investigation of dielectric properties of …the thesis presents an investigation of dielectric...

INVESTIGATION OF DIELECTRIC PROPERTIES OF SOME

LEAD BASED COMPLEX NIOBATE PEROVSKITES.

A THESIS

submitted by

Radha Ramani Vedantam

for the award of the degree

of

DOCTOR OF PHILOSOPHY

DEPARTMENT OF PHYSICS INDIAN INSTITUTE OF TECHNOLOGY MADRAS,

CHENNAI – 600 036, INDIA

DECEMBER 2004

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Dedicated to My PARENTS and My ETERNAL MASTER

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CERTIFICATE

This is to certify that the thesis entitled “Investigation of Dielectric properties of

some lead-based complex niobate perovskites” submitted by Ms. Radha Ramani

Vedantam to the Indian Institute of Technology, Madras, Chennai for the award of

degree of Doctor of Philosophy is a bonafide record of the research work carried out

by her under our supervision. The contents of the thesis, full or in parts, have not been

submitted and will not be submitted to any other Institute or University for the award

of any degree or diploma.

Research guides (V.SUBRAMANIAN) Chennai 600 036 (V. RAMA KRISHNA MURTHY) Date :

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TABLE OF CONTENTS

TITLE PAGE NO.

ACKNOWLEDGEMENTS ABSTRACT LIST OF TABLES LIST OF FIGURES ABBREVATIONS CHAPTER 1 INTRODUCTION 1.1 Ferroelectrics 1.2 Relaxor ferroelectrics 1.3 Polar micro regions 1.4 Correlation radius 1.5 Literature survey 1.6 Evidence of existence of polar micro regions 1.6 Relaxation behaviour of polar micro regions 1.6.1 Frequency dependence of Tmax 1.7 Theoretical models to explain the relaxor behaviour 1.8 Objective and scope of work CHAPTER 2 SYNTHESIS AND STRUCTURAL

CHARACTERIZATION OF (Pb1-xBax)(Zn1/3Nb2/3)O3, (Pb1-xSrx)(Zn1/3Nb2/3)O3, (Pb1-xBax)(Yb0.5Nb0.5)O3, (Pb1-xLax)(Yb0.5Nb0.5)O3, (Pb0.96-xLaxBa0.04)(Yb0.5Nb0.5)O3 AND

Pb(Fe0.5Nb0.5)O3 2.1. Synthesis and structural studies of Ba2+ and Sr2+

substituted Pb(Zn1/3Nb2/3)O3 compounds 2.2. Synthesis and structural studies of Pb(Yb0.5Nb0.5)O3

based compounds 2.2.1 Synthesis and structural studies of

Pb(Yb0.5Nb0.5)O3 2.2.2 Synthesis and structural studies of Ba2+

substituted Pb(Yb0.5Nb0.5)O3 2.2.3 Synthesis and structural studies of La3+ substituted

Pb(Yb0.5Nb0.5)O3 2.2.4 Synthesis and structural studies of La3+ and Ba2+

substituted Pb(Yb0.5Nb0.5)O3 2.3 Synthesis and structural studies of Pb(Fe0.5Nb0.5)O3

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TABLE OF CONTENTS (CONTD.)

TITLE PAGE NO.

CHAPTER 3 DIELECTRIC PROPERTIES OF

Pb(Fe0.5Nb0.5)O3 3.1 Low frequency dielectric measurements 3.2 Low frequency dielectric studies on Pb(Fe0.5Nb0.5)O3 CHAPTER 4 DIELECTRIC PROPERTIES OF PZN BASED

COMPOUNDS AND PYN BASED COMPOUNDS

4.1. Dielectric response of of Pb(Zn1/3Nb2/3)O3 based

samples 4.2. Dielectric response of Pb(Yb0.5Nb0.5)O3 based

compounds 4.2.1. Dielectric Response of Pb(Yb0.5Nb0.5)O3 and (Pb1-xBax)(Yb0.5Nb0.5)O3 4.2.2. Dielectric response of La3+ Substituted

Pb(Yb0.5Nb0.5)O3 4.2.3. Dielectric Response of La3+ and Ba2+ Substituted

Pb(Yb0.5Nb0.5)O3 4.3. High frequency dielectric measurements

CHAPTER 5 RAMAN STUDIES ON (Pb1-Bax)(Yb0.5Nb0.5)O3 5.1. Significance of Raman spectroscopic studies 5.2. Experimental set-up 5.3. Identification of modes based on Group theory analysis and

correlation.

CHAPTER 6 SUMMARY and CONCLUSIONS

REFERENCES

LIST OF PUBLICATIONS

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ACKNOWLEDGEMENTS My profound thanks to late Prof B M Sivaram, former Head of the Department, Physics, for allotting me to Microwave laboratory. I am thankful to my guides, Dr V Subramanian and Prof V R K Murthy, for the freedom they have given me in choosing the field of research and in pursuing it. I acknowledge the invaluable suggestions and encouragement they gave me through out my research work. I am thankful to the present Head, Department of Physics, Prof A Subrahmanyam for his useful suggestions and support in making the facilities available for the research work. I am very thankful to my Doctoral committee members for their useful suggestions during the meetings. I am thankful for IITM, Chennai, for providing the financial assistance through out the research period. I would like to express my gratitude to Dr. V Sivasubramanian, IGCAR, for his useful suggestions during the course of work. I am indebted to him for the academic discussions which helped a great deal in understanding the subject and also his useful suggestions in various stages of the work. I would like to thank my microwave lab mates Dr. M. Chitra, Dr. J. Venkatesh, Mr. Bibekanand Sundaray, Mr. Dibyaranjan Rout, Mr. E. D. V. Nagesh, Mr. G. Santosh Babu, Mr. D. V. B. Murthy, Mr. Jagadeesh Babu, Mr. T. Vishwam and, Mr. Ullash Kumar Barrick for their pleasant company during the period of my research. I am very thankful to Ms. P. Malar for her pleasant company through out the tenure. I appreciate the pleasant company of my colleagues Ms. R. Sri Latha, Dr. R. Nirmala, Ms. K. C. Lakshmi and others. I thank all the staff of the machine staff, Central XRD, Central Glass Blowing section for their timely help. I am very grateful for the moral support of my parents through out the period of my research work. I am very indebted to them, without whose help I could not have finished my work. I thank each and every one of my family members for their moral support and constant encouragement. I thank Mr. Kiran for his patience during the last stages of my work and his constant encouragement. Finally, I thank my Master for being with me and guiding me constantly. I am grateful for his blessings.

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ABSTRACT

Keywords: Relaxor ferroelectrics, Dielectric dispersion, Polar micro regions,

Relaxation, Raman spectroscopy, Local distortion, Diffuse transition.

The thesis presents an investigation of dielectric properties of certain lead-based

complex niobate perovskite oxides. The synthesis of the compositions is carried out

using conventional solid-state reaction route. Care was taken to avoid PbO

evaporation. The synthesis is carried out in single step or two-step or three-step

methods to avoid formation of secondary phases. Structural characterization is carried

out using X-ray diffraction.

The variation in the interaction between the polar micro regions is studied by

substituting isovalent ions with different polarizability and ionic radii in the Ba2+ and

Sr2+ substituted Pb(Zn1/3Nb2/3)O3. Shift in Tmax, the temperature corresponding to ε′max

with frequency is observed for both the series confirming the relaxor behaviour.

Degree of relaxation is more in the case of Sr2+ substituted compounds. The

decoupling of the ferroelectrically active octahedron is more in the case of Sr2+

substituted compounds resulting in decrease of both dielectric constant and loss and

Tmax. The relaxor behaviour of the compounds is explained using Vogel - Fulcher

relation, Power law and theoretical model proposed by Cheng et al.

The solid solution series Ba2+ substituted Pb(Yb0.5Nb0.5)O3, undergo a transition from

anti-ferroelectric orthorhombic to relaxor ferroelectric cubic at room temperature with

increase in Ba2+ concentration. B-site ordering is retained in the systems studied. The

crossover is attributed to rhombohedral local distortion using Raman spectroscopy.

Substitution of La3+ for Pb2+ in Pb(Yb0.5Nb0.5)O3 induces diffuseness around the

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transition temperature compared to Pb(Yb0.5Nb0.5)O3 whereas substitution of both

Ba2+ and La3+ in Pb(Yb0.5Nb0.5)O3 increases the sharpness of the transition.

Annealing the Pb(Fe0.5Nb0.5)O3, sintered at different temperatures, in oxygen

atmosphere results in decrease of both ε′ and ε″. This is attributed to variation in

oxidation state of iron and density of the samples before and after annealing.

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LIST OF TABLES

Table Title Page No. 2.1 Calcination and sintering temperatures, lattice parameters

and relative density of Pb(Zn1/3Nb2/3)O3 based compounds.

2.2 Calcination and sintering temperatures, lattice parameters

and relative density of Pb(Yb0.5Nb0.5)O3 based compounds.

2.3 Calcination, sintering temperatures, lattice parameters of Pb(Fe0.5Nb0.5)O3 sintered at different temperatures and relative density of the samples before and after annealing in oxygen atmosphere.

3.1 Frequency variation of Tmax for all the sintered samples before annealing and for PFN1 after annealing.

3.2 Variation in resistivity of the Pb(Fe0.5Nb0.5)O3 samples

before and after annealing. 4.1 Frequency dependence of Tmax of ε′ of (Pb1-xSrx)(Zn1/3Nb2/3)O3 and (Pb1- xSrx)(Zn1/3Nb2/3)O3 for x = 0.2 and 0.3. 4.2 ωo (Hz), To (K), Tf (K) and p obtained from V-F law and power law (eqns (1.1) and (1.2).) for (Pb1-xSrx)(Zn1/3Nb2/3)O3 and (Pb1- xSrx)(Zn1/3Nb2/3)O3 for x = 0.2 and 0.3. 4.3 ε∞ , ω0(Hz), α1, β1, δ, α and β obtained from Eqns. (1.9) and (1.11) for (Pb1-

xSrx)(Zn1/3Nb2/3)O3 and (Pb1- xSrx)(Zn1/3Nb2/3)O3 for x = 0.2 and 0.3. 4.4 D1 and D2 obtained from Eqns. 1.14(a) and 1.14(b).

4.5 m and n obtained from Eqns. 1.14(a) and 1.14(b).

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List of tables (Contd.) Page No. 4.6 ωo (Hz), To (K), Tf (K) and p obtained from V-F law and power law

(Eqns. (1.1) and (1.2)) (Pb1-xBax)(Yb0.5Nb0.5)O3. 5.1 Frequency (ω) and line-width (Γ) of the modes due to

cubic symmetry. 5.2 Frequency (ω) and line-width (Γ) of modes due to

symmetry lower than cubic. 5.3 Frequency (ω) and line-width (Γ) of the modes due to

orthorhombic symmetry.

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LIST OF FIGURES

Figure Title Page No. 1.1 Simple perovskite oxide structure. 1.2 Different perovskite structures. 1.3 (a) Hysterisis loop for ferroelectric and relaxor

ferroelectric. 1.3 (b) The temperature variation of polarization for

ferroelectric and relaxor ferroelectric. 1.3 ( c) Dielectric response of ferroelectric and relaxor

ferroelectric. 1.4 The variation in the polarization cloud with

variation in temperature. (a) gives the scenario at temperature T > Tm and (b) gives scenario at temperature T<<Tm.

1.5 Displacement of cations with respect to the oxygen

octahedra. 1.6 Distribution function of the relaxation times for the

relaxor ferroelectric 2.1 Configuration used for calcination and sintering of the

samples 2.2 Flow chart of the important steps involved in the

synthesis of the compositions. 2.3 X-ray Diffractograms of the (Pb1-xBax)(Zn1/3Nb2/3)O3 and

(Pb1-xSrx)(Zn1/3Nb2/3)O3 for x = 0.2 and 0.3.

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List of Figures (Contd.) Page No. 2.4 X-ray Diffractograms of the Pb1-

xBax(Yb0.5Nb0.5)O3 for x = 0, 0.05, 0.1, 0.15, 0.2, 0.25 and 0.3.at room temperature; O-Superlattice reflection corresponding to anti-parallel displacement of Pb2+ cations, -F-reflection due to B-site ordering.

2.5 Schematic projection view of PYN structure along

the [001]o zone axis: ----- Simple perovskite sublattice; (upper) block type arrangement; (lower) effective orthorhombic unit cell. The arrows indicate Pb2+ ions displacemen

2.6 Lattice relationship between high temperature prototype

and low temperature orthorhombic phases. The Pb2+ displacement is not taken into account and oxygen ion sites are omitted for clarity.

2.7 X-ray diffractograms of the La3+ substituted PYN and

La3+ and Ba2+ substituted PYN for x = 0.01, 0.02 and 0.04 at room temperature; O-Superlattice reflection corresponding to anti-parallel displacement of Pb2+ cations, -F-reflection due to B-site ordering.

2.8 X-ray diffractograms of PFN sintered at different

temperatures 1000 °C (PFN1), 1050 °C (PFN2), 1100 °C (PFN3) and 1150 °C (PFN4). 2.9 X-ray diffractograms of PFN samples after annealing

in oxygen atmosphere. 3.1 (a) The experimental set-up used for low frequency

dielectric measurements.

3.1 (b) The holder used for low frequency dielectric measurements. 3.2 (a) Temperature dependence of ε′ and ε″ of PFN sintered

at 1000 oC at various frequencies

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List of Figures (Contd.) Page No. 3.2 (b) Temperature dependence of ε′ and ε″ of PFN

sintered at 1050 oC at various frequencies. 3.2 (c) Temperature dependence of ε′ and ε″ of PFN

sintered at 1100 oC at various frequencies. 3.2 (d) Temperature dependence of ε′ and ε″ of PFN

sintered at 1150 oC at various frequencies. 3.3 (a) Temperature dependence of ε′ and ε″ of PFN1a

(PFN sintered at 1000 oC) at various frequencies. 3.3 (b) Temperature dependence of ε′ and ε″ of PFN2a

(PFN sintered at 1050 oC) at various frequencies. 3.3 (c) Temperature dependence of ε′ and ε″ of PFN3a (PFN

sintered at 1100 oC) at various frequencies 3.3 (d) Temperature dependence of ε′ and ε″ of PFN4a

(PFN sintered at 1150 oC) at various frequencies 4.1 Temperature dependence of ε′ and ε″ of (Pb1-xBax)(Zn1/3Nb2/3)O3 for x = 0.2 and 0.3 at

various frequencies. 4.2 Temperature dependence of ε′ and ε″ of (Pb1-

xSrx)(Zn1/3Nb2/3)O3 for x = 0.2 and 0.3 at various frequencies.

4.3. V-F law and Power law fit for the frequency

dependent Tmax (Pb1-xBax)(Zn1/3Nb2/3)O3 for x = 0.2 and 0.3.

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List of Figures (Contd.) Page No.

4.4. V-F law and Power law fit for the frequency dependent Tmax (Pb1-xSrx)(Zn1/3Nb2/3)O3 for x = 0.2 and 0.3.

4.5 Frequency dependence of ε′ for (Pb1-xBax)(Zn1/3Nb2/3)O3 for x = 0.2 and 0.3 and

(Pb1-xSrx)(Zn1/3Nb2/3)O3 for x = 0.2 and 0.3 at different temperatures.

4.6 Linear relation between A and B for (Pb1-xSrx)(Zn1/3Nb2/3)O3 for x = 0.2 and 0.3

and (Pb1-xBax)(Zn1/3Nb2/3)O3 for x = 0.2 and 0.3. 4.7 Fit of temperature dependence of A for (Pb1-xSrx)(Zn1/3Nb2/3)O3 for x = 0.2 and 0.3 and

(Pb1-xBax)(Zn1/3Nb2/3)O3 for x = 0.2 and 0.3 4.8 Theoretical fit of the experimental data for

temperature variation of ε′ at 100 kHz for (Pb1-xSrx)(Zn1/3Nb2/3)O3 for x = 0.2 and 0.3 and

(Pb1-xBax)(Zn1/3Nb2/3)O3 for x = 0.2 and 0.3 4.9 (a) Temperature dependence of ε′ and ε″ of

Pb(Yb0.5Nb0.5)O3 at various frequencies. 4.9 (b) Temperature dependence of ε′ and ε″ of (Pb1-xBax)(Yb0.5Nb0.5)O3 for x = 0.05 of Ba2+

content at various frequencies. 4.9 (c) Temperature dependence of ε′ and ε″ of (Pb1-xBax)(Yb0.5Nb0.5)O3 for x = 0.1 of Ba2+

content at various frequencies. 4.9 (d) Temperature dependence of ε′ and ε″ of (Pb1-xBax)(Yb0.5Nb0.5)O3 for x = 0.15 of Ba2+

content at various frequencies.

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List of Figures (Contd.) Page No 4.9 (e) Temperature dependence of ε′ and ε″ of (Pb1-xBax)(Yb0.5Nb0.5)O3for x = 0.2 of Ba2+

content at various frequencies. 4.9 (f) Temperature dependence of ε′ and ε″ of (Pb1-xBax)(Yb0.5Nb0.5)O3 for x = 0.25 of Ba2+

content at various frequencies. 4.9 (g) Temperature dependence of ε′ and ε″ of (Pb1-xBax)(Yb0.5Nb0.5)O3 for x = 0.3 of Ba2+

content at various frequencies. 4.10 (a) Temperature dependence of ε′ and ε″ of (Pb1-xLax)(Yb(1+x)/2Nb(1-x)/2)O3 for x = 0.01 at

various frequencies. 4.10 (b) Temperature dependence of ε′ and ε″ of

(Pb1-xLax)(Yb(1+x)/2Nb(1-x)/2)O3 for x = 0.02 at various frequencies. 4.10 (c) Temperature dependence of ε′ and ε″ of (Pb1-xLax)(Yb(1+x)/2Nb(1-x)/2)O3 for x = 0.04 at

various frequencies. 4.11 Temperature dependence of ε′ and ε″ at 100 kHz for Pb(Yb0.5Nb0.5)O3,

(Pb1-xLax)(Yb(1+x)/2Nb(1-x)/2)O3 for x = 0.01, 0.02 and 0.04.

4.12 (a) Temperature dependence of ε′ and ε″ of (Pb0.96-x LaxBa0.04)(Yb(1+x)/2Nb(1-x)/2)O3 for x = 0.01 at various frequencies. 4.12 (b) Temperature dependence of ε′ and ε″ of (Pb0.96-x LaxBa0.04)(Yb(1+x)/2Nb(1-x)/2)O3 for x = 0.02 at various frequencies. 4.13 Temperature variation of ε’ and ε’’ at 100 kHz

for (Pb1-xBax)(Yb0.5Nb0.5)O3 for x = 0.05, (Pb0.96-xLaxBa0.04)(Yb(1+x)/2Nb(1-x)/2)O3 for x = 0.01, 0.02

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List of Figures (Contd.) Page No. 4.14 (a) Coaxial holder used for dielectric measurements in

the frequency range (130 - 1000 MHz). 4.14 (b) The experimental set-up used for the measurements

in the frequency range (130 - 1000 MHz). 4.15 (a) Temperature dependence of ε′ and ε″ of (Pb1-xBax)(Zn1/3Nb2/3)O3 for x = 0.2 at various

frequencies. 4.15 (b) Temperature dependence of ε′ and ε″ of (Pb1-xBax)(Zn1/3Nb2/3)O3 for x = 0.3 at various

frequencies. 4.15 (c) Temperature dependence of ε′ and ε″ of (Pb1- xBax)(Yb0.5Nb0.5)O3 for x = 0.15 at various

frequencies. 4.15 (d) Temperature dependence of ε′ and ε″ of (Pb1-xBax)(Yb0.5Nb0.5)O3 for x = 0.2 at various

frequencies. 5.1 The experimental set-up used to record the Raman

spectra.

5.2 Raman spectra in the frequency region below 100 cm-1 at room temperature.

5.3 Raman spectra in the frequency range 100 - 400 cm-1 at room temperature.

5.4 Raman spectra in the frequency range 400 - 1000 cm-1 at room

temperature. 5.5 Atom vector displacements of the normal modes in the

paraelectric state of Pb(B′1/2B″1/2)O3.

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List of symbols and abbreviations

PR Remnant polarization

PS Spontaneous polarization

Tc Transition temperature

FE Ferroelectric

RFE Relaxor ferroelectric

n(T) refractive index

Tm, Tmax Temperature corresponding to ε′max for a particular frequency.

TB Burns temperature

TEM Transmission electron microscopy

HRTEM High resolution Transmission electron microscopy

ε′ Dielectric constant

ε″ Dielectric loss

P Polarisation

E Electric field

Ec Coercive field

rc Correlation radius

n Impurity concentration

a Lattice parameter

PSN Pb(Sc0.5Nb0.5)O3

PST Pb(Sc0.5Ta0.5)O3

PMN Pb(Mg1/3Nb2/3)O3

XAFS X-ray absorption fine structure

RDF Radial distribution function

ω Probing frequency

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ωo attempt or dipole or Debye frequency

Ea Activation energy of the relaxation process

Tf Depolarization or freezing temperature of polar regions

To Equivalent temperature of activation energy

p Indicator of degree of relaxation

LGD Landau-Ginsberg-Devonshire

τ1 The upper end of the relaxation time of the polar regions

τo The lower end of the relaxation time of the polar regions

εs Static dielectric constant

ε∞ Dielectric constant at high frequency

εL Dielectric response in low temperature region (T < Tmax)

δ Indicator of degree of relaxation

γ Diffuseness exponent

εmax Maximum dielectric constant

α Measure of concentration and dipole moment of dipoles

β Measure of rate of production of dipoles with decreasing temperature

εm Measured dielectric constant

εH Dielectric response in high temperature region (T > Tmax)

D1, D2 Weighing factors

ε1, ε2 Two polarization processes

Tm1 Dielectric constant maximum temperature of ε1

Tm2 Dielectric constant maximum temperature of ε2

PZN Pb(Zn1/3Nb2/3)O3

PYN Pb(Yb0.5Nb0.5)O3

PFN Pb(Fe0.5Nb0.5)O3

XRD X-ray diffraction

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PbO Lead oxide

PVA Poly Vinyl Alcohol

PBZN1 (Pb0.8Ba0.2)(Zn1/3Nb2/3)O3

PBZN2 (Pb0.7Ba0.3)(Zn1/3Nb2/3)O3

PSZN1 (Pb0.8Sr0.2)(Zn1/3Nb2/3)O3

PSZN2 (Pb0.7Ba0.3)(Zn1/3Nb2/3)O3

ZN ZnNb2O6

BZN Ba(Zn1/3,Nb2/3)O3

SZN Sr(Zn1/3Nb2/3)O3

PBYN1 (Pb0.95Ba0.05)(Yb0.5Nb0.5)O3

PBYN2 (Pb0.9Ba0.1)(Yb0.5Nb0.5)O3

PBYN3 (Pb0.85Ba0.15)(Yb0.5Nb0.5)O3


PBYN5 (Pb0.75Ba0.25)(Yb0.5Nb0.5)O3


PLYN1 (Pb0.99La0.01)(Yb.505Nb.495)O3

PLYN2 (Pb0.98La0.02)(Yb.510Nb.49)O3

PLYN3 (Pb0.96La0.04)(Yb.52Nb.48)O3

PBLYN1 (Pb0.95Ba0.04La0.01)(Yb.505Nb.495)O3

PBLYN2 (Pb0.94Ba0.04La0.02)(Yb.51Nb.49)O3

PBLYN3 (Pb0.92 Ba0.04La0.04)(Yb.52Nb.48)O3

PFN1 PFN sintered at 1000 oC




PFN1a PFN sintered at 1000 oC and annealed in oxygen atmosphere for 12 hrs


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BFN Ba(Fe0.5Nb0.5)O3

ε′max Maximum value of dielectric constant

ε″max Maximum value of dielectric loss

T′max Temperature corresponding to maximum value of loss

PLZT (Pb1-3x/2Lax)(ZryTi1-y)O3

Z' Real part of impedance

Z'' Imaginary part of impedance

Co Characteristic impedance of the transmission line

PMW Pb2MgWO6

F2g A-O stretching

F1g BO6 rotation

F1u B-localized

F2u Pb2+e- phonon coupling

F1u O-B-O asymmetric bending (ferroic)

F2g O-B-O symmetric bending

Eg B-O symmetric stretching

A1g B′ - O - B″ symmetric stretching

Γ (cm-1) Line-width of a mode in Raman Spectrum

ω (cm-1) Position of a mode in Raman Spectrum

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CHAPTER 1

INTRODUCTION

The family of compounds with general formula ABO3 is generally called perovskite

oxides, as their structure is similar to the naturally obtained mineral CaTiO3. The

study on these compounds is important as they find several applications in non-linear

optics, memory devices, pyroelectric, piezoelectric sensors etc. apart from the

academic point of view due to the physical properties they exhibit. The well-known

examples are BaTiO3, PbZrO3, PbTiO3 etc. The structure is presented in Fig 1.1. The

coordination number of A-site cation is 12 whereas the coordination number for the

B-site ion is 6. Initially, compounds with divalent ions in the A-site and tetravalent

ions in B-site were developed. Later on different valent ions were chosen to occupy A

and B sites. This structure is also called ‘simple’ perovskite.

The structure becomes ‘complex’ if two ions are of different valency and size in A as

well as B-sites. This structure is called complex perovskite with the general formula

(A’A”)(B’B’’)O3. First attempt on the synthesis of complex perovskite was reported

by Galasso and Pyle (1963) and Galasso and Pinto (1965) with the modification in the

B-site. The structures that result when there exists perfect ordering in B-site with

divalent and pentavalent ions in one set of compounds and trivalent and pentavalent

ions in other set of compounds are given in Fig 1.2. (A=Pb and Ba: B’=Mg, Zn, Y,

Fe, Nd and Gd etc., and B’’= Nb and Ta). Some of the well known complex

perovskites are Ba(Zn1/3Nb2/3)O3, (Onada (1982) and Colla et al (1993))

Sr(Zn1/3Nb2/3)O3 (Onada (1982) and Colla et al (1993)), (SrxLa1-x)MnO3 (Granado et

al (1999)), etc. The nature of dielectric response of these compounds find many

applications such as Pb2+ based relaxor ferroelectric transducers, actuators and

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Fig. 1.1 Simple perovskite oxide structure.

23

Fig. 1.2 Different perovskite structures.

24

multilayer capacitors and Ba2+ based dielectric resonator (DR) and microwave band

gap structure materials.

1.1 FERROELECTRICS To understand the dielectric response of these compounds, one has to probe the

micro-structural details (Thomas (1989)). In one set of perovskite systems, the ions

displace from their equivalent positions and lead to net dipole moment in the unit cell.

The compounds exhibiting this kind of permanent dipole moment are called

ferroelectrics. The displacement of ions is cooperative i.e., in the same direction for a

set of unit cells. This results in formation of domains (Fatuzzo and Merz (1967)). The

ferroelectrics are characterized by well-defined domain structure. The domain

structure results in certain unique properties to these systems. The properties are

discussed below.

The well-defined domain structure in ferroelectrics results in square hysteresis loop,

large coercive fields, large remnant polarization (PR) and spontaneous polarization

(Ps). Polarization vanishes at transition temperature (Tc). The vanishing is continuous

for second order transition while discontinuous for first order transition. The transition

from paraelectric to ferroelectric state is sharp in the dielectric response. The

temperature dependence of εr obeys Curie-Weiss law above Tc and thermal hysteresis

is observed in the dielectric response. No dispersion is observed in the radio

frequency region, independent of frequency. Dispersion is observed in microwave

region due to domain wall motion. The transition involves change in macroscopic

symmetry, which is evidenced from the appearance of shoulders or splitting of certain

lines indicating lowering of symmetry. The ferroelectric (FE) transition can be

thermodynamically either first order or second order. For transparent Ferroelectrics, a

25

change in the slope is observed at Tc in the temperature variation of the refractive

index, n(T).

Some materials may not have well defined domain structure due to the reasons

discussed later on. One set of such compounds is called relaxor ferroelectrics (Cross

(1994) and Samara (Solid state physics, vol. 56.)). Relaxor behavior is observed

normally in ferroelectric materials with compositionally induced disorder or

frustration. This behaviour has been observed and studied most extensively in

disordered ABO3 perovskite ferroelectrics and is also seen in mixed crystals of

hydrogen-bonded ferroelectrics and anti-ferroelectrics, the protonic glasses. The

salient features of the relaxor ferroelectric materials are explained in the following

section.

1.2 RELAXOR FERROELECTRICS

Relaxor ferroelectrics are characterized by slim hysteresis loop, small coercive fields,

small remnant polarization (PR) and spontaneous polarization (Ps). Polarization does

not vanish at transition temperature but vanishes at higher temperatures called Burns

temperature, TB. Relaxor ferroelectrics are characterized by diffused phase transition.

The dielectric permittivity of the relaxor attains a maximum value at a temperature

Tmax for a particular frequency. As the frequency increases, Tmax increases to higher

temperature. The temperature dependence of εr does not obey Curie-Weiss law just

above Tmax but obeys beyond TB (TB > Tmax) (Viehland et al (1992)). Thermal

hysteresis is not observed in dielectric response. Dispersion is observed in the radio

frequency region. The transition does not involve change in macroscopic symmetry.

In contrast to the displacive type of ferroelectrics, relaxors do not undergo any

structural phase transition as evidenced from X-ray and neutron diffraction studies (de

Mathan (1991a), (1991b)). The transition is thermodynamically neither first order nor

26

second order. A change in the slope is observed at TB in the temperature variation of

the refractive index, n(T) (Burns and Dacol (1983)). The differences in between

ferroelectrics and relaxor ferroelectrics are shown in Fig 1.3.

The reason for the differences is attributed to the existence of polar regions of nano

size (Burns and Dacol (1983)). The regions are named polar regions due to the

existence of hysteresis loop and also from the symmetry breaking in these regions as

evidenced from X-ray studies (La-Orauttapong et al (2001), Tkachuk and Chen

(2004), Frenkel et al (2004), Xu et al (2004)), TEM (Chen (1989)),, neutron

diffraction (Gehring et al (2001), (2004) and Conlon et al (2004)), Raman

spectroscopic studies (Lushnikov (2004)) and other techniques.

1.3 POLAR MICRO REGIONS

The possibility of the formation of the polar regions and their behaviour is discussed

in this section. In the ABO3 oxides, substituting ions of different sizes, valencies, and

polarizabilities at both A and B lattice sites produce dipolar defects and can introduce

a sufficiently high degree of disorder so as to break translational symmetry and

prevent the formation of a long-range ordered state (Dai et al (1993), (1995)). In these

highly polarizable host lattices (ferroelectric), the presence of a dipolar impurity on a

given site can induce dipoles in a number of adjacent unit cells within a correlation of

that site. The dipolar motion within this correlation length is correlated (diffused X-

ray scattering studies) leading to the formation of polar nanodomains.

27

Ferroelectric (Fatuzzo and Merz (1967))

Relaxor ferroelectric (Samara, Solid state Physics, Vol. 56)

Fig.1.3 (a) Hysteresis loop for ferroelectric and relaxor ferroelectric.

28

Fig 1.3 (b) The temperature variation of polarization for ferroelectric and relaxor ferroelectric (Samara (Solid state Physics, Vol. 56)).

Relaxor ferroelectric

Ferroelectric

29

Samara (Solid state physics, vol. 56))

Fig 1.3 (c) Dielectric response of ferroelectric and relaxor ferroelectric.

Relaxor ferroelectric 1 indicates 0.1 kHz and 9 indicates 1000 kHz (Lu and Calvarin (1995))

30

A variety of types of disorder in this lattice can produce dipolar defects and induce

relaxor behaviour. In PMN and related relaxors the disorder is brought about by

differences in valence, ionic radii and electro-negativities between the B-site ions that

introduce charge fluctuations and local ordering (Setter and Cross (1980), Chu and

Setter (1993), Viehland et al (1993), Viehland and Li (1994), Chu et al (1994) and

Rosenfeld and Egami (1995)). In La3+ substituted PZT (or PLZT) relaxors, the

substitution of La3+ for Pb2+ at the A-sites produces randomly distributed Pb2+

vacancies (one vacancy for every two La3+ ions) that, for high enough concentration

lead to relaxor state (Xi et al (1983), Dai et al (1993), (1995) and Gupta et al (1996))

and the substitution of Nb5+ for Ta5+ and Li+ for K+ in KTaO3 results in off-site

dipolar defects that lead to a relaxor state at low concentration (Toulouse et al (1994)

and Patnaik and Toulouse (1999)).

Thus it is evident from the above classification that two ingredients are essential for

observing the relaxor behaviour; the existence of lattice disorder (Chu and Setter

(1993), Chu et al (1994) Viehland and Li (1994b) Priya et al (2002) and Lu (2004))

and evidence for the existence of polar nano domains as islands in a highly

polarizable (soft-mode) host lattice (Viehland and Li (1994), Furuya et al (1994) and

Gupta et al (1996)).

Chemical substitution and lattice defects can introduce dipolar entities in mixed ABO3

perovskites, which is evident from the earlier discussion. At very high temperatures,

thermal fluctuations are very large that there are no well-defined dipole moments.

However, on cooling, the presence of these dipolar entities manifests itself at a

temperature (Burns temperature or also called dipolar temperature) TB >>Tmax. At and

below TB each dipolar entity will induce polarization (or dipoles) in adjoining unit

cells of its high polarizable host lattice, forming a dynamic polarization “cloud” as

shown in Fig 1.4 whose extent is determined by the polarizability or correlation length

31

for dipolar fluctuations, rc. Near TB>>Tmax, rc is small and the polarization clouds are

effectively small polar nano domains. As the temperature decreases the permittivity of

the host lattice increases increasing rc and hence the size of the nano domains. This

results in increase in the volume of the polar regions and the correlation between

them. The volume may increase to the extent that the polar regions percolate the

whole sample making it ferroelectric or on the other hand the volume does not

become large enough but slowing down of the fluctuations at T < Tmax leading to an

isotropic relaxor state with random orientation of polar domains. The variation in the

polarization cloud with temperature is shown in Fig 1.4 at two different temperatures,

T ≤ Tmax and T ≥ Tmax . This is the physical picture one could emerge following all

the characterization techniques.

1.4 CORRELATION RADIUS

The limiting case for the correlation radius, rc is expressed as follows by Vugmeister

and Glinchuk (1990). The limiting case is expressed in terms of the quantity nrc3

,

where n is the impurity concentration. Let N* be a characteristic quantity for a given

material system. For n rc3

< N*, the low concentration limit, where the separation r

between the dipoles is greater than rc, spatially inhomogeneous fluctuations of

polarization suppress ferroelectric order. Whereas for the case nrc3 > N*, the high

concentration limit, where rc is greater than the mean separation between the dipoles,

the crystal undergoes a ferroelectric phase transition accompanied by spontaneous

polarization.

32

Fig 1.4 The variation in the polarization cloud with variation in temperature (a) gives the scenario at temperature T > Tm and (b) gives scenario at temperature T<<Tm.

33

The cross over is defined by nrc3 = N*. For an ordinary polarizable crystal rc ~ a, the

lattice parameter whereas rc >> a for a highly polarizable soft optic mode lattice. For

nr3c < N*, the system exhibits a dipolar glass phase that transforms on heating to a

paraelectric phase while for nrc3

> N*, the system is in ferroelectric state and

transforms to paraelectric on heating. Though the case is found for the dipolar glasses

it is found that it is also applicable to relaxor ferroelectrics. For a critical

concentration of nrc3 ≅ 0.32 * 10-2, ferroelectric ordering occurs i.e., a non-zero

average dipole moment exists. Within the range 0.32 * 10-2 < nrc3 < 10-1 the spread of

the orientations of the dipole moments is substantial and the mean field theory is not

applicable whereas for n rc3

≥ 10-1, mean field theory is applicable.

1.5 LITERATURE SURVEY

1.5.1 Evidence of Existence of Polar Micro Regions

Smolensky and Agranovskaya (1959), and Smolensky et al (1959) first reported the

frequency dependent diffused phase transition in Pb(Mg1/3Nb2/3)O3 and

Pb(Ni1/4Nb3/4)O3. Diffused phase transition was thought to be due to compositional

fluctuations arising from B-site disordering. Fluctuation in composition leads to

fluctuation in local field component which results in distribution of Curie

temperatures. The theory seemed to be confirmed by the detailed studies on

Pb(Sc0.5Nb0.5)O3 and Pb(Sc0.5Ta0.5)O3. Ordered PST (Chu et al (1993)) and PSN (Chu

et al (1995)) show sharp transition whereas disordered showed relaxor behaviour .

However the theory could not explain the diffused phase transition in compounds that

do not have compositional heterogeneity. The presence of polar micro regions is

found to be the reason for the behaviour as explained below.

34

The profile analysis of diffuse scattering of X-ray and neutron diffraction indicates the

existence of regions of nanometer-sized regions with short-range correlated atomic

shifts (de Mathan (1991a), (1991b). The anti-parallel displacement of the cations with

respect to the oxygen octahedral is evident from small angle X-ray scattering and as

well diffuse X-ray scattering studies. The displacement is along the <111> direction,

indicating rhombohedral symmetry, as shown in Fig 1.5. Further studies using

synchrotron radiation have revealed existence of regions of further lower symmetry in

these systems (La-Orauttapong et al (2001), Tkachuk and Chen (2004), Frenkel et al

(2004), Xu et al (2004), Gehring et al (2001), (2004) and Conlon et al (2004)).

The presence of the nanometer-sized regions is seen from TEM and HRTEM studies

also. Chen (1989) observed 1:1 ordering in B-site along <111> in PMN from their

TEM studies. 1:1 ordering in the B-site results in charged regions and therefore

termed as polar micro regions. The negatively charged regions either lead to oxygen

vacancies or positive charged regions surround them. Randall and Bhalla (1989, 1990)

proposed that complex perovskites exhibiting relaxor behaviour have nanometer sized

regions exhibiting 1:1 ordering in the B-site whereas normal ferroelectric has long

range ordering in B-site. They classified the Pb2+ based systems based on TEM

studies. The classification is discussed in detail in later sections.

Burns and Dacol (1983) observed from the temperature dependence of refractive

index at different wavelengths that the deviation from linear behaviour starts at a

temperature TB very high than Tmax and proposed that polar micro regions start

forming at TB. Also TB is very much close to TCW, the temperature at which the

classical Curie-Weiss law begins to deviate.

35

Fig 1.5 Displacement of cations with respect to the oxygen octahedra.

36

The size of the PMR was found to increase with decrease in temperature as discussed

earlier. The relaxation frequency of the PMR depends on their size. To explain the

frequency dependence of Tmax it was proposed that ε′ (dielectric constant) decreases

when the probing frequency is greater than the relaxation frequency. The increase

with decrease of temperature above Tmax can be explained as due to increase in

polarization with increase in volume of PMR. Hence at a given temperature there

exists a distribution in the size of the polar micro regions.

Presence of first order Raman modes in PMN and other relaxor ferroelectric materials

indicate that the local symmetry is different from the mean cubic symmetry as there

cannot be any first order Raman modes for cubic symmetry. Raman spectroscopic

studies by Idnik and White (1994) indicate that the crystal structure of PMN

undergoes rhombohedral distortion around 200 K. Setter and Laulicht (1987) used

Raman spectroscopy to correlate the dielectric property variation of Pb(Sc1/2Nb1/2)O3

compound with the ordering of Sc and Ta ions. This is further discussed in detail in

chapter 5 dealing with Raman spectroscopic studies on Ba2+ substituted PYN.

X-ray absorption fine structure (XAFS) can give information on radial distribution

function (RDF) of the relative distance between the probe atom and its neighbour with

very high spatial resolution and with high sensitivity, distinguishing the type of

neighbours. Recent advances in theory and analysis have extended the range of

optimum reliable detailed information of the structural distribution from the first

neighbour to four or more neighbouring cells of atoms about the probe atom (Prouzett

et al (1993), Li et al (1994)). The RDF obtained from XAFS carried out on Nb k-

edge for PMN (Prouzett et al (1993)) (up to low temperature 5 K) indicate that shift of

Nb5+ along a <111> cubic axis give rise to two Nb – O bond lengths of 1.95 and 2.16

Å. The increase of intensity of Nb – Nb (Mg) in RDF on decreasing temperature

37

indicates the increase in correlation of the Nb shifts and increase in the volume of the

polar domains.

1.6 RELAXATION BEHAVIOUR OF POLAR MICRO REGIONS

1.6.1 Frequency Dependence of Tmax

Relaxor ferroelectrics exhibit frequency dependent dielectric properties as mentioned

earlier. Tmax, the temperature at which dielectric constant is maximum is frequency

dependent. To understand the frequency dependence of Tmax, several models are

proposed viz., Debye relation, Vogel – Fulcher relation, Power law etc. The dielectric

properties of the compounds exhibiting relaxor behaviour depend on the polar micro

regions that constitute them.

Cross proposed that the polar micro regions are thermally unstable and the behaviour

is analogous to superparamagnetism (1994). Consequently, Debye relation should

govern the frequency dependence of the Tmax. In Debye medium, the dipoles are free

to rotate and there are no interactions between the dipoles (can be frozen only at 0 K).

The erroneous values obtained in an attempt to explain the frequency dependence of

Tmax with Debye relation indicate that there exists interaction between the polar micro

regions. Viehland et al (1990) could successfully explain the frequency dependence of

Tmax of 0.9Pb(Mg1/3Nb1/3)O3-0.1PbTiO3 using V-F relation, which is given by

⎟⎟⎠

⎞⎜⎜⎝

⎛

−−=

)(exp

max f

ao TTk

Eωω (1.1)

where ω is the applied or probing frequency, ωo is attempt frequency of a dipole or

Debye frequency (should be less than 1013 - 1015 Hz, the order of attempt frequency of

38

ions in solid state), Ea is the activation energy for the relaxation process and Tf is the

depolarization or freezing temperature of the polar regions.

Experimental data indicates the existence of hysteresis loop below Tf. Tf coincides

with the Tmax of the extrapolated maximum of near zero frequency dielectric

permittivity. This indicates that the kinetics or fluctuations in dipolar moments are

responsible for the remnant polarization to cease beyond Tf. The hysteresis loop

observed below Tf indicates that the freezing is cooperative in nature as in spin

glasses or dipolar glasses and not thermal blocking as in superparamagnets. It is also

observed by Viehland et al (1991c) that the P-E measurements could be scaled

appropriately only on introduction of the concept of freezing temperature. The

possibility to explain the behaviour (of 0.9(Pb(Mg1/3Nb1/3)O3)-0.1(PbTiO3) using the

relation and the scaling behaviour of Polarisation – Electric field measurements

indicate that the compound is analogous to spin glass or dipolar glass with

polarization fluctuations above static freezing temperature (Viehland et al (1991c).

Reasonable values are obtained for a thermally activated system. The relation is found

to hold good for many compounds exhibiting relaxor nature viz., Pb(Mg1/3Nb2/3)O3

(Vugmeister and Rabitz, (2000), Levstik et al (1998)), Pb(Sc0.5Ta0.5)O3 (Chu et al

(1993)).

There exists controversy over the nature of polarization fluctuations at and below Tf.

Tagantsev (1994) showed that Vogel - Fulcher relation could be mathematically

obtained assuming a wide exponential distribution for the relaxation times of the

relaxators that constitute the relaxor ferroelectric and Tf as the temperature where

static dielectric permittivity attains maximum. In fact he showed that Tf did not

indicate freezing temperature. Tagantsev and Glazounov (1999) further evidenced this

from the non-linear susceptibility measurements, which do not show anomaly related

to freezing temperature in Pb(Mg1/3Nb2/3)O3.

39

Vogel - Fulcher relation can be interpreted as normal Debye relation with temperature

dependent activation energy that increases with decrease in temperature and becomes

undefined as the freezing temperature is approached. Ea is the activation energy

associated with single polar cluster and the temperature dependence arises due to the

development of short-range order between neighboring clusters with kTf being

measure of interaction. However, the close agreement of fit and the reasonable values

obtained indicate that the average value of Ea remains constant through out the

temperature range. Ea is expected to decrease with increase in the temperature since

there exists dispersion in the volume of the polar micro regions. The presence of a

mean value indicates that the interaction between dipoles plays an important role in

controlling the kinetics of polarization fluctuations in the radio frequency region

rather than the distribution in the volumes of the polar micro regions.

The relatively lower values of the fitted parameters, the pre-exponential factor and

activation energy, obtained indicate that there exists a freezing temperature or

depolarization temperature as observed for (PbxLa1-x)(ZryTi1-y)O3 (Xi et al (1983)).

The experimental observations made by Xi et al (1983) from the field dependent

dielectric and pyroelectric studies on PLZT indicate that the depolarisation

temperature Td′ depends on the applied field strength and much lower than Tmax. Td′ is

the temperature where stable ferroelectric state is induced in relaxor ferroelectric.

Similar observations are made in the field dependent studies of Pb(Mg1/3Nb2/3)O3. The

depolarisation temperature is found to be nearly the same as freezing temperature for

Pb(Mg1/3Nb2/3)O3. Hence there exists a depolarisation temperature or freezing

temperature for relaxors. It may not be single due to the distribution in the volumes of

polar regions but a distribution of freezing temperatures may exist. Vogel - Fulcher

relation does not give acceptable values to the parameters for certain compositions

40

(Cheng et al, (1996)). The reason might be due to the basic difference between the

glasses and relaxors. In glasses, the volume of the polar regions does not vary with

temperature whereas it is well known that in relaxors the volume of polar regions

increases with decreasing temperature.

Vogel - Fulcher relation exhibits intrinsic shortcomings in explaining the dielectric

relaxation in relaxor ferroelectric type materials. It does not characterize the

anomalous behaviour of the ferroelectrics at Tc, Curie temperature. It emphasizes the

dielectric nature of the compounds rather than the ferroelectric nature. Hence a

relation that emphasizes the ferroelectric nature is required to explain the frequency

dependence of Tmax. To explain the frequency dependence of Tmax, they proposed a

super exponential relation, power law, which is given by,

⎥⎥⎦

⎤

⎢⎢⎣

⎡⎟⎟⎠

⎞⎜⎜⎝

⎛−=

p

oo T

T

max

expωω (1.2)

where ωo is the attempt frequency of the dipole (or Debye frequency), To is the

equivalent temperature of the activation energy of the relaxation process, and p (>1) is

a constant, which connects with degree of dielectric relaxation in a RFE.

The relation emphasises the modified ferroelectric nature of relaxors. It can be seen

that for a particular temperature To = Tc and p equal to infinity, equation explains the

behaviour of a ferroelectric with transition temperature Tc. It is well known that the

relaxation is very weak in ferroelectrics. Hence the smaller is the value of p, the

stronger is the relaxation. For p = 1 the equation reduces to Debye relation which has

strongest dielectric relaxation. Hence p characterizes the degree of relaxation and the

relation emphasizes ferroelectric nature. The physical origin of the relation is not yet

clear though it gives parameters in a reasonable range.

41

In relaxor ferroelectric ωo is associated with the size and interaction between the polar

regions. The larger the size of the polar clusters and the stronger the interaction

between them, the smaller is the value of ωo. The size and the degree of interaction

are decided by the volume fraction of the polar clusters present in the material. The

higher the volume fraction of the polar clusters the higher the size of polar regions and

stronger the interaction between them. It is observed from the studies by Cheng et al

(1998a) that the variation of this parameter has this significance in power relation

whereas in Vogel - Fulcher relation the parameter does not hold any significance.

The frequency dependence of Tmax is discussed so far, which gives a broad view of the

nature of interactions between the polar micro regions. All the regions cannot have the

same relaxation time for relaxor ferroelectric. Hence a distribution function is

necessary to describe the behaviour of the relaxor ferroelectric. Moreover, the

mechanism of dispersion observed around Tmax is explained by Tsurmi (1994)

considering the variation in the size of the polar micro regions and their response to

the probing frequency with temperature. If the relaxation frequency of the polar micro

region becomes less than the measuring frequency, as the temperature decreases, ε′

maximum occurs and then begins to decrease. If the relaxation frequency of polar

micro region becomes greater than the measuring frequency, as the temperature

decreases, ε′′ maximum occurs and then decreases. It is obvious that the peak in the

dielectric response depends on the temperature dependence of τ. On the higher

temperature side, increase in the volume of the polar regions increases the electrically

induced polarization increases. Therefore, the theoretical model that describes the

relaxation mechanism has to consider the factors 1) the change in production and the

distribution of the volume of polar regions with temperature and hence the relaxation

time 2) the variation in the associated interaction among the polar regions and 3) the

frozen polar regions in the low temperature region. Certain theoretical models that are

42

proposed to explain the temperature and frequency dependence of dielectric constant

are discussed in the next section.

1.7 THEORETICAL MODELS TO EXPLAIN THE RELAXOR BEHAVIOUR

Bell (1993) initially tried explaining the dielectric behaviour based on ideal

superparaelectrics. He considered a fictional superparaelectric and carried out his

calculations. He considered different scenarios: an ensemble of independent, identical,

mono-sized superparaelectric clusters, then introduced a distribution in the size of the

clusters, temperature-dependent cluster sizes, and finally dipolar cluster interactions.

He assumed single transition temperature for all the regions. The calculations are

carried out employing LGD formalism for ferroelectrics to calculate the dielectric

function of an ensemble of clusters. Good results were obtained once the distribution

of the size of the polar clusters is introduced.

Glazounov (1995) introduced the possibility of distribution of local transition

temperatures for the polar regions. The model considers relaxors as an ensemble of

non-interacting polar regions and also they have unique size. Though to some extent

the static polarization and the real part of the permittivity could be explained the

behaviour of the imaginary part and the relaxation time spectrum could not be

accounted for completely. This indicates that distribution in the size of the polar

regions is very much essential in determining the behaviour of relaxors.

Lu and Calvarin (1995) assumed an exponential distribution of the polar region sizes.

The results of the model are better than that of the Bell’s model, but it predicts that the

dielectric absorption always increases with increasing frequency, which contradicts

the experimental results in the low-temperature range.

43

There are some artificial parameters in earlier models. They were based on a strong

inhomogeneous distribution of the polar region sizes. Hence in the present study the

model proposed by Cheng et al (1997, 1998) is used. Before going into the details of

the model the advantages of the present model are listed out.

Compared with the above models, the advantage is that the simulated dielectric

behavior in the present model can characterize all of the basic features of the RFE. In

addition, all of the parameters used in the fitting process are experimentally

determined in the present model, while the model is based on a homogeneous

distribution in some limited range. Thus the advantage of the present model indicates

that the distribution of the polar region size in the RFE is very smooth in a limited

range.

The temperature variation of ε′ is characterized by two different phenomena. The low

temperature dielectric response, i.e., below Tmax, the high degree of dielectric

dispersion depends on the freezing of the polar regions and the high temperature

response, i.e. above Tmax, the response is characterized by production and

concentration of dipoles and their orientation in the external field.

To consider the distribution in the volume of polar regions it is considered that the

least possible volume of the polar clusters can be the single unit cell. Even though the

volume of polar clusters increases with decrease in temperature, they do not increase

to the extent of domains in ferroelectrics, which can be evidenced from lack of

macroscopic phase transition and slim hysteresis loop. Hence there exists an upper

limit to the volume of the polar regions. It is obvious that lower end is independent of

temperature whereas upper end is dependent on temperature. The upper end increases

with decreasing temperature and the relaxation time associated with this polar region

(τ1) can be represented by power law. The lower end τo=1/ωo, is the attempt frequency

44

of polar regions or Debye frequency. The long limit increases with decreasing

temperature and in the mean time new polar regions appear in some non polar regions.

Therefore, it was assumed that the distribution [f(τ)] of τ is a constant from the short

end to the long end in the logarithmic scale as shown in Fig 1.6. Distribution of τ can

be expressed as

⎪⎪⎩

⎪⎪⎨

⎧

≤≤⎟⎠⎞⎜

⎝⎛

><

= )(ln

1),(0

))(ln(1

1

1

τττ

ττ

ττττ

τo

o

o

f (1.3)

where ⎥⎦

⎤⎢⎣

⎡⎟⎠⎞⎜

⎝⎛=

po

o TTT exp)(1 ττ . (1.4)

The Debye relation explains the dielectric relaxation response of each polar region.

ωτεε

εεεi

s

+−

=−=∆ ∞∞

∗∗

1 (1.5)

where ε*=(ε′-iε″) represents the total complex dielectric constant and ε∞ is the

dielectric constant at high frequency, which results from the electronic polarization,

ionic polarization and other polarization in the material with a rapid response time.

From the Debye relation and the proposed distribution function to characterize the

distribution of relaxation times, the variation of dielectric response in the region

below Tmax (εL) is given by

)ln(ln ωωεε −+= ∞ oL A (1.6)

where A is a intrinsic parameter that depends on temperature and independent of

frequency, ωo is relaxation frequency of a polar unit cell and represents the frequency

of internal vibration and hence independent of temperature. ε∞ is nearly independent

of temperature since relaxors do not involve any phase transition. Hence, low

temperature dielectric response depends mainly on the temperature dependence of A

which in turn depends on the freezing process of the polar regions since freezing

45

process characterizes the behaviour at low temperatures. Equation 1.6 can be modified

as

( ) ( ) ωε lnTATBL −= (1.7)

where

( )

( )⎟⎠⎞⎜

⎝⎛

=Β

⎟⎠⎞

⎜⎝⎛

⎟⎠⎞⎜

⎝⎛

=Α

o

s

o

o

s

T

T

ττε

ω

ττε

1

1

ln

,lnln

where B is given by

oAB ωε ln+= ∞ (1.8)

The values of A and B are obtained by fitting frequency dependence of ε′ at different

temperatures. By fitting A and B, ε∞ and ω0 are obtained.

The temperature dependence of the parameter A at temperatures much lower than

Tmax, can be fitted to the following empirical super exponential relation

⎟⎟

⎠

⎞

⎜⎜

⎝

⎛⎟⎟⎠

⎞⎜⎜⎝

⎛+=

+δ

βα

1

11exp)( TTA (1.9)

46

ln(τ)ln(τ

1)ln(τ

0)

f(τ)

1/ln

(τ 1/το)

Fig 1.6. Distribution function of the relaxation times for the relaxor ferroelectric.

where α1, β1 and δ are positive integers. From the observations on the earlier

compounds it is understood that δ indicates the degree of dielectric relaxation. Higher

is the value of δ, the more is degree of relaxation. It gives an idea of frozen rate of

polar regions. Lower the magnitude faster is the rate of freezing and vice versa.

Smolensky et al (1970) reported that the dielectric dispersion of relaxor ferroelectric

materials deviates strongly from Curie-Weiss law as the temperature Tmax was

approached from high temperature. They found that Curie-Weiss behaviour is retained

for the temperature range far greater than Tmax. The temperature, at which the

deviation from Curie-Weiss behaviour occurs, is close to the temperature of onset of

local polarization, TB due to the development of correlations between the dipoles. To

explain the low frequency dielectric dispersion in PMN, Smolensky proposed a

quadratic law. However, it was found that quadratic law is not suitable to explain the

behaviour of all relaxor compounds. A generalized semi-empirical relation given in

47

Eqn (1.10) is applied successfully to explain the phase transition modes of relaxor

type compounds.

( )CTT

T rr

γ

εεmax

'max,

'

1)(

1 −=⎟

⎟⎠

⎞⎜⎜⎝

⎛− (1.10)

where γ, the diffuseness exponent, varies from 1 to 2 is a measure of “relaxor nature”.

For γ=1, the equation reduces to Curie-Weiss law and for γ=2, equivalent to quadratic

law proposed by Smolensky. In the quadratic relation “C” remains constant at

temperatures higher than Tmax the fitted relation strongly deviates from the

experimental point (Tmax, εmax). However, it is observed that the parameter “C”

depends on the chosen temperature range and frequency near Tmax and this strongly

affects Tmax and εmax. This leads to indeterminacy in characterizing the relaxor

behaviour of relaxor ferroelectric. The generalized relation does not give a linear

relation. The parameters in this case also depend on the choice of temperature range

and frequency. Therefore γ cannot characterize the relaxation behaviour of the

compounds. Hence the two widely used equations cannot characterize the high

temperature side. Also from the earlier discussions it is quite obvious that the polar

regions start forming from temperatures high above Tmax and keep increasing in the

volume as result of coalescing. Hence the relation that characterizes the high

temperature region of relaxor ferroelectric should be a monotonous function. The two

relations are not monotonous functions. The relation that describes the dielectric

behaviour in high temperature side should be a monotonous function that emphasizes

the rate of formation of these regions and the varying concentration of the dipoles. It

is found that for temperatures higher than Tmax, the following exponential relation fits

well the dielectric behaviour (Cheng et al 1996, 1997)

48

)exp( TH βαε −= (1.11)

where α is a measure of concentration and dipole moment of dipoles and β is a

measure of rate of production of dipoles with decreasing temperature. It is observed

that the parameters remain stable with change in temperature and as well frequency.

For β=0, the equation characterizes the Debye medium, hence β indicates the degree

of relaxation. If the relaxation is strong, value of β is small.

The Eqns (1.9) and (1.10) describe the dielectric dispersion at temperatures less than

Tmax and greater than Tmax respectively. In the temperature dependence, if the

simulated results are close to the experimental results well below Tmax it is observed

that they deviate from the experimental results near Tmax. In the temperature

dependence, if the simulated results almost coincide with the experimental results

well above Tmax it is observed that the simulated results are less than the experimental

results below Tmax. This and the requirement of two equations exponential and super-

exponential relations to explain respectively the higher and lower temperature

response indicate that at least two polarization mechanisms are required to explain the

dielectric behaviour of relaxor ferroelectric. The measured dielectric response is thus

the sum of the contributions of these two polarization processes i.e., the dielectric

constant of relaxor ferroelectric can be expressed as

( ) ( ) ( )τωετωετωε ,,, 21 +=m (1.12)

where εm is the measured dielectric constant. ε1 and ε2 are the two polarization

processes. Both are dependent on temperature and frequency as εm. From the general

dielectric theory the dielectric response of both ε1 and ε2 can simply be written as

( ) ( )( ) ( )2,1

,1,

, =+

= iC

B

i

ii τω

τωτωε (1.13)

49

where Bi(ω,τ) and Ci(ω,τ) are both function of temperature and frequency. The

function forms of Bi(ω,τ) and Ci(ω,τ) are both dependent on polarization mechanism

and the material. At higher temperatures ε1 > ε2 and εm ≅ ε1 whereas at lower

temperatures ε2 > ε1and εm ≅ ε2. Therefore, the measured dielectric constant at very

high temperature can be used to determine some features of ε1, and that at very low

temperature can be used to determine some features of ε2.

For ε1, the dielectric behavior at high temperatures can be used to describe its static

dielectric constant. If one uses Eqn (1.11) to express B1, which increases with

decreasing temperature, C1 should be very small at high temperatures and increases

with decreasing temperature. At low temperatures, C1 should be larger than B1, so that

ε1 is much smaller than εm. Considering the general dielectric theory, both B1 and C1

are dependent on the intrinsic properties of the materials, such as the dipole moment

and concentration of the polar regions, the size and distribution of the polar regions,

the interaction among the polar regions, and the interaction between the polar and

non-polar regions. Therefore, C1 is related to B1.

For ε2, the dielectric behavior is not clear. Based on the above discussion, it is known

that the dielectric behavior at low temperature can be well described with Eqns (1.6)

and (1.9). Thus, if one uses Eqn (1.6) to express B2, which increases with increasing

temperature, C2 should be very small at low temperatures and it increases with

increasing temperature. At high temperatures, C2 should be larger than B2, so that ε2 is

much smaller than εm. B2 and C2 reflect the different features of the polarization

process. Both B2 and C2 are dependent on the intrinsic properties of the polarization

process. Thus, C2 is related to B2.

50

All of the measured relations between the temperature and dielectric constant for RFE

are smooth in the whole temperature range. Therefore, for the RFE, although there are

two different polarization processes, the weight of either ε1 or ε2 in εm changes with

the temperature smoothening. This indicates that both of them should have some

intrinsic relationship. Therefore, C2 is also related to B1, and C1 is related to B2.

Based on both the characteristics and physical significance of C1 and C2, both C1 and

C2 are dependent on both the temperature and frequency. Considering the above

discussion, the temperature dependence of both C1 and C2 should be determined from

Eqns (1.11) and (1.9). Thus, Eqn (1.13) can be written as

( ) ( )( )

( )

( ) ( )

( ))14.1(

ln)(1

,,

)14.1(

ln1,

2

2

1

1

b

TTAD

TT

a

TATD

TT

n

h

o

L

m

o

H

H

⎟⎠⎞⎜

⎝⎛+

=

⎟⎠⎞⎜

⎝⎛+

=

εω

ωεωε

ωε

εωε

where m(>1) and n(>1) are constants that are independent of frequency and

temperature and D1 and D2 are weighing factors that depend on frequency. Hence the

two expressions take care of the temperature variation in the low and high regions.

However the dielectric constant maximum for a frequency appears where the long end

of relaxation time is equal to the inverse of the frequency. It results in the simulated

frequency dependence of the dielectric behaviour, at the temperature around Tm,

having a little deviation from experimental results.

It is very interesting to compare the fitted temperature dependence of both ε1 and ε2

under different frequencies in order to study the basic features of both polarization

processes. The following features are noticed.

51

1. The value of ε1 rapidly decreases with decreasing temperature at the temperatures

lower than the temperature of ε1 maximum (Tm1);

2. The value of ε1 at Tm1 decreases with increasing frequency;

3. The value of Tm1 increases with increasing frequency;

4. At high temperature there is no dielectric dispersion, while at temperatures around

and lower than Tm1 there is a strong dielectric dispersion as the dielectric constant

always decreases with increasing frequency.

All these indicate that ε1 originates from a relaxation polarization process. The micro

origin of ε1 is the thermally activated flips of the polar regions in relaxor ferroelectric.

The following conclusions can be obtained from the temperature dependence of ε2 at

different frequencies.

1. ε2 is of a strong dielectric dispersion in the whole temperature range at the studied

frequencies.

2. With increasing frequency, ε2 increases at high temperatures while it decreases at

low temperatures.

3. The dielectric constant maximum temperature (Tm2) of ε2 increases with increasing

frequency.

4. The value of ε2 at Tm2 decreases with increasing frequency.

5. When the temperature is higher than Tm2, ε2 decreases rapidly with increasing

temperature.

It is impossible to explain all these features of ε2 with a relaxation polarization

process, as the dielectric constant contribution from the relaxation process always

decreases with increasing frequency. It seems that ε2 originates from a resonance

polarization. For this resonance polarization process, the following characteristics can

be derived from the above results. The polarization process does not exist in the

52

materials at high temperature. With decreasing temperature from the higher

temperature side, the polarization process appears rapidly in the material when the

temperature approaches Tm. For the contribution to the dielectric constant of the

materials, the lower the temperature the higher is the weight of the resonance process.

In the present study it is observed that the model could be successfully used to explain

the dielectric behaviour of relaxor-based compounds. It fails in analyzing the

behaviour of the compounds that undergo a transition from either ferroelectric or anti-

ferroelectric to relaxor ferroelectric.

Relaxors possess very large dielectric constants, attractive for capacitors;

exceptionally large electro-strictive coefficients, important for actuators and micro-

positioners; and larger electro-optic constants, useful for information storage, shutters,

and optical modulators (Yoon and Lee (2000)). In spite of being discovered three

decades earlier the mechanism of the relaxors is still not yet clear. These factors make

them a subject of interest. Hence the characteristics of certain lead-based relaxor

compounds are studied.

1.8 OBJECTIVE AND SCOPE OF WORK

The investigation involves the synthesis and dielectric studies of the polycrystalline

lead based complex perovskites. The compositions studied are Ba2+ and Sr2+

substituted Pb(Zn1/3Nb2/3)O3 (PZN), Ba2+ and La3+ substituted Pb(Yb0.5Nb0.5)O3

(PYN) and Pb(Fe0.5Nb0.5)O3 (PFN). The polycrystalline samples are synthesized using

conventional solid-state reaction route and the bulk samples are characterized using

X-ray diffraction (XRD), low frequency and high frequency dielectric studies. The

work is aimed at understanding the relaxation phenomenon involved in these

materials.

53

While disorder is energetically favoured for Pb2+ based relaxor ferroelectrics which

shows diffuse phase transition, ordering is easily favoured in the case of Ba2+ based

materials that has nearly temperature independent dielectric properties i.e., the

energitics of B′ and B″ ordering are dramatically altered by substituting Ba2+ for Pb2+

on the A-site (Burton and Cockayne (1999)). Recent microscopic model calculations

do indicate that the difference between these two extreme behaviours is mainly due to

the enhanced Pb-O hybridisation between Pb2+ 6s and O 2p states. Calculations

indicate that the long-range coulomb interactions, which drive B-site ordering in Ba2+

systems, do not dominate in Pb2+ systems. In other words hybridisation between Pb

6s and O 2p states leads to the near cancellation of long and short range interaction in

Pb(B’1/3B’’2/3)O3 systems and results in B-site disorder.

The hybridisation of atomic orbital distorts the local environment of a given ion. The

change in the degree of hybridisation of A-O (Pb-O and Ba-O) bonds and hence the

change in the local structure of Pb2+ and Ba2+ based complex perovskite systems

requires particular attention to get more insight into the variation in dielectric

properties. Therefore, the present thesis aims at studying the variation in the

interaction and volume of the polar micro regions, that dictate the dielectric properties

of relaxors, with the substitution of isovalent ions is studied in the Ba2+ and Sr2+

substituted Pb(Zn1/3Nb2/3)O3. The relaxor nature is analysed using the model proposed

by Cheng et al (1997, 1998), which has been discussed in detail in the earlier section.

Pb(Yb0.5Nb0.5)O3 is anti-ferroelectric at room temperature and on Ba2+ undergoes a

transition to relaxor ferroelectric. Local microscopic variations involved in the cross-

over from anti-ferroelectric to relaxor ferroelectric behaviour (for x ≥ 0.15 of Ba2+

concentration) in the solid solution series (BaxPb1-x)(Yb0.5Nb0.5)O3 are studied from

the behaviour of the Raman active phonon modes. The variations in the Raman

spectra are studied in conjecture with the structural and dielectric susceptibility on

54

substitution of Ba2+ for Pb2+. The dielectric behaviour of the samples exhibiting the

relaxor nature could not be analysed using the model proposed by Cheng et al. So far

the influence on the dielectric properties only on substitution of isovalent ions is

studied. Hence the effect of trivalent La3+ on the dielectric properties is studied by

substituting La3+ in the place of Pb2+.

Effect of annealing the polycrystalline samples of Pb(Fe0.5Nb0.5)O3, sintered at

different temperatures in oxygen atmosphere on the dielectric properties is studied.

Thus in this thesis, Chapter 2 deals with the synthesis and structural characterization

of the above said systems. Details of the difficulties involved in the synthesis of the

compositions and the precautions taken are discussed. Calcination and sintering are

carried out in the presence of atmosphere powder to avoid PbO loss. Two step method

proposed by Swartz and Shrout (1982) is followed to avoid formation of secondary

phases. The formation of single phase is confirmed using X-ray diffraction.

In chapter 3, the variations in the low frequency dielectric response on annealing

Pb(Fe0.5Nb0.5)O3 in oxygen atmosphere are presented. The results are discussed in

conjecture with room temperature resistivity measurements. The experimental set-up

used for low frequency dielectric measurements is explained.

The low and high frequency dielectric response of the Ba2+ and Sr2+ substituted

Pb(Zn1/3Nb2/3)O3 are discussed in chapter 4. The variation in the interaction due to the

two ions are studied using Vogel – Fulcher relation, Power law and the entire

temperature range is fitted to the model proposed by Cheng et al (1997, 1998) the

variation in the relaxor behaviour is discussed. The low and high frequency data of

Ba2+ substituted Pb(Yb0.5Nb0.5)O3 are also analysed. The above said relations and the

model could not be used to interpret the relaxor behaviour of the compounds. The low

55

frequency dielectric data of La3+ substituted Pb(Yb0.5Nb0.5)O3 and

(Ba0.04Pb0.96)(Yb0.5Nb0.5)O3 are analysed.

Chapter 5 concentrates on the Raman spectroscopic studies carried out on Ba2+

substituted Pb(Yb0.5Nb0.5)O3. The modes are assigned to different symmetries and the

variations in their behaviour with substitution of Ba2+ are discussed in detail. Finally

the summary and possible conclusions of all the studies are given in chapter 6 along

with future scope of the work. Each chapter is written with self-contained data along

with discussion of the results.

56

CHAPTER 2

SYNTHESIS AND STRUCTURAL CHARACTERIZATION

OF (Pb1-xBax)(Zn1/3Nb2/3)O3, (Pb1-xSrx)(Zn1/3Nb2/3)O3,

(Pb1-xBax)(Yb0.5Nb0.5)O3, (Pb1-xLax)(Yb0.5Nb0.5)O3,

(Pb0.96-x LaxBa0.04)(Yb0.5Nb0.5)O3 AND Pb(Fe0.5Nb0.5)O3

The synthesis of lead based compounds must take into consideration the loss of lead

oxide. Therefore, preventive measures have to be taken into consideration to avoid

the formation of secondary phases. Moreover, during the synthesis of the compounds,

one must be careful about the reactivity of each component. This chapter explains the

preventive measures adopted in the formation of single phase of the compounds

followed by the details on the synthesis and structural studies of the barium and

strontium substituted lead zinc niobate [(Pb1-xBax)(Zn1/3Nb2/3)O3 and (Pb1-

xSrx)(Zn1/3Nb2/3)O3 for x = 0.2 and 0.3], barium and lanthanum substituted lead

ytterbium niobate [(Pb1-xBax)(Yb0.5Nb0.5)O3 for x = 0 to 0.3 in steps of 0.05 and

(Pb1-x Lax)(Yb(1+x)/2Nb(1-x)/2)O3 for x = 0.01, 0.02 and 0.04], lanthanum substituted

lead barium ytterbium niobate [(Pb0.96-xLaxBa0.04)(Yb(1+x)/2Nb(1-x)/2)O3 for x = 0.01,

0.02 and 0.04] and lead iron niobate [Pb(Fe0.5Nb0.5)O3].

Two factors play major role in the synthesis of lead based complex perovskites viz.,

high volatality of PbO and its evaporation at 750 oC and high reactivity of B″ oxide

over B′ oxide with PbO in Pb(B′xB″1-x)O3. PbO evaporation results in vacancies at Pb

and O sites and also secondary phases deficient in lead (Smyth et al (1989), Cho et al

(1997)). The latter factor results in the formation of secondary phases, mainly A2B2O7

based pyrochlore phase. The secondary phases considerably affect the physical

properties of the compounds.

57

The arrangement suggested by Kingon and Clark (1982) is found to be more suitable

in reducing the loss of PbO in the presence of atmosphere powder or packing powder.

The arrangement used in the synthesis is given in Fig 2.1. PbZrO3 with 10% excess of

ZrO2 (PbZrO3 + 10% excess of ZrO2 present in PbZrO3) is used as packing powder

since it is effective in equilibrating the PbO vapour transport of the specimen with the

atmosphere powder and helps in maintaining constant activity of PbO (Atkin and

Fulrath (1971) and Holman and Fulrath (1972), (1973)). Though the studies were

done on PZT related systems in the references mentioned above for sintering

configuration and packing powder, it is observed that they are effective in the present

study also. Throughout the synthesis of lead based compounds during calcination and

sintering the same configuration is used to avoid PbO loss. No excess of PbO is added

at any stage to the compositions studied. The PbO loss is determined from the

difference in the mass of the samples before and after calcination/sintering. From this

difference, the amount of packing powder required was optimised for a given

composition. Change in the PbO content and the thermal parameters vary the activity

of PbO. Therefore, the packing powder required should be optimised for all the

compounds in solid solution series and also when the sintering temperature/duration

are changed.

Two-step process or precursor method proposed by Swartz and Shrout (1982) is

followed to avoid the formation of pyrochlore phase. In our study, the method is

slightly modified to ensure formation of single perovskite phase. Three different

methods are followed in the synthesis of the compounds to ensure single phase in the

present study. Pb(Zn1/3Nb2/3)O3 based compounds are synthesized using three-step

59

method, Pb(Yb0.5Nb0.5)O3 based compounds using single-step method and

Pb(Fe0.5Nb0.5)O3 using the two-step method. The details are given in the following

sections.

The main steps involved in the synthesis are given in the flow chart as shown in Fig

2.2. Whenever a precursor is required, additional step of weighing and calcination of

the precursor in alumina crucible is involved. The required reagents are taken in

stoichiometric proportions; dry mixed and then wet mixed with distilled water as

mediumUniform mixing of reagents is necessary for reproducible results. The amount

of water is just enough to form slurry so that after mixing, the selective sedimentation

of the reagents can be prevented. The calcination temperature and duration should be

optimised for the complete reaction of the reagents considered (Wang et al (1994),

Wu and Liou (1995)). A rough estimate of the calcination temperature is obtained

from the DTA measurements. Double calcination step is followed in certain cases as it

results in the formation of homogeneous and single phase (Adachi et al (1996) and Im

et al (1996)). Therefore for certain compositions the procedure is followed to ensure

single-phase compound. Prior to calcination, after drying, the slurry is ground for 30

minutes in agate mortar. The calcined powder is mixed with distilled water as medium

and dried at 150 oC for 12 hrs. The grinding helps to homogenize the compositional

variations, which may arise during calcination. The lead based compounds other than

PFN are calcined in the closed double alumina crucible. Calcination carried out in this

method ensured formation of single phase. Pellets are made after calcination by

mixing with poly vinyl alcohol (PVA), diluted in distilled water that acts as a binder.

It reduces brittleness and results in better compactness amongst the granules of the

materials. Cylindrical pellets are made using uniaxial isostatic cold press with the help

of tungsten carbide dyes. The pellets are kept at 500 oC for 12 hrs to evaporate PVA.

Sintering involves coordinated change of all grains in a powder compact to allow

60

Weighing in stoichiometric proportions

Dry mixing, wet mixing

Calcination

Phase confirmation (XRD)

Sintering (densification)

Polishing

Phase confirmation (XRD)

Electroding Raman study

Density measurement

Dielectric measurements

Fig. 2.2 Flow chart of the important steps involved in the synthesis of the compositions.

61

them change themselves in a space filling manner i.e., the grain centres move towards

each other, thereby reducing the size of the compact and eliminating the pores. The

reduction of surface and interface area is the driving force for the process. The

sintering is influenced by the particle size, distribution in the particle size and

agglomeration of the particles both before and after calcination. Calcination has

significant influence on the quality of sintering. Hence one should choose the

calcination temperature, duration of calcination carefully to ensure that the reagents

react well. High purity chemicals are used for the synthesis. This ensures high values

of density. The sintering temperature and minimum possible soaking time at the

temperature play significant role in determining and reproducibility of the physical

properties (Wang et al (1994) and Villegas et al (2000)). At each stage of calcination

and final sintering, the phases are confirmed with XRD.

The physical density is measured by Archimedes liquid displacement method and

compared with density calculated from X-ray data. These are referred as relative

density in the tables.

2.1. SYNTHESIS AND STRUCTURAL STUDIES OF Ba2+ and Sr2+

SUBSTITUTED Pb(Zn1/3Nb2/3)O3 COMPOUNDS This section deals with the synthesis of Ba2+ and Sr2+ substituted Pb(Zn1/3Nb2/3)O3. It

is well known that perovskite phase of Pb(Zn1/3Nb2/3)O3 cannot be stabilized in

polycrystalline form even using the two-step columbite precursor method. The

difficulty arises since Pb(Zn1/3Nb2/3)O3 is thermodynamically unstable over a wide

range of temperature (600 to 1400 oC), rapidly yielding pyrochlore phase and PbO as

decomposition products ruling out the possibility of forming pure polycrystalline

Pb(Zn1/3Nb2/3)O3 compound with single phase nature. Matsuo et al (1969) observed

that Pb(Zn1/3Nb2/3)O3 could be synthesized in polycrystalline form with stable

perovskite structure under high pressure at elevated temperatures (25 kbar, 800 to

62

1000 oC). To attain a stable perovskite phase in polycrystalline form under normal

conditions, solid solutions are being formed by substitutions either at A-site or B-site

with suitable ions. In Pb(Zn1/3Nb2/3)O3, substitutions at the A site by Ba2+ (Nomura S

and H Arima (1972), H Fan et al, (1998) Ahn B Y and N K Kim (2000a) and Zhu et

al (2001)) and Sr2+ (Fan H et al (1998)) or at the B-site by Zr (Lian et al (1991)), Fe

(G V Ramani and D C Agarwal (1993), Ta (Ahn B Y and N K Kim (2000b)), Ni

(Veirheilig et al (1992)) have been reported. Ahn and Kim (2000a) reported that the

perovskite phase is stabilised for x = 0.08 of Ba2+. The pure perovskite phase is

formed with x = 0.1 of Ba2+ and x = 0.2 of Sr2+ in the solid solution series (Pb1-

xBax)(Zn1/3Nb2/3)O3 (PBZN) and (Pb1-xSrx)(Zn1/3Nb2/3)O3 (PSZN) respectively in the

present study. However for comparing the characteristics of the two series, the

compositions from x = 0.2 for both the cases are considered.

Polycrystalline samples of (Pb1-xBax)(Zn1/3Nb2/3)O3 and (Pb1-xSrx)(Zn1/3Nb2/3)O3, for

x=0.2 and 0.3 (referred to PBZN1, PBZN2, PSZN1 and PSZN2 respectively

hereafter) were prepared by conventional solid-state reaction method in three stages to

avoid formation of any secondary phase. High purity reagents of PbO (99.95%),

BaCO3 (99.9%), SrCO3 (99.9%), Nb2O5 (99.95%) and ZnO (99.9%) were used for the

preparation of these ceramics.

In the first stage, ZnO and Nb2O5 were taken in stoichiometric proportions and

calcined at 1100 oC for 2 hrs to form ZnNb2O6 (ZN). In the second stage, ZN and

BaCO3 and SrCO3 were mixed in stoichiometric ratio and calcined for formation of

Ba(Zn1/3,Nb2/3)O3 (BZN) and Sr(Zn1/3Nb2/3)O3 (SZN) respectively. Double calcination

step was followed in calcination of the dried slurry. Calcination was carried out at

1200 oC for 3 hrs in each step, totally for 6 hrs. After each step of calcination the

powder was mixed with distilled water as medium in agate mortar and dried at 150 oC

for 12 hrs.

63

In the third stage, PbO, ZN, Ba(Zn1/3Nb2/3)O3 and Sr(Zn1/3Nb2/3)O3 were mixed in

stoichiometric ratio and calcined for the respective x. The calcination was carried out

in the range 1000 -1050 oC. After calcination, pellets were made for sintering. While

the pellets of PBZN1and PSZN1 were sintered at 1100 oC, the pellets of PBZN2 and

PSZN2 were sintered at 1150 oC. Care was taken to avoid PbO loss during sintering

and calcination by following the procedure given above.

The calcination and sintering temperatures, lattice parameters and density of the

pellets are given in Table 2.1. Figure 2.3 shows the XRD pattern for the

Pb(Zn1/3Nb2/3)O3 based compositions. Within the resolution of XRD the phase is

cubic perovskite and no secondary phases are observed. Peaks corresponding to

superlattice reflection are not observed for the compounds studied. The peaks shift

according to the variation in Ba2+ and Sr2+. The corresponding macroscopic symmetry

is cubic with Pm3m space group for all the compositions studied.

2.2 SYNTHESIS AND STRUCTURAL STUDIES OF Pb(Yb0.5Nb0.5)O3 BASED

COMPOUNDS This section deals with the synthesis and characterization of Pb(Yb0.5Nb0.5)O3 based

compounds viz., Ba2+ substituted Pb(Yb0.5Nb0.5)O3, La3+ substituted Pb(Yb0.5Nb0.5)O3,

La3+ and Ba2+ substituted Pb(Yb0.5Nb0.5)O3.

Lead Ytterbium Niobate, Pb(Yb0.5Nb0.5)O3, is synthesized using two-step method

whereas Ba2+ and La3+ substituted PYN are synthesized using single-step method.

Substitution in the A-site stabilizes the cubic perovskite phase.

64

10 20 30 40 50 60 70

(100

)

(220

)

(211

)

(200

)

(111

)

(110

)

2θ (deg)

x = 0.2 Sr2+

(100

)

(220

)

(211

)

(200

)

(111

)

(110

) Inte

nsity

(a.u

.)

x = 0.3 Sr2+(1

00)

(220

)

(211

)

(200

)

(111

)(1

11)

(110

)

x = 0.2 Ba2+

(220

)

(211

)

(200

)

(110

)

(100

)

x = 0.3 of Ba2+

Fig. 2.3 X-ray diffractograms of the (Pb1-xBax)(Zn1/3Nb2/3)O3 and (Pb1- xSrx)(Zn1/3Nb2/3)O3 for x = 0.2 and 0.3.

65

Table 2.1 Calcination and sintering temperatures, lattice parameters and relative density of Pb(Zn1/3Nb2/3)O3 based compounds.

Sample code

Calcination temperature (oC)

Sintering temperature (oC)

Lattice parameter (Å)

Relative density (%)

PBZN1 1000 1100 4.08 96

PBZN2 1050 1150 4.09 98

PSZN1 1000 1100 4.06 94

PSZN2 1050 1150 4.04 96

2.2.1 Synthesis and structural studies of Pb(Yb0.5Nb0.5)O3

Yb2O3 and Nb2O5 were taken in stoichiometric proportions to form YbNbO4. Double

calcination step was followed to calcine the powder, 1300 oC for 12 hrs each step, for

24 hrs. YbNbO4 and PbO were taken in stoichiometric ratio and mixed with distilled

water as medium. The dried slurry was calcined at 950 oC for 2 hrs in the closed

double alumina crucible method to avoid the loss of PbO. The pellets were sintered in

the closed crucible method in the presence of packing powder at 1100 oC for two hrs.

The calcination and sintering temperatures, lattice parameters and density of the

pellets are given in Table 2.2. XRD of the sintered Pb(Yb0.5Nb0.5)O3 is given in Fig

2.4. Pb(Yb0.5Nb0.5)O3 belongs to the family of highly ordered Pb2+ based compounds

such as PbCo0.5W0.5O3 and PbMg2WO6 with distinct super lattice reflections due to

long range ordering of B-site cations and with effective doubled unit cell about simple

perovskite structure (Choo et al (1993), Baldinozzi et al (1994) and Park (1998)).

Pb(Yb0.5Nb0.5)O3 is an anti-ferroelectric that undergoes paraelectric to anti-

ferroelectric phase transition at 275 K (Kwon et al (1991)). The space group of high

symmetry phase is Fm3m and that of low symmetry phase is Pnam. The XRD consists

of the reflections corresponding to anti-parallel displacement of Pb2+ and F reflections

corresponding to B-site ordering. Kwon et al (1991), from X-ray diffraction and

66

electron microscopy investigations, suggested that the true room temperature

symmetry is orthorhombic with lattice parameters ao=5.918 Å, bo=23.453 Å and

co=8.221 Å, and proposed a structural model consisting of anti-parallel lead-cation

displacements along the [110]p type directions of the cubic paraelectric phase shown

in Fig 2.5 “o” and “p” refer to orthorhombic and pseudocubic cells respectively.

Figure 2.6 shows the basic relation between the cubic and orthorhombic cells (Park

and Choo (1998)). The oxygen atoms are not shown for clarity. Symbol “c” represents

the cubic while “o” represents the orthorhombic structures. In the present case, the

observed lattice parameters deviated from the earlier reported values and the indexing

is done basing on the work of Kwon et al (1991).

2.2.2 Synthesis and structural studies of Ba2+ substituted Pb(Yb0.5Nb0.5)O3

Ceramic samples with the chemical formula (Pb1-xBax)(Yb0.5Nb0.5)O3 for x=0.05, 0.1,

0.15, 0.2, 0.25 and 0.3 (hereafter referred to PBYN1, PBYN2, PBYN3, PBYN4,

PBYN5 and PBYN6 respectively) were prepared by reacting the stoichiometric

proportions of high pure chemicals BaCO3, PbO, Yb2O3 and Nb2O5 using single-step

method. The addition of Ba2+ in A-site stabilizes with single perovskite phase

therefore single-step method was followed. Calcination was carried out from 900 -

1000 oC. Sintering was carried from the temperature 1100 - 1300 oC. The calcination

and sintering temperatures, lattice

67

10 20 30 40 50 60

.... o oooooooo

x = 0

2θ (deg)

x = 0.05

...

x = 0.1

Inte

nsity

(a.u

)

x = 0.15

(422

)

(400

)

(222

)

(220

)

(200

)

x = 0.2

(422

)

(400

)

(222

)

(220

)

(200

)

x = 0.25

.

...

. ...x = 0.3

(422

)

(400

)

(222

)

(220

)

(200

)

Fig 2.4 X-ray diffractograms of the (Pb1-xBax)(Yb0.5Nb0.5)O3 for x = 0, 0.05, 0.1,

0.15, 0.2, 0.25 and 0.3.at room temperature; O-Superlattice reflection corresponding to anti-parallel displacement of Pb2+ cations, - F-reflection due to B-site ordering.

70

Table 2.2 Calcination and sintering temperatures, lattice parameters and relative density of Pb(Yb0.5Nb0.5)O3 based compounds.

Sample code Calcination temperature (oC)


Lattice parameters (Å) a b c

Relative density (%)

PYN 900 1100 5.92 23.46 8.21 93

PBYN1 900 1150 5.92 23.47 8.23 93

PBYN2 950 1200 5.92 23.50 8.24 94

PBYN3 950 1250 5.93 23.52 8.24 96

PBYN4 1000 1300 8.41 8.41 8.41 96

PBYN5 1000 1300 8.42 8.42 8.42 96

PBYN6 1000 1300 8.46 8.46 8.46 97

PLYN1 900 1100 5.92 23.46 8.21 93

PLYN2 950 1100 5.92 23.46 8.21 93

PLYN3 950 1150 5.92 23.46 8.21 93

PBLYN1 900 1100 5.92 23.47 8.23 93

PBLYN2 950 1150 5.92 23.47 8.23 93

PBLYN3 950 1150 5.92 23.47 8.23 93

71

parameters and density are given in Table 2.2. X-ray diffractograms of the sintered

compounds are given in Fig 2.4. The XRD pattern consists of the reflections

corresponding to anti-parallel displacement of Pb2+ and F reflections corresponding to

B-site ordering. With increasing Ba2+ substitution, the intensity of the reflections

corresponding to anti-parallel displacement of Pb2+ gradually weaken and then

altogether disappear for x ≥ 0.15. However, the super lattice reflections corresponding

to B-site ordering are retained indicating doubling of unit cell. This also indicates that

Ba2+ substitution does not considerably affect the B-site ordering. The symmetry

changes from orthorhombic symmetry with space group Pnam to cubic symmetry

with space group Fm3m. The transition from orthorhombic to cubic occurs near x =

0.15 of Ba2+ in contradiction to x = 0.12 of Ba2+ content as observed by Choo and Kim

(1992). With the increase in Ba2+ concentration, the anti-ferroelectric

Pb(Yb0.5Nb0.5)O3 undergoes transition from anti-ferroelectric to ferroelectric to

relaxor ferroelectric with diffused phase transition, which is evident from the

hysteresis measurements (Choo and Kim (1992)). The indexing of the reflections is

carried out qualitatively basing on the work of Kwon et al (1991) and Kim et al

(2001).

2.2.3 Synthesis and structural studies of La3+ substituted Pb(Yb0.5Nb0.5)O3

Ceramic samples with the chemical formula (Pb1-xLax)(Yb(1+x)/2Nb(1-x)/2)O3 for x=0.01,

0.02 and 0.04 (hereafter referred to PLYN1, PLYN2 and PLYN3 respectively) were

prepared by reacting the stoichiometric proportions of high pure chemicals La2O3,

PbO, Yb2O3 and Nb2O5 using single-step method. Double calcination step was

followed to ensure formation of homogeneous and single phase. Calcination was

carried out around 900 - 950 oC for 2 hrs twice, thus totally for 4 hrs. Once the phase

was confirmed the pellets were sintered around 1150 -1200 oC for 2 hrs. At each stage

of calcination and final sintering the phases were confirmed with XRD. XRD of the

72

sintered compounds is given in Fig 2.7. The calcination and sintering temperatures,

lattice parameters and density are given in Table 2.2. Similar to PYN the XRD

consists of the reflections corresponding to anti-parallel displacement of Pb2+ and F

reflections corresponding to B-site ordering. The reflections are retained for all the

compositions studied.

2.2.4 Synthesis and structural studies of La3+ and Ba2+ substituted

Pb(Yb0.5Nb0.5)O3 La3+ and Ba2+ substituted Pb(Yb0.5Nb0.5)O3 compounds (Pb1-xBa0.04Lax)(Yb(1+x)/2Nb(1-

x)/2)O3 for x=0.01, 0.02 and 0.04 (hereafter referred as PBLYN1, PBLYN2 and

PBLYN3 respectively) were synthesized in single-step method. The starting reagents

BaCO3, La2O3, PbO, Yb2O3 and Nb2O5 were taken in stoichiometric proportions for

preparation of the compositions to study the low frequency dielectric properties.

Calcination was carried out around 900 -950 oC for 2 hrs. Addition of Ba2+ ensures

formation of single phase in single calcination step in contradiction to La3+

substitution alone. Pellets were sintered around 1150 - 1200 oC for 2 hrs. XRD of the

sintered compounds is given in Fig 2.7. There is shift in the peaks from PLYN1,

PLYN2 and PLYN3 corresponding to the substitution of Ba2+. The calcination and

sintering temperatures, lattice parameters and density are given in Table 2.2. The

reflections corresponding to anti-parallel displacement of Pb2+ and F reflections

corresponding to B-site ordering are retained for all the compositions studied as can

be observed from XRD similar to PBYN1.

2.3 SYNTHESIS AND STRUCTURAL STUDIES OF Pb(Fe0.5Nb0.5)O3

Synthesis of Pb(Fe0.5Nb0.5)O3 was carried out using conventional solid-state reaction

route following the two-step method proposed by Swartz and Shrout (1982). Fe2O3

73

10 20 30 40 50 60

.... ooo oooo

(1 1

2 2)

(280

)

(202

)

(080

)

(140

)

Inte

nsity

(a.u

.)

PLYN1

2θ (deg)

(1 1

2 2)

(280

)

(202

)(080

)

(140

)

PBLYN1

(1 1

2 2)

(280

)

(202

)

(080

)

(140

)

PLYN3

(1 1

2 2)

(280

)

(202

)

(080

)

(140

)

PLYN2

(1 1

2 2)

(280

)

(202

)

(080

)

(140

)

PBLYN2

(1 1

2 2)

(280

)

(202

)(080

)

(140

)

PBLYN3

Fig. 2.7 X-ray diffractograms of the La3+ substituted Pb(Yb0.5Nb0.5)O3 and La3+ and

Ba2+ substituted PYN for x = 0.01, 0.02 and 0.04 at room temperature; O- Superlattice reflection corresponding to anti-parallel displacement of Pb2+ cations, -F-reflection due to B-site ordering.

74

and Nb2O5 were taken in stoichiometric ratio to form FeNbO4 and calcined at 1000

oC for 4 hrs. FeNbO4 and PbO taken in stoichiometric proportions to form

Pb(Fe0.5Nb0.5)O3 were calcined at 700 oC for 3 hrs. The pellets were sintered at 1000,

1050, 1100 and 1150 oC (Hereafter referred as PFN1, PFN2, PFN3 and PFN4

respectively) for 2 hrs. XRD of the sintered compounds is given in Fig 2.8. No peaks

corresponding to secondary phase or ordering in B-site are observed. Here the phase

of Pb(Fe0.5Nb0.5)O3 is observed to be cubic perovskite according to JCPDS (35-522)

and no peak splitting corresponding to rhombohedral symmetry is present. The result

is in accordance to the observations of Ananta and Thomas (1999). The samples are

annealed at 800 oC for 12 hrs. No change is observed in the phase of the samples. The

XRD of the samples is given in Fig 2.9. The densities before and after annealing,

lattice parameters are given in Table 2.3.

The same samples of each composition prepared under identical conditions are used

for characterization. Pellets of nearly10 mm diameter and 1mm thickness are used for

the dielectric measurements at low frequencies and Raman study. For microwave

studies the sintered pellets are reduced to 3 mm diameter and 1 mm thickness with

polishing machine using fine emery sheets.

For dielectric measurements, the faces of the cylindrical sample are polished for

parallel faces and annealed at 500 oC to remove the strain due to polishing. Silver

paint for electrical contacts is applied to the parallel faces of the pellet and dried at

500 oC for 10 minutes.

75

10 20 30 40 50 60 70 80

(310

)(3

10)

(310

)(3

10)

(220

)

(211

)

(200

)

(111

)

(110

)

(100

)

1150 oC

(220

)

(211

)

(200

)

(111

)

(110

)

(100

)

1000 oC

2θ (deg)

(220

)

(211

)

(200

)

(111

)

(110

)

(100

)

1050 oC

Inte

nsity

(arb

. uni

ts)

(220

)

(211

)

(200

)

(111

)

(110

)

(100

)

1100 oC

Fig. 2.8 X-ray diffractograms of PFN sintered at different temperatures 1000 °C (PFN1), 1050 °C (PFN2), 1100 °C (PFN3) and 1150 °C (PFN4).

76

10 20 30 40 50 60 70 80

(310

)(3

10)

(310

)(3

10)

(220

)

(211

)

(200

)

(111

)

(110

)

(100

)

1150 oC

(220

)

(211

)

(200

)

(111

)

(110

)

(100

)

1000 oC

2θ (deg)

(220

)

(211

)

(200

)

(111

)

(110

)

(100

)

1050 oC

Inte

nsity

(arb

. uni

ts)

(220

)

(211

)

(200

)

(111

)

(110

)

(100

)

1100 oC

Fig. 2.9 X-ray diffractograms of PFN samples after annealing in oxygen atmosphere.

77

Table 2.3 Calcination, sintering temperatures, lattice parameters PFN sintered at different temperatures and relative density of the samples before and after annealing in oxygen atmosphere.

Sample code (before annealing)


Lattice parameters (Å)

Relative density before annealing (%)

Sample code (after annealing)

Relative density after annealing (%)

PFN1 1000 4.01 93 PFN1a 92

PFN2 1050 4.01 97 PFN2a 89

PFN3 1100 4.01 96 PFN3a 95

PFN4 1150 4.01 97 PFN4a 90

Thus in the present chapter, the synthesis methods followed to obtain single

phase of the compounds without any secondary phase are discussed. The

configuration suitable for calcination and sintering of lead-based compounds and the

usage of packing powder to compensate PbO loss are discussed. Basing on the

nature of the compound single or double or triple step is followed. Wherever

necessary double calcination step is followed to ensure formation of the phase.

78

CHAPTER 3

DIELECTRIC PROPERTIES OF Pb(Fe0.5Nb0.5)O3

The present chapter deals with the effect of sintering temperature and annealing on the

low frequency dielectric characterization of Pb(Fe0.5Nb0.5)O3. The dielectric behaviour

of the compounds is analysed in terms of presence of Fe2+ and Fe3+ and possible

confirmation with the resistivity and density measurements. In Section 3.1, the

experimental arrangement used for the low frequency measurements is explained and

Section 3.2 presents the experimental results followed by the analysis.

3.1. LOW FREQUENCY DIELECTRIC MEASUREMENTS

Low frequency dielectric measurements were carried out using the two-probe set-up

shown in Fig 3.1. The chamber used for the measurements was evacuated and filled

with helium gas before commencement of the measurements to avoid adsorption of

moisture on the surface of the sample. Temperature variation of dielectric response

was carried out at various frequencies viz., 0.1, 1, 5, 10, 25, 50, 100, 150 and 200 kHz.

Zentech - 1061 LCZ meter was used to measure the dielectric constant. The

arrangement can be used for a wide temperature range from 123 to 773 K. The

temperature was controlled using computer - Keithley nano-voltmeter - relay

arrangement up to an

79

Fig. 3.1 (a) The experimental set-up used for low frequency dielectric measurements.

80

Fig. 3.1 (b) The holder used for low frequency dielectric measurements.

81

accuracy of 0.1 K. Measurements were recorded for every 1 K. Samples were

subjected to several cooling and heating cycles for the measurement to be consistent.

3.2 LOW FREQUENCY DIELECTRIC STUDIES ON Pb(Fe0.5Nb0.5)O3

Lead Iron Niobate, Pb(Fe0.5Nb0.5)O3 (PFN), belonging to the complex perovskite

family of structures, exhibits frequency dependent dielectric properties. The very low

reactivity with silver (Lu and Lin (1997)), low sintering temperatures, easy

synthesizability and high permittivity of PFN make it a very interesting component in

the commercial electro ceramic materials. The possibility of existence of Fe in

multiple valences makes it a system of academic interest also. Mössbauer studies

carried out on pure PFN by Darlington (1991) showed the existence of only Fe3+

whereas Wang et al (1994) reported the existence of both Fe2+ and Fe3+ but doping a

little concentration of Mn resulted in only Fe3+. This factor of possibility of presence

of Fe3+/Fe2+ results in high conductivity in Fe-based systems and hence dissipation

factor, tanδ, is very high. The dielectric behaviour of these compounds might also

depend on the preparation conditions. Yokosuka (1993) observed that the sintering

temperature and other parameters significantly influence the resistivity and dielectric

properties. Ichinose and Kato (1994) also made a similar observation that annealing in

different atmospheres results a drastic change in the dielectric response. In a similar

material, Ba(Fe0.5Nb0.5)O3 (BFN), Yokosuka (1995) and Saha and Sinha (2002)

reported different kinds of dielectric dispersion. Yokosuka (1995) explained the

dielectric dispersion on the basis of the interfacial polarization model assuming the

coexistence of Fe2+ and Fe3+ at the interfaces of the grain boundary. Saha and Sinha

(2002) on the other hand, explained dielectric dispersion on the basis of the

characteristic relaxor type ferroelectric and their Mössbauer studies indicated the

presence of Fe3+ only. Hence the dielectric dispersion in Pb(Fe0.5Nb0.5)O3 and related

materials mainly depends on the synthesising conditions and the presence of Fe3+

82

and/or Fe2+. Sintering temperature and annealing the sintered samples in oxygen

atmosphere are chosen as the parameters to study and compare the variation in

dielectric characteristics.

To study the effect of sintering on the coexistence of Fe3+ and Fe2+ on the dielectric

dispersion, dielectric measurements on the four Pb(Fe0.5Nb0.5)O3 samples sintered at

1000, 1050, 1100 and 1150 oC are carried out. Temperature variation of dielectric

response at various frequencies viz., 0.1, 1, 5, 10, 25, 50, 100, 150 and 200 kHz is

carried out. Figure 3.2 shows the temperature dependence of the dielectric dispersion

for the samples PFN1, PFN2, PFN3 and PFN4 respectively. Table 3.1 gives Tmax (the

temperature at which the dielectric constant (ε′) is maximum for a given frequency)

frequency dependence. Even though a diffused transition is observed, there is no shift

of Tmax or T′max (the temperature corresponding to maximum value of ε′′) with

frequency. This indicates that all these samples do not exhibit the features of classical

relaxor behaviour. Randall and Bhalla (1989, 1990) indicated that there should exist

an ordering in B-site in nano-scale for observing the shift of Tmax with frequency i.e.,

to observe the classical relaxor behaviour. The dielectric response and XRD in the

present study (Chapter 2, Figs 2.8 and 2.9) are in accordance to this and do not

indicate any B-site ordering for Pb(Fe1/2Nb1/2)O3.

To explain the very high increase in dielectric constant and dissipation factor with

temperature, two different factors can be proposed. Any residual content of FeNbO4

leads to high conductivity with temperature since the compound exhibits

semiconductor

83

0

10000

20000

30000

40000

50000

60000

300 325 350 375 400 425

0

40000

80000

120000

160000

1000 oC

ε'

0.1 kHz 1 kHz 5 kHz 10 kHz 25 kHz 50 kHz 100 kHz 150 kHz 200 kHz

ε''

Temperature (K)


Fig. 3.2 (a) Temperature dependence of ε′ and ε″ of PFN sintered at 1000 oC at various frequencies.

84

0

20000

40000

60000

80000

300 315 330 345 360 375 390 405 420

0

40000

80000

120000

160000

1050 oC


ε'


ε''

Temperature (K)

Fig. 3.2 (b) Temperature dependence of ε′ and ε″ of PFN sintered at 1050 oC at various frequencies.

85

0

10000

20000

30000

40000

50000

60000

300 325 350 375 400 4250

20000

40000

60000

1100 oC


ε'


ε''

Temperature (K)

Fig. 3.2 (c) Temperature dependence of ε′ and ε″ of PFN sintered at 1100 oC at various frequencies.

86

0

15000

30000

45000

60000

75000

90000

300 325 350 375 400 425

0

100000

200000

300000

1150 oC


ε'


ε''

Temperature (K)

Fig. 3.2 (d) Temperature dependence of ε′ and ε″ of PFN sintered at 1150 oC at

various frequencies.

87

Table 3.1 Frequency variation of Tmax for all the sintered samples before annealing and for PFN1 after annealing.

Temperature Tmax (K)

Frequency

(kHz)

PFN1 PFN1a

(1000 °C)

PFN2

(1050 °C)

PFN3

(1100 °C)

PFN4

(1150 °C)

0.1 - 401 405 400 -

1 396 403 403 399 404

5 395 409 403 399 401

10 395 411 403 399 401

25 394 416 402 399 400

50 394 417 402 399 400

100 394 417 402 398 400

150 394 414 402 398 400

200 394 413 402 398 400

properties (Schmidbauer and Schneider (1997)). The other factor is the co-existence

of Fe2+ and Fe3+ ions on equivalent crystallographic sites leading to electron hopping

type of conduction at lower frequencies. In the present case, the results are discussed

considering the variation in the ratio of divalent and trivalent iron since within the

resolution of XRD (Chapter 2, Figs 2.8 and 2.9), the structure was single cubic

perovskite and no extra peaks were observed.

Ananta and Thomas (1999) observed a monotonous increase in the dielectric constant

and dissipation factor with increase in sintering temperature. In our study though an

increase is seen, it is not as high as in the earlier reported case. It can be observed that

for a given single sintering temperature, the transition is diffusive at low frequencies

and with increase in frequency it becomes sharp. It can be observed from Fig 3.1 that

ε″ is high at low frequencies for all the samples.

From the dielectric response (in all the cases except for the sample sintered at 1100

oC), it is observed that the dielectric constant and loss increases with increase in the

88

sintering temperature. This can be due to the increase in the concentration of divalent

iron. Annealing these sintered samples in oxygen atmosphere is expected to increase

the amount of Fe3+. Therefore, the dielectric dispersion studies are carried out on the

samples annealed at 800 oC for 12 hrs in oxygen atmosphere.

Figure 3.3 shows the temperature variation of real and imaginary parts of relative

permittivity for frequency region between 0.1 and 200 kHz for the annealed samples

(PFN1a, PFN2a, PFN3a, and PFN4a). It may be inferred that Tmax shifts to higher

temperatures after annealing. It may also be noted that though Tmax shifts with

frequency for PFN1a, it could not be considered as a relaxor type of variation, since

there is no consistent variation in ε′′ with frequency.

Annealing is found to decrease both dielectric constant and loss considerably. This is

in contrast to the reports of Dhirendra Mohan et al (2001). In their study it was

observed that the dielectric constant increases on annealing. They attributed the factor

to removal of excess of lead from the grain boundaries, which improved the dielectric

constant. However since the annealing is carried out at a lower temperature, i.e., 800

oC in the present case rather than at 1000 oC as reported the increase is not found.

Therefore, the change in the dielectric response due to annealing is explained as

below.

At 100 Hz, the maximum value of ε′ and ε′′ decreases by 4 and 50 times respectively

for sample PFN1. Similarly, in the case of PFN2, ε′ falls by 10 times and ε′′ falls by

26 times. For PFN3, ε′ value reduces by 3.5 times and ε′′ reduces by 2 times. The

89

2000

4000

6000

8000

10000

12000

14000

300 325 350 375 400 425

0

500

1000

1500

2000

2500

3000

PFN1a

ε'

0.1 kHz 1kHz 5kHz 10kHz 25kHz 50kHz 100kHz 150kHz 200kHz

PFN1a

ε''

Temperature (K)

0.1 kHz 1kHz 5kHz 10kHz 25kHz 50kHz 100kHz 150kHz 200kHz

Fig. 3.3 (a) Temperature dependence of ε′ and ε″ of PFN1a (PFN sintered at 1000 oC)

at various frequencies.

90

0

2000

4000

6000

8000

300 325 350 375 400 425

0

2000

4000

6000

PFN2a

ε'


PFN2a

ε''

Temperature (K)


Fig. 3.3 (b) Temperature dependence of ε′ and ε″ of PFN2a (PFN sintered at 1050 oC)


91

0

5000

10000

15000

20000

300 325 350 375 400 425

0

10000

20000

30000

40000

PFN3a

ε'


PFN3a

ε''

Temperature (K)


Fig. 3.3 (c) Temperature dependence of ε′ and ε″ of PFN3a (PFN sintered at 1100 oC) at various frequencies.

92

0

2000

4000

6000

8000

300 325 350 375 400 425

0

5000

10000

15000

20000

PFN4a

ε'

0.1 kHz 1 kHz 5 kHz 10 kHz 25 khz 50 kHz 100 kHz 150 kHz 200 kHz

PFN4a

ε''

Temperature (K)

0.1 kHz 1 kHz 5 kHz 10 kHz 25 khz 50 kHz 100 kHz 150 kHz 200 kHz

Fig. 3.3 (d) Temperature dependence of ε′ and ε″ of PFN4a (PFN sintered at 1150 oC)


93

value of ε′ decreases by 11 times and ε′′ falls nearly by 16 times for PFN4.

Moreover, T′max shifts to higher temperatures for PFN1a.

The common feature observed for all the compositions before and after annealing is

that both dielectric constant and loss increase drastically for 0.1 kHz compared to

other frequencies. The increase is observed more in the case of dielectric loss. The

difference between 0.1 kHz and higher frequencies increases with increase in

sintering temperature, with maximum difference being observed for PFN4 and

PFN4a. The difference between the lower and higher frequencies is prominent for

samples that are not annealed. The increase of loss with temperature is probably due

to increase in hopping conduction with temperature. This is mainly due to the

coexistence of divalent and trivalent iron. The formation of divalent iron increases

with increase in sintering temperature, which is evident from the increasing difference

in 0.1 kHz and higher frequency response with sintering temperature. Annealing in

oxygen atmosphere reduces the concentration of divalent iron. The difference in the

response between the samples annealed and that not annealed indicate that the

dielectric dispersion in PFN is dependent on the ratio of divalent and trivalent iron.

This is in accordance with the mechanism proposed by Ananta and Thomas. The

mechanism for formation of Fe2+ is

Fe3++e- ⇔ Fe2+.

Resistivity measurements further illustrate the difference in the conduction, due to the

simultaneous existence of both oxidation states, because of annealing. The values are

tabulated in Table 3.2. The increase in the resistivity by an order on annealing

explains the decrease in magnitudes of ε′ and ε″ after annealing. This indicates that all

the samples possess Fe2+ and Fe3+ and annealing the samples in oxygen atmosphere

decreases the ratio between the concentration of Fe2+ and Fe3+. The ratio between the

94

Table 3.2 Variation in resistivity of the Pb(Fe0.5Nb0.5)O3 samples before and after

annealing

Sample code

Sintering temperature

(°C)

Resistivity before annealing (ρ)

Ω.cm

Sample code

Resistivity after annealing (ρa)

Ω.cm

Ratio between resistivities

(ρa/ρ) PFN1 1000 3.7x104 PFN1a 5.0x105 13.5

PFN2 1050 5.6x104 PFN2a 6.0x105 10.7

PFN3 1100 2.4x104 PFN3a 1.0x105 4.2

PFN4 1150 1.0x104 PFN4a 2.5x105 25.0

resistivity before and after annealing is very high for sample PFN4. While considering

the change in the dielectric response due to annealing, it is also essential to take into

account the effect of the change in the density (Chapter 2, Table 2.3). It is well known

that the decrease in the density results in an increase in the resistivity and decrease in

the dielectric constant since the connectivity between the grains decreases. The

density variation between PFN1 and PFN1a, PFN3 and PFN3a is not appreciable

whereas the variation in the density between PFN2 and PFN2a, PFN4 and PFN4a is

appreciable (Table 2.3). Hence, the observed variation in the dielectric dispersion in

the case of PFN1a and PFN3a is mainly due to the change in the oxidation state of

iron. It may also be inferred that the observed variation in the dielectric dispersion for

PFN2a and PFN4a is due to both the decrease in the density and the change in the

oxidation state of iron. This is clear from the observed data, which indicates the fall

in magnitudes of ε′ and ε′′ is more for PFN2a and PFN4a compared to other two

samples.

The possible conclusions drawn from the dielectric, room temperature resistivity

and density measurements are summarised as follows. The dielectric constant as

well dielectric loss were found to increase with increase in sintering temperature

(except for sample sintered at 1100 oC). This is attributed to increase in Fe2+ with

95

sintering temperature. On annealing the samples in oxygen atmosphere it is observed

that the dielectric constant as well dielectric loss decreased for all the samples. The

resistivity of the samples also came down by one order indicating that there was a

variation in Fe2+/Fe3+ ratio. The decrease in the dielectric parameter in two of the

samples (PFN1 and PFN3) might be mainly due to change in the ratio between Fe2+

and Fe3+ whereas in the other two samples (PFN2 and PFN4) decrease in the

dielectric parameter might be attributed to both density and the ration between Fe2+

and Fe3+.

96

CHAPTER 4

DIELECTRIC PROPERTIES OF PZN BASED COMPOUNDS

AND PYN BASED COMPOUNDS

The chapter deals with the dielectric characterization of Ba2+ and Sr2+ substituted

Pb(Zn1/3Nb2/3)O3, Ba2+ substituted Pb(Yb0.5Nb0.5)O3, La3+ substituted

Pb(Yb0.5Nb0.5)O3 and La3+ substituted (Pb0.96Ba0.04)(Yb0.5Nb0.5)O3. Section 4.1 deals

with experimental results obtained for Pb(Zn1/3Nb2/3)O3 based compounds followed

by the analysis using the relations and the model proposed by Cheng et al (1997,

1998) discussed in Chapter 1. Section 4.2 discusses the low frequency dielectric

properties of Pb(Yb0.5Nb0.5)O3 based compounds. Finally, Section 4.3 presents results

and discussions on the dielectric measurements carried out in the high frequency

region.

4.1. DIELECTRIC RESPONSE OF Pb(Zn1/3Nb2/3)O3 BASED SAMPLES The dielectric measurements were carried out in the temperature range 123 to 423 K

using the experimental set-up discussed in Chapter 3, Section 3.1. The low frequency

dielectric response of the four compositions is shown in Figs 4.1 and 4.2. Only five

frequencies are shown for representation. The temperature corresponding to

maximum value of real part of dielectric constant, Tmax, and the temperature

corresponding to maximum value of imaginary part of dielectric constant, T′max,

increases with increase in frequency. T′max is less in magnitude compared to Tmax for a

given frequency. The peak value corresponding to real part of dielectric constant

maximum ε′max decreases with increase in frequency. The peak value of dielectric

loss, ε″max increases with increase in frequency. These features indicate that the

97

100 150 200 250 300 350 400 4500

500

1000

1500

2000

2500

3000

100 150 200 250 300 350 400 4500

50

100

150

200

250

100 150 200 250 300 350 400 450200

400

600

800

1000

1200

1400

100 150 200 250 300 350 400 4500

20

40

60

80

100

ε'

x = 0.2 Ba2+

ε'

Temperature (K)

1 kHz 10 kHz 100 kHz 150 kHz 200 kHz

x = 0.2 Ba2+


ε''

Temperature (K)


x = 0.3 Ba2+

Temperature (K)

1 kHz 10 kHz 100 kHz 150 kHz 200 kHzε''

x = 0.3 Ba2+

Temperature (K)

Fig. 4.1 Temperature dependence of ε′ and ε″ of (Pb1-xBax)(Zn1/3Nb2/3)O3 for x = 0.2 and 0.3 at various frequencies.

98

100 200 300 400

400

500

600

700

800

900

100 200 300 400

0

10

20

30

40

50

100 200 300 400 500200

400

600

800

1000

1200

1400

1600

1800

2000

2200

100 200 300 400 500

0

20

40

60

80

100

120

140

160

x = 0.3 Sr2+

Temperature (K)


ε'' x = 0.3 Sr 2+

Temperature (K)



ε'

x = 0.2 Sr2+

ε'

Temperature (K)


ε''

x = 0.2 Sr2+

Temperature (K)

Fig. 4.2 Temperature dependence of ε′ and ε″ of (Pb1-xSrx)(Zn1/3Nb2/3)O3 for x = 0.2 and 0.3 at various frequencies.

99

relaxor nature is retained in PBZN and PSZN for the compositions studied. It is

observed that addition of Ba2+ and Sr2+ decreases not only the maximum value of

dielectric constant but also shifts the Tmax to the lower temperature. The variation in

Tmax with frequency is tabulated in Table 4.1 for all the compositions.

The 9 pairs of (ω, Tmax) for the measured frequencies are analysed using Levenberg-

Marquardt non-linear fitting to Eqns (1.1) and (1.2) given in chapter 1 as shown in

Figs 4.3 and 4.4 to solve for To, ωo, Tf and p. The results are tabulated in Table 4.2. It

can be seen that ωo obtained from V-F law for PBZN is in the expected range but for

PSZN it is higher. Even though, ωo is in the expected range for Ba2+ based

compounds, it is seen from the Table 4.2 that the activation energies for all the

compositions are high and erroneous for a thermally activated system. Hence V-F

relation does not give acceptable parameters that represent the relaxor behaviour for

the compositions studied. Cheng et al (1996) observed a similar contradiction. The

values of ωo and To obtained for the four compositions from the power law are quite

reasonable for a thermally activated system. Hence the Eqn (1.2) correctly describes

the relaxation phenomena of the studied compositions.

The theoretical model mentioned in chapter 1 proposed by Cheng and Katiyar (1997,

1998a, 1998b) is used to describe the variation in the relaxor nature of the PBZN1,

PBZN2, PSZN1 and PSZN2. The linear fit between logarithm of probing frequency

and ε′ is given in Fig 4.5 for two temperatures. From the linear fit at different

temperatures in the region well below Tmax, A and B are obtained from the slope and

intercept respectively. The A vs B plot (Fig 4.6) gives ε∞ and ωo. The intrinsic

parameter A follows the super-exponential relation given in Eqn (1.9) as can be

100

6 8 10 12 14

4.4

4.6

4.8

5.0

6 8 10 12 14

4.4

4.6

4.8

5.0

6 8 10 12 143.6

3.7

3.8

3.9

4.0

4.1

6 8 10 12 143.6

3.7

3.8

3.9

4.0

4.1

1000

/T

x = 0.3 Ba2+

power law

ln ω

expt fit

x = 0.3 Ba3+

VF Law

ln ω

expt fit

x = 0.2 Ba2+

V-F Law10

00/T

max

ln(ω)

expt fit

ln(ω)

expt fit

x = 0.2 Ba2+

Power Law

Fig. 4.3 V-F law and Power law fit for the frequency dependent Tmax (Pb1-xBax)(Zn1/3Nb2/3)O3 for x = 0.2 and 0.3.

101

6 8 10 12 144.8

5.0

5.2

5.4

5.6

6 8 10 12 144.2

4.3

4.4

4.5

4.6

4.7

6 8 10 12 144.2

4.3

4.4

4.5

4.6

4.7

6 8 10 12 144.8

5.0

5.2

5.4

5.6

x = 0.3 Sr2+

Power law

ln (ω)

expt fit

ln (ω)

1000

/Tm

axx = 0.2 Sr2+

V-F law

expt fit

ln (ω)

x = 0.2 Sr2+

Power law

expt fit

ln (ω)

1000

/Tm

ax

expt fit

x = 0.3 Sr2+

V-F law

Fig. 4.4 V-F law and Power law fit for the frequency dependent Tmax (Pb1-xSrx)(Zn1/3Nb2/3)O3 for x = 0.2 and 0.3.

102

Table 4.1 Frequency dependence of Tmax of ε′ of (Pb1-xSrx)(Zn1/3Nb2/3)O3 and (Pb1- xSrx)(Zn1/3Nb2/3)O3 for x = 0.2 and 0.3.

Table 4.2 The values of ωo (Hz), To (K), Tf (K) and p obtained from V-F law and

power law (Eqns (1.1) and (1.2).) for (Pb1-xSrx)(Zn1/3Nb2/3)O3 and (Pb1-

xSrx)(Zn1/3Nb2/3)O3 for x = 0.2 and 0.3. Composition ωo (Hz)

Eqn (1.1) Eqn (1.2)

To (K)

Eqn (1.1) Eqn (1.2)

Tf (K)

Eqn (1.1)

p

Eqn (1.2)

x = 0.2 Ba2+ 4.7 x 1010 2.10 x 108 574 318 216 10.12

x = 0.3 Ba2+ 5.3 x 1012 3.71 x 109 1176 331 151 5.60

x = 0.2 Sr2+ 1.6 x 1016 3.86 x 1011 1955 385 150 5.12

x = 0.3 Sr2+ 4 .0x 1017 1.12 x 1013 2665 467 105 3.36

Tmax (K) Frequency

(kHz) x = 0.2

Ba2+

x = 0.3

Ba2+

x = 0.2

Sr2+

x = 0.3

Sr2+

0.1 250 204 214 183

1 253 208 219 189

5 256 213 223 193

10 258 215 225 196

25 261 219 228 198

50 266 224 230 201

100 268 225 232 204

150 269 227 234 204

200 270 228 235 205

103

8 10 12 14400

600

800

1000

1200

6 8 10 12 14 16400

800

1200

1600

2000

2400

4 6 8 10 12 14 16360

400

440

480

520

560

4 6 8 10 12 14 16350

400

450

500

550

600

650

ln (ω)

ε'

x = 0.3 Ba2+

Expt. data fit

140 K

180 K

ln (ω)

ε'

x = 0.2 Ba2+

140 K

210 K

Expt. data fit

ln (ω)

ε'

Expt. data fit

x = 0.2 Sr2+

117 K

101 K

ln (ω)

ε'

Expt. data fit

x = 0.3 Sr2+

138 K

99 K

Fig. 4.5 Frequency dependence of ε′ for (Pb1-xBax)(Zn1/3Nb2/3)O3 for x = 0.2 and 0.3 and (Pb1-xSrx)(Zn1/3Nb2/3)O3 for x = 0.2 and 0.3 at different temperatures.

104

10 20 30 40400

600

800

1000

1200

1400

10 20 30400

600

800

1000

1200

0 40 80 120 1600

1000

2000

3000

4000

0 20 40 600

400

800

1200

1600

x = 0.2 Sr2+B(

T)

A(T)

Expt. data fit

Expt. data fit

A(T)

B(T)

x = 0.3 Sr3+

x = 0.2 Ba2+

B(T

)

Expt. data fit

A(T)

x = 0.3 Ba2+

A(T)

B(T

)

Expt. data fit

Fig. 4.6 Linear relation between A and B for (Pb1-xSrx)(Zn1/3Nb2/3)O3 for x = 0.2 and 0.3 and (Pb1-xBax)(Zn1/3Nb2/3)O3 for x = 0.2 and 0.3.

105

observed in Fig 4.7. The values of α1, β1 and δ obtained from the non-linear fit are

tabulated in Table 4.3. The exponential relation is used for the temperature region

above Tmax and α and β are tabulated in Table 4.3.

Table 4.3 The values of ε∞ , ω0(Hz), α1, β1, δ, α and β obtained from Eqns (1.9) and

(1.11) for (Pb1-xBax)(Zn1/3Nb2/3)O3 and (Pb1- xSrx)(Zn1/3Nb2/3)O3 for x = 0.2 and 0.3.

Composition ε∞ ω0(Hz) α1 β1 δ α β

x = 0.2 Ba2+ 256.3 1.25 x 1010 0.98 90.2 0.6 9.84 0.00677

x = 0.3 Ba2+ 212.7 1.18 x 1010 0.151 55.12 0.23 8.19 0.0041

x = 0.2 Sr2+ 238.2 1.8 x 1012 1.87015 127.7 1.78 8.96 0.0053

x = 0.3 Sr2+ 197 2 x 1015 1.72737 142.5 1.59 7.53 0.003

Figure 4.8 shows the fit for the entire temperature range for the frequency 100 kHz. It

can be observed that there exists discrepancy around Tmax whenever the response is

broad as for PBZN1 and PBZN2. Table 4.4 gives the parameters D1 and D2 for the

compositions for all the frequencies. D1 and D2 do not follow any regular trend with

frequency. The values of m and n tabulated in Table 4.5 remain approximately the

same in the entire frequency range.

From Table 4.1 it can be observed the shift in Tmax for the Sr2+ substituted compounds

is more than Ba2+ substituted compounds from Pb(Zn1/3Nb2/3)O3. It can also be

observed from Figs 4.1 and 4.2 that ε′ is less for the Sr2+ compositions. The pre-

exponential factor ωo of the Eqn 1.2 gives an idea about the size and the degree of

interaction between the polar clusters in relaxor ferroelectric materials. From Table

4.2, it is clear that the value of ωo is consistently

106

80 100 120 140 160

10

20

30

40

80 100 120 140 160 1805

10

15

20

25

30

90 120 150 180 2100

40

80

120

100 120 140 160 18010

20

30

40

50A(

T)A(

T)

x = 0.2 Sr2+

A(T)

Expt. data fit

x = 0.3 Sr2+

Expt. data fit

Temperature (K)Temperature (K)

x = 0.2 Ba2+

A(T)

Temperature (K)

Expt. data fit

x = 0.3 Ba2+

Temperature (K)

Expt. data fit

Fig. 4.7 Fit of temperature dependence of A for (Pb1-xSrx)(Zn1/3Nb2/3)O3 for x = 0.2 and 0.3 and (Pb1-xBax)(Zn1/3Nb2/3)O3 for x = 0.2 and 0.3

107

100 200 300 400 500400

800

1200

1600

2000

100 200 300 400 500400

500

600

700

800

900

100 200 300 400 5000

500

1000

1500

2000

2500

3000

100 200 300 400 500

400

600

800

1000

1200

1400

ε'

expt. data fit

x = 0.2 Sr2+ε'

expt. data fit

x = 0.3 Sr2+

expt. data fit

x = 0.2 Ba2+

Temperature (K)

x = 0.3 Ba2+

Temperature (K)

expt. data fit

Fig. 4.8 Theoretical fit of the experimental data for temperature variation of ε′ at 100 kHz for (Pb1-xSrx)(Zn1/3Nb2/3)O3 for x = 0.2 and 0.3 and (Pb1-

xBax)(Zn1/3Nb2/3)O3 for x = 0.2 and 0.3.

108

Table 4.4 The values of D1 and D2 obtained from Eqns 1.14(a) and 1.14(b).

Frequency

(kHz)

x = 0.2 Ba2+

D1 D2

x = 0.3 Ba2+

D1 D2

x = 0.2 Sr2+

D1 D2

x = 0.3 Sr2+

D1 D2

1 13.36 0.39 9.3 0.41 4.2 0.67 6.15 0.36

10 14.37 0.35 5.5 0.31 3.8 0.61 7.58 0.32

100 17.98 0.25 1.01 347 1.22 1.05 9.17 0.29

150 18.87 0.24 1.09 82 1.02 1.34 9.35 0.29

200 19 0.23 1.15 50 0.98 1.5 9.6 0.28

Table 4.5 The values of m and n obtained from Eqns 1.14(a) and 1.14(b).

Composition m n

x = 0.2 Ba2+ 1.13 1.54

x = 0.3 Ba2+ 1.15 2.43

x = 0.2 Sr2+ 1.34 1.35

x = 0.3 Sr2+ 1.63 2.19

low for PBZN than for PSZN by two to three orders of magnitude. This indicates that

for PBZN, the size of the polar clusters is large and the interaction between the polar

clusters is stronger than for PSZN. Also the volume fraction of the polar clusters is

higher for PBZN than for PSZN. The large size of the polar clusters results in the

high Tmax and the stronger interaction between them results in a broader response

around Tmax.

It can be observed that though the value of ωo is in acceptable range there exists

discrepancy between the values obtained from the power law and the theoretical

model used. Power law gives averaged response and hence it is difficult to get an

accurate value. But it can be observed that the overall trend remains the same for both

109

power law and the theoretical model and the earlier explanation holds well. From

Table 4.2, it can be noted that the value of p decreases with increase in Ba2+ or Sr2+.

The degree of relaxation increases rapidly between x=0.2 and x=0.3 for PBZN than

for PSZN. The value of p determines the degree of relaxation and hence the rate of

growth of polar clusters. As mentioned earlier, the smaller the value of p, the stronger

the degree of relaxation. This in turn means the smaller rate of growth of polar

clusters. The value of p for same x is lower for PSZN than that of PBZN. This

indicates that the growth of the polar clusters is inhibited more in PSZN than PBZN.

This is further supported by the values of β which indicate the production rate of polar

regions with decreasing temperature is less for the Sr2+ substituted compounds. In the

present case it is seen that δ (Table 4.3) does not signify the change in the degree of

relaxation. With increase in Ba2+ and Sr2+ content the value decreases, which indicate

a decrease in degree of relaxation. However between PBZN and PSZN the degree of

relaxation is high for Sr2+ based compounds. The value of δ for Ba2+ substituted

compounds are almost in the same range as that obtained for 0.87(Pb1-x

Lax/2Kx/2)(Zn1/3Nb2/3)O3-0.8PbTiO3-0.05BaTiO3 with x = 0.04, 0.08, 0.12 whereas for

Sr2+ based compounds the value is high (Cheng et al (1998a)). This indicates that the

degree of relaxation is high in Sr2+ based Pb(Zn1/3Nb2/3)O3 compounds. The fact is

further supported by the value of β which is very low for both Ba2+ and Sr2+

substituted compared to the above said compounds. This indicates that the equivalent

substitution in A-site results in more degree of dielectric relaxation since this does not

involve the space charge effects.

To get more quantitative insight into the differences in the dielectric relaxation

between PBZN and PSZN, it is essential to understand the origin of relaxation process

in relaxor materials. Thomas (1990) proposed a theoretical framework in that indirect

coupling of ferroelectrically active NbO6 octahedra through Pb2+ is important to

110

observe the relaxor behaviour. According to this model, evolution of micro polar

regions (polar clusters) takes place through the indirect coupling of NbO6 through

Pb2+ ion in the unit cell. Butcher and Thomas (1991) applied this theoretical model to

study the variation in relaxation process in Ba2+ substituted Pb(Mg1/3Nb1/3)O3. They

observed that even for the large concentration of Ba2+, the polar micro regions are

retained showing weak relaxor behaviour. From the detailed analysis based on the

computer simulation using the theoretical model and from with the experimental

observation of fall of ε′max, ε″max and Tmax, they inferred that the substitution of

Barium ion prevents coupling of neighbouring NbO6 octahedra to the ferroelectric

network and a decrease in the number of octahedra coupled together in the

ferroelectric network. There is a progressive breakdown of relatively large Pb2+ rich

regions into smaller regions, which is evident from decrease of Tmax with increase in

x. The fact that Pb(Zn1/3Nb1/3)O3 is a relaxor ferroelectric like Pb(Mg1/3Nb1/3)O3

whereas Ba(Zn1/3Nb1/3)O3 and Sr(Zn1/3Nb1/3)O3 (Onada et al (1982) Colla et al

(1993)) are dielectrics signifies the importance of indirect coupling of NbO6 octahedra

through Pb2+. Increase in Ba2+ or Sr2+ for Pb2+ disrupts the coupling and leads to

decrease in volume of micro polar regions. As discussed earlier, the change of ωo

(from Eqn 1.1) with Ba2+ and Sr2+ content reflects the change associated with size and

interaction between the polar clusters. It can be seen from Table 4.1 that for a given

x, Tmax, ε′max and ε″max decrease rapidly for PSZN than PBZN. This indicates that the

decoupling of neighbouring NbO6 octahedra to the ferroelectric network is more for

Sr2+ than for Ba2+. These factors indicate that though relaxor nature is observed in all

the compositions studied, Ba2+ substituted compounds retain the relaxor nature more.

111

4.2 DIELECTRIC RESPONSE OF Pb(Yb0.5Nb0.5)O3 BASED COMPOUNDS

4.2.1 Dielectric Response of Pb(Yb0.5Nb0.5)O3 and (Pb1-xBax)(Yb0.5Nb0.5)O3

The low frequency measurements are carried out as explained earlier. The dielectric

response of the compositions is shown in Fig 4.9. For pure Pb(Yb0.5Nb0.5)O3, the anti-

ferroelectric to paraelectric transition is very sharp (Kwon et al (1991)). Tmax is

frequency independent. It can be observed that with increase in Ba2+ concentration the

dielectric constant increases and the diffuseness in the response around Tmax increases.

From Fig 4.9 it can be seen that with increase in ‘x’, ε′ increases up to x = 0.1 and

then decreases with further increase in ‘x’. This is against the expectations, since

polarisability of Pb2+ is more compared to Ba2+. Choo and Kim (1992) observed

similar behaviour. From hysteresis measurements at room temperature, they attributed

this behaviour to the onset of ferroelectric nature due to the change in the nature of

chemical bonds with increase in volume of unit cell on substitution of Ba2+ for Pb2+.

According to Migoni et al (1976) the driving factor for ferroelectricity in perovskite

oxides is the oxygen polarisability along B-O bond, which in turn strongly depends on

the surroundings. Increase in the unit cell volume leads to increase in polarisability of

O2, which leads to onset of ferroelectricity. However, the observed diffuse phase

transition with further increase in Ba2+ indicates that the coherence length of

ferroelectric order parameter is short ranged. This factor is discussed further in

Chapter 5 dealing with the Raman spectroscopic measurements on this solid solution

series.

It is also observed that the dielectric constant and the rate of increase of dielectric

constant much below Tmax are higher with increase in ‘‘x”. From x = 0.15, the relaxor

properties are predominantly observed (Kim et al (2001), Kim and Choo (2002)).

112

100

200

300

400

500

600

250 300 350 400 450 500 550 600 650-5

0

5

10

15

20

25

30

35

40

PYN

Temperature (K)

ε'



ε''

Fig. 4.9 (a) Temperature dependence of ε′ and ε″ of Pb(Yb0.5Nb0.5)O3 at various frequencies.

113

100

200

300

400

500

600

250 300 350 400 450 500 550 600

0

20

40


x = 0.05 Ba2+

ε'

ε''

Temperature (K)


Fig. 4.9 (b) Temperature dependence of ε′ and ε″ of (Pb1-xBax)(Yb0.5Nb0.5)O3 for x = 0.05 of Ba2+ content at various frequencies.

114

500

600

700

800

900

1000

1100

300 350 400 450

0

5

10

15

20

25

30

35

40

45


x = 0.1 Ba2+

ε'

ε''

Temperature (K)


Fig. 4.9 (c) Temperature dependence of ε′ and ε″ of (Pb1-xBax)(Yb0.5Nb0.5)O3 for x = 0.1 of Ba2+ content at various frequencies.

115

150 200 250 300 350 400 4500

15

30

200

300

400

500

600

700

800

900


ε''

Temperature (K)

x = 0.15 Ba2+

ε'


Fig. 4.9 (d) Temperature dependence of ε′ and ε″ of (Pb1-xBax)(Yb0.5Nb0.5)O3 for x = 0.15 of Ba2+ content at various frequencies.

116

200

300

400

500

600

700

800

900

1000

150 200 250 300 350 400 4500

10

20

30

40

x = 0.2 Ba2+

ε'



ε''

Temperature (K)

Fig. 4.9 (e) Temperature dependence of ε′ and ε″ of (Pb1-xBax)(Yb0.5Nb0.5)O3 for x = 0.2 of Ba2+ content at various frequencies.

117

50 100 150 200 250 300 350 400 450

100

150

200

250

300

350

400

450

500

100 150 200 250 3000

5

10

15

20

25

30

ε'


x = 0.25 Ba2+

Temperature (K)

ε''

10 kHz 100 kHz 150 kHz 200 kHz

Fig. 4.9 (f) Temperature dependence of ε′ and ε″ of (Pb1-xBax)(Yb0.5Nb0.5)O3 for x = 0.25 of Ba2+ content at various frequencies.

118

100 200 300 400100

150

200

250

300

350

100 150 200 250

5

10

15

20


x = 0.3 Ba2+

ε'


Temperature (K)

ε''

Fig. 4.9 (g) Temperature dependence of ε′ and ε″ of (Pb1-xBax)(Yb0.5Nb0.5)O3 for x = 0.3 of Ba2+ content at various frequencies.

119

They are characterized by diffused phase transition around Tmax and frequency

dependent dielectric properties. Tmax and T′max (temperature corresponding to ε′′max)

shift to higher temperatures with increase in frequency. ε′max decreases with increase

in frequency. The temperature T′max is lower than Tmax for a given frequency. ε′′max

increases with increase in frequency.

Table 4.6 The values of ωo (Hz), To (K), Tf (K) and p obtained from V-F law and

power law (Eqns (1.1) and (1.2)) (Pb1-xBax)(Yb0.5Nb0.5)O3.

Composition T0 (K) ω0 (Hz) p x = 0.15 352 4.3x105 84

x = 0.2 363 3.8x107 19

x = 0.25 283 2.5x106 69

x = 0.3 314 2.7x107 12

It can be observed from Table 4.6 that p decreases and ω0 increases with increase in

Ba2+. Very high values are obtained for p and ω0. This can be either due to the fact

that the volume of the domains is large compared to ordinary relaxors since the

transition observed is from anti-ferroelectric to relaxor with increase in Ba2+ content

or power law is not applicable for these compositions. Taking analogy from

(PbxLa1-x)(ZryTi1-y)O3 (Cheng et al (1998)), one can conclude that the law is not

applicable for these compositions. Therefore, the theoretical model cannot be applied

for these compositions. The reasons behind the variation in the anti-ferroelectric to

relaxor ferroelectric are discussed basing on the Raman spectroscopic studies that are

discussed in Chapter 5.

120

4.2.2. Dielectric response of La3+ Substituted Pb(Yb0.5Nb0.5)O3

The low frequency dielectric response is given in Fig 4.10. It is observed that with

substitution of La3+ the diffuseness of the transition around Tmax increases. However

Tmax is not frequency dependent. Fig 4.11 gives the temperature variation of ε′ and ε″

at 100 kHz for the three samples comparing with pure PYN. From Fig. 4.11, it may be

inferred that while there is no regular variation in the ε′ and ε″ with the substitution of

La3+, there is a clear increase in the diffuseness of the dielectric response. The reason

for the diffuseness as observed from the earlier studies can be either due to disordered

nature in B-site or creation of vacancies as in (Pb1-3x/2Lax)(ZryTi1-y)O3 (PLZT) (Xi et

al (1983), Dai and Viehland (1995)). XRD (Chapter2, Fig 2.7) indicates no noticeable

variation in the intensity of the F-reflection indicating B-site ordering is observed.

Therefore, the diffuseness is mainly due to the vacancies created by the substitution of

La3+. In the case of PLZT x/65/35 where x, 65 and 35 are the mol % of La3+, Zr4+ and

Ti4+ respectively, creation of vacancies resulted in the formation of polar micro

regions, which eventually are responsible for the diffuseness in the dielectric response

(Viehland et al (1991), (1992a), (1992b), Tsurumi et al (1994)). This diffuseness

increases with La3+ substitution and for x > 6%, it was possible to experimentally

observe relaxor nature (Dai et al (1993)). Therefore, in the present case also, it is

possible to infer that the creation of vacancies may lead to the polar micro regions.

Probably, at higher concentration of La3+, one may expect to experimentally observe

the relaxor nature of the compound.

121

50

100

150

200

250

300

350

300 350 400 450 500 550 600 650

0.0

2.5

5.0

7.5

x = 0.01 La3+

ε' 10 kHz 100 kHz 150 kHz 200 kHz


ε''

Temperature (K)

Fig. 4.10 (a) Temperature dependence of ε′ and ε″ of (Pb1-xLax)(Yb(1+x)/2Nb(1-x)/2)O3 for x = 0.01 at various frequencies.

122

100

150

200

250

300

350

400

450

250 300 350 400 450 500 550 600 6500

2

4

6

8

10

12


x = 0.02 La3+

ε'


ε''

Temperature (K)

Fig. 4.10 (b) Temperature dependence of ε′ and ε″ of (Pb1-xLax)(Yb(1+x)/2Nb(1-x)/2)O3 for x = 0.02 at various frequencies.

123

250 300 350 400 450 500 550 600 650

0

10

20

30

40

50

100

150

200

250

300

350

400

ε''

Temperatre (K)



x = 0.04 La3+

ε'

Fig. 4.10 (c) Temperature dependence of ε′ and ε″ of (Pb1-xLax)(Yb(1+x)/2Nb(1-x)/2)O3 for x = 0.04 at various frequencies.

124

100

200

300

400

500

250 300 350 400 450 500 550 600 650

0

8

16

24

32

40

Temperature (K)

ε' x = 0 x = 0.01 x = 0.02 x = 0.04

x = 0 x = 0.01 x = 0.02 x = 0.04

ε''

Fig. 4.11 Temperature dependence of ε′ and ε″ at 100 kHz for Pb(Yb0.5Nb0.5)O3, (Pb1-xLax)(Yb(1+x)/2Nb(1-x)/2)O3 for x = 0.01, 0.02 and 0.04.

125

4.2.3. Dielectric Response of La3+ and Ba2+ Substituted Pb(Yb0.5Nb0.5)O3 The low frequency dielectric response is given in Fig 4.12. Tmax is not frequency

dependent. It is observed that with substitution of La3+ the transition around Tmax

becomes sharp. Fig 4.13 presents the temperature variation of ε′ and ε″ for the two

samples in comparison with PBYN1, since the Ba2+ is almost same. Increase in ε′ and

Tmax with increase in La3+ might indicate an induction of ferroelectric nature. The

value of ε″ decreases drastically with the substitution of La3+. But from Fig 4.13 at

100 kHz the loss is more for PBLYN1.

Though individual substitution of Ba2+ and La3+ brings diffuseness around Tmax, the

diffuseness observed is more for small amount of La3+ than Ba2+. The presence of

both La3+ and Ba2+ gives an entirely different response. The difference observed in the

dielectric behaviour of the two solid solution series with substitution of Ba2+ requires

further investigation.

4.3. HIGH FREQUENCY DIELECTRIC MEASUREMENTS

In the present section, initially the experimental set-up used for the measurements in

high frequency (130 – 1000 MHz) is discussed in detail followed by the formulae

used for analysing the data and the results of the experiment.

The experimental set-up used is shown in Fig 4.14. The set-up was completely

computer controlled. The high frequency measurements were carried out using an

indigenously prepared cylindrical co-axial holder of characteristic impedance 50 Ω.

The set-up could be used in a limited temperature range; 123 – 423 K due to the

presence of Teflon in between the metal cylinders. The impedance measurements

were carried out using HP network analyser in the Smith chart mode in frequency

domain. Temperature was controlled upto 0.1 K and measurements were recorded for

126

100

200

300

400

500

600

700

300 350 400 450 500 550 600

0

4

8

12

16

20

24

28


x = 0.01 La3+

ε'


ε''

Temperature (K)

Fig. 4.12 (a) Temperature dependence of ε′ and ε″ of (Pb0.96-xLaxBa0.04)- (Yb(1+x)/2Nb(1-x)/2)O3 for x = 0.01 at various frequencies.

127

300 350 400 450 500 550 600

400

600

800

1000

1200

1400

x = 0.02 La3+

ε'

Temperature (K)


Fig. 4.12 (b) Temperature dependence of ε′ and ε″ of

(Pb0.96-xLaxBa0.04)(Yb(1+x)/2Nb(1-x)/2)O3 for x = 0.02 at various frequencies.

128

250

500

750

1000

1250

250 300 350 400 450 500 550 600

0

5

10

15

20

25

ε' x = 0.05 Ba2+

x = 0.01 La3+

x = 0.02 La3+

x = 0.05 Ba2+

x = 0.01 La3+

ε''

Temperature (K)

Fig. 4.13 Temperature variation of ε′ and ε″ at 100 kHz for (Pb1-xBax)(Yb0.5Nb0.5)O3

for x = 0.05, (Pb0.96-xLaxBa0.04)(Yb(1+x)/2Nb(1-x)/2)O3 for x = 0.01, 0.02.

129

Fig. 4.14 (a) Coaxial holder used for dielectric measurements in the frequency range (130 - 1000 MHz).

130

Fig. 4.14 (b) The experimental set-up used for the measurements in the frequency range (130 - 1000 MHz).

131

every 1 K in the temperature range measurements are carried out. The measured

impedance is converted into dielectric constant and loss with the following formulae.

Co is the characteristic capacitance of the transmission line, ω is the probing

frequency and Z’ and Z’’ are the real and imaginary parts of the impedance.

The dielectric constant and loss of the samples PBZN1, PBZN2, PBYN3, and PBYN4

are given in Figs 4.15.

It can be seen from the Figs 4.15 that the dielectric constant increases with increase in

frequency. It is evident from the dielectric behaviour that two polarization phenomena

play significant role (Colla et al (1992), Guo et al (1998)). The relaxations might be

due to the relaxation of the wall of the polar regions (Glazounov et al (1996),

Tagantsev and Glazounov (1998), Glazounov and Tagantsev (2000)),

superparaelectric relaxation (Guo et al (1998)), and relaxation of the chain of the

ferroelectrically active B-site ions (Kittel (1951), Poplavko et al (1969), Demyanov

(1971), Ikegami (1963), Stanford (1961)). The increase in the dielectric constant

might indicate that the relaxation is resonance in character. Micro imaging and

dielectric data in between region (200 kHz - 130 MHz) are required to completely

characterize the relaxation behaviour.

oCωε

⎟⎟⎟⎟

⎠

⎞

⎜⎜⎜⎜

⎝

⎛

+

=2''Z'2Z

''Z- r'

oCωε

⎟⎟⎟⎟

⎠

⎞

⎜⎜⎜⎜

⎝

⎛

+

=2''Z'2Z

'Z '' r

132

0

100

200

300

400

100 200 300 4000

25

50

75

100

125

150

x = 0.2 Ba2+

200 MHz 250 MHz 300 MHz 350 MHz 400 MHz 500 MHz 600 MHz 700 MHz 800 MHz 900 MHzε'

200 MHz 250 MHz 300 MHz 350 MHz 400 MHz 500 MHz 600 MHz 700 MHz 800 MHz 900 MHz

ε''

Temperature (K)

Fig 4.15 (a) Temperature dependence of ε′ and ε″ of (Pb1-xBax)(Zn1/3Nb2/3)O3for x = 0.2 at various frequencies.

133

Fig. 4.15 (b) Temperature dependence of ε′ and ε″ of (Pb1-xBax)(Zn1/3Nb2/3)O3 for x = 0.3 at various frequencies.

20

40

60

80

100

100 200 300 4000

5

10

15

20

25

x = 0.3 Ba2+

200 MHz 250 MHz 300 MHz 350 MHz 400 MHz 500 MHz 600 MHz 700 MHz 800 MHz 900 MHz 1000 MHz

ε'

200 MHz 250 MHz 300 MHz 350 MHz 400 MHz 500 MHz 600 MHz 700 MHz 800 MHz 900 MHz 1000 MHz

ε''

Temperature (K)

134

Fig. 4.15 (c) Temperature dependence of ε′ and ε″ of (Pb1-xBax)(Yb0.5Nb0.5)O3 for x = 0.15 at various frequencies.

25

50

75

100

125

200 300 4000

10

20

30

130 MHz 150 MHz 200 MHz 250 MHz 300 MHz 350 MHz 400 MHz 500 MHz 600 MHz 700 MHz 800 MHz 900 MHz 1000 MHz

x = 0.15 Ba2+

ε'

ε''

Temperature (K)

130 MHz 150 MHz 200 MHz 250 MHz 300 MHz 350 MHz 400 MHz 500 MHz 600 MHz 700 MHz 800 MHz 900 MHz 1000 MHz

135

Fig. 4.15 (d) Temperature dependence of ε′ and ε″ of (Pb1-xBax)(Yb0.5Nb0.5)O3 for x = 0.2 at various frequencies.

0

70

140

210

200 300 4000

25

50

x = 0.2 Ba2+

130 MHz 300 MHz 350 MHz 400 MHz 500 MHz 600 MHz 700 MHz 800 MHz 900 MHz 1000 MHzε'

130 MHz 300 MHz 350 MHz 400 MHz 500 MHz 600 MHz 700 MHz 800 MHz 900 MHz 1000 MHz

ε''

Temperature (K)

136

Thus the proposed conclusions based on the results in this chapter are as follows:

It has been observed from the dielectric studies on Pb(Zn1/3Nb2/3)O3 based systems

that even though the ionic radii of Pb2+ and Sr2+ are almost same, the variation in

polarizability of the two molecules plays a drastic role in determining the dielectric

behaviour of the compounds. The decrease in the dielectric constant with decrease in

Pb2+ signifies the importance of hybridisation of Pb 6s and O 2p orbitals in the

determining the properties of the lead-based systems (Burton and Cockayne (1999)).

This also emphasizes the stereochemistry of the Pb2+ ion and the lone pair effect in

forming lobe shaped structure on admixture of s and p character (Ram Seshadri

(2001)).

Power law explains the variation in the relaxor behaviour of Pb(Zn1/3Nb2/3)O3-based

systems but could not be applied to the Pb(Yb0.5Nb0.5)O3-based systems in the low

frequency region though with increase in Ba2+ concentration diffuseness around Tmax

and relaxor behaviour become predominant. Hence it can be concluded that power

law proposed by Cheng et al., (1996) is applicable for systems that are basically

exhibiting relaxor behaviour. It cannot be applied for systems that undergo a transition

from either ferroelectric or anti-ferroelectric to relaxor ferroelectric as mentioned

earlier.

Individually when Ba2+ and La3+ substituted in Pb(Yb0.5Nb0.5)O3 the diffuseness at

Tmax increases with increase in the concentration of both Ba2+ and La3+. Further

increase in La3+ may induce relaxor behaviour in the system also. On substitution of

La3+ and Ba2+ together the transition becomes sharp with increase in both ε′ and Tmax

whereas ε″ decreases drastically. Further investigation is required to understand the

behaviour of the two solid solution series. Measurements in the region 200 kHz - 130

MHz are required to understand the relaxation mechanism completely of the systems

for which the dielectric measurements are carried out in the high frequency region.

137

CHAPTER 5

RAMAN STUDIES ON (Pb1-xBax)(Yb0.5Nb0.5)O3

The system (Pb1-xBax)(Nb0.5Yb0.5)O3 undergoes a transition from anti-ferroelectric to

relaxor ferroelectric for x ≥ 0.15. Therefore, one must study in detail the micro-

structural aspects of the system as the XRD confirms the presence of B-site ordering.

In this chapter, one of the tools that is useful to probe the phase transitions, Raman

spectroscopy, is employed to study the photon – phonon interaction to identify the

micro-structural aspects. The chapter starts with a brief introduction to the

significance of Raman spectroscopy in detecting the local symmetry followed by the

details on the experimental arrangement. The results are analysed in conjecture with

the XRD and dielectric measurements carried out on the above set of compounds at

the end of the chapter.

5.1. SIGNIFICANCE OF RAMAN SPECTROSCOPIC STUDIES

Raman effect is caused by modulation of susceptibility of the medium by vibrations.

It involves the coupling between incident photons and quasi particle excitations such

as phonons, magnons and electronic single particle or collective excitations within a

sample. In crystalline solids, Raman effect deals with phonons. A phonon is Raman

active if the first derivative of the polarizability with respect to the vibrational normal

co-ordinate has a non-zero value. The possible Raman modes depend on the

symmetry of the solid considered. Decrease of degree of order leads to broadening of

the Raman lines, the disappearance of their eventual splitting and increased

diffuseness of evolution near the phase transition temperature. Lowering of symmetry

lifts degeneracy of certain modes.

138

Raman scattering is the appropriate technique to get more insight into the local

distortions present in any systems. Studies on Raman active optical phonon modes

have been reported for many lead based complex perovskites. It is easy to interpret the

Raman spectrum from the highest possible symmetry and later on include all the

possible and required distortions. Group theory forbids the first order Raman activity

in the cubic phase (the paraelectric phase) with space group Pm3m. However, for

certain ferroelectrics like BaTiO3 weak lines are observed in the paraelectric phase

(Baskaran et al (2002)). These lines are attributed to cation disorder. The average

macroscopic structure of the widely studied lead based relaxors is cubic with Pm3m

symmetry. All oxygen octahedrons are equivalent in Pm3m structure. In this case, the

oxygen atoms ought to occupy the local positions with an inversion centre. No Raman

active modes initiated by O2 vibrations could appear in such materials. The presence

of the Raman active modes indicates cation disorder as in BaTiO3 and therefore the

difference in the local and global symmetry. In the case of BaTiO3 the disorder is the

off-centre positions of Ti4+.

In complex perovskites, B-site is occupied by two ions. In some compounds the B-site

is completely ordered according to the stoichiometry and in other compounds it does

not happen so. The presence of A1g (a non-degenerate mode discussed in latter

sections) mode in all the lead-based complex perovskites indicates the presence of

some chemical ordering at B-site. Due to different ionic sizes and force constants for

B′ and B′′, two adjacent sharing corner oxygen octahedrons may become non-

equivalent. If two octahedrons are not equivalent, the constituent oxygen atoms occur

in local positions without inversion centre and their vibrations become Raman active.

As the B-site ions are distributed throughout the B sites, there is a distribution of

phonon frequencies, resulting in a broad band, characteristic of disordering type.

Since this type of band is enhanced in intensity and narrower for compounds

139

exhibiting B-site ordering it is perhaps more correct to interpret its presence as

evidence of non-random distribution of B′ and B′′.

The intensity of the peaks is very high indicating that the activity corresponding to the

vibration is very high even though the compounds are notorious for their disordered

nature. One common feature observed in the paraelectric phase, even in the low

degrees of order in the B-ion sub lattice is occurrence of Raman spectra which

disappear at high enough temperatures (Güttler et al (2003)). A decrease in degree of

order leads to broadening of Raman lines, the disappearance of their eventual splitting

and increased diffuseness of evolution near the phase transition temperature.

Disappearance of Raman activity takes place for Pb(Sc0.5Nb0.5)O3 and

Pb(Sc0.5Ta0.5)O3 at which the annealing procedures are usually carried out (Kania et al

(1995)). In Pb(Mg1/3Nb2/3)O3 and Pb(Zn1/3Nb2/3)O3, Raman activity is found to

disappear beyond Tmax, around TB (Burns temperature). This might be due to the

disappearance of polar micro regions at TB.

Raman scattering is also helpful in studying the dynamics of structure by analyzing

the characteristic modes associated with nano regions. The selection rules are very

sensitive to the local and global symmetries. The Raman spectra of Pb(Zn1/3Nb2/3)O3

(Ohwa et al (1998a)) and Pb(Mg1/3Nb2/3)O3 (Ohwa et al (1998b)) are different since

there is difference in the crystal symmetry in the low temperature range.

Pb(Mg1/3Nb2/3)O3 is pseudo cubic (Bonneau et al (1989), de Mathan (1991a, 1991b))

whereas Pb(Zn1/3Nb2/3)O3 is rhombohedral (Mulvihill et al (1997)). In addition, the

existence of ferroelastic domain wall structure in Pb(Zn1/3Nb2/3)O3 results in

distribution of polarization of incident and scattered light. The temperature dependent

Raman spectra of Pb(Mg1/3Nb2/3)O3-based (Idnik and White, (1994) and Ohwa et al

140

(1998)) and Pb(Zn1/3Nb2/3)O3-based (Iwata et al (2001), Jiang and Kojima (1999), and

Kamba et al (2003)) compositions also behave different.

Relaxor ferroelectric Pb(Mg1/3Nb2/3)O3 exhibits complex Raman spectra though the

macroscopic structure is cubic symmetry (Idnik and White, (1994)). Raman spectra of

Pb(Mg1/3Nb2/3)O3 (Husson et al (1990), Ohwa et al (2001)) have been interpreted in

terms of existence of 1:1 ordered nano-clusters and of local structural distortion

whose symmetry is lower than cubic (Kim (2002)). Recently Jiang et al (2000, 2001)

reported the Raman studies on nano-scale 1:1 B-site ordering in PMN with partial

substitution of Na+, Bi3+ and La3+ for Pb2+. They obtained the degree of B site

ordering from the full width at half maximum (FWHM) of Raman modes

corresponding to 1:1 ordering. The changes in the degree of ordering for the quenched

and annealed Pb(Sc0.5Ta0.5)O3 (Bismayer et al (1989)) have been reported by Raman

spectra studies . Recently Mihailova et al (2002) assigned the symmetry of Raman

modes for disordered Pb(Sc0.5 Nb0.5)O3 and Pb(Sc0.5Ta0.5)O3 based on normal mode

calculations.

The present solid solution series exhibits a crossover from anti-ferroelectric to relaxor

behaviour for x ≥ 0.15 (Choo and Kim (1992), Kim et al (2001)), hence it is important

to understand the behaviour of Raman active phonon modes in the solid solution

system. The changes in the Raman spectra are discussed in conjecture with the

structural and dielectric susceptibility on substitution of Ba2+ for Pb2+. Raman

spectroscopy and X-ray diffraction are used to study the variations in the nature of

chemical bonds. It is evident from the first principle calculations by Cohen (1992) that

there exists hybridisation between Pb2+ and O2- whereas the nature of interaction is

ionic between Ba2+ and O2-. Hence there is expected a change in the nature of bonds

on substitution of Ba2+ for Pb2+.

141

Raman studies are carried out at room temperature on the ceramic samples. This has

advantages and disadvantages. The advantage being that the spectrum can be recorded

at one stretch regardless of the geometric orientation of the crystal with respect to

propagation and polarization of light. The disadvantage being that the FWHM is

larger i.e., the peaks are wider. This may lead to overlapping of certain peaks and

cause difficulty in interpretation of peak parameters.

5.2. EXPERIMENTAL SET-UP

The sintered pellets were polished on one side using 0.25 µm diamond paste and

subsequently annealed at 500 oC for 8 hrs to remove the residual surface stress left

from polishing. Raman spectra were recorded in the back scattering geometry using

200 mW power of 488 nm line from an Ar-ion laser. Scattered light was analysed

using a double monochromator (SPEX 14018) and detected using a photo-multiplier

tube (FW ITT130) operating in the photon counting mode. The experimental set-up is

shown in Fig 5.1. The position, intensity and line-width (FWHM) of Raman spectra

were obtained using Jandel peak fit program. The Lorentzian line shape was used to

describe the peak shapes in the spectrum.

142

S AMP L E

LASER

MONO- CHROMATOR PMT

AMPLIFIER

COUNTER

PC

Fig. 5.1 The experimental set-up used to record the Raman spectra

143

5.3. IDENTIFICATION OF MODES BASED ON GROUP THEORY ANALYSIS AND CORRELATION

Pb(Yb0.5Nb0.5)O3 is an anti-ferroelectric with orthorhombic symmetry at room

temperature possessing the same space group as Pb2MgWO6, Pnam (Choo et al

(1993), Baldinozzi et al (1995) Park (1998)). Pb2MgWO6 undergoes transition from

paraelectric to anti-ferroelectric at 310 K (Kania et al (1995)), from higher symmetric

cubic with space group Fm3m to orthorhombic Pnam. The symmetry of paraelectric

and anti-ferroelectric phases of both Pb(Yb0.5Nb0.5)O3 and Pb2MgWO6 are same

(Choo et al (1993)). Hence the group theory analysis for the classification of phonon

modes of PMW by Baldinozzi et al (1996) is followed for Pb(Yb0.5Nb0.5)O3 in the

present study. The total number of phonon modes in the orthorhombic phase is

Γ = 18A1g+18B1g+12B2g+12B3g+12A1u+12A2u+18B2u+18B3u. Of which only 60

are Raman active. They are listed below.

ΓRaman = 18Ag + 18B1g + 12B2g + 12B3g.

In the high symmetry cubic phase, the total number of phonon modes at Γ point is

Γ = A1g + Eg + F1g +2F2g + 5 F1u + F2u.

The number of Raman active phonon modes with cubic phase is as follows.

ΓRaman = A1g + E g+ 2F2g.

The F1u modes are IR-active modes and F1g, F2u and F2g are silent modes.

The entire frequency range of Raman spectra is plotted in three figures for

convenience. The spectra of all the compositions for the frequency region below 100

cm-1 are given in the Fig 5.2. The region between 100 and 400 cm-1 and between 400

and 1000 cm-1 are given in Figs 5.3 and 5.4. The corresponding position and line-

width of modes are tabulated in Tables 5.1, 5.2 and 5.3 for clarity.

144

In the present case it is observed that, in the orthorhombic phase, the number of

modes is less than 60. This can be due to merging of certain modes because of thermal

broadening, low polarizability and degeneracy of certain modes. In Pb2MgWO6 as

many 40 modes have been reported at 10 K (Kania et al (1995)). In the cubic phase,

the number of modes observed is more than predicted by group theory analysis. The

reason for this is explained in the later section.

Qualitative mode assignment for lead based relaxor ferroelectrics poses difficult

problem owing to the extensive broadening of the modes. Based on the normal mode

calculations for a pseudo-cubic perovskite structure of Pb(B′1/2B″1/2)O3 type

Mihailova et al (2002) assigned the symmetries to the respective modes for disordered

Pb(Sc0.5Nb0.5)O3 and Pb(Sc0.5Ta0.5)O3.

Possible modes are

• A-O stretching (F2g)

• BO6 rotation (F1g)

• B-localized (F1u)

• Pb2+e- phonon coupling (F2u)

• O-B-O asymmetric bending (ferroic) (F1u)

• O-B-O symmetric bending (F2g)

• B-O symmetric stretching (Eg)

• B′ - O - B″ symmetric stretching (A1g)

The ions involved in each vibration and the modes of vibration are given in Fig 5.5.

145

40 60 80 100

x = 0.3

x = 0.25

x = 0.2

x = 0.15

x = 0.1

x = 0.05

x = 0

Ram

an in

tens

ity (a

.u)

Raman shift (cm-1)

Fig. 5.2 Raman spectra in the frequency region below 100 cm-1 at room temperature.

146

100 150 200 250 300 350 400100 150 200 250 300 350 400100 150 200 250 300 350 400100 150 200 250 300 350 400

Raman Shift (cm-1)

x = 0.3

x = 0.25

x = 0.2

x = 0.15

x = 0.1

x = 0.05

x = 0

Ram

an In

tens

ity (a

.u.)

Fig. 5.3 Raman spectra in the frequency range 100 - 400 cm-1 at room temperature.

147

400 500 600 700 800 900 1000

x = 0.3

x = 0.25

x = 0.2

x = 0.15

x = 0.1

x = 0.05

x = 0

Ram

an In

tens

ity (a

.u.)

Raman Shift (cm-1)

Fig. 5.4 Raman spectra in the frequency range 400 - 1000 cm-1 at room temperature.

148

Table 5.1 Frequency (ω (cm-1)) and line-width (Γ (cm-1)) of the modes due to cubic symmetry.

0.30 0.250.200.150.100.050.00 Composition (x)

528 528526525520511512 ω

O-B-O symmetric bending

65 706574716553 Γ F2g

772 774789783791766757 ω

B-O symmetric stretching

37 333635323514 Γ Eg

822 823821822819806803 ω

B′-O-B′′ symmetric stretching

16 181417171820 Γ A1g

52 505555596161 ω

Pb-O stretching

15 1713151066 Γ F2g

149

Table 5.2 Frequency (ω cm-1)) and line-width (Γ (cm-1)) of modes due to symmetry

lower than cubic.

0.30 0.250.200.150.100.050.00 Composition (x)

206 206209208207194192 ω

BO3 rotation 39 38 43 44 40 17 30 Γ F1g

260 260261261263269270 ω

B-localized 16 17 16 22 27 14 22 Γ F1u

303 301303301302318303 ω

30 33 38 38 44 31 42 Γ

361 358357353351353345 ω

Pb2+ e- - phonon

coupling

10 12 17 19 18 16 16 Γ

F2u

421 421422420422426- ω

O-B-O Asymmetric

bendi

21 21 21 23 25 18 - Γ F1u

150

Table 5.3 Frequency (ω) and line-width (Γ) of the modes due to orthorhombic symmetry.

Composition (x)

ω

(cm-1)

Γ

(cm-1)

105 9

107 6

111 5

113 2

0.00

0.05

0.10

0.15

0.20

0.25

0.30

-

-

-

-

-

-

Orthorhombic distortion

142

167

5

10

165

172

6

9

170 10

- -

0.00

0.05

0.10

0.15

0.20

0.25

0.30

-

-

-

-

-

-

Orthorhombic distortion

152

Accordingly the mode observed at 55 cm-1 involving Pb-O stretching vibration is

assigned to F2g symmetry. The existence of non-identical ions in the B-site leads to

modes at 200, 265 and 812 cm-1. The mode at 200 cm-1 corresponding to BO3 rotation

is assigned to F1g symmetry while mode near 265 cm-1 corresponding to the localized

motion of B-ions is assigned to F1u symmetry. The movement of only oxygen atoms

along B′-O-B′′ axis results in an asymmetric mode near 812 cm-1 assigned to A1g

symmetry. Two F2u symmetry modes are observed at 303 and 353 cm-1. It can be

seen from fig 5.4 that the mode at 421 cm-1 begins to appear from x = 0.05 and with

further increase in Ba2+ content, the intensity of the mode increases. This mode is not

observed at room temperature for Pb(Yb0.5Nb0.5)O3. This mode is also assigned to F1u

symmetry and involves the asymmetric O-B-O bending. The O-B-O symmetric

bending observed at 520 cm-1 is also assigned to F2g symmetry. The mode at 772 cm-1

corresponds to Eg symmetry and does not involve the cations.

Two F2g phonon modes observed at 55 and 520 cm-1 are triply degenerate in cubic

symmetry and split into three lines as the symmetry reduces to orthorhombic. In the

present case the splitting is not prominently seen for both modes as was observed for

Pb2MgWO6 (Kania et al (1995), Baldinozzi et al (1995)), Pb(Sc0.5Nb0.5)O3 and

Pb(Sc0.5Ta0.5)O3 (Mihailova et al (2002)). However, for Pb(Yb0.5Nb0.5)O3 and for the

compound x = 0.05, a faint shoulder near 70 cm-1 can be seen. For the compositions

beyond x = 0.05, the splitting could not be observed. The mode at 55 cm-1

corresponds to Pb-O stretching. The mode is influenced by the mass of A-site cation

and A-O binding force. Hence the corresponding mode occurs in the low frequency

region. For many lead based complex perovskites, this mode is observed in the range

50 – 60 cm-1 (Kania et al (1995), Baldinozzi et al (1995) and Mihailova et al (2002)).

It is expected that the frequency of this mode should increase with increase in Ba2+

content, as the mass of Ba (137.3) is less than Pb (207.2). With increase in Ba2+

153

content, the frequency of this mode decreases to 50 cm-1 and FWHM increases to 17

cm-1. This indicates considerable softening of the force constant of the corresponding

vibration. The broadening observed with increase in Ba2+ may be due to the

disordered distribution of Ba2+ ions. The mode at 520 cm-1 due to symmetric O-B-O

bending shows an increase in intensity with increase in substitution of Ba2+ as can be

seen from Fig 5.4. The FWHM does not exhibit any uniform variation.

The intensity of the modes at 105 and 167 cm-1 decreases monotonically and vanishes

at x = 0.20 which corresponds to the disappearance of the diffraction peaks associated

with the anti-parallel displacement of Pb2+ ions beyond x = 0.15. In the absence of

detailed lattice calculations, quantitative assignment of these modes is not possible but

may be assigned to orthorhombic distortion due to Pb2+ions.

The presence of ions of different valence and ionic size in the B-site results in the

relative rotation of octahedron due to size mismatch in B′-O-B″ bond. This gives rise

to F1g mode at 200 cm-1. With increase in Ba2+ content, the frequency of the mode

changes marginally. The intensity of this mode increases with increase in Ba2+

concentration.

Two of the four F1u phonon modes observed at 265 and 420 cm-1, are sensitive to the

mass and symmetry of B-site ions. The mode at 265 cm-1 corresponds to localization

of B-site cations. The frequency of this mode decreases slightly whereas intensity

decreases drastically with increase in Ba2+.

Two F2u modes at 303 and 353 cm-1 arise due to electron-phonon coupling of Pb2+

lone pair electrons (Burton and Cockayne (1999) and Chen (1996)). The frequency

and the FWHM of these two modes do not show significant variation with increase in

Ba2+ substitution. The F2u mode consists of O2- vibrations along the Pb-O bonds, i.e.,

it appears as a Pb-O bond-stretching mode in lead-oxygen system. This mode

154

becomes Raman active under the lack of centre of inversion that arises from off-

centred displacement of Pb2+ ions. The Pb2+ cations can easily form elongated lone

pairs if they are linked with B cations of different valence. The atoms may shift from

ideal positions due to difference in covalency of the B′ - O and B″ - O bonds and in

such a manner lone pairs oriented along the direction of the shift in the B cations

appear. The shift in the position of Pb2+ ions, and the orientation of lone pair electrons

depend on the local symmetry. The XRD pattern (Chapter 2, Fig 2.4) indicates that

the intensity of reflection peaks corresponding to anti-parallel off-centred

displacement of Pb2+ ions gradually decreases with increase in Ba2+ concentration and

cease to exist for x > 0.15. According to Mihailova et al, (2002), the ratio of

intensities of the peaks I353/I303 is a measure of the chemical ordering at B-site. If

ordering exists in the B-site the orientations of lone pairs are correlated and all Pb2+

atoms shift in the same direction with respect to O2- atoms. If the ordering does not

exist there is random shift of the lone pairs and hence atoms. The higher the ratio the

more is the ordering and vice versa. The ratio is high for x = 0 and x = 0.05 and then

decreases as can be observed from Fig 5.3. The decrease in the chemical ordering

should also result in the broadening of the A1g phonon mode (near 812 cm-1), which is

not observed in our study. Therefore, the decrease in the intensity ratio (I353/I303) of

the peaks is attributed to the decrease in the concentration of lone pair of electrons due

to substitution of Ba2+ ions and not due to the chemical ordering in B-site.

The other F1u mode at 420 cm-1 begin to appear from x = 0.05. At room temperature

this mode is not seen for Pb(Yb0.5Nb0.5)O3. However, for Pb2MgWO6 some low

intensity modes in the range 400 - 410 cm-1 and 440 - 450 cm-1 are observed at 10 K

(Kania et al (1995)). Since both Pb(Yb0.5Nb0.5)O3 and Pb2MgWO6 are structurally

similar, one can expect modes in the above-mentioned range in the low temperature

Raman spectra of Pb(Yb0.5Nb0.5)O3. In the present work, with the room temperature

155

data alone for Pb(Yb0.5Nb0.5)O3, it is very difficult to conclude about the presence of

the mode around 420 cm-1. Low temperature Raman spectra for some of the

compounds in (Pb1-xBax) (Yb0.5Nb0.5)O3 solid solution is necessary to have more

discussion on the characteristics of the mode. However, in relaxor ferroelectric

compounds such as Pb(Mg1/3Nb2/3)O3, Pb(Sc0.5Nb0.5)O3 and Pb(Sc0.5Ta0.5)O3, modes

in the range 420 – 440 cm-1 are observed over a wide temperature range ( Idnik and

White (1994), Iwata et al (2001), Ohwa et al (1998), Mihailova et al (2002)) .

Mihailova et al (2002) based on phonon mode calculations assigned the modes in the

frequency range 420 – 440 cm-1 to the asymmetric O-B-O bending vibration having

F1u symmetry arising from rhombohedral structural distortion. In the present (Pb1-

xBax)(Yb0.5Nb0.5)O3 solid solution series, the other end of the composition is

Ba(Yb0.5Nb0.5)O3. This compound belongs to other Ba2+ series of compounds such as

Ba(Y0.5Nb0.5)O3 and Ba(Y0.5Ta0.5)O3. The Raman spectra of these series of

compounds do not exhibit any mode at 420 cm-1 (Gregora et al (1995) and Siny et al

(1998)). Therefore it can be expected that the intensity of this mode may begin to

decrease for x > 0.30. In Ba2+ based complex perovskite compounds, Ba2+ ion and B

ions occupy the cubo-octahedron and octahedral centres formed by oxygen atoms;

whereas in Pb2+ based complex perovskite compounds, both Pb2+ and B ions exhibit a

shift from cubo-octahedron and octahedral centre positions. The off-centred positions

of Pb2+ and B ions are responsible for ferroelectric behaviour in these compounds.

From XRD pattern (Chapter 2, Fig 2.4), it can be seen that the intensity of reflections

due to off-centred displacement of Pb2+ ions decreases with increase in Ba2+ and

completely vanishes beyond x = 0.15 indicating a structural change from

orthorhombic to cubic. For cubic Fm3m symmetry, group theoretical analysis predicts

only 4 Raman active modes. However nine modes are clearly observed in the spectra

for the compositions x = 0.20 – 0.30. This indicates the existence of some lower

symmetry structure in addition to 1:1 ordering. Choo and Kim (1992) attributed the

156

evolution of hysterisis loop and broadening and disappearance of heat capacity

anomaly in Pb1-xBax (Yb0.5Nb0.5)O3 solid solution series to the appearance of local

polar regions of low symmetry within non-polar matrix. In the case of

Pb(Mg1/3Nb2/3)O3, detailed X-ray and neutron diffraction studies indicate in addition

to the average cubic symmetry, the existence of nano-meter size polar clusters of local

rhombohedral R3m symmetry (de Mathan (1991b)). The dielectric response of relaxor

ferroelectrics is viewed as the relaxation of these polar clusters over a wide

temperature and frequency ranges. Recently, nano-scale phase separation has been

observed in perovskite type manganites between ferromagnetic metallic and non-

ferromagnetic insulating phases, which is very similar to that observed in relaxor

ferroelectrics (Bibes et al (2001) and Kimura et al (1999)). In La1-ySryMnO3, solid

solution series y = 0.1 is of orthorhombic symmetry whereas y = 0.2 is of

rhombohedral symmetry (Granado et al (1998) and Bjorrnsson et al (2000)). The

presence of mode at 420 cm-1 in the Raman spectrum in addition to the orthorhombic

modes at 30 K for y = 0.1, is attributed to the existence of orthorhombic phase with

rhombohedral distortion. The presence of mode at 420 cm-1 for y = 0.2 further

validates the assignment of this mode to rhombohedral symmetry. Thus the

appearance of the mode at 420 cm-1 from x = 0.05 in the present study can be

attributed to the existence of rhombohedral symmetry.

The presence of ordered regions with a particular symmetry allows the appearance of

specific Raman modes that are otherwise silent. Presence of A1g phonon mode (812

cm-1) in all the spectra in our case indicates the existence of chemical ordering in the

B-site. This mode is a simple motion of oxygen atoms along B′-O-B′′ axis. This is

similar to the breathing type of a free octahedron without involving A or B cations.

All the cations are at rest and the cationic mass effect does not come into picture. The

corresponding frequencies depend on the B′-O and B′′-O binding forces. The

157

vibrations occur at the highest frequencies of the spectrum since it does not involve

the heavy cations. The degree of ordering is estimated by the FWHM of the A1g

phonon mode. Based on Raman studies on La3+ Substituted Pb(Mg1/3Nb2/3)O3, Jiang

et al (2000, 2001) attributed the narrowing of the A1g mode (772 cm-1) from 56 to 38

cm-1 to increase in the B-site ordering. However, in the present study marginal change

is only observed in the FWHM of A1g mode indicating no effective change in the B-

site ordering on substitution of Ba2+. This is further proved from the existence of the

F reflection peaks in XRD (Chapter 2, Fig 2.4). The frequency of this mode is

expected to decrease with Ba2+ substitution, as the ionic radius is greater than that of

Pb2+. (Siny et al (1998)) In the present case, an opposite trend is observed indicating

an increase in the force constant of B-O bond.

The Eg symmetry mode at 772 cm-1 does not involve the motion of cations. This

mode is predominantly observed for the composition x = 0.25 and x = 0.3.

Thus from the earlier discussions the following conclusions can be drawn. The

phonon modes at 55, 520, 772 and 812 cm-1 are the modes due to true Raman activity

for the space group Fm3m. The presence of additional modes at 200, 265 and 420 cm-

1 indicate the existence of lower symmetry structure, which in the present study is

attributed to the local rhombohedral distortion. The electron-phonon coupling due to

Pb2+ lone pair electrons leads to modes at 303 and 353 cm-1. This explains the

presence of nine modes in contradiction to four possible modes for Fm3m. The modes

at 105, 142, 167, 192 and 650 cm-1 correspond to orthorhombic symmetry. The modes

due to orthorhombic symmetry gradually disappear which is further evidenced by the

disappearance of the reflections corresponding to anti-parallel displacement of Pb2+

ions. The intensity of the modes at 200 and 420 cm-1 increases with increase in the

Ba2+ concentration. The increase in the intensity of the lines with increase in Ba2+

content indicates increase in the number of such polar regions with local

158

rhombohedral distortion. Correspondingly the dielectric response becomes more

diffused and exhibits relaxor behaviour. Even though the dielectric response begins to

show relaxor behaviour from x = 0.1, the Raman spectra indicates the appearance of

rhombohedral distortion from x = 0.05. The reason is that the fraction of the cells

exhibiting the local distortion might be very less. Therefore for x = 0.05, the present

dielectric studies could not detect the frequency dispersion of low fraction polar

regions. Since Raman scattering probes the variation within few unit cells, the local

distortion could be detected in the Raman spectra from x = 0.05.

The cubic symmetry with local rhombohedral distortion without any trace of

orthorhombic symmetry commences around x = 0.2. The presence of F2g (55 cm-1)

and A1g (812 cm-1) modes in all the spectra indicates the doubling at the unit cell,

which is in accordance to the presence of F-reflections for all the compositions.

159

CHAPTER 6

SUMMARY AND CONCLUSIONS

In this section the studies conducted on the PZN based compounds, PYN based

compounds and PFN are summarised and the possible conclusions arrived at are

presented.

The present work deals with the synthesis and investigation of some lead based

complex niobate perovskites. Lead based compounds exhibit diverse properties

depending on the ordering in the B-site. In the present study the PZN based relaxor

compounds, the solid solution series (Pb1-xBax)(Yb0.5Nb0.5)O3, which undergoes a

transition from anti-ferroelectric to relaxor ferroelectric, La3+ substituted PYN and

La3+ and Ba2+ substituted PYN and the ferroelectric PFN are chosen. All the

compositions were synthesized taking precautions to avoid PbO loss. X-ray analysis

was carried out to confirm the formation of single phase within the resolution of XRD

without any secondary phase.

In PZN based compounds, the compositions remain pseudo cubic with space group

Pm3m. The Ba2+ and Sr2+ substituted Pb(Zn1/3Nb2/3)O3 exhibit the relaxor behaviour.

The substitution of barium or strontium in the place of lead results in a decrease of ε′,

ε″ and Tmax. The frequency dependent Tmax is analysed using V-F relation and Power

law. The temperature variation of the dielectric response for every frequency is

analysed using the model proposed by Cheng et al. It has been observed that Power

law is more suitable for the PZN-based compounds. For PBZN, the size of the polar

clusters is large and the interaction between the polar clusters is stronger than for

PSZN. The volume fraction of the polar clusters is higher for PBZN than for PSZN.

The large size of the polar clusters results in the high Tmax and the stronger interaction

160

between them results in a broader response around Tmax. The degree of relaxation

increases rapidly between x=0.2 and x=0.3 for PBZN than for PSZN. The value of p

for same x is lower for PSZN than that of PBZN. This indicates that the growth of the

polar clusters is inhibited more in PSZN than PBZN. The production rate of polar

regions with decreasing temperature is less for the Sr2+ substituted compounds which

has been observed from the parameters obtained from the theoretical model used.

Indirect coupling of ferroelectrically active NbO6 octahedra through Pb2+ is important

to observe the relaxor behaviour. Increase in Ba2+ or Sr2+ for Pb2+ disrupts the

coupling and leads to decrease in volume of micro polar regions. The decoupling of

neighbouring NbO6 octahedra to the ferroelectric network is more for Sr2+ than for

Ba2+. It has been observed from the dielectric studies on PZN-based systems that even

though the ionic radii of Pb2+ and Sr2+ are almost same, the variation in polarizability

of the two molecules plays a drastic role in determining the dielectric behaviour of the

compounds. The decrease in the dielectric constant with decrease in Pb2+ signifies the

importance of hybridisation of Pb 6s and O 2p orbitals in the determining the

properties of the lead-based systems. This emphasizes the stereochemistry of the Pb2+

ion, the lone pair effect in forming lobe shaped structure on admixture of s and p

character.

In Ba2+ substituted PYN, the major concentration was on studying the local distortions

involved in the transition from anti-ferroelectric to relaxor ferroelectric. The system

undergoes a structural phase transition from orthorhombic Pnam for x = 0 to cubic

Fm3m for x > 0.15 of Ba2+ content at room temperature. XRD indicates that the B-site

ordering is retained. Tmax decreases with increase in Ba2+ content. εmax increases with

increase in Ba2+ content up to x = 0.10 and then decreases. Increase in the

polarizability of oxygen due to increase in the volume of the unit cell might be the

161

reason. However, the ordering developed is short range ordering, which is evident

from the diffused phase transition (x = 0.15 of Ba2+). Substitution of Ba2+ breaks the

coupling of ferroelectrically active oxygen octahedra and results in decrease in the

dielectric constant.

Very low pre-exponential values are obtained on application of power law to the

frequency dependent Tmax. The power law could not explain the relaxor behaviour of

the compositions exhibiting frequency dependent Tmax. Therefore, the present

theoretical model could not be used to characterize this set of compositions. The

crossover is characterized using Raman spectroscopic studies. The relaxor behaviour

has been attributed to the presence of local rhombohedral distortion, which is

evidenced from the presence of a mode at 420 cm-1. Modes due to lack of centre of

inversion are observed. B-site ordering is retained on substitution of Ba2+. Cubic

symmetry with local rhombohedral distortion without orthorhombic symmetry is

obtained around x = 0.2 of Ba2+ content.

It is observed that with substitution of La3+ for Pb2+ in PYN, the diffuseness of the

transition around Tmax increases. However Tmax is not frequency dependent for the

compositions studied. The reason for the diffuseness might be due to the vacancies

created on substitution of La3+ for Pb2+. further increase in La3+ may induce relaxor

behaviour.

It is observed that with substitution of La3+ and Ba2+ for Pb2+ in PYN, the transition

around Tmax becomes sharp. Tmax is not frequency dependent. Increase in ε′ and Tmax

with increase in La3+ might indicate an induction of ferroelectric nature. ε″ decreases

drastically with substitution of La3+. The difference in the behaviour of the two series

requires further investigation.

162

The microwave measurements are carried out using co-axial probe technique. The

coaxial probe used for the measurements is indigenously fabricated. It is evident from

the dielectric behaviour that two polarization phenomena play significant role. The

relaxations might be due to the relaxation of the wall of the polar regions,

superparaelectric relaxation, relaxation of the chain of the ferroelectrically active B-

site ions. The increase in the dielectric constant might indicate that the relaxation is

resonance in character. Requires micro imaging and dielectric data in between region

to completely characterize the relaxation behaviour.

In PFN, XRD and dielectric response indicate that there is no ordering in B-site. Only

diffused phase transition is observed. The difference between the 0.1 and 200 kHz

dielectric response increases with increase in sintering temperature. This increase

might be due to variation in the ratio of trivalent and divalent iron. The divalent iron

increases with increase in the sintering temperature. Decrease in the dielectric

constant and loss are observed on annealing the samples in oxygen atmosphere. The

difference in dielectric response between the 0.1 kHz and 200 kHz decreased and

resistivity decreased by an order on annealing. Annealing in oxygen atmosphere

increases the trivalent iron reducing the dielectric constant and loss.

6.1 FUTURE SCOPE OF THE WORK

a) Small angle X-ray studies, XAFS and XANES studies as a function of temperature

can help in significant understanding of the microscopic phenomena of the relaxors.

Band theory calculations based on the XAFS measurements and the computations

basing on the first principles can throw light on the anomalous behaviour associated

with the lead based compositions. Detailed temperature and pressure dependent

Raman spectroscopic studies also help in understanding the behaviour of relaxors.

AFM Mapping enhances the understanding of the relaxors.

163

The difference in the relaxation properties of the La3+-based compounds studied can

be further understood using Raman spectroscopic studies.

b) XAFS is the fine structure that occurs in the absorption coefficient on the high

energy side of X-ray absorption edges. The absorption edges occur as X-ray photons

attain enough energy to just dislodge electrons bound in atoms. The fine structure

occurs only when the atoms are in the condensed state and dislodged can back scatter

from the surrounding atoms and interfere with the out going portion of its wave

function. By appropriately analyzing this XAFS the arrangement of atoms about the

X-ray absorbing atom the probe atom can be determined. Recent advances in theory

and analysis have extended the range of optimum reliable detailed information of the

structural distribution from the first neighbour to four or more neighbouring cells of

atoms about the probe atom. XAFS can give information on pair probability

distribution function (PDF) of the relative distance between the probe atom and its

neighbour with very high spatial resolution and with high sensitivity, distinguishing

the type of neighbours. Due to its short range nature XAFS can equally probe highly

ordered crystalline solids, highly disordered amorphous materials with no long range

order and materials with disorder intermediate of these extremes.

As the degree of disorder increases with substitution of Pb2+ for Ba2+ in Ba2+ based

complex perovskite materials, the systematic change in the local structure thus

obtained using XAFS can further enhance the understanding of the variation in

dielectric properties. The distinct advantage with the XAFS is its ability to probe the

dynamical distortions in the time scale of the order of 10-15 seconds comparing to the

other techniques like Raman scattering and magnetic resonance whose characteristic

time scale of measurement is 10-10 seconds or longer.

164

REFERENCES

1. Adachi, M., T. Toshima, J. Yachizaka and A. Kawabata (1996)

Preparation and properties of Pb(Sc1/2Nb1/2)O3-Pb0.85La0.15Ti0.96O3 (PSN-

PLT) solid-solution ceramics. Jpn.J.Appl.Phys. 35, 5094-5098.

2. Ahn, B. Y. and N. Kim (2000a) Effects of barium substitution on

perovskite formation, dielectric properties, and diffuseness characteristics

of lead zinc niobate ceramics. J. Am. Ceram. Soc. 83, 1720-1726.

3. Ahn, B. Y. and N. Kim (2000b) Perovskite phase developments and

dielectric characteristics in barium-substituted lead zinc tantalate system.

Mater. Res. Bull. 35, 1677.

4. Ananta, S. and N. W. Thomas (1999) Relationships between sintering

conditions, microstructure and dielectric properties of lead iron niobate. J.

Eur. Ceram. Soc. 19, 1873.

5. Ananta, S. and N. W. Thomas (1999) A modified two-stage mixed oxide

synthetic route to Lead magnesium niobate and lead iron niobate. J. Eur.

Ceram. Soc. 19, 155-163.

6. Atkin, R. B. and R. M. Fulrath (1971) Point defects and sintering of lead

zirconate-titanate. J. Am. Ceram. Soc. 54, 265-270.

7. Baldinozzi, G. and Ph. Sciau (1995) Crystal structure of the

antiferroelectric perovskite perovskite Pb2MgWO6. Acta

Cryatallographica B51, 668-673.

8. Baldinozzi, G., Ph. Sciau and A. Bulou (1996) Raman study of the

structural phase transition in the ordered perovskite Pb2MgWO6. J. Phys:

Condens. Matter 7, 8109-8117.

9. Baskaran, N., A. Ghule, C. Bhongale, R. Murugan and H. Chang

(2002) Phase transformation studies of ceramic BaTiO3 using thermo-

Raman and dielectric constant measurements. J. Appl. Phys. 91, 10038.

10. Bell, A. J. (1993) Calculations of dielectric properties from the

superparaelectric model of relaxors. J. Phys. Condens. Matter 5, 8773.

11. Bjorrnsson, P., M. Rubhausen, J. Backstrom, M. Kail, S. Eriksson, J.

Eriksen and L. Borjesson (2000) Lattice and charge excitations in La1-

xSrxMnO3. Phys. Rev. B 61, 1193-1197.

165

12. Bibes, M., L. Balcells, S. Valencia, J. Fontcuberta, M. Wojcik, E

Jedryka, and S. Nadolski (2001) Nanoscale Multiphase Separation at

La2/3Ca1/3MnO3/SrTiO3 Interfaces. Phys. Rev. Lett. 87, 067210.

13. Bismayer, U., V. Devarajan and P. Groves (1989) Hard mode Raman

spectroscopy and structural phase transition in the relaxor ferroelectric lead

scandium tantalate, Pb(Sc0.5Ta0.5)O3. J. Phys: Condens. Matter 1, 6977-

6986.

14. Bonneau, P., P. Garnier, E. Husson and A. Morell (1989) Structural

study of PMN ceramics by X-ray diffraction between 297 and 1023 K.

Mat. Res. Bull. 24, 201-206.

15. Burns, G. and. F. H. Dacol (1983a) Glassy polarization behavior in

ferroelectric compounds Pb(Mg1/3Nb2/3)O3 and Pb(Zn1/3Nb2/3)O3. Solid

State Commun. 48, 8532.

16. Burns, G. and F. H. Dacol (1983b) Crystalline ferroelectrics with glassy

polarization behavior. Phys. Rev. B 28, 2527.

17. Butcher S. J. and N. W. Thomas (1991) Ferroelectricity in the system

Pb1-xBax(Mg1/3Nb2/3)O3. J. Phys. Chem. Solids. 52, 595.

18. Burton B. P. and E. Cockayne (1999) Why Pb(B,B')O3 perovskites

disorder at lower temperatures than Ba(B,B')O3 perovskites. Phys. Rev. B

60, R12542–R12545.

19. Chen, J., H. M. Chan and M. P. Harmer (1989) Ordering structure and

dielectric properties of undoped and La/Na doped Pb(Mg1/3Nb2/3)O3. J.

Am. Ceram. Soc. 72, 593.

20. Chen, I. W., P. Li, and Y. Wang (1996) Structural origin of relaxor

perovskites. J. Phys. Chem. Solids 57, 1525-36.

21. Cheng, Z. Y., L. Y. Zhang and Xi Yao (1996) Investigation of glassy

behavior of lead magnesium niobate relaxors. J. Appl. Phys. 79, 8615.

22. Cheng, Z.Y. and R. S. Katiyar (1997) Dielectric behavior of lead

magnesium niobate relaxors. Phys. Rev. B 55, 8165.

23. Cheng, Z.Y. and R. S. Katiyar (1998a) Dielectric properties and glassy

behaviour in the solid-solution ceramics Pb(Zn1/3Nb2/3)O3 -PbTiO3 -

BaTiO3. Philos. Mag. B 78, 279.

24. Cheng, Z.Y. and R. S. Katiyar (1998b) Temperature dependence of the

dielectric constant of relaxor ferroelectrics. Phys. Rev. B 57, 8166.

25. Cheng, Z. Y., Aqiang Guo, X. Yao and R. S. Katiyar (1998c) Dielectric

behaviour of quenched PLZT 7/70/30 ceramics. IEEE 521-524.

166

26. Cho, E. S., J. Kim and S. L. Kang (1997) Effect of PbO content on the

microstructure and dielectric constant of 0.8Pb(Zn1/3Nb2/3)O3-0.1BaTiO3-

0.1PbTiO3. Jap. J. Appl .Phys. 36, 5562-5565.

27. Choo, W. K., and H. Y. Kim (1992) Diffuse phase transition of barium-

substituted lead-ytterbium-niobate ceramics. J. Phys: Condens. Matter 4,

2309-2321.

28. Choo, W. K., H. J. Kim, J. H. Yang, H. Lim, J. Y. Lee, J. R. Kwon and

C. H. Chun (1993) Crystal structure and B-site ordering in

Antiferroelectric Pb(Mg1/2W1/2)O3, Pb(Co1/2W1/2)O3 and Pb(Yb1/2Nb1/2)O3. Jap. J. Appl. Phys. 32, 4249-4253.

29. Chu, F., N. Setter and A. K. Tagantsev (1993) The spontaneous relaxor-

ferroelectric transition of Pb(Sc0.5Ta0.5)O3. J. Appl. Phys. 74, 5129-5134.

30. Chu, F., I. M. Reaney, and N. Setter (1995) Spontaneous (zero-field)

relaxor–to–ferroelectric-phase transition in disordered Pb(Sc1/2Nb1/2)O3. J.

Appl. Phys. 77, 1671-1676.

31. Colla, E. L., I. M. Reaney and N. Setter, (1993) Effect of structural

changes in complex perovskites on the temperature coefficient of the

relative permittivity. J. Appl. Phys. 74, 3414-3425.

32. Colla, E. V., E. Y. Koroleva, N. M. Okuneva and S. B. Vakhrushev

(1992) Low-frequency dielectric response of PbMg1/3Nb2/3O3. J. Phys:


33. Cohen, R.E (1992) Origin of ferroelectricity in oxide ferroelectrics and

the difference in ferroelectric behavior of BaTiO3 and PbTiO3. Nature 358,

136-138.

34. Conlon, K. H., H. Luo, D. Viehland, J. F. Li, T. Whan, J. H. Fox, C.

Stock, and G. Shirane (2004) Direct observation of the near-surface layer

in Pb(Mg1/3Nb2/3)O3 using neutron diffraction. Phys. Rev. B 70, 172204.

35. Cross, L. E. (1994) Relaxor ferroelectrics: an overview. Ferroelectrics

151, 305-320.

36. Dai, X., A. DiGiovanni, and D. Viehland (1993) Dielectric properties of

tetragonal lanthanum modified lead zirconate titanate ceramics. J. Appl.

Phys. 74, 3399-3405.

37. Dai, X., Z. Xu, and D. Viehland (1995) Normal to relaxor ferroelectric

transformations in lanthanum-modified tetragonal-structured lead zirconate

titanate ceramics. J. Appl. Phys. 79, 1021-1026.

167

38. Darlington, C. N. W. (1991) Studies of transitions in ordered and

disordered perovskites: x-ray and Mössbauer scattering experiments. J.

Phys. Condens. Matter 3, 4173-4185.

39. de Mathan, N., E. Husson and A. Morell (1991a) Structural study of a

poled PbMg1/3Nb2/3O3 ceramic at low temperature. Mater. Res. Bull. 26,

1167.

40. de Mathan, N., E. Husson, G. Calverin, J.R. Gavarri, A.W. Hewat and

A. Morell (1991b) A structural model for the relaxor Pb(Mg1/3Nb2/3)O3 at

5K. J. Phys. Condens. Matter 3, 8159-8171.

41. Demyanov, V. V. (1971) An experimental check of the theory of

microwave dispersion of the permittivity ε of BaTiO3 -type ferroelectrics.

Sov. Phys. - Solid State 8, 1921-1925.

42. Dhirendra Mohan, Ram Prasad and S. Banerjee (2001) Effect of post

sinter annealing on the dielectric constants of PMN and PFN. Cerams. Int.

27, 243-246.

43. Fan, H., L Kong, Lianying Zhang, and Xi Yao (1998) Structure-

property relationships in lead zinc niobate based ferroelectric ceramics. J.

Appl. Phys. 83, 1625-1630.

44. Fatuzzo, E. and W. J. Merz (1967) Ferroelectricity. North Holland

publishing company- Amsterdam.

45. Frenkel, A. I., D. M. Pease, J. Giniewicz, E. A. Stern, D. L. Brewe, M.

Daniel and J. Budnick (2004) Concentration-dependent short-range order

in the relaxor ferroelectric (1–x)Pb(Sc,Ta)O3-xPbTiO3. Phys. Rev. B 70,

014106.

46. Furuya, M., T. Mori, and A. Ochi (1994) Transmission electron

microscopy study of B-site cation configurations in perovskite-structured

Pb(Mg1/2W1/2)O3-Pb(Ni1/3Nb2/3)O3-PbTiO3 ceramics J. Appl. Phys. 75,

4144-4151.

47. Galasso, F. and J. Pyle (1963) Ordering in compounds of

A(B′0.33B″0.66)O3 type. Inorg. Chem. 2, 482.

48. Galasso, F. and J. Pinto (1965) Growth of single crystals of

Ba(B′0.33B″0.66)O3 perovskite-type compounds. Nature 207, 70.

49. Gehring, P. M., S. E. Park and G. Shirane (2001) Dynamical effects of

the nanometer-sized polarized domains in Pb(Zn1/3Nb2/3)O3. Phys. Rev. B

63, 224109.

168

50. Gehring, P. M., K. Ohwada, and G. Shirane (2004)Electric-field effects

on the diffuse scattering in PbZn1/3Nb2/3O3 doped with 8% PbTiO3 Phys.

Rev. B 70, 014110.

51. Glazounov, A. E., A. K. Tagantsev and A. J. Bell (1996) Evidence for

domain-type dynamics in the ergodic phase of the PbMg1/3Nb2/3O3 relaxor

ferroelectric. Phys. Rev. B 53, 11281–11284.

52. Glazounov, A. E., A. J. Bell and A. K. Tagantsev (1995) Relaxors as

superparaelectrics with distributions of the local transition temperature. J.

Phys: Condens. Matter 7, 4145-4168.

53. Glazounov, A. E. and A. K. Tagantsev (2000) Phenomenological Model

of Dynamic Nonlinear Response of Relaxor Ferroelectrics. Phys. Rev. Lett.

85, 2192–2195.

54. Granado, E., O. Moreno, A. Gracia, J. A. Sanjurjo, C. Rettori, I.

Torriani, S. Oseroff, J. J. Neumeier, K. J. McClallan, S. W. Cheong

and Y. Tokura (1998) Phonon Raman scattering in R1-xAxMnO3+ delta

(R=La,Pr; A=Ca,Sr). Phys. Rev. B 58, 11435-11440.

55. Gregora, I., J. Petzelt, J. Pokomy, V. Vorlicek, Z. Zikmund, R.

Zurmuhlen and N. Setter (1995) Raman spectroscopy of the zone centre

improper ferroelastic transition in ordered Ba(Yb1/2Nb1/2)O3 complex

perovskite ceramic. Solid State Commun. 94, 899-903.

56. Guo, H. K., G. Fu, X. G. Tang, J. X. Zhang and Z. X. Chen (1998) The

dielectric relaxation relationship of PMN - PT ceramics. J. Phys: Condens.

Matter 10, L297-L302.

57. Gupta, S. M., and D. Viehland (1996) Role of charge compensation

mechanism in La-modified Pb(Mg1/3Nb2/3)O3–PbTiO3 ceramics: Enhanced

ordering and pyrochlore formation. J. Appl. Phys. 80, 5875-5883.

58. Güttler, B., B. Mihailova, R. Stosch, U. Bismayer and M. Gospodinov

(2003) Local phenomena in relaxor-ferroelectric PbSc0.5B″0.5O3 (B″=Nb,

Ta) studied by Raman spectroscopy. J of Molecular Structure 661-662,

469-479.

59. Holman, R. L. and R. M. Fulrath (1972) Intrinsic nonstoichiometry in

single-phase Pb(Zr0.5Ti0.5)O3. J. Am. Ceram. Soc. 55, 192-195.

60. Holman, R. L. and R. M. Fulrath (1973) Intrinsic nonstoichiometry in

lead zirconate-titanate system determined by Knudsen effusion. J. Appl.

Phys. 44, 5227-5236.

169

61. Husson, E., L. Abello and A. Morell (1990) Short range order in

PbMg1/3Nb2/3O3 ceramics by Raman spectroscopy. Mat. Res. Bull. 25, 539-

545.

62. Ichinose, N. and N. Kato (1994) Dielectric properties of

Pb(Fe1/2Nb1/2)O3-based ceramics. Jpn. J. Appl. Phys. 33, 5423-5426.

63. Ikegami Seiji (1963) Mechanism of microwave dielectric dispersion in

polycrystalline BaTiO3. J of Phys. Soc. Jpn. 18, 1203-1213.

64. Idink, H. and W. B. White (1994) Raman spectroscopic study of order-

disorder in lead magnesium niobate. J. Appl. Phys. 76, 1789-1793.

65. Im, K. V., W. K. Choo and C. K. K. Choo (1996) Structural phase

transition in La-substituted Pb[(Yb1/2Nb1/2)0.88Ti0.12]O3 relaxor system.

Jpn.J.Appl.Phys. 35, 5217-5219.

66. Iwata, M., N. Tomisato, H. Orihara, H. Ohwa, N. Yasuda and Y.

Ishibashi (2001) A Raman study of phase transition in the (1-

x)Pb(Zn1/3Nb2/3)O3 - x PbTiO3 system. Ferroelectrics 261, 83-88.

67. Jiang, F. and S. Kojima (1999) Raman scattering of

0.91Pb(Zn1/3Nb2/3)O3-0.09PbTiO3 relaxor ferroelectric single crystals. Jpn.

J. Appl. Phys. 38, 5128-5132.

68. Jiang, F., S. Kojima, C. Zhao and C. Feng (2000) Raman scattering on

the B-site order controlled by A-site substitution in relaxor Perovskite

ferroelectrics. J. Appl. Phys. 88, 3608-3612.

69. Jiang, F., S. Kojima, C. Zhao and C. Feng (2001) Chemical ordering in

lanthanum-doped lead magnesium niobate relaxor ferroelectrics probed by

A1g Raman mode. Appl. Phys. Lett. 79, 3938-3940.

70. Kamba, S., E. Buixaderas, J. Petzelt, J. Fousek, J. Nosek and P.

Bridenbaugh (2003) Infrared and Raman spectroscopy of

[Pb(Zn1/3Nb2/3)O3]0.92–[PbTiO3]0.08 and [Pb(Mg1/3Nb2/3)O3]0.71–

[PbTiO3]0.29 single crystals. J. Appl. Phys. 93, 933-939.

71. Kania, A., J. E. Kugel, G. E. Roleder and M. Hafid (1995) A Raman

investigation of the ordered complex perovskite PbMg0.5W0.5O3. J. Phys:


72. Kim, H. J. and W. K. Choo (1992) Dipolar relaxation of (Pb1-

xBax)(Yb1/2Nb1/2)O3 in the diffuse phase transition. Ferroelectrics 158,

265-270.

73. Kim, H. S. and W. K. Choo (2002) Phase transitions of Pb(Yb1/2Nb1/2)O3

as the Ba2+ substituting in A-site. Ferroelectrics 269, 147-152.

170

74. Kim, H. S., J. H. Kim, W. K. Choo and N. Setter (2001) Phase transition

behaviours of (1–x)Pb(Yb1/2Nb1/2)O3–xBa(Yb1/2Nb1/2)O3 ceramics. J. Eur.

Ceram Soc. 21, 1665-1668.

75. Kim, B. K. (2002) Probing of nanoscaled nonstoichiometric 1:1 ordering

in Pb(Mg1/3Nb2/3)O3-based relaxor ferroelectrics by Raman spectroscopy.

Mat. Sci. Engg. B 94, 102.

76. Kimura, T., Y. Tomioka, R. Kumai, Y. Okimoto, and Y. Tokura

(1999) Diffuse Phase Transition and Phase Separation in Cr-Doped

Nd1/2Ca1/2MnO3: A Relaxor Ferromagnet. Phys. Rev. Lett. 83, 3940–3943.

77. Kingon, A. I. and B. Clark (1982) Sintering of PZT ceramics: I,

Atmosphere control. J. Am. Ceram. Soc. 66, 253-256.

78. Kingon, A. I. and B. Clark (1982) Sintering of PZT ceramics: II, Effect

of PbO content on densification kinetics. J. Am. Ceram. Soc. 66, 256-260.

79. Kittel, C (1951) Domain Boundary Motion in Ferroelectric Crystals and

the Dielectric Constant at High Frequency. Phys. Rev. 83, 458.

80. Kwon, J. R., C. K. K. Choo and W. K. Choo (1991) Dielectric studies

and X-ray Diffraction studies in highly ordered complex perovskite

Pb(Yb1/2Nb1/2)O3. Jpn. J. Appl. Phys. 30 1028-1033.

81. La-Orauttapong, D., J. Toulouse, J. L. Robertson, and Z. G. Ye (2001)

Diffuse neutron scattering study of a disordered complex perovskite

Pb(Zn1/3Nb2/3)O3 crystal. Phys. Rev. B 64, 212101.

82. Levstik, A., Z. Kutnjak, C. Filipic, and R. Pirc (1998) Glassy freezing

in relaxor ferroelectric lead magnesium niobate. Phys. Rev. B 57, 11204–

11211.

83. Li, P., Y. Wang and I. Chen (1994) Local atomic structure of PZN and

related perovskites I. An XANES study of ionicity/covalency.

Ferroelectrics 158, 229-234.

84. Lian, J. Y. and T. Shiosaki (1991) Phase transition characteristics in

PbZrO3 based PZT-PZN solid solution ceramics. IEEE Trans. on

ultrasonics, ferroelectrics and frequency control 38, 564-568.

85. Lu, C. and J. Lin, (1997) Interaction between lead iron niobate/tungstate

ceramics and silver/palladium metals Ceram. Int. 23, 223-228.

86. Lu Yalin (2004) Dielectric and ferroelectric behaviors in

Pb(Mg1/3Nb2/3)O3–PbTiO3 rhombohedral/tetragonal superlattices. Appl.

Phys. Lett. 85, 979-981.

171

87. Lu, Z. G. and G. Calvarin (1995) Frequency dependence of the complex

dielectric permittivity of ferroelectric relaxors. Phys. Rev. B 51, 2694.

88. Lushnikov, S., S. Gvasaliya and R. S. Katiyar (2004) Behavior of

optical phonons near the diffuse phase transition in relaxor ferroelectric

PbMg1/3Ta2/3O3. Phys. Rev. B 70, 172101.

89. Matsuo, Y., H. Sasaki, S. Hayakawa, F. Kanamaru, and M. Koizumi,

(1969) J. Am. Ceram. Soc. 52, 516.

90. Migoni, R., H. Bilz, and D. Bäuerle (1976) Origin of Raman Scattering

and Ferroelectricity in Oxidic Perovskites. Phys. Rev. Lett 37, 1155-1158.

91. Mihailova, B., U. Bismayer, B. Guttler, M. Gospodinov and L.

Konstantinov (2002) Local structure and dynamics in relaxor-ferroelectric

PbSc1/2Nb1/2O3 and PbSc1/2Ta1/2O3 single crystals. J. Phys: Condens.

Matter 14, 1091.

92. Mulvihill, M. L., L. E. Cross, W. Cao and K. Uchino (1997) Domain-

Related Phase Transition like Behavior in Lead Zinc Niobate Relaxor

Ferroelectric Single Crystals J. Am. Ceram. Soc. 80, 1462-1468.

93. Nomura, S. and H. Arima, (1972) Dielectric and piezoelectric properties

in the ternary system of Pb(Zn1/3Nb2/3)O3- Ba(Zn1/3Nb2/3)O3-PbTiO3. Jap.

J. Appl. Phys. 11, 358-364.

94. Ohwa, H., M. Iwata, N. Yasuda and Y. Ishibashi (1998a) Raman

scattering in relaxor Pb(Zn1/3Nb2/3)O3. Jap. J. Appl. Phys. 37, 5410-5412.

95. Ohwa, H., M. Iwata, N. Yasuda and Y. Ishibashi (1998) Temperature

Dependence of the Raman spectra in Pb(Mg1/3Nb2/3)O3. Ferroelectrics

218, 53-61.

96. Ohwa, H., M. Iwata, H.Orihara, N. Yasuda and Y. Ishibashi (2001)

Raman Scattering in (1-x)Pb(Mg1/3Nb2/3)O3-xPbTiO3 J Phys. Soc. Jpn. 70,

3149-3154.

97. Onada, M., J. Kuwata, K. Kaneta, K. Toyama and S. Nomura (1982)

Ba(Zn1/3Nb2/3)O3- Sr(Zn1/3Nb2/3)O3 solid solution ceramics with

temperature-stable high dielectric constant and low microwave loss. Jpn.

J. Appl. Phys. 21, 1707-1710.

98. Park, K. H. and W. K. Choo (1998) Crystal structure and domain-wall

orientations of antiferroelectric Pb(Yb1/2Nb1/2)O3. J. Phys: Condens.

Matter 10, 5995-6007.

172

99. Pattnaik, R. K. and J. Toulouse (1999) Dielectric relaxation and

resonance in relaxor ferroelectric K1-xLixTaO3. Phys. Rev. B 60, 7091–

7098.

100. Poplavko, Y., M. Tsykalov and V. I. Molchanov (1969) Microwave

dielectric dispersion of the ferroelectric and paraelectric phases of Barium

titanate. Sov. Phys. - Solid State 10, 2708-2709.

101. Priya, S. and D. Viehland (2002) Importance of structural irregularity on

dielectric loss in (1–x)Pb(Mg1/3Nb2/3)O3–(x)PbTiO3 crystals. Appl Phys

Lett. 80, 4217-4219.

102. Prouzet, E., E. Husson, N. deMathan and A. Morell (1993) A low-

temperature extended X-ray absorption study of the local order in simple

and complex perovskites. II. PMN (PbMg1/3Nb2/3O3). J. Phys: Condens.

Matter 5, 4889-4902.

103. Ramani, G. V. and D. C. Agarwal, (1993) Stabilization of the perovskite

phase and dielectric properties in Pb(Zn1/3Nb2/3)O3-Pb(Fe1/2Nb1/2)O3

relaxor ferroelectrics. Ferroelectrics 150, 291-301.

104. Randall, C. A. and A. S. Bhalla (1990) Nanostructural-property relations

in complex lead perovskites. Jpn. J. Appl. Phys. 29, 327-333.

105. Randall, C. A. and A. S. Bhalla (1989) Classification and consequences

of complex lead perovskite ferroelectrics with regard to B-site Cation

Order. J. Mater. Res. 5, 829-834.

106. Rosenfeld, H. D. and T. Egami Short and intermediate range structural

and chemical order in the relaxor ferroelectric lead magnesium niobate.

Ferroelectrics 164, 133-141.

107. Samara, G. A. Ferroelectricity revisited - advances in materials and

physics. Solid State Physics 56, 239-459.

108. Schmidbauer, E. and J. Schneider (1997) Electrical resistivity,

thermopower, and 57Fe Mössbauer study of FeNbO4 J Sol. State Chem.

134, 253-264.

109. Setter, N. and L. E. Cross (1980) The role of B-site cation disorder in

diffuse phase transition behavior of perovskite ferroelectrics. J Appl Phys.

51, 4356-4360.

110. Setter, N. and I. Laulicht (1987) The observation of B-site ordering by

Raman scattering in A(B'B'')O3 perovskites Appl. Spec. 41, 526-528.

173

111. Siny, I. G., R. Tao, R. S. Katiyar, R. Guo and A. S. Bhalla (1998)

Raman spectroscopy pf Mg-Ta order-disorder in Ba(Mg1/3Ta2/3)O3. J Phys.

Chem. Solids 59, 181-195.

112. Smolenskii, G. A. and A. I. Agranovskaya (1959) Dielectric polarization

of a number of complex compounds. Sov. Phys. Solid State 1, 1429-1437

113. Smolenskii, G. A., V. A. Isupov and A. I. Agranovskaya (1959) New

ferroelectrics of complex composition of the type A22+(BI

3+BII5+)O6. I. Sov.

Phys. Solid State 1, 150-151

114. Smyth, D. M., M. P. Harmer and P. Peng (1989) Defect chemistry of

relaxor ferroelectrics and the implications for dielectric degradation. J. Am.

Ceram. Soc. 72, 2276-2278.

115. Saha, S. and T. P. Sinha (2002) Structural and dielectric studies of

BaFe0.5Nb0.5O3. J.Phys.: Condens. Matter 14, 249-258.

116. Stanford, A. L., Jr. (1961) Dielectric Resonance in Ferroelectric Titanates

in the Microwave Region. Phys. Rev 124, 408–410.

117. Swartz, S. L. and T. R. Shrout (1982) Fabrication of perovskite lead

magnesium niobate. Mat. Res. Bull. 17, 1245-1250.

118. Tagantsev, A. K. (1994) Vogel-Fulcher relationship for the dielectric

permittivity of relaxor ferroelectrics. Phys. Rev. Lett. 72, 1100–1103

119. Tagantsev, A. K. and A. E. Glazounov (1999) Does freezing in

PbMg1/3Nb2/3O3 relaxor manifest itself in nonlinear dielectric

susceptibility? Appl Phys Lett. 74, 1910-1912.

120. Tagantsev, A. K. and A. E. Glazounov (1998) Mechanism of

polarization response in the ergodic phase of a relaxor ferroelectric. Phys.

Rev. B 57, 18–21.

121. Thomas, N. W. (1990) A new frame work for understanding relaxor

ferroelectrics. J. Appl. Chem. Solids 51, 1419-1431.

122. Toulouse, J., B. E. Vugmeister, and R. Pattnaik (1994) Collective

Dynamics of Off-Center Ions in K1-xLixTaO3: A Model of Relaxor

Behavior Phys. Rev. Lett. 73, 3467–3470

123. Tsurumi, T., K. Soejima, T. Kamiya and M. Daimon (1994)

Mechanism of Diffuse phase transition in relaxor ferroelectrics. Jap. J.

Appl. Phys. 33 1959-1964.

174

124. Viehland, D., S. J. Jang, L. E. Cross and M. Wuttig (1990) Freezing of

the polarization fluctuations in lead magnesium niobate relaxors J. Appl.

Phys. 68, 2916-2921.

125. Viehland, D., S. J. Jang, L. E. Cross and M. Wuttig (1991a) Internal

strain relaxation and the glassy behavior of La-modified lead zirconate

titanate relaxors. J. Appl. Phys., 69, 6595-6602.

126. Viehland, D., S. J. Jang, L. E.Cross and M. Wuttig (1991b) Local polar

configurations in lead magnesium niobate relaxors. J. Appl. Phys. 69 414-

419.

127. Viehland, D., J. F. Li, S. J. Jang, L. E. Cross and M. Wuttig (1991c)

Dipolar-glass model for lead magnesium niobate. Phys. Rev. B 43, 8316–

8320.

128. Viehland, D., S. J. Jang, L. E. Cross and M. Wuttig (1992) Deviation

from Curie-Weiss behavior in relaxor ferroelectrics. Phys. Rev. B 46,

8003–8006.

129. Viehland, D., J. F. Li, S. J. Jang, L. E. Cross and M. Wuttig (1992)

Glassy polarization behavior of relaxor ferroelectrics. Phys. Rev. B 46,

8013–8017.

130. Viehland, D. and J. Li (1993) Compositional instability and the resultant

charge variations in mixed B-site cation relaxor ferroelectrics. J. Appl.

Phys. 74, 4121-4124

131. Viehland, D. and J. Li (1994a) Dependence of the glasslike

characteristics of relaxor ferroelectrics on chemical ordering J. Appl. Phys.

75, 1705-1709

132. Viehland, D. and J. Li (1994b) The role of local compositional instability

in mixed B-site cation relaxors. Ferroelectrics 158, 381-386.

133. Vierheilig, A., A. Safari and A. Halliyal (1992) Phase stability and

dielectric properties of ceramics in the Pb(Zn1/3Nb2/3)O3-Pb(Ni1/3Nb2/3)O3-

PbTiO3 relaxor ferroelectric system. Ferroelectrics 135, 147-155.

134. Villegas, M., A. C. Caballero, C. Moure, P. Duran and J. F. Fernandez

(2000) Influence of processing parameters on the sintering and electrical

properties of Pb(Zn1/3Nb2/3)O3-based ceramics. J. Am. Ceram. Soc. 83,

141-146.

135. Vugmeister, B. E. and M. D. Glinchuk (1990) Dipole glass and

ferroelectricity in random-site electric dipole systems. Rev. Mod. Phys. 62,

993–1026

175

136. Vugmeister, B. E. and H. Rabitz (2000) Coexistence of the critical

slowing down and glassy freezing in relaxor ferroelectrics. Phys. Rev. B

61, 14448–14453.

137. Wang, S. F., U. Kumar, Y. S. Chou, P. Marsh and H. Kunkel (1994)

Effect of preparation parameters on the induced piezoelectric and

mechanical properties of 0.9PMN-0.1PT ceramics. Ferroelectrics 158,

393-398.

138. Wang, X., Z. Gui, L. Li and X. Zhang (1994) Mössbauer study on

valency state of iron ions in Pb(Fe1/2Nb1/2)O3 ceramics. Mat. Lett. 20, 75-

78.

139. Wu, L. and Y. Liou (1995) Properties of PMN and 0.9PMN-0.1PT

ceramics sintered with various heating rates. Ferroelectrics 168, 251-259.

140. Xi, Y., C. Zhili, and L. E. Cross (1983) Polarization and depolarization

behavior of hot pressed lead lanthanum zirconate titanate ceramics. J.

Appl. Phys. 54, 3399-3403.

141. Xu, G., Z. Zhong, H. Hiraka, and G. Shirane (2004) Three-dimensional

mapping of diffuse scattering in Pb(Zn1/3Nb2/3)O3-xPbTiO3. Phys. Rev. B

70, 174109

142. Yokosuka, M., (1995) Dielectric dispersion of the complex perovskite

oxide Ba(Fe1/2Nb1/2)O3 at low frequencies. Jap.J.Appl.Phys. 34 5338-5340.

143. Yokosuka M., (1993) Electrical and Electromechanical properties of hot

pressed Pb(Fe1/2Nb1/2)O3 ferroelectric ceramics. Jap.J.Appl.Phys. 32 1142-

1146.

144. Zhu, W., A. l. Kholkin, P. Q. Mantas, J. L. Baptista (2001)

Morphotrophic phase boundary in Pb(Zn1/3Nb2/3)O3-BaTiO3-PbTiO3

system. J. Am. Ceram Soc. 84, 1740-1744.

176

LIST OF PUBLICATIONS

Publications in refereed journals:

1. R R Vedantam, V. Subramanian, V. Sivasubramanian and V. R. K.

Murthy (2003) Low frequency dielectric study of Barium and Strontium

substituted Pb(Zn1/3Nb2/3)O3 Ceramics. Jap. J. Appl. Phys., 42, 7392-7396,

2. R R Vedantam, V. Subramanian, V. Sivasubramanian and V. R. K.

Murthy (2004) Low frequency Dielectric studies on Pb(Fe1/2Nb1/2)O3. Mat.

Sci. and Eng. B 113, 136-142.

3. R R Vedantam, V Subramanian, V Sivasubramanian and V. R. K.

Murthy Dielectric and Raman studies in (BaxPb1-x)(Yb0.5Nb0.5)O3. Accepted

in J. Phys: Condens. Matter.

Conferences:

1. V Radha Ramani, V Sivasubramanian, V Subramanian and V R K

Murthy, Preparation and dielectric characterization of (Pb1-

xBax)(Zn1/3Nb2/3)O3. XI National Seminar on Ferroelectrics and Dielectrics,

Jammu, Nov. 1-3, 2000.

2. Radha Ramani V, V Subramanian, V Sivasubramanian and V R K

Murthy, Preparation and dielectric characterization of Pb(Fe0.5Nb0.5)O3. XII

National Symposium on Ferroelectrics and Dielectrics, Indian Institute of

Science, Bangalore, December 2002.

3. R R Vedantam, V Subramanian, V Sivasubramanian and V R K Murthy,

Low Frequency dielectric studies of Strontium Substituted Pb(Zn1/3Nb2/3)O3.

Asian Meet on Ferroelectrics, Indian Institute of Science, Bangalore,

December 2003.

investigation of dielectric properties of …the thesis presents an investigation of dielectric...

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