3rd march final bhatti sb. phd(physics) thesis hasan...

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Effect of Divalent and Trivalent Cations on the Electrical and

Magnetic Properties of Hexa-ferrites

Ph.D Thesis

Hasan Mehmood Khan

Session: (2009-2012)

Department of Physics Bahauddin Zakariya

University

Multan, Pakistan

(2016)

Ph.D Thesis

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Effect of Divalent and Trivalent Cations on the Electrical and

Magnetic Properties of Hexa-ferrites

By

Hasan Mehmood Khan

PhD Scholar

Supervised By

Prof. Dr. Misbah-ul-Islam

A thesis submitted in partial fulfilment of the requirement for the Degree of

Doctor of Philosophy in Physiscs

Department of Physics Bahauddin Zakariya University Multan

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DEDICATED

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To

My Parents and Family

CERTIFICATE This is to certify that the work presented in this thesis entitled “Effect of

Divalent and Trivalent Cations on the Electrical and Magnetic Properties of Hexa-

ferrites” has been carried out under my supervision at the Department of Physics,

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

Electronics, University of York, United Kingdom. In my opinion, this work is fully

adequate in the scope and quality of the award for the degree of Doctor of

Philosophy in Physics.

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Supervisor:

Professor Dr. Misbah-ul-Islam

Department of Physics

Bahauddin Zakariya University

Multan, Pakistan.

Declaration of Originality

I hereby declare that I have not submitted this research work titled, “Effect of

Divalent and Trivalent Cations on the Electrical and Magnetic Properties of Hexa-

ferrites” leading to the degree of Ph.D in Physics to other university with in the country

or outside Pakistan. 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.

I also declare that I do understand the terms “copyright” and “plagiarism”. In case of any

copy right violation and plagiarism found in this work, I will be held fully responsible of the

consequences of any such violation.

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Signature------------------

Hasan Mehmood Khan

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

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

whose life is forever guidance for the humanity. I would like to express my sincere

gratitude to my worthy supervisor Dr. Misbah Ul Islam, Associate Professor, Department

of Physics, Bahauddin Zakariya University Multan, whose continuous guidance,

stimulating suggestions and encouragement helped me at every step during my Ph.D

research work. Many thanks to him for suggesting me this kind of research project and

guided me the ways to approach a research problem and the need to be persistent to

accomplish any goal. I am grateful to Higher Education Commission of Pakistan (HEC)

for the financial support for this project under HEC Indigenous and International

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

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

me to broaden my view and knowledge. I am really grateful to Prof. Dr. Javed Ahmed,

Chairman Department of Physics B.Z.U (Multan), Prof. Dr. Tariq Bhatti, Prof. Dr. Ejaz

Ahmed, Dr Amir Zia, Dr Niaz Ahmed and Dr Abdul Shakoor, for his scientific guidance and

support during the progress of my work. Many thanks to my respected father Dr. Muhammad

Latif Khan and my elder brother Dr. Tariq Mehmood for their support and co-operation in

every aspect of life. I can’t help without appreciating and thanking for the unconditional

support of Prof. Yongbing Xu, Department of Electronics, University of York, United

Kingdom, for providing lab facilities and valuable suggestions during my Ph.D. work.

I also pay thanks to Dr. Ian D. Flintoft and Dr. Ian will for valuable suggestions and

providing facilities for microwave, VSM, and structural properties measurements during

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my six months stay at University of York United Kingdom. I am thankful to my colleagues

Dr. Ishaque, Dr. Muhammad Azhar Khan, Dr. Irshad Ali, Dr. Col. Asif iqbal, Mudassir and

Fida Hussain, Aziz and Sajjad for their moral support during my studies.

Hasan Mehmood Khan

ABSTRACT Three series of M-type hexagonal ferrite samples with the chemical compositions

Ca0.5Ba0.5-xTbxZnyFe12-yO19 (x= 0.00–0.10; y= 0.00–1.00), Ca0.5Ba0.5-xPrxNiyFe12-yO19, (x =

0.00– 0.10; y = 0.00–1.00) and Ca0.5Ba0.5-xNdxZnyFe12-yO19, (x = 0.00–0.10; y = 0.00–1.00)

were prepared by Sol-gel auto-combustion method. FTIR profiles of the selected samples

were measured in the wave number range 370-4000 cm-1 indicating M-type hexagonal ferrite

structure. The XRD analysis confirmed single phase M-type hexa-ferrite structure for all

three series of samples namely Ca0.5Ba0.5-xTbxZnyFe12-yO19 (x= 0.00–0.10; y= 0.00–1.00),

Ca0.5Ba0.5xPrxNiyFe12-yO19, (x = 0.00–0.10; y = 0.00–1.00) and Ca0.5Ba0.5-xNdxZnyFe12-yO19,

(x = 0.00–0.10; y = 0.00–1.00). The lattice parameters were found to increase as the contents

of the substituted cations increased, which is attributed to the ionic sizes of the implicated

cations. The c/a ratio was found be in the range 3.97-4.04 which is in the acceptable range.

The room temperature resistivity decreases from 8.6 × 109 to 24 × 108 ohm-cm in all three

series. Temperature dependent resistivity exhibits semiconducting behaviour due to increase

in drift mobility of the charge carriers by indicating their importance in switching

applications. The dielectric constant was measured in the frequency range from 10 to 100

kHz, which follows Maxwell Wagner model. The dielectric loss decreases substantially with

increasing frequency and reaches a constant value later on. This decrease with increasing

frequency is attributed to the hopping frequency of the charge carriers that cannot follow the

applied external field beyond a certain frequency. The SEM profiles show regular hexagonal

platelets with homogeneous grain size ranging from 0.5 to 10 µm. The values of particle size

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calculated by TEM were found to be in the range of 0.5–10nm. The coercivity values of all

samples are in the range of M-type hexaferrites and are consistent with reduction in grain

size and these changes in coercivity are resulted due to domain wall pinning fields at grain

boundaries. Permeability, permittivity and insertion loss are measured in the frequency range

0.5-12GHz. The values of permittivity for the ferrites are lower at high frequencies and are

favourable for impedance matching. The values of permeability are favourable for

microwave surface impedance match because the wavelength in microwave absorber

decreases as the frequency increases for all samples. The attenuation frequency of these

hexaferrites strongly depends upon thickness and can be tuned for the desired frequency by

varying the thickness of the sample.

Table of Contents

Contents Page No.

CHAPTER 1

INTRODUCTION 02

1.1 Ferrite 02

1.2 Soft Ferrites 02

1.3 Hexa-Ferrites 03

1.4 M-type Hexaferrites 04

1.5 Applications of hexaferrites 06

1.6 Electrical Properties 07

1.6.1 Electrical Resistivity 07

1.6.2 Conduction Mechanism 07

1.7 Saturation Moments 08

1.8 The Magnetic Interactions 09

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1.9 Domains in Ferrites 10

1.10 Magnetostatic Energy 11

1.11 Magnetocrystalline Anisotropy Energy 11

1.12 Magnetostrictive Energy 12

1.13 Domain Wall Energy 12

1.14 Hysteresis Loop 13

1.15 Permeability 14

1.16 Different Techniques used for the Synthesis of Ferrites 21

1.16.1 Solid State Synthesis 21

1.16.2 Chemical Co-precipitation 21

1.16.3 Sol-gel 21

1.16.4 Hydrothermal 22

1.16.5 Spray pyrolysis 22

1.16.6 Glass crystallization 23

1.17 Motivation of Work 23

References 25

CHAPTER 2 THEORETICAL

BACKGROUND 2.1 Magnetic materials 30

2.1.1 Types of magnetic materials 30

(i) Diamagnetic Materials 31 (ii) Paramagnetic Materials 31 (iii)

Ferromagnetic Materials 32

(iv) Antiferromagnetic Materials

32

(v) Ferrimagnetic Materials 33

2.2 Ferrites and their Uses

33

2.3 Crystal structure 35

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(i) Spinel or Soft Ferrites

35

(ii) Garnet 36 (iii) Ortho Ferrites 36

(iv) Hexagonal Ferrites 37

2.4 Hopping Model of Electrons 39

2.5 Magnetic Properties 40

2.6 Magnetization in Ferrites 41

2.7 Neel’s Theory of Ferrimagnetisms 41

2.8 Molecular Field Theory of Ferrimagnetism 42

2.9 Literature review 44

References 61

CHAPTER 3 Materials and Methods 3.1 Composition of Ferrite-samples 68

3.2 Fabrication Technique 68

3.3 Characterization 71

3.3.1 Thermo gravimetric Analysis 71

3.3.2 FTIR 71

3.3.3. Principle of FTIR 72

3.3.4 X-Ray Diffraction 72

3.4 Dielectric Measurements 74

3.5 Electrical Resistivity Measurements 74

3.6 Bulk Density Measurements 75

3.7 Scanning Electron microscopy and EDXS 75

3.8 Vibrating Sample Magnetometer (VSM) 76

3.9 Plasma Surface Technology 76

3.10 Transmission Electron microscopy 77

3.11 Radio-frequency and microwave attenuation 78

References 82

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CHAPTER 4 Results and

Discussions Ca0.5Ba0.5-xTbxZnyFe12-yO19 Series

4.1 Fourier Transform Infrared Spectroscopy (FTIR) 85

4.2 X-ray Diffraction Analysis 85

4.3 Magnetic Measurements 87

4.4 Scanning and Transmission Electron Microscopy 90


4.5.1 Room Temperature Resistivity 96

4.5.2 Temperature Dependent Resistivity 96

4.5.3 Drift Mobility 100

4.6 Dielectric Properties 100

4.6.1 Dielectric Constant 100

4.6.2 Dielectric Loss 101

4.7 AC Conductivity 101

4.8 Conduction Mechanism 102

4.9 Temperature dependent M-H loops 106

4.10 Complex permittivity and permeability 109

4.11 Microwave absorption 111

Ca0.5Ba0.5-xPrxNiyFe12-yO19 Series

4.12 Fourier Transform Infrared Spectroscopy (FTIR) 114

4.13 X-ray Diffraction Analysis 115


4.15 Scanning and Transmission Electron Microscopy 121





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Ca0.5Ba0.5-xNdxZnyFe12-yO19 Series

4.23 Thermal Analysis 144

4.24 FTIR Spectroscopy 144

4.25 X-ray diffraction Analysis 146


4.27 Scanning Electron Microscopy, EDS and TEM 152













Comparison of all three series 176

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Conclusions 179

References 180

Fig. No. List of Figures Page No.

1.1 Applications of Ferrites 02

1.2 Unit cell of barium hexaferrite 05

1.3 Illustration of the BaFe12O19 structure 05

1.4 Magnetic interactions Adapted from Gorter 09

1.5 Magnetization in Domains. a) single domain,

b,c) closure domains 11

1.6 Typical hysteresis loop 14

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1.7 A circular coil carrying current I 15

1.8 A solenoid carrying current I 16

1.9 Equivalent circuit of a torroid 19

2.1 Magnetic structure of Paramagnetic materials 31

2.2 Magnetic structure of Ferromagnetic materials 32

2.3 Magnetic structure of Antiferromagnetic materials 33

2.4 Magnetic structure of Ferrimagnetic materials 33

2.5 Manufactured ferrites 35

2.6 Compositional phase diagram for hexagonal ferrites 38

3.1 Flow chart for Sol-gel process 70

3.2 DTA/TGA analyzer 71

3.3 FTIR Spectrometer 72

3.4 3.5

3.6

X-ray Diffractometer Two probe sample holder for electrical

measurements 73 74

Scanning Electron Microscope 75

3.7 ADE Model 10 VSM 76

3.8 Femto Diener plasma cleaner Model 2011 77

3.9 TEM: JEOL Japan 2011 (with LaB6 filament) 78

3.10 Dimensions of reference and load samples 79

3.11 ASTM4935 coaxial transverse electromagnetic wave cell

and an HP 8753D vector network analyzer 79

4.1 FTIR of Ca0.5Ba0.5-xTbxZnyFe12-yO19(x = 0.02,0.06, 0.10) 86

4.2 XRD patterns of Ca0.5Ba0.5-xTbxZnyFe12-yO19

(x = 0.00-0.10; y =0.00–1.00). 86

4.3 Lattice parameters for Ca0.5Ba0.5-xTbxZnyFe12-yO19

(x = 0.00-0.10; y =0.00–1.00). 88

4.4 VSM analysis of Ca0.5Ba0.5-xTbxZnyFe12-yO19

(x = 0.00-0.10; y =0.00–1.00). 88

4.5 Variation of Coercivity of Ca0.5Ba0.5-xTbxZnyFe12-yO19

(x = 0.00-0.10). 89

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4.6 Variation in Ms and Mr Vs Tb. contents of

Ca0.5Ba0.5-xTbxZnyFe12-yO19 (x = 0.00-0.10). 89

4.7 SEM analysis of Ca0.5Ba0.5-xTbxZnyFe12-yO19 ( x=0.02). 91

4.8 SEM analysis of Ca0.5Ba0.5-xTbxZnyFe12-yO19 (x=0.06). 91

4.9 SEM analysis of Ca0.5Ba0.5-xTbxZnyFe12-yO19 (x=0.10). 92

4.10 TEM analysis of Ca0.5Ba0.5-xTbxZnyFe12-yO19 ( x=0.02). 92



4.13 Room temperature resistivity of Ca0.5Ba0.5-xTbxZnyFe12-yO19

(x = 0.00–0.10; y = 0.00–1.00). 98

4.14 Temperature dependent resistivity of Ca0.5Ba0.5-xTbxZnyFe12-yO19

(x = 0.00–0.10; y = 0.00–1.00). 98

4.15 Activation energy for Ca0.5Ba0.5-xTbxZnyFe12-yO19

(x = 0.00–0.10; y = 0.00–1.00). 99

4.16 Drift mobility of Ca0.5Ba0.5-xTbxZnyFe12-yO19

(x = 0.00–0.10; y = 0.00–1.00). 103

4.17 Dielectric constant of Ca0.5Ba0.5-xTbxZnyFe12-yO19

(x = 0.00–0.10; y = 0.00–1.00). 103

4.18 Dielectric loss of Ca0.5Ba0.5-xTbxZnyFe12-yO19

(x = 0.00–0.10; y = 0.00–1.00). 104

4.19 Ac conductivity of Ca0.5Ba0.5-xTbxZnyFe12-yO19

(x = 0.00–0.10; y = 0.00–1.00).

4.20 Conduction Mechanism of Ca0.5Ba0.5-xTbxZnyFe12-yO19

104

(x = 0.00–0.10; y = 0.00–1.00)

4.21 Temperature dependant M-H loops for

105

Ca0.5Ba0.5TbZnFe12O19 sample. 107

4.22 Coercivity of Ca0.5Ba0.5TbZnFe12O19 sample.

4.23 Saturation and remanence magnetization for

107

Ca0.5Ba0.5TbZnFe12O19 sample.

4.24 Real and Imaginary part of permittivity of

108

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Ca0.5Ba0.4Tb0.10Zn1.00Fe11O19 in ASTM4935 cell.

4.25 Real and Imaginary part of permeability

110


4.26 Loss dependence on thickness for

110


4.27 FTIR analysis of Ca0.5Ba0.5-xPrxNiyFe12-yO19

112

x = 0.02, 0.06, 0.10; y = 0.20, 0.60,1.00

4.28 XRD patterns of Ca0.5Ba0.5-xPrxNiyFe12-yO19,

114

x = 0.00-0.10; y =0.00 116

4.29 Variation of lattice parameters for Ca0.5Ba0.5-xPrxNiyFe12-yO19,

x = 0.00-0.10; y =0.00–1.00 116

4.30 VSM analysis of Ca0.5Ba0.5-xPrxNiyFe12-yO19

x = 0.00-0.10; y =0.00–1.00 119

4.31 Variation of Coercivity of Ca0.5Ba0.5-xPrxNiyFe12-yO19

x = 0.00-0.10; y =0.00–1.00 119

4.32 Variation in Ms and Mr of Ca0.5Ba0.5-xPrxNiyFe12-yO19

x = 0.00-0.10; y = 0.00–1.00 120

4.33 SEM analysis of Ca0.5Ba0.48Pr0.02Ni0.20Fe11.8O19

x=0.02,y=0.20 122

4.34 SEM analysis of Ca0.5Ba0.44Pr0.06Ni0.60Fe11.4O19

x=0.06,y=0.60 122

4.35 SEM analysis of Ca0.5Ba0.4Pr0.10Ni1.00Fe11O19

x=0.10,y=1.00 123

4.36 TEM analysis of Ca0.5Ba0.48Pr0.02Ni0.20Fe11.8O19

x=0.02,y=0.20 123

4.37 TEM analysis of Ca0.5Ba0.44Pr0.06Ni0.60Fe11.4O19

( x=0.06,y=0.60). 124

4.38 TEM analysis of Ca0.5Ba0.4Pr0.10Ni1.00Fe11O19

( x=0.10,y=1.00). 124

4.39 Room temperature resistivity of Ca0.5Ba0.5-xPrxNiyFe12-yO19

(x = 0.00–0.10; y = 0.00–1.00). 128

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4.40 Temperature dependent resistivity of Ca0.5Ba0.5-xPrxNiyFe12-yO19

(x = 0.00–0.10; y = 0.00–1.00). 128

4.41 Activation energy of Ca0.5Ba0.5-xPrxNiyFe12-yO19

(x = 0.00–0.10; y = 0.00–1.00). 129

4.42 Drift mobility of Ca0.5Ba0.5-xPrxNiyFe12-yO19

(x = 0.00–0.10; y = 0.00–1.00). 133

4.43 Dielectric constant of Ca0.5Ba0.5-xPrxNiyFe12-yO19

(x = 0.00–0.10; y = 0.00–1.00). 133

4.44 Dielectric loss of Ca0.5Ba0.5-xPrxNiyFe12-yO19

(x = 0.00–0.10; y = 0.00–1.00). 134

4.45 Ac conductivity of Ca0.5Ba0.5-xPrxNiyFe12-yO19

(x = 0.00–0.10; y = 0.00–1.00). 134

4.46 Conduction Mechanism of Ca0.5Ba0.5-xPrxNiyFe12-yO19

(x = 0.00–0.10; y = 0.00–1.00). 135

4.47 Temperature dependant M-H loops for Ca0.5Ba0.5PrNiFe12O19 137

4.48 Coercivity for Ca0.5Ba0.5PrNiFe12O19 sample 137

4.49 Mr and Ms for Ca0.5Ba0.5PrNiFe12O19 sample 138


Ca0.5Ba0.4Pr0.10Ni1.00Fe11O19 in ASTM4935 cell 140





4.53 TG/DTA of Ca0.5Ba0.44 Nd0.06 Zn0.60Fe11.4O19 hexaferrite 145

4.54 FTIR spectra of Ca0.5Ba0.5-xNdxZnyFe12-yO19

(x = 0.02, 0.06, 0.10; y = 0.20, 0.60, 1.00) hexaferrites 145

4.55 XRD patterns of Ca0.5Ba0.5-xNdxZnyFe12-yO19

(x = 0.00–0.10; y = 0.00–1.00). 147

4.56 Variation of lattice parameters for Ca0.5Ba0.5-xNdxZnyFe12-yO19

(x = 0.00–0.10,y= 0.00–1.00). 147

4.57 VSM analysis of Ca0.5Ba0.5-xPrxNiyFe12-yO19

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x = 0.00-0.10; y =0.00–1.00 150

4.58 Variation of Coercivity of Ca0.5Ba0.5-xPrxNiyFe12-yO19

x = 0.00-0.10; y =0.00–1.00 150

4.59 Variation in Ms and Mr of Ca0.5Ba0.5-xPrxNiyFe12-yO19

x = 0.00-0.10; y = 0.00–1.00 151

4.60 SEM analysis of Ca0.5Ba0.48Nd0.02Zn0.20Fe11.8O19

x=0.02,y=0.20 153

4.61 SEM analysis of Ca0.5Ba0.44Nd0.06Zn0.60Fe11.4O19

x=0.06,y=0.60 153

4.62 SEM analysis of Ca0.5Ba0.4Nd0.10Zn1.00Fe11O19

x=0.10,y=1.00 154

4.63 TEM analysis of Ca0.5Ba0.48Nd0.02Zn0.20Fe11.8O19

x=0.02,y=0.20 154

4.64 TEM analysis of Ca0.5Ba0.44Nd0.06Zn0.60Fe11.4O19

( x=0.06,y=0.60). 155

4.65 TEM analysis of Ca0.5Ba0.4Pr0.10Ni1.00Fe11O19

( x=0.10,y=1.00). 155

4.66 Room temperature resistivity of Ca0.5Ba0.5-xNdxZnyFe12-yO19

(x = 0.00–0.10; y = 0.00–1.00). 158

4.67 Temperature dependent resistivity of Ca0.5Ba0.5-xNdxZnyFe12-yO19

(x = 0.00–0.10; y = 0.00–1.00). 158

4.68 Activation energy of Ca0.5Ba0.5-xNdxZnyFe12-yO19

(x = 0.00–0.10; y = 0.00–1.00).

4.69 Drift mobility of Ca0.5Ba0.5-xNdxZnyFe12-yO19

159

(x = 0.00–0.10; y = 0.00–1.00).

4.70 Dielectric constant of Ca0.5Ba0.5-xNdxZnyFe12-yO19

162

(x = 0.00–0.10; y = 0.00–1.00).

4.71 Dielectric loss of Ca0.5Ba0.5-xNdxZnyFe12-yO19

162

(x = 0.00–0.10; y = 0.00–1.00).

4.72 Ac conductivity of Ca0.5Ba0.5-xNdxZnyFe12-yO19

165

(x = 0.00–0.10; y = 0.00–1.00).

4.73 Conduction Mechanism of Ca0.5Ba0.5-xNdxZnyFe12-yO19

165

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(x = 0.00–0.10; y = 0.00–1.00)

4.74 Temperature dependant M-H loops for

166

Ca0.5Ba0.5NdZnFe12O19 170

4.75 Coercivity for Ca0.5Ba0.5NdZnFe12O19 170

4.76 Ms and Mr for Ca0.5Ba0.5NdZnFe12O19


171

Ca0.5Ba0.4Nd0.10Zn1.00Fe11O19 in ASTM4935 cell.


173

Ca0.5Ba0.4Nd0.10Zn1.00Fe11O19 in ASTM4935 cell.


173

Ca0.5Ba0.4Nd0.10Zn1.00Fe11O19 in ASTM4935 cell. 175

Overall discussion about thesis and goals achieved 178

Conclusions 179

References 180

Table.No. List of Tables Page No.

2.1 Subclasses of Hexaferrites 39

3.1 XRD Measurement conditions 73

4.1 Magnetic and lattice parameter values for

Ca0.5Ba0.5-xTbxZnyFe12-yO19 (x = 0.00- 0.10). 94

4.2 EDS analysis of M-type hexa-ferrite

Ca0.5Ba0.5-xTbxZnyFe12-yO19 powders (x=0.02,0.06,1.00) 94

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4.3 2θ values, relative intensities, d-values and hkl’s for

Ca0.5Ba0.5-xTbxZnyFe12-yO19 hexa-ferrites ( x = 0.00-0.10) 95

4.4 Magnetic properties, lattice parameters, Porosity, grain size

for Ca0.5Ba0.5-xPrxNiyFe12-yO19 hexa-ferrites ( x = 0.00-0.10)

125

4.5 EDXS analysis of Ca0.5Ba0.5-xPrxNiyFe12-yO19

(x = 0.02, 0.06, 1.00) powders 125

4.6 2θ values, relative intensities, d-values and hkl’s for

Ca0.5Ba0.5-xPrxNiyFe12-yO19 hexa-ferrites ( x = 0.00-0.10)

126 4.7 Lattice Constants (a,c), Crystallite Size and Bulk

density of

Ca0.5Ba0.5-xNdxZnyFe12-yO19 (x = 0.00–0.10; y = 0.00–1.00) 167

4. 8 2θ values, relative intensities, d-values and hkl’s for

Ca0.5Ba0.5-xNdxZnyFe12-yO19 hexa-ferrites ( x = 0.00-0.10) 168

Table, Comparison of the all three series 177

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Chapter 1

INTRODUCTION

INTRODUCTION 1.1. Ferrites

Ferrites with unique magnetic and electrical properties have always been of great interest for

engineers and scientists. Ferrites are non-conductive ferrimagnetic ceramic chemical

compound derived from iron oxides such as hematite Fe2O3 or magnetite Fe3O4 as well as

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oxides of other metallic elements. Ferrites like most other ceramics are hard, nonconductive

and brittle. Ferrites are used to make ferrite cores for transformers, permanent magnets, and

microwave devices and in magnetic recording media. Ferrite stuff was initially prepared in

1930 by Y’ogoro Kato and Takeshi Takei of the Tokyo institute of Engineering Japan [1 -2].

According to basics of their magnetic properties, the ferrites are often classified as "soft" or

"hard", which refers to their low or high magnetic coercivity. Fig. 1.1 shows the various

applications of ferrites.

Figure. 1.1 Applications of ferrites [3].

1.2. Soft Ferrites

Soft magnetic material is one that can be both facilely magnetized and demagnetized,

so that it can store or transfer magnetic energy in alternating or other transmuting wave forms

(sine, pulse, square, etc). Soft ferrites have been under excruciating investigations for decades

due to their electromagnetic characteristics and number of applications. Ferrites are the best

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

such as radio wave circuits, high quality filters and operating contrivances. Ferrites become

captivating materials due to their utilization as magnetic semiconductors and electric insulators

[4-6].

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1.3. Hexa-Ferrites

Permanent ferrite magnets are made of hard ferrites, with high coercivity and high

remanence after magnetization. These are composed of Ba, Sr or Ca based with iron oxide as

principal component. The high coercivity means the materials that are very resistant of

becoming demagnetized, an essential characteristic for a permanent magnet. They also conduct

magnetic flux well and have a high magnetic permeability. This enables these socalled ceramic

magnets to store stronger magnetic fields than iron itself. They are cheap, and are widely used

in household products such as refrigerator magnets, cars, automobiles and computers. The

maximum magnetic field B is about 0.35 tesla and the magnetic field strength H is about 30 to

160 kilo ampere turns per meter or (400 to 2000 oersteds). The density of ferrite magnets is

about 5g/cm3.

The most common hard ferrites are:

• Strontium ferrite, SrFe12O19 (SrO·6Fe2O3), a common material for permanent magnet

applications.

• Barium ferrite, BaFe12O19 (BaO·6Fe2O3), common material for permanent magnet

applications. Barium ferrites are robust ceramics that are generally stable to moisture and

corrosion-resistant. They are used in magnets and as a medium for magnetic recording, e.g.

on magnetic stripe cards [7].

Hexa-ferrites continue to be very attractive materials for technological applications due to their

unique electrical and magnetic properties. Hard ferrites of Ba or Sr-hexa ferrites are the major

permanent magnetic materials. The M -type hexa-ferrites MFe12O19 (M = Ba, Sr or Pb) are

important ferrimagnetic oxides. Their magnetic properties make them potential materials for

use as permanent magnets, recording media, micro wave and high frequency devices because

of their high intrinsic coercivity, fairly large crystal anisotropy and low cost. Besides, these

they are very stable and have very high electrical resistivity. The M-type family of hexaferrites

has traditionally served as permanent magnets in applications for dielectric media [6–9]. Due

to their magneto-dielectric properties, hexaferrites play an important role in the electronic

industry. The low cost, easy manufacturing, and interesting electric and magnetic properties

has resulted in this polycrystalline ferrite being one of the most important materials and it has

many technological applications [11–12].

Chapter.1

Page 24

1.4 M-type Hexaferrites

Fig. 2.7 shows the unit cell of barium hexaferrites and fig.2.8 shows illustration of

barium ferrite structure showing the RSR*S* stacking sequence. The BaFe12O19 unit cell is a

combination of two structural blocks aligned in the direction of the hexagonal c-axis: RSR*S*,

* indicates the 180° rotation of the structural block with respect to the c-axis. The ‘S’ block has

a spinel structure with cubic close-packed O ions and Fe ions on its tetrahedral and octahedral

sites. The ‘R’ block is formed of hexagonally close-packed O ions and one Ba ion. Fe ions

occupy the interstitial, tetrahedral, octahedral and bipyramidal sites. The main intrinsic

magnetic properties results from the specific site occupancy of the magnetic Fe ions. Magnetic

properties can be varied by substituting the Fe ions with another substitution. Rare earth RE

elements along with a divalent can drastically affect the electromagnetic properties of ferrites

[19-20]. Hexagonal ferrites exhibit excellent magnetic properties in hyper frequency could

meet the need of soft magnetic materials for chip components [21]. Strontium hexaferrite has

great importance due to its numerous technological applications in fields such as recording

devices, telecommunication, magneto-optical, microwave devices and permanent magnets [22-

24]. Study of magnetic properties of Sr-hexaferrite have been attempted in the past by several

workers by replacing its Sr2+ and Fe3+ ions with Al3+ ,Cr3+, Sm3+, La3+ etc. and various bivalent

tetravalent cation combinations such as Ti–Co, Ti–Mn, Ti–Zn, Ir–Zn, Zr–Zn, Zr–Mn and Zr–

Ni [25–30].

Chapter.1

Page 25

Fig. 1.2. Unit cell of barium hexaferrite based on two formula units of BaFe12O19 [24].

Fig. 1.3. Illustration of the BaFe12O19 structure, showing the RSR*S* stacking sequence (the*

indicates a 180 rotation around c-axis). For a clear representation of the stacking, the structural

blocks are represented for four unit cells. Large circles correspond to O2 anions, the large white

Chapter.1

Page 26

circles to Ba2 cations and the small circles to Fe3 cations Ba2Fe8O14. Astrik (*) shows that the

corresponding block is rotated 180° around the hexagonal c-axis [24].

1.5 Applications of hexaferrites

M-type hexaferrites have continuously made inroads in applications such as plasto

ferrites, injection-molded pieces, microwave devices, and magnetic recording media. With

proper design and substitutions, passive elements including mm-wave circulators can be

constructed from hexaferrites. Hexaferrite with proper design and substitution are used

as passive elements at microwave frequencies [15]. Radar absorbing paint made from

ferrites is used to coat military aircrafts for stealth operation and in the expensive

absorption tiles lining the rooms used for electromagnetic compatibility measurements.

Other applications of hexaferrite materials include Common Mode Chokes, EMI filters,

Current Sensors, Handheld Devices, Spike Suppression and Gate Drive Transformers,

shield beads, snap-on cores, flat cable beads (Figure 1.1), automotive industry and consumer

goods [16].

Hexaferrites having the intrinsic characteristics are also used in

(i) Computers and peripherals

(ii) Communication Systems

(iii) Automobiles

(iv) Switch Mode Power Supplies

(vi) Ignition coil

Chapter.1

Page 27

1.6 Electrical Properties

1.6.1 Electrical Resistivity

The ferrites have resistivity in the range 10-2-1011 ohm-cm depending upon their

chemical composition. It was observed that the resistivity was caused by the simultaneous

presence of ferrous and ferric ions on octahedral sites. A lot of research work has been carried

out [17-18] on improving the electrical resistivity of ferrites. A small amount of foreign ions,

about 1 % can be incorporated in an oxide and if these ions have different valency to those

already present e.g titanium ions in Fe2O3, then these ions may force some ions into different

valency sites. In order to have high resistivity, the number of ferrous ions in stoichiometric

ferrites should be less. The temperature dependent resistivity of ferrites obeys the following

relation [19,20 ].

ρ = ρ 0 exp ( Ea/kT) (1.1)

Where ρ is the resistivity, k is Boltzman constant and Ea is the activation energy which can be

illustrated as the energy needed to release an electron from the ion for a jump to the neighboring

ion. The value of activation energy lies between 0.1 and 0.5 eV. It has been noticed that the

high activation energy usually the high resistivity of ferrite at room temperature.

1.6.2 Conduction Mechanism

Ferrites are key materials and exhibit interesting properties owing to which these are

useful in electronic devices. Ferrites which are ferrimagnetic semiconductor led to the synthesis

of new ferrites to achieve optimum resistivity. The substitution of different cations like

manganese and cobalt can also alter the resistivity in ferrites. To produce low loss ferrites, an

extensive research work has been done to study mechanism of electrical transport properties

and the influence of various substitutions on these properties. The conduction mechanism in

ferrites is entirely different than semiconductors. In ferrites charge carriers are localized at the

magnetic atoms. The conductivity is affected by the temperature dependent mobility while

carrier concentration remains unchanged by the variation of temperature. The cations are

surrounded by the close packed oxygen anions and the first order approximation can be

regarded as an isolated from each other. There will be a small overlap of the anions charge

Chapter.1

Page 28

clouds or orbital. The electrons related to a particular ion will usually remain isolated and hence

localized electron model is more applicable in ferrites rather than collective electron model

(band model). The conduction in ferrite is due to the exchange of 3d electrons, localized at the

metal ions, from Fe3+ to Fe2+ [21].

1.7 Saturation Moments

The saturation magnetization of ferrite can be calculated at 0K by knowing the moment

of each ion, the distribution of ions on A and B sites and the interaction between the two sites

is negative [22]. In Ni ferrite, all Ni2+ ions reside on B-sites and Fe3+ ions are randomly

distributed on both A and B-sites. The moments of Fe3+ ions cancel and the net moment is that

of the Ni2+ ion, which is 2μ B. Thus it can be generalized that the saturation magnetization of

any inverse ferrite is simply the moment of the divalent ion. The Zn ferrite has normal

structure. The Zn2+ ions are of zero moments occupies A sites. Hence there can be no AB

interaction. The negative BB interaction then occurs, Fe3+ ions on B sites tend to have

antiparallel moments and there is no net moment. Magnesium ferrite is a well known mixed

ferrite. If its structure were completely inverse, its net moment would be zero, because

the moment of Mg2+ ion is zero. It was noted earlier that 0.1 of the Mg2+ ions are on Asites

and these displaces an equal number of Fe3+ ions to B-sites. Hence Mg ferrite giving an

expected net moment of 1.0 μ B. This is very close to the experimental value of 1.1 μ B. In

mixed ferrites containing zinc, it is remarkable that the addition of nonmagnetic zinc

increases the saturation magnetization. Suppose a mixed ferrite containing 10 molecular

percent Zn ferrite in Ni ferrite. The Zn2+ ions are of zero moments go to A sites in pure Zn

ferrite and Fe3+ ions of Zn ferrite have parallel moments in B-sites because of the strong

AB interaction. The expected net moment increases from 2.0μ B, for pure Ni ferrite to 2.8μ B

for the mixed ferrite. If this increase of 0.8μ B per 10 molecular percent of Zn ferrite continued

with further additions, we would expect pure Zn ferrite to have moment of 10 μ B. This does

not happens because the A moments will soon become too weak to affect the B moments and

the net moment begin to decrease. The discrepancies between the theoretical and experimental

moments may be ascribed to the following;

• Orbital moments may not be completely quenched.

Chapter.1

Page 29

• The structure may not be completely inverse.

• The degree of inversion can sometimes be changed by heat treatment. Hence the

saturation becomes a temperature sensitive property.

1.8 The Magnetic Interactions

In ferrimagnets, the metal ions occupy the two crystallographic sites, namely A-sites

and B-sites. Three kinds of magnetic interactions between the metal ions are possible

through O2- ions. These are A-A interactions, B-B interactions and A-B interactions. It

has been experimentally noted that the energies of these interactions are negative and

thus induce an antiparallel orientation. The magnitude of interaction energy between the

magnetic ions depends upon the distances from these ions to the oxygen ion through which the

interaction occurs and the angle between these two magnetic ions. An angle of 180° will

give rise to the greatest exchange energy and the energy decreases very rapidly with

increasing distance. The various possible configurations of the ions pairs in spinel ferrites

with favourable distances and angles for an effective magnetic interaction [23] are shown

in Figure 1.2. On the basis of the values of the distance and the angle φ , it may be concluded

that of the three possible interactions, the A-B interaction has the greatest magnitude. From the

figure 1.2 it is evident that the two configurations for the A-B interaction have small distances

and the values of the angle φ are fairly high. In the B-B interaction the first configuration will

be effective since in the second configuration the distance is too large for effective interaction.

Fig.1.4 Magnetic interactions Adapted from Gorter [23].

The A-A interaction is the weakest as the distance is large and the angle φ is ~ 80°. Thus with

only A-B interaction predominating, the spins of the A and B-site ions, in ferrimagnets will be

Chapter.1

Page 30

oppositely magnetized sublattices, with a resultant magnetic moment equal to the difference

between those of A and B site ions.

1.9 Domains in Ferrites

The magnetic materials are subdivided into domains. Domains contain 1012 to 1016

atoms and their dimensions [23] are of the order of microns. In general, the magnetic

orientations are distributed at random, depending upon the microstructure of its crystals. In

each domain the magnetic moments of the atoms are mutually parallel. Within each

domain, the magnetization is uniform and is equal to saturation magnetization. But

different domains are magnetized in different directions. Domains are formed basically to

reduce the magnetostatic energy which is the magnetic potential energy contained in the field

lines, connecting north and south poles outside of the material. In Figure 2.7 the arrows

indicate the direction of the magnetization and consequently the direction of spin alignment in

the domain. We can substantially reduce the length of the flux path through the unfavorable air

space by splitting that domain into two or more smaller domains. This splitting process

continues to lower the energy of the system until the point that more energy is required to

form the domain boundary than is decreased by the magnetostatic energy change. When

a large domain is split into n domains, the energy of the new structure is about l/nth of the

single domain structure. In Fig. 1.3, the moments in adjacent domains are oriented at an angle

of 180° to each other. Other configurations may occur which lead to lowering of the energy

of the system. The triangular domains are called closure domains. In this configuration,

the magnetic flux path never leaves the boundary of the material. Therefore, the

magnetostatic energy is reduced. This type of structure may also be found at the outer

surfaces of a material. The size and shape of a domain may be determined by the minimization

of several types of energies.

Chapter.1

Page 31

Fig.1.5. Magnetization in Domains. a) single domain, b,c) closure domains [23].

1.10 Magnetostatic Energy

The magnetostatic energy is the work needed to put magnetic poles in special

geometric configurations. It is also the energy of demagnetization. It can be calculated for

simple geometric shapes. Neel 1944 and Kittel 1946 have calculated the magnetostatic energy

of flat strips of thickness, d, magnetized to intensity, M, alternately across the thickness

of the planes. The equation is;

Ep = 0.85 dM2 (1.2)

The general formula for the calculations of other shapes is

Ep = constant x dM2 (1.3)

Therefore the magnetostatic energy is decreased as the width of the domain decreases.

This mathematically confirms the assumption that splitting of domains into smaller widths

decreases the energy from the magnetostatic view.

1.11 Magnetocrystalline Anisotropy Energy

In most magnetic materials, the domain magnetization tends to align itself along one of

the main crystal directions. This direction is called the easy direction of magnetization.

Sometimes it is an edge of the cube and at other times, it may be a body diagonal. The difference

in energy of a state where the magnetization is aligned along an easy direction and one where

it is aligned along a hard direction is called the magnetocrystalline anisotropy energy.

Chapter.1

Page 32

This magnetocrystalline anisotropy energy is also that needed to rotate the moment from the

easy direction to another direction. The energy of the domain can be lowered by this

amount by having the spins or moments align themselves along these directions of easy

magnetization. Magnetocrystalline anisotropy is due to the fact that there is not complete

quenching of the orbital angular momentum.

1.12 Magnetostrictive Energy

When a magnetic material is magnetized, a small change in the dimensions

occurs. The relative change is on the order of several parts per million and is called

magnetostriction. The converse is also true. That is, when a magnetic material is stressed, the

direction of magnetization will be aligned parallel to the direction of stress in some

materials and at right angles to it in others. The energy of magnetostriction depends

on the amount of stress and on a constant characteristic of the material called the

magnetostriction constant

E = 3/2λσ (1.4)

where λ is magnetostriction constant and σ is applied stress.

If the magnetostriction is positive, the magnetization is increased by tension and also the

material expands when the magnetization is increased. On the other hand, if the

magnetostriction is negative, the magnetization is decreased by tension and the material

contracts when it is magnetized. Stresses can be introduced in ferrites which can affect the

directions of the moments.

1.13 Domain Wall Energy

Bloch 1932 was the first to present the idea of magnetic domains, with domain wall

boundaries separating them. In the domain structure of bulk materials, the domain wall

is the region where the magnetization direction in one domain is gradually changed to the

direction of the neighboring domain. If δ is the thickness of the domain wall which is

proportional to the number of atomic layers through which the magnetization is to

change from the initial direction to the final direction, the exchange energy stored in the

transition layer due to the spin interaction is;

Chapter.1

Page 33

Ee = kTc/a (1.5)

where kTc is thermal energy at the Curie point and ‘a’ is the distance between atoms. Therefore

the exchange energy is reduced by an increase in the width of the wall or with the number of

atomic layers in that wall. However, in the presence of an anisotropy energy or preferred

direction, rotation of the magnetization from an easy direction increases the energy so the

wall energy due to the anisotropy is;

Ek = kλ (1.6)

In this case, the energy is increased as the domain width or number of atomic layers

is increased. The two effects oppose each other and the minimum energy of the wall

per unit area of wall occurs according to the following equation;

Ew = 2(KaTc/a)1/2 (1.7) where Ka is the Anisotropy

constant

If magnetostriction is a consideration, the equation is modified to;

Ew = 2(kaTc/a)1/2 (Ka+3 λsσ/2)1/2 (1.8) where

λs is magnetostriction constant. Typical values of domain wall energies are on the order of

1-2 ergs/cm2

1.14 Hysteresis Loop

In soft magnetic materials, we want a high induction for a low field. In this case, H is

very small compared to 4πM and B is essentially equal to 4πM. If we start with a demagnetized

specimen and increase the magnetic field, the induction increases as shown in Fig. 1.4. At

high fields, the induction flattens out at a value called the saturation induction, Bs. If,

after the material is saturated, the field is reduced to zero and then reversed in the

opposite direction, the original magnetization curve is not reproduced but a loop commonly

called a hysteresis loop is obtained. It is noticed that there is a lag in the induction with respect

to the field. This lag is called hysteresis. As a result, the induction at a given field strength

has two values and cannot be specified without a knowledge of the previous magnetic history

of the sample. The area included in the hysteresis loop is a measure of the magnetic losses

incurred in the cyclic magnetization process. The hysteresis losses can also be correlated

with the irreversible domain dynamics. The value of the induction after saturation when the

field is reduced to zero is called the remanent induction or remanence. The values of the reverse

Chapter.1

Page 34

field needed after saturation to reduce the induction to zero is called the coercive force or

coercivity, Hc. Most polycrystalline sintered samples of ferrites with spinel structure have

a relatively low coercive force and hexagonal structure have high coercive force.

Fig.1.6. Typical hysteresis loop along with initial magnetization curve for soft and

hard magnetic materials [24].

1.15 Permeability

In ferromagnetic and ferrimagnetic materials one is concerned with the total flux

density, B, and it is more convenient to define a very important parameter, ‘μ ’ the

magnetic permeability which is the ratio of induction, B to magnetizing field, H.

However, this parameter can be measured under different sets of conditions. For example,

if the magnetizing field is very low, approaching zero, the ratio will be called the initial

permeability μ 0. It is defined as follows; μ 0 = lim( ) (1.9)

→

This parameter will be important in telecommunication applications where very low drive

levels are involved. On the other hand, when the magnetizing field is sufficient to bring the B

level up to the point of inflection, the highest permeability occurs. This can be seen by

visualizing the permeability as the slope of the line from the origin to the end point of the

Chapter.1

Page 35

excursion. Since the magnetization curve flattens out after the point, the μ will decrease.

It is important to know the position of the maximum permeability and the course of μ versus

B. The Biot and Savart law could be used [25] to define the magnetic flux density B due to a

circular coil carrying a current I and hence permeability. In Fig. 1.5, ‘a’ is the radius of the

circular coil.

Let us calculate the magnetic flux density at the point P at a distance z0 from point ‘O’ on the

axis of the coil.

Fig.1.5 A circular coil carrying current I [48].

The element dl of the current carrying loop at the top of the coil points perpendicularly

out of the page. The point P and the current element ‘Idl’ of the coil are separated by a distance

‘r’. The magnetic field produced by the element dl is dB, which is normal to dl and ‘r’. This

will act in the direction shown in the figure. On integrating round the coil, the sum of the

components of dB, normal to the axis, is zero. The magnitude of the component parallel

to the axis is given by [26]:

Chapter.1

Page 36

µ

dB = cosψ (1.10)

where ‘ψ’ is the angle between the axis and magnetic field dB.

Integrating equation 1.10, the magnetic flux density

is given by:

B=µ = µ

(1.11)

B= (1.12)

The above derivation could be used to calculate the field on the axis of a solenoid having N

number of turns. In Fig. 1.6, the point P the axis of the solenoid is at a distance z0 from O.

Fig. 1.6 A solenoid carrying current I [48].

∫

cos

ψ

dl=

µ

ψ

2

µ

[

]

Chapter.1

Page 37

If the turns are equally spaced and closely wound, we may consider the current is flowing

uniformly round the cylinder. That is, if we consider the length to be divided into elements

dz,

as shown at a distance z from O, the current in this section of the coil is dzI, [

( ) ]

dB = µ (1.13)

Integrating the equation 1.13, the magnetic flux density is given by:

B = µ [ + ] (1.14)

For infinite solenoid α = β = 0

Hence the equation 1.14, can be simplified as

µ

B = (1.15)

The total flux produced by the coil is given by

Φ = BA (1.16)

where A denote the cross-sectional area of the solenoid.

When ac current will flow through the coil, the magnetic flux through the coil will change as a

function of time and an electromotive force, e will be produced. According to Faradays law,

Lenz’s law induced emf, e is directly proportional to the rate of change of

Flux

,

e -N (1.17)

Chapter.1

Page 38

where N is the number of turns in the winding which senses. The negative sign indicates that

the emf induced opposes the changes in flux. Since, the magnetic flux is proportional to

the current one can write:

= − (1.18)

where L is the self inductance. For an inductor the inductance can further be defined as:

L = (1.19)

where, ϕ is the total linkage of the one turn inductor and ‘I’ is the current through the inductor.

An inductor having N-turn, the inductance can be defined as:

L = = = µ (1.20)

Any magnetic material as a core inside the solenoid having magnetic permeability, will

change the self inductance. Mathematically;

Ĺ = µ µ (1.21)

Or

µ = ΄ (1.22)

where, L΄ is the self-inductance of the solenoid with magnetic core, µr is the relative

magnetic permeability and µ = µrµ0 is the magnetic permeability in the presence of a dc

magnetic excitation. In a coil with varying magnetic field, the magnetic permeability is

Chapter.1

Page 39

measured as the ratio of the mean induction across the specimen cross-section to the applied

field. For ac excitation, the magnetic field strength, H and induction, B are two

sinusoidally varying functions of the same frequency but not of the same phase in the

presence of losses. It is well known that the magnetic permeability is the result of

macroscopic atomic currents, which produce magnetic moments within the ferromagnetic

materials. As an ac current flows through the core material, a circular magnetic field is

produced around it. This induces the atomic magnetic dipole moments with in the core.

The induced magnetic moment is proportional to the external applied field. In the absence of

an external applied field these magnetic moments are randomly oriented. An applied field tends

to orient these moments along the field direction. Each magnetic dipole moment makes an

average angle with the field direction. An equivalent solenoid current surrounding the

specimen can replace this magnetic effect of the material.

This current is called the amperian surface current.

Now, during ac excitation, the net magnetic moment of the material rotates according

to the magnitude and the polarity of the induced field. The average angle of the dipole moment

direction with the field direction changes in each cycle, which changes the magnetic

induction. Finally, the magnetic induction becomes periodic due to the periodic magnetic field

strength. In this situation the observed magnetic permeability µ can no longer be expressed by

only real quantities. Magnetic permeability, µ then can be referred to as “Apparent

Permeability, µd”. This quantity consists of a real and an imaginary part. The part of magnetic

induction that is in phase with the applied field can be attributed to the real part whereas,

the out of phase part can be considered as the imaginary part.

Mathematically, the apparent permeability can be expressed as a complex number:

µa = µʹa − µʺa (1.23)

where µʹ is real part of apparent permeability and µʺ imaginary part of apparent

permeability. The real part of the permeability is a measure of how much energy is stored in a

material. The imaginary part of the permeability is a measure of how much energy is lost in

materials. So, the apparent permeability is the net change in energy, i.e. the difference between

the real and imaginary parts of the permeability [26].

Chapter.1

Page 40

Fig. 1.7. Equivalent circuit of a torroid [27].

For the toroidal specimen used in this work, wound with at least 25 equally spaced

turns fig.1.7, the equivalent series circuit representing the magnetic core of the coil is a

selfinductance Lm in series with an intrinsic resistance Rm related to the complex apparent

permeability. The permeability is a complex quantity expressing the loss of energy

which occurs as the magnetization alternates, so that the impedance of the winding is not purely

reactive but has also resistive component [28]. The total impedance of this series circuit could

be expressed as:

Z= Rm + jωLm= jωLʹ (1.24)

Or, jωLʹ = Rm + jωLm (1.25)

Or, j2ωLʹ = jRm + j2ωLm (1.26)

Or, Lʹ = Lm – j (1.27)

Comparing eqn. 1.25 and 1.26, the apparent permeability can be related to impedence as

follows:

µa = Lm – j (1.28)

Chapter.1

Page 41

From eqn. 2.37 the real and imaginary part of permeability can be expressed as follows;

µʹa = (1.29)

real part of relative permeability,

µʹa= µ ʹ

(1.30)

µ

µʺa = (1.31)

complex part of relative permeability

µʺa= µ ʺ (1.32)

µ

the imaginary part of complex permeability henceforth, is referred to as permeability loss µʺ,

sometimes it is divided by µʹ to form loss factor, tanδ = µ ʺ

µʹ

Chapter.1

Page 42

1.16 Different Techniques used for the Synthesis of Ferrites

There are several proved techniques available to form barium hexaferrite. The method

chosen is dependent upon the final application; which will set the total sample mass, particle

size and magneto-dielectric properties required. Other considerations are availability of

equipment, lab facilities and the expense of chemical precursors and apparatus needed for

synthesis. Listed below are the main processes, then follows a brief overview of each:

• Solid state synthesis;

• Chemical co-precipitation;

• Sol-gel;

• Hydrothermal;

• Spray pyrolysis;

• Glass crystallization.

These methods are used to produce bulk materials, while spray pyrolysis and glass

recrystallization processes listed above are suitable for producing thin films of barium

hexaferrite.

1.16.1 Solid state synthesis

Solid state synthesis is the traditional method of forming barium hexaferrite. In this

method oxides and carbonates of precursor materials are mixed together and then heated to

form the final compound. This method benefits from the simplicity in forming relatively large

quantities of material and does not require expensive laboratory equipment.

1.16.2 Chemical co-precipitation

In chemical co-precipitation of barium hexaferrite, separate solutions containing barium

and ferrite ions are precipitated from the solution usually a nitrate or citrate and the solid then

dried out. This forms a fine powder which is then mixed and heated to react together in a similar

way to the solid state synthesis method [29-31]. This method has been driven by the need for

ever smaller particle sizes within the final barium hexaferrites compound. This results in a more

eff ective material for perpendicular recording media because higher storage densities can be

achieved [32]. Variations of the method produce a range of grain sizes in the final product from

Chapter.1

Page 43

0.1 µm to 0.5µm [33-34]. These procedures have been further refined such that material

produced currently has grain sizes of 80-120nm. Another benefit of co-precipitation is the

reduction in intermediate phases present in the final product [35-37].

1.16.3 Sol-gel

A sol is a substance where fine particles less than 0.1µm are dispersed in a liquid.The

sol then has introduced, or is partially evaporated resulting in a gel of well mixed reactants

being formed. This mixture can then be heated to form barium hexaferrites [38].The chemistry

of the sol-gel method results in final products which are homogeneous and form barium

hexaferrites at a lower temperature as much as 500 K lower than the solid state method [39-

40].

1.16.4 Hydrothermal

Hydrothermal experiments are performed within an autoclave, where reactants can be

subjected to temperatures and pressures higher than normal conditions. Barium hexaferrites is

formed by reacting aqueous solutions of ferric nitrate and barium nitrate at diff erent

temperatures for diff erent lengths of time [41-42]. At a temperature of 300°C, particles of less

than 0.1µm can be formed. Starting solutions using chlorides instead of nitrates have also been

used, resulting in nano-sized particles of barium hexaferrites average size 12nm at lower

temperatures of 140-180°C [43-44]. In recent years this method has been advanced by the use

of super critical water within the autoclave to achieve greater control over particle size and thus

electro-magnetic properties of the resulting compound [45-46].

1.16.5 Spray pyrolysis

In spray pyrolysis, a thin film is formed by spraying a solution on to a heated surface.

The reaction to form the compound occurs on the surface where a suitable temperature is

chosen [47]. This process is used in conjunction with other methods such as citrate precursors

all owing greater control over particle size from 100nm to50-80nm [48-49], or focusing on

forming barium hexaferrites at lower temperatures 700°C while still producing grain sizes in

Chapter.1

Page 44

the nm range. When used in conjunction with co-precipitation, barium hexaferrites powder

with particle size of 30-60 nm can be formed at a temperature of 550°C [50-51].

1.16.6 Glass crystallization

This method was developed with magnetic recording applications in mind; the size,

shape and magnetic properties of the barium hexaferrites particles must have fine tolerance

limits. In this scheme, reactant oxides are melted with a glass forming component, quenched,

crystallized and then followed by chemical separation of the barium hexaferrites from the

unwanted materials [52]. Early work resulted in particles of 80nm, later work studied

controlling experimental temperatures from 200-780°C to form crystals ranging from 50330nm

as selected by the user [53-55].

1.17. Motivation of Work

M-type hexaferrite BaFe12O19 have been a favorite magnetic material for stealth

technology, electromagnetic interference suppression and microwave devices. The reported

[56-58] absorption parameters and related properties for BaFe12O19 ferrite are listed in the table

given below.

Samples εʹ ε ʺ μʹ μ ʺ Ref.loss

(CoTi)xBaFe(12-2x)O19,

x=(0.00-0.10) [56]

23(11GHz) 6.7(12GHz) 0.82(8-

12GHz)

1.2(8-

12GHz)

-21.15dB

(9.54GHz)

BaFe12x(Ti0.5Co0.5)xO19

x=(0.00-0.10) [57]

15 (1GHz) 18 (5GHz) 5.5

(1MHz)

16 (2GHz) -10dB

(10GHz)

BaCe0.05Fe(11.95)O19,

[58]

3(11GHz) 1.73(12GHz) 2.9(8-

12GHz)

0.96(9.9GHz) -17.28(8-

13GHz)

To enhance these properties and absorption ability of M-type ferrites upto X-band (8.4-10.5

Ghz) Ca was selected as base alongwith Ba and rare earth elements with divalent transition

metal ions were substituted. Ca has got the ability to improve these properties and lowers the

sintering temperature. Moreover, Ca is more abundant than Sr and Ba on earth with low cost.

Ca also belong to the same group of periodic table and same electronic configuration as that of

Ba and Sr. Whereas the rare earth element may enhance the resistivity, electric and magnetic

storage capabilities. It may also be interesting that unfilled 4f electrons of rare earth and 3d

electrons of transition metal ions may also enhance the AB- interactions thereby magnetization

Chapter.1

Page 45

may increase. The above mentioned facts motivated me to investigate the CaBa based M-type

hexaferrites substituted with rare earth and transition metal ions [13-14]. In order to achieve

the required goals following three series were selected and investigated thoroughly.

1. Ca0.5Ba0.5-xTbxZnyFe12-yO19 (x = 0.00–0.10; y = 0.00–1.00).

2. Ca0.5Ba0.5-xPrxNiyFe12-yO19 (x = 0.00–0.10; y = 0.00–1.00).

3. Ca0.5Ba0.5-xNdxZnyFe12-yO19 (x = 0.00–0.10; y = 0.00–1.00).

References [1] Carter, C. Barry; Norton, M. Grant"Cer. materials: science and engineering" Springer,

(2007). ISBN 0-387-46270-8.

[2] http://www.global.tdk.com/about_tdk/code of conduct/chapter two.htm.

[3] http://www.pro-perfect.com/

[4] M.A. Ahmed, E.Ateia, S.I. El-dek, Mater. Lett. 57 (2003) 4256.

http://www.global.tdk.com/about_tdk/codehttp://www.global.tdk.com/about_tdk/codehttp://www.pro-perfect.com/

Chapter.1

Page 46

[5] Mansoor Al-Haj, J.Magn Magn Mater. 299 (2006) 435.

[6] http://arxiv.org/pdf/cond-mat/0606631.

[7] W. Hort, Iron oxides for hard/soft ferrites, in: Proceedings of the Conference, Pittsburgh,

(1996).

[8] G.K. Thompson, B.J. Evans, J. Appl. Phys. 73 (1993) 6295.

[9] E. Kreber, U. Gonser, A. Trautwein, F.E. Haris, J. Phys. Chem. Solids 36 (1975) 263.

[10] B.D. Cullity, Introduction to Magnetic Materials, Addison-Wesley, New York, 1972.

[11] S. Hussain, M.A. Rehman, A. Maqsood, M.S. Awan, J. Cryst. Growth. 297 (2006) 403.

[12] F. Leccabue, O.A. Muzio, M.S.E. Kany, G. Calestani, G. Albanese, J. Magn. Magn.

Mater. 68 (1987) 201.

[13] T.Y. Chien, Y.C. Ko, J. Mater. Sci. 25 (1990) 1711.

[14] B. Kaur, M. Bhat, F. Licci, R. Kumar, P. N. Kotru, K. K. Bamzai, Nucl. Instr. and

Meth. in Phys. Res. B, 222 (2004) 175.

[15] S. R. Shinde, A. Bhagwat, S. I. Patil, S. B. Ogale, G. K. Mehta, S. K. Date, G. Marest,

J.

Magn. Magn. Mater, 186 (1998) 342.

[16] J.W. Lee, Y.S. Cho, V.R.W. Amarakoon, J. Appl. Phys. 85 (1999) 5696.

[17] Muhammad Javed Iqbal, Muhammad Naeem Ashiq, Iftikhar Hussain Gul, J. Magn.

Magn. Mater, 322 (2010) 1720.

[18] Muhammad Javed Iqbal, Saima Farooq, Materials Research Bulletin 46 (2011) 662.

[19] D. Mishra, S. Anand, R.K. Panda , R.P. Das, Materials Chemistry and Physics 86 (2004)

132.

[20] H. Luo , B.K. Rai, S.R. Mishra , V.V. Nguyen , J.P. Liu, Journal of Magnetism and

http://arxiv.org/pdf/cond-mat/0606631

Chapter.1

Page 47

Magnetic Materials 324 (2012) 2602.

[21] Shahid Hussain, A. Maqsood, J. Magn. Magn. Mater., 316 (2007) 73.

[22] B. D. Cullity, “Introduction to Magnetic Materials”, Addison-Wesley Publishing

Company, Notre Dame, (1972).

[23] E. W. Gorter, Philips Res. Report 9 (1954) 295, 321, 403.

[24] www.electronics-tutorials.ws.

[25] Alex Goldman, Modern Ferrite Technology”, Van Nostrand Reinhold, New York,

(1990).

[26] M. Kamruzzaman, Ph. D. Thesis, (2003). Department of Physics, University of

Limerick, Limerick, Ireland.

[27] B. B. Laud, “Electromagnetics”, Wiley Eastern, (1983).

[28] A. Berkowitz, and E. Kneller, Magnetism and Metallurgy. 1, Academic

Press, New York. 838 (1969).

[29] E. C. Snelling and A. D. Giles, “Ferrites for Inductors and Transformers”, John

Willey & Sons, (1983).

[30] K.J.Standley,“Oxide Magnetic Materials”, 2nd Ed., Clarendon Press, Oxford (1972).

[31] J.Daintith, J.Clark, H.M.Clarke, R.Cutler, D.Cooper, D.E.Edwards, R.Rennie, and

D.E.Ward. Dictionary of Chemistry Oxford University Press, 2008.

[32] T.O gasawara and M.A.S.Oliveira, J. Magn. Magn. Mater. 217 (2000) 147.

[33] J.Matutes Aquino, S.Diaz Castanon, M. Mirabal Garcia, and S.A. Palomares Sanchez.

Scripta Materialia, 42 (2000) 295.

[34] K. Haneda, C.Miyakawa, and H.Kojima. Preparation of high-coercivity BaFe12O19.

Journal of the American Ceramic Society, 57 (1974) 35.

[35] C.D.Mee and J.C.Jeschke, Journal of Applied Physics, 34 (1963) 1271.

http://www.electronics-tutorials.ws/

Chapter.1

Page 48

[36] S.E.Jacobo, C. Domingo Pascual, R.Rodriguez Clemente, and M.A. Blesa, Journal of

Materials Science, 32 (1997) 1025.

[37] J.Huang, H.Zhuang, and W.Li, Materials Research Bulletin, 38 (2003) 149.

[38] M.Radwan, M.M.Rashad, and M.M. Hessien. Journal of Materials Processing

Technology, 181 (2007) 106.

[39] W.Roos, Journal of the American Ceramic Society, 63 (1980) 601.

[40] Encyclopaedia Britannica Online. Advanced Ceramics. http://www.britannica.com/ E.B

checked / topic / 6657 / advanced-ceramics, Accessed: March 2009.

[41] F. Licciand, T.Besagni, IEEE Transactions on Magnetics, MAG-20(5) (1984)1639.

[42] C.Surig, K.A. Hempel, and Ch.Sauer, Journal of Magnetism and Magnetic Materials,

157/158 (1996) 268.

[43] C.H.Lin, Z. W. Shih, T.S.Chin, M.L.Wang, and Y.C.Yu, IEEE, Transactions on

Magnetics, 26 (1990) 15.

[44] H.Kumazawa, Y.Maeda, and E.Sada, Journal of Materials Science Letters, 14 (1995)

68.

[45] E.Sada, H.Kumazawa, and H-M.Cho., Industrial and Engineering Chemistry Research,

30 (1991) 1319.

[46] S.Che, J.Wang, and Q.Chen, Journal of Physics: Condensed Matter, 15 (2003) L335.

[47] T.Adschiri, Y.Hakuta, and K.Arai, Industrial and Engineering Chemistry Research,

39

(2000) 4901.

[48] S-C.Nam and G-J.Kim, Korean Journal of Chemical Engineering, 21 (2004) 582.

[49] J.B.Mooney and S.B.Radding, Spray pyrolysis processing. Annual Review of Materials

Science, 12 (1982) 81.

http://www.britannica.com/

Chapter.1

Page 49

[50] T. Gonzalez Carreno, M.P.Morales, and C.J.Serna, Materials Letters, 43 (2000) 97.

[51] V. K. Sankaranarayanan, R.P.Pant, and A.C.Rastogi, Journal of Magnetism and

Magnetic Materials, 220 (2000) 72.

[52] H-F.Yu and H-Y.Lin, Journal of Magnetism and Magnetic Materials, 283 (2004) 190.

[53] V. V.Pankov, Inorganic Materials, 40 (2004) 979.

[54] L. Rezlescu, E.Rezlescu, P.D.Popa, and N.Rezlescu. Journal of Magnetism and

Magnetic Materials, 193 (1999) 288.

[55] O.Kubo, T.Ido, and H.Yokoyama, IEEE Transactions on Magnetics, 18 (1982) 1122.

[56] S.B.Narang, P.Kaur, S.bahel, Ch.Singh, Journal of Magnetism and Magnetic Materials,

405 (2016) 17.

[57] Takanori Tsutaoka , Aiko Tsurunaga, Nobuyoshi Koga, Journal of Magnetism and

Magnetic Materials, 399 (2016) 64–71

[58] S. Chang, S. Kangning, C.Pengfei, Journal of Magnetism and Magnetic Materials, 324

(2012) 802.

Chapter.2

Page 50

Chapter 2

THEORETICAL

BACKGROUND &

LITERATURE

SURVEY

Chapter.2

Page 51

THEORETICAL BACKGROUND

2.1 Magnetic materials

Material Science and engineering plays an imperative role in this modern age of science

and technology. The tremendous progress in the development and growth of electronic

ceramics since the era of post Second World War II has played a major role in the

transformation of the society from steel age to the information age. Satellite communications

from coast to coast and around the world would not be possible without simultaneous advances

in semiconductors, dielectrics, ferroelectrics, ferrites and optoelectronics. The continued

developments in these fields have been matched, and perhaps eventually superseded with

advances in superconducting ceramics, photonics, and optical waveguides and potentially in

optical computing and information processing [1]. In connection with advances in

communication technologies, magnetic ceramics have been investigated due to their vastly

intriguing properties such as magnetization behaviour, high magnetic permeability and high

electrical resistivity [2]. These intrinsic material properties have made them indispensably the

most versatile engineering ceramics for high frequency applications including power

transformers, antennas, faraday rotators, etc [3]. A magnetization, M can occur as a result of

more or less alignment of elementary magnets known as magnetic dipole (electron orbits or

electron spins) present in a matter. In order to produce this alignment of magnetic dipole, an

external magnetic field (H) is to be applied. When magnetization is relatively small, it increases

proportionally with an applied field according to the relation, M = χH, where χ is the

susceptibility per cm3 [4]. Magnetism in the material can be classified in terms of the

arrangements of magnetic dipoles in the solid and depending upon the sign and the value of

susceptibility (χ). These dipoles can be thought of a little imprecisely, as microscopic bar

magnets attached to the various atoms present.

2.1.1 Types of magnetic materials

Magnetic materials are divided in to five groups namely; Diamagnetic, Paramagnetic,

Ferromagnetic, Antiferromagnetic and Ferrimagnetic.

Chapter.2

Page 52

(i) Diamagnetic Materials

Materials with no elementary magnetic dipoles are known as diamagnetic. The

magnetic susceptibility (χ) of a diamagnetic substance is negative and very slightly less than 1

and of the order of 10-5. There is no appreciable variation of diamagnetism with temperature.

In the absence of applied magnetic field, each atom has net zero magnetic dipole moment. In

the presence of an applied magnetic field, the angular velocities of the electronic orbits are

changed. These induced magnetic dipole moments align themselves opposite to the applied

field. Diamagnetism can be a big effect in superconductors and in artificial materials.

Diamagnetic materials are repelled from either pole of a magnet. Water, gold, bismuth, copper,

zinc, mercury are examples of diamagnetic materials.

(ii) Paramagnetic Materials

Fig. 2.1 shows magnetic structure of paramagnetic materials. Paramagnetic materials

are those in which some of the atoms, ions or molecules making up the solid possess a

permanent magnetic dipole moment. These dipoles are isolated from one another. In the

absence of applied magnetic field, each atom has net non-zero magnetic dipole moment. These

magnetic dipole moments are randomly oriented so that the net macroscopic magnetization is

zero. In the presence of an applied magnetic field, the magnetic dipoles align themselves with

the applied field so that magnetic susceptibility, χm > 0 and of the order less than 10-2.

Paramagnetic materials are weakly attracted to either pole of a magnet. Examples of

paramagnetic substances are aluminium, platinum, lithium, oxygen and in general all

magnetically diluted solution of elements which have an incomplete atomic orbital.

Fig.2.1 Magnetic structure of Paramagnetic materials.

Chapter.2

Page 53

(iii) Ferromagnetic Materials

Fig. 2.2 shows magnetic structure of ferromagnetic materials. Ferromagnetic materials

include iron, nickel, cobalt and compounds containing these elements. In the absence of an

applied external magnetic field, each atom has very strong magnetic dipole moments due to

uncompensated electron spins. Regions of many atoms with aligned dipole moments called

‘domains’. In the absence of an applied magnetic field, the domains are randomly oriented so

that the net macroscopic magnetization is zero. In the presence of an applied magnetic field,

the domains align themselves with the applied field. The effect is a very strong one with χm >>

0. Ferromagnetic materials are strongly attracted to either pole of a magnet. The permeability

is very non-linear and it depends on the previous history of the material and it is much larger

than the permeability of free space. The relationship, B = µH can be illustrated by means of a

magnetization curve also called hysteresis loop. Where, B is the magnetic flux density, µ is

permeability and H is magnetic field strength.

Fig.2.2 Magnetic structure of Ferromagnetic materials.

(iv) Antiferromagnetic Materials

Fig. 2.3 shows magnetic structure of antiferromagnetic materials. In antiferromagnetic

materials, the magnetic moments of

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