increases, the charge

carriers start hopping from one site to another, hence the conduction process increases.

Also the Figs. 4.105 and 4.106 revealed that the samples having high resistivity have low

value of drift mobility. The drift mobility drops from 1.26 x 10-10

to 4.49 x 10-12

cm2V

-1S

-1

as the terbium concentration is increased from 0.00 to 0.2.

The Verwey’s hopping model [89] can be employed to explain the conduction

mechanism in these ferrite systems. According to this model the conduction mechanism

in ferrites is mainly attributed to the transfer of electrons between the ions of the same

element occurring in more than one valence state, and these have random distribution on

crystallographically equivalent lattice sites. The ferrites form closed packed oxygen

lattices with the cations over the tetrahedral (A) and octahedral (B) sites. The separation

between two metal ions residing on the octahedral (B) sites is smaller than the separation

between a metal ion on the octahedral (B) sites and ion on the tetrahedral (A) sites. Hence

the probability of electron hopping between octahedral (B) and tetrahedral (A) sites is

very small as compared to the ions occurring on the octahedral (B) sites only.

The electron hopping among the ions of the tetrahedral sites is not possible as

there are only Fe3+

ions. The Fe2+

ions occupy only on octahedral sites. The hopping

probability depends on the distance between the metal ions and the mobility of the charge

carriers. The presence of terbium ions on the octahedral sites (as discussed in FTIR

analysis) increase the distance between the metal ions of the octahedral sites and impedes

the electron transfer between the iron ions. Hence increase in resistivity and decrease in

the drift mobility is expected. The following conduction mechanism may also be possible

in these ferrites:

Mg2+

+ Fe3+

↔ Mg3+

+ Fe2+

(4.15)

As Tb3+

ions are stable [3] below 1300 ºC and do not change their valence state from

Tb3+

to Tb4+

ions. The incorporation of Tb3+

ions may cause in the blocking of the

conduction mechanism. It is supposed that Tb3+

ions behave like scattering centres in the

electron exchange mechanism between the ions of different valencies situated on

crystallographically positions in the lattice and enhances the resisitivity of these ferrites.

4.5

5

5.5

6

6.5

7

2 2.2 2.4 2.6 2.8 3 3.2 3.4

1000/T (K-1)

Lo

g ρ

(Ω

-cm

)

x = 0.00x = 0.02x = 0.04x = 0.06x = 0.08x = 0.10

Fig. 4.103. Plot of logρ vs 1000/T for Mg1-xTbxFe2O4 ferrites (0.00 ≤ x ≤ 0.10).

5

5.5

6

6.5

7

7.5

8

2 2.5 3 3.5

1000/T (K-1)

Lo

g ρ

(Ω

-cm

)

x = 0.12

x = 0.14

x = 0.16

x = 0.18

x = 0.20

Fig. 4.104. Plot of logρ vs 1000/T for Mg1-xTbxFe2O4 ferrites (0.12 ≤ x ≤ 0.20).

0.E+00

5.E-10

1.E-09

2.E-09

2.E-09

3.E-09

3.E-09

4.E-09

300 320 340 360 380 400 420 440 460 480 500

T (K)

μd (

cm

2.v

-1.S

-1)

x = 0.00

x = 0.02

x = 0.04

x = 0.06

x = 0.08

x = 0.10

Fig. 4.105. The plot of drift mobility (μd) with temperature for Mg1-xTbxFe2O4

ferrites (0.00 ≤ x ≤ 0.10).

0.E+00

2.E-10

4.E-10

6.E-10

8.E-10

1.E-09

1.E-09

300 320 340 360 380 400 420 440 460 480 500

T (K)

μd(c

m2.v

-1.S

-1)

x = 0.12

x 0.14

x = 0.16

x = 0.18

x = 0.20

Fig. 4.106. The plot of drift mobility (μd) with temperature for Mg1-xTbxFe2O4

ferrites (0.12 ≤ x ≤ 0.20).

The activation energy, deduced from the temperature variation of resistivity as a

function of terbium concentration is shown in Fig. 4.107. A small increase in the

activation energy is observed up to x = 0.10 and later it increases more rapidly with

increasing concentration of terbium ions. The higher activation energy values correspond

to the higher resistivity values may be due to the formation of insulating intergranular

secondary phase (TbFeO3) which impedes the conduction phenomenon. The increase in

activation suggests the partial incorporation of terbium ions on the octahedral sites, which

causes the blockage of electron transfer between the Fe3+

and Fe2+

. The activation energy

values of the samples under investigation are comparable to the reported trivalent

substituted magnesium ferrites [67, 90, 91].

0.2

0.24

0.28

0.32

0.36

0 0.04 0.08 0.12 0.16 0.2

Terbium contents (x)

Acti

vati

on

en

erg

y (

eV

)

Fig. 4.107. Plot of activation energy vs terbium concentration

for Mg1-xTbxFe2O4 ferrites.

4.18 Dielectric Properties

Figs. 4.108 and 4.109 show the variation of dielectric constant (ε') with frequency

from 10 Hz to 10MHz of Mg1-xTbxFe2O4 ferrites at room temperature. It can be observed

that the dielectric constant decreases with an increase in frequency. This decrease of

dielectric constant is due to the reason that the ions contributing in the polarizability

exhibit lagging behind the applied field beyond a certain frequency, which is normal

ferrimagnetic behaviour. [1]. The electron exchange between Fe2+

and Fe3+

in n-type

semi-conducting Mg-Tb ferrites can not follow the changes in the applied ac field.

Therefore the values of dielectric constant decrease with an increase in frequency. All the

samples have high values of dielectric constant in the order of 103-10

4 at low frequencies.

This may be due to oxygen vacancies, voids, grain boundary defects, etc [2]. These high

values of dielectric constant at lower frequencies may be due to the Maxwell-Wagner

interfacial polarization [2-3] for inhomogeneous dielectric structure which is in

agreement with Koops phenomenological theory [4].

The inhomogeneous dielectric structure was composed of two layers. The first

layer consists of well conducting large ferrite grains and the second thin layer comprises

poorly conducting grain boundaries. The ferrite grains having high conductivity and low

dielectric constant are more effective in the high frequency region while the resistive

grain boundaries are more effective in the low frequency region [5]. The samples with

terbium (Tb) contents x = 0.18 and x = 0.20 have low values of dielectric constant as

compared to all other compositions in the low frequency region. This can be attributed to

the space charge polarization [6] or interfacial polarization which is the result of

inhomogeneous dielectric structure.

0.E+00

1.E+04

2.E+04

3.E+04

4.E+04

5.E+04

6.E+04

7.E+04

8.E+04

10 100 1000 10000 100000 1000000 10000000

Frequency (Hz)

Die

lectr

ic c

on

sta

nt

x = 0.00

x = 0.02

x = 0.04

x = 0.06

x = 0.08

x = 0.10

Fig. 4.108. Dielectric constant (ε') vs frequency of Mg1-xTbxFe2O4 (x = 0.0- 0.10) ferrites.

0.E+00

2.E+03

4.E+03

6.E+03

8.E+03

1.E+04

1.E+04

1.E+04

2.E+04

2.E+04

10 100 1000 10000 100000 1000000 10000000

Frequency (Hz)

Die

lectr

ic c

on

sta

nt

x = 0.12

x = 0.14

x = 0.16

x = 0.18

x = 0.20

Fig. 4.109. Dielectric constant (ε') vs frequency of Mg1-xTbxFe2O4 (x = 0.12- 0.20)

ferrites.

Figs. 108 and 109 revealed that the dielectric constant decreases as the terbium

contents are increased in the mixed Mg-Tb ferrite system. A physical interpretation of

dielectric polarization can be done on the basis of electric dipoles formed by the cations

Fe3+

, Mg2+

and Tb3+

of the structure with their surrounding O2-

ions. But the main source

of dielectric polarization in ferrites is the change of Fe3+

ions to Fe2+

ions on the

octahedral sites, leads to a local displacement of electric charge carriers, thereby

participating in the dielectric polarization and relaxation phenomenon [7]. In MgFe2O4

ferrite, most of the Mg ions occupy on the octahedral sites [8] while Fe ions occupy on

both octahedral (B-sites) and tetrahedral (A-sites) sites.

The increase of Tb ions substitution on B-sites replaces some Mg ions. The

reduction of Mg ions on B-sites leads to the decrease in population of Fe2+

ions (Mg2+

+

Fe3+

↔ Mg3+

+ Fe2+

) on the B-sites. Also the electron exchange interaction (conduction

mechanism) happening at B-sites between the Fe3+

ions to Fe2+

ions retarded due to the

presence of Tb ions on the B-sites that increases the hopping length of conduction

electrons. Since the dielectric polarization mechanism in ferrites is similar to the

electronic conduction mechanism [9]. The number of electrons exchanged between the

cations involved results in the local displacements in the direction of the applied external

field which determines the dielectric polarization. This explains the decrease in the

dielectric constant with the increasing concentration of Tb ions.

Similar behaviour of dielectric constant has been reported [10] when different

rare-earths elements substituted in Mn-Zn ferrites. The materials with higher dielectric

constant are useful [11] in capacitors of dynamic random access memories (DRAM) of

personal computers and work stations.

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

1.1

10 100 1000 10000 100000 1000000 10000000

Frequency (Hz)

Die

lectr

ic l

oss

x = 0.00

x = 0.02

x = 0.04

x = 0.06

x = 0.08

x = 0.10

Fig. 4.110. Dielectric loss (tanδ) vs frequency of Mg1-xTbxFe2O4 (x = 0.0- 0.10) ferrites.

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

1.1

10 100 1000 10000 100000 1000000 10000000

Frequency (Hz)

Die

lectr

ic l

oss

x = 0.12

x = 0.14

x = 0.16

x = 0.18

x = 0.20

Fig. 4.111. Dielectric loss (tanδ) vs frequency of Mg1-xTbxFe2O4 (x = 0.12- 0.20) ferrites.

The materials of the present study may have potential application in this regard.

The variation of dielectric loss (tanδ) with frequency at room temperature for Mg1-

xTbxFe2O4 (x = 0.0- 0.20) ferrites is shown in Figs. 4.110 and 4.111. The figures 4.110

and 4.111 revealed that the values of dielectric loss more or less decreases with

substitution of terbium ions in magnesium ferrites. It can be seen that the dielectric loss

first decreases as the frequency increases and then increases rapidly beyond 100 KHz.

Qualitatively the formation of dielectric loss peaks may be owing to the following

reasons.

A strong correlation has been reported [12] between the conduction mechanism

and dielectric behaviour. The conduction phenomenon in ferrites is considered due to the

hopping of electrons between divalent and trivalent iron ions present over the octahedral

sites. The dielectric loss peak is observed when the jump frequency of the local charge

carriers (f = 1/τrelaxation) is approximately equal to the frequency of external applied

field [5, 13, 14]. The sharp peak can be observed when both the frequencies exactly

matched with each other.

Eddy current losses are inversely proportional to the resistivity of the ferrite

material. Hence the high resistivity is the key aspect for the ferrite material in order to

reduce the eddy current losses. It is seen that the minima occurred in the dielectric loss

for all the samples shifts towards the lower frequency region. The loss peak increase as

the terbium concentration is increased from 0.00 to 0.10 as shown in Fig. 4.110. The

dielectric loss peak is decreased as the terbium concentration is varied from 0.12 to 0.20

as indicated in Fig. 4.111. The irregular behaviour of the loss peak may be related to the

jump or hopping probability of the material. A decrease in the loss peak with increasing

terbium concentration indicates that the hopping or jump probability is decreasing. The

probable reason for this decrease is the population of Fe2+

ions on the octahedral sites,

which are responsible for the polarization in these ferrites, decreases with the increase of

terbium concentration.

Hence it can be inferred that the jump or hopping frequencies for all the samples

showing peaking behaviour lie in the range 1 to 10 MHz. The samples having nominal

compositions Mg.82Tb.18Fe2O4 and Mg.84Tb.16Fe2O4 exhibit minimum dielectric loss and

dielectric constant. These mentioned compositions have higher resistivity as compared to

all other compositions. Similar trends of the dielectric loss (tanδ) were also been reported

by other researchers [15, 16].

0

0.005

0.01

0.015

0.02

0.025

1.E+01 2.E+06 4.E+06 6.E+06 8.E+06 1.E+07

Frequency (Hz)

σ a

c (

oh

m-1

cm

-1)

x = 0.00

x = 0.02

x = 0.04

x = 0.06

x = 0.08

x = 0.10

Fig. 4.112. The variation of ac conductivity with frequency for Mg1-xTbxFe2O4

(x = 0.0- 0.10) ferrites.

0

0.005

0.01

0.015

0.02

0.025

1.E+01 2.E+06 4.E+06 6.E+06 8.E+06 1.E+07

Frequency (Hz)

σ a

c (

oh

m-1

cm

-1)

x = 0.12

x =0.14

x =0.16

x =0.18

x =0.20

Fig. 4.113. The variation of ac conductivity with frequency for Mg1-xTbxFe2O4

(x = 0.12- 0.20) ferrites.

Figs. 112 and 113 show the variation of ac conductivity with frequency at room

temperature for Mg-Tb ferrites. The ac conductivity (σac) increases with an increase if

frequency. The frequency dependence conductivity behaviour can be explained with the

help of Maxwell-Wagner double layer model. The ferrous ions are formed in the samples

while sintering the ferrites powders which lead to the high conductive grains. When

theses ferrite powders are cooled in an oxygen atmosphere, the low conductive grains are

possible to form. The ferrites which have high conductive grains are considered

inhomogeneous dielectric materials. The high conductive grains and grain boundaries

(low conductive grain) have different properties. The grain boundaries are more active in

the low frequency region. The hopping frequency of electron between Fe2+

and Fe3+

ions

is very low.

As the frequency increases conductive grains become more active by promoting

the hopping of electrons between Fe2+

and Fe3+

ions, hence increase the hopping

frequency. Thus ac conductivity increases as the frequency increases. The ac conductivity

decreases generally as the Tb-contents are increased in the samples as shown in Figs.

4.112 & 4.113. This decrease in σac can be explained on the basis that Tb-ions occupy on

the octahedral sites in these Mg-Tb ferrites. The Tb-ions are expected to lockup with Fe2+

ions and it reduces the hopping between the iron ions Fe2+

↔ Fe3+

. This decrease the

probability of hopping of charge carriers and the conductivity decreases.

The ac conductivity is observed to decrease in all Tb-substituted samples except x

= 0.18, which is anomaly in these plots. Also the sample Mg.96Tb.04Fe2O4 exhibit has high

conductivity values in high frequency region (MHz) as compared to the neighbouring

compositions. The decrease in conductivity beyond 8MHz is attributed to the occurance

of loss peak in tanδ. A decrease in ac conductivity has been reported [10] when different

rare-earths were substituted in Mn-Zn ferrites.

Conclusions

In the present work two series of Tb-substituted spinel ferrites namely Ni1−xTbxFe2O4

(x = 0, 0.02, 0.04, 0.06, 0.08, 0.10, 0.12, 0.14, 0.16, 0.18, 0.20) and Mg 1-x Tb x Fe2O4

(x = 0, 0.02, 0.04, 0.06, 0.08, 0.10, 0.12, 0.14, 0.16, 0.18, 0.20) were prepared by solid

state reaction technique.

The XRD analysis of Ni1−xTbxFe2O4 and Mg 1-x Tb x Fe2O4 ferrites revealed that

all samples are cubic spinel ferrites.

The substitution of terbium for x > 0.08 in nickel ferrites leads to the formation of

a secondary phase (TbFeO3) where as in Mg 1-x Tb x Fe2O4 ferrites the second

phase appeared at x = 0.06 as shown in the XRD patterns.

The appearance of secondary phase suggests the solubility limit in both series.

A non-linear behavior of lattice constant is found in both series and this is

attributed to the difference of ionic radii of Ni, Mg and Tb cations.

The bulk density of Ni1−xTbxFe2O4 and Mg 1-x Tb x Fe2O4 increases from 5.13 to

5.69 g/cm3 and from 3.55 to 4.6 g/cm

3 while X-ray density lies in the range ~ 5.4 -

5.86 g/cm3 and 4.55 – 5.16 g/cm

3 as the concentration of terbium is increased

from 0 to 0.2.

An appreciable decrease in porosity has been observed in both series caused by

the incorporation of terbium ions.

The FTIR analysis of both series indicate two absorption peaks thereby

confirming the spinel structure of these ferrites.

These absorption peaks revealed that terbium substitution for nickel and

magnesium ions occur at octahedral sites.

An inhomogeneous grain size distribution has been observed by the

microstructural analysis (SEM) and grain size is found to decrease by the

incorporation of terbium ions in Ni1−xTbxFe2O4 and Mg1-xTbxFe2O4 ferrites.

The micrographs also exhibit a few agglomerates and existence of secondary

phase.

The EDX analysis indicates the elemental percentage of the elements present in

each composition.

In Ni1−xTbxFe2O4 ferrites, the saturation magnetization is decreased from 34 to 27

emu/gram with the substitution of terbium.

The substitution of terbium in these ferrites leads to the dilution of B-sublattice

magnetization by the replacement of nickel magnetic ions by Tb in Ni1−xTbxFe2O4

ferrites and hence decreases the net magnetization.

The coercivity of Ni1−xTbxFe2O4 ferrites is decreased from 40 to 23.5 Oe as the

concentration of terbium is varied from 0 to 0.14 while for higher concentration (x

> 0.14), the coercivity increases.

In Mg 1-x Tb x Fe2O4 series the saturation magnetization lies in the range 30 - 26

emu/gram.

The substitution of terbium for magnesium in Mg 1-x Tb x Fe2O4 ferrites also takes

place at the octahedral sites and the redistribution of the cations involved results

in the decrease of the net magnetization.

The coercivity of Mg 1-x Tb x Fe2O4 ferrites decreases linearly with porosity up to

x = 0.06 and thereafter the coercivity deviates from linearity. The coercivity lies

in the range 47 to 34 Oe.

The FMR spectra of both the series showed single and slightly asymmetric

resonance peaks.

The linewidth (ΔH) observed have lower values (593 Oe for Ni.94Tb.06Fe2O4) as

compared to the reported linewidth of spinel ferrites and showed better correlation

with magnetization.

The large values of linewidth (ΔH) are attributed to the sample’s inhomogeneities.

A remarkable decrease in the initial permeability with increasing terbium

concentration in both series has been observed.

The magnetic loss factor of Ni1−xTbxFe2O4 ferrite indicates a very small value of

= 3.44 x 10 -7

at x = 0.2.

The magnetic loss factors of Mg 1-x Tb x Fe2O4 ferrites are also very low and for x

= 0.2 its value is ~ 1.02 x 10-6

.

The resistivity of Ni1−xTbxFe2O4 ferrites increased from 1.7 x 105 to 3.9 x 10

5 Ω-

cm while the resistivity of Mg 1-x Tb x Fe2O4 ferrites increases from 2.33 x 106 to

5.71 x 107 Ω-cm with the increasing concentration of terbium.

The temperature dependent resistivity revealed that all the investigated

compositions show semiconducting behaviour.

The increase in drift mobility of the charge carriers of both series at higher

temperature is owing to thermal activation.

The activation energy increases with an increase in Tb-concentration in a similar

manner as that of resistivity.

The dielectric constant and dielectric loss decreases in both series by the terbium

incorporation.

Ni1−xTbxFe2O4 ferrites exhibited an abnormal dielectric loss.

The dielectric loss of Ni1−xTbxFe2O4 ferrites remains in the range 0.98-0.21 while

for Mg 1-x Tb x Fe2O4 ferrites it lies in the range 0.99-0.37 in the frequency range

from 10 Hz to 10 MHz.

References

[1] B. D. Cullity. Elements of X-ray Diffraction. Addison-Wesley; 1959.

[2] Sagar E. Shirsath, B. G. Toksha, K. M. Jadhav,Mater. Chem. Phys. 117 (2009)

163-168.

[3] N. Rezlescu, E. Rezlescu, C. Pasnicu, M. L. Craus. J. Phys. Condens . Matter 6

(1994) 5707- 5716.

[4] A. A. Pandit, A. R. Shitre, D. R. Shengule, K. M. Jaghav . J. Mater. Sci. 40 (2005)

423-428.

[5] M. U. Islam, I. Ahmed, T. Abbas, Proceeding of the sixth International Symposium

on Advanced Materials (1999) 155-158.

[6] D. R. Lide, CRC Hand Book of Chemistry and Physics, 76th

ed.,CRC press,

London,1995.

[7] N. Rezlescu, E. Rezlescu, P. D. Popa, L. Rezlescu. J. Alloys Comp. 275- 277

(1998) 657-659.

[8] O. M. Hemeda, M. Z. Said, M. M. Barakat, J. Magn. Magn. Mater. 224 (2001)132-

142.

[9] L. John Berchmans, R. Kalai Selvan, P.N. Selva Kumar, C.O. Augustin, Mater. Lett.

58 (2004) 1928 – 933.

[10] L. John Berchmans, R. Kalai Selvan, P.N. Selva Kumar, C.O. Augustin, J. Magn.

Magn. Mater. 279 (2004) 103-110.

[11] William E. Lee, W. Mark Rainforth, Ceramic Microstructures: Property control by

processing. Kluwer Academic Publishers, 1994.

[12] E. Rezlescu, N. Rezlescu, C. Pasnicu, M. L. Craus, P. D. Popa, Cryst. Res. Technol.

31 (1996) 343-352.

[13] I. Neel, Ann. Phys. 3 (1948) 137-198.

[14] C. N. Chinnasamy, A. Nareyanasamy, N. Ponpandian, K. Chattopadhyay, K.

Shinoda, B. Jeyadevan, K. Tohji, K. Nakatauka, T. Furubayashi, I. Nakatani, Phys.

Rev. B 63 (2001) 184108-1 - 184108-6

[15] H. Perron. T. Mellier, C. Domain, J Roques, E. Simoni, R Drot and H Catalette, J.

Phys. Condens. Matter, 19 (2007) 346219-1 – 346219-10.

[16] M. Azhar Khan, M.U. Islam, M. Ishaque, I.Z. Rahman, A. Genson, S. Hampshire,

Mater. Charact. 60 (2009) 73-78.

[17] N. Rezlescu and E. Rezlescu, Solid State Commun. 88 (1993) 139-141.

[18] A. Goldman, Modern Ferrite Technology, Van Nostrand Reinhold , New York,

1990.

[19] D. Jiles, Introduction to Magnetism and Magnetic Materials, Chapman & Hall,

London, 1991.

[20] B. Parvatheeswara Rao, O. F. Caltun, J. Optoelectron. Adv. Mater. 8, (3) (2006)

991- 994.

[21] B. Parvatheeswara Rao, A. Mahesh Kumar, K. H. Rao, Y. L .N. Murthy, O. F.

Caltun, I. Dumitru, L. Spinu, J. Optoelectron. Adv. Mater. 8 (5) (2006) 1703-1705.

[22] K. J. Standley, Oxide Magnetic Materials, Oxford: Claredon Press, 1962.

[23] R. F. Soohoo and A. H. Morrish, J. Appl. Phys. 50 (1979) 1639-1641.

[24] T. Nakamura, J. Appl. Phys., 88 (2000) 348-353.

[25] A. M. Sankpal, S. V. Kakatkar, N. D. Chaudhari, R. S. Patil, S. R.Sawant, J. Mater.

Sci. Mater. Sci. in Electronics 9 (1998) 173-179.

[26] J. Smit, H. P. J. Wijn, Ferrites, Philips Technical Library, Eindhoven,

Netherlands 1959.

[27] A. Globus. M Guyot, IEEE Trans. Magn., 6(1970) 614-617.

[28] A. Globus, M Guyot, Phys. Stat. Sol. (b), 52 (1972) 427-431.

[29] A. Globus, Paul Duplex and Marcel Guyot, IEEE Trans. Magn. MAG-7 (1971) 617-

622.

[30] Su-il Pyun, Jong-Tae Baek, Am. Ceram. Soc. Bull. 64 (1985) 602-605.

[31] A. Globus, P Duplex, Phys. Stat. Sol. 31 (1969) 875-881

[32] G. T. Rado, R. W. Wright, W. H. Emerson, Phys. Rev. 80 (1950) 273-280

[33] A. Verma, T. C. Goel, R. G. Mendiratta, P. Kishan, J. Magn. Magn. Mater. 208

(2000) 13-19.

[34] S. Chikazumi, Physics of Magnetism, Wiley, New York, 1964.

[35] C. Kittel, An introduction to Solid State Physics, 5th

Ed., Wiley, New York, London,

1976, P.170.

[36] N. Rezlescu, E. Rezlescu, P. D. Popa, L. Rezlescu, J. Alloys Compd. 275- 277

(1998) 657-659.

[37] N. Rezlescu, E. Rezlescu, Solid State Commun. 88, 2, (1993) 139-141.

[38] Misbah ul-islam, Tahir Abbas, M. Ashraf Chaudhry, Mater. Lett. 53 (2002)

30-34.

[39] M.U. Islam, Faiza Aen, Shahida B. Niazi, M. Azhar Khan, M. Ishaque,

T. Abbas, M.U. Rana, Mater. Chem. Phys. 109 (2008) 482-487.

[40] D. S Birajdar, D. R. Mane, S. S. More, V. B. Kawade, K. M. Jadhav, J. Mater. Lett.

59 (2005) 2981-2985

[41] M. K. Shobanaa, S. Sankara, V. Rajendranb, Mater. Chem. Phys. 113 (2009) 10-13.

[42] A. K. M. Akhtar Hossain, S. T. Mahmud, M. Seki, T. Kawai, H. Tabata, J. Magn.

Magn. Mater. 312 (2007) 210-219.

[43] M. Z. Said, Mater. Lett. 34 (1998) 305-307.

[44] J.C. Maxwell, Electricity and Magnetism, Oxford University Press,

Landon, 1973.

[45] K.W. Wagner, Ann. Phys. 40 (1913) 817-825.

[46] C.G. Koop, Phys. Rev. 83 (1951) 121-127.

[47] N. Sivakumar, A. Narayanasamy, B. Jeyadevan, R. Justin Joseyphus, J. Phys. D:

Appl. Phys. 41 (2008) 245001-1 – 245001-5

[48] A. M. Abdeen, J. Magn. Magn. Mater. 192 (1999) 121-129.

[49] A. M. M. Farea, Shalendra Kumar, Khalid Mujasam Batoo, Ali Yousef, Chan Gyu

Lee, Alimuddin, J. Alloys Compd. 469 (2009) 451-457.

[50] D.C. Agarwal, Asian J. Phys. 6 (1997) 108-115.

[51] M. F. Fayek, M. K. Elnimr, F. Sayed Ahmed, S. S. Ata-Allah, M. Kaiser, Solid State

Commun. 115 (2000) 109-113.

[52] R. V. Mangalaraja, S. Ananthakumar, P. Manohar, F. D. Gnanam, J. Magn. Magn.

Mater. 253 (2002) 56-64.

[53] B. Parvatheeswara Rao, K. H. Rao, J. Mater. Sci. 32 (1997) 6049-6054.

[54] M. A. Ahmed, N. Okasha, M. M. El-Sayed, Ceram. Int. 33 (2007)

49-58.

[55] K. S. Nalwa, A. Garg, A. Upadhyaya, Mater. Lett. 62 (2008) 878-881

[56] S. D. Chhaya, M. P. Pandya, M. C. Chhantbar, K. B. Modi, G. J. Baldha, H. H.

Joshi, J. Alloys Comp. 377 (2004) 155-161.

[57] Mansour Al-Haj, J. Magn. Magn. Mater. 299 (2006) 435-439.

[58] N. Okasha, Mater. Chem. Phys. 84 (2004) 63-70.

[59] N. Rezlescu, C. Doroftei, E. Rezlescu, P. D. Popa, Sensors and Actuators B 115

(2006) 589-595.

[60] C. B. Kolekar, P. N. Kamble, A. S. Vaingankar, J. Magn. Magn. Mater. 138

(1994) 211-215.

[61] P. P. Hankare, V. T. Vader, N. M. Patil, S. D. Jadhav, U. B. Sankpal, M. R. Kadam,

B. K. Chougule, N. S. Gajbhiye, Mater. Chem. Phys. 113 (2009) 233-238.

[62] M. U. Islam, M. A. Chaudhry, T. Abbas, M. Umar, Mater. Chem. Phys. 48 (1997)

227-229.

[63] B. K. Labde, Madan C. Sable, N. R. Shamkuwar, Mater. Lett. 57 (2003) 1651-1655.

[64] Qiang-Min Wei, Jian-Biao Li, Yong-Jun Chen, J. Mater. Sci. 36 (2001) 5115-5118.

[65] A. M. Shaikh, S. A. Jadhav, S. C. Watawe, B. K. Chougule, Mater. Lett. 44

(2000) 192-196.

[66] M. A. Ahmed, E. Ateia, S. I. El-Dek Vibrational Spectroscopy 30 (2002) 69-75.

[67] M. A. Ahmed, E. Ateia, F. M. Saleem, Physica B 381 (2006) 144-155.

[68] S. C. Watawe, B. D. Sutar, B. D. Sarwade, B. K. Chougule, Int. J. Inorg. Mater. 3

(2001) 819-823.

[69] S. A. Mazen, M. H. Abdallah, B. A. Sabrah, H. A. M. Hashem, Phys. Stat. Sol. (a)

134 (1992) 263-271.

[70] A. A. Sattar, A. M. Samy, R. S. El-Ezza and A. E. Eatah, Phys. Stat. Sol. (a) 193

(2002) 86-93.

[71] N. N. Jani, Bismal S. Trivedi, H. H. Joshi, R. G. Kulkarni, Hyperfine Interact.

110 (1997) 227-237.

[72] Mansour Al-Haj, Phys. Stat. Sol. (a) (2) 203 (2006) 343-348.

[73] Yaping Wang, Feng Xu, Liangchao Li, Hui Liu, Haizheng Qiu, Jiang Jing, Mater.

Chem. Phys. 112 (2008) 769-773.

[74] Ana Cristina, F. M. Costa, Marcio R. Morelli, Ruth H. G. A. Kiminami, J. Mater.

Sci. 39 (2004) 1773-1778.

[75] L. Gama, A. P. Diniz, A. C. F. M. Costa, S. M. Rezende, A. Azevedo, D. R.

Cornejo, Physica B 384 (2006) 97-99.

[76] L. Ben Tahar, M. Artus, S. Ammar, L. S. Smiri, F. Herbst, M.-J. Vaulay,

V. Richard, J.-M. Greneche, F. Villain, F. Fievet, J. Magn. Magn.

Mater. 320 (2008) 3242-3250.

[77] B. Parvatheeswara Rao, K. H. Rao, P. S. V. Subba Rao, A. Mahesh Kumar, Y. L. N.

Murthy, K. Asokan, V. V. Siva Kumar, Ravi Kumar, N. S. Gajbhiye, O. F. Caltun,

Nucl. Instr. Meth. Phys. Res. B 244 (2006) 27-30.

[78] B. Parvatheeswara Rao, Ovidiu caltun, Ioan Dumitru, Leonard Spinu, J. Magn.

Magn. Mater. 304 (2006) e752-e754.

[79] Marshal Sparks, “Ferromagnetic relaxation theory” McGraw-Hill, New york 1964

P10.

[80] M. Yan, J. Hu, W. Luo, W.Y. Zhang, J. Magn. Magn. Mater. 303 (2006) 249–255.

[81] S. A. Ghodake, U. R. Ghodake, S. R. Sawant, S. S. Suryavanshi, P. P. Bakare, J.

Magn. Magn. Mater. 305 (2006) 110-119.

[82] VivekVerma, S. P. Gairola, Vibhav Pandey, J. S. Tawale, Hua Su, R. K. Kotanala, J.

Magn. Magn. Mater. 321 (2009) 3808-3812.

[83] S. E. Jacobo, W. G. Fano, A. C. Razzitte, Physica B 320 (2002) 261-263.

[84] N. Rezlescu, E. Rezlescu, C. Pasnicu and M. L. Craus, J. Magn. Magn. Mater. 136

(1994) 319-326.

[85] E. Rezlescu, N. Rezlescu, P. D. Popa, L. Rezlescu, C. Pasnicu, Phys. Stat. Sol. (a)

162 (1997) 673-678.

[86] M.U. Islam, T. Abbas, Shahid B. Niazi, Zubair Ahmad, Sadia Sabeen M.Ashraf

Chaudhry, Solid. State Commun.130 (2004) 353-356.

[87] M. Ishaque, M.U.Islam, M. Azhar Khan, I. Z. Rahman, A.Genson, S.Hampshire,

Physica B 405 (2010) 1532–1540.

[88] A. G Bhosale, B. K. Chougule, Mater. Lett. 60 (2006) 3912-3915

[89] E. J. W. Verwey and J. H. De Boer, Rec. Trans. Chim. des pays-Bas. 55 (1936)

531-540.

[90] Y. Purushotham, M. B. Reddy, Pran Kishan, D. R. Sagar, and P. Venugopal Reddy,

Mater. Lett. 17 (1993) 341-345.

[91] M. Kaiser, and S. S. Ata Allah, Phys. Stat. Sol. (b) 15, 242 (2005) 3138-3148.

[92] R. G. Kharabe, R. S. Devan, C. M. Kanamadi, B. K. Chougule, Smart Mater. Struct.

15 (2006) N36.

[93] B. Kunar, G. P. Srivastava, J. Appl. Phys. 75 (10) (1994) 6115-6117.

[94] F. M. Pontes, E. R. Leite, E. Longo, J. A. Varela, E. B. Araujo and J. A. Eiras,

Appl. Phys. Lett. 76 (2000) 2433-2435.

[95] W. Jing, Z. Hong, B. Shuxin, C. Ke, Changrui, J. Magn. Magn. Mater, 312 (2007)

310-313.

[96] Kh. Roumaih, J. Alloys Comp. 465 (2008) 291-295.

[97] Muhammad Javed Iqbal, Zahoor Ahmad, J. Power Sources 179 (2008) 763-769.

[98] J. Azadmanjiri, Mater. Chem. Phys. 109 (2008) 109-112.

[99] M. B. Reddy, P. V. Reddy, J. Appl. Phys. (U.K.) 24 (1991) 975-981.

[100] M. K. Fayek, S. S. Ata –Allah, H. A. Zayed, M. Kaiser, S. M. Ismail, J. Alloys

Comp. 469 (2009) 9-14.

[101] S. S. Bellad, B. K. Chougule, Mater. Chem. Phys. 66 (2000) 58-63.

[102] S. C. Watawe, B. D. Sarwade, S. S. Bellad, B. D. Sutar, B. K. Chougule, J. Magn.

Magn. Mater, 214 (2000) 55-60.

Appendix A

Conversion Factors

Principal unit systems in Magnetism[*]

Quantity Symbol SI

(Summerfield)

SI

(Kennelly)

CGS-EMU

(Gaussian)

Field H A.m-1

A.m-1

Oe (Oersted)

Induction B Tesla Tesla G (Gauss)

Magnetization M A.m-1

- emu. cm-3

Intensity of

Magnetization

I - Tesla -

Flux Φ weber Weber maxwell

Moment M A.m-1

Weber meter emu

Pole strength p A.m weber emu. cm-1

Field equation B = μ0 (H+M) B = μ0 H + I B = H + 4πM

Conversion Factors.

1 Oe = (1000 / 4 π). A. m-1

= 79.58 A. m-1

1 G = 10-4

Tesla

1 emu. cm-3

= 1000 A. m-1

[* ] D. Jiles, Introduction to Magnetism and Magnetic Materials, Chapman and Hall,

London, 1996, 11-12.

Appendix B

Abbreviations, Symbols and Physical Constants

Ms Saturation magnetization

B Magnetic induction

μ Permeability

μi′ Relative initial permeability

Hc Coercivity

λ Wave length of X-ray

tanδ Loss factor

u Oxygen parameter

rA Tetrahedral ionic radius

rB Octahedral ionic radius

a Lattice constant

A-sites Tetrahedral sites

B-sites Octahedral sites

H Magnetic field

T Temperature

Tc Curie temperature

K1 Magnetocrystalline anisotropy constant

Dx X-ray density

Db Bulk density

M Molecular weight

N Avogadro’s number

P Percentage of porosity

f frequency

hkl Miller indices

ρt Density of toluene at the measurement temperature

Wa Weight of the sample in air

Wt Weight of the sample in toluene

FMR Ferromagnetic resonance

∆H Linewidth

ρ Resistivity

έ Dielectric constant d Thickness of the pellet in meters

C Capacitance

FTIR Fourier Transform infrared Spectroscopy

N No. of turns of wound wire

n 0rder of reflection

Lm Self-inductance

Rm Intrinsic resistance

Z Impedance

VSM Vibrating Sample Magnetometer

SEM Scanning Electron Microscopy

EDX Energy Dispersive X-ray Spectroscopy

XRD X-ray Diffraction

d Interplaner spacing

Ea Activation energy

List of Publications Published

1- M. Azhar Khan, M. U. Islam , M. Ishaque, I.Z. Rahman, Ceram. Int. 37 (2011)

2519- 2526.

2- M. Ishaque, M. U. Islam, M. Azhar Khan, I. Z. Rahman, A. Genson, S.

Hampshire, Physica B, 405 (2010) 1532-1540.

3- M. Azhar Khan, M. U. Islam, M. Ishaque, I. Z. Rahman, A. Genson, S.

Hampshire, Mater. Charact. 60 (2009) 73-78.

4- M.U. Islam, Faiza Aein, Shahida B. Niazi, M.Azhar Khan, M.Ishaque, T,Abbas

and M.U. Rana, Mater. Chem. Phys. 109 (2008) 482-487.

5- M.U.Islam, M.Azhar Khan, Zulfiqar Ali, Shahida B.Niazi, M. Ishaque and T.

Abbas, Int. J. Modern Phys. B Vol.21 No.15, (2007) 2669-2677.

Submitted

1-M. Azhar Khan, M. U. Islam, M. Ishaque, Magnetic, Electrical and Dielectric

properties of Terbium-substituted Nickel Ferrites.

2- Muhammad Azhar Khan, M. U. Islam, M. Ishaque, I.Z. Rahman, Magnetic and

Dielectric behavior of Terbium substituted Mg1-xTbxFe2O4 Ferrites.

Date post:	14-Mar-2022
Category:	Documents
Upload:	others
View:	14 times
Download:	0 times

FABRICATION AND CHARACTERIZATION

Documents