prr.hec.gov.pkprr.hec.gov.pk/jspui/bitstream/123456789/1945/1/1415S.pdf · I hereby declare that I have not submitted this research work of mine entitled “Physical Properties of

PHYSICAL PROPERTIES OF YTTRIUM SUBSTITUTED FERRITES

Ph.D. Thesis

Muhammad Ishaque

Department of Physics Bahauddin Zakariya University

Multan, Pakistan. (2011)

PHYSICAL PROPERTIES OF YTTRIUM SUBSTITUTED FERRITES

Ph.D. Thesis Muhammad Ishaque

A thesis submitted in partial fulfillment of the requirement for the degree of Doctor of

Philosophy in Physics Department of Physics

Bahauddin Zakariya University Multan, Pakistan (2011)

Declaration

I hereby declare that I have not submitted this research work of mine entitled “Physical

Properties of Yttrium Substituted Ferrites” leading to the degree of Ph.D. in Physics to any other

university within 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 Ishaque.

Acknowledgements

All praises and blessings to Allah the most Gracious and Merciful. It is with great

submission that I bow my head before Him for giving me the courage to complete this work.

I wish to express my deepest gratitude to Dr. Misbah-ul-Islam, Dr. Tahir Abbas, Dr.

Anwar-ul-Haq, Dr. Mazhar Uddin Rana, Dr. M.Y. Nadeem, Dr. Tariq Bhatti, Dr. Ijaz Ahmad,

Dr. Amer Basher Ziya, Dr. Javeed Ahmad and Dr. Ishtiaq Ahmad Soomro for their inspiring

guidance and consistent encouragement for the completion of this work. Their valuable

suggestions helped me in comprehending the intricacies involved in this work.

My deep appreciations to the chairman, Department of Physics and other staff members

who provided me research facilities available both in and out of the department.

I am thankful to Prof. Dr. I. Z. Rahman, Prof. Dr. Stuart Hampshire and Dr. Annaik Genson

University of Limerick, Ireland for providing me an access to their research laboratories. I am

also indebted to Dr. Carl E. Patton for providing magnetic properties measurement facilities on

VSM and FMR at the department of Physics, Colorado State University, USA.

Thanks are due to Sir Anwar Manzoor Rana, Sir Asim Javed, M. Wasiq (Ph.D. Scholar), M.

Azhar Khan (Ph.D. Scholar), M. Irshad Ali (Ph.D. Scholar), Hafiz Tahir (Ph.D. Scholar), Faiza

(Ph.D. Scholar), M. Ishfaq (Ph.D. Scholar) and Sher Atta Khan Khosa for their valuable help

from start to end.

Finally, this arduous task would have not been done without the moral support, good

wishes, consistent encouragement and patience of my wife and sons.

I want to especially thank to the Higher Education Commission (HEC) of Pakistan for the

financial assistance under HEC Indigenous scheme and International Research Support Initiative

Program (IRSIP).

Muhammad Ishaque

To My Parents, Family & Friends

ABSTRACT

This dissertation presents a systematic study on five series of spinel ferrites. Three series

of spinel ferrites, namely, NiY-ferrites (NiY2xFe2-2xO4, x = 0.0 – 0.12, step: 0.02), MgY-ferrites

(MgY2xFe2-2xO4, x = 0.0 – 0.12, step: 0.02) and NiZnY-ferrites (Ni0.6Zn0.4Y2xFe2-2xO4, x = 0.0 -

0.1, step: 0.02) were fabricated in a polycrystalline form by double sintering ceramic method.

Two series of CoZnY-ferrites (Co1-xZnxY0.15Fe1.85O4, x = 0.0, 0.2, 0.4, 0.6, 0.8, 1.0) and CoY-

ferrites (CoFe2O4 + x Y2O3, x = 0 wt %, 1 wt %, 3 wt %, 5 wt %) were fabricated by co-

precipitation method. The samples were characterized by X-ray diffraction (XRD), Scanning

Electron Microscopy (SEM), Fourier Transform Infrared Spectroscopy (FTIR), Vibrating

Sample Magnetometery (VSM) and Impedance spectroscopy and Ferromagnetic Resonance.

Phase analysis of NiY-, MgY- and NiZnY-ferrites from XRD patterns has shown cubic

spinel single phase along with few traces of second phase identified as orthorhombic phase. This

phase becomes more conspicuous for higher concentration of yttrium. The lattice constant as a

function of yttrium contents changes non-linearly. The behavior of the lattice parameter was

explained on the basis of differences in ionic radii of the constituent ions. Analysis of the XRD

patterns of the CoZnY-ferrites confirms the formation of cubic spinel phase along with second

phase of YFeO3. The lattice seems to expand to accommodate the increased number of Zn2+ ions

of relatively larger ionic radii. The phase analysis of the XRD patterns of CoY-ferrites shows

that all the samples are dual phase except the sample with x = 0 wt %. The lattice constant was

found to decrease with yttrium contents. The lattice seems to compress by the presence of second

phase due to difference in thermal expansion coefficients. X-ray density and physical density

was found to increase whereas porosity was found to decrease with the increase of yttrium

contents. The morphology of the samples shows non-homogeneous distribution of grains in all

the samples except CoZnY-ferrites. The near uniform distribution of grain size was observed in

CoZnY ferrites. FTIR spectra of NiY-, MgY- and NiZnY-ferrites observed at room temperature

in the wave number range 370 – 1100 cm-1 exhibit splitting of the two fundamental absorption

bands, thereby confirming the solid state reaction. FMR spectra of NiY- and MgY-ferrites were

measured at room temperature at X-band (9.5 GHz). The nominal compositions MgY0.04Fe1.96O4

and NiY0.12Fe1.88O4 have small linewidth, ΔH = 269 Oe and 282 Oe respectively. Hence these

ferrites have potential for high frequency applications. A systematic study of variations in

resistivity with different concentration of yttrium has been carried out to optimize the resistivity.

The room temperature resistivity shows an increasing trend in all series whereas it was decreased

in case of Co-Zn-Y ferrites. The addition of Y3+ ions in place of Fe3+ ions reduce the degree of

conduction by blocking Verwey’s hopping mechanism resulting in an increase of resistivity. The

temperature dependent dc resistivity was found to decrease linearly with rise in temperature. The

observed decrease in dc resistivity with temperature is normal behavior for semiconductors

which follows the Arrhenius relation. It was observed that the samples having higher values of

resistivity also possessed higher activation energy. The saturation magnetization was observed to

decrease with yttrium contents which are due to redistribution of cations on the tetrahedral and

octahedral sites. The coercivity was observed to increase with yttrium contents. The smaller

grains may obstruct the domain wall movement. As a result, the values of initial permeability (

iμ′ ) decreased from 110 to 35, 27 to 6 and 185 to 87 at 1 MHz in NiY-, MgY- and NiZnY-

ferrites respectively. The values of magnetic loss tangent decreased from 0.23 to 0.03, 0.04 to

0.007, 1.2 to 0.41 in NiY-, MgY- and NiZnY-ferrites respectively. This may be attributed to the

increase in resistivity that reduces the eddy current loss. The frequency dependent behaviors of

dielectric constant follow the Maxwell–Wagner’s interfacial polarization in accordance with

Koops phenomenological theory. The introduction of yttrium ions decreases the dielectric

constant and dielectric loss tangent (tan δ). The results obtained are of great interest for the

development of modified spinel ferrites for various industrial applications.

Table of Contents Acknowledgments

Abstract

Contents Page No.

CHAPTER 1

Introduction 1.1 Ferrites 1

1.2 Literature Survey 2

1.3 Aims & Objectives of the Present Work 28

References 29

CHAPTER 2 Theories and Models 2.1 Soft Magnetic Materials 36

2.2 Spinel Structure of Ferrites 37

2.3 Electrical Properties 40

2.3.1 Conduction mechanism in ferrites 40

2.3.1.1 Hopping model of Electrons 41

2.3.1.2 Polaron model 42

2.4 Dielectric properties 43

2.4.1 Electronic Polarization 44

2.4.2 Ionic Polarization 44

2.4.3 Dipolar or Orientational polarization 44

2.4.4 Space Charge Polarization or Interfacial polarization 45

2.4.5 Frequency Dependence of Dielectric Constant 46

2.5.1 Magnetic Materials 47

2.5.1.1 Diamagnetic Materials 47

2.5.1.2 Paramagnetic Materials 48

2.5.1.3 Ferromagnetic Materials 49

2.5.1.4 Antiferromagnetic Materials 49

2.5.1.5 Ferrimagnetic Materials 50

2.6 Origin of Magnetic Moments 50

2.6.1 Electronic Structure 50

2.6.2 Bonding 52

2.6.2.1 Ionic Bonding 52

2.6.2.2 Covalent Bonding 53

2.6.2.3 Metallic Bonding 54

2.7 The origin of Magnetic interactions in Ferrites 54

2.7.1 Indirect Exchange Interaction 55

2.7.2 Super-exchange interaction 55

2.7.3 Double-exchange interaction 57

2.7.4 Molecular Field Theory 57

2.7.5 Neel theory of Ferrimagnetism 59

2.8 Magnetic interactions 60

2.8.1 The Magnetization in Ferrite Domains 60

2.8.2 Magnetostatic Energy 61

2.8.3 Magnetocrystalline Anisotropy Energy 62

2.8.4 Magnetostrictive energy 62

2.8.5 Domain wall Energy 63

2.9. Hysteresis loop 64

2.10 Introduction to Ferromagnetic Resonance 66

2.10.1 The System of Units 66

2.10.2 The Magnetization Time Evolution Equation 67

2.10.3 Ferromagnetic Relaxation 70

2.10.4 Gilbert Damping Model 70

2.10.5 Landau-Lifshitz Model 70

2.10.6 Other Ferromagnetic damping Models 71

References 72

Chapter 3

Fabrication and Characterization Techniques

3.1 Sample Preparation 74

3.1.1 Standard Ceramic Method 74

3.1.2 Co-precipitation method 75

3.2 Characterization Techniques 80

3.2.1 X-ray Diffraction (XRD) 80

3.2.2 Scanning Electron Microscopy (SEM) 83

3.2.3 Bulk Density Measurement 84

3.2.4 DC Resistivity 84

3.2.5 Dielectric Properties 85

3.2.6 Vibrating Sample Magnetometer (VSM) 85

3.2.7 Impedance Analyser 87

3.2.8 Ferromagnetic Resosnance (FMR) 88

3.2.9 Initial Permeability ( iμ ) 89

References 90

CHAPTER 4 Results and Discussions

4.1 NiY2xFe2-2xO4 ferrite series 91

4.1.1 X-ray diffraction Analysis 91

4.1.1.1 Lattice Parameters 93

4.1.1.2 Bulk Density, X-Ray Density and Porosity 93

4.1.1.3 Average Grain Size 96

4.1.2 FTIR Analysis 98

4.1.3 Electrical resistivity 101


4.1.4.1 Compositional dependence of dielectric behavior 103

4.1.4.2 Frequency dependence of dielectric constant 104

4.1.4.3 Variation of dielectric loss tangent with frequency 105

4.1.4.4 Relationship between dielectric constant and resistivity 106

4.1.5 M-H Loops Analysis 107

4.1.6 Initial Permeability ( iμ ) 109

4.1.7 Ferromagnetic Resonance (FMR) 112

4.2 MgY2xFe2-2xO4 ferrite series 115











4.2.4.4 Relationship between dielectric constant and resistivity 128

4.2.5 M-H loops Analysis 129

4.2.6 Initial permeability ( iμ ) 131

4.2.7 Ferromagnetic Resonance (FMR) 133

4.3 Ni0.6Zn0.4Y2xFe2-2xO4 ferrite series 136










4.3.4.3 Variation of dielectric loss tangent (tan δ) with frequency 149

4.3.5 Magnetic properties 149

4.3.5.1 MH-loops 149

4.3.5.2 Initial permeability ( iμ ) 151

4.3.5.3 Magnetic loss tangent (tan) 152

4.4 Co1-xZnxY0.15Fe1.85O4 Ferrite System 154

4.4.1 X-Ray Diffraction Analysis 154


4.4.1.2 Average Crystallite Size 156

4.4.1.3 X-ray density, Physical Density and Porosity 159

4.4.2 Electrical Resistivity 162

4.4.3 Dielectric properties 166

4.4.3.1Compositional Dependence of dielectric constant 166

4.4.3.2 Frequency Dependence of dielectric constant 166


4.4.3.4 Relationship between dielectric constant (ε ′ ) and Resistivity (ρ) 168

4.5 CoFe2O4 + x Y2O3 Ferrite System 170

4.5.1 X-Ray Diffraction Analysis 170



4.5.1.3 Physical Density 175

4.5.2 dc Resistivity 176

4.5.3 Dielectric properties 179

4.5.3.1 Compositional Dependence of dielectric constant 179

4.5.3.2 Frequency Dependence of dielectric constant 179

4.5.3.3 Variation of dielectric loss tangent (tan δ) with frequency 180

4.5.3.4 Relationship between dielectric constant (ε ′ ) and Resistivity (ρ) 181

4.5.4.1 Conclusion 182

4.5.4.2 Future work 185

References 186

Appendix A 190

Appendix B 191

List of Publications 193

List of Figures Fig. 4.1 X- ray diffraction patterns for NiY2xFe2-2xO4 (0 ≤ x ≤ 0.12), * indicate

YFeO3 peak. 92

Fig. 4.2 X-ray density (Dx), physical density (DP), percentage porosity

Vs. Y Concentration (x) for NiY2xFe2-2xO4 (0 ≤ x ≤ 0.12). 95

Fig. 4.3 SEM micrograph of NiY2xFe2-2xO4 ferrite: (a) x = 0.0. (b) x = 0.08

(c) x = 0.12 98

Fig. 4.4 Typical FTIR spectra of NiY2xFe2-2xO4 ferrites: x = 0.0, 0.02,

0.04, 0.06, 0.08, 0.1. 100

Fig. 4.5 Variation of room temperature resistivity Vs. Y-concentration

for NiY2xFe2-2xO4 ferrites (x = 0.0, 0.02, 0.04, 0.06, 0.08, 0.1,

0.12). 101

Fig. 4.6 Variation of Log ρ Vs. 1000/ T (K) for NiY2xFe2-2xO4 ferrites

(x = 0.0, 0.02, 0.04, 0.06, 0.08, 0.1, 0.12). 102

Fig. 4.7 Activation energy Vs. Y concentration for NiY2xFe2-2xO4

(0 ≤ x ≤ 0.12) 103

Fig. 4.8 Variation of dielectric constant as a function of frequency for

NiY2xFe2-2xO4 ferrites (0 ≤ x ≤ 0.12). 104

Fig. 4.9 Plot of loss tangent (tan δ) Vs frequency at room temperature

for NiY2xFe2-2xO4 ferrites (0 ≤ x ≤ 0.12) 105

Fig. 4.10 MH- loops for NiY2xFe2-2xO4 ferrites (x = 0.0, 0.02, 0.04, 0.06,

0.08, 0.1, 0.12). 108

Fig. 4.11 Frequency variation of initial permeability ( iμ ) for NiY2xFe2-2xO4

ferrites (x = 0.0, 0.02, 0.04, 0.06, 0.08, 0.1). 110

Fig. 4.12 Ms2 Vs. Initial permeability ( iμ ) for NiY2xFe2-2xO4 ferrites. 110

Fig. 4.13 Frequency variation of magnetic loss tangent for NiY2xFe2-2xO4 ferrites

(x = 0.0, 0.02, 0.04, 0.06, 0.08, 0.1, 0.12). 111

Fig. 4.14 FMR spectra of NiY2xFe2-2xO4 ferrites (x = 0.0, 0.02, x = 0.04, 0.06,

0.08, 0.1, 0.12. 114

Fig. 4.15 X- ray diffraction patterns for MgY2xFe2-2xO4 (0 ≤ x ≤ 0.12) 116

Fig. 4.16 X-ray density (Dx), physical density (DP), percentage porosity Vs. Y

concentration for MgY2xFe2-2xO4 (0 ≤ x ≤ 0.12) ferrites. 118

Fig. 4.17 SEM micrograph of MgY2xFe2-2xO4 ferrite: (a) x = 0.0, (b) x = 0.06,

(c) x = 0.1. 120

Fig. 4.18 FTIR spectra of MgY2xFe2-2xO4 ferrite: (a) x = 0.0, 0.02, 0.04, 0.06,

0.08, 0.1. 122

Fig 4.19 Variation of Log ρ Vs. 1000/ T (K) for MgY2xFe2-2xO4 ferrites

(x = 0.0, 0.02, 0.04, 0.06, 0.08, 0.1, 0.12). 124

Fig. 4.20 Plot of Activation energy Vs. Y concentration for

MgY2xFe2-2xO4 (0 ≤ x ≤ 0.12) 125


MgY2xFe2-2xO4 (0 ≤ x ≤ 0.12) ferrites. 126


MgY2xFe2-2xO4 (0 ≤ x ≤ 0.12) ferrites. 128

Fig. 4.23 Hysteresis loops for MgY2xFe2-2xO4 ferrites (x = 0.0, 0.02, 0.04, 0.06,

0.08, 0.1, 0.12). 130

Fig. 4.24 Frequency variation of initial permeability for NiY2xFe2-2xO4 ferrites

(x = 0.0, 0.02, 0.04, 0.06, 0.08, 0.1). 132

Fig. 4.25 Frequency variation of magnetic loss tangent for MgY2xFe2-2xO4 ferrites

(x = 0.0, 0.02, 0.04, 0.06, 0.08, 0.1, 0.12). 132

Fig. 4.26 FMR spectra of MgY2xFe2-2xO4 ferrites (x = 0.0, 0.02, x = 0.04, 0.06,

0.08, 0.1, 0.12) 135

Fig. 4.27 X-ray diffraction patterns for Ni0.6-2xZn0.4+2xY2xFe2-2xO4 system

(x = 0.0, 0.02, 0.04, 0.06, 0.08, 0.1), * indicate FeYO3 peak. 137


Concentration (x) for NiY2xFe2-2xO4 (0 ≤ x ≤ 0.1). 138

Fig. 4.29 SEM micrograph of Ni0.6-2xZn0.4+2xY2xFe2-2xO4 ferrite

for x = 0.0, 0.8, 0.1. 141

Fig. 4.30 FTIR spectra of Ni0.6Zn0.4Y2xFe2-2xO4 ferrites (x = 0.0, 0.02, 0.04,

0.06, 0.08, 0.1). 143

Fig. 4.31 Variation of Log ρ Vs. Y-concentration for Ni0.6Zn0.4Y2xFe2-2xO4 ferrites

(x = 0.0, 0.02, 0.04, 0.06, 0.08, 0.1). 145

Fig. 4.32 Variation of Log ρ Vs. 1000/ T(K) for Ni0.6Zn0.4Y2xFe2-2xO4 ferrites

(x = 0.0, 0.02, 0.04, 0.06, 0.08, 0.1). 146

Fig. 4.33 Activation energy Vs. Y-concentration (x) for Ni0.6Zn0.4Y2xFe2-2xO4 ferrites

(x = 0.0, 0.02, 0.04, 0.06, 0.08, 0.1). 146

Fig. 4.34 Variation of dielectric constant Vs frequency for Ni0.6Zn0.4Y2xFe2-2xO4

ferrites (x = 0.0, 0.02, 0.04, 0.06, 0.08, 0.1). 147

Fig. 4.35 Plot of loss tangent (tan δ) Vs. frequency for Ni0.6Zn0.4Y2xFe2-2xO4 ferrites

(x = 0.0, 0.02, 0.04, 0.06, 0.08, 0.1). 149

Fig. 4.36 Hysteresis loops for Ni0.6Zn0.4Y2xFe2-2xO4 ferrites (x = 0.0, 0.02, 0.04, 0.06,

0.08, 0.1). 150

Fig. 4.37 Frequency variation of initial permeability for Ni0.6Zn0.4Y2xFe2-2xO4 ferrites

(x = 0.0, 0.02, 0.04, 0.06, 0.08, 0.1). 152

Fig. 4.38 Frequency variation of magnetic loss tangent for Ni0.6Zn0.4Y2xFe2-2xO4

ferrites (x = 0.0, 0.02, 0.04, 0.06, 0.08, 0.1). 153

Fig. 4.39 X-ray diffraction patterns for Co1-xZnxY0.15Fe1.85O4 ferrites (x = 0.0, 0.2, 0.4,

0.6, 0.8, 1.0). * indicates YFeO3 peaks. 155

Fig. 4.40 SEM micrograph of Co1-xZnxY0.15Fe1.85O4 ferrite (a)x = 0.0, (b) x = 0.4,

(c) x = 1.0. 159

Fig. 4.41 X-ray density (Dx), Physical density (Dp), percentage porosity Vs. Zn2+

concentration for Co1-xZnxY0.15Fe1.85O4 ferrites (x = 0.0, 0.2, 0.4, 0.6,

0.8, 1.0). 161

Fig. 4.42 Arrhenius plots for Co1-xZnxY0.15Fe1.85O4 ferrites (x = 0.0, 0.2, 0.4,

0.6, 0.8, 1.0). 165

Fig. 4.43 Variation of dielectric constant Vs frequency for Co1-xZnxY0.15Fe1.85O4

ferrites (x = 0.0, 0.2, 0.4, 0.6, 0.8, 1.0). 167

Fig. 4.44 Plot of loss tangent (tan δ) Vs frequency for Co1- xZnxY0.15Fe1.85O4

ferrites (x = 0.0, 0.2, 0.4, 0.6, 0.8, 1.0). 168

Fig. 4.45 X- ray diffraction patterns for CoFe2O4 + x Y2O3 (a) x = 0, (b) x = 1 wt %,

(c) x = 3 wt %, (d) x = 5 wt %). (*) indicates secondary phase. 171

Fig. 4.46 SEM micrograph of CoFe2O4 + x Y2O3 ferrite system (a) x = 0 wt%,

(b) x = 1 wt %, (c) x = 5 wt %). 175

Fig. 4.47 Variation of Physical density with Yttrium concentration for CoFe2O4 +

x Y2O3 ( x = 0 wt%, 1 wt %, x = 3 wt %, x = 5 wt %). 176

Fig. 4.48 Variation of room temperature resistivity Vs. Y-concentration for CoFe2O4

+ x Y2O3 ( x = 0 wt %, 1 wt %, 3 wt %, 5 wt %). 177

Fig. 4.49 Variation of Log ρ vs. 1000 / T(K) for CoFe2O4 + x Y2O3 ( x = 0 wt %,

1 wt %, 3 wt %, 5 wt %). 177

Fig.4.50 Activation energy Vs. Y-Concentration for CoFe2O4 + x Y2O3 ferrite system

(x = 0 wt%, 1 wt %, 3 wt %, 5 wt %). 178

Fig. 4.51 Variation of dielectric constant as a function of frequency for CoFe2O4 +

x Y2O3 ferrite system (x = 0 wt %, 1 wt %, 3 wt %, 5 wt %). 180

Fig.4.52 Plot of loss tangent (tan δ) vs frequency at room temperature for CoFe2O4 +

x Y2O3 (x = 0, 1 wt %, 3 wt %, 5 wt %). 181

List of Tables Table 4.1 Miller indices (hkl) and interplanar spacing (d) for NiY2xFe2-2xO4

(0.0 ≤ x ≤ 0.12). 94

Table 4.2 Phases, lattice constant (a), X-ray density (Dx), physical density (Dp),

percentage porosity (P %) and grain size of the NiY2xFe2-2xO4

(0.0 ≤ x ≤ 0.12). 94

Table 4.3 FTIR absorption bands for NiY2xFe2-2xO4 (x = 0.0, 0.02, 0.04, 0.06,

0.08, 0.1) ferrites. 99

Table 4.4. Variation of dielectric constant (ε ′ ) and resistivity ( ρ ) in the case

of Ni-Y ferrites. 106

Table 4.5 Compositional variation of saturation magnetization and coercivity for

NiY2xFe2-2xO4 ferrites (x = 0.0, 0.02, 0.04, 0.06, 0.08, 0.1). 107

Table 4.6 Compositional variation of linewidth (Oe) for NiY2xFe2-2xO4 ferrites

(x = 0.0, 0.02, 0.04, 0.06, 0.08, 0.1). 112

Table 4.7 Miller indices (hkl) and interplanar spacing (d) for MgY2xFe2-2xO4 (0.0 ≤ x

≤0.12) ferrites. 117

Table 4.8 Phases, lattice constant, X-ray density, bulk density, percentage porosity

and grain size of the MgY2xFe2-2xO4 (0.0 ≤ x ≤ 0.12) ferrites. 117

Table 4.9 FTIR absorption bands for MgY2xFe2-2xO4 ferrites. 121

Table 4.10 Variation of dielectric constant (ε ′ ) and resistivity ( ρ ) in the case of

MgY2xFe2- 2xO4 ferrites. 129

Table 4.11 Compositional variations of saturation magnetization and coercivity for

MgY2xFe2-2xO4 ferrites (x = 0.0, 0.02, 0.04, 0.06, 0.08, 0.1, 0.12). 131

Table 4.12 Compositional variations of linewidth and FMR Position for

MgY2xFe2-2xO4 ferrites (x = 0.0, 0.02, 0.04, 0.06, 0.08, 0.1). 133

Table 4.13 Miller indices (hkl) and interplanar spacing (dhkl) for

Ni0.6-2xZn0.4+2xY2xFe2- 2xO4 (0.0 ≤ x ≤ 0.1) ferrites. 139

Table 4.14 Lattice constant, phases X-ray density, physical density, percentage

porosity and grain size of the Ni0.6Zn0.4Y2xFe2-2xO4 (0.0 ≤ x ≤ 0.1). 140

Table 4.15 FTIR absorption bands for Ni0.6Zn0.4Y2xFe2-2xO4 ferrites (x = 0.0, 0.02,

0.04, 0.06, 0.08, 0.1). 142

Table 4.16 Compositional variation of saturation magnetization and coercivity

for Ni0.6Zn0.4Y2xFe2-2xO4 ferrites (x = 0.0, 0.02, 0.04, 0.06, 0.08, 0.1). 151

Table 4.17 Miller indices (hkl) and interplanar spacing (d) for Co1-xZnxY0.15Fe1.85O4

(0.0 ≤ x ≤ 0.1). 160

Table 4.18 Lattice constant, phases, X-ray density, Physical density, percentage

Porosity and particle size of the Co1-xZnxY0.15Fe1.85O4

(0.0 ≤ x ≤ 0.1). 160

Table 4.19 Resistivity (ρ), Activation energy (eV) and transition temperature for

Co1-xZnxY0.15Fe1.85O4 ferrites (x = 0.0, 0.2, 0.4, 0.6, 0.8, 1.0). 163


CoZnY-ferrites. 168

Table 4.21 Miller indices (hkl) and interplanar spacing (d) for CoFe2O4 + x Y2O3

(x = 0, 1 wt %, 3 wt %, 5 wt %). 170

Table 4.22 Phases, lattice constant, X-ray density, physical density and

grain size for CoFe2O4 + x Y2O3 ferrites. 172

Table 4.23Variation of dielectric constant (ε ′ ) and resistivity ( ρ ) in the case of

CoFe2O4 + x Y2O3 ferrites. 181

Chapter 1 INTRODUCTION

1.1 Ferrites Ferrites or ferromagnetic cubic spinels with chemical formula MFe2O4 (M is a divalent

transition metal ion) are ceramic materials [1] and are inexpensive, stable, black in appearance,

hard, fragile and easily manufactured. Due to non parallel arrangements of the strongly coupled

magnetic moments, ferrites [2] possessed spontaneous magnetization below Curie temperature. It

exhibits phenomena of hysterisis owing to self saturated domains. It has been considered as

highly important electronic material for more than seven decades. It has several advantages over

ferromagnetic alloys such as lower cost, low eddy current losses at very high frequencies, better

temperature and corrosion resistance.

Spinel ferrite plays an important role in a variety of technical fields, for example, ferrites

has been used in telecommunication, switched mode power supplies, ac and dc motors,

communication systems, digital memories, power distribution transformers, surface mount

devices, multilayer chip inductors, video and audio applications, radar and satellite

communications. Beyond 1950s, researchers made microwave devices such as switches,

modulators, circulators, limiters, waveguide and strip line isolators which depend upon ferrite

applications at microwave frequencies. New applications in the field of microwave engineering

and information technology are rapidly expanding. Research activities in these technical fields

has generated an increasing demand for quality ferrite materials for power supplies, transformer

cores, deflection yokes, recording and interface suppression [1]. Many researchers achieved

remarkable results both in the basic research as well as in the applied study of ferrites. On the

other hand, investigators have not been succeeded in making an ideal ferrite product which

fulfills all the requirement of electronic industry particularly in the field of microwave

engineering and telecommunications. Each ferrite product has its own advantages and

disadvantages. Scientists still have not been able to make hard and fast rules about a single

property. It is not easy to make novel ferrite materials. However, the search for quality material

is going on to prepare new materials which have optimum parameters of ferrites like high

saturation magnetization, high resistivity, high permeability, low eddy current losses, low FMR

linewidths and good homogenous material.

It is believed that the production of ferrite material will increase in future. A large

number of scientists and engineers are involved in exploring the world of ferrites both in the

basic research and in the applied study of ferrites. It is not an easy job to collect all the

informations about all types of ferrites. However, in the present study efforts have been made to

present experimental results of Y-substituted / doped Ni-, Mg-, Ni Zn-, Co- and Co Zn- ferrites

with improved structural and electrical properties.

1.2 Literature Survey Ferrites have been investigated since 1935, when Snoek started research on ferrites in

1935. Since then these materials are under investigations over the decades. In 1947, it was

reported that Mn-Zn and Ni-Zn have excellent magnetic properties [3]. Verway and Heilmann

[4] in Netherland studied the distribution of metal ions over the tetrahedral and octahedral sites.

Neel [5] presented the theory about the magnetic properties of ferrites. It was reported that the

magnetic properties depends upon cation distribution among tetrahedral sites (A) and octahedral

sites (B) which aligned their magnetic moments in opposite directions. Negative exchange

interaction exists among A-A, B-B, and A-B sites. The unpaired spins at A and B sites will be

magnetized antiparallel below a transition temperature when A-B exchange interaction is

dominant one. When A-A or B-B exchange interaction is dominant then Neel reported that the

material remain paramagnetic down to the lowest temperature.

The properties of ferrites have been improved through extensive research. In 1950,

ferrites attract worldwide attention because new applications such as microwave devices,

electronic media, computer and telephone industry were rapidly expanding. Quality ferrites

continued to be prepared having new properties. Among the noteworthy are barium and

strontium ferrite [6] and Mn-Mg ferrites [7] with a square type hysterisis loop for magnetic

memories, acicular fine γ-Fe2O3 particles, Yttrium Iron Garnet (YIG) [8]. In United States of

America, many researchers studied ferrites from 1950 through 1970. In 1952, Hogan [9] studied

microwave ferrite devices. Yafet et. al. [10] studied antiferromagnetic arrangements in ferrites.

They extended the Neel theory and showed that tetrahedral (A-site) and octahedral (B-site)

sublattices could be further subdivided into sub-lattices in such a way that the resultant magnetic

moments of the sub-lattices are again aligned in opposite directions to each other, leading to

ferrimagnetism.

Albers-Schoenberg [7] prepared Mn-Mg ferrites suitable for magnetic memories in 1954.

Uitert reported [11] dc resistivity in the Ni and Ni-Zn ferrite system prepared by solid-state

reaction method. It was pointed out the close relationship between conductivity and Fe2+ ions. It

was found that in NiZn ferrites having deficiency in Fe2+ ions have high resistivity. Beyond

1300 °C, all Ni and NiZn samples exhibit low resistivities due to formation of Fe2+ ions. The

loss of Zinc in NiZn materials at high temperature is expected to introduce Fe2+ ions. Addition

of small amount of excess iron in NiZn ferrite was reported to have low resistivity and high

conductivity.

The influence of minor addition of Mn or Co in high resistivity nickel ferrite prepared by

solid-state reaction method was reported by Uitert reported [12]. It was found that the

incorporation of small amount of Mn or Co oxides considerably decreased the conductivity and

hence increased the resistivity of Ni ferrite. The amount of Mn or Co required to obtain

maximum resistivity depends upon manufacturing process. The maxima was achieved for each

sintering temperature and moved to higher Mn concentration as sintering temperature increased.

The maxima obtained can be related to maximum activation energies. Kedem et. al. [13] studied

internal fields in nickel ferrite. It was found that NiFe2O4 itself have Yafet-Kittel type ordering

from their mossbauer measurements. Bobeck [14] worked on magnetic bubbles in 1967. Dillon

[15] developed magneto optical devices in 1969. Koops [16] reported that both dielectric

constant and resistivity of Ni0.4Zn0.6Fe2O4 fall with rising frequency. Rowen et. al. [17] reported

the dependence of dielectric loss factor at 9.4 GHz on dc resistance for nickel ferrite. It was

concluded that tan δ decreases sharply with the increase of specific resistance. Fairwether [18]

investigated the dependence of dielectric constant of Mg ferrite and Mg-Al ferrite. It was

reported that dielectric and conductivity increases with temperature at high and low frequency.

The Y-K angles in ZnxNi1-xFe2O4 (x = 0.0-0.75. step: 0.25) ferrites prepared by ceramic

method were reported by Murthy et. al. [19]. The magnetic structure was investigated by using

neutron diffraction technique. It was observed that all the samples except NiFe2O4 exhibit non-

collinear Y-K type of magnetic ordering. It increased with Zn contents and decreased with

increasing temperature. NiFe2O4 has Neel type ordering at all temperatures.

Linewidth (∆H) gives information about the losses of ferrites at microwave frequency.

The smaller the line width, the less lossy the specimen is due to lower dispersion and vice versa.

It is reported that anisotropy and porosity contribute to the line broadening for polycrystalline

ferrites [20]. Berkowitz et. al. [21] reported spin pinning at ferrite-organic interfaces. It was

observed from the mossbauer spectra that the ultrafine particles of nickel ferrite coated with

organic molecules made large angles with external applied field of 68.5 KOe, where as uncoated

ultrafine Ni-ferrite particles do not exhibit such behavior.

The dc resistivity of Ni0.62Zn0.40Fe1.98O4 + xV2O5 (x = 0.002-0.01; Step: 0.002) prepared

by solid-state reaction method were reported by Jain et. al. [22]. It was found that the smallest

value of electrical conductivity was observed at 0.4 mol % of V2O5 content. The results were

explained on the basis of solubility limit of V2O5 in the spinel lattice. Joshi et. al. [23] reported

magnetization, Curie temperature, and Y-K angles of Cu substituted Ni-Zn mixed ferrites. Neel

type of spin is observed in NiFe2O4, Zn0.2Ni0.8Fe2O4, Ni0.8Cu0.2Fe2O4 and Zn0.2Ni0.6Cu0.2Fe2O4.

All other samples including Ni0.6Zn0.4Fe2O4 show noncollinear spin arrangement due to presence

of YK-angles. The increase in YK angles is attributed to the decrease in A-B interaction which

leads to lowering of Curie temperature. The magnetization as well as Curie temperature of Ni-

Zn ferrites decreases with the addition of Cu which is attributed to smaller magnetic moment of

copper. Hiti et. al. [24] reported dc conductivity for ZnxMg0.8-xNi0.2Fe2O4 (x = 0, 0.2, 0.4, 0.8)

prepared by ceramic method. It decreases with increasing zinc contents and porosity while it

increases with increasing temperature. The activation energy for conduction increases while

both magnetic transition temperature and Curie temperature decreases with the increasing

concentrations of zinc ions. The dielectric constant was directly proportional to the root mean

square of the dc conductivity.

The effects of rare-earth oxides on physical properties of Ni0.7Zn0.3Fe1.98R0.02O4, where R

= Yb, Er, Dy, Tb, Gd, Sm, or Ce ferrite synthesized by ceramic method was reported by

Rezlescu et. al. [25]. It was concluded that the permeability increases with the size of ionic

radius. For Ce substitutions, initial permeability enhances continuously up to Curie temperature.

The formation of thin insulating grain boundaries of ortho ferrites enhances electrical resistivity

and thereby reducing the eddy current losses at higher frequencies. Rare-earth ions having large

size and stable valence of 3+ were found to be the best subsistent in order to improve electrical

and magnetic properties. Gadolinium was found to be the best substituent. Pigram et. al [26]

investigated the effect of binder additions on the green and sintered properties of Mn-Zn ferrite.

An overall comparison of the binders indicated that PVA, PEG and PAM all show excellent

binding properties. Samples prepared by using higher binder contents had marginally lower bulk

densities and lower initial permeabilities. The solid hydrocarbon residue left after the low

temperature burnout of PVA and PAM binder does not affect magnetic properties and

microstructures of sintered products. PEG was found to be the least favorable of the three

binders.

The milling affect on the properties of NiFe2O4 ferrite were studied by Jovalekic et. al.

[27]. Its fabrication started from a mixture of crystalline NiO and α -Fe2O3 powders. The

samples of Ni-ferrite was treated mechanochemically for various milling times show remarkably

different specific electrical resistivity which strongly depends on the milling time of the powder

and decreases by four orders of magnitude as the milling time increases from 0 to 50 h. The

spine1 phase was first observed initially after 10 h of milling and its formation was completed

after 35 h of milling. The NiFe2O4 ferrite has a nanocrystalline structure with a particle size of

about 6 nm. It was concluded that mechanochemical treatment can be used for changing the

properties of NiFe2O4 ferrite. Nam et. al. [28] reported the effect of Cu substitution on the

physical properties of NiZn ferrite prepared by solid-state reaction method. It was found that the

dc resistivity increased up to x ≤ 0.2 and then decreased with the substitution level x. The

samples sintered up to 1300 °C shows P-type conductivity mechanism. The bulk density of the

samples sintered at 1000 °C increased with Cu contents that might be attributed to atomic

mobility of copper atoms at low temperature and above 1000 °C, the sintering density was found

to be decreased due to intergranular porosity and exaggerated grain growth. It was concluded

that NiZnCu ferrite can be prepared at low temperature than NiZn ferrite. Copper substitution

improved its electrical and magnetic properties and is the best material than NiZn ferrite at RF

frequency region.

The dc resistivity on two series of Ni0.65Zn0.35Fe2-xScxO4 and Ni0.65-xZn0.35+xFe2-xScxO4

were reported by Rao et. al. [29]. The resistivity has been found to increase with the increase of

Sc/Zn content in both the series. In first series, large Sc3+ions replace smaller ions Fe3+ions. As a

result, bond length increases which limits the hopping probability. In second series, resistivity

slightly enhances because hopping mechanism between Ni3+ and Ni2+ reduces owing to

successive replacement of nickel by zinc ions. Bhise et. al. [30] reported the role of MnTi and

MnSn substitutions on the electrical properties of Ni-Zn ferrites. The conduction mechanism was

found to be due to hopping of polarons at high temperatures. Thermoelectric power was found to

be negative showing that the majority charge carriers were electrons and the materials is n type

semiconductors. In case of MnSn substituted samples, the binding energy was found to be in the

range 0.1 eV and in case of MnTi substituted samples, it was found to be in the range of 0.2 eV.

This behavior may be attributed to the formation of stable bonds of Ti4+ with Fe2+. Temperature

dependent thermo-emf of the samples shows that these samples are non-degenerate

semiconductors.

Dias et. al. [31] reported isothermal sintering behavior of Ni0.38Zn0.53Fe2.09O4 prepared by

hydrothermal process. The investigations showed high density ferrites with different

microstructures depends upon the sintering conditions. The densification process without any

remarkable grain growth was observed at 1100°C and at 1200°C. The remarkable grain growth

was observed beyond 1300°C. The influence of rare-earth ions on the electrical and mechanical

properties of Ni-Zn ferrites were reported by Rezlescu et. al. [32]. It was concluded that the

incorporation of small amount of rare-earth ions second phase and formed inhomogeneous solid

solution and thereby increasing the resistivity. Abdullah et. al. [33] reported the dielectric

behavior of Mg-Zn ferrites in the frequency range of 1MHz-10MHz. It was concluded that the

dielectric properties were due to interfacial polarization.

High insulating thin grain boundaries in doped MnZn ferrites for high frequency power

supplies were reported by Drofenik et. al. [34]. The eddy current loss at higher frequencies

depends upon grain size and grain boundary permittivity to thickness ratio. A low oxygen

concentration during sintering process causes smaller grain size and produces Fe2+ ions which

decrease the thickness of intrinsic grain boundary. As a result, samples with highest amount of

Fe2+ show the largest eddy current loss, irrespective of the smallest average grain size. Shabasy

et. al. [35] reported dc electrical properties of ZnxNi1-xFe2O4 (x = 0, 0.02, 0.04, 0.06, 0.08, 0.1)

ferrites prepared by ceramic method. The dc electrical resistivity, Curie temperature and

activation energies for electric conduction decreases with zinc contents. All the samples show

semiconductor behavior as resistivity decreases with rise in temperature. The activation energies

for electric conduction in the ferrimagnetic region was less than that in paramagnetic region. The

range of activation energies for ferromagnetic region was reported from 0.348 eV to 0.181 eV

and for paramagnetic region it was from 0.744 eV to 0.19 eV.

Shinde et. al. [36] reported electrical and dielectric properties of Co1+xSixFe2-2x O4

ferrites. The decrease in DC resistivity with increasing Si4+ contents was attributed to the

Verwey mechanism. These results reveal that Si substitution increases the values dielectric

constant with increasing temperature and tan decrease with rise in temperature. Zaag et. al. [37]

reported the effect of grain size on the intragranular domain walls and initial permeability in

MgMnZn-ferrite. Intragranular domain state was found to change from mono to two domain

state at D = 2.9 mμ2.0± . This change did not affect the initial permeability dependence on the

grain size.

The diffusion of tracer oxygen atoms in Ni ferrites were reported by Fetisov et. al. [38]. It

was concluded that the oxygen vacancies may take part in the local rearrangement of the

structure that determines the thermomagnetic characteristics of ferrites.

N. Rezlescu [39] studied the effects of rare-earth oxides on the physical properties of

Li0.3Zn0.4Fe1.96 R0.04O4 where R = Yb, Er, Dy, Tb, Gd, Sm. It was reported that only pure Li-Zn

ferrite is monophasic. R-containing samples are biphasic. Some of the atoms of rare earth do not

become part of the lattice and may segregate at the grain boundaries due to its large ionic radius

that limit the grain growth, lower the porosity and improve the temperature dependence of initial

permeability. Resistivity has been reported to increase by the addition of Rare earth. Said [40]

reported structural and electrical properties of NiGdxFe2-xO4 ferrites. The reduction of Fe3+ ions

in the B-sites with increasing Gd3+ contents results in the increase of lattice parameters which

was explained on the basis of ionic radii. X-ray density and bulk density increases while porosity

decreases with Gd3+ contents. The increase of bulk density with Gd contents was correlated with

atomic weight of Gd (157.25 amu) and Fe (55.847 amu).

The temperature dependent ferromagnetic resonance study of Ni-Zr-substituted non-

stoichiometric barium ferrite sample were reported by Misra et .al. [41]. It was found that

anisotropy field reduces with the increase of Ni-Zr substitution. Resonance field values increases

with rise in temperature owing to faster reduction in demagnetization field as compare to

anisotropy field. The linewidths were large and decrease with temperature which might be

attributed to random orientations of the crystallites and distribution of demagnetizing fields

within the samples. Byeon et. al. [42] reported that the systematic increase in linewidth observed

in Mn0.47Zn0.47Fe2.06O4 polycrystalline samples was attributed to the increase in Fe2+

concentration with decreasing oxygen partial pressure. Gazeau et. al. [43] reported magnetic

resonance of ferrite nanoparticles of maghemite (γ-Fe2O3). The anisotropy of the system was

found to be uniaxial and positive. At low temperature, an extra line broadening is caused by

surface disorder of small particles. The degree of spin frustration rises with decrease in particle

size. The distribution of canting angles of frustrated spin at the surface increases the linewidth.

Flores et. al. [44] reported two-magnon processes and ferromagnetic linewidth calculation in

manganese ferrite. It was concluded that, the two magnon theory developed for ferromagnetic

relaxation is not valid for ferrites. An experimental set up should be devised to asses the porosity

contribution to the linewidth. The anisotropy contribution in polycrystalline ferrites is neglected

while porosity and eddy-current contribution to the line width also appear.

The electrical properties of Ni1-xCuxFe2O4 prepared by standard ceramic method were

reported by Islam et. al. reported [45]. The dc resistivity reduces with the increase of Cu

concentration that may be owing to migration of Fe2+ ions from B-site to A- site. The activation

energies decrease from 0.31 to 0.067 eV with Cu contents which may be attributed to the

creation of oxygen vacancies. Mohan et. al. [46] studied dielectric properties of NixZn1-xFe2O4

(x = 0.2-1.0) in the frequency range 100 KHz-1 MHz. The dielectric constant was found to be

approximately inversely proportional to the square root of the resistivity. It was observed that

the composition Ni0.6Zn0.4Fe2O4 exhibits the lowest real part of dielectric constant (ε ′ ), complex

dielectric constant (ε ′′ ), dielectric loss tangent ( δtan ) and the lowest electrical conductivity

due to the lowest Fe2+ ions concentration. The dielectric constant decreases with rise in

frequency. The dispersion of dielectric constant was maximum for the sample with x = 0.8

which was explained on the basis of available Fe2+ ions on octahedral sites.

Mazhar et. al. [47] reported cation distribution of Mn1-xCuxFe2O4, with x = 0, 0.25, 0.50,

0.75, 1.0 prepared by ceramic method. R-factor method was used for the determination of cation

distribution. It was concluded that the distribution of cations on A and B sites has shown that all

the samples belong to the family of partially inverse spinel ferrites. The lattice constant decreases

with Cu contents up to x = 0.25 and beyond this the lattice constant increases with Cu contents.

This irregular behavior of lattice constant was attributed to occupation of both Cu and Mn for the

octahedral sites. Ravinder et. al. [48] reported the dielectric behavior of MgxZn1-xFe2O4 (x = 0.0-

1.0, step = 0.02) in the frequency range 1 KHz to 100 KHz at room temperature. Dielectric

constant, dielectric loss tangent and complex dielectric constant decreases with the decrease of

Fe2+ ions till x = 0.4. At x > 0.4, these parameters shows an increasing trend. Zn-ferrite exhibit

the highest dielectric constant because it contains maximum number of ferrous ions which

involve in the phenomena of exchange between Fe2+ and Fe3+ giving rise to maximum

polarization. The value of the dielectric constant reduces with rise in frequency because the

electron exchange between the Fe2+ and Fe3+ ions can not follow the alternating field beyond a

certain frequency of the externally applied field.

Dias et. al. [49] studied dielectric properties of Ni0.38Zn0.53Fe2.09O4. It was concluded that the

dielectric response shows greater dependence on the grain size as compare to the density of the

samples. It was observed from EDS analysis that zinc loss did not occur significantly. The

permittivity values were reported to be of the order of 105 in the frequency range 102-104 Hz for

all compositions.

The localized canting in Zn substituted Ni ferrites were reported by Bercoff et. al. [50].

The magnetic properties of all the samples were explained by three sublattice model (

). It was assumed that B-sites may split into two sublatticesBandBA ′,, BandB ′ . Only B′

is occupied by Fe3+ and Ni2+ and is affected by canting. This model give a good description of

canting under the assumption that JAA = 0. Singh et.al [51] reported electrical and dielectric

properties of Mg-Mn-Al ferrites for high frequency applications. The decreasing behavior of

lattice constant of lattice constant has been explained on the basis of difference in ionic radii.

The addition of Al3+ ions in place of Fe3+ions reduce the degree of conduction by blocking

Verwey’s mechanism resulting in an increase of resistivity. The increase in dc resistivity has

been observed at the expense of deterioration in the values of initial permeability, saturation

magnetization and Curie temperature. The samples were reported to have high resistivity, low

dielectric loss and low values of saturation magnetization. It was proposed that these samples

may use in microwave devices operating in L, S and C bands.

The structural disorder and magnetic evolution in magnesium ferrite were reported by

Sepelak et. al. [52]. The concentration of Fe3+ ions on tetrahedral sites reduced due to mechanical

treatment. It was concluded that the degree of inversion decreases with milling time while spin

canting increases with increasing milling time which may be attributed to the mechanically

induced noncollinear spin structure of near-surface atoms. Hemeda et. al [53] reported spectral

and transport phenomena in NiGdxFe2-xO4. It was concluded that the electrical resistivity

enhances while line width ∆H reduces with Gd3+ contents. The decreasing trend of ∆ H shows

that the material is less lossy at higher frequency which can which can be used as the core for

transformers in microwave region. The FTIR spectra Gd3+ ions occupy B sites. The dielectric

behavior of Mn0.58Zn0.37Fe2.05-xErxO4 (x = 0.2-1.0, step = 0.2) as a function of frequency was

investigated in the range 1-13 MHz reported in the literature [54]. It was concluded that the

maximum value of dielectric constant was found to be 446 for x = 1.0 at 1 MHz. This high value

of dielectric constant may be attributed to the highest concentration of Fe2+ ions which involve in

the phenomena of exchange between Fe2+ and Fe3+ giving rise to maximum polarization. The

dielectric constant, dielectric loss tangent, and complex permittivity depend upon the

concentration of Fe2+ ions. The value of dielectric constant falls continuously with rise in

frequency which is a normal dielectric behavior. This reduction occurs because beyond a certain

frequency of the applied electric field where the exchange between ferrous and ferric ions can

not follow the alternating field. Maximum loss tangent was observed at 5 MHz for x = 0.2, 0.4,

0.6 and beyond x = 0.6, the maximum loss tangent was observed at 7 MHz. It was concluded that

the dielectric constant was found to be approximately inversely proportional to the square root of

resistivity.

Rane et. al. [55] reported dielectric behaviour of MgFe2O4 in the frequency range from 10

Hz – 1 MHz synthesized by chemically beneficiated iron ore rejects. The values of dielectric

constant lie between 12-15 at 10 Hz and decreases continuously with rise in frequency which is a

normal dielectric behaviour of ferrites. Loss tangent shows decreasing trend with frequency up to

1 KHz and, thereafter, it attains almost constant value. Menzel et.al. [56] studied

mechanochemical reduction of nickel ferrite. The mechanical treatment of NiFe2O4 results in the

formation of nano scale ferrite particles. The fraction of the reduced phases increases with the

increase of milling time. It was concluded that the nanocrystalline materials of the

mechanochemical reduction are metastable with respect to structural and compositional changes

at high temperatures. The range of the thermal stability extends up to about 600 K in a nitrogen

atmosphere. Beyond 600 K, the nanoscale products gradually begin to crystallise.

The ferromagnetic resonance of zinc ferrite and cobalt-doped zinc ferrite nanoparticles

were reported by Hochepied et. al. [57]. FMR spectra of both samples are characterized by an

invariant point at a given field . The equation of the form 0H αRHH −03..2)( PPHΔ was

suggested that interrelates the linewidth PPHΔ and resonance field shift ( being the

resonance field). Ravinder et. al. [58] reported high frequency (1-15 MHz) behavior of

Ni0.7Zn0.3GdxFe2-xO4 (x = 0.0-1.0, step: 0.2). It was found that the composition

Ni0.7Zn0.3Gd1.0Fe1.0O4 has the highest value of dielectric constant (21.13) which may be

attributed to highest number of ferrous ions whose exchange with Fe3+ give rise to maximum

dielectric polarization. The composition Ni0.7Zn0.3Fe2O4 has the lowest dielectric constant due to

minimum ferrous ion concentration. The composition Ni0.7Zn0.3Gd0.6Fe1.4O4 exhibits the lowest

value of the dielectric loss tangent (

RHH −0 RH

δtan = 0.061). It was found that the dielectric constant is

inversely proportional to the square root of resistivity. The materials with low resistivity exhibit

high dielectric losses and vice versa. Wei et. al. [59] reported cation distribution and infrared

properties of NixMn1-xFe2O4 ferrites (x = 0, 0.1, 0.25, 0.5, 0.75, 1) prepared by standard double

sintering ceramic method. The cation distribution using XRD data has shown that the present

samples belong to the family of mixed or partially inverse spinel ferrites. The FTIR spectra show

the band 1ν shift towards higher frequency while the band 2ν remains constant with increasing

nickel ions which can be attributed to the cation distribution.

Sindhu et. al. [60] studied ac conductivity of nickel zinc ferrites. It was reported that ac

electrical conductivity increases with rise in frequency initially and beyond 5 MHz, it exhibits

small dip which was explained on the basis of Maxwell-Wagner two layer model. The

compositional dependence shows an increasing trend of ac conductivity with zinc content up to x

= 0.6, and thereafter it reduces. This behavior was explained on the basis of porosity of the

samples. Ponpandian and Narayanasamy [61] reported the effect of structural changes and grain

size ranging from 7 to 115 nm on electrical properties of zinc ferrite synthesized by mechanical

milling. It was concluded that the conduction mechanism was found to be due to the hopping of

charge carriers. The conductivity and dielectric loss factor decreases while activation energy

enhances with the decrease of grain size. The samples having grain size of 74 and 115 nm shows

that the conduction mechanism was due to electrons while the samples having grain size of 7 and

13 nm shows that the conduction mechanism was due to both electrons and holes. The p-type

charge carriers were introduced by oxygen vacancies created by high energy ball milling. It was

found that the hole hopping has higher activation energy than the electron hopping.

The influence of R2O3 (R = La, Gd) on dielectric properties of Ni-Zn ferrite in the

frequency range of 1 – 40 MHz were reported by Sun et. al. [62]. It was concluded that the

values of dielectric constant increases with the increasing concentration of R2O3 where as δtan

decreases with increasing R2O3. The R2O3 substitutions decreases bulk density and increases

lattice parameters. Kumar et. al. [63] reported the electrical conductivity of Ni0.7Zn0.3Fe2-xGdxO4

(x = 0.0,0.2) . It was concluded that these ferrites belong to semiconductor because Seebeck

coefficient was negative. Conductivity was found to increases with the increase of Gd

concentration from 5.62 × 10-8 to 4.17 × 10-7 Ω-1 cm-1. El-Sayed [64] studied the influence of

chromium substitution on the physical properties of Ni0.6Zn0.4CrtFe2-tO4 synthesized by ceramic

method. Lattice parameter, bulk density, and X-ray density increases while porosity and grain

size decreases with chromium concentration. The replacement of iron with chromium at B-sites

resulted into decrease in cation vacancies which may lead to decrease of both porosity and grain

size.

The characterization of Ni1-xCuxFe2O4 prepared by standard ceramic technique were

reported by Hoque et. al. [65]. SEM micrographs show second phase for x > 0.2 which lead to

poor sintered product and exaggerated grain growth. Resistivity decreases with the increase of

Cu contents. Initial magnetic permeability and saturation magnetization is maximum for the

composition x = 0.2, which can be attributed to the maximum sintered density. For 0 ≤ x ≤ 0.5,

the increasing trend in initial permeability is accompanied by a shift in the dispersion toward low

frequencies. Nanocrystalline magnetite (Fe3O4) and nickel ferrites (NiFe2O4) have been

synthesized [66] from metallic precursors by radio frequency plasma torch. An average particle

size of 20-30 nm was achieved. The coercivity and Neel temperature of Ni ferrite sample was

found to be 58 Oe and 590 °C respectively.

Sattar et. al. [67] reported the dielectric properties of Cu0.5Zn0.5Fe2-xRx O4 (R = La, Nd,

Sm, Gd; x = 0, 0.1) in the frequency range 50-105 Hz and temperature up to 800 K. The real part

of dielectric constant (ε ′ ) and dielectric loss tangent ( δtan ) show decreasing trend with

increasing frequency while ac conductivity (σac) is generally increased. ε ′ , δtan , and σac are

increased with the temperature. The decrease ofε ′with increasing frequency is due to the fact

that the frequency of electron exchange between ferrous and ferric ions can not follow the

applied electric field frequency. The decrease of ε ′ , δtan and the increase of σac as a function

of frequency was explained by Koop’s model.

The effect of Ti ions substitution on the conductivity and dielectric properties of

Co0.4Zn0.6+XTiXFe2-2XO4 ferrites prepared by ceramic method were reported by Meaz et. al [68].

It was found that the electrical conductivity decreases as Ti ions substitution increases. The

results of electrical conductivity were explained on the basis of polaron conduction mechanism.

Tan is also found to be compositionally dependent where its value decreases with increasing Ti

and Zn ions content. Ahmed et. al. [69] investigated influence of yttrium ions on the magnetic

properties of Ni–Zn ferrites prepared in polycrystalline form using the standard ceramic

technique. The magnetic constants have been determined from DC magnetic susceptibility

measurements. The transition from ferrimagnetic to the paramagnetic state is accompanied by an

increase in the thermo-emf. It was observed that the magnetic moment and the Curie temperature

decreased with Zn2+ contents. This means that some cation on the B sites migrate to the A site

which control the physical properties of the system. The magnetization increases with Yttrium

content (y) up to the level y = 0.04 and beyond this the magnetization decreases with increasing

magnetic field intensity. The expected replacement of the nonmagnetic Y3+ in place of Fe3+ ions

on the B site was responsible for such abnormal behavior. This is because the migration of some

Fe3+ ions to the A site enhances the AB interaction. This replacement may influence the hopping

process (Fe2+ Fe+3 + e) that takes place on octahedral sites. The magnetic susceptibility

decreases after y = 0.04 which may be attributed to the microstrain which was produced from the

replacement of Fe3+ ions with larger ionic radius of Y3+ ions. It was concluded that the higher

concentration of Y3+ in the substituted samples cannot enter the spinel lattice but produce lattice

strains that impede the domain wall displacement which may reduce the permeability.

⇔

Modi et. al. [70] studied structural properties of magnesium and aluminium co-

substituted lithium ferrite prepared by double-sintering ceramic method. The simultaneous

substitution for Li1 + and Fe3 + by Mg2 + and Al3 + in Li0.5Fe2.5O4 has shown the B-site preference

of cations involved. The bond length was calculated theoretically. Therefore, it is important to

consider the influence of structural parameters on transport properties while synthesizing the

ferrite materials for particular applications.

The dielectric response of Li0.5-0.5xMgxFe2.5-0.5xO4 (x = 0.1-0.9, step: 0.2) in the frequency

range 1 to 13 MHz were reported by Ravinder et. al. [71]. It was found that the real part of

dielectric constant (ε ′ ) and dielectric loss tangent ( δtan ) reduces with reduction of Fe2+

concentration whose exchange with ferric ions give rise to maximum polarization. The

composition Li0.45Mg0.1Fe2.45O4 exhibits the highest value of ε ′ , ε ′′ and δtan because it has

maximum divalent iron ion concentration. Therefore, it was concluded that the number of ferrous

ions on the octahedral sites that play dominant role in the process of conduction as well as

polarization. The dielectric constant of Li0.45M g0.1Fe2.45O4 decreases from 624 at 1 MHz to 150

at 13 MHz. This reduction occurs because the electronic exchange between charge carriers

cannot follow the alternating field above certain frequency of the externally applied electric field.

The frequency dependence of δtan is found to be abnormal because some peaks were seen at

certain frequency. A maximum loss tangent can be observed when hopping rate is nearly equal to

that of the externally applied electric field.

Kumar et. al. [72] studied high frequency (1-13 MHz) behaviour of Ni0.7Zn0.3ErxFe2-xO4

(x = 0.2-1.0, step: 0.2). The real part of dielectric constant (ε ′ ),and dielectric loss tangent ( δtan

) shows increasing trend with the increase of Er contents. The composition Ni0.7Zn0.3Er1.0Fe1.0O4

has a maximum value of dielectric constant of 882 at 1 MHz because it contains maximum

number of Fe2+ ions. ε ′ decreases continuously with frequency. A maximum of δtan was

observed at 7 MHz because hopping frequency was nearly equal to the applied electric field at

this stage. ε ′ was approximately inversely proportional to the square root of resistivity. It was

found that the materials with low resistivity exhibit high dielectric losses and vice versa.

The structural and FTIR studies of Ni1+xPbxFe2-xO4 (x = 0, 0.1, 0.2, 0.3, 0.4, 0.5) prepared

by ceramic technique were reported by Labde et.al. [73]. The lattice constant increases with Pb4+

contents which can be explained on the basis of difference in ionic size. The tetrahedral force

constant Kt increases with bond length RA and the octahedral force constant Ko increase with RB.

The IR bands shift towards the lower frequency side with the addition of Pb4+ ions for x = 0.0-

0.2 suggesting the increase in lattice parameter. Ravinder et. al. [74] reported the electric

properties of cadmium-substituted nickel ferrites having compositional formula Ni1-xCdxFe2O4 (x

= 0.2-0.8, step = 0.2). It was found that these ferrites are n-type semiconductor material because

their Seebeck coefficient is negative. Thus, the conduction mechanism was due to hopping of

electrons. The conductivity was reported to be varying from 3.96 × 10-8 to 1.00 × 10-4 Ω-1 cm-1

and decreases continuously with cadmium contents. Islam et. al. [75] reported electrical

properties of Ni1-xZnxFe2O4 ferrites prepared by co-precipitation method. It was concluded from

dc resistivity measurements that the conduction mechanism in these ferrites was due to hopping

of small polarons. It was found that all the compositions are degenerate type semi-conductors on

the basis of thermopower measurements.

Azadmanjiri et. al. [76] reported the effect of sintering condition on the microstructure

and phase development of nickel ferrite powder prepared by sol-gel autocombustion method.

The samples with particle size of less than 100 nm were achieved by this preparation method. It

was observed that different calcinations and different iron to nickel ratio influence the particle

size of the compositions. The single phase NiFe2O4 was synthesized at 1000 °C. Ahmed et. al.

[77] reported transport and magnetic properties of Co-Zn-La ferrite. It was concluded that the

reduction in resistivity is due to thermally activated mobility. The electrical resistivity

measurements showed that there is more than one conduction mechanism taking part in

conductivity. The values of the activation energy show the semi-conducting behavior of the

investigated samples. The magnetic susceptibility decreases with rise in temperature. It was

observed that the values of effective magnetic moment decreases with Zn2+ contents.

Berchmans et. al. [78] reported the dielectric properties of Ni1-xMgxFe2O4 as a function of

frequency in the range 50 Hz to 10 KHz at room temperature. The dielectric constant decreases

with rise in frequency which was explained on the basis of Maxwell-Wagner model. The lower

dielectric constant was observed for the Ni0.1Mg0.9Fe2O4 sample due to lowest concentration of

Fe2+ ions in the octahedral sites. The relaxation peaks were observed at frequency of 2 KHz in

the dielectric loss properties which may be owing to both p and n type charge carriers (Rezlescu

model).

The effect of rare earth on structural and magnetic properties of Zn0.5Ni0.5R0.02Fe1.98O4,

with R = Y, Gd, Eu fabricated by combustion method were reported by Jacobo et. al. [79]. Curie

temperature was found to decrease while coercivity increases with rare earth substitution.

Chhaya et. al. [80] reported magnetic and electrical properties of Mg1-xCaxFe2O4 (x = 0.0-0.35).

It was concluded that maximum 23 % of Ca2+ can be substituted for Mg2+. The cation

distribution confirms the substitutional limit and the percentage formation of fcc phase. The

variation of magneton number as a function of Ca-content follow the Neel’s collinear model.

Rezlescu et. al. [81] reported effects of some ionic substitutions on the properties of

Mg0.5Cu0.5Fe2–xMe3x/nO4, where Me = Y, La, Ga, Ti and Nb, x = 0 and 0.2). The magnetic and

electrical properties of MgCu ferrite change with the substituent species. La ions play useful role

in increasing the density. The saturation magnetization and electrical resistivity was increased

while density was found to decrease with Ga substitution. The results are explained in terms of

microstructural changes induced by the substitutions. Conclusions are made concerning the

optimization of response time to humidity change for the development of ceramic humidity

sensors which are chemically and thermally stable than polymeric sensors. A dense MgCu ferrite

can be fabricated at modest temperatures if the type of cation substituent is carefully selected. Nb

ions enhance the density of the MgCu ferrite by about 50% on heating at a relatively low

temperature of 1000 °C. Haijum et. al. [82] reported the ultrafine nanocrystalline MgAl2O4

synthesized by citrate sol-gel process. It was found that the initial crystallization temperature was

600 °C and the lattice constant at this temperature was about 8.08 Å. As the calcining

temperature increases to 1350°C, the lattice constant increases to 8.17 Å. There were two kinds

of particles: plate like particles and spherical like particles having grain size 30-50 nm and 200

nm respectively.

The magnetic properties of Mg0.5Cu0.5YxFe2−xO4 ferrites prepared by the solid state

reaction method were reported by Mansour [83]. A single spinel phase was confirmed by XRD

data in the range 0 ≤ x ≤ 0.08. The lattice constant was found to increase with substitution level x

except at x = 0.08 due to distortion in the lattice. The saturation magnetization was found to

decrease with Y3+ content, which may be attributed to the replacement of the magnetic Fe3+ ions

by the nonmagnetic Y3+ ions at B sites. Dogra et. al [84] investigated structural and magnetic

studies of NiMn0.05TixMgxFe1.95−2xO4 ferrites. The decrease in the lattice constant and the

increase in the bond length with Mg and Ti concentration are explained on the basis of size

difference of the substituents. The magnetic moment decreases due to the occupation of

substituted non-magnetic ions at B site which in turn decreases the saturation magnetization,

Curie temperature and initial permeability.

Mangalaraja et. al. [85] reported dielectric properties of Ni0.6Zn0.4Fe2O4 synthesized by

microwave-assisted flash combustion technique. It was found that the dielectric constant and

dielectric loss factor are slightly higher than ferrites synthesized by flash combustion technique

in normal heating. High density was obtained in case of microwave heating. Kaiser et. al. [86]

reported low frequency conductivity study of Mg0.5Cu0.5GaxFe2-xO4. Electrical properties were

investigated from room temperature up to in the frequency range 100 Hz-10 KHz. The transition

temperature Tc was found to decrease linearly with increasing Ga concentration. The activation

energy for electrical conduction in the ferrimagnetic region has little variation with frequency

due to substitution of Ga in these compounds. The activation energy in the paramagnetic region

shows undefined behavior showing the nature of this disordered state. For low concentration of

Gallium (x= 0.1, 0.2), small polaron mechanism was predominant. Widatallah et. al. [87]

reported the cation distribution of aluminium substituted Li-ferrites. The cation distribution was

investigated by using Rietveld refinement of the X-ray powder diffraction data. It was found that

the Al3+ ions replaced both Fe3+ and Li+ ions on octahedral sites and the substituted Li+ ions

replaced Fe3+ ions at tetrahedral sites.

The magnetic properties of Mn0.5Ni0.1Zn0.4AlxFe2-xO4 (x = 0-0.15, step: 0.025)

synthesized by conventional ceramic method were reported by Sattar et. al. [88]. The IR analysis

confirms the distribution of Al-ions on both A and B sites. The saturation magnetization, dc

resistivity, initial permeability and Curie temperature are increased for all substituted samples.

These results were promising for high frequency applications. Arulmurugan et. al. [89] studied

magnetic properties of Co1-xZnxFe2O4 with x ranging from 0.1 to 0.5. The magnetic parameters

such as saturation magnetization, coercivity, Curie temperature and particle size were found to

decrease with the increase in zinc substitution. It was concluded that the partial substitution of

zinc with cobalt for x > 0.5 can bring down the Curie temperature close to the room temperature.

The low Curie temperature can be used for the preparation of temperature-sensitive ferrofluid.

Rao et. al. [90] studied the influence of V2O5 additions on the resistivity and dielectric properties

of Ni-Zn ferrites. It was found that the dielectric loss tangent increases with the increasing

concentration of vanadium. The dielectric constant and the dielectric loss tangent are found to

exhibit normal dielectric behavior up to lower megahertz region while showing peaks around 4

MHz. The dielectric dispersion was explained on the basis of Koop’s two layer model and

Maxwell-Wagner polarization theory.

Arulmurugan et. al. [91] reported the influence of zinc substitution on Co-Zn

nanoparticles prepared by chemical co-precipitation method. The saturation magnetization, Curie

temperature and particle size estimated showed a decreasing trend with the increase in zinc

concentration. It was concluded that the Co-Zn ferrite particles can be used to prepare ferrofluids

with higher magnetization. Xinhua et. al. [92] fabricated Fe-deficient NiZn ferrite powders

synthesized by sol-gel processing. No secondary phase was observed when annealing

temperature was less than 700 °C. Beyond this, it was found to be biphasic. It was observed that

the lattice parameters annealed at lower temperature are larger than those annealed at higher

temperature and vary slowly with increasing Fe deficiency due to lattice expansion in the nano

particles.

The ac conductivity and dielectric properties for Mg1-xZnxFe2O4 (x = 0.0-0.6) was

reported by S. F. Mansour [93]. It was observed that the ac conductivity does not depend upon

the frequency below 10 KHz. Beyond this, conductivity increases strongly with rise in

frequency. The dispersion in ac conductivity has been explained by Koop’s theorem which

assumed that ferrite sample acts as a multilayer capacitor. The conductivity increases because the

effect of multilayer condenser rises with frequency. The dielectric constant and dielectric loss

decreases with increasing frequency. This behavior may be explained by assuming the

mechanism of the polarization process in ferrite is similar to that of the electronic polarization.

The relaxation time was estimated about 2 × 10-6 seconds for all the samples. Rao et. al. [94]

reported the dielectric properties of Ni0.65Zn0.35+xFe1.99-2xIn0.01TixO4 (x = 0.0-0.125, step = 0.025).

It was concluded that the dc resistivity increased with titanium concentration. It was found that

the dielectric constant of these ferrites has been found to be of the order of 103 and the samples

containing titanium exhibited lower dielectric losses compared to the basic composition because

titanium ions on B-sites impede the hopping process. Frequency responses of dielectric constant

and dielectric loss tangent reveal that these materials exhibit normal behavior up to 2 MHz.

Rao et. al. [95] reported distribution of In3+ ions in indium-substituted Ni-Zn-Ti ferrites.

The results indicate improvements in resistivity while retaining the magnetization at higher

levels, thus, making them useful for power applications at higher frequencies. It is concluded that

the indium ions occupy tetrahedral sites for substitutional level x = 0.1, and beyond this it begin

to occupy octahedral sites until they dissolve in the matrix.

The dielectric properties of mixed Li-Ni-Cd ferrites as a function of frequency in the

range 100 Hz- 1 MHz were reported by Kharabe et. al. [96]. It was found that the dielectric

constant decreases with rise in frequency which was explained on the basis of Maxwell-Wagner

type of interfacial polarization in accordance with Koop’s phenomenological theory. Dielectric

constant was roughly inversely proportional to the square root of resistivity. Souilah et. al. [97]

prepared NiZnCu ferrite particle by sol-gel technique. Short processing time of gel preparation,

homogeneity and well defined microstructure with small grain size were achieved in this study.

Rao et. al. [98] reported the ferromagnetic resonance of ball milled ferrite nanoparticles

of the system Ni0.65Zn0.375InxTi0.025Fe1.95-xO4 ferrites. All the samples exhibit single asymmetric

resonance peaks. The line broadening is attributed to the reduction of the quantity of Fe3+ ions.

The observed linewidths show large values ranges from 1400-1800 Oe. Bhosale et. al. [99]

reported electrical properties of NiAlxFe2-xO4 prepared by standard ceramic technique. The

resistivity was found to increase with the increase in Al content. Thermoelectric power shows

that both n-type and p-type of charge carriers are present. Ataa et. al. [100] reported initial

magnetic permeability and ac electrical conductivity of Li0.5-0.5xCoxFe2.4-0.5xR0.1O4 (where x =

0.0, 0.5 and R = Y, Yb, Eu, Ho and Gd) prepared by standard ceramic techniques. The ac

electrical conductivity measurements exhibit dispersion with frequency at low temperatures. The

hopping mechanism is the predominant one in these samples. The behavior of the initial

magnetic permeability with temperature shows multidomain structure for the samples with x = 0

and single domain structure for all other compositios.

The structural and IR analysis of Polycrystalline soft ferrite, Cu1+xSixFe2-2xO4 (x = 0.0,

0.05, 0.1, 0.15, 0.2 and 0.3) prepared by standard ceramic technique were reported by Zaki et. al.

[101]. The X-ray analysis confirmed the single phase formation of the samples starting by x =

0.05-0.1 and beyond this the secondary phase was observed. The lattice parameter was found to

decrease with increasing both Cu and Si ions which is may be due to ionic size difference of

metal ions involved. The FTIR spectra of Cu–Si ferrite system have been analyzed in the

frequency range 200–1200 cm-1. It showed two bands 1ν and 2ν which are assigned to

tetrahedral and octahedral sites, respectively. The position of the highest frequency band lies

around 575 cm-1 while the lower frequency band lies around 400 cm-1. The position of the extra

peak is around 800 cm-1 in the IR absorption spectrum corresponding to SiO2.

Masti et. al. [102] studied magnetization (Ms) of CdxMg1-xFe2-yCryO4 (x = 0-1.0, step:

0.2; y = 0, 0.05, 0.1). Results of Ms are explained by Neel’s two-sublattice model for x ≤ 0.4 and

thereafter YK-model is applicable. The Ms and magnetic moment decreases with Cr3+ contents

which was attributed to the dilution of B-B site interaction. Gul et. al. [103] reported physical

and magnetic properties of CoFe2-2xZrxZnxO4 ferrites prepared at low temperature by chemical

co-precipitation technique. The particle size estimated showed an increasing trend with Zn2+ and

Zr4+ contents and lies in the range from 12–23 nm. The DC electrical resistivity and Curie

temperature were found to decrease with Zn2+ and Zr4+ concentration. The decrease of Tc with

increasing Zn2+ and Zr4+ concentration may be explained on the basis of A–B exchange

interaction strength due to the change of the Fe3+ distribution between two sub-lattice sites.

Activation energy lies in the range from 0.554 to 0.440 eV. It has been observed that drift

mobility increases with temperature due to decrease in DC electrical resisitivity. The dielectric

constant and loss factor decrease with increasing frequency for all the samples. Gama et. al.

[104] studied magnetic and structural properties of nanosize Ni-Zn-Cr ferrite particles. A

secondary phase of hematite was observed in all the samples without chromium. The sample

with 0.1 mol of chromium exhibit only Ni-Zn cubic phase. The grain size slightly reduced with

the increase of chromium concentration. The magnetic saturation was reduced by 34 % and

coercivity by 77 % with the inclusion of chromium. This material has a high frequency

transformer application.

Ajmal et. al. [105] investigated the influence of zinc substitution on structural and

electrical properties of Ni1−xZnxFe2O4 ferrites. The substitution of Zn in the Ni1−xZnxFe2O4

ferrites produced remarkable changes in its physical properties. Particle size reached the

maximum limit of 6.16 nm. Unit cell parameters ‘a’ increased from 8.337 to 8.490 Å. Porosity

decreased up to 10.2 %. The resistivity varied from 1.629×106 to 3.0×103 Ω. cm at 360 K and

activation energy decreased from 0.388 to 0.217 eV. The value of dielectric constant approaches

to 31580 with the increase in Zn concentration at 100 kHz. All the samples follow the Maxwell–

Wagner’s interfacial polarization. Loss factor decreases from 9.057 to 0.456 with the variation

in frequency from 80 Hz to 1 MHz. Hossain [106] reported the structural, electrical and magnetic

properties of Ni1-xZnxFe2O4 (x = 0.2, 0.4) synthesized by ceramic method. The electrical

resistivity, activation energy and Tc decrease while the magnetization, initial permeability

increases with Zn contents. The decreasing behavior of dc resistivity shows that the samples are

semiconductors. The initial permeability changes with bulk density. The permeability sharply

decreases fr due to occurrence of ferrimagnetic resonance. This factor limits the frequency at

which a magnetic material can be used. The material having high permeability tends to have its

permeability decreases at a relatively lower frequency. This is due to the fact that the addition of

Zn content enhances the permeability and reduces the resonance frequency by lowering the

anisotropy.

The grain size effect on the dielectric behavior of nanostructured Ni0.5Zn0.5Fe2O4 spinel

ferrite were reported by Sivakumar et.al. [107]. It was concluded that the sample having 14 nm

shows lower dielectric loss compared to that of the bulk nickel zinc ferrite. The unusual increase

in tan with milling was because of the decrease in resistivity due to oxygen vacancies

introduced upon milling. The relaxation frequency was found to decrease with milling due to

increasing interaction among charge carriers arising out of oxygen vacancies introduced by

milling process. The mechanism for the electrical conduction as well as polarization was found

to be similar. Hua et. al. [108] studied the effects of composition and sintering temperature on

properties of NiZn and NiCuZn ferrites. It was concluded that:

Initial permeability increases with the slight increase of Fe2O3 for both NiZn and NiCuZn

ferrites while slight excess or deficiency of Fe2O3 has no remarkable effect on magnetic flux

density.

Power losses of NiCuZn ferrite were found to be less than that of NiZn ferrite samples at any

sintering temperature.

The influence of V2O5 on the magnetic properties of Ni0.64Zn0.36Fe2O4 were reported by Mirzaee

et. al. [109]. The V2O5 was doped in Ni-Zn ferrite in the range from 0 to 3.2 wt. %. The

maximum grain size was observed at about 1.6 wt. % of V2O5. Different mechanisms of grain

growth were discussed. Capillary forces between ferrite particles facilitate densification and

grain growth. The grain growth development may be due to the segregation of V5+ on the grain

boundaries. The presence of V5+ increased pore mobility due to excess cation vacancies which

may be helpful to grain growth. It was found that the Curie temperature increased about 5 % by

adding about 0.8 wt. % of V2O5. Melagiriyappa et. al. [110] investigated dielectric behavior and

ac electrical conductivity study of Mg1−xZnxFe2−ySmyO4 (x = 0, 0.2, 0.4, 0.6, 0.8 and 1.0; y = 0,

0.05 and 0.10) prepared by usual standard ceramic method. The dielectric properties were

studied at room temperature as a function of frequency and composition. The experimental

results show that dielectric constant and dielectric loss tangent decrease where as ac electrical

conductivity increases with rise in frequency. The ac electrical conductivity is derived from the

dielectric data. The dielectric behavior is attributed to the Maxwell–Wagner type interfacial

polarization. The conduction mechanism in these ferrites is owing to electron hopping between

Fe2+ and Fe3+ ions on adjacent octahedral sites. The dielectric constant and ac conductivity

increases with increase in Zn2+ ion substitution. The dielectric constant decreases with the

increase of Sm3+ content.

The electrical properties of NixZn1-xFe2O4 ferrite were reported by Sheikh et. al. [111].

SEM graphs show that grain size increases with sintering temperature. The nature of temperature

dependent dc resistivity at various sintering temperature shows the change in conduction

behavior. The anomalous behavior may be due to change in cation distribution. Shinde et. al.

[112] studied dc resistivity of Ni1-xZnxFe2O4 synthesized by oxalate precipitation method. The dc

resistivity ferrites increase from 0.42 × 109 Ω cm to 6.3 × 109 Ω. cm. The higher values of

resistivity may be attributed to greater homogeneity and smaller grain size. Gul et. al. [113]

reported Electrical and magnetic characterization of nanocrystalline Ni–Zn ferrite synthesis by

chemical co-precipitation route. The presence of Zn2+ ions causes remarkable change in physical

properties. The lattice constant ‘a’ increases linearly with zinc contents from 8.359 to 8.438 Å.

The grain size was found within the range 7–15 nm. It decreases with Zn2+ concentration. DC

electrical resistivity of the samples at room temperature was found to be decreased from

1.67×109 to 4×109 Ω. cm with Zn2+ content. The activation energy calculated from the DC

electrical resistivity vs. temperature for all the samples ranges from 0.507 to 0.705 eV. The

activation energy increases with Zn2+ contents. The drift mobility was also calculated from the

resistivity measurement. It has been observed that drift mobility increases with increasing

temperature. The dielectric constant of all the samples decreases with rise in frequency.

The effects of microstructure on permeability and power loss characteristics of

Ni0.35Zn0.55Cu0.1Fe2O4 prepared by the standard conventional ceramic method were reported by

Hua et.al. [114]. It was found samples having different microstructures, has same initial

permeability values. This fact was attributed to the advantage of big grain size. The sample with

maximum grain size had poor frequency stability due to the low-frequency resonance induced by

large grain size. When samples exposed under large flux density, the sample with large grain size

and closed pores could have minimum power loss. However, the sample having small grain size

had better performance in our testing frequency range for the low induction condition. These

results were described in terms of the effects of grain boundaries and closed pores to the domain

wall movement. Nayak et. al. [115] reported the properties of cadmium ferrites prepared by a

simple combustion method. The initial grain size was 106 nm, which on further heating has

enhanced to 115 nm. Electron spin resonance (ESR) results reveal varying effect of heating for

g-values, line-width and resonance field.

Islam et. al. [116] reported the the influence of SiO2 on the electrical properties of

Co0.5Zn0.5Fe2O4 ferrites. The resistivity at room temperature increases from105 to 109 (Ω. cm),

which may be attributed to the grain boundary resistance owing to segregation of Si at or near

the grain boundaries. Temperature dependent DC resistivity decreases with rise in temperature

showing semi-conducting behavior. Activation energy obtained from mobility is nearly close to

the activation energy obtained from Arrhenius equations which shows the polaron hopping

process. Thermopower coefficient (α) shows that p and n types of charges take part in conduction

process. The value of (α) changes with temperature for all the samples exhibiting degenerate type

semi-conducting behavior of these samples. The mobility of charge carriers increase with

temperature which may be due to the fact that as the temperature increases, charge carriers start

hopping from one site to another and hence conduction increases. Valezuela et. al. [117] reported

that low field microwave absorption (LFA) depends upon the anisotropy of the specimen and

clearly different from the ferromagnetic resonance (FMR). It is directly linked with the spin

rotation absorption driven by the AC field in the unsaturated sample.

The ac conductivity of Ni1−xCuxFe2O4 were reported by Roumaih [118]. The results

obtained for these materials show a semiconductor–metallic–semiconductor behavior as Cu

content increase. All studied samples show a transition with the conductivity versus temperature.

This blocking temperature was found to decrease with increasing Cu concentration. The

dielectric parameter (ε) and loss (tan δ) were measured as a function of temperature in the

frequency range 100 Hz–100 kHz. The conduction mechanism is discussed on the basis of the

hopping mechanism. The thermoelectric power for all the samples is positive at room

temperature, indicating p-type behavior. It tends towards negative values, indicating n-type

behavior at higher temperature.

Iqbal et. al. [119] studied physical properties of CoFe2xMxO4 synthesized by substitution

of the combination of metallic elements M = Zr–Mg by the microemulsion method.

Thermogravimetric analysis shows that the spinel phase can be obtained by heat treatment as low

as 700 °C. The substitution results in a slight shrinkage of the unit cell due to large binding

energy of substituted oxides of zirconium and magnesium. The electrical resistivity, the

activation energy and A–B interactions increases with doping Zr–Mg in cobalt ferrite because of

the change in distribution of Fe3+ and Fe2+ ions in the lattice. The susceptibility data suggest that

the migration of Fe3+ to tetrahedral site lead to an increase in A–B interactions which in turn

increase the blocking temperature (TB) as observed in samples having dopant content x = 0.1.

Kharabe et.al. [120] reported structural and electrical properties of Li0.5Ni0.75-x/2Cdx/2Fe2O4

(where x = 0. 0.1, 0.3, 0.5, 0.7, 0.9) ferrite. The temperature dependent dc resistivity shows that

conduction takes place by hopping mechanism. The room temperature dc resistivity shows

decreasing trend with Cd content up to 0.3 and then it enhances with further increase in Cd

contents. The variation of Seebeck coefficient with temperature reveals that the samples with x =

0. 0.5, and 0.7 shows p-type conduction whereas the samples with substitution level x = 0.1, 0.3

and 0.9 show transition from n-type to p-type charge carriers. The average grain diameter was

found to increase while the Curie temperature decreases linearly with cadmium content.

The effect of Mg and Cr substitution on physical properties of Ni0.5Zn0.5-x-yMgxCryFe2O4

ferrites was reported by Hossain et. al. [121]. The lattice parameter, bulk density, and the average

grain diameter shows decreasing trend with increasing Mg and Cr contents. The increase in

lattice parameter was explained on the basis of difference in ionic radii. The increase in bulk

density was explained in terms of atomic masses. The composition Ni0.5Zn 0.5Fe2O4 heated at

1350 °C shows maximum bulk density (4.98 g cm-3) and average grain size (12.5 μm). The real

part of the initial permeability ( iμ′ ) and the saturation magnetization (Ms) decreased with Cr and

Mg contents whereas the Neel temperature enhances. The highest value which are 432 of iμ′was

obtained for Ni0.5Zn 0.5 Fe2O4 sintered at 1350 °C with correspondence resonance frequency (fr)

of 2 MHz. The observed Ms and iμ′ values depend upon the grain size, nature of grain

boundaries and chemical composition. The increase of iμ′was occurred with the decrease of fr ,

which confirm the Snoek relation.

Roy et. al. [122] reported electromagnetic properties of Ni0.25Cu0.2Zn 0.55 SmxFe2-xO4

synthesized through the nitrate-citrate auto-combustion method. It was concluded that the bulk

density, permeability and saturation magnetization (Ms) were increased while magnetic loss was

decreased with Sm substitution up to x = 0.05. An increase in the permeability was attributed to

the increase in grain size and better densification which not only enhance the spin rotational

contribution but also reduced demagnetizing field owing to reduction of pores. Beyond x = 0.05,

permeability decreased due to the formation of significant amount of non magnetic SmFeO3. An

increase in Ms was attributed to higher permeability of substituted ferrites. Ghodake et. al. [123]

reported the electrical properties of Co substituted Ni–Zn ferrites. Nanocrystalline Ni–Co–Zn

ferrites have been prepared by chemical co precipitation method, using oxalate precursors. The

resistivity was found to increase with Co2+ content. The values of resistivity was found to be

varied almost linearly up to the Curie temperature where a break occurs indicating a change of

magnetic ordering from ferrimagnetism to paramagnetism. The values of activation energy in

paramagnetic region are found to be higher than those in ferrimagnetic region, which shows that

the process of conduction is affected by the change in magnetic ordering. Dielectric constant and

dielectric loss tangent decreases with the addition of Co2+ contents.

The effect of calcining treatment in the temperature range 300-750 °C on the magnetic

properties of Ni0.206Cu0.206Zn0.618Fe1.94O4-δ prepared by co precipitation method were reported by

Kim et. al. [124]. Calcining temperature significantly effect microstructure, density and magnetic

properties. It was found that the calcining temperature near 450 °C resulted in the highest bulk

density of 4.9g/cm3, saturation magnetization of 3000 G and initial permeability of 170. This

sample showed higher quality factor of 3.5 times at 1 MHz than one prepared by the

conventional ceramic method. Kaiser [125] reported the influence of Ni substitutions on some

properties of Cu0.8-xZn0.2NixFe2O4 synthesized by ceramic method. The critical temperature was

increased linearly with the increase of nickel concentration while the activation energies were

found to decrease with Ni contents. The study of conductivity as a function of temperature and

frequency shows metallic to semiconductor transformation occurs with the increase of nickel

concentration. It was found that the over large hopping mechanism was present at higher nickel

concentration.

Zhang et. al. [126] reported the influence of Co doping on the structural and magnetic

properties of Mn–Zn ferrite nanoparticles, synthesized by the co-precipitation method. It was

concluded that Co ions are easily soluble into the lattice of the ferrites and never induce crystal-

structure changes. The lattice parameters increase almost linearly with Co content. All the Co-

doped ferrite nanoparticles show superparamagnetism at room temperature and the crystallite

size lies between 24.5 and 27.0 nm. The saturation magnetization Ms increases with increasing

Co content, reaching a maximum value of approximate 73 emu/g for Co content 1.0 at% and

decreases with further increasing Co content. The experiment results obtained are of interest for

further research and development of soft-magnetic ferrites for various industrial and

technological applications. Rao et. al [127] reported cation distribution of CoFe2−xTixO4 where x

varies from 0.00 to 0.30 in steps of 0.05 prepared by standard ceramic method. All the titanium

containing cobalt ferrite compositions have favored the formation of TiFe2O5 secondary phase.

Lattice constant, saturation magnetization and dc resistivity have confirmed the occupancy of

titanium ions to octahedral site. Improvement in the electrical resistivity by three orders in

magnitude has been explained on the basis of formation of Ti4+–Fe2+ ion locking pairs besides

TiFe2O5 (monoclinic) additional phase. The reduced Curie temperatures may help in developing

suitable materials for stress sensor applications.

The effect of highly activated hopping process on the physical properties of Co1-

xZnxLayFe2-yO4 , 0.1 ≤ x ≤ 0.9, y = 0.25, prepared using standard ceramic technique was reported

by Ahmad et. al [128]. The real part of dielectric constant for each sample was found to increases

with temperature up to transition temperature and decreases with frequency. Also it decreases

with increasing Zn content as the result of changing polarization of the sample due to changing

hopping mechanism. The dielectric transition temperature increases continuously with the

increase of Zn contents depending on frequency.

1.3 Aims & Objectives of the Present Work Now a day’s researchers are looking for high quality ferrites with optimum properties like

high saturation magnetization, high resistivity, low coercivity, high permeability, low eddy

current losses, low FMR linewidths and good homogeneity. The enhancement in the properties is

being investigated by substituting or doping rare earth/ rare earth transition metal ions and other

ions with large radii. Rezlescu et. al. [25] have reported these kinds of ferrites with small amount

of rare earth substitution for Fe (Iron). Yttrium is also a potential candidate for the enhancement

of properties and the work on Y-substituted / doped ferrites have not yet been reported frequently

in the literature to the best of my knowledge. There was a need to fill this gap. To tailor this end,

five series of yttrium substituted / doped ferrites were prepared. Three series of yttrium

substituted MgY-, NiY- and NiZnY ferrites with chemical formula MgY2xFe2-2xO4, NiY2xFe2-

2xO4, and Ni0.6Zn0.4Y2xFe2-2xO4 (x = 0.0, 0.02, 0.04 0.06, 0.08, 0.1, 0.12) were fabricated in a

polycrystalline form by double sintering ceramic method. Two series of Co1-xZnxY0.15Fe1.85O4 (x

= 0.0, 0.2, 0.4, 0.6, 0.8, 1.0) and CoFe2O4 + x Y2O3 (x = 0, 1 w t%, 3 wt %, 5 wt %) were

synthesized by co-precipitation method. These five series were prepared in order to thoroughly

investigate the effect of yttrium on the structural, electrical and magnetic properties for

applications of these ferrites in electromagnetic interference (EMI), ferrofluids, TV deflection

yokes, microwave devices like isolators, circulators and phase shifters.

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Chapter 2 Theories and Models

2.1 Soft Magnetic Materials The wide variety of magnetic materials can be divided into two groups, the magnetically

soft and the magnetically hard materials. The term soft magnet refers to temporary magnetism

having low coercivity which can be easily magnetized and demagnetized. High permeability, low

coercivity, low anisotropy, small magnetostriction and large saturation magnetization in a small

applied field is the distinguish characteristics of soft magnetic materials. It exhibit magnetic

properties in the presence of magnetizing force. It differs from the hard magnetic materials in the

sense that hard magnetic materials (hard to magnetize and demagnetize) has high coercivity and

are permanent. There are lots of applications of soft ferrites. They are generally used to enhance

the flux generated by the current carrying coil. They are used as a core material for small special

purpose transformer, inductor particularly in communication equipment. They are used in

microwave devices, computers and in magnetic amplifiers. Ferrites are developed for a wide

range of applications where high permeability and low loss were the main requirements. The

range of permeabilities extends from about 15 for nickel ferrite to more than 10000 for

manganese zinc ferrite grades. The combination of good magnetic properties and high

resistivities made ferrites very suitable as a core materials in the field of telephony transmission

where carrier systems required large number of high performance inductors and transformers

mainly operating in the frequency range from about 40 KHz to 500 KHz. Ferrites could be made

in more functional shapes than there metallic counterparts and their better performance enabled

frequency division multiplex (FDM) telephony to be extended to higher frequency [1].

Soft magnetic materials should have a narrow hysteresis loop because an amount of

energy equal to its area is dissipated each time the loop is traversed. It should not have a large

magnetostriction, because that can give rise to induced anisotropy. The relative importance of the

material is determined primarily by the frequency of oscillations of the magnetizing field. The

best material is the one with the largest saturation magnetization at zero frequency. For low

frequency oscillating field, high permeability, large saturation magnetization, and low coercivity

becomes important. As the frequency is increases, high permeability and low coercivity rises

relative to large saturation magnetization, because the power loss due to hysteresis is

proportional to frequency. The power loss due to eddy currents is proportional to square of the

frequency. The good soft magnetic materials should have large resistivity to overcome eddy

current losses particularly at high frequency [2].

2.2 Spinel Structure of Ferrites The ideal crystal structure of spinel ferrites is formed by cubic close-packed face centred

cubic array of 32 oxygen ions with in between a large number of interstitial sites partially filled

with metal ions [3]. The role of ions and their arrangement is important in determining the

structural, electrical and magnetic properties of ferrites. There are two types of interstitial sites

known as tetrahedral or A-site and octahedral or B-site. In a unit cell of 32 oxygen ions, there are

64 A-sites and 32 B-sites. If all the interstitial sites are filled with metal ions then structure will

not be electrically neutral because positive charge would be greater than negative charge. For

electrically neutral structure, only 8 A-sites and 16 B-sites are filled by cations. The unit cell [4]

consists of eight formula units (8 ×AB2O4). The general formula of spinel ferrites is

where423 OMFeM xx ′′′ −+ M ′ is a divalent cation or combination of cations with an average valence

of two. M ′′ is a trivalent cation or combination of cations with an average valence of three.

Those ferrites in which x = 0 is known as simple ferrite. The solid solution between simple

ferrites is called mixed ferrite. The structure belongs to the space group O7h-F3dm and is cubic.

The coordinates of the equivalent positions of this space group which are relevant for the spinel

structure are given in Table 2.1.

Spinel structure is face centered cubic. The coordinates of the additional positions can be

obtained by translations (0 0 0, 021

21 ,

21 0

21 ,

21

21 0) and μ =

83 .

In real spinel crystals, the closed cubic packing of the oxygen ions is distorted by the metal ions.

The tetrahedral interstitial sites are too small to contain the cations and the oxygen ions move

away from their ideal positions along the 111 direction away from the central tetrahedral ions.

A quantitative measure of this displacement is the oxygen parameterμ which provides

information about the exact position of the oxygen lattice sites. The value of the oxygen

parameter is equal to 0.375 if there is no enlargement of the tetrahedrons. Figure 2.1 gives the

schematic picture of the unit cell of the spinel structure.

Table 2.1: Co-ordinates of ions in the elementary cell of spinel structure expressed as a

fraction of the lattice parameters [5]

A-sites (8 ions) 000; 41

41

41

B-sites (16 ions) 85

85

85 ;

85

87

87 ;

87

85

87 ;

87

87

85

O2- sites (32 ions) μ , μ , μ ;μ , μ , μ ; μ−

41 , μ−

41 , μ−

41 ;

μ−41 , μ+

41 , μ+

41 ; μ , μ , μ ; μ , μ , μ

μ+41 , μ−

41 , μ+

41 ; μ+

41 , μ+

41 , μ−

41

The symmetry of the space group O7h-F3dm is only applicable for normal distributions of

cations. For example, in MgAl2O4, all magnesium ions occupy tetrahedral sites and all aluminum

ions occupy octahedral sites. Cation distribution is another important parameter which not only

affects the crystal symmetry but also change physical properties of ferrites.

O-2

A

B

Tetrahedral site octahedral site

(A site: 64 per unit cell) (B site: 32 per unit cell)

Fig. 2.1 Primitive cell of the spinel structure.

2.3 Electrical Properties

2.3.1 Conduction mechanism in ferrites The resistivity of ferrites is higher than metals by several orders of magnitude. This is the

main advantage of ferrites over ferromagnetic materials because high resistivity results in low

energy losses. The resistivity of ferrites can vary from 10-2 Ω-cm to 1011 Ω-cm depending upon

the chemical composition of ferrites [6]. The main cause of low resistivity of ferrites is the

simultaneous presence of Fe3+ and Fe2+ ions on B-sites [7]. The extra electron on Fe2+ ions need

little energy to move to similarly situated adjacent Fe3+ ions. The valence states of the two ions

interchanged. These extra electrons take part in jumping or hopping from one iron ion to the

next under the influence of an electric field. It is necessary to ensure that there are no Fe2+ ions in

the stoichiometric ferrite in order to obtain ferrite samples with high resistivity.

Temperature dependent resistivity of ferrites follows Arrhenius relation [6]

)(exp0 kTEaρρ = (2.1)

where oρ is pre-exponential constant, ρ is resistivity and Ea is activation energy which

can be interpreted as the energy required for hopping of electrons from one lattice site to another.

The high activation energy is associated with the high the resistivity. Sometimes, the graph

between Log ρ and 1/T show a break which occur in the curves at temperature correspond to the

ferrimagnetic Curie temperature (Tc). The electrical resistance of ferrites drops with rising

temperature and therefore, they are classified as semiconductors. Guillaud and Bertrand [8] have

measured the electrical resistivity of pure magnesium ferrite at room temperature and they found

ρ = 63 MΩ cm and at -100°C something over 105 Ω cm.

Ferrites are playing a useful role in magnetic applications owing to low electrical

conductivity in comparison with that of magnetic metals. The increasing demand of low loss

ferrites at high frequency resulted in extensive investigation on conductivity and therefore

control of resistivity is essential in ferrites. Ferrites are ferromagnetic semiconductor but

conduction mechanism is quite different from semiconductor materials. In ferrites, carrier

concentration does not depend upon temperature variations. Only mobility is a function of

temperature. The band type conduction does not occur in ferrites due to isolation of metal ions

surrounded by oxygen ions. This shows the insulating nature of ferrites.

The conduction in spinel ferrites which are affected by doping can be classified into two

types: excess or oxidation type and deficit or reduction type, and valence controlled action. The

other mechanisms which can affect the resistivity of ferrites are: grain boundary and structure

distortion. The resistivity increases with the addition of lower valent cations and decreases with

addition of higher valent cations in case of excess type. The inverse relationship occurs in the

deficit type. It can be seen that Ni-ferrite belongs to the deficit type while Mg-ferrite belongs to

excess type. This valence controlled action was observed at high impurity concentration because

the substitution can not produce enough ferrous ions to affect the resistivity at low concentration.

It was found that there are some exceptions in which the addition of impurity increases the

resistivity of the excess type to a maximum and then causes a decrease. These impurities do not

form a solid solution or form a solid solution which is not homogeneous. They tend to segregate

at the grain boundaries and form highly resistivity substance [9].

Several mechanisms have been suggested for conductivity in ferrites. These are as follows:

1- Hopping model.

2- Small polaron model.

2.3.1.1 Hopping model of Electrons Jonker [10] proposed that those materials in which the carrier mobility is extremely low

then there is a strong probability of exchanging the valence of metal ions particularly iron ions.

The ions occasionally come close together during lattice vibration for charge transfer. The lattice

vibration brings about the conduction. According to hopping model, a charge carrier can move

from one place to another via jumping or hopping. The carrier mobility for jumping of electrons

and holes are given by:

TK

TKEfleB

)(exp 111

1

−

=μ (2.2)

TK

TKEfleB

)(exp 222

2

−

=μ (2.3)

1μ and 2μ represent mobilities for electrons and holes. and represent jumping

length. and are lattice frequencies active in the jumping process, and are

activation energies involved in the required lattice deformation..

1l 2l

1f 2f 1E 2E

The mathematical expression for total conductivity for materials having two types of

conductivities can be given as:

2211 . μμσ enen += (2.4)

The temperature variations do not affect the number of charge carriers in the sample. It

only influences the charge carrier mobility. For hopping conduction, it was concluded that:

The mobility has the lowest value much smaller than the limiting value of 0.1 cm2/Vs

taken as a minimum for band conduction.

∗

The numbers of charge carriers are fixed in hopping model. ∗

2.3.1.2 Polaron model A small polaron is a defect created when electron is trapped in a self-induced potential

well and may polarize the molecule. The entire defect (carrier plus distortion) then migrates by

an activated hopping mechanism. The combination of the electron and its induced polarization

field can be considered as quasi-particle which is called a polaron [11]. Small polaron formation

can take place in those materials whose conduction electrons belong to incomplete inner d or f

shells which tend to form extremely narrow bands [12] due to small electron overlap. The size of

the polaron depends upon the region over which the lattice distortion or deformation due to

polarization is introduced. In ionic crystals, the radius of the distorted region is much bigger than

a lattice constant because the electron-phonon coupling arises from the long range strong

coulomb interaction between the electron and optical lattice modes. The polarons in ionic

crystals are called “large polarons”. In molecular crystals, the radius of the distorted region lies

within the order of lattice constant because the electron-phonon coupling arises from the short

range strong coulomb interaction between the electron and optical lattice modes. The polarons in

ionic crystals are called “small polarons”. The self trapping was first introduced by Landau [13].

But still the occurrence of self trapping of electrons in crystal lattice is not confirmed.

Theoretical study of polaron based on perturbation theory or vibrational principles may not be

valid for the actual interaction between an electron distorted crystal surroundings where the

lattice deformation or distortion in shape and extension is a function of electron velocity.

2.4 Dielectric properties A dielectric, or an electrical insulator, is a substance that is highly resistant to the flow of

an electric current. Dielectric materials can be solid, liquid, or gases. There are lots of

applications of dielectric. For example, a capacitor containing dielectric can be subjected to

higher voltage because dielectric is more resistant to ionization than dry air. The use of dielectric

in capacitors provides higher capacitance. The relative dielectric constant is a measure of the

extent to which it concentrates electrostatic lines of flux.

Ferrites naturally combine magnetic and dielectric properties, therefore, they are known as

natural magnetodielectrics. The dielectric property of ferrites depends upon several factors such

as method of preparation, sintering conditions, chemical composition, and micro structure such

as grain size. Ferrites are important magnetic materials with a variety of applications due to their

magnetic properties and dielectric loss. In 1971, Iwauchi presents a strong correlation between

dielectric behavior and conduction mechanism of ferrites. The conduction mechanism of ferrites

can be explained by hopping mechanism of electrons between ions of the same element present

in more than one valence state. The hopping between Fe2+ and Fe3+ on octahedral sites is the

dominant mode of conduction observed in a large number of ferrites. The higher concentration of

Fe2+ leads to higher conductivity because the conduction in ferrites is due to electron hopping

between Fe2+ and Fe3+ on the octahedral sites of spinel structure. It is observed that high

conductivity ferrites exhibit high dielectric constant. It is the number of Fe2+ ions that play an

important role in conduction as well as dielectric polarization [14]. It is observed by various

authors [15, 16] that the dielectric constant is high at low frequency and decreases with the

increase of frequency. It is low at high frequency and becomes less dependent upon the

frequency.

2.4.1 Electronic Polarization It arises as a result of the displacement of electrons in an atom relative to the nucleus

[17]. The individual atom has no dipole moment in the absence of applied field. When a field E

is applied then the electric field displaces the electron density relative to the nucleus it surrounds

and the atom acquires a dipole moment P as shown in Fig. 2.2. This dipole moment is directly

proportional to E so that we may write EP α= whereα the polarizability of the atom is.

Fig. 2.2 The electronic polarization, the electron cloud is displaced due to applied electric

field.

2.4.2 Ionic Polarization This type of polarization arises when applied electric field produces relative displacement

of the anion and cation charge centers that causes net dipole moment. The magnitude of the

dipole moment can be calculated from the relation: idqP = where q is the charge of dipole and

is relative displacement in meters. The nature of electronic and ionic polarization is same

because are caused by the displacement of bound charges with respect to each other in the

direction of the applied electric field.

id

2.4.3 Dipolar or Orientational polarization

It is important only for those materials which contain complex ions having permanent

dipole moment. These dipoles are free to rotate in liquid or a gas but they can not rotate in solids.

These dipoles orient along the direction of the applied electric field as

without field with field

Fig. 2.3 The orientational polarization, the already exist dipoles are aligned in the

direction of the external field.

shown in Fig. 2.3 and the material will acquire a net moment. This is called orientational

polarization. Thermal agitation tends to randomize the dipoles. It is because of this reason the

calculation of dipolar polarization has to be made under thermal equilibrium.

2.4.4 Space Charge Polarization or Interfacial polarization This type of polarization arises as a result of accumulation of charges locally as they drift

through the material locally. The nature of this polarization is different from the electronic,

orientational and ionic polarization. In case of space charge polarization, several factors are

responsible for large scale distortion of the electric field [17, 18]. These factors are:

1- Pile up of charges in the volume or on the surface of the dielectric.

2- Change in conductivity at boundaries, cracks and defects, and boundary region between

the crystalline and amorphous regions within the polymer.

3- Pile up of charges in the volume or on the surface of the dielectric.

It may be assumed that a polycrystalline ferrites consist of large domains of well conducing

material which is separated by thin layers of relatively poor conducting material. We

consider the example of Maxwell-Wagner to drive the ωε −′ and ωε −′′ characteristics due

to space charge polarization that exist between two layers of polycrystalline ferrite material

that have different conductivity.

221 τωεε

εε+−

+=′ ∞∞

S (2.5)

2221 1

)()(

1τωεεωτ

ωε

+−

++

=′′ ∞S

o RRC (2.6)

The dielectric constant given by equation (1) gives the ωε −′ characteristics for space charge

polarization. It is identical to the Debye equation, which is the dispersion for interfacial

polarization, is identical with dipolar polarization although the relaxation time for the former

could be much longer. The relaxation spectrum given by equation 2.6 consist of two terms;

the first term due to conductivity makes an increasing contribution to the dielectric loss as the

frequency becomes smaller. Fig.2.4 shows the

Fig. 2.4 Relaxation spectrum of a two layer dielectric

relaxation spectrum of a two layer dielectric. The second term is identical to the Debye

relaxation and at higher frequencies the relaxation for the interfacial polarization is

indistinguishable from dipolar relaxation.

2.4.5 Frequency Dependence of Dielectric Constant Fig. 2.5 shows the contribution of polarization mechanism to the dielectric constant and their

relaxation frequencies for materials having inhomogeneous structure. The dielectric constant

becomes smaller as each process relaxes because the contribution to polarization from that

mechanism ceases.

Fig. 2.5 Frequency dependence of the real and imaginary parts of the dielectric

constant.

The dielectric constant is given by the equation beyond the optical frequencies. The

interfacial polarization may involve several mechanisms of charge build up at the electrode

dielectric interface or in the amorphous and crystalline regions of a semi-crystalline polymer.

Different types of charge carriers are involved depending upon the mechanism of charge

generation. In dipolar liquids, the orientational polarization occurs in the radio frequency to

microwave frequency range. In polymers, the dipoles may be constrained to rotate or move to a

limited extent depending upon whether dipole is the part of main chain or side group.

Correspondingly the relaxation frequency may be smaller, of the order of a few hundred KHz. In

solids, there is a range of allowed frequencies, making the present treatment considerably

simplified.

2n=∞ε

2.5 Magnetic Materials

2.5.1.1 Diamagnetic Materials Electrons in an atom consist of two types of movements: spinning about its own axis and

moving in its own orbit. The magnetic moment (vector quantity) is associated with each kind of

movement. The net magnetic moment in an atom is the vector sum of all its electronic

movements. Magnetic susceptibility (χ ) is an important parameter for characterizing magnetic

materials which can be defined by the relation. HM

=χ where M is a magnetization and H is an

applied field. Diamagnetic substances are those substances which has no intrinsic [19] magnetic

movement and exhibit negative magnetism which leads to negative susceptibility. These

materials have negative susceptibilities lying in the range 10-6 which are independent of

temperature. Atoms which have closed shell electronic structure are usually diamagnetic. The

monatomic rare gases He, Ne, A, etc., which have closed shell electronic structures are

diamagnetic. Similarly Na+ and Cl- have closed shell are diamagnetic. Elements like diamond,

Silicon, Germanium are diamagnetic due to closed shell structure. Superconductor is a perfect

diamagnetic [20].

2.5.1.2 Paramagnetic Materials Paramagnetic substances are those substances in which an atom has an intrinsic magnetic

moment [19] due to non-cancellation of spin and orbital components. Atoms such as transition

metals, rare earth ions and their compounds are paramagnetic because they can have large

magnetic moment owing to their incomplete inner shell. Magnetic moments of transition metals

are entirely due to spin and orbital components being largely quenched. The transition metal salts

usually obey the Curie law or Curie-Weiss law with small value of θ.

χ = C / (T – θ) where C is a Curie constant and T is temperature in

Kelvin degrees. θ is a constant. These materials have positive susceptibilities lying in the range

between 10-3 and10-6 [20]. The ferromagnetic and ferrimagnetic materials at temperature above

the Curie temperature are paramagnetic [20]. Magnetic susceptibilities of some Diamagnetic and

Paramagnetic elements are listed in table 2.2.

Table 2.2: Magnetic susceptibilities of some Diamagnetic and Paramagnetic elements [21]

Element MAGNETIC SUSCEPTABILITY (χ)

Sb

Cu

Pb

-7.0 x 10-5

-0.94 x 10-5

-1.7 x 10-5

Ag

Al

Pt

O2(NTP)

-2.6 x 10-5

+0.21x 10-4

+2.9 x 10-4

+17.9 x 10-7

2.5.1.3 Ferromagnetic Materials Those materials in which a large number of atoms (1013 to 1014) produces a region where

all atomic spins within the region aligned parallel (positive exchange interaction) is called

ferromagnetic materials [3] for example Ni, Co, Fe, and some of the rare earths. In 1933, Bethe

shows the dependence of magnetization energy as function of the ratio of atomic separation to

the diameter of unfilled electronic shell (3d or 4f electrons). The region which allows positive

exchange interaction is known as magnetic domains. In 1907, Weiss gave the idea of domain. He

presented the concept of “molecular field” which produced positive exchange interaction. In

1928, Hesinberg named this molecular field to quantum mechanical exchange forces [3].

In ferromagnetic materials, the susceptibility is a function of field strength. The relation

between magnetization and field strength is characterized by hysteresis. There exist elementary

regions of magnetization below Curie temperature known as weiss domain. The magnetic

moment of electron spins produces spontaneous magnetization of a weiss domain. The

ferromagnetism in liquids or gases is not possible because it is associated with particular crystal

lattice formation [20]

2.5.1.4 Antiferromagnetic Materials These materials have susceptibilities of the order of 10-3 but they increase with the rise of

temperature, up to a critical temperature and then decrease again. The temperature at which

antiferromagnetism disappears is called the Neel temperature. Many compounds are

antiferromagnetic for example manganese oxide, iron oxide, nickel oxide, iron chloride, and

manganese selenide [20].

2.5.1.5 Ferrimagnetic Materials The general formula for these materials is MO.Fe2O3 where M stands for divalent

metallic ion (iron, nickel, magnesium). These oxides usually have spinel type structure. Only

inverse spinels are ferromagnetic [20]. These materials have two different lattice sites known as

tetrahedral and octahedral sites and have negative exchange interaction. The magnetic moments

on two sites are not equal and thus, complete cancellation did not occur. The net magnetic

moments are the difference in the moments on two sites. This phenomena is known as

ferrimagnetism or uncompensated antiferromagnetism [3].

2.6 Origin of Magnetic Moments

2.6.1 Electronic Structure The moving charges produce magnetic fields. Ampere (1775-1836) proposed the

existence of small molecular currents in matter [19]. By 1905, it was agreed that molecular

current responsible for magnetism in matter were due to electrons circulating in the atom [3].

The motion of electrons around the nucleus can be characterized by four quantum numbers

1- The principal quantum number n determines total energy of the electrons in each state

and is given by:

22

222 44 hn

meEo

nπ

πε ⎟⎟⎠

⎞⎜⎜⎝

⎛−=

where e is the charge on electron, oε the permittivity of free space, h is the Planck’s

constant, m is the mass and n is a positive integer.

2- The orbital quantum number l is associated with the electron angular momentum Po, as

[ ]π2

)1( 21 hllPO +=

For a given n, can have values: l 1....,,.........3,2,1,0 −= nl

3- The magnetic quantum number is related to the components of the electron angular

momentum when magnetic field is applied to the atom. The permitted values of are:

lm

lm

lml l +≤≤−

The several electron states with the same energy (same n) can exist. This condition is known

as degenerate states.

4- The spin quantum number is related to the intrinsic angular momentum of electron with

value [ ]π2

)1( 21 hSSPS +=

S have two values s = 21

± .

The total angular momentum can be expressed as:

[ ]π2

)1( 21 hjjPtotal += where j = + s. The magnetic dipole moment, M, of a moving particle

of mass m, charge Q and angular momentum A is

l

Am

QM ⎟⎟⎠

⎞⎜⎜⎝

⎛=

2 .

The atomic magnetic moments are quantized in units of π22h

me⎟⎟⎠

⎞⎜⎜⎝

⎛ called Bohr magneton

Bμ = 9.274 × 10-24 Am2. The ratio γ=me

2 is called gyromagnetic ratio. The various

magnetic moments are:

[ ] Bl ll μμ 21

)1( += for orbital magnetic moment

[ ] BS SS μμ 21

)1(2 += for spin magnetic moment

[ ] Bj jj μμ 21

)1( += for total angular magnetic moment

The occupancy of states can be determined by Hund’s rule in free atoms

Rule 1- Electrons occupy states in each orbital with maximum total spin number. The total

spin number for orbital, S, can be calculated as S = s∑ .

Rule 2- The next priority is to achieve maximum total orbital momentum L as L = l∑ .

Rule 3- The total angular, J, is determined as SLJ −= for an orbital less than half-full, and

SLJ += for an orbital more than half-full. For an exactly half-filled orbital, L = 0, J = S.

Magnetic moment for atoms having multi electrons are calculated using the following

expression:

[ ] Beff JJg μμ 21

)1( += (2.7)

where g is Lande factor, introduced to account for the difference in orbital and spin

contribution to total orbital momentum.

)1(2)1()1(

23

++−+

+=JJ

LLSSg (2.8)

2.6.2 Bonding The atoms in the bonded state are in a more stable energy condition than when they are

unbonded. The valence electrons have to be modified in such a way as to maximize attractive

forces and minimize repulsive forces.

2.6.2.1 Ionic Bonding In this type of bonding, large interatomic forces are developed by an electron transfer

from one atom to another to produce ions [19]. These positively and negatively charged ions are

bonded together by strong coulombic forces. It is a strong nondirectional bond. Generally ionic

bonds formed between highly electropositive (metallic) and highly electronegative (nonmetallic)

elements. Electrons are transferred from electropositive elements to atoms of electronegative

elements producing positive and negative cations in the ionization process. The general trend in

ionic bonding is to form ions with complete filled orbitals which resulted in zero magnetic

moments. In transition series elements, the first ionization step involves transfer of the 4s2

electrons to form divalent cations in Fe, Ni, Co, Ti, V, Mn, Sc, and of the 4s1 electrons in Cr and

Cu to form monovalent cations. This process would not bring any change in 3d magnetic

moments. Further ionization involves 3d electrons and also would change the total spin moment.

The magnetic moment increases if the 3d orbital is more than half filled and decreases if it is half

full or less than half full. The total magnetic moment of the first transition series are different to

those of the corresponding atoms, even if the 3d orbitals are unchanged. The reason is that the

cations are influenced by crystal field produced by anions surrounding cation sites. The spin

moments are changed but the orbital magnetic moments are decreased or eliminated due to

presence of crystal field. This phenomenon is called orbital quenching. The crystal field can

result in orbitals with decreased or even zero spin moments for certain symmetries,

independently of the Hund’s rule. An example is trivalent rhodium Rh3+ (Z = 45), with 4d6 as the

outermost occupied orbital, in an octahedral site. Hund’s rule would lead to 4 Bμ in a weak

crystal electric field as shown in the Fig. The first five electrons occupy all the states of spin 21 ,

one in each orbital (dxy, dyz, dzx, dx2

-y2, and dz

2), and the sixth occupies the state s = 21

− in dxy to

give the high spin configuration. The occupancy of orbitals dx2

-y2 and dz

2 can be prevented by the

repulsion of the negative anion charge along the Z-axis for a strong crystal field. The electrons

are forced to occupy the available states, with spin 21

− , in orbitals dyz and dzx. The Pauli

principle leads to antiparallel spins in the three occupied orbitals and therefore to zero spin

moment. This is the low spin configuration. Theses effects are virtually absent in rare earth

cations because orbitals with magnetic moments (4f) are shielded from the crystal field by 5s and

5p orbitals.

2.6.2.2 Covalent Bonding Relatively large interatomic forces are created by the sharing of electrons to form a bond

with a localized direction. This type of bonding takes place between atoms with small

differences in electronegativity and which are close to each other in the periodic table. The atoms

most commonly share their outer s and p electrons with other atoms so that each atom attains the

noble gas electron configuration. Each covalent bond is formed by two electrons, one from each

atom with opposite spins. It is a directional bonding, depending upon the geometry of the orbitals

involved. This bonding has little effect on the magnetic moments of transition series atoms.

2.6.2.3 Metallic Bonding Relatively large interatomic forces are created by the sharing of electrons in a delocalized

manner to form strong nondirectional bonding between atoms. This type of bonding takes place

between atoms of the same type, when they are in close proximity, as a result of interactions, the

original atomic levels splits into new level, with small difference of energy between them at the

equilibrium interatomic separation. Interactions of N atoms lead to 2N band levels (N with spin

up and N with spin down) for an s atomic orbital, 6N band for p orbital, 10N band levels for d

atomic orbital.

2.7 The origin of Magnetic interactions in Ferrites In ferrites, magnetic moments are antiparallel but uncompensated and resulted into net

magnetic moment. Consider a simple system of two atoms ‘a’ and ‘b’ having one electron each.

The distance between two atoms is very small, giving rise to electron interaction. Electron wave

function can be expressed as linear combination of the original atomic wave function [19]. The

total energy can be written as:

exba JQEEE ±++=

exE

(2.9) where

and are the energies of the electrons, Q is the electrostatic interaction energy and is the

exchange energy. arises when electron of atom ‘a’ orbits around nucleus of atom ‘b’ and

electron of atom ‘b’ moves around nucleus of atom ‘a’. The spin orientation is the important

factor. The parallel spins will be resulted into positive and antiparallel spins will be resulted

into negative . Heisenberg showed that exchange energy between two atoms having spins

and can be represented by the relation:

aE bE exJ

exJ

exJ

iex SS

exJ iS

jS jJ2−= where is the exchange integral.

It is the measure of the extent to which the electronic charge distribution of two electrons under

consideration overlaps one another.

exJ

The magnetic ions in ferrites occupy the interstitial sites of a close packed oxygen lattice.

Thus the probability of direct overlap of the electronic charge distribution is very small. In 1934,

Kramers gave a new idea of exchange mechanism between metal ions through the intermediary

oxygen ions. Neel formulated his new theory for ferrites.

2.7.1 Indirect Exchange Interaction In magnetic oxides as well as in many ionic crystals the exchange energy J < 0 which

support anti-parallel alignment. In such substances, cations are separated by anions and direct

exchange interaction is not possible because they are located too far apart each other. Oxygen O2-

ion like inert gas have closed shell configuration and offer no spin coupling in ground state. This

state will be disturbed by the neighboring ions. One of the electrons in oxygen ions exchange

with the unpaired electron of the metal ions (A-site) by the principle of the superposition states.

According to Pauli Exclusion Principle, oxygen spin will be opposite to that of metal ion. The

other spin of oxygen ion paired with the unpaired spin of another metal ion.

In 1951, Zener presented double exchange mechanism. Cations of same element having

different valence, exchange electron through oxygen ions. For example Fe2+ O2- Fe3+ can change

to Fe3+ O2- Fe2+.

2.7.2 Super-exchange interaction In ferrites direct interaction is not possible due to the following reasons:

1- Large distance between the magnetic cations.

2- The non magnetic anions such as oxygen is situated in the line joining magnetic cations.

Kramers (1934), Anderson (1950) and Van Vleck (1952) proposed a mechanism called super-

exchange interaction.

The probability of interaction of oxygen ions in the ground state with magnetic

cations is extremely small [21]. However, its interaction with metallic ions is possible in excited

state. The possible excitation mechanism can be explained in the following way.

)2( 6p

Consider the interaction between oxygen and ferric ions. The ground state of these ions can be

shown as:

)3( 53 dFe + )2( 62 pO −

↓ ↑↓

↓ ↑↓

↓ ↑↓

↓

↓

The ions have 5 electrons in 3d shell and according to Hund’s rule, the alignment of 5 spins

in d shell is shown in the fig. The six electrons of the oxygen ion form three pairs. In excited

state, one p-electron leaves the oxygen ions and becomes the part of iron ion temporarily and

converts the ferric ion for a very short time to ferrous ion. These ions can be shown as:

+3Fe

)3( 6d

) 3( 62 dFe + )2( 52 pO −

↑↓ ↓

↓ ↑↓

↓ ↑↓

↓

The excited oxygen ion having one unpaired spin is now paramagnetic and overlaps p orbital

with the ferric ion orbital produces exchange forces.

Thus the other spin in the oxygen ion free to pair with the unpaired spin of other metal ions

located opposite to the original metal ion. The second spin of the oxygen ion can only couple

with a spin which is opposite to the original metal ion. This mechanism of interaction suggests

the antiparallel alignment of the two metal ions adjacent to the oxygen ion.

It is generally assumed that the super exchange interaction decreases rapidly with the

increase of distance between metal ions and non magnetic anion (oxygen ion). The dumb bell

shape of the 2p orbit makes it a reasonable assumption that the exchange forces will be greatest

for an angle of 180° and also where the interatomic distances are shortest. The interaction will be

very small for an angle of 90°. The best combination of distances and angles are found in A-B

interactions while A-A interaction is very weak and B-B interaction is probably intermediate.

2.7.3 Double-exchange interaction In 1951, Zener proposed this mechanism to explain the cause of interaction between

adjacent metal ions of parallel spins through neighboring oxygen ions [21]. The argument

requires the presence of ions of the same metal in different valence states. In magnetite, Zener’s

argument would envisage the transfer of one electron from the Fe2+ ions to the nearby oxygen

ions and the simultaneous transfer of an electron with parallel spins to the Fe3+ ion nearby. This

process is shown below.

)3( 62 dFe + ) −2O 3( 53 dFe + )3( 53 dFe + −2O )3( 62 dFe +

↓↑ ↑↓ ↓ ↓ ↑↓ ↓ ↑

↓ ↑↓ ↓ ↓ ↑↓ ↓

↓ ↑↓ ↓ ↓ ↑↓ ↓

↓ ↓ ↓ ↓

↓ ↓ ↓ ↓

exchangethebefore exchangetheafter

This mechanism is similar to the conduction mechanism proposed by De Boer and Verway

(1937) to explain the reasons for electrical conductivity of certain conducting materials. This

mechanism favors positive interaction.

2.7.4 Molecular Field Theory It is the simplest theory of ordered magnetic moments in solids. In 1907, P. Weiss

suggested [19] that ordering results from fictive field, the molecular field, which depends upon

magnetization:

MH w λ=

where is the molecular field, the magnetization and wH M λ the molecular field coefficient.

The total field experienced by magnetic moments is:

HHH wT +=

where H is the external field. The Curie law is now:

THM

TC==χ

Replacing by wH Mλ and solving for M:

CTCHMλ−

= .

with CTC =λ . Expressing the susceptibility as a function of only the external field leads to:

CTTC−

=χ

which is the Curie-Weiss law. This leads to linear behavior of χ1 for T > Tc. At T = Tc, χ

becomes infinity; since HM

=χ , it can be interpreted as the existence of finite magnetization at

zero field, i.e., a spontaneous magnetization.

The order of magnitude of the magnetic interaction energy for one spin, wB Hμ , can be

compared with the thermal energy at the Curie transition, kTc

. CwB TkH ≈μ B

Cw

kTH

μ≈

Taking Bμ = 1.165 × 10-29 J m/A, k = 1.381 × 10-23 J/K and Tc = 1000K. leads to Hw ≈1.2 × 109

A/m. The actual field produced by a spin on its neighbors is ≈ 8 × 104 A/m. The weiss molecular

field is not a real field, but a simplified representation of the exchange interaction. In the most

simple case, with two sublattices in spinel ferrites, the net magnetization at temperature T(at T <

Tc) is simply:

)()( TMTMM tetoct −=

where are the magnetization of octahedral and tetrahedral sublattices

respectively. For T < Tc, the Curie-Weiss expression becomes:

)()( TMandTM tetoct

θχχ −−+=

Tb

CT

O

11

where bandO θχ , are associated with molecular field coefficients. At high temperature, the last

term on the right – hand side becomes negligible and:

OCT

χχ11

+= (2.10)

2.7.5 Neel theory of Ferrimagnetism

Neel divided the crystal lattice into two sublattices formed by tetrahedral (A) and

octahedral (B) sites in a spinel structure [21]. He assumed one type of magnetic ions only. He

supposed that λ fraction of magnetic ions appeared on A-sites and remaining fraction of

magnetic ions μ appeared on B-sites. Thus

λ + μ = 1 (2.11)

The general formula of spinel ferrites is MFe2O4 which satisfies Neel’s assumptions. M is a non-

magnetic ion while Fe3+ is a magnetic ion. The formula can be written as:

422212 ][ OMFeMFe λμλλ − where bracket ions represent octahedral sites. The several

interactions between magnetic ions can be classed as A-A, B-B and A-B interactions.

According to Neel theory, A-B interactions dominate over other interactions and net magnetic

moments of A-sites are more or less anti-parallel with the magnetic moment of B-sites. Each

ferric ion has magnetic moment of 5 Bμ . The moment of ferrite molecule is 2 (λ - μ ) 5 Bμ due

to anti-parallel arrangement of magnetic moments on A and B sites. The Neel theory predicts

much smaller moments as compare to theoretical one. Experimental observations also support

Neel theory. The magnetic field acting upon an ion can be written as mO HH H += where

OH

AH

BH

AH

AH

is an external applied field and is internal molecular field. By applying the idea of

molecular field in ferrites, we have the equations:

mH

ABAA HH +=

BABB HH +=

is a molecular field acting on A-ions. is a molecular field acting on B-ions. is a

molecular field due to neighboring A-ions. is a molecular field due to neighboring B-ions.

The molecular field components can be written as:

BH

ABHAAH

AAA Mγ= , BABAB MH γ= , BBB MH , ABABA MH γ= . = γBB

s'γ are the molecular field coefficients and are the magnetic moments of the A and B

sublattices. It may be shown that

AM BM

BAABγ γ= , but BAAA γγ ≠ unless the two sublattices are identical.

Neel showed that 0∠ABγ due to anti-parallel arrangement of and , gives rise to

ferrimagnetisms. The total magnetic field in the presence of external field can be written as

AM BM

BABAAAAOa MMHHHH + γ + γO=+= (2.12)

AABBBBBOb MMHHHH + γ + γO=+= (2.13)

2.8 Magnetic interactions The exchange forces between two metal ions [3] on different sites depend upon two factors:

1- Distance between cations and oxygen ions.

2- Angle among the cations and oxygen ions.

The exchange force between cations is maximum for an angle of 180° and where the distance

between the cations and oxygen ions is the shortest. For ideal spinel, A-O-B angles are 125°

and 154° while B-O-B angles are 90° and 125° (B-O distance is large) and A-O-A angle is

80° [3]. A-O-B is the strongest interaction while AA and BB interactions are weak. In 1948,

Neel explained the phenomena of ferrimagnetism on the basis of A-B interaction which

orients the unpaired spins of these ions antiparallel.

2.8.1 The Magnetization in Ferrite Domains

It is a region in ferro- or ferromagnetic material where all moments are aligned. Each

domain consists of a number of atoms about 1012 to 1015 whose resultant moments are mutually

parallel. The concept of magnetic domains enables us to describe the phenomena of hysterisis

and the magnetic process that determines it. It is supposed that a magnetic body below its Curie

temperature consist of a large number of small domains each spontaneously magnetized to

saturation.

Domains are formed in order to minimize the magnetostatic energy. This type of energy is the

magnetic potential energy contained in the flux lines connecting north and south poles. Fig.

shows the magnetic lines in a particle with single domain. The arrows show the direction of spin

alignment in the domain. The magnetic energy can be reduced to a minimum or even zero for

certain domain structure by dividing a crystal into two or more domains. When a domain is split

into n domains the magnetic energy can be reduced in to 1/n of single domain structure. F.g.

shows the magnetic moments in adjacent domains are oriented 180° to each other.

Certain other domain configurations may occur which lead to reducing the magnetic energy of

the system in cubic crystal structure. Fig. shows triangular domain structure called closure

domains. In this configuration, the magnetic flux path never leaves the boundary of the magnetic

material. Therefore, the magnetostatic energy is eliminated by the formation of closure domains.

Landau and Lifshitz have shown that a domain structure is a natural consequence of various

energies contributing towards the total energy of the magnetic material. They are:

1- Magnetostatic Energy

2- Magnetocrystalline anisotropy energy

3- Magnetostrictive energy

4- Domain wall Energy

2.8.2 Magnetostatic Energy It is the energy needed to put magnetic poles in special geometric configurations. In 1951,

Bozorth presented a mathematical expression for magnetostatic energy per cm3 for an infinite

sheet magnetized at right angles to the surface. The equation is 22 SP ME π= (2.14)

Neel (1944) and Kittel (1946) derived an equation for the magnetosatic energy of flat strips of

thickness, d, and magnetization, M. The equation is

285.0 MdEP = (2.15)

The above equation shows that the magnetostatic energy decreases with the decrease of width of

the domain. It confirmed the fact that the splitting of domains into smaller widths decreases the

magnetostatic energy.

2.8.3 Magnetocrystalline Anisotropy Energy The domain magnetization tends to align itself along one of the main crystal direction

called easy direction of magnetization. It may be edge or diagonal of the cube. The difference of

energy between state where magnetization is aligned along easy direction to a state and a state

where it is aligned hard direction is called magnetocrystalline anisotropy energy. This energy is

required to rotate magnetization from easy direction to another direction. The energy of the

domain can be minimized by anisotropy energy by aligning the moments along easy direction of

magnetization. The adjacent domain have the tendency to align itself along the same axis but in

opposite direction i.e. 180° wall is found between two adjacent domains [3].

Anisotropy arises from the crystalline nature of most magnetic materials. The magnetization

vector in a crystal is anisotropic. The total energy of crystal depends upon the direction of

magnetization vector. The minimum energy is along the easy direction. In cubic crystals, <100>

or <111> are easy directions. This phenomenon is called magnetocrystalline anisotropy and all

magnetization process depends upon anisotropy rules. The energy required to deviate the

magnetization vector from an easy direction can be represented by series expansion of the

cosines of angles between magnetization and crystal axes [19]:

LLL++++= )()( 23

22

212

21

23

23

22

22

211 ααααααααα KKEK (2.16)

where and are the magnetocrystalline constants, and 1K 2K 1α , 2α , 3α are angle cosines. The

sign of and depends upon the easy directions. For <100>, is positive while for

<111>, is negative. Magneticrystalline anisotropy originates from spin-orbit interaction.

Applied field not only deviate the spin from easy direction but it also tends to rotate the orbit due

to spin-orbit coupling. The rotation of the orbit needed more energy than the rotation of the spin

because orbits are strongly associated with the lattice.

1

1

K

K2K 1K

2.8.4 Magnetostrictive energy

A small change in the dimension of the magnetic materials occurs when it is magnetized.

This phenomena is called magnetostriction which is related to spin-orbit coupling. The change in

spin direction is related to change in orbital orientation resulted in modifying the length of the

sample. The strain produced by a saturating magnetic field is called magnetostriction constant

Sλ : O

S LLΔ

=λ , is the initial length. OL

Magnetostriction is an isotropic phenomena. The value of LΔ in a single crystal is different for

different field orientations. In polycrystals, Sλ is an average of the single crystal values.

Stress also affects the magnetization process which can also be related to spin-orbit

coupling. Stress affects the process of orbital rotation under the influence of magnetic field. The

energy of magnetostriction depends upon the amount of stress and on a contstant characteristic of

the material called magnetostriction constant.

λσ2/3=E (2.17)

where λ = magnetostriction constant

σ = applied stress

In case of positive magnetostriction, the magnetization is increased by tension and the material

expand when the magnetization increased. If the magnetostriction is negative, the magnetization

is decreased by tension and the material contracts when it is magnetized [3].

2.8.5 Domain wall Energy In 1932, Bloch presented the idea of magnetic domains with domain walls separating

them. In bulk materials, domain wall is that region where magnetization direction in one domain

is gradually changed to the direction of the neighboring domain. Suppose δ is the thickness of

the domain wall, the exchange energy stored in the transition layer resulting from the spin

interaction is

aTK

E Ce =

where is the thermal energy at Curie temperature and ‘a’ is the distance between atoms.

Thus exchange energy decreased with the increase in the width of the wall. In the presence of

CTK

anisotropy energy, rotation of magnetization from easy direction increases the energy. The wall

energy resulting from the anisotropy is

δkEK =

Therefore, the energy is increased as the domain width is increased. The two effects oppose each

other and the minimum energy of the wall per unit area of walls occurs according to the

following equation:

21

2 ⎟⎠⎞

⎜⎝⎛=

aTK

E CaW

where is anisotropy constant. aK

If magnetostriction is a consideration, the equation is modified to

21

21

23

2 ⎟⎠⎞

⎜⎝⎛ +⎟

⎠⎞

⎜⎝⎛=

σλSaW K

aTKE

where Sλ is a magnetostriction constant. The domain wall thickness for the condition of

minimum energy is given by the equation

21

)tan( ⎟⎠⎞

⎜⎝⎛×=

KEatconsδ (2.18)

The value of δ for some soft magnetic material may be about 10-6 cm.

2.9 Hysteresis loop In magnetic applications, the most important matter is how much magnetization an

applied magnetic field can create. The material is said to be magnetically soft if small field is

enough to produce saturation. When soft magnetic material is subjected to an increasing applied

magnetic field (H), magnetization begins to increase from zero to saturation value and the curve

M vs H from demagnetized state to saturation is called initial or virgin or induction curve. The

value of magnetization for which H = 0 is called retentivity or residual magnetization. The

magnetization will decrease to zero when applied field is reversed. The value of the negative

field at which magnetization will decrease to zero is called coercivity Hc. If the reverse field is

further increased the saturation will reach at -MS. If the reverse field is reduced to zero and then

increased in the positive direction, magnetization will follow the curve –Ms, -Mr, +Ms. The loop

traced out is known as major hysteresis loop. This curve is symmetric about the origin. The area

contained in the hysteresis loop is the measure of the energy on taking the material through the

hysteresis cycle and is given by the formula: ∫= dMHW

There are two processes responsible for the hysteresis in ferromagnetic materials: domain wall

displacement and rotation. Rotation process is the intrinsic property of the material and is

independent upon the structure while domain wall displacement depends upon the structure. In

ferrites, the shape and area depends not only on the composition (intrinsic property) but it also

depends upon the porosity, size and shape of pores, and grain size (related to structure). Smith

reported magnetic properties of Ni0.5Zn0.5Fe2O4 and related coercivity (Hc) with porosity. In this

case, Hc increases with the increase of porosity. This linearity deviates at high values of porosity.

This deviation is related to the fact that higher porosity samples consist of smaller particles

which lead to greater coercive force. The hysteresis loop can be classified into four main types:

Normal loops, Rectangular loops, Perminvar loops, Isoperm loops.

The normal hysteresis loops is S-shaped and have remanence value 50-75 % of

saturation. Polycrystalline isotropic materials having no preferred direction possess this loop.

Ferrites having moderate permeability possess normal hysteresis loop. Those materials having

remanence value 80-100 % of saturation has rectangular Hysteresis loops. A very high

remanence value always found in the direction of easiest magnetization. It occur in those ferrite

materials which possess excessive crystal anisotropy. Rectangular loops can be induced in by

applying suitable external stress. Some ferrites exhibit spontaneous rectangular hysteresis loops

inspite of the fact that there is no stress anisotropy or no orientation of the of the crystallites.

Albers [22] fabricated Mg-Mn ferrites which show spontaneous rectangular hysteresis loop.

There is another class of ferrite which do not show rectangular loop initially but it can be

induced by other means. For example, remanence value can be raised in all ferrites by applying

mechanical stress. Some ferrites shows unusual shapes of hysteresis loop which can be changed

by heat treatment or by changes in the composition. The permeability of such materials remains

constant at low applied field with low hysteresis losses. Iron-rich ferrite composition exhibit

perminvar effect. At low temperature (-80 °C), this effect was observed in Mn-Zn and Ni-Zn

ferrites of low iron content [23]. In some ferrites, the change in permeability is very small with

increasing field strength. Guillaud et. al. observed isoperm loop in Mn ferrite whose remanence

was 10 % of the saturation value [20]. Isoperm ferrites usually have high initial permeability

particularly in Mn- Zn ferrite and are isotropic.

2.10 Overview of Ferromagnetic Resonance At very high frequencies, domain walls can not follow the field and the only remaining

magnetization mechanism is spin rotation within domains. This mechanism shows dispersion

which takes the form of resonance. The spins experience a torque when an external field is

applied. The response of spins is not instantaneous. Spins precess around the field direction for a

certain time (relaxation time) before adopting the field direction. The frequency of this

precession is given by the Larmor frequency. If an ac field is applied to the sample,

ferromagnetic resonance occurs. FMR experiment is performed by saturating the sample with

strong dc field and applying a small, perpendicular ac field at constant frequency. The dc field is

then slowly varied to achieve resonance conditions, measuring the power absorption in the

sample. Resonance is plotted as power absorption as a function of dc field, for a given constant

frequency [19].

The first resonance experiment was performed in 1946. Considerable progress toward a

complete understanding of relaxation progress has been made. This progress includes the

discovery of Anderson and Suhl of the portion of magnon spectrum degenerate with the uniform

precession. Many of the theoretical methods for treating relaxation problems were discussed by

various authors in the U.S.S.R. In Russia, work has been principally concerned with relaxation

frequencies averaged over a thermal distribution of magnons rather than the relaxation

frequencies of individual magnons [24].

2.10.1 The System of Units It is common to use Gaussian units (cgs units) rather than SI units when dealing with

magnetism. It is important to look at the magnetic flux density B in order to compare the units of

magnetic parameters in different system of units:

)( MHB oSI += μ

MHBcgs π4+=

The conversion to SI units is as follows

[ ] )(10.41 3 cgsOemAH SI

−== π

The unit of magnetization is Gauss:

[ ]GaussM 14 =π

2.10.2 The Magnetization Time Evolution Equation Electrons have both spin magnetic moment and orbital magnetic moment μr , which is

proportional to the spin Sr

moment. Usually the orbital magnetic moment is small compared to

the spin [25, 26]

Srr γμ =

γ is the gyromagnetic ratio of the electron:

cmeg

e2−=γ , where e being the charge and is the rest mass of the electron, c being the speed

of light and g being the Landé factor of the electron:

em

2≈g

Since the Bohr magneton is

cme

eB 2

h=μ

The gyromagnetic ratio of the electron is

hBg μ

γ −=

Numerically this is equal to 1117 .8.210.76.1 −−− −=−= OeMHzOeSγ

If magnetic field is applied to the sample, the spin magnetic moments will be parallel to this

field. If there is a perturbation from this situation, a torque

Hrrr

×= μτ

will be created, which will be equal to the time derivative of the angular momentum (spin) Sr

.

The time derivative of the spin magnetic moment can be written as

Htd

d rrr

×−= μγμ

which is the torque equation.

Due to exchange interaction between neighboring magnetic moments the spin magnetic moment

of adjacent atoms in a homogeneously magnetized sample prefer to be oriented in the same

direction.

One can summarize the resulting effect by using the magnetization ),( trM rr, which characterize

an ensemble of atoms in a small volume VΔ :

VVtrM V

V Δ=

Δ= Δ

Δ∑ μ

μr

rrr 1),(

The magnetization time evolution equation can be expressed in terms of the magnetization:

),(),(),( trHtrMtd

trMdeff

rrrrrr

×−= γ (2.19)

where is the total magnetic field, summarizing the the externally applied field and

internal fields in the sample. These internal fields in turn depend upon the magnetization. Hence

the magnetization time evolution equation 2.19 actually is non-linear equation for

),( trH effrr

Mr

and does

not contain any loss terms. But losses are very important to explain the FMR line width.

The magnetization and the total magnetic field have static (homogeneous) and dynamic (location

and time dependent, exerted by microwave radiation) contributions. Usually the dynamic

contribution is much smaller than the static one and varies harmonically.

0),();,(),( MtrmtrmMtrM o

rrrrrrrr∠∠+=

),(),(),( trHtrMtd

trMdeff

rrrrrr

×−= γ (2.20)

where is the total magnetic field, summarizing the externally applied field and internal

fields in the sample. These internal fields in turn depend upon the magnetization. Hence the

magnetization time evolution equation does not contain any loss terms. But losses are very

important to explain the FMR linewidth.

),( trH effrr

The magnetization and the total magnetic field have static (homogeneous) and dynamic

(location and time dependent, exerted by microwave radiation) contributions. Usually the

dynamic contribution is much smaller than the static one. The dynamic contribution varies

harmonically.

0),();,(),( MtrmtrmMtrM o

rrrrrrrr∠∠+=

0),();,(),( HtrhtrhHtrH oeff

rrrrrrrr∠∠+=

For the dynamic contributions lower case letters are used.

( )hmHmhMHM

hHmMtd

trMd

oooo

oo

rrrrrrrr

rrrrrr

×+×+×+×−=

+×+−=

γ

γ )()(),(

For low power microwave radiation the last term hmrr

× can be neglected. This approximation is

called small signal limit.

At static equilibrium

0=× oo HMrr

One can introduce a coordinate system, in which magnetization at static equilibrium points in the

z-direction. In the small signal limit, the deviation from this situation is very small and can be

neglected. This results in zMM So)r

= .

oS MMr

=

is a conserved quantity, i.e. the length of the static magnetization vector does not change.

)(),(oS HmhzM

tdtrMd rrr)

rr

×+×−= γ

Due to the condition of static equilibrium

zHH zo)r

=

)(),( mHhMztd

trmdzSrr)

rr

−×−= γ

or

)),(),((),(

trhMtrmHtd

trmdySyz

x rrrr

−−= γ (2.21)

)),(),((),(

trhMtrmHtd

trmdxSxz

y rrrr

−−= γ (2.22)

2.10.3 Ferromagnetic Relaxation

The power absorbed by the sample is limited due to microwave losses. This process is

called ferromagnetic relaxation. If these losses are present, Eq. 2.19 will not be valid any more.

Instead one has to add loss term:

lossestrHtrMtd

trMdeff +×−= ),(),(),( rrrrrr

γ (2.23)

This phenomenological approach will be discussed for uniform-mode relaxation.

It would be very complicated to explicitly include all causes of damping in the magnetization

time evolution equation as a sum of various terms. However they can be summarized by some

phenomenological models. Doing this, some parameters that can be determined experimentally,

account for the amount of losses.

2.10.4 Gilbert Damping Model Aphenomenological model of ferromagnetic relaxation has been proposed by Gilbert

[27]. If there is a driving force and damping in a physical system, the damping force will

counteract the driving one.

In the Gilbert model, the damping force is proportional to the rate of change of the

magnetization, which is the macroscopic dynamical variable in the magnetic system. This is

analogous to the mechanical damping in a viscous medium, which depends upon the velocity.

This is taken into account by a damping field that reduces the actual magnetic field to a field

dttrMd

MtrH

S

Geff

),(),(rr

rr

γα

− or

+×−= ),(),(),( trHtrMdt

trMdeff

rrrrrr

γdt

trMdM

trM

S

G ),()( rrrr

×α (2.24)

Gα is the Gilbert damping parameter, which is material-dependent constant.

This model is capable of describing intrinsic damping.

2.10.5 Landau-Lifshitz Model Landau-Lifshitz developed another model of ferromagnetic relaxation, according to

which the loss terms in Eq. 2.24 is proportional to the component of the magnetic field that is

perpendicular to the magnetization.

[ ]),(),(),(),(),(),( trHtrMtrMM

trHtrMdt

trMdeff

S

LLeff

rrrrrrrrrrr

××−×−=α

γγ

LLα is the Landau-Lifshitz damping parameter, the above equation can be cast into

dttrMdtrM

MtrHtrM

dttrMd

S

LLeffLL

),(),(),(),()1(),( 2rr

rrrrrrrr

×+×+−=α

αγ (2.25)

2LLα is usually a very small number, hence it can be ignored. In that case the Landau-Lifshitz

model will become equivalent to the Gilbert damping model, describing intrinsic ferromagnetic

damping in thin metal films.

One can approximate

ααα ≈≈ GLL

Thus this ferromagnetic damping parameter will be calledα .

2.10.6 Other Ferromagnetic damping Models Bloembergen and Wang [28] developed a model, according to which the relaxation of the

transverse components of the magnetization are independent from one of the longitudinal

component. These relaxations are characterized by the relaxation times T1 and T2. According to

this model the magnetization relaxation is described by the Bloch equations. That is why it is

called the Bloch-Bloembergen model.

2

)()(

)( ),()),(),((

),(T

trMtrHtrM

dttrMd yx

yxeffyx

rrrrr

rr

−×−= γ

1

)),(),((),(T

MMtrHtrM

dttrMd Sz

zeffz −

−×−=rrrrrr

γ (2.26)

The length of the magnetization vector is not conserved in this model.

If the condition

),(.),(),().,(),(

1

2

trHtrMtrHtrMtrHM

TT

eff

effeffSrrrr

rrrrr−

=

is fulfilled, the length of the magnetization vector will stay constant.

),(.),(),(),((),(1),(),((

),(

2 trHtrMtrHtrMtrM

TtrHtrM

dttrMd

eff

effeff rrrr

rrrrrrrrrr

rr××

−×−= γ (2.27)

which is equivalent to the Landau-Lifshitz model with a field dependent α .

References [1] E.C. Snelling, “Soft Ferrites Properties and Applications”, Second Edition,

Butterworths, London (Chapter 1).

[2] B.D. Cullity, “Introduction to magnetic materials”, Addison-wesley publishing

company, 1972 p. 493.

[3] Alex Goldman, “Modern Ferrite Technology”, 1990: Van Nostrand Reinhold, New

York. p. 21, 15.

[4] B. Viswanathan, V.R.K. Murthy, Ferrite Materials Science and Technology, Narosa

publishing company, 1990. p. 2.

[5] Wohlfarth, P.E., “Ferromagnetic Materials”, A handbook on the properties of

magnetically ordered substances, 1982, North-Holland Publishing Company.

[6] J. Smith, H.P.J. Wijn, “Ferrites”, 1959: John Wiley & Sons, New York, p.228

[7] E. J. W. Verwey, J. H. van de Boer, Rec. trav. Chim. Pays Bas, 55, 531-540 (1936).

[8] Guillaud, C., and Bertrand, R. J. Rech. 11 (1950) 73-82.

[9] Long Wu, Tien-Shou, Chung-Chuang Wei, J. Phys. D: Appl. Phys, 13 (1980) 259-

266.

[10] G. H. Jonker, J. Phys. Chem. Solids 9 (1959) 165.

[11] H. Frohlich, F. Seitz. Phys. Rev. 79 (1950) 526-527.

[12] R. Manjula, “Ferrite Materials”, Narosa Publishing House, New Delhi. P. 30

[13] L. Landau, J. Phys. Z. Sowjetunion 3 (1933) 664-665

[14] S. F. Mansour, Egypt. J. Solids, 28 (2005) 263-273.

[15] R.G. Kharabe, R.S. Devan, C.M. Kanamadi, B.K. Chougule, Smart Mater. Struct. 15

(2006) N36-N39.

[16] D. Ravinder, A. Chandrashekhar Reddy, Materials Letters 57 (2003) 2855-2860.

[17] Gorur G. Raju, “Dielectric in Electric Fields”, Marcel Dekker. Inc. Newyork. (2004). [18] B. Taeev, “Physics of Dielectric Materials”, Mir Publishers (1979).

[19] Raul Valenzuela, “Magnetic Ceramics”, 1994: Cambridge University Press, p-113,

114, 98, 106, 116, 121, 138.

[20] Dr-Ing. Carl Heck, “Magnetic Materials and their Applications”, Butterworth & Co

(Publishers) Ltd. (1974). P.17, 16, 18, 158

[21] K.J. Standley “Oxide Magnetic Materials”, 2nd edition, Clarendon Press, Oxford

(1972) p. 90, 92, 46.

[22] Elbers-Schoenberg, E. Ceram. Bull 35 (7) (1956) 276-279.

[23] Kornetzki, Perminvarferrite. ETZ-A 80 (17) (1959) 605-609.

[24] Marshall Sparks: Ferromagnetic relaxation Theory, Mcgraw-Hill company, New

York, pp. 1.

[25] 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.

[26] B. Lax and K. Button, “Microwave Ferrites and Ferrimagnetics”, McGraw-Hill

(1962).

[27] T. L. Gilbert, IEEE Trans. Magn. 40 (2004) 2443.

[28] N. Bloembergen, S. Wang, Phys. Rev. 93 (1953) 72.

Chapter 3 Fabrication and Characterization Techniques

3.1 Sample Preparation

3.1.1 Standard Ceramic Method

Three series of yttrium substituted Ni-, Mg- and Ni0.6Zn0.4- ferrites with chemical

formulas NiY2xFe2-2xO4, (x = 0.0 – 0.12, step: 0.02), MgY2xFe2-2xO4 (x = 0.0 – 0.12, step: 0.02)

and Ni0.6Zn0.4Y2xFe2-2xO4 (x = 0.0-0.1, step: 0.02) were fabricated in a polycrystalline form by

double sintering ceramic method in air atmosphere keeping in view their valances for

maintaining the charge neutrality. The weight percentage of various oxides was calculated using

the following chemical reactions.

42223232 )1( OFeYMgOFexOYxMgO xx −→−++

42223232 )1( OFeYNiOFexOYxNiO xx −→−++

42224.06.03232 )1(4.06.0 OFeYZnNiOFexOYxZnONiO xx −→−+++

The weight percentage (wt %) of each composition was calculated by using the following

relation:

ncompositiorequiredofweightMolecularsampleofweightquiredoxidesofweightMolecularoxidesofWeight Re% ×

=

The starting materials were AR grade oxides Fe2O3 (99.90%), Y2O3 (99.99%), NiO (99.99%),

ZnO (99.99%) and MgO (96%) supplied by E Merck and Aldrich. The oxides were wet milled

for three hours according to their stoichiometric proportion to promote better mixing of raw

materials. The fine dry powder was presintered at 900 °C for 24 hours and cooled slowly in the

furnace. The mixture was milled again for three hours to obtain a homogeneous material.

Polyvinyl alcohol was used as a binder. The mixture with 5 % polyvinyl alcohol was pressed into

pellets under pressure of 4 tons/in2. MgY2xFe2-2xO4 were finally sintered at 1240 °C for 8 hours,

NiY2xFe2-2xO4 were finally sintered at 1225 °C for 8 hours, and Ni0.6Zn0.4Y2xFe2-2xO4 were

finally sintered at 1200°C

for 8 hours. All the three series were left in the furnace after final sintering in order to slowly

cool to room temperature.

For FTIR analysis, 0.1 mg sample powder and 0.99 mg of potassium bromide (KBr)

powder were mixed and dried in an oven at 105 °C for 20 hours. Using a pestle and mortar, the

powder was mixed for three minutes. The powder was then pressed into discs of approximately

1mm thick under the pressure of 4 tons/in2. A pure KBr disc was prepared as a reference sample

in order to eliminate the background from the spectrum.

The sample in the form of toroid was used for permeability measurement. The toroid was

covered with electrically insulating cellophane tape and then it was wound with 22 equally

spaced turns of insulated copper wire. After that, it was wound again with the cellophane tape.

The two extended wires of the wound sample are connected in a die-cast box by soldering.

Sintering is a critical step in processing of ferrites. It is defined as the process of

obtaining fully dense materials by reduction of porosity. During sintering powder does not melt

but particles joined together. As a result, reduction of porosity occurred by atomic diffusion in

the solid state. The driving force for sintering is the reduction in surface free energy of the

powder [1] and the part of this energy is utilized into the formation of grain boundaries in the

resulting polycrystalline samples. It is known that reduction in surface free energy promote

atomic diffusion process that lead to densification by transport of matter from grain boundaries

into pores. In solid sate sintering, the material is in a solid phase during the whole process.

Sintering process can be divided into three stages. In first stage, shrinkage occurs. The contact

area between particles increases by surface diffusion. Grain boundaries began to form at the

interface between the particles. In second stage, porosity changes from open to closed pores. The

most of densification occurred during this stage.

3.1.2 Co-precipitation method Co-precipitation method was used to prepare Co-Zn-Y Ferrites with chemical

formula ZnxCo1-xY0.15Fe1.85O4 (x = 0.0-0.1, step: 0.02). The flow chart showing the preparation

steps is shown in Fig.3.1. The chemical used in the synthesis of samples were FeCl3, ZnCl2,

CoO4C4H6.4H2O, Y2O3, NaOH and Na2CO3. All chemicals were of

analytical grade. The amounts of the constituents for the mixtures according to stoichiometric

calculations are given in table 3.1. All the chemicals were soluble in deionized water except

Y2O3 which was made soluble by using small quantity of HCl and heated up to 70 °C. In order to

obtain the desired compositions, the solution of the required concentrations were prepared by

dissolving stoichiometric amounts of FeCl3, ZnCl2, CoO4C4H6.4H2O, NaOH and Na2CO3 in

deionized water. These solutions of desired compositions were mixed in a beaker. Solution of

NaOH and Na2CO3 were dropped slowly into the former solution. The brown precipitates formed

by pouring the solution of NaOH and Na2CO3. The prepared solution was mechanically stirred

for three hours. The pH was found to be around 10. The precipitates were settled down and

filtered by a filter paper placed on a suction flask operating on a water pump. These precipitates

were also contained sodium and chloride ions. These precipitates were thoroughly washed with

deionized water until the precipitates were free from sodium and chloride ions. The solution was

tested by adding few drops of AgNO3. The removal of sodium and chloride ions were confirmed

if no precipitates occur by adding drops of AgNO3. The product was dried in furnace at 90 °C for

10 hours to remove water contents. The dried precipitates were mixed homogeneously in an

agate mortar and pestle for 30 minutes. The load of 25 KN was applied on each sample for 4

minutes using Paul-Otto Weber Hydraulic Press. The pellets were pre sintered in digital electric

furnace at temperature 550 °C for 5 hours followed by furnace cooling. The final sintering was

carried out at 1150 °C for 8 hours followed by furnace cooling.

Table 3.1 Stoichiometric calculations for wet method

Stoichiometric

composition of

ZnxCo1-xY0.15Fe1.85O4

Chemical Weight

(g)

Molecular Weight

(g/mol)

X = 0.0

NaOH 3.3068 40.00

Na2CO3 4.3814 105.99

C4H6CoO4.4H2O 5.1481 249.09

FeCl3 6.2016 162.2

Y2O3 0.7 225.8

X = 0.2

NaOH 3.3068 40.00

Na2CO3 4.3814 105.99

C4H6CoO4.4H2O 4.1184 249.09

FeCl3 6.2016 162.2

Y2O3 0.7 225.8

ZnCl2 0.5634 136.29

X = 0.4

NaOH 3.3068 40.00

Na2CO3 4.3814 105.99

C4H6CoO4.4H2O 3.088 249.09

FeCl3 6.2016 162.2

Y2O3 0.7 225.8

ZnCl2 1.1266 136.29

X = 0.6

NaOH 3.3068 40.00

Na2CO3 4.3814 105.99

C4H6CoO4.4H2O 2.059 249.09

FeCl3 6.2016 162.2

Y2O3 0.7 225.8

ZnCl2 1.69 136.29

X = 0.8

NaOH 3.3068 40.00

Na2CO3 4.3814 105.99

C4H6CoO4.4H2O 1.0296 249.09

FeCl3 6.2016 162.2

Y2O3 0.7 225.8

ZnCl2 2.2534 136.29

X = 1.0

NaOH 3.3068 40.00

Na2CO3 4.3814 105.99

FeCl3 6.2016 162.2

Y2O3 0.7 225.8

ZnCl2 2.8168 136.29

ZnCl2 Y2O3 FeCl3

Deionized water

Na2CO3 NaOH

Deionized water HCl + 70 °C

CoO4C4H6.4H2O

NaOH + Na2CO3

Drops Solution, RT °C

Dried in furnace At 110 °C for 10 hours

Filtration and wash until all Chlorides are eliminated

Suspension stirrer 3 h (precipitates)

Sintering

Grinding

Characterization

Fig.3.1 Flow chart for co-precipitation method.

CoFe2O4 + x Y2O3 with x = 0, 1 wt %, 3 wt %, 5 wt % have been synthesized. Co-

precipitation method was used to prepare CoFe2O4. The chemical used in the synthesis of

samples were FeCl3.6H2O, CoO4C4H6.4H2O, Y2O3, NaOH and Na2CO3 of analytical grade

having 99.99 % purity. The amounts of the constituents for the mixtures according to

stoichiometric calculations are given in table 3.2. All the steps mentioned for the preparation of

Co-Zn ferrites have been followed except final sintering was carried out at 1100 °C for 8 hours.

Yttrium Oxide (1 wt %, 3 wt % and 5 wt %) was added in CoFe2O4. Each sample was ground for

two hours in agate and mortar. Final sintering was carried out at 1100 °C for 8 hours.

Table 3.2. Stoichiometric calculations for wet method Stoichiometric Composition

Chemical formula

Weight (g)

Molecular Weight (g/mol)

CoFe2O4

NaOH 1.98 40.00

Na2CO3 5.247 105.99

C4H6CoO4.4H2O 4.1098 249.09

FeCl3.6H2O 8.9199 270.32

3.2 Characterization Techniques Different characterization techniques were used in order to explore the properties of

ferrite samples. The physical, structural, magnetic, electrical, and dielectric properties were

investigated in order to realize the characteristics of MgY2xFe2-2xO4, NiY2xFe2-2xO4, and

Ni0.6Zn0.4Y2xFe2-2xO4 ferrites. The several techniques were used for this work are discussed as

follow.

3.2.1 X-ray Diffraction (XRD) In 1912, the phenomenon of X-ray diffraction by crystals was discovered provided new

techniques for studying fine structure of matter. Diffraction can indirectly show the details of

internal structure of the order of 10-8 cm [2] in size. XRD measurements are taken on ferrite

samples using a Philips X’ Pert X-ray Diffraction machine with PC-APD diffraction software.

XRD was performed over 2θ range of 20-70°. X-ray patterns were taken using using a CuKα

radiation having wavelength of 1.540562 A°. Typical conditions for XRD measurements are

listed in Table 3.1:

Table 3.1: XRD parameters

Filter Nickel

Target Copper

Voltage 40 KV

Tube Current 35 mA

Scanning Range 20-70°

Diffraction is a scattering phenomenon. A diffraction beam is defined as a beam made of two or

more scattered waves mutually reinforcing each other [2]. Consider a parallel, monochromatic

beam of x-rays falls upon a crystal at an angle θ with a family of Bragg planes whose spacing is

. The atoms act as scattering centers. The scattering radiation occurs in all directions. The

scattering is strong in few directions which satisfy the Bragg law. This can be stated

mathematically using Bragg’ s law[2] :

d ′

θλ sin2 dn ′= (3.1)

where is interplanar spacing. d ′The lattice constant ‘ a ’ can be obtained from the following equation [3]:

222222

sin2lkhlkhda ++=++′=

θλ

(3.2)

where is a planar spacing and d ′ lkh ,,

a

are miller indices of cubic planes being

considered. The value of lattice parameter ‘ ’ is subjected to a number of systematic errors

which may originate from the inaccurate measurement of line position, X-ray absorption, and

sample being off centred. In 1945, Nelson and Riley analyzed the various sources of errors and

showed that collectively these errors vary according to the following equation:

)cossin

cos(22

θθ

θθ+=

Δ Kdd

(3.3)

The bracketed terms are called Nelson and Riley function [2]. The lattice constant ‘a ’ for

each composition was found by plotting ‘a ’ against the Nelson and Riley function and

extrapolating this line to a-axis. In this way, the more accurate value of lattice constant was

obtained.

The X-ray densities (Dx) were computed from the values of lattice parameter using the formula

[4].

3

8Na

MDx = (3.4)

Fig. 3.2 Line broadening of XRD patterns due to particle size effect.

where M is a molecular weight, N is Avogadro’ s number and ‘ a ’ is the lattice parameter of

the sample.

In 1918, Scherrer formulate an equation [2] which is used to estimate the grain size. He

discovered that the half width of the peak ( 2/1β ) in terms of diffraction 2θ (measured in radians)

as shown in Fig 3.2.

θβλ

cos9.0

2/1

=t (3.5)

where ‘ t ’ is the grain size and 2/1β is the full width half maximum of the (311) peak.

3.2.2 Scanning Electron Microscopy (SEM) Scanning Electron Microscopy is used to investigate surface morphological distinctive

characteristics about the size, shape, and arrangement of particles on the surface of the specimen.

In SEM, electron beam is scanned across the sample’s surface. A number of signals are

generated when a focused beam of electrons hit the specimen surface due to interaction of

primary electron with metal. These signals are recorded by the detector which provides

information about the surface of the sample or its chemical content. SEM has two major

improvements over optical microscope: The picture magnetization can be enhanced from X1000

to X2000 up to X30,000 to X60,000 and it also improves the depth of resolution by a factor of

approximately 300.

In SEM, electron beam incident upon a small spot and as a result electron ejects out of

the surface of the sample. These electrons are known as secondary electrons. These low energy

secondary electrons have a small mean free path. Therefore, the information is coming from a

depth of approximately 10 nm. The signal of backscatter electron detector is formed by

scattering of primary electrons owing to interaction between nucleus of an atom of the specimen

and beam of primary electrons. The intensity of the backscatter electron increased with the

increase of atomic number and hence signal contains information about the chemical

composition.

JEOL JSM-840 scanning electron microscope was used in this study which is configured

with secondary and backscattered electron detectors as well as an energy dispersive X-ray

spectrometer. The accelerating voltage is 3-35 KV with resolution of 4nm.

3.2.3 Bulk Density Measurement The bulk density of each sample has been measured using the Satorius Determination Kit.

Arcimedean principle was applied for determining the bulk density. Each sample was immersed

in toluene and was exposed to the force of buoyancy. The bulk density of all samples under

investigation was determined by using the following relation:

weightofLosstolueneofdensityairinsampletheofWeightD ×

=

WtWa

Wa t

−×

=ρ

(3.6)

where Wa is the weight of the sample in air, Wt is the weight of the sample in toluene and tρ

is the density of the toluene.

The percentage porosity of each sample was determined by using the following equation:

%1001 ×⎟⎟⎠

⎞⎜⎜⎝

⎛−=

xDDP (3.7)

The ratio of physical density and X-ray density which is being subtracted from unity gives

porosity in the samples. It is multiplied by 100 in order to yield percentage porosity. The

physical density is always smaller than X-ray density due to the presence of pores.

3.2.4 DC Resistivity DC resistivity was measured by two probe method. A sample holder equipped with two

electrodes made up of copper, with effective area of 0.95 cm2 was used for the resistivity

measurements. Silver paste was used on both surfaces of each sample to obtain good ohmic

contact. A sensitive Electrometer model 610 Keithley and dc power supply was connected in

series with the sample holder. One can measure the corresponding current by varying the voltage

from power supply. The resistance of each sample was calculated by using the following

relation:

tAR

=ρ (3.8)

where R is the resistance of the sample, A is the area of electrode in contact with the sample and

t is the thickness of the sample. There was no concern about the contact resistance. The pressure

contacts were used. The behavior of the samples was ohmic up to 200 °C. Temperature

dependent dc resistivity was measured by inserting the sample holder in a small furnace

equipped with alumal-chromel thermocouple. The temperature was varied with the step of 10 °C

and the corresponding current was measured on Electrometer with fixed 10 V applied across the

sample. Then the gradient of the plot of Log ρ Vs 1000/T gives the activation energy.

3.2.5 Dielectric Properties The high frequency impedance has been measured by using the Solartron 1260

Impedance Analyser. The analyzer was connected to the computer with GPIB interface SMART

(Solartron Materials & Research) version 1.2 software controlled whole operation. The analyzer

saved the data as real, imaginary, and magnitude of impedance in ohms. In this work, dielectric

properties have been studied over the frequency range from 100 Hz to 10 MHz. The values of

dielectric constant (ε ′ ) and dielectric loss tangent (tan δ) was determined using the formula:

δεεε

ε

tan′=′′

=′oAtC

(3.9)

where oε is an electrical constant known as permittivity of free space, C is the capacitance of the

sample, t is the thickness of the sample and A is the area of the sample, ε ′′ is the complex

dielectric constant.

3.2.6 Vibrating Sample Magnetometer (VSM) VSM is one of the most capable instrument which is devised to measure and characterize

magnetic materials. The principle of this technique is based on Faraday’s law of induction. i.e.

the changing magnetic field will produce an electric field:

Edtd

−=Φ

where dtdΦ

is the rate of change of magnetic flux and E is the induced voltage.

This electric field E can be measured which give information about the changing magnetic

field. It is usually calibrated with standard Nickel specimen of known magnetic moment. The

sample to be studied is placed within suitably pick up coils in a costant magnetic field and is

made to under go mechanical motion. The constant magnetic field will magnetize the sample.

The magnetized sample will create magnetic field around it. This magnetic field will become

time varying owing to the up and down vibration of the sample and can be sensed by the pick-up

coils. According to Faraday’s law of induction, the time varying magnetic field will induce an

electric field (current) in pick-up coils. This current will be directly proportional to the

magnetization of the sample which is amplified by the lock-in amplifier. By using computer

interface, the apparatus will tell us

Fig.3.3 Schematic diagram of Vibrating Sample Magnetometer.

about the magnetization of the sample. A plot of magnetization (M) versus applied field (H) is

generated.

The VSM consist of following parts:

Water cooled electromagnet amplifier Power supply Vibrator Sample holder

Pick-up coils Lock-in amplifier Control chassis Computer interface.

The water cooled electromagnetic with power supply generate applied field H. The

sample holder is attached to vibrator which moves the sample up and down at a set frequency

(usually less than 100 Hz). The sample produces induced emf (alternating current) in pick-up

colis at the same frequency set for sample vibration. This current will give information about the

magnetization of the sample. Amplifier will amplify the signal created by pick-up coils. Control

chassis control the oscillations of the vibrator. Lock-in amplifier is tuned to pick-up only signals

at the vibrating frequency which eliminates noise from the environment. Fig.3.3 shows the

schematic diagram of Vibrating Sample Magnetometer.

3.2.7 Impedance Analyser The high frequency impedance was measured by using solartron 1260 Impedance

Analyser. The troidal shaped samples as shown in Fig. 3.4 were connected to the analyzer by

connecting wires. The high frequency impedance was measured by using two probe methods.

The analyzer was connected to the GPIB interface. The whole operation was controlled by

Solartron Materials Research & Test (SMART) version 1.2 software. Solartron 1260 Impedance

Analyser saved data as real, imaginary and magnitude of impedance in ohms. The permeability

has been calculated from real and imaginary parts of the impedance over the frequency range

from 0.1 KHz to 1 MHz. These values are then used to determine the values of real and apparent

permeability. The toroidal shaped sample was covered with cellophane tape and then it was

wound with 22 equally spaced turns of copper wire (30 SWG). After that the sample was

covered again with the cellophane tape to wind the wire tightly with the sample. The two

extended wires of the toroidal sample were connected in a die-cast box by soldering. This box

was finally connected with the Impedance analyzer to measure the impedance. Fig. 3.4 shows the

diagram of the toroid.

(a) (b)

Fig. 3.4 (a) Schematic diagram of toroid sample which is wound with copper wire and (b)

dimension of toroid sample.

3.2.8 Ferromagnetic Resosnance (FMR) FMR experiments were performed at room temperature using a standard spectrometer

operated at 9.45 GHz. The TE102 mode rectangular reflection cavity was used. The first

derivative dHdP

of the power absorption “ P ” was recorded as a function of the applied field (H).

The reference resonance field with X-band spectrometer at 9.45 GHz was γω

=refH = 3.375

KOe where γ is the gyromagnetic ratio of free electrons. The resonance field can be defined as

the field for which dHdP

= 0. The distance PPHΔ between the bounding peaks of the first

derivative of the absorption line define the FMR linewidth. The samples were put in a small

quartz tube and held in the cavity. DC field was applied in parallel configuration to the sample

and perpendicular to the high frequency AC field. The FMR line width is determined by

monitoring the reflected wave in a cylindrical cavity working at 9.45 GHz. The sample is always

saturated owing to static magnetic field in ferromagnetic resonance measurements. FMR can be

thought as a spin rotation process occurring during the magnetic saturation.

3.2.9 Initial Permeability ( iμ )

It is the property of the magnetic materials which refers to the ease with which a material

can be magnetized. It is the measured permeability of the material with nearly zero applied field.

It would be resolved into two types of mechanisms, such as contribution from the domain wall

motion [5] and contribution from spin rotation. It was reported [6] that domain wall component

starts to decrease at lower frequencies and spin rotational components remains active in higher

frequencies region. iμ was calculated using the formula [7, 8]

⎟⎠⎞

⎜⎝⎛

=

rRhN

L

o

i

ln

22 μ

πμ (3.10)

where L is the inductance, N is the number of turns of inductor, h is the height of toroid, R and r

are the outer and inner radius of the toroid, and oμ is the magnetic permeability of vacuum. In

this report, samples have been characterized up to 1 MHz due to limitation of the formula used

for determining initial permeability. An inductor of ferrite material has self resonance in

frequencies more than 1 MHz. Therefore, it is necessary to make measurements up to 1 MHz [9].

References [1] Raul Valenzuela, “Magnetic Ceramics”, Cambridge University Press 1994. p. 62.

[2] Cullity, D.B., “Elements of X-ray Diffraction”, second ed. 1977: Addison- Wesley

publishing company, p. 3, 84, 102, 356.

[3] William F. Smith, “Principles of Materials science and Engineering”, P-90, Mcgraw-

Hill, Inc.

[4] K.B.Modi, J.D. Gajera, M.C. Chhantbar, K.G. Saija, G.J. Baldha, H.H. Joshi,


[5] Naito, Y. in Proc. 1st Int. Conf. on Ferrites. 1970.

[6] Nakamura, T., J. Magn. Magn. Mater. 168 (1997) 285-291.

[7] Mamata Maisnam, Sumitra Phanjoubam, H.N.K. Sarma, L. Radhapiyari Devi, O.P.

Thakur, Chandra Prakash Physica B 352 (2004) 86-90.

[8] Dr. moIng. Carl Heck, “Magnetic Materials and their Applications”, London

Butterworths p. 30.

[9] A.C. Razzitte, S.E. Jacobo, W.G. Fano, Journal of Applied Physics 87 (2000) 6232-

6234.

CHAPTER 4

Results and Discussions According to the procedure described in Chapter 3, following five series of ferrites were

prepared: 1. NiY2xFe2-2xO4, x = 0.0 – 0.12, step: 0.02

2. MgY2xFe2-2xO4, x = 0.0 – 0.12, step: 0.02

3. Ni0.6Zn0.4Y2xFe2-2xO4, x = 0.0 - 0.1, step: 0.02

4. Co1-xZnxY0.15Fe1.85O4, x = 0.0 – 1.0, step: 0.2

5. CoFe2O4 + x Y2O3, x = 0 wt %, 1 wt %, 3 wt %, 5 wt %

These samples were characterized for structural analysis by X-ray diffraction (XRD),

Scanning Electron Microscopy (SEM) and Fourier Transform Infrared spectroscopy (FTIR). For

electrical transport properties, electrical resistivity and dielectric measurements were carried out.

For magnetic properties, initial permeability and Ferromagnetic resonance (FMR) was measured.

The M-H loops of each composition were obtained. Now we will present in the following pages,

the results and discussion about each series.

4.1 NiY2xFe2-2xO4 ferrite series 4.1.1 X-ray diffraction Analysis

X-ray diffraction patterns of NiY2xFe2-2x O4 series samples were obtained over the 2θ

range of 10-70o, using Philips X’ Pert analytical diffractometer with Cu Kα1 radiation. X-ray

diffraction patterns of NiY2xFe2-2x O4 (x = 0.0, 0.02, 0.04, 0.06, 0.08, 0.1, 0.12) ferrite system are

shown in Fig. 4.1. All the samples show good crystallization, with well-defined diffraction lines.

For x ≤ 0.06, the samples produced eight well defined diffraction peaks. The presence of the

strong diffraction peaks corresponding to the planes (111), (220), (311), (222), (400), (422),

(511/333), (440) indicates the presence of cubic spinel phase. While, for x ≥ 0.08, the samples

showed nine well defined diffraction peaks that is one more than the above mentioned samples.

The extra peak is, but well defined and appeared at 2θ = 33.1o (indicated by * in Fig. 4.1). The

intensity of this peak increases with the increase of yttrium concentration. On the basis of one

peak it is not possible to identify the unknown phase. However, it can only be speculated. This

peak can be identified as the (1 2 1) reflection of the FeYO3 phase (Iron Yttrium Oxide) matched

with ICDD PDF # 39-1489. The secondary phase on the grain boundaries appears due to high

reactivity of Fe3+ ions with Y3+ ions [1]. Miller indices (hkl) and interplaner spacing (dhkl) for

NiY2xFe2-2xO4 ferrites are listed in table 4.1.

Fig. 4.1 X- ray diffraction patterns for NiY2xFe2-2xO4 (0 ≤ x ≤ 0.12), * indicate

YFeO3 peak.

4.1.1.1 Lattice Parameters

The average lattice constant ‘a ’ for each composition was found by plotting it against the

Nelson and Riley [2] function. The composition of the phases precipitated, the lattice constants

and other physical properties of this series are listed in table 4.2. A slight increase in the values

of the lattice constant ( a ) is noted for all the compositions. The variation can be explained on the

basis of difference in ionic radii of the substituted ions. It is assumed that the replacement of the

smaller Fe3+ ions (0.64 Å) with larger Y3+ ions (0.95 Å) causes an expansion of the host spinel

lattice which results in the increase of lattice constant. This observation is consistent with the

results reported by various authors where it has been reported that the substitutions of yttrium

ions increases the lattice constant [3, 4]. The lattice parameter for biphasic samples still increases

with yttrium contents which enables us to conclude that the spinel lattice is not compressed by

secondary phase. Thus, it may be concluded that, there is no solubility limit for yttrium ions

(rare-earth transition metal) in Ni ferrite in the given range (0 ≤ x ≤ 0.12). Such observation in

the lattice constant in rare-earth substituted ferrites has been reported by Hemeda et. al. [5] in

case of NiGdxFe2-xO4.

4.1.1.2 Bulk Density, X-Ray Density and Porosity From the lattice parameter value “a”, we also calculated the X-ray density (Dx) using the relation

[6].

3

8aNMDX = (4.1)

Where 8 represents the number of molecules in a unit cell of spinel lattice [6], M is the

molecular weight of the sample, “a” is the lattice constant and N is the Avogadro’s number. The

physical density was measured using a Sartorius density determination kit. The Archimedean

principle was applied and liquid toluene was used. The physical density (Dp) and percentage

porosity (P) was computed using the equation mentioned in ref. [7].

Table 4.1 Miller indices (hkl) and interplanar spacing (d) for NiY2xFe2-2xO4 (0.0 ≤ x ≤

0.12).

S.No hkl x = 0.0

d(Å )

x = 0.02

d(Å )

x = 0.04

d(Å )

x = 0.06

d(Å )

x = 0.08

d(Å )

x = 0.1

d(Å )

x = 0.12

d(Å )

1 111 4.807 4.802 4.804 4.804 4.802 4.801 4.807

2 220 2.944 2.942 2.944 2.943 2.944 2.944 2.945

3 311 2.511 2.51 2.51 2.511 2.511 2.511 2.512

4 222 2.405 2.405 2.405 2.405 2.404 2.404 2.405

5 400 2.083 2.082 2.083 2.083 2.083 2.083 2.083

6 422 1.701 1.701 1.701 1.701 1.701 1.701 1.702

7 511/333 1.604 1.603 1.603 1.604 1.604 1.604 1.604

8 440 1.473 1.473 1.473 1.473 1.473 1.473 1.473

Table 4.2 Phases, lattice constant (a), X-ray density (Dx), physical density (Dp),

percentage porosity (P %) and grain size of the NiY2xFe2-2xO4 (0.0 ≤ x ≤ 0.12).

S.

N0.

Composition

(x)

Secondary

phase

Lattice

parameter

a(Å )

X-Ray

Density

(g/cm3)

Physical

Density

(g/cm3)

Percentage

Porosity

(P %)

Grain

Size(μm)

Scherrer

1 NiFe2O4 - 8.335 5.376 4.699 12.59 1.479

2 NiY0.04Fe1.96O4 - 8.336 5.405 4.828 10.68 1.302

3 NiY0.08Fe1.92O4 - 8.338 5.432 4.878 10.20 1.143

4 NiY0.12Fe1.88O4 8.339 5.469 4.924 9.980 1.038

5 NiY0.16Fe1.84O4 YFeO3 8.351 5.489 4.952 9.772 0.942

6 NiY0.20Fe1.80O4 YFeO3 8.362 5.502 4.994 9.235 0.916

7 NiY0.24Fe1.76O4 YFeO3 8.374 5.516 5.016 9.065 0.620

Table 4.2 presents X-ray density (Dx), physical density (Dp), percentage porosity (P %) and

average grain size of all the samples. The influence of yttrium concentration on X-ray density

(Dx), physical density (Dp) and percentage porosity are shown in Fig. 4.2. It is worth mentioning

that the values of X-ray density are higher than the physical density. This may be due to porosity

in the samples. X-ray density exhibits an increasing trend with yttrium contents as it mainly

depends upon the molecular weight of the samples. It increases from 5.376 to 5.516 g/cm3. The

physical density also increases with yttrium contents from 4.699 to 5.016 g/cm3 which is

attributed to the difference in atomic weight of Yttrium (88.90585 amu) and iron (55.845 amu)

as described in CRC book [8]. The formation of secondary phase (YFeO3) fills intergranular

voids and exhibit good densification. Therefore, a decrease in porosity can be expected with

yttrium contents. This is consistent with previous work as reported by Rezlescu et. al. [4] in case

of Mg0.5Cu0.5Fe2-xY3x/nO4 ferrite system.

0.00 0.02 0.04 0.06 0.08 0.10 0.12

4.7

4.8

4.9

5.0

5.1

5.2

5.3

5.4

5.5

Dx DP Porosity

Y-Concentration (x)

Den

sity

(g/c

m3 )

8

10

12

Porosity (%

)


Concentration (x) for NiY2xFe2-2xO4 (0 ≤ x ≤ 0.12).

4.1.1.3 Average Grain Size

The average grain size was estimated using the Scherrer formula [2] using FWHM of

(311) line. The average grain sizes calculated by Scherrer formula are listed in table 4.2. It

decreases with yttrium contents. It is an established fact that the grain growth depends upon the

grain boundary mobility. A possible reason for the decreasing trend of grain size is that the

increasing concentration of yttrium reduces the grain growth probably due to segregation on or

near the grain boundaries which hampers its movement.

The morphological features of the samples were studied using a JEOL JSM-840 Scanning

Electron Microscope. These micrographs exhibit the inhomogeneous grain size distribution. The

values of grain size obtained by SEM micrograph for three representative samples with x = 0.0,

0.08, 0.12 were 1.62 mμ , 0.997 mμ and 0.581 mμ respectively, which are comparable to the

values of average grain size obtained by Scherrer’s formula using XRD data. Few representative

SEM micrographs are shown in Fig. 4.3.

(a)

Fig. 4.3 SEM micrograph of NiY2xFe2-2xO4 ferrite: (a) x = 0.0. (b) x = 0.08 (c) x = 0.12

4.1.2 FTIR Analysis Fig. 4.4 shows FTIR spectra of all the samples. For all the samples, three absorption

bands were observed in the wave number range 370-1100 cm-1. The band positions for selected

compositions are tabulated in table 4.3. The absorption bands are in the expected range which

confirms the formation of the spinel structure. In spinel ferrites, the absorption band around 600

cm-1 ( 1ν ) is attributed to stretching vibrations of tetrahedral complexes and the band around 400

cm-1 ( 2ν ) is attributed to octahedral complexes. The higher frequency band 1ν (599-602 cm-1)

and lower frequency band 2ν (403-421 cm-1) are assigned to tetrahedral and octahedral groups

respectively. The higher frequency band 1ν is nearly constant for all investigated compositions.

The lower frequency band 2ν slightly shifts to higher frequency side and broadening of the

spectral bands is also observed with increasing yttrium contents. The broadening of the spectral

bands and shift in 2ν to higher frequency side may be attributed to the occupancy of yttrium ions

on octahedral (B) sites due to its higher atomic weight and larger ionic radius than iron ions

which affect Fe3+ - O2- distances on B sites. Similar observations were reported by Gadkari et.al.

[1] in case of Mg1-xCdxFe2O4 + 5% Y3+ ions. The absorption band 3ν is assigned to Fe2+ - O2-

vibration [5]. It can be seen from the table 4.3 that 3ν decreases with the increase of yttrium

contents. The decreasing trend of 3ν is attributed to the decreasing concentration of Fe2+ ions [5]

at octahedral sites. As the yttrium contents increases the concentration of Fe3+ ions gradually

decreases and thus the corresponding decrease of Fe2+ ions is expected along with which results

into the observed fall in the values of absorption band 3ν .

Table 4.3 FTIR absorption bands for NiY2xFe2-2xO4 (x = 0.0, 0.02, 0.04, 0.06, 0.08, 0.1)

ferrites.

S. No. Composition )1(1

−cmν )( 12

−cmν )( 13

−cmν

1 NiFe2O4 600 403 470

2 NiY0.04Fe1.96O4 599 405 465

3 NiY0.08Fe1.92O4 601 408 462.5

4 NiY0.12Fe1.88O4 599 412 457

5 NiY0.16Fe1.84O4 602 417 454

6 NiY0.20Fe1.80O4 602 421 443

Fig. 4.4 Typical FTIR spectra of NiY2xFe2-2xO4 ferrites: x = 0.0, 0.02, 0.04, 0.06, 0.08,

0.1. 1ν and 2ν indicate tetrahedral and octahedral absorption bands respectively.

4.1.3 Electrical resistivity The room temperature dc resistivities of NiY2xFe2-2xO4 was measured by two probe

method. The results as a function of Y- concentration are listed in table 4.4. It was found that the

resistivity increases with the increase of yttrium concentration from 4.85 ×106 to 7.48 ×108 Ω.

cm. Fig. 4.5 shows the variation of Log ρ Vs. Y-concentration for NiY2xFe2-2xO4 ferrites (x = 0.0,

0.02, 0.04, 0.06, 0.08, 0.1, 0.12). It has been reported that yttrium ions occupy octahedral sites

[9] owing to its large ionic radius. The concentration of Fe3+ ions gradually decreases at B-sites

when yttrium is substituted in place of iron. The hopping rate of electron transfer will decrease

with the decrease of Fe3+ ions concentration. Consequently, it enhances the dc resistivity with the

increase of yttrium concentration. Another possible reason for increase in resistivity on

increasing yttrium is due to the fact that the occupation of yttrium ions at B-sites will increase

the separation between Fe3+ and Fe2+ ions in proportion to its ionic radius. It obstructs the

movement of electron transfer between ferrous and ferric ions and hence increases the resistivity

and activation energy. These results are consistent with the results reported by different authors

[10, 11].

6.6

7.1

7.6

8.1

8.6

9.1

0 0.02 0.04 0.06 0.08 0.1 0.12

Y-concentration (x)

Log ρ

(ohm

.cm

)

Fig. 4.5 Variation of room temperature resistivity Vs. Y-concentration for NiY2xFe2-2xO4

ferrites (x = 0.0, 0.02, 0.04, 0.06, 0.08, 0.1, 0.12).

Conduction mechanism in the present samples may be due to hopping of electrons from

Fe2+ to Fe3+ and hole transfer from Ni3+ to Ni2+ ions.

+−+

−++

⇔+

+⇔23

32

NieNieFeFe

Combining these two equations,

Ni2+ + Fe3+ Ni3+ + Fe2+ ⇔

Temperature dependent dc resistivity has been measured in the temperature range 25 -

200°C. The Arrhenius plots are shown in Fig. 4.6. The figure shows that the dc resistivity

decreases linearly with temperature for all the samples. This can be attributed to the increase in

drift mobility of thermally activated charge carriers. The observed decrease in dc resistivity with

temperature is normal behavior for semiconductors which follows the Arrhenius relation.

5

5.5

6

6.5

7

7.5

8

8.5

9

1.9 2.1 2.3 2.5 2.7 2.9 3.1 3.3

103/T (K)

Log ρ

(ohm

.cm

)

x = 0x = 0.02x = 0.04x = 0.06x = 0.08x = 0.1x = 0.12

Fig. 4.6 Variation of Log ρ Vs. 1000/ T (K) for NiY2xFe2-2xO4 ferrites (x = 0.0, 0.02,

0.04, 0.06, 0.08, 0.1, 0.12).

The activation energies were calculated from the slope of Arrhenius plots and are plotted

in Fig. 4.7. It is observed that the activation energy and the electrical resistivity show similar

behavior with composition. The sample with higher resistivity has higher

0.250.270.290.310.330.350.370.390.410.430.45

0 0.02 0.04 0.06 0.08 0.1 0.12

Y-Concentration (x)

E (e

v)

Fig. 4.7 Activation energy Vs. Y concentration for NiY2xFe2-2xO4 (0 ≤ x ≤ 0.12)

values of activation energies and vice versa. Since the resistivity has been found to increase with

yttrium concentration, a rise in activation energies with yttrium concentration is expected.

The higher values of activation energy at higher yttrium concentration show the strong

blocking of the conduction mechanism between ferrous and ferric ions due to presence of yttrium

ions at B-sites. A possible reason for the increasing behavior of activation energy can be

attributed to the increase in lattice constant. In ferrites, the interionic distances increases with the

increase in the values of lattice constant. This gradual increase in interionic distance enhances

the barrier height encountered by the charge carriers. Consequently, it enhances the activation

energy.

4.1.4 Dielectric Properties

4.1.4.1 Compositional dependence of dielectric behavior

The variation of dielectric constant (ε ′ ) determined in the frequency range from 10 Hz to

10 MHz is shown in Fig. 4.8. It can be seen from the figure that the dielectric constant (ε ′ ) of

the mixed Ni-Y ferrites decreases with the increase of yttrium concentration. Iwauchi [12]

reported that the mechanism for the electrical conduction is similar to that of the dielectric

polarization. The compositional dependence of dielectric constant can be explained on the basis

of this theory. In ferrites, the electronic exchange between Fe2+ ⇔ Fe3+ in octahedral sites

results in the local displacement of electrons in the direction of the applied electric field which

determines electric polarization behavior of the ferrites.

It is known that Y3+ ions occupy octahedral sites [9] due to its larger ionic radius. The

concentration of Fe3+ ions at B sites decreases gradually with increasing concentration of

yttrium. The reduction in the values of dielectric constant with increasing concentration of

yttrium is due to depleting concentration of iron ions at B sites which play a dominant role in

dielectric polarization. The electron transfer between Fe2+ and Fe3+ ions (Fe2+ ↔ Fe3+ + e–) will

be hindered i.e. the polarization decreases. Consequently, dielectric constant decreases with

yttrium contents.

Fig. 4.8 Variation of dielectric constant as a function of frequency for NiY2xFe2-2xO4

ferrites (0 ≤ x ≤ 0.12).

4.1.4.2 Frequency dependence of dielectric constant

Fig. 4.8 shows the variation of the dielectric constant as a function of frequency at room

temperature for all the samples in the frequency range from 10 Hz to 10 MHz. It is clear from the

figure that dielectric constant shows dispersion with frequency. The values of dielectric constant

are high at low frequency and then decreases rapidly with the rise in frequency. Ultimately, it

attains a constant value which is the general trend for all the ferrite samples [13]. The above

dielectric dispersion depends upon two factors: 1- Electron hopping between Fe2+ and Fe3+ ions.

0

20

40

60

80

100

120

10 100 1000 10000 100000 00 10000000

Frequency (Hz)

Diel

ectri

c co

nsta

nt

10000

x = 0x = 0.02x = 0.04x = 0.06x = 0.08x = 0.1x = 0.12

2- Space charge polarization due to the presence of an inhomogeneous dielectric structure.

Koops [14] suggested a theory in which the samples having heterogeneous structure contain well

conducting grains separated by highly resistive thin grain boundaries. This causes localized

accumulation of charge under the applied electric field which builds up space charge

polarization. Hence a high value of dielectric constant is expected at low frequency [14, 15]. The

electron reverses their direction with the increase of field reversal frequency of electric field. The

chances of electron accumulation at grain boundaries decreased thereby decreasing polarization.

Therefore, dielectric constant decreases with rise in frequency and reaches almost constant value

as is observed.

4.1.4.3 Variation of dielectric loss tangent with frequency

The variation of dielectric loss tangent (tan δ) with increasing frequency for mixed

NiY2xFe2-2xO4 ferrites is shown in Fig. 4.9. It is clear from the figure that tan δ decreases with

increasing yttrium concentration. This can be attributed to the increase in resistivity which causes

reduction in tan δ.

0

0.2

0.4

0.6

0.8

1

1.2

10 100 1000 10000 100000 1000000 10000000

Frequency (Hz)

tan δ

x = 0x = 0.02x = 0.04x = 0.06x = 0.08x = 0.1x = 0.12

Fig. 4.9 Plot of loss tangent (tan δ) Vs frequency at room temperature for NiY2xFe2-

2xO4 ferrites (0 ≤ x ≤ 0.12)

It is clear from the figure that tan δ is high at low frequency and decreases rapidly at high

frequency. It is an established fact that [16] ferrites consist of well conducting grains and poorly

conducting grain boundaries. It is known that thin insulated grain boundaries are more effective

at low frequency while well conducting grain boundaries are more effective at high frequency

region. Therefore, it is expected that energy loss is high at low frequency region while it is low at

high frequency region. Hence tan δ is high in low frequency region because more energy is

needed for hopping process of charge carriers. tan δ is low in high frequency region because little

energy is needed for hopping process of charge carriers in this region [17].

4.1.4.4 Relationship between dielectric constant and resistivity

The values of dielectric constant and resistivity are given in table 4.4. It can be seen

from the table that dielectric constant is approximately inversely proportional to the square root

of resistivity for those ferrite materials in which conduction mechanism plays fundamental role

in the polarization process. The product ρε ′ remains nearly constant as shown in table 4.4.

Similar relationship between ε ′ and ρ was observed by Ravinder [13.].

Table 4.4. Variation of dielectric constant (ε ′ ) and resistivity ( ρ ) in the case of Ni-Y ferrites.

Ferrite

Composition Hzat10ε ′

MHzat10ε ′

).( cmΩρ

).( 2/12/1 cmΩ

ρHzat10ρε ′

MHzat10ρε ′

Ni Fe2O4 106.08 8.02 4.85×106 2202.27 2.3×105 1.76×104

NiY0.04Fe1.96O4 86.96 6.46 9.18×106 3029.85 2.6×105 1.95×104

NiY0.08Fe1.92O4 82.98 5.71 3.16×107 5621.39 4.7×105 3.2×104

NiY0.12Fe1.88O4 76.34 4.79 8.63×107 9289.78 7.09×105 4.4×104

NiY0.16Fe1.84O4 68.25 3.89 1.47×108 12124.36 8.27×105 4.7×104

NiY0.20Fe1.80O4 23.86 3.81 2.58×108 16062.38 3.83×105 6.1×104

NiY0.24Fe1.76O4 18.94 3.85 7.48×108 27349.59 5.18×105 10.5×104

4.1.5 M-H Loops Analysis The M-H loops for each compositions of NiY2xFe2-2xO4 ferrite were obtained using

computer controlled Lake Shore (model 7300) vibrating sample magnetometer (VSM). The

maximum applied field was up to 6 KOe. The VSM was calibrated with Ni standard having

magnetization 3.475 emu at 5000 G. Data on saturation magnetization and coercivity are listed in

table 4.5. The variation of magnetization (M) of all the samples with the applied magnetic field, H, (up to

6000 Oe) is shown in Fig. 4.10. Each loop is clearly exhibiting low coercivity (Hc < 59.08 Oe),

indicating that all the samples belong to the family of soft ferrites. It was observed from the

experimental results that the value of saturation magnetization goes on


NiY2xFe2-2xO4 ferrites (x = 0.0, 0.02, 0.04, 0.06, 0.08, 0.1).

nCompositio

(x)

nCompositio )/( gmemuM S )(OeH C

0.0 NiFe2O4 50.98 15.54

0.02 NiY0.04Fe1.96O4 48.64 18.66

0.04 NiY0.08Fe1.92O4 46.65 24.88

0.06 NiY0.12Fe1.88O4 45.93 31.1

0.08 NiY0.16Fe1.84O4 45.57 55.98

0.10 NiY0.20Fe1.80O4 44.74 56.69

0.12 NiY0.24Fe1.76O4 41.44 59.08

-6000 -4000 -2000 0 2000 4000 6000-60

-40

-20

0

20

40

60

x = 0.0

M (e

mu)

H (Oe)-6000 -4000 -2000 0 2000 4000 6000

-60

-40

-20

0

20

40

60

x = 0.02

M (e

mu)

H (Oe)-6000 -4000 -2000 0 2000 4000 6000

-60

-40

-20

0

20

40

60

x = 0.04

M (e

mu)

H (Oe)

-6000 -4000 -2000 0 2000 4000 6000-60

-40

-20

0

20

40

60

x = 0.06

M (e

mu)

H (Oe)-6000 -4000 -2000 0 2000 4000 6000

-60

-40

-20

0

20

40

60

x = 0.08

M (e

mu)

H (Oe)-6000 -4000 -2000 0 2000 4000 6000

-60

-40

-20

0

20

40

60

x = 0.1

M (e

mu)

H (Oe)

-6000 -4000 -2000 0 2000 4000 6000

-40

-20

0

20

40 x = 0.12

M (e

mu)

H (Oe)

Fig. 4.10 MH- loops for NiY2xFe2-2xO4 ferrites (x = 0.0, 0.02, 0.04, 0.06, 0.08, 0.1, 0.12).

decreasing with the increase of yttrium concentration. This can be explained on the basis of

assumed cation distribution. It is known that nickel prefer octahedral sites [18]. Thus the cation

distribution for NiFe2O4 ferrites can be written as (Fe) [Ni Fe] O4. When non-magnetic yttrium

ions are substituted with iron ions, they tend to occupy octahedral sites [3]. The substituting non-

magnetic yttrium ions enter into the B-sites and replaces Fe3+ ions. Therefore, the magnetization

of B-sublattice decreases keeping the magnetization of A-sublattice constant. Thus the resultant

magnetization ( AB MMM −= ) decreases which results into the observed fall in saturation

magnetization (Ms). Similar report about saturation magnetization has been quoted earlier [3].

The values of coercivity are listed in table 4.5. From the table, it is seen that coercivity

increases with the increase of yttrium concentration. It is inversely proportional to the grain size

[19]. In the present samples, grain size decreases with the increase of yttrium concentration. The

gradual increase of coercivity (Hc) with the increase of yttrium concentration may be attributed

to the decrease in grain size.

4.1.6 Initial Permeability ( iμ )

Fig. 4.11 shows the initial permeability ( iμ ) at room temperature for all compositions as

a function of frequency. The figure shows that iμ decreases with the increase of yttrium

contents. This decreasing behavior can be explained on the basis of following equation [20].

1

2

KDM mS

i =μ

where is saturation magnetization, is the average grain size and is the

magnetocrystalline anisotropy constant. Fig. 4.12 shows a linear relation between

SM mD 1K

iμ and .

This linear relationship indicates that initial permeability is directly proportional to and

is not playing a significant role. In present samples, grain size decreases with the increase of

yttrium contents. The decreasing trend of grain size increases resistance against domain wall

motion due to increased number of grain boundaries. Therefore, initial permeability decreases

with the decrease of grain size and increase of grain boundaries [21].

2SM

1K2SM

0

20

40

60

80

100

120

0 200 400 600 800 1000

Frequency (KHz)

Initi

al p

erm

eabi

lity

x = 0.0x = 0.02x = 0.04x = 0.06x = 0.08x = 0.1x = 0.12

Fig. 4.11 Frequency variation of initial permeability ( iμ ) for NiY2xFe2-2xO4 ferrites (x =

0.0, 0.02, 0.04, 0.06, 0.08, 0.1).

1500

1800

2100

2400

2700

60 70 80 90 100 110 120

Initial Permeability

Ms2

Fig. 4.12 Ms2 Vs. Initial permeability ( iμ ) for NiY2xFe2-2xO4 ferrites.

Without Y2O3, pure nickel ferrite is aligned as (Fe3+) [Ni2+ Fe3+] O2-4 [22]. It is well established

that non-magnetic Y3+ ions tend to occupy octahedral B-sites [3]. The substituted non-magnetic

yttrium ions enter into the B-sites and replaces B-site Fe3+ ions. Therefore, the magnetization of

B-sublattice decreases keeping the magnetization of A-sublattice constant. Thus the resultant

magnetization ( AB MMM −= ) is expected to decrease which results into the observed fall

in MS and initial permeability.

Fig. 4.11 shows that iμ slightly decreases with the increase of frequency which may be

due to the fact that domain wall components starts to decrease at lower frequencies [24] In soft

ferrites iμ would be resolved into two types of mechanism such as domain wall motion

magnetic mechanism and domain rotation magnetic mechanism. The domain wall motion

magnetic mechanism remains active at low frequency region. At high frequency region, initial

permeability can be described mainly using domain rotation magnetic mechanism.

Fig. 4.13 shows the frequency variation of magnetic loss tangent for NiY2xFe2-2xO4 ferrites. The

figure shows that magnetic loss tangent decreases with the increase of yttrium concentration. It is

known that magnetic losses decreases with the increase in resistivity and decrease in the average

grain size and vice versa [25]. In present samples, average grain size decreases while resistivity

increases with the increase of yttrium contents. The substantial reduction in the loss factor might

be attributed to the increase in resistivity and decrease in the average grain size.

0

0.1

0.2

0.3

0.4

0.5

0 200 400 600 800 1000

Frequency (KHz)

Mag

netic

Los

s Ta

ngen

t x = 0.0x = 0.02x = 0.04x = 0.06x = 0.08x = 0.1x = 0.12

Fig. 4.13 Frequency variation of magnetic loss tangent for NiY2xFe2-2xO4 ferrites (x = 0.0,

0.02, 0.04, 0.06, 0.08, 0.1, 0.12).

4.1.7 Ferromagnetic Resonance (FMR) FMR experiments were performed with a standard spectrometer at 9.45 GHz. The TE102 mode

rectangular reflection cavity was used. The first derivative dHdP

of the power absorption “ P ”

was recorded as a function of the applied field (H). The reference resonance field with X-band

spectrometer at 9.45 GHz was γω

=refH = 3.375 KOe where γ is the gyromagnetic ratio of

free electrons. The resonance field can be defined as the field for which dHdP

= 0. The difference

between the bounding peaks of the first derivative of the absorption line define the FMR

linewidth. Fig. 4.14 depicts the FMR spectra of all the samples. The line width of all the samples

is listed in table 4.6.

PPHΔ

Compositio

Table 4.6 Compositional variation of linewidth (Oe) for NiY2xFe2-2xO4 ferrites (x = 0.0,

0.02, 0.04, 0.06, 0.08, 0.1).

n

(x)

nCompositio Line width

(Oe)

FMR Position

(Oe)

0.0 NiFe2O4 472 4360

0.02 NiY0.04Fe1.96O4 461 4485

0.04 NiY0.08Fe1.92O4 371 4483

0.06 NiY0.12Fe1.88O4 282 4437

0.08 NiY0.16Fe1.84O4 325 4533

0.10 NiY0.20Fe1.80O4 526 4592

0.12 NiY0.24Fe1.76O4 735 4150

It can be seen from the table that line width decreases with the increase of yttrium

concentration for the substitution level 0 ≤ x ≤ 0.06. Beyond this, the line width increases with

the increase of yttrium concentration.

The decreasing trend of linewidth impurity [26] with yttrium contents is attributed to the

valence-exchange mechanism, or charge transfer relaxation mechanism (Fe2+ ↔ Fe3+). Fe2+ ions

contain one more electrons than Fe3+ ions. The energy of the ferrite material is changed if one of

the extra electrons hops from one iron ion to another. This hopping can obviously give rise to

electrical conductivity. It can also give rise to linewidth. The line width is determined by the

integral over the complete precession cycle of the rate of transfer of energy to the lattice. The

substitution of yttrium ions gradually reduces Fe3+ ions in the composition. A corresponding

decrease in Fe2+ ions is also expected along with. The Y3+ ions impedes the electron transfer

between Fe2+ and Fe3+ ions and thereby decreasing the hopping rate The reduction of linewidth

with the increase of yttrium concentration is attributed to the decrease of Fe3+ ions and hence

expected corresponding decrease of Fe2+ ions on each step. Similar observations are reported by

Flores et. al. [27]

The line width increases with the increase of yttrium concentration for the substitution

level 0.08 ≤ x ≤ 0.12. The increasing trend of linewidth is attributed to the sample

inhomogenities caused by secondary phase. High concentration of yttrium diffused to the grain

boundaries and formed inhomogeneous solid solution. Magnetic properties are not necessarily

constant throughout the biphasic samples. Hence several different resonance peaks are

superposed and the resulting linewidth is broadened.

0 2000 4000 6000 8000

0

Der

ivativ

e of

the

FMR

abs

orpt

ion

curv

e

Applied field (Oe)0 2000 4000 6000 8000

-2

0

2

Applied field (Oe)0 2000 4000 6000 8000

-2

0

2

x = 0.04

Applied field (Oe)

0 2000 4000 6000 8000

-2

0

2

x = 0.06

Der

ivativ

e of

the

FMR

abs

orpt

ion

curv

e

Applied field (Oe)0 2000 4000 6000 8000

-2

0

2

x = 0.08

Applied field (Oe)0 2000 4000 6000 8000

-2

0

2

x = 0.1

Applied field (Oe)

0 2000 4000 6000 8000

0

x = 0.12

x = 0.02x = 0.0

Der

ivativ

e of

the

FMR

abs

orpt

ion

curv

e

Applied field (Oe)

Fig. 4.14 FMR spectra of NiY2xFe2-2xO4 ferrites (x = 0.0, 0.02, x = 0.04, 0.06, 0.08, 0.1, 0.12)

4.2 MgY2xFe2-2xO4 ferrite series

4.2.1 X-ray diffraction Analysis X-ray diffraction patterns of MgY2xFe2-2xO4 (x = 0.0, 0.02, 0.04, 0.06, 0.08, 0.1,

0.12) ferrite system are shown in Fig. 4.15. X-ray diffraction patterns were obtained over the 2θ

range 10-70o using Philips X’ Pert analytical diffractometer with Cu Kα radiation operated at

1400 watt. For x ≤ 0.02, the samples produced six well defined diffraction peaks. The presence

of the strong diffraction peaks corresponding to the planes (220), (311), (400), (422), (511/333),

(440) indicates the presence of cubic spinel phase. While, for x ≥ 0.04, the samples showed

seventh well defined diffraction peaks that is one more than the above mentioned samples. The

extra peak is, but well defined and appeared at 2θ = 33.2o (indicated by * in Fig. 4.15). The

intensity of this peak increases with the increase of yttrium concentration. On the basis of one

peak it is not possible to identify the unknown phase. However, it can only be speculated. This

peak can be identified as the (1 2 1) reflection of the FeYO3 phase (Iron Yttrium Oxide) matched

with ICDD PDF # 39-1489. The secondary phase on the grain boundaries appears due to high

reactivity of Fe3+ ions with Y3+ ions [1]. Miller indices (hkl) and interplaner spacing (dhkl) for

MgY2xFe2-2xO4 ferrites are listed in table 4.7.

4.2.1.1 Lattice Parameters The average values of lattice constant ‘a ’ for all compositions was found by using the

Nelson-Riley [2] function. A slight increase in the values of the lattice constant ( ) is noted for

the samples with x = 0.0, 0.02 and for higher yttrium concentration it decreases. A slight increase

in lattice constant with the increase of yttrium concentration can be explained on the basis of the

ionic radii of the substituent ions. It is assumed that the replacement of smaller Fe3+ ions (0.64

Å) with the larger Y3+ ions (0.95 Å) on the octahedral sites causes the unit cell to expand which

results in the increase of lattice constant [4]. A possible explanation for the decrease of lattice

constant for 0.04 ≤ x ≤ 0.12 is that some of the yttrium ions no longer dissolve in the spinel

lattice but diffuse to the grain boundaries reacting with Fe to form FeYO3. It is possible that the

spinel lattice is compressed by the intergranular secondary phase due to the differences in the

thermal expansion coefficients [28].

a

Fig. 4.15 X- ray diffraction patterns for MgY2xFe2-2xO4 (0 ≤ x ≤ 0.12)

4.2.1.2 Bulk Density, X-Ray Density and Porosity Table 4.8 presents X-ray density (Dx), physical density (Dp), percentage porosity (P %)

and average grain size of all the samples. The influence of yttrium concentration on X-ray

density (Dx), physical density (Dp) and percentage porosity are shown in Fig. 4.16. The physical

density (Dp) was measured using a Sartorius density determination kit. The Archimedean

principle was applied and liquid toluene was used. X-ray density increases with yttrium

contents as it mainly depends upon the molecular weight of the samples. It increases from 4.503

g cm-3 to 4.693 g cm-3 while physical density also increases from 3.924 g cm-3 to 4.292 g cm-3

with the increase of yttrium concentration from x = 0 to x = 0.12. The increasing trend of

physical density with yttrium content can also be attributed to the difference in atomic weight

of Y (88.90585 amu) and Fe (55.845 amu) as described in CRC book [8]. The formation of

YFeO3 secondary phase as confirmed by XRD patterns fills intergranular voids and shows good

densification. The decrease in porosity can be expected with the increase of yttrium

concentration (x). Our results of physical density and porosity are consistent with the results

reported by Rezlescu et. al. [4] in case of Mg0.5Cu0.5Fe2-xY3x/nO4.

Table 4.7 Miller indices (hkl) and interplanar spacing (d) for MgY2xFe2-2xO4 (0.0 ≤ x

≤0.12) ferrites.

Sr.no hkl x = 0.0

d(Å )

x = 0.02

d(Å )

x = 0.04

d(Å )

x = 0.06

d(Å )

x = 0.08

d(Å )

x = 0.1

d(Å )

x = 0.12

d(Å )

1 220 2.955 2.954 2.954 2.953 2.977 2.956 2.958

2 311 2.521 2.520 2.520 2.519 2.537 2.523 2.524

3 400 2.091 2.090 2.091 2.091 2.101 2.093 2.094

4 422 1.707 1.708 1.708 1.708 1.715 1.709 1.710

5 511 1.610 1.610 1.611 1.611 1.612 1.612 1.613

6 440 1.479 1.479 1.480 1.479 1.481 1.481 1.481

Table 4.8 Phases, lattice constant, X-ray density, bulk density, percentage porosity and

grain size of the MgY2xFe2-2xO4 (0.0 ≤ x ≤ 0.12) ferrites.

S.No. Composition Lattice

Constant

a, (Å )

Secondary

phase

X-ray

density

g cm-3

Physical

density

g cm-3

Porosity

(%)

Grain

size(μm)

Scherrer

1 MgFe2O4 8.3867 - 4.503 3.924 12.873 1.987

2 MgY0.04Fe1.96O4 8.3885 - 4.530 3.978 12.188 1.809

3 MgY0.08Fe1.92O4 8.3848 YFeO3 4.566 4.036 11.605 1.651

4 MgY0.12Fe1.88O4 8.3803 YFeO3 4.603 4.071 11.558 1.478

5 MgY0.16Fe1.84O4 8.3794 YFeO3 4.635 4.167 10.08 1.277

6 MgY0.20Fe1.80O4 8.378 YFeO3 4.660 4.225 9.339 1.195

7 MgY0.24Fe1.76O4 8.3758 YFeO3 4.693 4.292 8.541 1.166

0.00 0.02 0.04 0.06 0.08 0.10 0.123.9

4.0

4.1

4.2

4.3

4.4

4.5

4.6

4.7

Dx DP Porosity

Y-Concentration (x)

Den

sity

(g/c

m3 )

8

10

12

14P

orosity (%)

Fig.

4.16 X-ray density (Dx), physical density (DP), percentage porosity Vs. Y

concentration for MgY2xFe2-2xO4 (0 ≤ x ≤ 0.12) ferrites.

4.2.1.3 Average Grain Size The average grain size calculated from Scherrer formula [2] from the width of the (311)

line is tabulated in table 4.8. It is observed from the table that average grain size decreases with

increasing yttrium contents (x) for all the compositions. The grain growth depends upon the

grain boundary mobility [1]. The presence of yttrium ions at or near the grain boundaries limits

the grain boundary movement. Hence grain size decreases with yttrium contents as is observed.

Fig. 4.17 SEM micrograph of MgY2xFe2-2xO4 ferrite: (a) x = 0.0, (b) x = 0.06, (c) x = 0.1. The surface morphology of the samples was studied using a JEOL JSM-840 Scanning Electron

Microscope. The decrease in grain size is confirmed by SEM micrographs of few representative

samples as shown in Fig. 4.17 (x = 0.0, 0.06, 0.1). The values of grain size obtained by SEM

micrograph were 2.14 μm, 1.42 μm and 1.23 μm respectively which are comparable to the grain

size obtained by Scherrer formula. These micrographs show inhomogeneous grain size

distribution.

4.2.2 FTIR Analysis Fig. 4.18 shows FTIR spectra of a few representative samples exhibiting the two major

absorptions bands in the wave number range 370 – 1100 cm-1. The band position for the

selected compositions is listed in table 4.9. In spinel ferrites, the absorption band around 550-

600 cm-1 is attributed to tetrahedral complexes and the band around 400 cm-1 is attributed to

octahedral complexes [29]. The higher frequency band 1ν (571-575 cm-1) and lower frequency

band 2ν (408-418 cm-1) are assigned to tetrahedral and octahedral complexes respectively.

Table 4.9 FTIR absorption bands for MgY2xFe2-2xO4 ferrites.

S. No. Composition )( 11

−cmν )( 12

−cmν

1 MgFe2O4 572 408

2 MgY0.04Fe1.96O4 572 410

3 MgY0.08Fe1.92O4 571 411

4 MgY0.12Fe1.88O4 574 414

5 MgY0.16Fe1.84O4 574 415

6 MgY0.20Fe1.80O4 575 418

The absorption bands of the present samples are found to be in the expected ranges which

confirm the completion of solid state reaction. 1ν band is almost constant for all investigated

samples. The band frequency 2ν slightly shifts to higher frequency side

Fig. 4.18 FTIR spectra of MgY2xFe2-2xO4 ferrite: (a) x = 0.0, 0.02, 0.04, 0.06, 0.08, 0.1, 1ν and 2ν

indicate tetrahedral and octahedral absorption bands respectively.

and also band broadens with increasing yttrium concentration. The broadening of the spectral

bands and increase in 2ν may be attributed to the yttrium substitution for iron on octahedral

sites due to its higher atomic weight and larger ionic radius than iron which affect Fe3+ - O2-

distances on octahedral sites. Similar observations were reported by Gadkari et.al. [1] in case of

Mg1-xCdxFe2O4 + 5% Y3+ ions .

4.2.3 Electrical Resistivity The dc resistivity was measured by using two probe method using silver paste contacts.

A Sensitive Electrometer model 610-C Keithley and dc power supply was used. The resistivity

of each sample was calculated using the relation: ρ = RA / t where ‘R’ is the resistance of the

sample, ‘A’ is the area of electrode and ‘t’ is the thickness of the sample. The thickness of the

sample used for resistivity measurement was 2 mm. The room temperature dc resistivities of

MgY2xFe2-2xO4 were measured by two probe method and the results as a function of Y-

concentration are listed in table 4.10. It was found that the resistivity increases with the increase

of yttrium concentration from 7.4×107 to 1.8×1010 Ω.cm. This increase in resistivity may be due

to the reason that the yttrium ions occupy octahedral sites preferentially due to its large ionic

radius (0.95 Å) [9]. On increasing non-magnetic Y3+ ions substitution on B-sites, the Fe3+ ions

concentration at B-sites will decrease. This will reduce the number of electronic jump

probability between Fe2+ and Fe3+ and thereby increases the resistivity. Yttrium formed

inhomogeneous solid solution when it is substituted in place of iron. It is expected that Y3+

tends to segregate on the grain boundaries and formed highly resistive substance YFeO3

(secondary phase), consequently, resistivity is enhanced. Another reason for increase in

resistivity on increasing yttrium is due to the fact that the occupation of yttrium ions on B-sites

hinders the movement of Fe3+ ↔ Fe2+ ions in the conduction process, thus causes a decrease in

conductivity. These results are consistent with the results reported in the literature [11].

Temperature dependent dc resistivity has been measured in the temperature range 25 -

200°C. The Arrhenius plots are shown in Fig. 4.19.

Fig 4.19 Variation of Log ρ Vs. 1000/ T (K) for MgY2xFe2-2xO4 ferrites (x = 0.0, 0.02,

0.04, 0.06, 0.08, 0.1, 0.12).

It can be observed from the figure that the dc electrical resistivity shows a linear decrease with

temperature for all the samples. This can be attributed to the increase in drift mobility of

electric charge carriers, which are thermally activated upon an increase in temperature [28, 30

and 31]. The observed decrease in resistivity with temperature is normal behavior for

semiconductors which follows the arrhenius relation The activation energies were calculated

from the slope of Arrhenius plots and are plotted in Fig. 4.20. It has been noted that the

activation energy and the electrical resistivity show similar behavior with composition. The

sample with higher resistivity has higher values of activation energies and vice versa [32, 33].

Since the resistivity has been found to increase with yttrium concentration, a rise in activation

energies with yttrium concentration is expected. The higher values of activation energy at

higher yttrium concentration show the strong blocking of the conduction mechanism between

ferrous and ferric ions due to presence of yttrium ions at B-sites.

0.39

0.44

0.49

0.54

0.59

0.64

0.69

0 0.02 0.04 0.06 0.08 0.1 0.12

Y-Concentration (x)

E (e

v)

Fig. 4.20 Activation energy Vs. Y concentration for MgY2xFe2-2xO4 (0 ≤ x ≤ 0.12)

4.2.4 Dielectric Properties The high frequency impedance has been measured by using the Solartron 1260

Impedance Analyser. Dielectric properties were studied over the frequency range from 10 Hz to

10 MHz. The values of dielectric constant (ε ′ ) and dielectric loss tangent (tan δ) were

computed using the formula given in ref. [34].

4.2.4.1 Compositional dependence of dielectric behavior Variation of dielectric constant (ε ′ ) determined in the frequency range from 10 Hz to 10

MHz, as a function of yttrium concentration is shown in Fig. 4.21. It is observed that the

dielectric constant (ε ′ ) of the mixed Mg-Y ferrites decreases with the increase of yttrium

concentration. The compositional dependence of dielectric constant can be explained on the

basis of the assumption that the mechanism for the electrical conduction is similar to that of the

dielectric polarization. Usually the electronic exchange between Fe2+ and Fe3+ in octahedral

sites results in local displacement of electrons in the direction of the applied electric field which

determines electric polarization behavior of the ferrites.

0

10

20

30

40

50

60

10 100 1000 10000 100000 1000000 10000000

Frequency (Hz)

Die

lect

ric

cons

tant

x = 0x = 0.02x = 0.04x = 0.06x = 0.08x = 0.1x = 0.12

Fig. 4.21 Variation of dielectric constant as a function of frequency for MgY2xFe2-2xO4

(0 ≤ x ≤ 0.12) ferrites.

It is known that Y3+ ions occupy octahedral sites [29] due to its larger ionic radius. In present

samples, the concentration of Fe3+ ions at B sites gradually decreases with the increase of

yttrium concentration. As a result, the probability of hopping between Fe3+ and Fe2+ ions at B

sites decreases. Hence the electron transfer between Fe2+ and Fe3+ ions (Fe2+ ↔ Fe3+ + e–) will

be hindered i.e. the polarization decreases. Consequently, dielectric constant decreases with the

increase of yttrium concentration. Among all the ferrites, the specimen with composition

MgY0.24Fe1.76O4 (x = 0.12) exhibits drastic decrease of dielectric constant.

4.2.4.2 Frequency dependence of dielectric constant The variation of the dielectric constant as a function of frequency for mixed MgY2xFe2-

2xO4 ferrites for different compositions of yttrium are shown in Fig. 4.21. The figure shows that

the value of dielectric constant decreases rapidly with the rise in frequency and ultimately

attains a constant value which is the general trend for all the ferrite samples [35, 36 and 37].

The frequency dependent behaviors of dielectric constant in ferrites follow the Maxwell–

Wagner’s interfacial polarization in accordance with Koops [14] phenomenological theory.

Koops suggested a theory in which the samples having heterogeneous structure can be assumed

to consist of two layers. The first layers consist of good conducting grains and the second layer

consists of highly resistive insulating thin grain boundaries. Thus the dielectric behavior is

attributed to interfacial polarization resulting from their heterogeneous structure consist of

grains and thin grain boundaries. The electrons reach the insulating grain boundaries through

hopping mechanism and accumulate there due to its high resistivity. This accumulation of

localized charges under the influence of applied field result in increasing the interfacial

polarization. Hence dielectric constant is high at low frequency. The dielectric constant

naturally decreases with the increase of field reversal frequency because the charge carriers in

inhomogeneous dielectric structure require finite time to line up their axes parallel to an

alternating electric field. The decrease in dielectric constant with increasing frequency is

attributed to the fact that polarization decreases with rise of frequency. Ultimately, it reaches a

constant value because beyond a certain critical frequency of external field the electronic

exchange between ferrous and ferric ions can not follow the alternating field.

4.2.4.3 Variation of dielectric loss tangent with frequency The variation of tan δ with increasing frequency for mixed MgY2xFe2-2xO4 ferrites is

shown in Fig. 4.22. The figure shows that tan δ is also compositionally dependent where its

values decrease with increasing yttrium contents. This may be attributed to the increase in

resistivity which causes reduction in tan δ [38].

The dielectric loss tangent also depends upon the frequency. At low frequency, its value

is high. It decreases continuously with the rise in frequency. It is known that ferrites consist of

well conducting grains separated by poorly conducting grain boundaries. At low frequency,

grain boundaries are more effective. The energy loss is high at low frequency because more

energy is needed for hopping process of charge carriers. Hence tan δ is high at low frequency.

The well conducting grains are more effective at high frequency. Thus energy loss is low

because low energy is needed for hopping mechanism of charge carriers. Hence tan δ is low at

high frequency [17].

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

10 100 1000 10000 100000 1000000 10000000

Frequency (Hz)

tan δ

x = 0x = 0.02x = 0.04x = 0.06x = 0.08x = 0.1x = 0.12

Fig.4.22 Variation of dielectric constant as a function of frequency for MgY2xFe2-2xO4

(0 ≤ x ≤ 0.12) ferrites.

4.2.4.4 Relationship between dielectric constant and resistivity

There are several mechanisms for the dielectric behavior in ferrites. Dielectric

constant is approximately inversely proportional to the square root of resistivity for those ferrite

materials in which conduction mechanism plays fundamental role in the polarization process.

The product ρε ′ remains nearly constant as shown in table 4.10. Similar relationship

between ε ′ and ρ was reported by other researchers [39, 40 and 41].


MgY2xFe2-

2xO4 ferrites.

Ferrite

Composition Hzat10ε ′

MHzat10ε ′

).( cmΩρ

).( 2/12/1 cmΩ

ρHzat10ρε ′

MHzat10ρε ′

MgFe2O4 57.93 9.07 7.4×107 8602.3 4.9×105 7.8×104

MgY0.04Fe1.96O4 39.87 7.56 1.2×108 11090.5 4.4×105 8.4×104

MgY0.08Fe1.92O4 34.38 6.80 2.2×108 14594.5 5.0×105 9.9×104

MgY0.12Fe1.88O4 28.40 6.01 4.4×108 20976.2 5.9×105 12.6×104

MgY0.16Fe1.84O4 24.30 5.18 7.2×108 26832.8 6.5×105 13.9×104

MgY0.20Fe1.80O4 18.76 4.74 1.8×109 42426.4 7.9×105 20.1×104

MgY0.24Fe1.76O4 7.66 4.25 1.8×1010 134164.1 10.3×105 57×104

4.2.5 M-H loops Analysis The MH loops were plotted at room temperature using computer controlled Lake

Shore (model 7300) vibrating sample magnetometer (VSM). The maximum applied field

was up to 6 KOe. The VSM was calibrated with Ni standard having magnetization 3.475

emu at 5000G.

The values of saturation magnetization (Ms) and coercivities for various

MgY2xFe2-2xO4 samples (x = 0.0, 0.02, 0.04, 0.06, 0.08, 0.1, 0.12) are listed in table 4.11.

The M-H loops are depicted in Fig. 4.23. It is seen from the table that the substitution of

Y3+ ions in MgY2xFe2-2xO4 results in a decrease in saturation magnetization and increase

in coercivity. The sublattices [22] of pure magnesium ferrite having partially inverse

spinel structure are aligned as (Mg0.1Fe0.9) [Mg0.9Fe1.1] O4. It is known that non-magnetic

Y3+ ions tend to occupy octahedral sites [3]. When adding Y2O3, non-magnetic Y3+ ions

enter into the ferrite lattice and probably replace Fe3+ ions on octahedral B-sites, thus

reducing magnetization on B-sites. The magnetization at B-sublattice decreases while the

magnetization at A-sublattice remains constant. The result is a decrease in the net

magnetization due to antiferromagnetic coupling.

It is an established fact that coercivity is inversely proportional to the grain size

[42]. In present samples, grain size decreases with the increase of yttrium

concentration. The gradual

-6000 -4000 -2000 0 2000 4000 6000

-30

-20

-10

0

10

20

30

x = 0.0

M (e

mu)

H (Oe)-6000 -4000 -2000 0 2000 4000 6000

-30

-20

-10

0

10

20

30

x = 0.02

M (e

mu)

H (Oe)-6000 -4000 -2000 0 2000 4000 6000

-30

-20

-10

0

10

20

30

x = 0.04

M (e

mu)

H (Oe)

-6000 -4000 -2000 0 2000 4000 6000-30

-20

-10

0

10

20

30

x = 0.06

M (e

mu)

H (Oe)-6000 -4000 -2000 0 2000 4000 6000

-30

-20

-10

0

10

20

30

x = 0.08

M (e

mu)

H (Oe)-6000 -4000 -2000 0 2000 4000 6000

-30

-20

-10

0

10

20

30

x = 0.1

M (e

mu)

H (Oe)

-6000 -4000 -2000 0 2000 4000 6000-30

-20

-10

0

10

20

30

x = 0.12

M (e

mu)

H (Oe)

Fig. 4.23 Hysteresis loops for MgY2xFe2-2xO4 ferrites (x = 0.0, 0.02, 0.04, 0.06, 0.08,

0.1, 0.12).

increase of coercivity (Hc) with yttrium contents may be attributed to the decrease in

grain size. Similar observations was reported by Jacobo et. al. [43] about the slight

decrease of saturation magnetization and increase of coercivity in Ni0.5Zn0.5Y0.02Fe1.98O4

ferrites. From the table, it is observed that saturation magnetization (Ms) can be related to

coercivity (Hc) through Brown’s relation [44]:

MsKH

oc μ

12= (4.2)

This relation shows that Hc is inversely proportional to Ms. This is consistent with our

experimental results.

Table 4.11 Compositional variations of saturation magnetization and coercivity for

MgY2xFe2-2xO4 ferrites (x = 0.0, 0.02, 0.04, 0.06, 0.08, 0.1, 0.12).


MgFe2O4 29.97 18.658

MgY0.04Fe1.96O4 26.66 21.768

MgY0.08Fe1.92O4 25.28 24.878

MgY0.12Fe1.88O4 24.75 27.988

MgY0.16Fe1.84O4 23.29 31.097

MgY0.20Fe1.80O4 22.19 37.317

MgY0.24Fe1.76O4 21.86 39.884

4.2.6 Initial permeability ( iμ )

Fig. 4.24 shows the influence of Y3+ ions on the initial permeability ( iμ ) as a

function of frequency. It is observed from the figure that yttrium decreases the magnitude

of iμ . The decreasing behavior of iμ may be explained on the basis of lattice strains and

weaker super exchange interaction between tetrahedral A-sites and octahedral B-sites.

The substitution of yttrium reduces the spin rotational magnetization because yttrium

may reduce the magnetic exchange interaction between A sites and B sites. The addition

of yttrium contents distorts the lattice and form inhomogeneous solid solution, thereby

causing deterioration in initial permeability with the increase of yttrium concentration [9].

. .

0

5

10

15

20

25

30

35

0 200 400 600 800 1000

Frequency (KHz)

Initi

al p

erm

eabi

lity

x= 0.0x= 0.02x = 0.04x = 0.06x= 0.08x = 0.1x = 0.12

Fig. 4.24 Frequency variation of initial permeability for MgY2xFe2-2xO4 ferrites (x = 0.0,

0.02, 0.04, 0.06, 0.08, 0.1).

Fig. 4.25 shows the frequency variation of magnetic loss tangent for MgY2xFe2-2xO4

ferrites. Tan gradually decreases with the increase of yttrium concentration.

0

0.02

0.04

0.06

0.08

0.1

0 200 400 600 800 1000

Frequency (KHz)

Mag

netic

Los

s ta

ngen

t x = 0.0x = 0.02x = 0.04x = 0.06x = 0.08x = 0.1x = 0.12

Fig. 4.25 Frequency variation of magnetic loss tangent for MgY2xFe2-2xO4 ferrites (x =

0.0,

0.02, 0.04, 0.06, 0.08, 0.1, 0.12).

Magnetic losses depend upon resistivity. As the resistivity increases with yttrium

contents, the eddy current losses decrease. The lower values of Tan with yttrium

contents are attributed to the low eddy current losses as a result of higher resistivity [11].

4.2.7 Ferromagnetic Resonance (FMR)

FMR spectra of each sample was taken on a standard FMR spectrometer at X-

band (9.5 GHz) for MgY2xFe2-2xO4 at room temperature. The TE102 mode rectangular

reflection cavity was used. The first derivative dHdP

of the power absorption “ P ” was

recorded as a function of the applied field (H). The resonance occurs if the FMR

condition is fulfilled. The resonance field can be defined as the field for which dHdP

= 0.

Fig. 4.26 shows the room temperature typical FMR spectra of the ferrite samples.

The linewidth and FMR position of all the samples is listed in table 4.12. It can be seen

from the table that line width decreases with the increase of yttrium concentration for the

substitution level x = 0 to x = 0.02. Beyond this, the linewidth increases with the increase

of yttrium concentration.

Table 4.12 Compositional variations of linewidth and FMR Position for MgY2xFe2-2xO4

ferrites

(x = 0.0, 0.02, 0.04, 0.06, 0.08, 0.1).

nCompositio Linewidth

)(OeHΔ

FMR Position

(Oe)

MgFe2O4 333.7 4469

MgY0.04Fe1.96O4 269 4880

MgY0.08Fe1.92O4 348 4581

MgY0.12Fe1.88O4 637.5 4804

MgY0.16Fe1.84O4 684.1 4750

MgY0.20Fe1.80O4 750 4241

MgY0.24Fe1.76O4 768.3 4452

The decreasing behavior of linewidth is attributed to the valence-exchange mechanism

[26]. The hopping of electrons between Fe2+ ions (3d6) and Fe3+ ions (3d5) is the

possible source of linewidth and increase in electrical conductivity. In the present

samples, the substitution of Y3+ ions reduces Fe3+ ions in the composition and the

corresponding reduction in Fe2+ ions is also expected. The reduction of linewidth with the

increase of yttrium concentration is attributed to the decrease of Fe3+ ions and hence

expected corresponding decrease of Fe2+ ions on each step. Similar observations are

reported by Flores et. al. [27].

At x > 0.02, the increase in yttrium concentration lead to the increase in line

width. This may be attributed to the sample inhomogenities due to the presence of second

phase. High concentration of yttrium diffused to the grain boundaries and formed

inhomogeneous solid solution. Magnetic properties are not necessarily constant

throughout the biphasic samples. Hence several different resonance peaks are superposed

and the resulting line width is broadened.

2000 4000 6000 8000

-2

0

2x = 0.0

Der

ivativ

e of

the

abso

rptio

n cu

rve

Applied field (Oe)

0 2000 4000 6000 8000 10000

-2

0

2 x = 0.02

Applied field (Oe)

3000 4000 5000 6000 7000-2

0

2x = 0.04

Applied field (Oe)

3000 4000 5000 6000 7000 8000

0

2

x = 0.06

Der

ivativ

e of

the

abso

rptio

n cu

rve

Applied field (Oe)

2000 4000 6000 8000

-0.3

0.0

0.3

0.6x = 0.08

Applied field (Oe)

2000 4000 6000 8000

-0.8

-0.4

0.0

0.4

0.8x = 0.1

Applied field (Oe)

2000 3000 4000 5000 6000 7000

-0.6

-0.3

0.0

0.3

0.6

x = 0.12

Der

ivativ

e of

the

abso

rptio

n cu

rve

Applied field (Oe)

Fig. 4.26 FMR spectra of MgY2xFe2-2xO4 ferrites (x = 0.0, 0.02, x = 0.04, 0.06,

0.08, 0.1, 0.12)

4.3 Ni0.6Zn0.4Y2xFe2-2xO4 ferrite series

4.3.1 X-ray diffraction Analysis

X-ray diffraction patterns of the samples were obtained over the 2θ range of 10-

70o using Philips X’ Pert analytical diffractometer using Cu Kα radiation. Fig. 4.27

shows the XRD patterns of all the samples. The patterns were indexed for phase

confirmation. All the samples show good crystallization, with well-defined diffraction

lines. The presence of the reflection planes (111), (220), (311), (222), (400), (422),

(511/333), (440) confirms the formation of cubic spinel structure. For x ≤ 0.06, the

samples produced eight well defined diffraction peaks. While, for x ≥ 0.08, the samples

showed nine well defined diffraction peaks that is one more than the above mentioned

samples. The extra peak is, but well defined and appeared at 2θ = 33.1o (indicated by * in

Fig. 4.27). The intensity of this peak increases with the increase of yttrium concentration.

On the basis of one peak, it is not possible to identify the unknown phase. However, it

can only be speculated. This peak can be identified as the (1 2 1) reflection of the FeYO3

phase (Iron Yttrium Oxide) matched with ICDD PDF # 39-1489. The appearance of

second phase may be attributed to the high reactivity of Fe3+ ions with Y3+ ions at the

grain boundaries. The second phase is also reported in rare earth substituted ferrites by

several investigators [45, 1]. Miller indices (hkl) and interplanar spacing (d) for Ni-Zn-Y

ferrites are listed in table 4.13.

4.3.1.1 Lattice Parameters The values of lattice constants and the phases precipitated in the samples are

listed in table 4.14. The average value of the lattice constant ‘a ’ for each composition

was calculated using Nelson and Riley [2] function. From the table, it can be seen that the

lattice constant increases slightly for 0.0 ≤ x ≤ 0.06 and for higher yttrium concentration

it decreases. It is reported that Y3+ ions occupy B-sites [3]. It is assumed that the

replacement of the smaller Fe3+ ions (0.64 Å) with larger Y3+ ions (0.95 Å) causes an

expansion of the host spinel lattice which results in the increase of lattice constant. This

observation is consistent with the results reported by several researchers [3, 4] where it

has reported that the addition of Y3+ ions increases the lattice constant. A possible

explanation for the decrease of lattice constant for x = 0.08, 0.1 is that some of the

yttrium ions no longer dissolve in the spinel lattice but diffuse to the grain boundaries

reacting with Fe to form FeYO3. It is possible that the spinel lattice is compressed by the

intergranular secondary phase due to the differences in the thermal expansion coefficients

[28].

Inte

nsity

(arb

. uni

ts)

Fig. 4.27 X-ray diffraction patterns for Ni0.6Zn0.4Y2xFe2-2xO4 system (x = 0.0, 0.02,

0.04, 0.06, 0.08, 0.1), * indicate FeYO3 peak.

4.3.1.2 Bulk Density, X-Ray Density and Porosity

The X-ray densities (Dx) were computed from the molecular weight and values of

lattice parameter using the formula reported in Ref. [7]. The physical density and

percentage porosity (P) of all the sintered ferrites samples under investigation were

determined by using the equations mentioned in ref. [22]. Table 4.14 presents X-ray

density (Dx), physical density (Dp) and percentage porosity (P %). The influence of

yttrium concentration on X-ray density (Dx), physical density (Dp) and percentage

porosity are shown in Fig. 4.28. From the table, it is seen that Dx increases with yttrium

contents. It increases from 5.37 to 5.54 g/cm3. This increase is due the increase in

molecular weight of the samples. The physical density also increases with yttrium

contents from 4.81 to 4.99 g/cm3 which is attributed to the difference in atomic weight of

Yttrium (88.90585 amu) and iron (55.845 amu) as described in CRC book [8]. It is worth

mentioning that the values of X-ray density are higher than the physical density. This

may be due to porosity in the samples. In present samples, porosity decreases with

increase in yttrium contents and can be attributed to the increase in physical density.

0.00 0.02 0.04 0.06 0.08 0.10

4.8

4.9

5.0

5.1

5.2

5.3

5.4

5.5

5.6

Dx DP Porosity

Y-Concentration (x)

Den

sity

(g/c

m3 )

9.9

10.0

10.1

10.2

10.3

10.4

10.5

Porosity (%

)


able 4.13 Miller indices (hkl) and interplanar spacing (dhkl) for Ni0.6-2xZn0.4+2xY2xFe2-

Concentration (x) for Ni0.6Zn0.4Y2xFe2-2xO4 (0 ≤ x ≤ 0.1). T

2xO4 (0.0 ≤ x ≤ 0.1) ferrites.

Sr.No hkl x = 0.0 x = 0.02 x = 0.04 x = 0.06 x = 0.08 x = 0.1

d(Å ) d(Å ) d(Å ) d(Å ) d(Å ) d(Å )

1 111 4.817 4.824 4.818 4.815 4.814 4.806

2 220 2.953 2.957 2.953 2.954 2.954 2.953

3 311 2.520 2.522 2.520 2.521 2.521 2.521

4 222 2.412 2.415 2.414 2.415 2.416 2.413

5 400 2.090 2.092 2.091 2.091 2.090 2.091

6 422 1.707 1.709 1.709 1.709 1.709 1.707

7 511/333 1.610 1.611 1.610 1.610 1.611 1.610

8 440 1.479 1.480 1.479 1.479 1.480 1.479


The average grain size of each sample calculated using Scherrer formula [2] from

the wid

th of the (311) line is listed in table 4.14. From the table, it is seen that average

grain size decreases for all the samples with increasing yttrium contents (x). The presence

of yttrium ions at or near the grain boundaries hinders the grain growth, thus limiting the

grain boundary mobility. Hence grain size decreases with yttrium contents. The surface

morphology of the compositions was studied using JEOL JSM-840 SEM. In this study,

JEOL JSM-840 SEM was used to study the surface morphology of the samples. The

SEM micro graphs of few representative samples (x = 0.0, 0.08, 0.1) are shown in Fig.

4.29. The values of grain size obtained by SEM micrograph for three representative

samples with x = 0.0, 0.08, 0.1 were 1.39 mμ , 0.82 mμ and 0.74 mμ respectively,

which are comparable to the values of averag ain siz tained by S rrer’s formula

using XRD data. These micrographs show inhomogeneous grain size distribution. It is

e gr e ob che

clear from SEM micrographs that morphology of yttrium substituted samples deviate

from fine structure of pure ferrites [1].

Table 4.14 Lattice constant, phases X-ray density, physical density, percentage porosity

and grain size of the Ni0.6Zn0.4Y2xFe2-2xO4 (0.0 ≤ x ≤ 0.1).

Composition

(x)

Secondary

phase

Lattice

parameter

a(Å )

X-Ray

Density

(g/cm3)

Physical

Density

(g/cm3)

Percentage

porosity

Average

grain

Size(μm)

Scherrer

Ni0.6Zn0.4Fe2O4 - 8.369 5.37 4.81 10.46 1.28

Ni0.6Zn0.4Y0.04Fe1.96O4 - 8.374 5.40 4.84 10.34 1.10

Ni0.6Zn0.4Y0.08Fe1.92O4 - 8.376 5.43 4.87 10.32 0.97

Ni0.6Zn0.4Y0.12Fe1.88O4 - 8.381 5.46 4.90 10.20 0.84

Ni0.6Zn0.4Y0.16Fe1.84O4 FeYO3 8.379 5.50 4.94 10.18 0.77

Ni0.6Zn0.4Y0.2Fe1.80O4 FeYO3 8.377 5.54 4.99 9.93 0.71

(a)

(b)

Fig. 4.29 SEM micrograph of Ni0.6Zn0.4Y2xFe2-2xO4 ferrite for x = 0.0, 0.08, 0.1.

4.3.2 FTIR Analysis Fig. 4.30 shows the FTIR spectra of few representative samples of

Ni0.6Zn0.4Y2xFe2-2xO4 ferrites. The two major absorption bands were observed in the wave

number range 370-1100 cm-1 for all the investigated samples. The band positions for

selected compositions are listed in table 4.15. In the present study, the absorption bands

are found to be in the expected range which confirms the completion of solid state

reaction. In spinel ferrites, the absorption band around 600 cm-1 ( 1ν ) is attributed to

stretching vibrations of tetrahedral metal-oxygen bond and the band around 400 cm-1 ( 2ν

) is attributed to stretching vibrations of octahedral metal-oxygen bond [5]. The high

frequency absorption band 1ν lies in the range 576-579 cm-1 and low frequency

Table 4.15 FTIR absorption bands for Ni0.6Zn0.4Y2xFe2-2xO4 ferrites (x = 0.0, 0.02, 0.04, 0.06, 0.08, 0.1). S. No. Composition )( 1

1−cmν )( 1

2−cmν

1 Ni0.6Zn0.4Fe2O4 576 390

2 Ni0.6Zn0.4Y0.04Fe1.96O4 576.5 394

3 Ni0.6Zn0.4Y0.08Fe1.92O4 578 399

4 Ni0.6Zn0.4Y0.12Fe1.88O4 579 403

5 Ni0.6Zn0.4Y0.16Fe1.84O4 577 406

6 Ni0.6Zn0.4Y0.20Fe1.80O4 577 410

absorption band 2ν lies in the range 390-410 cm-1. The high frequency band 1ν is nearly

constant for all investigated samples. The absorption band 2ν slightly shifts to higher

frequency side and also band broadens which suggesting the occupancy of Y3+ ions on B-

sites. The low frequency band 2ν continues to widen with yttrium contents. This may be

due to larger ionic radius and higher atomic weight of yttrium than Fe3+ ions which affect

Fe3+ - O2- distances on B sites. Similar observations were reported by Gadkari et.al. [1] in

case of Mg1-xCdxFe2O4 + 5% Y3+ ferrites.

Fig. 4.30 FTIR spectra of Ni0.6Zn0.4Y2xFe2-2xO4 ferrites (x = 0.0, 0.02, 0.04, 0.06, 0.08,

0.1). 1ν and 2ν indicate tetrahedral and octahedral absorption bands respectively.

4.3.3 Electrical resistivity The two probe method was used for measuring dc resistivity of the present samples.

The surface of the samples were polished and then coated with silver paste as a contact

material for electrical measurements. A sensitive Keithley Electrometer 610-C was used.

The effect of temperature on dc resistivity has been studied in the temperature range 25-

200 °C.

Fig. 4.31 shows the dc resistivity at room temperature for all the compositions as a

function of yttrium concentration. The substitution of yttrium in place of iron may bring

the following changes in conduction process.

(A) In all the present samples, Fe3+ ions are being replaced by Y3+ ions. Since the

ionic radius of Y3+ ions is larger than ionic radius of Fe3+, the substitution

increases the bond length resulting in a reduction of hopping probability. This

process increases the resistivity.

(B) Y3+ ions do not take part in conduction process rather decreases the hopping rate

of electrons by blocking the Verwey’s hopping mechanism resulting in an

increase of resistivity.

(C) High concentration of Y3+ ions diffused to the grain boundaries and formed

inhomogeneous solid solution. It may tend to segregate at the grain boundaries

and formed highly resistive yttrium iron oxide FeYO3 (secondary phase as

confirmed by XRD) which enhances the resistivity

(D) In the present samples, Y3+ ion replaces Fe3+ ions at octahedral B-sites. The

concentration of Fe3+ ions decreases continuously when yttrium is incorporated in

place of iron. The probability of hopping rate of electron transfer is expected to

decrease with the decrease of Fe3+ ions. Consequently, dc electrical resistivity

increases with yttrium contents.

5

6

7

8

9

0 0.02 0.04 0.06 0.08 0.1

Y-Concentration (x)

Log ρ

(ohm

.cm

)

Fig. 4.31 Variation of Log ρ Vs. Y-concentration for Ni0.6Zn0.4Y2xFe2-2xO4 ferrites (x =

0.0, 0.02, 0.04, 0.06, 0.08, 0.1).

Further, it is known that resistivity decreases with the decrease in grain size [46]. In

the present samples, grain size gradually decreases and thereby increasing the

resistivity. This is consistent with previous work where it has been reported that the

substitution of yttrium increases the resistivity of Ni-Zn ferrites [11].

Temperature dependent dc resistivity for all the samples has been measured in the

temperature range 25-200 °C. Fig. 4.32 shows the Arrhenius plots of Ni0.6Zn0.4Y2xFe2-

2xO4 ferrites. It is seen from the figure that the temperature dependent resistivity of all

the samples is observed to decrease with the rise of temperature. This can be

attributed to the increase in drift mobility of charge carriers with the rise in

temperature.

The values of activation energies corresponding to the slope of Arrhenius plots for all

the compositions have been estimated. Fig. 4.33 shows that the activation energy

increases with the increase in yttrium contents. The increase in activation energy is

expected because the resistivity has been found to increase for the whole range of

yttrium concentration. Yttrium impedes the electron transfer between Fe2+ and Fe3+

ions and thereby enhances the activation energy.

4

5

6

7

8

9

10

1.8 2 2.2 2.4 2.6 2.8 3 3.2 3.4103/T(K)

Log ρ

(ohm

.cm

)

x = 0x = 0.02x = 0.04x = 0.06x = 0.08x = 0.1

Fig. 4.32 Variation of Log ρ Vs. 1000/ T(K) for Ni0.6Zn0.4Y2xFe2-2xO4 ferrites (x = 0.0,

0.02, 0.04, 0.06, 0.08, 0.1).

Fig. 4.33 Activation energy Vs. Y-concentration (x) for Ni0.6Zn0.4Y2xFe2-2xO4 ferrites (x =

0.15

0.19

0.23

0.27

0.31

0.35

0 0.02 0.04 0.06 0.08 0.1

Y-Concentration (x)

E (e

V)

0.0, 0.02, 0.04, 0.06, 0.08, 0.1).

4.3.4 Dielectric Properties Dielectric properties were investigated at room temperature over the frequency range

from 10 Hz to 10 MHz by using the Solartron 1260 Impedance Analyser. The values of

dielectric constant (ε ′ ) and dielectric loss tangent (tan δ) were determined using the

relations given in ref. [34]

4.3.4.1 Compositional dependence of dielectric behavior

Fig. 4.34 depicts the variation of dielectric constant for all the samples measured

at room temperature in the frequency range 10 Hz-10 MHz. The magnitude of dielectric

constant decreases with the increase of yttrium concentration. The compositional

0

10000

20000

30000

40000

50000

10 100 1000 10000 100000 1000000 10000000

Frequency (Hz)

Die

lect

ric

cons

tant

x = 0x = 0.02x = 0.04x = 0.06x = 0.08x = 0.1

Fig. 4.34 Variation of dielectric constant Vs frequency for Ni0.6Zn0.4Y2xFe2-2xO4 ferrites

(x = 0.0, 0.02, 0.04, 0.06, 0.08, 0.1).

dependence of dielectric constant can be explained by assuming that the conduction

mechanism is similar to the mechanism of dielectric polarization as reported in the

literature [13]. The hopping of electrons between Fe2+ and Fe3+ determines the

polarization and thus the dielectric constant of ferrites. Fe2+ ions are formed at high

sintering temperature due to partial reduction of Fe3+ ions. In the present samples, Y3+

ions replaces Fe3+ ions at B-sites when gradually increasing concentration of Y3+ ions are

incorporated in the Ni-Zn ferrites. This may be attributed to the reduction of Fe2+ / Fe3+

ions at B-sites. As yttrium concentration further increased, the iron contents will be

continuously decreased. The n type charge carrier will also be reduced as a result of

decreasing iron contents. Consequently, space charge polarization decreases with

increasing yttrium content which is clearly manifested by the relative decrease of

dielectric constant values from x = 0.0 to x = 0.1.

4.3.4.2 Frequency dependence of dielectric constant Fig. 4.34 depicts the variation of dielectric constant as a function of frequency at

room temperature for all the compositions of Ni-Zn-Y ferrites. It can be observed from

the figure that dielectric constant decreases continuously with rise in frequency. The

decrease is larger at low frequency region and it attains nearly constant value at high

frequency region. In ferrites, the dielectric structure was assumed to be made of two

layers. The first layer consists of well conducting grains and the second layer consists of

highly resistive grain boundaries. At low frequency, the electrons reach the grain

boundaries through hopping process and accumulate there due to its high resistivity. This

causes the localized accumulation of charges under the applied field, which results in

interfacial polarization. Hence dielectric constant is high at low frequency region. At high

frequency, the electronic exchange between Fe2+ and Fe3+ ions cannot follow the applied

alternating field, which reduces the contribution of interfacial polarization and thereby

decreasing the dielectric constant at high frequency. As the frequency of the applied field

further increased, a point will come when charge carriers can not line up their axes

parallel to the field and thereby reducing the space charge polarization. This will reduce

the dielectric constant with rise in frequency and attains almost constant value at high

frequency [13]. This type of dielectric behaviour is observed by several investigators

[46, 33].

4.3.4.3 Variation of dielectric loss tangent (tan δ) with frequency Fig. 4.35 depicts the variation of dielectric loss tangent (tan δ) with increasing frequency

for Ni0.6Zn0.4Y2xFe2-2xO4 ferrites. The figure shows that tan δ decreases with yttrium

contents. This can be attributed to the increase in resistivity which causes reduction in

tanδ.

0

0.2

0.4

0.6

0.8

1

10 100 1000 10000 100000 1000000 10000000

Frequency (Hz)

tan δ

x= 0x = 0.02x = 0.04x = 0.06x = 0.08x = 0.1

Fig. 4.35 Plot of loss tangent (tan δ) Vs. frequency for Ni0.6Zn0.4Y2xFe2-2xO4 ferrites (x

= 0.0, 0.02, 0.04, 0.06, 0.08, 0.1).

It is known that ferrites consist of good conducting grains separated by poorly conducting

grain boundaries. The grain boundaries are more effective at low frequency region. Thus

the more energy is required for hopping process. Therefore the energy loss is high at low

frequency. Hence tan δ is high in this low frequency region. At high frequency region,

well conducting grains are more effective. Therefore, the energy loss is low because low

energy is needed for hopping mechanism of charge carriers. Hence tan δ is low at high

frequency [17].

4.3.5 Magnetic properties 4.3.5.1 MH-loops Fig. 4.36 shows the MH-loops of all the samples for the Ni0.6Zn0.4Y2xFe2-2xO4 system.

The MH-loops of the present samples are narrow S-type with small coercivity. The

values of magnetic parameters e.g. saturation magnetization and coercivity are listed in

table 4.16.

-6000 -3000 0 3000 6000-100-80-60-40-20

020406080

M (e

mu)

H (Oe)

-6000 -3000 0 3000 6000-80-60-40-20

020406080

M (e

mu)

H (Oe)

-6000 -3000 0 3000 6000-80-60-40-20

020406080

M (e

mu)

H (Oe)

-6000 -3000 0 3000 6000-80-60-40-20

020406080

M (e

mu)

H (Oe)

-6000 -3000 0 3000 6000-80-60-40-20

020406080

M (e

mu)

H (Oe)

-6000 -3000 0 3000 6000-80-60-40-20

020406080

M (e

mu)

H (Oe)

Fig. 4.36 Hysteresis loops for Ni0.6Zn0.4Y2xFe2-2xO4 ferrites (x = 0.0, 0.02, 0.04, 0.06,

0.08, 0.1).

It is observed that the value of saturation magnetization decreases with the increase of

yttrium concentration. This can be explained on the basis of assumed cation distribution.

It is known that zinc prefer tetrahedral sites while nickel prefers octahedral sites [18].

Thus the assumed cation distribution for Ni0.6Zn0.4Fe2O4 ferrites can be written as

(Zn0.4Fe0.6) [Ni0.6Fe1.4] O4. When non-magnetic yttrium ions are introduced on the

expense of iron ions, they tend to occupy octahedral sites [9] and probably replace Fe3+

ions on this site. Thus the magnetization of octahedral sublattice decreases keeping the

magnetization of tetrahedral sublattice constant. Due to antiferromagnetic coupling, the

net magnetization is expected to decrease which results in the observed fall in saturation

magnetization. Similar kind of observations was reported by Jacobo et. al. [43] about the

slight decrease of saturation magnetization and increase of coercivity in

Ni0.5Zn0.5Y0.02Fe1.98O4 ferrites as compared to the unsubstituted sample.


Ni0.6Zn0.4Y2xFe2-2xO4 ferrites (x = 0.0, 0.02, 0.04, 0.06, 0.08, 0.1).

nCompositio

(x)


0.0 Ni0.6Zn0.4Fe2O4 75.31 12.87

0.02 Ni0.6Zn0.4Y0.04Fe1.96O4 71.68 17.32

0.04 Ni0.6Zn0.4Y0.08Fe1.92O4 71.52 19.45

0.06 Ni0.6Zn0.4Y0.12Fe1.88O4 68.34 24.81

0.08 Ni0.6Zn0.4Y0.16Fe1.84O4 66.56 29.45

0.1 Ni0.6Zn0.4Y0.20Fe1.80O4 60.83 32.37

It is known that coercivity is inversely proportional to the grain size [19]. The

gradual increase of coercivity (Hc) with the increase of yttrium concentration in the

present samples may be attributed to the decrease in grain size.

4.3.5.2 Initial permeability ( iμ )

Fig. 4.37 shows the variation of initial permeability ( iμ ) over a frequency range

(100 Hz ≤ f ≤ 1 MHz) of Ni-Zn-Y ferrites with six different compositions of the form

(Ni0.6Zn0.4Y2xFe2-2xO4) with x = 0.0, 0.02, 0.04, 0.06, 0.08, 0.1 The effect of increasing

yttrium concentration results in a decrease of initial permeability. From figure, it has been

observed that the initial permeability slightly decreases and above 100 KHz the values

remains nearly constant for all the samples. The iμ depends upon two magnetic

mechanisms: the domain wall motion and spin rotational magnetization. It is known that

yttrium ions has a high preference for B-sites [9] and the substitution of yttrium reduces

the spin rotational magnetization because it may reduce the magnetic exchange

interaction between tetrahedral (A) sites and octahedral (B) sites and thereby reducing the

saturation magntization. It is known that iμ is related to the average grain size, saturation

magnetization (Ms) and magnetocrystalline anisotropy constant (K1) [20].

1

2

KDM mS

i =μ

The microstructure of these samples shows that average grain size decreases with

the increase of yttrium concentration which hinders the domain wall motion. Therefore, a

decrease of iμ with increasing yttrium contents is expected. The observed fall in iμ

could be due to combined effect of average grain size and saturation magnetization. The

observed fall in iμ also suggest that K1 is not playing a dominant role.

Fig. 4.37 Frequency variation of initial permeability for Ni0.6Zn0.4Y2xFe2-2xO4 ferrites (x

= 0.0, 0.02, 0.04, 0.06, 0.08, 0.1).

4.3.5.3 Magnetic loss tangent (tan)

Magnetic loss tangent (tan) decreases with the increase of yttrium contents as

shown in Fig. 4.38. Maisnam et.al. [25] reported that the magnetic loss decreases with

507090

110130150170190

210

0 200 400 6 800 1000

Frequency (K

Initi

al P

erm

eabi

lity x = 0

x = 0.02x = 0.04x = 0.06x = 0.08x = 0.1

00

Hz)

decrease in the average grain size and vice versa. In the present samples, electrical

resistivity increases with yttrium contents. Hence the eddy current loss decreases with

yttrium contents. The lower values of tan with yttrium contents are attributed to the low

eddy current loss as a result of higher resistivity and decrease in the average grain size.

0

0.2

0.4

0.60.8

1

1.2

1.4

1.6

0 200 400 600 800 1000

Frequency (KHz)

Mag

netic

Los

s Ta

ngen

t

x = 0x = 0.02x = 0.04x = 0.06x = 0.08x = 0.1

Fig. 4.38 Frequency variation of magnetic loss tangent for Ni0.6Zn0.4Y2xFe2-2xO4 ferrites

(x = 0.0, 0.02, 0.04, 0.06, 0.08, 0.1).

4.4 Co1-xZnxY0.15Fe1.85O4 Ferrite System 4.4.1 X-Ray Diffraction Analysis

X-ray diffraction patterns were taken by using X-ray diffractometer JDX-3532

JEOL Japan using αKCu radiation. The operating voltage and current were kept at 40

KV and 300 mA. The samples were scanned through 15 - 70° to identify the phases

developed and to confirm the completion of chemical reaction.

Fig 4.39 shows the XRD patterns of Co1-xZnxY0.15Fe1.85O4 ferrites (x = 0.0, 0.2,

0.4, 0.6, 0.8, 1.0). The peaks of all the XRD patterns were analyzed and indexed.

Analysis of the XRD patterns confirms the formation of cubic spinel phase as main phase

along with few traces of secondary phase. The strongest reflection comes from (311)

plane which denotes the formation of spinel structure [45]. The presence of allowed fcc

peaks corresponding to the planes (220), (311), (222), (400), (422), (511) and (440)

confirms the formation of cubic spinel structure. It was observed that all the samples are

biphasic. The reflections of second phase which are identified as YFeO3 appeared at 2θ =

23.14°, 39.28°, 68.1° (indicated by the * in Fig. 4.39). These peaks are identified as

(110), (221), (041) reflection of YFeO3 (JCPDS # 80150). A possible explanation for the

appearance of second phase is that some yttrium ions cannot enter the spinel lattice

rather diffuse to the grain boundaries and react with Fe to form YFeO3 (second phase)

[1]. Miller indices (hkl) and interplanar spacing (d-values) for Co-Zn-Y ferrites are listed

in table 4.17.

4.4.1.1 Lattice Parameters The average value of the lattice constant for all the samples was calculated using

the Nelson-Riley function [2].

⎥⎦

⎤⎢⎣

⎡+=

θθ

θθθ

22

21)( Cos

SinCosF (4.3)

The variations of lattice constant as a function of zinc concentration are listed in table

4.18. The lattices constant was found to increase form 8.378 Å to 8.438 Å with increasing

zinc contents. The increasing behavior of lattice constant can be explained on the basis of

difference in ionic radii of the constituent ions (Zn2+ and Co2+). As zinc ions (0.82 Å)

10 20 30 40 50 60 70-200

0

200

400

600

800

1000

1200

1400

1600

x = 0.0

440

511

422

40022

2

220

***

Inte

nsity

(Cou

nts)

Inte

nsity

(Cou

nts)

2 Theta (degrees)10 20 30 40 50 60 70

0

500

1000

1500

2000

2500

3000

x = 0.2

440

511

422400222

311

220

***

2 Theta (degrees)

10 20 30 40 50 60 70

0

300

600

900

1200

1500

1800

x = 0.444

051

142

2

40022

231

122

0

***

Inte

nsity

(Cou

nts)

Inte

nsity

(Cou

nts)

2 Theta (degrees)10 20 30 40 50 60 70

0

500

1000

1500

2000

2500

x = 0.6

440

511

422

40022

231

1

311

220

***

2 Theta (degrees)

10 20 30 40 50 60 70

0

500

1000

1500

2000

2500x = 0.8

440

511

422

40022

231

122

0

***Inte

nsity

(Cou

nts)

2 Theta (degrees)10 20 30 40 50 60 70

0

300

600

900

1200

1500

1800x = 1.0

440

511

422

40022

231

122

0

***

Inte

nsity

(Cou

nts)

2 Theta (degrees)

Fig. 4.39 X-ray diffraction patterns for Co1-xZnxY0.15Fe1.85O4 ferrites (x = 0.0, 0.2, 0.4,

0.6, 0.8, 1.0). * indicates YFeO3 peaks.

increases at the expense of cobalt ions (0.78 Å), the lattice seems to expand to

accommodate the increased number of zinc ions of relatively larger ionic radii. However,

as far as the author is aware, no data is available in the literature to compare the values of

lattice parameter of Co1-xZnxY0.15Fe1.85O4 ferrites (x = 0.0, 0.2, 0.4, 0.6, 0.8, 1.0). The

lattice constant of CoFe2O4 is reported as 8.395 Å and ZnFe2O4 is 8.451 Å [47]. The

lattice constant of zinc substituted samples was found to be slightly below the range of

the lattice constants of CoFe2O4 and ZnFe2O4. This may be attributed to the presence of

second phase of YFeO3. Similar observations were reported by Gadkari et.al. [1].

4.4.1.2 Average Crystallite Size The average crystallite size of each sample under investigation was determined

from the full width at half maximum (FWHM) of the most intense peak (311) using

Debye Scherrer formula [2]:

θβλ

CosD 94.0= (4.4)

where λ is the wavelength, β is the full width at half maximum (FWHM), θ is the

Bragg’s diffraction angle. Here ( ) 2/122SM βββ −= , Mβ is the full width at half maximum

(FWHM) of the most intense peak (311) and Sβ is the standard instrumental broadening

[1]. The values of average crystal size are listed in table 4.18. The average crystal size

was found to decreases from 38.41 nm to 14.25 nm with the increase of Zn contents. The

variation in crystalline size depends upon the preparation condition which gives rise to

different rates of ferrite formation for different concentration of zinc. Such observations

in the variation of particle size for different zinc contents have been reported by several

researchers [47, 48].

The SEM micro graphs of few representative samples (x = 0.0, 0.4, 1.0) are

shown in Fig.4.40. The average grain size estimated from SEM micrographs of the

present samples with substitution level x = 0.0, 0.4, 1.0 are 0.226 µm, 0.223 µm and

0.219 µm respectively. The average grain size estimated from SEM picture is larger than

the particle size estimated from XRD data, suggesting the size of many grains. SEM

picture may be the aggregation of more than one particle due to strong inter-particle

interactions [49]. SEM micrographs indicate nearly uniform distribution of grains.

(a)

(b)

(c)

Fig. 4.40 SEM micrograph of Co1-xZnxY0.15Fe1.85O4 ferrite (a)x = 0.0, (b) x = 0.4, (c) x =

1.0.

4.4.1.3 X-ray density, Physical Density and Porosity The X-ray densities (Dx) were computed from the values of lattice parameter

using the formula reported in Ref. [6]. The influence of yttrium concentration on X-ray

density (Dx), physical density (Dp) and percentage porosity are listed in table 4.18. X-ray

density (Dx) shows increasing trend with the increase in zinc concentration. It increases

from 5.414 to 5.442 g/cm3. This increase is attributed to the increase in molecular weight.

The atomic weight of Zn (65.38 amu) is greater than Co (58.9332 amu). The influence of

zinc concentration on X-ray density (Dx) and physical densities (Dp) are shown in Fig.

4.41.

Table 4.17 Miller indices (hkl) and interplanar spacing (d) for Co1-xZnxY0.15Fe1.85O4 (0.0

≤ x ≤ 1.0).

Sr.No hkl x = 0.0

d(Å )

x = 0.2

d(Å )

x = 0.4

d(Å )

x = 0.6

d(Å )

x = 0.8

d(Å )

x = 1.0

d(Å )

1 220 2.980 2.978 2.966 2.964 2.974196 2.970

2 311 2.528 2.532 2.536 2.541 2.546075 2.550

3 222 2.416 2.420 2.422 2.426 2.42378 2.418

4 400 2.088 2.098 2.093 2.094 2.096141 2.096

5 422 1.714 1.715 1.714 1.716 1.715 1.625

6 511 1.615 1.619 1.620 1.623 1.624 1.715

7 440 1.483 1.485 1.485 1.486 1.492 1.493

Table 4.18 Lattice constant, phases, X-ray density, physical density, percentage porosity

and average crystallite size of the Co1-xZnxY0.15Fe1.85O4 (0.0 ≤ x ≤ 1.0).

Composition

(x)

Lattice

parameter

a(Å )

Secondary

phase

X-Ray

Density

(g/cm3)

Physical

Density

(g/cm3)

Percentage

porosity

Average

crystallite

size (nm)

Scherrer

formula

CoY0.15Fe1.85O4 8.378 YFeO3 5.414 3.954 26.977 38.41

Co0.8Zn0.2Y0.15Fe1.85O4 8.391 YFeO3 5.418 4.026 25.684 36.32

Co0.6Zn0.4Y0.15Fe1.85O4 8.405 YFeO3 5.42 4.187 22.755 27.07

Co0.4Zn0.6Y0.15Fe1.85O4 8.419 YFeO3 5.422 4.281 21.046 26.41

Co0.2Zn0.8Y0.15Fe1.85O4 8.429 YFeO3 5.431 4.365 19.619 16.59

ZnY0.15Fe1.85O4 8.438 YFeO3 5.442 4.421 18.763 14.25

The physical densities of the sintered samples have been measured using

Archimedes principle and are tabulated in table 4.18. The bulk density of all the samples

increases with the increase of zinc concentration. The physical density increases from

3.954 to 4.421 g/cm3.The increase in physical densities are again due to difference in

Fig. 4.41 X-ray density (Dx), Physical density (Dp), percentage porosity Vs. Zn2+

concentration for Co1-xZnxY0.15Fe1.85O4 ferrites (x = 0.0, 0.2, 0.4, 0.6, 0.8, 1.0).

ionic radii of Zn2+ and Co2+ ions. It was observed that the bulk density values are smaller

than X-ray density which indicates the presence of pores. In the present samples, the

porosity decreases with increase in zinc contents and can be attributed to the increase in

physical density.

4.4.2 Electrical Resistivity The room temperature dc resistivity of Co1-xZnxY0.15Fe1.85O4 ferrite was measured

by using two probe method. A Source meter model 2400 (Keithley) was used. The

resistivity of the sintered samples was determined by using the relation: ρ = RA/t where

‘R’ is resistance, ‘A’ is the area of electrode and ‘t’ is thickness of the sample.

Temperature dependent dc resistivity has been measured in the temperature range 25-200

°C. The results of dc resistivity are listed in table 4.19. It was found that the resistivity

decreases with the increase of Zn concentration from 9.20 ×107 Ω. cm to 5.26 ×106 Ω.

cm.

The substitution of zinc in place of cobalt may bring the following changes in

conduction process.

It is known that some Fe2+ ions may be formed during sintering process at high

temperature due to volatilization of Zn2+ ions and partial reduction of Fe3+ ions [50]. It

was reported that Fe2+ ions have a strong preference to occupy B-sites [8] and Zn2+ ions

occupy tetrahedral sites [51]. It is, therefore, expected that the conduction process occurs

due to exchange of electrons between Fe2+ and Fe3+ ions. The concentration of Fe2+ ion

gradually increases at B-sites for higher concentration of zinc. The hopping rate will

increase.

On adding Zn2+ ions, Fe3+ are partially replaced by Zn2+ ions which also have a

strong tetrahedral site preference. Some of the Fe3+ ions will migrate from A-sites to B

sites as a result of increasing concentration of Zn2+ ions [52]. It seems that there is an

increase in the number of Fe2+/Fe3+ ions pairs at B-sites due to corresponding migration

of some of the Fe3+ ions from A sites to B-sites, consequently deceasing the resistivity as

well as activation energy.

Another possibility may occur in the hopping process among cobalt ions with

different valences states. The Co2+ ions are change into Co3+ ions (Co2+ Co3+ + e). The

hole hopping is the dominant one in this process as reported in the literature [51]

→

So the overall effect of the increasing concentration of Zn2+ ions enhances the probability

of formation of Fe2+ ions and thereby decreasing the resistivity.

Temperature dependent dc resistivity has been measured in the temperature range

25 - 200°C. The Arrhenius plots are shown in Fig.4.42. The figure shows that the dc

resistivity decreases linearly with temperature for all the samples. This can be attributed

to the increase in drift mobility of thermally activated charge carriers. These samples

exhibit semi-conducting behavior and the samples are showing the temperature

dependence and are therefore known as degenerate semi-conductors. The observed

decrease in dc resistivity with temperature is normal behavior for semiconductors which

follows the arrhenius relation. The activation energy of all the samples has been

determined from the slope of Arrhenius plots and are listed in table 4.19.

Table 4.19 Resistivity (ρ), Activation energy (eV) and transition temperature for Co1-

xZnxY0.15Fe1.85O4 ferrites (x = 0.0, 0.2, 0.4, 0.6, 0.8, 1.0).

Ferrite Composition ).( cmΩ

ρ

Activation energy (eV)

Ferri Para

Transition temperature (K)

CoY0.15Fe1.85O4 9.20 × 107 0.52 - -

Co0.8Zn0.2Y0.15Fe1.85O4 5.73 × 107 0.49 - -

Co0.6Zn0.4Y0.15Fe1.85O4 4.28 × 107 0.46 - -

Co0.4Zn0.6Y0.15Fe1.85O4 1.74 × 107 0.33 0.45 373

Co0.2Zn0.8Y0.15Fe1.85O4 1.29 × 107 0.26 0.40 333

ZnY0.15Fe1.85O4 0.526 × 107 0.17 0.36 313

4.6

5.4

6.2

7

7.8

2 2.4 2.8 3.2

1000/T(K)

Log ρ

(Ω. c

m)

x = 0.0x = 0.2x = 0.4

4.75

5.25

5.75

6.25

6.75

7.25

2.1 2.4 2.7 3 3.3

1000/T(K)

Log ρ

(Ω. c

m)

x = 0.6

4.75

5.25

5.75

6.25

6.75

7.25

2.1 2.4 2.7 3 3.3

1000/T(K)

Log ρ

(Ω. c

m)

x = 0.8

4.6

5.1

5.6

6.1

6.6

2.1 2.4 2.7 3 3.3

1000/T(K)

Log ρ

(Ω. c

m)

x = 1.0

Fig. 4.42 Arrhenius plots for Co1-xZnxY0.15Fe1.85O4 ferrites (x = 0.0, 0.2,

0.4, 0.6, 0.8, 1.0).

The variation of resistivity as a function of temperature is linear up to transition

temperature. The conduction mechanism changes above the transition temperature. This

may be the Curie temperature. It is clear from the figure that the slope of the samples

with substitution level x = 0.6, 0.8, 1.0 changes at transition temperature. The values of

activation energy and transition temperature are listed in table 4.19. The table shows that

the activation energy in the para region is greater than activation energy in ferri region.

The charge carriers in para region need more energy to be activated.

4.4.3 Dielectric properties

4.4.3.1Compositional Dependence of dielectric constant Dielectric properties were studied over the frequency range from 100 Hz to 100

KHz by using 1689 M digibridge. The behavior of both dielectric constant (ε ′ ) and

dielectric loss tangent (tan δ) with composition is similar to that of electrical resistivity.

This behavior can be explained on the basis of the assumption that there exist a strong

correlation between electrical resistivity and dielectric behavior.

The dielectric constant is found to increase with the increase of Zn2+ contents as

shown in the Fig. 4.43 . The variation in the values of dielectric constant can be explained

on the basis of space charge polarization and Koop’s two layer model. According to

Koop’s two layer model, the ferrite is supposed to be made of well conducting grains

separated by insulating grain boundaries. The conduction in ferrite materials occurs due

to hopping of electrons between Fe2+ and Fe3+ at B-sites. The electrons reach the grain

boundaries through hopping mechanism and pile up at grain boundaries due to its higher

resistivity and produce space charge polarization. The substitution of Zn2+ ions would

continuously increase the Fe2+ concentration at B-sites due to its volatilization. This in

turn increases the piling up of charges at grain boundaries and thereby enhancing the

space charge polarization. The value of dielectric constant, therefore, increases with

increasing Zn contents.

4.4.3.2 Frequency Dependence of dielectric constant Fig.4.43 shows the variation of dielectric constant as a function of frequency in

the range 100 Hz to 100 KHz. It is clear from the figure that the values of dielectric

constant decreases with frequency. It is low at high frequency and then decreases sharply

with the increase in frequency. This behavior is known as dielectric dispersion which

depends upon space charge polarization. It was suggested by Koops [14] that ferrites

consist of well conducting grains separated by thin insulating grain boundaries. This

causes the localized accumulation of charges under the applied external field and thereby

enhancing the space charge polarization. Hence high value of dielectric constant is

expected at low frequency. As the frequency of the applied field further increases, a stage

will reach when space charge carriers can not line up their axes parallel to the field and

thereby reducing the contribution of space charge polarization. This in turn decreases the

dielectric constant with increase in frequency and attains almost constant value as is

observed. Similar behavior has been observed in the literature [8].

4.4.3.3 Variation of dielectric loss tangent with frequency The variation of dielectric loss tangent (tan δ) with increasing frequency for

mixed Co1-xZnxY0.15Fe1.85O4 ferrites is shown in Fig.4.44. It is seen from the figure that

tan δ increases with increasing zinc concentration. This can be attributed to the decrease

in resistivity which in turn increases the tan δ. The Figure also shows that tan δ decreases

with increasing frequency. The more energy is needed for hopping process in the low

frequency region which corresponds to high resistivity (due to insulating grain

boundaries). Hence tan δ is high in low frequency region. A small energy is required for

hopping of charge carriers in the high frequency region which corresponds to low

resistivity (due to well conducting grains). Therefore, tan δ is low at high frequency

region [8].

0

1

2

3

0 20 40 60 80

Frequency (KHz)

Die

lect

ric

Cons

tant

100

x = 0.0x = 0.2x = 0.4x = 0.6x = 0.8x = 1.0

Fig. 4.43 Variation of dielectric constant Vs frequency for Co1-xZnxY0.15Fe1.85O4 ferrites

(x = 0.0, 0.2, 0.4, 0.6, 0.8, 1.0).

0

0.4

0.8

1.2

1.6

0 20 40 60 80

Frequency (KHz)

Die

lect

ric L

oss

Tang

ent

100

x = 0.0x = 0.2x = 0.4x = 0.6x = 0.8x = 1.0

. Fig. 4.44 Plot of loss tangent (tan δ) Vs frequency for Co1- xZnxY0.15Fe1.85O4 ferrites (x

= 0.0, 0.2, 0.4, 0.6, 0.8, 1.0).

4.4.3.4 Relationship between dielectric constant (ε ′ ) and Resistivity (ρ)

The values of resistivity (ρ), dielectric constant (ε ′ ), square root of resistivity (

ρ ), the product ( ρε ′ ) are listed in table 4.20 . It is seen from the table that the

Table 4.20 Variation of dielectric constant (ε ′ ) and resistivity ( ρ ) in the case of Co-Zn-

Y ferrites.

Composition

(x) Hzat100ε ′

KHzat100

ε ′).( cmΩ

ρ

).( 2/12/1 cmΩ

ρHzat100

ρε ′

KHzat100ρε ′

0.0 0.397 0.143 9.2×107 9593.75 3.8×103 1.37×103

0.2 0.581 0.19 5.7×107 7569.68 4.4×103 1.44×103

0.4 0.683 0.261 4.3×107 6542.17 4.5×103 1.71×103

0.6 1.137 0.317 1.7×107 4171.33 4.7×103 1.32×103

0.8 1.521 0.321 1.3×107 3591.66 5.5×103 1.15×103

1.0 2.81 0.319 5.3×106 2293.47 6.4×103 0.73×103

dielectric constant is found to be roughly inversely proportional to the square root of

resistivity and the product ρε ′ remains nearly constant. Such relationship was

reported by several researchers in the literature [53, 34].

4.5 CoFe2O4 + x Y2O3 Ferrite System 4.5.1 X-Ray Diffraction Analysis

X-ray diffraction patterns were taken by using X-ray diffractometer JDX-3532

JEOL Japan using αKCu radiation. The operating voltage and current were kept at 40

KV and 300 mA. The samples were scanned through 15 - 80° to identify the phases

developed and to confirm the completion of chemical reaction.

Fig. 4.45 shows the XRD patterns of CoFe2O4 + x Y2O3 (x = 0 wt%, 1 wt %, 3 wt

%, 5 wt %). The peaks of all the XRD patterns were indexed and cubic spinel phase was

identified as main phase along with few traces of second phase. The presence of allowed

fcc peaks corresponding to the planes (111), (220), (311), (222), (400), (422), (511/333)

and (440) confirms the formation of cubic spinel structure. It was observed that all the

samples are biphasic except the sample with x = 0 (CoFe2O4). The diffraction pattern of

CoFe2O4 (x = 0) matched well with JCPDS card 22-1086 for Co-ferrite. The sample

CoFe2O4 showed a single phase spinel structure with no impurities in the XRD pattern.

The reflection peaks of second phase which were identified as YFeO3 appeared at 2θ =

23.1°, 39.6°, 45.51° (indicated by the * in Fig.). These peaks can be identified as (110),

(211), (122) reflection of YFeO3 (JCPDS # 80150). Miller indices (hkl) and interplanar

spacing (d) for Co-Y ferrite system are listed in table 4.21.

Table 4.21 Miller indices (hkl) and interplanar spacing (d) for CoFe2O4 + x Y2O3 (x = 0, 1 wt %, 3 wt %, 5 wt %).

Sr.No hkl x = 0.0

d(Å )

x = 1

d(Å )

x = 3

d(Å )

x = 5

d(Å ) 1 111 4.843 4.870 4.881 4.875

2 220 2.968 2.964 2.966 2.962

3 311 2.532 2.536 2.546 2.550

4 222 2.422 2.427 2.421 2.420

5 400 2.101 2.097 2.094 2.091

6 422 1.713 1.711 1.711 1.709

7 333 1.615 1.619 1.617 1.616

8 440 1.477 1.480 1.483 1.486

10 20 30 40 50 60 70 80 90-500

0

500

1000

1500

2000

2500

3000

3500

4000

440

511

422

40022

231

122

0

111

(a)In

tens

ity (C

ount

s)

2 Theta (degrees)10 20 30 40 50 60 70 80 90

-500

0

500

1000

1500

2000

2500

3000

3500

4000

440

511

422

*

400

*

222

311

220

*

111

(b)

Inte

nsity

(Cou

nts)

2 Theta (degrees)

10 20 30 40 50 60 70 80 90

0

500

1000

1500

2000

2500

300044

051

142

2

*400

*

222

311

220

*

111

(c)

Inte

nsity

(Cou

nts)

2 Theta (degrees)10 20 30 40 50 60 70 80 90

-500

0

500

1000

1500

2000

2500

3000

3500

220

111

*

440

511

422

*400

*

222

311(d)

Inte

nsity

(Cou

nts)

2 Theta (degrees)

Fig. 4.45 X- ray diffraction patterns for CoFe2O4 + x Y2O3 (a) x = 0, (b) x = 1 wt %, (c) x

= 3 wt %, (d) x = 5 wt %). (*) indicates secondary phase.

4.5.1.1 Lattice Parameters The average value of the lattice constant for all the samples was calculated using

the Nelson-Riley function [2].

⎥⎦

⎤⎢⎣

⎡+=

θθ

θθθ

22

21)( Cos

SinCosF (4.5)

The lattice constant as a function of yttrium concentration is listed in table 4.22. The

lattices constant are found to decrease form 8.385 Å to 8.348 Å with increasing yttrium

contents. This means that the addition of yttrium in the samples cannot enter the spinel

lattice and it may diffuse to the grain boundaries and react with Fe to form YFeO3

(secondary phase). It is possible that the spinel lattice is compressed by the intergranular

secondary phase due to the differences in the thermal expansion coefficients [28]. The

lattice constant of bulk CoFe2O4 is reported as 8.395 ± 0.005 Å [54].

Our value of lattice constant for CoFe2O4 comes out to be 8.385 Å. The difference

in the value of lattice constant of CoFe2O4 may be due to different sintering atmosphere

and the method of preparation. The doping of Y2O3 in CoFe2O4 affects not only the phase

composition but also the size of the spinel lattice. Such a reduction in the lattice constant

has been reported in the literature [1].

Table 4.22 Phases, lattice constant, X-ray density, physical density and grain size for

CoFe2O4 + x Y2O3 ferrites.

Composition (x)

Lattice parameter a(Å )

Secondary phase

Lattice parameter a(Å )

Average grain Size(μm) SEM

Physical Density g/cm3

Average crystallite size (nm) Scherrer formula

CoFe2O4 8.385 - 8.385 0.689 4.129 48.51 CoFe2O4 + 1 wt% of Y2O3

8.375 YFeO3 8.375 0.680 4.311 46.31

CoFe2O4 + 3 wt% of Y2O3

8.361 YFeO3 8.361 - 4.391 39.28

CoFe2O4 + 5 wt% of Y2O3

8.348 YFeO3 8.348 0.65 4.463 34.11


The average crystallite size of each sample under investigation was determined

from the full width at half maximum (FWHM) of the most intense peak (311) using

Debye Scherrer formula [2]:

θβλ

CosD 94.0= (4.6)

where λ is the wavelength, β is the full width at half maximum (FWHM), θ is

the Bragg’s diffraction angle. Here ( ) 2/122SM βββ −= , Mβ is the full width at half

maximum (FWHM) of the most intense peak (311) and Sβ is the standard instrumental

broadening [1]. The values of average crystal size are listed in table 4.22. The average

crystal size was found to decreases from 48.51 nm to 34.11 nm with the increase of

yttrium contents.

Fig. 4.46 shows the SEM micrographs of samples with doping level x = 0 wt%, 1

wt %, 5 wt % and the grain size calculated from these micrographs are listed in table

4.22. These micrographs exhibit the non-uniform grain size distribution. It is clear that

yttrium added compositions deviate from the fine structure of pure Co-ferrite. It is seen

from the table that grain size decreases with the increase of yttrium addition. It is known

that grain growth depends upon the grain boundary mobility. The addition of yttrium

reduces the grain growth which may be due to the segregation of yttrium at or near the

grain boundary which in turns hampers its motion [1]. The grain size of these samples

decreases from 0.689 to 0.65 µm.

The average grain size estimated from SEM picture is larger than the average

particle size estimated from XRD data, suggesting the size of many grains. SEM picture

may be the aggregation of more than one particle due to strong inter-particle interactions

[49].

(a)

(b)

(c)

Fig. 4.46 SEM micrograph of CoFe2O4 + x Y2O3 ferrite system (a) x = 0 wt%, (b) x = 1

wt %, (c) x = 5 wt %).

.4.5.1.3 Physical Density The physical density (Dp) of the sintered samples have been measured using

Archimedes principle. The values of physical density are listed in table 4.22. Fig. 4.47

shows the variation of physical density with yttrium contents. The figure shows that the

physical density of all the samples increases with the increase of yttrium addition. The

addition of yttrium induces second phase (YFeO3) as confirmed by XRD patterns. The

formation of second phase fills intergranular voids and thereby enhances the physical

density with the increasing concentration of yttrium. Our results of density are consistent

with the reported literature [1].

Fig. 4.47 Variation of Physical density with Yttrium concentration for CoFe2O4 + x Y2O3

( x = 0 wt%, 1 wt %, x = 3 wt %, x = 5 wt %).

4.5.2 dc Resistivity

Fig. 4.48 shows the influence of yttrium addition on dc resistivity at room

temperature. It is seen from the figure that resistivity increases with the increase of

yttrium addition. The increasing trend of dc resistivity may be due to the formation of

insulating intergranular layers. High concentration of Y3+ ions diffused to the grain

boundaries and formed inhomogeneous solid solution. It may tend to segregate at or near

the grain boundaries and formed highly resistive yttrium iron oxide YFeO3 (secondary

phase) which enhances the resistivity. Further, it is known that resistivity increases with

the decrease in grain size [46]. In the present samples, grain size gradually decreases and

thereby enhances the resistivity.

6.6

6.9

7.2

7.5

7.8

8.1

0 1 2 3 4 5Y-concentration (x)

Log ρ

(ohm

.cm

)

Fig. 4.48 Variation of room temperature resistivity Vs. Y-concentration for CoFe2O4 + x

Y2O3 ( x = 0 wt %, 1 wt %, 3 wt %, 5 wt %).

Temperature dependent dc resistivity for all the samples has been measured in

the temperature range 25-200 °C. Fig. 4.49 shows the Arrhenius plots of all the samples.

It is seen from the figure that the temperature dependent resistivity of all the samples is

observed to decrease with the increases of temperature. This can be attributed to the

increase in drift mobility of charge carriers. These samples exhibit semi-conducting

behavior, therefore, known as degenerate semi-conductors.

4

5

6

7

8

2.1 2.5 2.9 3.3

103/T (K)

Log ρ

(ohm

.cm

)

x = 0x = 1x = 3x = 5

Fig. 4.49 Variation of Log ρ vs. 1000 / T(K) for CoFe2O4 + x Y2O3 ( x = 0 wt %, 1 wt %,

3 wt %, 5 wt %).

The values of activation energies corresponding to the slope of Arrhenius plots for

all the compositions have been estimated. Fig 4.50 shows that the actvation energy

increases with the increase in yttrium addition. The increase in activation energy is

expected because the resistivity has been found to increase for the whole range of yttrium

addition. It is concluded that the samples having high activation energy have high

resistivity and vice versa.

In present samples, activation energy obtained is greater than 0.4 eV, according to

Klinger [55] the conduction is due to polaron hopping. The value of activation energy of

the present Y-doped cobalt ferrites lies in the range from 0.41 eV to 0.57 eV. In ferrites,

the activation energy is a function of mobility of the charge carriers. The conduction

occurs in ferrites via hopping process. The rate of hopping is associated with activation

energy, which depends upon the electrical energy barrier experienced by the electrons

during hopping. Activation energy also depends upon the grain size [56]. A small grain

size implies a decreased grain to grain contact area for the electrons to flow through,

which, lead to higher barrier height. In present samples, grain size decreases with the

addition of yttrium. Therefore, activation energy increases with the addition of yttrium

contents.

0.4

0.44

0.48

0.52

0.56

0.6

0 1 2 3 4

Y-concentration (x)

E (e

v)

5

Fig. 4.50 Activation energy Vs. Y-Concentration for CoFe2O4 + x Y2O3 ferrite system (x

= 0 wt%, 1 wt %, 3 wt %, 5 wt %).

4.5.3 Dielectric properties

4.5.3.1 Compositional Dependence of dielectric constant

Fig. 4.51 shows the variation of dielectric constant as a function of frequency at

room temperature in the range 0.1 KHz to 100 KHz. The figure shows that dielectric

constant decreases with increasing content of Y3+ ions. Dielectric constant may be

affected by the increased inhomogeneous dielectric structure when an increased

concentration of Y3+ ions is successively incorporated in Co-ferrite. The addition of

yttrium seems to prevent the development of the microstructure, thus contributing to the

increase in resistivity and decrease of dielectric constant with increasing content of Y3+

ions. Similar behavior was reported in the literature [57]. It is reported that a composition

with high DC resistivity acquires low values of dielectric constant and vice versa [58]. In

the present samples, DC resistivity increases with the increase of yttrium addition.

Therefore, the decrease of dielectric constant is expected with increasing content of Y3+

ions.

4.5.3.2 Frequency Dependence of dielectric constant It is observed from the Fig. 4.51 that the values of dielectric constant decreases

continuously with the increase of frequency. The values of dielectric constant are high at

low frequency and become less sensitive at high frequency. The observed variation can

be explained on the basis of space charge polarization. The high value of dielectric

constant is expected at low frequency due to localized accumulation of charges under the

influence of applied external field leading to build up of space charge polarization. The

probability of electron accumulation at the grain boundaries is reduced, thereby reducing

the polarization with the increase of frequency. Therefore, dielectric constant decreases

with rise in frequency as observed. Koops [14] presented a theory in order to explain the

frequency response of dielectric constant in ferrite materials. It was suggested that ferrites

consist of well conducting grains separated by low conducting grain boundaries and

therefore formed inhomogeneous dielectric structure. In inhomogeneous dielectric

structure, space charge carriers always require some time to move their axes parallel to an

external alternating electric field. As the frequency of the alternating field increases, a

stage will come when space charge carriers just started to move before the field reverses

and make little contribution to the space charge polarization. It is, therefore, dielectric

constant decreases sharply with rise in frequency and attain nearly constant values at high

frequency. Similar behavior has been reported in the literature [13].

1

10

100

1000

10000

0 10 20 30 40 50 60 70 80 90 100

Frequency (KHz)

Diel

ectr

ic c

onst

ant

x = 0x = 1x = 3x = 5

Fig. 4.51 Variation of dielectric constant as a function of frequency for CoFe2O4 + x Y2O3

ferrite system (x = 0 wt %, 1 wt %, 3 wt %, 5 wt %).

4.5.3.3 Variation of dielectric loss tangent (tan δ) with frequency Fig 4.52 shows the plot of loss tangent with frequency for the present samples. It

is observed from the figure that the loss tangent decreases continuously with frequency

for all the samples. The value of tan δ is high at low frequency region while it is low at

high frequency region. At low frequency, thin grain boundaries are more effective while

at high frequency well conducting grains are more effective. It is, therefore, expected that

energy loss is high in low frequency region (insulating grain boundary) because more

energy is needed for hopping of charge carriers in this region. Therefore, tan δ is high in

this region. Energy loss is low in high frequency region (well conducting grains) because

small energy is required for hopping of charge carriers in this region. Therefore, tan δ is

low in this region.

The figure also shows that tanδ is found to be composition dependent. Its value

decreases with the addition of yttrium contents. In present samples, resistivity of all the

samples increases with the increase of yttrium contents. The increase in resistivity may

give rise to reduction in tan δ [17].

0

1

2

3

4

5

6

0 10 20 30 40 50 60 70 80 90 10

Frequency (KHz)

Die

lect

ric

Loss

Tan

gent

0

x = 0x = 1x = 3x = 5

. Fig.4.52 Plot of loss tangent (tan δ) vs frequency at room temperature for CoFe2O4 + x

Y2O3 (x = 0, 1 wt %, 3 wt %, 5 wt %).

4.5.3.4 Relationship between dielectric constant (ε ′ ) and Resistivity (ρ)

Table 4.23 shows the values of resistivity (ρ), dielectric constant (ε ′ ), square root

of resistivity ( ρ ) and the product ( ρε ′ ). It is seen from the table that the dielectric


CoFe2O4 + x Y2O3 ferrites.

Composition

(x wt%) Hzat100ε ′

KHzat100

ε ′).( cmΩ

ρ

).( 2/12/1 cmΩ

ρHzat100

ρε ′

KHzat100ρε ′

0 1873.61 7.63 4.95×

106

2224.86 4.16×106 1.69×104

1 267.86 4.65 9.7×106 3108.05 0.83×106 1.44×104

3 57.78 3.01 4.31×

107

6565.06 0.38×106 1.97×104

5 57.47 1.92 8.39×

107

9159.69 0.53×106 1.76×104

constant is found to be roughly inversely proportional to the square root of resistivity and

the product ρε ′ remains nearly constant. Such relationship was reported by several

researchers in the literature [53, 34].

CONCLUSION & FUTURE WORK 4.5.4.1 Conclusions In this work, NiY-ferrites (NiY2xFe2-2xO4), MgY-ferrites (MgY2xFe2-2xO4),

NiZnY-ferrites (Ni0.6Zn0.4Y2xFe2-2xO4), CoZnY-ferrites (Co1-xZnxY0.15Fe1.85O4, x = 0.0,

0.2, 0.4, 0.6, 0.8, 1.0) and CoY-ferrites (CoFe2O4 + x Y2O3, x = 0 wt %, 1 wt %, 3 wt

%, 5 wt %) were prepared. From the XRD analysis, it was found that all the samples have

fcc phase along with few traces of second phase (YFeO3). The lattice constant was

increased slightly with the increase of yttrium contents up to x ≤ 0.02 and x ≤ 0.06 in

MgY- and NiZnY-ferrites respectively while for higher values of concentration level x,

lattice parameter decreases with yttrium contents due to presence of second phase. In NiY

ferrites, lattice constant increases with yttrium contents. In CoY ferrites, lattice constant

decreases with the increase of yttrium doping level due to presence of second phase

whereas it increases with the increase of Zn contents in CoZnY ferrites.

The presence of second phase influences the grain growth, that is the average grain size

are decreased from 1.48 to 0.83 µm, 1.99 to 1.17 µm, 1.28 to 0.71 µm and 0.69 to 0.65

µm in NiY-, MgY-, NiZnY- and CoY-ferrites respectively. The average particle size is

decreased from 38.41 nm to 14.25 nm in CoZnY-ferrites. This indicates that yttrium

addition may segregate at or near the grain boundaries that hinders the grain growth. The

physical densities are increased from 4.70 to 5.02 g/cm3, 3.92 to 4.29 g/cm3, 4.81 to 4.96

g/cm3, 3.95 to 4.42 g/cm3 and 4.13 to 4.50 g/cm3 in NiY-, MgY-, NiZnY-, CoZnY- and

CoY-ferrites respectively. The percentage porosity was decreased from 12.59 to 9.07,

13.21 to 7.68, 10.46 to 10.15, 26.97 to 18.76 in NiY ferrites, MgY ferrites, NiZnY and

CoZnY ferrites respectively.

These interesting structural properties with the variation of yttrium in NiY-, MgY- and

NiZnY-ferrites influence the static (Ms, Hc) and dynamic ( iμ′ ) magnetic properties. The

saturation magnetization was decreased from 50.98 to 41.44 emu/g, 29.97 to 21.86

emu/g, 75.31 to 58.82 emu/g in NiY-, MgY- and NiZnY-ferrites respectively. The

decreasing behavior of Ms with increasing yttrium contents may be due to the fact that

yttrium addition leads to the magnetic dilution of B sublattice through the removal of Fe

magnetic ions and thereby decreasing the net magnetization. The coercivity values are

increased from 15.54 to 59.08 Oe, 18.66 to 39.88 Oe and 12.87 to 35.31 Oe in NiY-,

MgY- and NiZnY-ferrites respectively. The increasing trend of Hc may be attributed to

the gradual decrease in grain size with the increase of yttrium contents. The smaller

grains may obstruct the domain wall movement, as a result, the values of initial

permeability ( iμ′ ) are decreased from 110 to 35, 27 to 6 and 185 to 87 at 1 MHz in NiY-,

MgY- and NiZnY-ferrites respectively. The values of magnetic loss tangent decreased

from 0.23 to 0.03, 0.04 to 0.007, 1.2 to 0.41 in NiY-, MgY- and NiZnY-ferrites

respectively. This may be attributed to the increase in resistivity that reduces the eddy

current losses.

FTIR spectra of NiY-, MgY- and NiZnY-ferrites obtained at room temperature in

the wave number range 370 – 1100 cm-1 show splitting of the two fundamental

absorption bands, thereby confirming the completion of solid state reaction. The

absorption band around 600 cm-1 ( 1ν ) is attributed to stretching vibrations of tetrahedral

metal-oxygen bond and the band around 400 cm-1 ( 2ν ) is attributed to stretching

vibrations of octahedral metal-oxygen bond. The high frequency band 1ν is nearly

constant for all the investigated samples. The absorption band 2ν slightly shifts to higher

frequency side and also band broadening suggested the occupancy of Y3+ ions on B-sites.

The low frequency band 2ν continues to widen with yttrium contents. This may be due to

larger ionic radius and higher atomic weight of Y3+ ions than Fe3+ ions which affect Fe3+

- O2- distances on B sites.

The dc electrical resistivity is increased with the increase of yttrium concentration

from 4.85 106 – 7.48× 108 Ω. cm, 7.4 × × 107 – 1.8 × 1010 Ω. cm, 5.02 × 105 – 2.51 × 108

Ω. cm and 4.95 × 106 – 8.32 107 Ω. cm in NiY-, MgY-, NiZnY- and CoY ferrites

respectively. It makes NiY-, MgY- and NiZnY-ferrites suitable for high frequency

applications. The dc electrical resistivity decreased with the increase of zinc

concentration from 9.12 × 107 – 5.25

×

× 106 Ω. cm in CoZn-ferrites. The temperature

dependent dc resistivity decreases with the increase of temperature which may be

attributed to the semiconducting behavior of all the samples under investigation. It was

observed that the samples having higher values of resistivity also possessed higher

activation energy and vice versa. The high dc resistivity and low dielectric losses are the

desired characteristics of NiY-ferrites used to prepare microwave devices

The dielectric constant of all the samples shows dispersion with frequency. The

values of dielectric constant are high at low frequency and then decreases rapidly with the

rise in frequency. Dielectric loss tangent (Tan δ) of all the samples decreases with

increasing frequency. The values of dielectric constant (ε ′ ) of NiY-, MgY-, NiZn- and

CoY-ferrites ferrites decreases with the increase of yttrium concentration whereas it

decreases with the increase of zinc contents in CoZn-ferrites. The reduction in the values

of dielectric constant with increasing concentration of yttrium is due to depleting

concentration of iron ions at B sites which play a dominant role in dielectric polarization.

The electron transfer between Fe2+ and Fe3+ ions (Fe2+ ↔ Fe3+ + e–) will be hindered i.e.

the polarization decreases. Consequently, dielectric constant decreases with yttrium

contents. The high dc resistivity, low dielectric losses and low values of saturation

magnetization are the desired characteristics of MgY-ferrites used to prepare microwave

devices operating in L, S and C bands. CoZnY-ferrites can be used to prepare ferrofluids

and magnetic coating.

In this study, we have observed FMR spectra of NiY- and MgY-ferrites. It was

observed that the linewidth decreases from 472 to 282 Oe and 333.7 Oe to 269 Oe takes

place up to x ≤ 0.06 and x ≤ 0.02 in NiY ferrites and MgY ferrites respectively. The

composition MgY0.04Fe1.96O4 have minimum linewidth, ΔH = 269, which is the minimum

of the reported linewidths for spinel ferrites. The decreasing trend of linewidth may be

attributed to the valence exchange mechanism or charge transfer relaxation mechanism. It

was observed from FMR spectra that linewidth increases from 325 to 735 Oe for 0.08 ≤ x

≤ 0.12 and 348 to 768.3 Oe for 0.04 ≤ x ≤ 0.12 in NiY- and MgY-ferrites respectively.

The increasing trend of linewidth may be attributed to the sample inhomogenities due to

presence of second phase.

4.5.4.2 Future Work

In this study, some aspects have been evolved that need further investigations.

Future work in the following areas would be interesting:

In this work, we have observed that the crystalline ferrite material is formed by

agglomerates of nanoparticles in CoZnY ferrites and CoY ferrites prepared by chemical

coprecipitation method, which cannot be individually resolved by SEM techniques. To

get the accurate values of particle size, one has to use high resolution Transmission

Electron microscopy (TEM), which is useful instrument for studying materials in the

angstrom range structural details.

Impedance is performed using Solartron Impedance Analyzer having frequency

range from 10 Hz to 10 MHz. For high frequency applications of ferrites, it is important

to get accurate information of the resonance frequency and to find Snoek’s limit, which

can be used for technical applications in the frequency range above 500 Hz to several

GHz.

The low temperature susceptibility can be measured for further investigations of

magnetic interactions.

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Appendix A: Conversion Factors*

Quantity Symbol SI CGS

Field H A.m-1 Oe (Oersted)

Induction B Tesla G (Gauss)

Magnetization M A.m-1 emu. Cm-3

Intensity of

Magnetization

I Tesla -

Flux Ф weber Maxwell

Moment M weber meter emu

Pole Strength P weber emu. Cm-1

Field equation B = IHo +μ B = MH π4+

Conversion Factors:

1 Oe = (1000 / 4π ) A. m-1 = 79.58 A. m-1

1 G = 10-4 Tesla

1emu. Cm-3 = 1000 A. m-1

* From D. Jiles, Introduction to Magnetism and Magnetic Materials, Chapman and Hall,

London, 1996, 11-12.

Appendix B: Abbreviations, Symbols & Physical Constants

Ms Saturation magnetization

B Magnetic induction

iμ Initial permeability

cH Coercivity

λ Wavelength of X-ray

χ Susceptibility

tan Loss factor

Ar Tetrahedral ionic radius

Br Octahedral ionic radius

a Lattice parameter

A-sites Tetrahedral sites

B-sites Octahedral sites

H Magnetic field

T Temperature

Tc Curie temperature

K1 Magnetocrystalline anisotropy constant

XD X-ray density

PD Physical density

M Molecular weight

XRDd

o

Crystallite size calculated from XRD

β Instrument broadening

Bk Boltzmann constant

P Porosity

f frequency

ρ resistivity

n order of reflection

hkl Miller indices

N Number of turns of wound wire

ON Avogadro’s number

Z Impedance

FTIR Fourier Transform Infrared

VSM Vibrating sample Magnetometer

XRD X-ray diffraction

SEM Scanning Electron Microscope

List of Publications

1- M. Ishaque, M. U. Islam, M. Azhar Khan, I. Z. Rahman, A. Genson, S.

Hampshire, Physica B 405 (2010) 1532-1540.

2- M. U. Islam, M. Azhar Khan, Zulfiqar Ali, M. Ishaque, Shahida B. Niazi, T.

Abbas, International Journal of Modern Physics B 21 (2007) 2669-2677.

3- M. U. Islam, Faiza Aein, Shahida B. Niazi , M. Azhar Khan, M. Ishaque, T.

Abbas, M. U. Rana, Mater. Chem. Phys. 109 (2008) 482-487.

4- M. Azhar Khan, M. U. Islam, M. Ishaque, I. Z. Rahman, A. Genson, S.

Hampshire Materials Characterization 60 (2009) 73-78.

5- M. Azhar Khan, M. U. Islam, M. Ishaque, I. Z. Rahman, Ceramics International

37 (2011) 2519 – 2526.

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