PROJECT REPORT

ON

PREPARATION AND ANALYSIS OF BaPr 1.33Ti3O9 & BaPr2Ti4O12

MICROWAVE DIELECTRIC CERAMICS

A Project report submitted in partial fulfillment of the requirement for the award of

Bachelor of technology

In

Electronics and communication engineering

Under the guidance of: Submitted By:

Er. Shalini Bahel Amit Mahajan(74544)

Dr. S. Bindra Narang

Dept. of Electronics & Communication Engineering

Guru Nanak Dev University

Amritsar

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CERTIFICATE FROM GUIDE

This is to certify that the project titled “PREPARATION AND ANALYSIS OF BaPr1.33Ti3O9& BaPr2Ti4O12 MICROWAVE DIELECTRIC CERAMICS” has been carried out by Amit Mahajan under my supervision in partial fulfillment of the requirements for the Degree of Bachelor of Technology in Electronics & Communication Engineering of the Guru Nanak Dev University, Amritsar during the academic year 2009- 2010.

_______________________

(Er. Shalini Bahel)

COUNTERSIGNED

_______________________________

Dr. M.L Singh

Head of the Department,

Electronics & Communication Engineering

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ACKNOWLEDGEMENT

The completion of any project brings with it a sense of satisfaction, but it is never complete without thanking those people who made it possible and whose constant support has crowned our efforts with success. One cannot even imagine the power of the force that guides us all and neither can we succeed without acknowledging it. My deepest gratitude to Almighty God for holding my hands and guiding me throughout my life.

I am thankful to my esteemed faculty member Prof. Sukhleen Bindra Narang for her expert guidance, encouragement and valuable suggestions. I would like to express my gratitude to Er. Shalini bahel, my guide, for her lectures on dielectric ceramics which constantly inspired me towards the attainment of everlasting knowledge throughout the course. I am thankful to the Head of Department Dr. M.L.Singh, without his incredible support and steady involvement; the project would not have been fruitful. I would also like to thank research scholar Ms. Dalbir Kaur for explaining me various concepts of microwave dielectric ceramics. I am grateful to the Thapar University and PU, Chandigarh for providing me the facility to carry out the experimental work. I would like to thank all the staff members of ECE dept. for providing me with the required facilities and support towards the completion of the project. I am extremely happy to acknowledge and express my sincere gratitude to my parents for their constant support and encouragement and last but not the least, friends and well wishers for their help and cooperation and solutions to problems during the course of the project.

Amit Mahajan

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ABSTRACT

In the field of microwave dielectric ceramics, BaO-R2O3-TiO2 (R=La, Nd, Sm, Pr) is the most valuable material system, which is used for microwave components such as multi-layer ceramic chip capacitor (MLCC), single-layer ceramic chip capacitor (SLC), dielectric resonator & filter, voltage control oscillator (VCO) and antenna, etc. Also microwave dielectric ceramics has received much attention due to rapid growth of the wireless communication industry. In this project we are concerned with the development of microwave resonator materials. The three vital properties required for these materials are:

1) A high dielectric constant for miniaturization.2) A high quality factor (which is inverse of loss tangent, tanδ) for better frequency stability.3) A good temperature stability or near zero temperature coefficient of resonant frequency.

Dielectric ceramics materials in ternary system BaO-R2O3-TiO2 (R=Rare earth, La, Pr, Nd, Sm, Gd) has gained importance due to their high dielectric constants, high quality factor and near zero temperature coefficient of resonant frequency. The ceramics system with general formulas BaPr1.33Ti3O9 & BaPr2Ti4O12 has been synthesized by mixed oxide method using reagent grade powders BaCo3, Pr6O11 and TiO2. The samples have been calcinated at 1100°C for 2 hrs in silica crucibles in a linear programmable furnace in order to bring about a thermal decomposition, phase transition and removal of a volatile fraction.

Microwave dielectric properties can be adjusted widely by ionic or structural modification. The effect of such substitution on microstructures and microwave dielectric properties at room temperature has been investigated. Various analytical tools are used for the study of structural and dielectric properties. The most common analytical tool for structural studies is crystal diffraction using x-rays that undergo wave interface with the regular arrangements of atoms in a crystalline lattice. This technique is x-ray powder diffraction (XRD) and can be used to give both

qualitative and quantitative data for the crystal structure. It is expected that substitution of Pr in

ceramics would result in promising material with high dielectric constant and low loss.

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CONTENTS

ABSTRACT Page No.CHAPTER 1 Introduction

1.1 Microwave dielectric ceramics 8 Ceramics

1.1.1 Origin of ceramics 1.1.2 Examples of ceramics

1.2 Properties of ceramics 91.2.1 Mechanical properties1.2.2 Refractory behavior1.2.3 Electrical behavior

1.2.3.1 Electrical insulation and dielectric behavior1.2.3.2 Ferroelectric, piezoelectric and pyroelectric

1.2.4 Semi conductivity1.2.5 Superconductivity

1.3 Processing of ceramic material 111.3.1 In situ manufacturing1.3.2 Sintering based method

1.4 Other applications of ceramics 121.5 Aim of the project 141.6 Project report layout 14

CHAPTER 2 Dielectric Properties2.1 Dielectric constant 15

2.1.1 Definition2.1.2 Generalizations

2.2 Capacitance 172.2.1 Definition2.2.2 Charge Stored2.2.3 Energy Stored2.2.4 Capacitive Reactance Xc2.2.5 Time Constant2.2.6 Uses of Capacitors

2.3 Loss Tangent ( tanδ) and Q factor 192.3.1 Definition2.3.2 Electromagnetic Field perspective2.3.3 Loss tangent component2.3.4 Q factor

2.4 Polarization of Dielectrics 22

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2.4.1 Definition2.4.2 Effect of Dielectrics

2.5 Dielectric A.C Conductivity 232.5.1 Definition

2.6 Temperature Coefficient of Resonance frequency 242.6.1 Definition

CHAPTER 3 Preparation and Analysis3.1 Weighing 25

3.1.1 Definition3.1.2 Techniques of Weighing

3.1.2.1 Spring Scale3.1.2.2 Analytical Balance

3.2 Ball Milling 263.2.1 Definition

3.3 Calcination 273.3.1 Definition3.3.2 Examples of Calcination process3.3.3 Calcination Reactions

3.4 Post Mixing 293.4.1 Definition

3.5 Granulation and Sieving 293.5.1 Definition of Granulation3.5.2 Definition of Sieving

3.6 Compaction 303.6.1 Definition

3.7 Sintering and Polishing 313.7.1 Definition

3.8 X-ray powder diffraction 31

3.8.1 Definition 3.9 Apparatus required for X-ray powder diffraction 33

3.9.1 Diffractometer

CHAPTER 4 RESULT AND DISCUSSION

4.1 X-Ray Diffraction 35

4.2 Density Measurement 36

4.3 Dielectric Properties 37

4.3.1 Dielectric Constant

4.3.2 Loss Tangent

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4.3.3 AC Conductivity

CHAPTER 5 Conclusions 43

BIBLIOGRAPHY

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CHAPTER 1

INTRODUCTION

1.1 Microwave dielectric ceramics :

Temperature-stable, medium-permittivity dielectric ceramics have been used as resonators in filters for microwave (MW) communications for several years. The growth of the mobile phone market in the 1990s led to extensive research and development in this area. The main driving forces were the greater utilization of available bandwidth, that necessitates extremely low dielectric loss (high-quality factor), an increase in permittivity so that smaller components could be fabricated, and, as ever in the commercial world, cost reduction. Over the last decade, a clear picture has emerged of the principal factors that influence MW properties. Proper selection of ceramics materials is necessary in order to achieve suitable dielectric properties. Dielectric ceramics can be selected from a wide range of materials. These materials include titanates, nitrates, tantalates, niobates, silicates, etc. such as – Alumina, Aluminium nitride, Barium Titanates (BaTiO3), Barium Strontium Titanates, and Lithium Niobates.

The Barium Titanates (BaTiO3) is used extensively in ceramics because of its high dielectric constant compared with other ceramics. It is rarely used without modification, because difficulty in controlling grain size during sintering. BaTiO3 is slightly doped with rare earth oxides (up to a concentration of around 0.3-0.5%) and is used for the preparation of switching and regulating devices. Ceramics in the vicinity of BaO: R2O3:4TiO2 are used in microwave resonators. It will be beneficial to explain ceramics at this point.

1.2 CERAMICS : 1.2.1 Origin of ceramics

The word ceramic is derived from Greek, and strictly refers to clay in all its forms. However, modern usage of the term broadens the meaning to mean inorganic non-metallic materials. Until 1950s or so, the most important of these was the traditional clays, made into pottery, bricks, tiles and similar, along with cements and glass. The traditional crafts are described in the article on pottery. The classic ceramic materials are hard, porous and brittle. The study of ceramics consists to a large extent of methods to mitigate the problems, and accentuate the strengths of the materials, as well as to offer up unusual uses for these materials.

1.2.2 Examples of Ceramic Materials

Silicon nitride (Si3N4), which is used as an abrasive powder. Boron carbide (B4C), which is used in some helicopter and tank armor. Silicon carbide (Si C ), which is used as a succeptor in microwave furnaces, a commonly

used abrasive, and as a refractory material. Magnesium diboride (MgB2), which is an Unconventional superconductor. Zinc oxide (Zn O ), which is a semiconductor, and used in the construction of transistors.

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Ferrite (Fe3O4), which is ferromagnetic and is used in the core of electrical transformers and magnetic core memory.

Steatite is used as an electrical insulator. Bricks (mostly aluminum silicates), used for construction. Uranium oxide (UO2), used as fuel in nuclear reactors. Yttrium barium copper oxide (Y Ba 2Cu3O7-x),a high temperature superconductor

1.3 Properties of Ceramics

1.3.1Mechanical properties :

Ceramic materials are usually ionic or glassy materials. Both of these almost always fracture before any plastic deformation takes place, which results in poor toughness in these materials. Additionally, because these materials tend to be pours, the pores and other microscopic imperfections act as stress concentrators, decreasing the toughness yet further, and reducing the tensile strength. These combine to give catastrophic failures, as opposed to the normally much more gentle failure modes of metals.

It is not true to say that these materials do not show plastic deformation. However, due to the rigid structure of the crystalline materials, there are very few available slip systems for dislocations to move, and so they deform very slowly. With the non-crystalline (glassy) materials, viscous flow is the dominant source of plastic deformation, and is also very slow. It is therefore neglected in many applications of ceramic materials. These materials have great strength under compression, and are capable of operating at elevated temperatures. Their high hardness makes them widely used as abrasives, and as cutting tips in tools.

1.3.2 Refractory behavior:

Some ceramic materials can withstand extremely high temperatures without losing their strength. These are called refractory materials. They generally have low thermal conductivities, and thus are used as thermal insulators. For example, the belly of the Space Shuttles are made of ceramic tiles which protect the spacecraft from the high temperatures caused during reentry. The most salient properties required for a good refractory material is that it not soften or melt, and that it remains unreactive at the desired temperature. This latter point covers both self decomposition, and reacting with other compounds in its vicinity - either of which would be detrimental.

Porosity takes on additional relevance with refractories. As the porosity is reduced, the strength, load bearing ability and environmental resistance decreases as the material gets denser. However as the density increases the resistance to thermal shock (cracking as a result of rapid temperature change) and insulation characteristics are reduced. Many materials are used in a very porous state, and it is not uncommon to find two materials used - a porous layer, with very good insulating properties, with a thin coat of a more dense material to provide strength. It is perhaps surprising to find that these materials can be used at temperatures where part of them is a liquid. For example, silica firebricks used to line steel making furnaces is used at temperatures up to

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1650°C (3000°F), where some of the brick will be liquid. Designing for such a situation unsurprisingly requires a substantial degree of control over all aspects of construction and use.

1.3.3 Electrical behavior :

One of the largest areas of progress with ceramics was their application to electrical situations, where they can display a bewildering array of different properties.

1.3.3.1 Electrical insulation and dielectric behavior:

The majority of ceramic materials has no mobile charge carriers, and thus do not conduct electricity. When combined with strength, this leads to uses in power generation and transmission. Power lines are often supported from the pylons by porcelain discs, which are sufficiently insulating to cope with lightning strikes, and have the mechanical strength to hold the cables. A sub category of their insulating behavior is that of the dielectrics. A good dielectric will maintain the electric field across it, without inducting power loss. This is very important in the construction of capacitors. Ceramic dielectrics are used in two main areas. The first is the low-loss high frequency dielectrics, used in applications like microwave and radio transmitters. The other is the materials with high dielectric constants (the ferroelectrics). Whilst the ceramic dielectrics tend not to outmatch other options for most purpose, they fill these two niches very well.

1.3.3.2 Ferroelectric, piezoelectric and pyroelectric :

A ferroelectric material is one the can spontaneously generate a polarization, in the absence of an electric field. These materials exhibit a permanent electric field, and this is the source of their extremely high dielectric constants.

A piezoelectric material is one where an electric field can be changed or generated by applying a stress to the material. These find a range of uses, principally as transducers - to convert a motion into an electric signal, or vice versa. These appear in devices such as microphones, ultrasound generators, strain gauges and many more.

A pyroelectric material develops an electrical field when heated. Some ceramic pyroelectrics are so sensitive they can detect the temperature change caused by a person entering a room (approximately 40 micro Kelvin). Unfortunately, such devices lack accuracy, so they tend to be used in matched pairs - one covered, the other not, and only the difference between the two used.

1.3.4 Semi conductivity:

There are a number of ceramics that are semiconductors. Most of these are transition metal oxides that are II-VI semiconductors, such as zinc oxide. Whilst there is talk of making blue LEDs from zinc oxide, ceramicists are most interested in the electrical properties that show grain boundary effects. One of the most widely used of these is the transistor. These are devices that exhibit the unusual property of negative resistance. Once the voltage across the device

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reaches a certain threshold, there is a breakdown of the electrical structure in the vicinity of the grain boundaries, which results in its electrical resistance dropping from several mega-ohms down to a few hundred. The major advantage of these is that they can dissipate a lot of energy, and they self reset - after the voltage across the device drops below the threshold, its resistance returns to being high.

This makes them ideal for surge protection applications. As there is control over the threshold voltage and energy tolerance, they find themselves in all sorts of applications. The best demonstration of their ability can be found in electricity sub stations, where they are employed to protect the infrastructure from lightning strikes. They have rapid response, are low maintenance, and do not appreciable degrade from use, making them virtually ideal devices for this application. The semiconducting ceramics can also be found employed as gas sensors. When various gases are passed over a polycrystalline ceramic, its electrical resistance changes. With tuning to the possible gas mixtures, very inexpensive devices can be produced.

1.3.5 Superconductivity:

Under some conditions, such as extremely low temperature, some ceramics exhibit superconductivity. The exact reason for this is not known, but there are two major families of superconducting ceramics. The complex copper oxides are exemplified by Yttrium barium copper oxide, often abbreviated to YBCO, or 123 (after the ratio of metals in its stiochiometric formula YBa2Cu3O7-x). It is particularly well known because it is quite easy to make, does not require any particularly dangerous materials to do so, and has a superconducting transition temperature of 90K (which is above the temperature of liquid nitrogen (77K)). The x in the formula refers to the fact that fully stiochiometric YBCO is not a superconductor, so it must be slightly oxygen deficient, with x typically around 0.3.

The other major family of superconducting ceramics is magnesium diboride. It is currently in a family all of its own, and its behavior is not particularly remarkable, other than its very different from all other superconductors (not being either a complex copper oxide, nor a metal), and thus it is hoped that studying it will reveal more information about why superconductivity exists, which will feed into high temperature superconductivity research.

1.4 Processing of Ceramic Materials :

Non-crystalline ceramics, being glasses, tend to be formed from melts. The glass is shaped when either fully molten, by casting, or when in a toffee like viscosity, by methods such as blowing to a mould.

Crystalline ceramic materials are not amenable to a great range of processing. Methods for dealing with them tend to fall into one of two categories - either make the ceramic in the desired shape, by reaction in situ, or by forming powders into the desired shape, and then sintering to form a solid body. A few methods use a hybrid between the two approaches.

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1.4.1 In situ manufacturing:

The most common use of this type method is in the production of cement and concrete. Here, the dehydrated powders are mixed with water. This starts hydration reactions, which result in long, interlocking crystals forming around the aggregates. Over time, these result in a solid ceramic.

The biggest problem with this method is that most reactions are so fast that good mixing is not possible, which tends to prevent large scale construction. However, small scale systems can be made by deposition techniques, where the various materials are introduced above a substrate, and react and form the ceramic on the substrate. This borrows techniques from the semiconductor industry, such as chemical vapor deposition, and it very useful for coatings. These tend to produce very dense ceramics, but do so slowly.

1.4.2 Sintering based methods:

The principles of sintering based methods are simple. Once a roughly held together object is made (called a "green body"), it is baked in a kiln, where diffusion processes cause the green body to shrink, and close up the pores in it, resulting in a denser, stronger product. The firing is done at a temperature below the melting point of the ceramic. There is virtually always some porosity left, but the real win of this method is that the green body can be produced in any way imaginable, and still be sintered. This makes it a very versatile route.

There are thousands of possible refinements that can be added to this process. Some of the most common are pressing the green body, to give the densification a head start, and reduce the sintering time needed. Sometimes organic binders are added, to hold the green body together, which burn out during the firing. When pressing, something organic lubricants are added, to get maximum density from pressing. It's not uncommon to combine these, and add binders and lubricants to a powder, then press. Rather than a powder, a slurry can be used, and then cast into a desired shape, dried and then sintered. Indeed, the traditional pottery is done with this type of method, using a plastic mixture worked with the hands. If a mixture of different materials is used together in a ceramic, it sometimes is that the sintering temperature is above the melting point of one minor component - a liquid phase sintering. This results in faster sintering times over solid state sintering.

1.5 Applications of ceramics :

Ceramics are used in the manufacture of knives. The blade of a ceramic knife will stay sharp for much longer than that of a steel knife, although it is more brittle and can be snapped by dropping it on a hard surface.

Ceramics such as alumina and boron carbide have been used in ballistic armored vests to repel large-caliber rifle fire. Such plates are known commonly as small-arms protective inserts (SAPI). Similar material is used to protect cockpits of some military airplanes, because of the low weight of the material.

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Ceramic balls can be used to replace steel in ball bearings. Their higher hardness means that they are much less susceptible to wear and can offer more than triple lifetimes. They also deform less under load meaning they have less contact with the bearing retainer walls and can roll faster. In very high speed applications, heat from friction during rolling can cause problems for metal bearings; problems which are reduced by the use of ceramics. Ceramics are also more chemically resistant and can be used in wet environments where steel bearings would rust. The major drawback to using ceramics is a significantly higher cost. In many cases their electrically insulating properties may also be valuable in bearings.

In the early 1980s, Toyota researched production of an adiabatic ceramic engine which can run at a temperature of over 6000°F (3300°C). Ceramic engines do not require a cooling system and hence allow a major weight reduction and therefore greater fuel efficiency. Fuel efficiency of the engine is also higher at high temperature, as shown by Carnot's theorem. In a conventional metallic engine, much of the energy released from the fuel must be dissipated as waste heat in order to prevent a meltdown of the metallic parts. Despite all of these desirable properties, such engines are not in production because the manufacturing of ceramic parts in the requisite precision and durability is difficult. Imperfection in the ceramic leads to cracks, which can lead to potentially dangerous equipment failure. Such engines are possible in laboratory settings, but mass-production is not feasible with current technology.

Work is being done in developing ceramic parts for gas turbine engines. Currently, even blades made of advanced metal alloys used in the engines' hot section require cooling and careful limiting of operating temperatures. Turbine engines made with ceramics could operate more efficiently, giving aircraft greater range and payload for a set amount of fuel.

Recently, there have been advances in ceramics which include bio-ceramics, such as dental implants and synthetic bones. Hydroxyapatite, the natural mineral component of bone, has been made synthetically from a number of biological and chemical sources and can be formed into ceramic materials. Orthopedic implants made from these materials bond readily to bone and other tissues in the body without rejection or inflammatory reactions. Because of this, they are of great interest for gene delivery and tissue engineering scaffolds. Most hydroxyapatite ceramics are very porous and lack mechanical strength and are used to coat metal orthopedic devices to aid in forming a bond to bone or as bone fillers. They are also used as fillers for orthopedic plastic screws to aid in reducing the inflammation and increase absorption of these plastic materials. Work is being done to make strong, fully dense nano crystalline hydroxyapatite ceramic materials for orthopedic weight bearing devices, replacing foreign metal and plastic orthopedic materials with a synthetic, but naturally occurring, bone mineral. Ultimately these ceramic materials may be used as bone replacements or with the incorporation of protein collagens, synthetic bones.

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High-tech ceramic is used in watch making for producing watch cases. The material is valued by watchmakers for its light weight, scratch-resistance, durability and smooth touch. IWC is one of the brands that initiated the use of ceramic in watch making. The case of the IWC 2007 Top Gun edition of the Pilot's Watch Double chronograph is crafted in high-tech black ceramic.

1.6Aim of the project:

The aim of the present project work is:

1. To process (BaPr1.33Ti3O9) & (BaPr2Ti4O12 ) microwave dielectric ceramics.2. To analyze the structural and dielectric properties of the prepared microwave

dielectric ceramics.

1.7 Pr oject report layout:

The project report is divided into following five chapters:

Chapter 1: It presents an introduction to the microwave dielectric ceramics.

Chapter 2: This is about the dielectric properties such as capacitance, dielectric constant loss tangent, temperature coefficient of the resonant frequency, polarization and ac conductivity.

Chapter 3: Processing of ceramic samples using conventional mixed oxide is presented in this chapter.

Chapter 4: This chapter deals with structural and Dielectric characterization of synthesized samples.

Chapter 5: It gives the conclusions derived from various measurements carried out on synthesized samples.

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CHAPTER 2

DIELECTRIC PROPERTIES

2.1 Dielectric constant

2.1.1 Definition

The Dielectric constant (or relative permittivity) is an intrinsic property of dielectric material. Under given conditions is a measure of the extent to which it concentrates electrostatic lines of flux. It is the ratio of the amount of stored electrical energy when a potential is applied, relative to the permittivity of a vacuum. The relative static permittivity is the same as the relative permittivity evaluated for a frequency of zero. The relative permittivity describes the ease by which a dielectric medium may be polarized. The capacitance of a capacitor is proportional to εr.

The dielectric constant (relative static permittivity) is represented as εr or sometimes κ or K. It is defined as

εr= ε/ε0

Where ε is the static permittivity of the material, and ε0 is the electric permittivity of the free space(which is equal to 8.854*10-12 F/m)

The relative permittivity is complex and frequency dependent, which gives the static relative permittivity for ω = 0.

Propagation of waves in dielectric materials

When two electric charges are placed inside a dielectric, the electrostatic force between the charges is changed by a factor 1/εr. Empirically it is observed that the force between two charges never increases (the force stays the same or decreases) by the presence of any dielectric medium, hence the relative permittivity εr ≥ 1. Only the vacuum has εr = 1 (exact). All dielectrics have values larger than one (but some materials, such as non-dense inert gases, have relative permittivity very close to the vacuum value of unity).

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Other terms for dielectric constant are relative static permittivity, or relative dielectric constant, or static dielectric constant.

If σ is the charge density on the plate (charge per surface, in SI units C/m2), the strength E of the field E is given by

E = σ/ (2 ε0εr),

Where ε0 is the electric permittivity of free space. When the charge density σ is positive the electric field (a vector) E points away from the plate. Of course, plates of infinite size do not exist, but this formula is applicable when the height is much smaller than the dimensions of the plate, so that border effects can be neglected.

In parallel-plate capacitors border effects can usually be ignored and because both plates have the same charge density (but of opposite sign), the electric field inside a capacitor, filled with a dielectric with εSr, is double that of one plate

E = σ/ (ε0εr).

If the plates have surface area A, they carry a total charge Q = σ A (positive on one plate, negative on the other),

Q = ε0εr A E.

The distance between the plates is d,

then the voltage difference V between the plates is (E / d).

The capacitance C of a capacitor is by definition (Q / V), so that we find that the capacitance of a parallel-plate capacitor is linear in the relative permittivity εr:

C = εr C0 with C0 ≡ (ε0 A) / d.

Clearly, C0 is the capacity with vacuum between the plates, and one may define

εr is equal to the ratio of the capacitance of a capacitor filled with the dielectric to the capacitance of an identical capacitor in a vacuum without the dielectric material.

Because εr > 1, the insertion of a dielectric between the plates of a parallel-plate capacitor always increases its capacitance, or ability to store opposite charges on each plate.

The relative permittivity is defined as a macroscopic property of dielectrics.

The static relative permittivity of a medium is related to its static electric susceptibility, χe by

εr = 1+ χe

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The relative static permittivity, εr, can be measured for static electric fields as follows: first the capacitance of a test capacitor, C0, is measured with vacuum between its plates. Then, using the same capacitor and distance between its plates the capacitance Cx with a dielectric between the plates is measured. The relative dielectric constant can be then calculated as

εr = Cx / C0

For time-variant electromagnetic fields, this quantity becomes frequency dependent and in general is called relative permittivity.

2.1.2 Generalizations

The relative permittivity of a dielectric is a function of temperature and, when the dielectric is a gas. For low-symmetry dielectrics (solids and liquid crystals) it may happen that the constant is a second rank tensor, which is represented with respect to a Cartesian coordinate system by a 3 × 3 matrix.

For frequency-dependent (time-dependent) electric fields the relative permittivity is in general a function of the angular frequency ω.

Electric field above infinite plate

An infinitesimal surface element in cylinder coordinates times the surface charge density σ gives an infinitesimal charge in the plate,

dQ= σrdrdΨ

where σ is assumed constant over the plate and for convenience sake we take it positive (hence the field points in the positive z direction).

2.2 CAPACITANCE

2.2.1 Definition

In electromagnetism and electronics, capacitance is the ability of a body to hold an electrical charge. Capacitance is directly proportional to the surface area of the conductor plates and inversely proportional to the separation distance between the plates.

C= (Aε/d)

Where ε= ε0 εr

ε0 is the permittivity of free space where ε0 = 8.854x d-12 F/m

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d is the separation between the plates, measured in metres.

Capacitance between two plates

2.2.2 Charge Stored

The amount of charge (symbol Q) stored by a capacitor is given by:

Charge, Q = C × V

Where Q = charge in coulombs (C)

C = capacitance in farads (F)

V = voltage in volts (V)

2.2.3 Energy stored

The energy (measured in joules) stored in a capacitor is equal to the work done in moving dq from one plate to the other against the potential difference V = q/C requires the work dW.

When they store charge, capacitors are also storing energy:

Energy, E = ½QV = ½CV²

where E = energy in joules (J).

Note that capacitors return their stored energy to the circuit. They do not 'use up' electrical energy by converting it to heat as a resistor does.

2.2.4 Capacitive Reactance Xc

Capacitive reactance (symbol Xc) is a measure of a capacitor's opposition to AC (alternating current).

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Capacitive reactance, Xc = 1 / (2fC)

Where Xc = reactance in ohms ()

f = frequency in hertz (Hz)

C = capacitance in farads (F)

The reactance Xc is large at low frequencies and small at high frequencies. For steady DC which is zero frequency, Xc is infinite (total opposition), hence the rule that capacitors pass AC but block DC.

2.2.5 Time constant

Time constant = R × C

where Time constant is in seconds (s)

R = resistance in ohms (Ώ)

C = capacitance in farads (F)

The time constant is the time taken for the charging (or discharging) current (I) to fall to 1/e of its initial value (Io). 'e' is the base of natural logarithms, an important number in mathematics e = 2.71828

2.2.6 Uses of Capacitors

Capacitors are used for several purposes:

Timing -for example with a 555 timer IC controlling the charging and discharging.

Smoothing -for example in a power supply.

2.3 Loss tangent (tanδ) and Q-factor

2.3.1 Definition

The loss tangent is a parameter of dielectric material that quantifies its inherent dissipation of electromagnetic energy. The term refers to the angle in a complex plane between the resistive (lossy) component of an electromagnetic field and its reactive (lossless) component.

2.3.2 Electromagnetic Field Perspective

For time varying electromagnetic fields, the electromagnetic energy is typically viewed as waves propagating either through free space, in a transmission line, or through a waveguide. Dielectrics

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are often used to mechanically support electrical conductors and keep them at a fixed separation. Maxwell’s equations are solved for the electric and magnetic field components of the propagating waves that satisfy the boundary conditions of the specific environment's geometry. In such electromagnetic analyses, the parameters permittivity ε, permeability μ, and conductivity σ represent the properties of the media through which the waves propagate. The permittivity can have real and imaginary components such that

ε = ε' − jε'' .

The component ε′ represents the familiar lossless permittivity, is s measure of how much energy from an external electric field is stored in material, which is given by the product of the free space permittivity and the relative permittivity,

ε′ = ε0 εr.

ε′ is mostly greater than 1 for solids and liquids.

where ε″ is the imaginary amplitude of permittivity attributed to bound charge and dipole relaxation phenomena, which is a measure of how dissipative or lossy a material is to an external field. ε″ is usually greater than 1, bt less than ε′.

2.3.3 Loss tangent component

The loss tangent is then defined as the ratio (or angle in a complex plane) of the lossy reaction to the electric field E in the curl equation to the lossless reaction:

tanδ= (ω ε''+σ)/ ω ε'

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For dielectrics with small loss, this angle is << 1 and tan(δ)~δ. For electromagnetic wave, the power decays with propagation distance z as

P = Poe − δkz ,

where Po is the initial power,

k= ω (µ ε') ½ = (2π/λ)

ω is the angular frequency of the wave, and

λ is the wavelength in the dielectric.

Also, a similar analysis could be applied to the permeability where

μ = μ' − jμ'' ,

with the subsequent definition of a magnetic loss tangent

tanδ = (μ''/ μ')

where C is the lossless capacitance.

2.3.4 Q-factor

A capacitor's loss tangent is sometimes stated as its dissipation factor, or the reciprocal of its quality factor Q, as follows

tanδ = DF= 1/Q

DF= Dissipation factor

Graph representing losses and Q-factor

Dielectrics should be selected in such a way that the DF of dielectrics be low or Q be high in order to reduce the losses.

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2.4 Polarization of Dielectrics

2.4.1 Definition

If a material contains polar molecules, they will generally be in random orientations when no electric field is applied. An applied electric field will polarize the material by orienting the dipole moments of polar molecules. This decreases the effective electric field between the plates and will increase the capacitance of the parallel plate structure. The dielectric must be a good electric insulator so as to minimize any DC leakage current through a capacitor.

The amount of charge stored in a capacitor is the product of the voltage and the capacity. The voltage can be increased, but electric breakdown will occur if the electric field inside the capacitor becomes too large. The capacity can be increased by expanding the electrode areas and by reducing the gap between the electrodes One method for increasing capacity is to insert dielectric material (an insulating material with no free charges) between the plates that reduces the voltage because of its effect on the electric field.

When the molecules of a dielectric are placed in the electric field, their negatively charged electrons separate slightly from their positively charged cores because of forces in opposite direction. With this separation, referred to as polarization, the molecules acquire an electric dipole moment. A cluster of charges with an electric dipole moment is often called an electric dipole.

Polarization

The electric dipole moment p of two charges +q and −q separated by a distance d is a vector of magnitude p = qd with a direction from the negative to the positive charge. An electric dipole in an external electric field is subjected to a torque τ = pE sin θ, where θ is the angle between p and E. The torque tends to align the dipole moment p in the direction of E. The potential energy of the dipole is given by Ue = −pE cos θ, or in vector notation Ue = −p · E.

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The electric susceptibility χe relates the polarization to the electric field as P = χ eE. In general, χe

varies slightly depending on the strength of the electric field. The dielectric constant κ of a substance is related to its susceptibility as κ = 1 + χe /ε0; it is a dimensionless quantity.

2.4.2 Effects of dielectric s

The presence of a dielectric affects many electric quantities. A dielectric reduces by a factor K the value of the electric field and consequently also the value of the electric potential from a charge within the medium. The insertion of a dielectric between the electrodes of a capacitor with a given charge reduces the potential difference between the electrodes and thus increases the capacitance of the capacitor by the factor K. For a parallel-plate capacitor filled with a dielectric, the capacity becomes C = Κε0A/d. A third and important effect of a dielectric is to reduce the speed of electromagnetic waves in a medium by the factor √K .

Effect of polarization

2.5 DIELECTRIC A.C CONDUCTIVITY

2.5.1 Definition

Dielectric conductivity sums all the dissipative effects and represents actual conductivity caused by migrating the charge carriers. For good dielectric materials, the conductivity should be very low, because basically dielectrics act as insulators and insulators should not allow the passage of electricity or current through them. The dielectric conductivity (σ) can be calculated using the following relation:

σ = ε0ωtanδ = ε''ε0ω

where, ε0 (8.854*10-12 F/m) is the permittivity of free space and ω (=2πf) is the angular frequency. This is the frequency at which the prepared dielectric materials vibrate and allow only such frequencies to pass through them, blocking the others.

2.6 TEMPERATURE COEFFICIENT OF RESONANCE FREQUENCY

2.6.1 Definition

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The temperature coefficient of resonance frequency (τf) represents the variation of resonance frequency with change in temperature (in ppm/C). Generally all the dielectric materials used in communication field work at particular frequency i.e. they block all the frequencies except the selected frequency and showing an infinite attenuation at other frequencies. But with slightly change in temperature, the desired resonance frequency of dielectrics changes producing losses at the desired frequency and interfering with other frequencies. So while selecting the dielectric materials, it is taken into consideration that the temperature coefficient of resonant frequency should be very-very small for the selected material.

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CHAPTER 3

PREPARATION AND ANALYSIS

3.1 WEIGHING

3.1.1 Definition

A weighing scale is a measuring instrument for measuring the weight or mass of an object.

There are two techniques used for measurements: Spring scale Measurement Analytical Measurement

3.1.2 Techniques of weighing

3.1.2.1 Spring scale

A spring scale measures weight by the distance a spring deflects under its load. A balance compares the unknown weight to a standard weight using a horizontal lever. This process uses a spring with a known spring constant (see Hooke's law) and measure the displacement of the spring by any variety of mechanisms to produce an estimate of the gravitational force applied by the object. Weighing scales are used in many industrial and commercial applications, and products from feathers to loaded tractor-trailers are sold by weight. Specialized medical scales and bathroom scales are used to measure the body weight of human beings. Spring scales measure weight, the local force of gravity on an object, and are usually calibrated in units of force such as Newton or pounds-force

3.1.2.2 Analytical balance

An analytical balance is an instrument that's used to measure mass to a very high degree of precision. The weighing pan(s) of a high precision (.01 mg or better) analytical balance are inside a transparent enclosure with doors so dust does not collect and so any air currents in the room do not affect the delicate balance. The use of a vented balance safety enclosure that has uniquely designed acrylic airfoils allows a smooth turbulence-free airflow that prevents balance fluctuation and the weighing of mass down to 1μg without fluctuations or loss of product. Also, the sample must be at room temperature to prevent natural convection from forming air currents inside the enclosure, affecting the weighing.

Analytical precision is achieved by maintaining a constant load on the balance beam, by subtracting mass on the same side of the beam that the sample is added. The final balance is achieved by using a small spring force rather than subtracting fixed weights.

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Electronic Weighing Machine (Analytical Balance)

Generally the high purity materials are weighed in appropriate molar proportion using an Electronic Weighing machine called Analytical Balance with an accuracy of 10-4. The regent grade oxide powders are BaCO3, TiO2, Pr6O11, which are used as raw materials for ceramics processing.

3.2 BALL MILLING

3.2.1 Definition

Ball Milling is a process in which grinding of raw materials takes place in a liquid agent (e.g. distilled water, ethanol and methanol). These agents are required for proper mixing. The grinded materials are thoroughly mixed in Agate Mortar for about 12 hrs to get a homogeneous mixture. Generally we use methanol as a liquid agent.

An Agate Mortar is a type of grinder used to grind materials into extremely fine powder to form homogeneous mixture for use in paints and ceramics. Agate Mortar, a type of grinder, is a device used in grinding (or mixing) materials like ores, chemicals, ceramic raw materials and paints. Agate Mortar rotate around a horizontal axis. It consists of containers partially filled with the material to be ground plus the grinding medium.

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Agate Mortar

3.3 CALCINATION

3.3.1 Definition

Calcination (also referred to as calcining) is a thermal treatment process applied to ores and other solid materials in which powder mixtures are pre-heated at 1100°C for 2 hrs in silica crucibles in a linear programmable furnace in order to bring about a thermal decomposition, phase transition, or removal of a volatile fraction. The calcination process normally takes place at temperatures below the melting point of the product materials. Calcination is to be distinguished from roasting, in which more complex gas-solid reactions take place between the furnace atmosphere and the solids.

The process of calcination derives its name from its most common application, the decomposition of calcium carbonate (limestone) to calcium oxide (lime) and carbon dioxide, in order to produce cement. The product of calcination is usually referred to in general as "calcine". Calcination is carried out in furnaces or reactors (sometimes referred to as kilns) of various designs including shaft furnaces, rotary

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Calcination process

rotary kilns, multiple hearth furnaces, and fluidized bed reactors.

3.3.2 Examples of calcination processes:

Decomposition of carbonate minerals, as in the calcination of limestone to drive off carbon dioxide;

Decomposition of hydrated minerals, as in calcination of bauxite, to remove crystalline water as water vapor;

3.3.3 Calcination Reactions

Calcination reactions usually take place at or above the thermal decomposition temperature (for decomposition and volatilization reactions) or the transition temperature (for phase transitions). This temperature is usually defined as the temperature at which the standard Gibb's free energy of reaction for a particular calcination reaction is equal to zero.

Examples of chemical decomposition reactions common in calcination processes, and their respective thermal decomposition temperatures include:

CaCO3 = CaO + CO2; 848°C

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3.4 POST MIXING

3.4.1 Definition

The mixing powders which have been calcined at 1100°C in furnace are then crushed manually (with the help of hands), because after calcination, powder becomes hard, so powder is crushed and again mixed in Ball Mill for 12 hrs with liquid mixing agent (methanol ) in order to get a more homogeneous mixture .

3.5 GRANULATION AND SIEVING

3.5.1 Definition of granulation

Granulation is the process or an act of forming or crystallizing into grains.

Granulation is often required to improve the flow of powder mixtures and mechanical properties. Granules are usually obtained by adding liquids (binder or solvent solutions). Larger quantities of granulating liquid produce a narrower particle size range and coarser and harder granules, i.e. the proportion of fine granulate particles decreases. The optimal quantity of liquid needed to get a given particle size should be known in order to keep a batch-to-batch variations to a minimum. Wet granulation is used to improve flow, compressibility, homogeneity, electrostatic properties, and stability of solid dosage forms. The particle size of the granules is determined by the quantity and feeding rate of granulating liquid. Generally the fine powders are granulated using an organic binder, 3 wt % PVA (Poly Vinyl Alcohol), to provide strength and flow ability to granules.

3.5.2 Definition of sieving

Sieving is a process of separation of a mixture of a various sized particles, either dry or suspended in a liquid, into two or more portions by passing through a screens of specified mesh sizes. A representative weighed sample is poured into the top sieve which has the largest screen openings. Each lower sieve in the column has smaller openings than the one above. At the base is a round pan, called the receiver. The column is typically placed in a mechanical shaker. The shaker shakes the column, usually for some fixed amount of time.

Generally the granulated powder is passed through sieves of 60-80 mesh B.S.S (250-100 µm approx.) to get a homogeneous mixture of desired granular size.

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Sieves

3.6 COMPACTION

3.6.1 Definition

The compaction is the process in which the granule powders are compacted to the pallets which can be of rectangular (23mm Χ 10 mm) and circular (12mm diameter and 3-4mm thickness) shapes under a pressure of 98 kN with the help of dyes (palletizer) having cavities of desired shapes .The pallets are formed in order to study the properties of these dielectric materials with the help of scanning electron microscopy and X-ray diffraction

Hydraulic press circular and rectangular dyes

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3.7 SINTERING AND POLISHING

3.7.1 Definition

The pallets which have been formed with the help of palletizer are sintered in linear programmable furnace. These sintered pallets are polished with fine emery paper to make the surface smooth, flat and parallel for measurements, because smoothed surfaces show excellent properties under microscope. Then the samples are coated with silver plating in order to make the surface gleaming. Finally, ceramic samples of desired shapes and of shiny surfaces are ready for characterization.

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Chapter 4

RESULTS AND DISCUSSIONS

This chapter deals with the results obtained from experimental procedures for dielectric

behaviour of Barium praseodymium titanate ceramic materials.

4.1 X-Ray diffraction

The X-ray diffraction patterns of synthesized samples BaPr1.33Ti3O9 and BaPr2Ti4O12

(namely, sample 1 and sample 2 respectively) are shown below:

Figure 4.1: XRD patterns of synthesized samples BaPr 1.33Ti3O9 & BaPr2Ti4O12

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Sample 2

Sample1

Sample 2

It shows that tungsten bronze type structure is formed with an orthorhombic symmetry.

The variation in relative intensities of peaks may be related to the occupation of lattice sites by

the substituted ions.

4.2 DENSITY MEASUREMENT

The density of the synthesized samples has been measured by archimedies method at

30˚C using distilled water as displacement fluid. The equation used to calculate density is as

under.

Density of sample =

mass in air ×density of distilled water mass of sample and wire∓ mass of wire

For sample 1 (BaPr1.33Ti3O9), the density was measured to be 5.4 gm/cm3:

Mass of sample

in air(gm)

Mass of sample

and wire(gm)

Mass of

wire(gm)

Density of

distilled water(at

30˚c)(gm/cm3)

Density of the

sample

(gm/cm3)

1.1857 0.2244 0.0061 0.996 5.409790

For sample 2 (BaPr2Ti4O12), the density was measured to be 5.24 gm/cm3:

Mass of sample

in air(gm)

Mass of sample

and wire(gm)

Mass of

wire(gm)

Density of

distilled water(at

30˚c)(gm/cm3)

Density of the

sample

(gm/cm3)

1.9301 0.3729 0.3729 0.996 5.23664

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It is observed that the ceramics with higher Pr contents have a high value of bulk density. The

substituted ions might have caused decrease in intergranular pores, which is ascribed to small

ionic radius of substituted Pr ions (1.013Å) than Ba ions(1.35Å).

4.3 DIELECTRIC PROPERTIES

The amount of Rare earth element present in barium rare earth titanate produces

significant change in the dielectric behaviour of. The dielectric properties of the synthesized

samples have been found out to be a function of Pr contents and temperature.

4.3.1 Dielectric constant

Figure 4.2 shows the variation of dielectric constant (ε') synthesized samples as a

function of frequency (100 Hz to 1MHz) at room temperature. This shows that dielectric

constant changes from 106.89 to 101.67 for sample 1 and 115.29 to 112.57 for sample 2 as

frequency changes from 100 Hz to 1 MHz. The dielectric constant is affected by three factors: (i)

volume of TiO6 octahedra, (ii) tilting of octahedral strings and (iii) polarizabilities of R and Ba

ions. As the Pr3+ ions substitute for the Ba2+ ions, not only the vacancies were created to maintain

the charge neutrality but also the lattice parameters were changed due to the difference in ionic

radius between Pr3+ and Ba2+. The difference of ion radius directly affect the length of c-axis,

which is the important characteristic of the tungsten-bronze type structure.

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Dielectric constant Vs Frequency

100102104106108110112114116118

100 1000 10000 100000 1000000Frequency (in Hz)

Die

lect

ric

Co

nst

ant

Sample 1

Sample 2

Figure 4.2: Dielectric constant of synthesized samples as a function of frequency

Figure 4.3 and 4.4 shows the variation of dielectric constant (ε') as a function of

temperature (room temp. to 200 0C) at five frequencies ( 100 Hz, 1 KHz, 10 KHz, 100 KHz and

1MHz) for sample 1 and 2 respectively.

Dielectric Constant Vs Temperature

98100102104106108110112114116118

25 75 125 175

Temperature (in C)

Die

lect

ric

Co

nst

ant

100 Hz

1 KHz

10 K Hz

100 K Hz

1 M Hz

Figure 4.3: Variation of dielectric constant of sample 1 as a function of temperature at

five different frequencies

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Dielectric Constant Vs Temperature

90

95

100

105

110

115

120

125

25 75 125 175

Temperature (in C)

Die

lect

ric

Co

nst

ant

100 Hz

1 KHz

10 K Hz

100 K Hz

1 M Hz

Figure 4.4: Variation of dielectric constant of sample 2 as a function of temperature at five

different frequencies

4.3.2 Loss Tangent

Figure 4.5 shows the variation of loss tangent (tanδ) as a function of frequency for both

the samples.

Loss tangent Vs Frequency

-0.002

0

0.002

0.004

0.006

0.008

0.01

0.012

0.014

0.016

0.018

100 1000 10000 100000 1000000Frequency (in Hz)

Lo

ss T

ang

ent

Sample 1

Sample 2

Figure 4.5: Variation of loss tangent (tanδ) as a function of frequency for both samples

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Many factors were believed to affect the microwave dielectric loss (loss tangent) and

could be divided into two fields, the intrinsic and extrinsic losses. The intrinsic losses were

mainly caused by lattice variation modes while the extrinsic losses were dominated by second

phases, oxygen vacancies, grain sizes and densification or porosity.

Figures 4.6 and 4.7 show the variation of loss tangent as a function of temperature (room

temp. to 200 0C) at five frequencies ( 100 Hz, 1 KHz, 10 KHz, 100 KHz and 1MHz) for sample 1

and 2 respectively. It is observed that the variation of loss tangent with temperature for a

particular sample is not linear.

Loss Tangent Vs Temperature

0

0.005

0.01

0.015

0.02

0.025

0.03

0.035

0.04

25 75 125 175

Temperature (in C)

Lo

ss T

ang

ent 100 Hz

1 KHz

10 K Hz

100 K Hz

1 M Hz

Figure 4.6: Variation of Loss tangent (tanδ) as a function of temperature for sample 1.

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Loss Tangent Vs Temperature

0

0.005

0.01

0.015

0.02

0.025

0.03

0.035

25 75 125 175

Temperature (in C)

Lo

ss T

ang

ent 100 Hz

1 KHz

10 K Hz

100 K Hz

1 M Hz

Figure 4.7: Variation of Loss tangent (tanδ) as a function of temperature for sample 2.

4.3.3 AC Conductivity

AC conductivity (σ) is derived from the dielectric constant and loss tangent using the following

relation:

σ = ε0ωtanδ = ε''ε0ω

where, ε0 (8.854*10-12 F/m) is the permittivity of free space and ω (=2πf) is the angular

frequency.

The plots for ac conductivity of synthesized samples are shown in figure 4.8 as a function

of frequency at room temperature. Very low conductivity has been observed for the prepared

samples. It basically decreased with increase in Pr contents, but increased with frequency.

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Actually, the dielectric conductivity (σ) sums over all the dissipative effects of the

material. Conductivity might have originated caused by migrating charge carriers and it may also

refer to an energy loss associated with the dispersion of ε', for example, the friction

accompanying the orientation of dipoles. Also, the defect centres and impurities could contribute

to the conductivity which are generally randomly distributed in dielectrics. Moreover, the excess

electrons or excess holes due to their interaction with lattice ions generally distort the

surroundings in such a way that the potential well thereby generated is deep enough to introduce

localization leading to the existence of conduction. No doubt, its value remains very low in the

case of dielectrics but it does exist.

AC Conductivity Vs Frequency

0.00E+00

5.00E-10

1.00E-09

1.50E-09

2.00E-09

2.50E-09

3.00E-09

3.50E-09

100 1000 10000 100000 1000000Frequency (in Hz)

AC

Co

nd

uct

ivit

y (M

ho

/cm

)

Sample 1

Sample 2

Figure 4.8: Variation of AC Conductivity with frequency at room temperature

Page 39

Chapter 5

CONCLUSIONS

1. Results obtained from X-ray diffraction powder patterns of barium praseodymium

titanate confirms the formation of tungsten bronze type crystal structure with

orthorhombic symmetry.

2. Dielectric constant (ε') as a function of frequency at room temperature decreases for

increasing Pr contents for sample 1 and 2.

3. Loss tangent decreases with increasing Pr content linearly as a function of frequency

from 100 Hz to 1 MHz.

4. Very low AC conductivity has been observed for the prepared samples. It basically

decreased with composition, but increased linearly with frequency.

5. Variations of dielectric constant as a function of temperature at different frequencies, 100

Hz, 1 KHz, 10 KHz, 100 KHz and 1MHz, are investigated and it is found that variation in

dielectric constant as a function of temperature decreases with increase in Pr contents.

6. It can be easily concluded that reasonably good dielectric properties have been obtained

for the two synthesized samples and could be used in wireless communication.

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