Barrier Layer Concepts in Doped BaTiO 3 Ceramics

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2 Barrier Layer Concepts in Doped BaTiO 3 Ceramics A dissertation submitted to the Graduate School of the University of Cincinnati in partial fulfillment of the requirements for the degree of DOCTOR OF PHILOSOPHY (PhD) in the Department of Chemical and Materials Engineering of the College of Engineering and Applied Science By Harshani Tennakone B.S. University of Peradeniya, Sri Lanka M.S. University of Peradeniya, Sri Lanka January 2013 Committee Chair: Professor Relva C. Buchanan Committees: Dr. R. D. Roseman Dr. J. A. Sekhar Dr. V. Vasudevan

3 Abstract Barium titanate is one of the most extensively studied dielectric and ferroelectric ceramic, continuing to be the material of choice for many applications. Its use as a dielectric for capacitors, thermisters, piezoelectric transducers and memory devices are well known. This research reveals that exceptionally high dielectric constants and other attributes desired for electronic and energy storage device applications are achievable by selected isovalent and aliovalent doping of barium titanate. Doping of barium titanate with Nd 3+ and co-doping with Zr 4+ is being studied to elucidate the complex interactions involved in the formation of grain boundary and surface barrier layers and other morphological characteristics. Observed dielectric relaxations of the system are related to charge compensation mechanisms and dielectric properties in terms of equivalent circuits, brick layer and Maxwell Wagner-Debye models. The perovskite structure of barium titanate admits either isovalent or aliovalent substitutions depending on dopant ionic radii. Isovalent substitutions generally modify the morphology of the ceramics and induce phase changes. Aliovalent substitutions, notably trivalent rare earth ions such as Nd, modulate electronic properties inducing semiconductivity at lower concentrations. At higher concentrations or under oxidizing conditions, ionic compensation retains insulation. The most remarkable feature observed in this study is the oxygen partial pressure driven solubility of Nd in barium titanate at intermediate dopant concentrations, generating surface barrier layer morphologies with gradient variations in Ti 3+ from surface to the interior, exhibiting complex relaxation mechanisms. The study confirmed that macroscopic barrier layers over the sample surface and microscopic barrier layers in the grain boundaries profoundly influence dielectric properties, offering avenues for developing materials of high dielectric constant, low loss and good stability. Nd 2 O 3 doping from 0.3 to 0.5 mol% was identified as the region where a ii

4 diffused surface barrier layer and grain boundary barrier layers coexist. Variation of charge composition and processing parameters within this range enabled producing a material of room temperature dielectric constant exceeding and a loss ~ 0.1. Aliovalent co-doping with ZrO 2 yielded a structure with semiconducting cores and insulating grain boundaries, enhancing the dielectric constant while maintaining a low loss. Doping Nd 2 O 3 ( mol %) and ZrO 2 (1-2 mol %) produced a stable material of exceptionally high dielectric constant (~ ) and low loss (tan δ = 0.03) suitable for high energy density capacitor applications. Grain boundary segregation of ZrO 2, the higher solubility of Nd 2 O 3 in ZrO 2 than in barium titanate and oxygen diffusion dependent Nd 2 O 3 solubility, were identified as the crucial phenomena involved in modulating the structures of surface and grain boundary barrier layers. The dielectric relaxation mechanisms observed are explained on the basis of brick layer model separating relaxation into Debye and Maxwell Wagner schemes. The model explains the sensitivity of the dielectric properties to the variation of the dimensions of barriers layers and the mode of charge compensation, suggesting that effective medium theories of composite dielectrics do not rule out the possibility of achieving high static dielectric constant at relatively low loss in mixed phase systems such as Nd 2 O 3 and ZrO 2 doped barium titanate. iii

5 Copyright 2013 Harshani Tennakone iv

6 ACKNOWLEDGEMENT First and foremost I want to thank my advisor Prof. Relva C. Buchanan for his teaching, guidance, encouragement and patience during my graduate studies at the University of Cincinnati. Further, it has been an honor to work with him as a Ph.D student and his enthusiasm for research was courageous and motivated me even at the hardship of the Ph.D pursuit. I also want to thank my committee members, Dr. V. Vasudevan, Dr. R.D. Roseman and Dr. J. A. Sekhar for their support and valuable suggestions through this study. Further, I take this opportunity to thank them for their commitment for my excellence. The members of my group, Dr. Yunus Balogon, Dr. Xian Gao, Arun Surendranath, Siddharth Vaidyanathan, Yungkun Zou and Yuxuan Gong are also kindly acknowledged. Their contribution to my research as well as my personal life was immense. I am further grateful to all the support given by the students at Advanced Material Characterization Center at the University of Cincinnati for helping me analyzing the samples and the input given. This work is supported by the National Science Foundation, under grants DMR# and DMR# , which support is gratefully acknowledged. I would like to pay my gratitude to my husband for his encouragement throughout this study and the sacrifices made to keep me focused and make my research successful. Finally, I would like to thank my parents for their unconditional encouragement. I am especially thankful to my dear father, for being an excellent example for me through my life. Without him, I will never be able to acquire this greatest achievement in my life. v

7 TABLE OF CONTENTS Title i Abstract......ii Acknowledgement. v Table of Contents vi List of Tables. x List of Figures....xi Chapter 1. Introduction Chapter 2. Background and Literature Review Ferroelectric Barium Titanate Crystalline Structure and Phase Transitions Capacitance and Dielectric Properties Semiconduction in BT Site Substitution Core Shell Structures and Barrier Layers (BLs) in Doped BT Core Shell Structure Barrier Layer Capacitors (BLC) Combined Core Shell Barrier Layer Capacitors Polarization and Dielectric Relaxation Mechanisms in Doped BT Dielectric Polarization Dielectric Relaxation The Effective Medium Theory and Brick Layer Model vi

8 2.4 Oxygen Diffusion in Doped BT Kinetics of Diffusion Oxygen Diffusion and Dopant Solubility in BT Chapter 3. Motivation and Objective Chapter 4. Experimental Sample Preparation Sintering and Heat Treatment Density Measurement Dielectric and Electrical Measurements Dielectric Measurement Impedance Measurement Resistivity Measurement Microstructural Measurements X-Ray Diffraction Optical Microscopy Scanning Electron Microscopy (SEM) Secondary Ion Mass Spectroscopy (SIMS) Atomic Force Microscopy (AFM).. 57 Chapter 5. Results and Discussion Densification and Microstructure Effect of Dopant Composition Effect of Sintering Profile and Temperature vii

9 5.1.3 Effect of Binder Content and Applied Pressure Summary Characteristics of Structural Inhomogeneities Compositional Dependence Variation of Resistivity X-Ray Diffraction Analysis Analysis of the Valence State of Ti within the BL Structure Effect of Annealing Summary Dielectric Characteristics in Core-shell/ BL Structures Dielectric and Relaxation Properties of Pure BT Dielectric and Relaxation Properties of Nd/ Zr Doped BT Relaxation Behavior of the Oxidized and the Reduced Regions of the SBL Structure Summary Effect of Oxidation and Dopant Site Substitution in BL Formation Oxidation Dopant Substitution Summary Effect of Zr in Core-Shell BL Development Dielectric and Electrical Property Variation Variation of Structural Properties Summary viii

10 Chapter 6. Mathematical Model Model Description Summary Chapter 7. Summary Discussion Barrier Layer Phenomenon Induced BL Phenomenon by Annealing Combined effect of BL generation in Zr/Nd Doped BT Systems Chapter 8. Conclusions Chapter 9. Suggestions for Future Work References Appendix 1: Complex Permittivity and Dielectric Relaxation Appendix 2: Unique Oscillatory Behavior of the Dielectric Constant in 0.7 mol% Nd2O3/ 1 mol% ZrO2 Doped BT..164 ix

11 LIST OF TABLES Chapter 5 Table 5.1 Average grain sizes for specimens sintered at C for 90 minutes Table 5.2 Variations in unite cell parameters with different Nd/Zr concentrations for BT samples sintered at C, 90 minutes...88 Table 5.3 Isotopes of Ti, atomic number and the abundance..90 Table 5.4 Maximum peak intensities determined for 144Nd + and Ti 2 O 3 + in SIMS atomic mass spectrum.. 92 Table 5.5 Oxidized layer thickness measured and the calculated diffusion coefficient for 0.2 mol% Nd 2 O 3 doped BT sintered at C for 90 min and annealed for different time periods Table 5.6 Variation of the grain size over the surface and the interior region in 0.2 mol% Nd 2 O 3 doped BT samples sintered at C for 90 min and annealed for 0 to 16 hrs Table 5.7 Measured oxidized layer thicknesses and diffusion coefficients calculated using Eqn. 9(6) Table 5.8 Oxidation changes in Nd and Nd/Zr doped BT specimens sintered at C for 90 minutes. 115 Table 5.9 Calculation of the tolerance factor for Nd 3+ substitution..118 Table 5.10 Cell parameters calculated using XRD analysis for 0.7 mol% of Nd 2 O 3 1 mol% ZrO 2 doped BT sintered at C for 90 minutes 126 Chapter 7 Table 7.1 Measured oxidized layer thicknesses and the calculated diffusion coefficients for Nd/Zr doped BT sintered at C for 90 min..144 x

12 Chapter 2 LIST OF FIGURES Fig.2.1. (a) Cubic Perovskite BT structure (b) Tetragonal BT structure below the Curie temperature (T C )....7 Fig.2.2. Phases of BaTiO 3 indicating the directions of polarization Fig.2.3. (a) Six polarization/strain directions of Tetragonal structure (b) Schematic diagram showing the separation of phase boundaries Fig.2.4. (a) Circuit representation of a parallel plate capacitor (b) Charge separation under an applied electric field. 10 Fig.2.5. (a) Schematic representation of parallel plate capacitor with a dielectric medium 11 Fig.2.6. Phase transformation around the Curie temperature for a typical BT sample. 14 Fig.2.7. Mobility of a polaron inside a crystal lattice Fig.2.8. Nearest neighbors of a trivalent dopant (a) in A-site (b) in B-site Fig.2.9. Plot of atomic number vs. ioni radii for lanthanide 3 + ions, using XRD data.. 20 Fig (a) TEM image of a core-shell structure of Nb 2 O 5 doped BaTiO 3 (b) TEM analysis of Zr distribution inside a typical core-shell grain (c) Experimental Ba, Ti, Zr concentration profiles Fig Dielectric response of pure BT and BT doped with Zr sintered at C for 2hrs Fig Formation of Schottky Barrier Fig BL core-shell structure and the equivalent circuit Fig A schematic representation of Core-shell development in doped BT Fig Dielectric permittivity spectrum of a material Fig (a) Polarization of a dielectric as a function of time, t (b) Relaxational dispersion of dielectric constant ε(ω), corresponding P(t) in (a) Fig Polarization as a function of temperature for BT xi

13 Fig The equivalent electrical circuit and the corresponding Cole-Cole plot for a Debye system. 34 Fig Maxwell Wagner and Debye Models Fig The equivalent electrical circuit for a two-layer system Fig (a) MW Microstructure consisting of a large array of conducting spheres (white) surrounded by a less conducting material (black). The volume ratio of the interior to the exterior remains constant for all the coated spheres. (b) An SEM micrograph showing the microstructure of a Yitria stabilized Zirconia ceramic.(c) Corresponding Cole-cole diagram for the system Fig Schematic representation of the ideal Brick Layer Model.. 41 Fig Chemical diffusion coefficient of doped BT with Y as a function of p(o2) for different temperatures.. 45 Fig Phase diagram of BaTiO 3 solid solution Chapter 4 Fig.4.1. Flow Chart for processing doped BT ceramics Fig.4.2. Schematic of the setup for measuring the temperature dependent dielectric constant...52 Fig.4.3. Schematic setup of the sample holder to measure the frequency dependent dielectric constant Fig Schematic of the mass analyzer in SIMS...57 Fig.4.5. Setup for domain observation using AFM..57 Chapter 5. Fig.5.1. (a) % Relative density (b) room temperature dielectric constant vs. sintering temperature variations for BT powders with stoichiometric compositions and Fig.5.2. Low angle XRD spectrum for BT powders with stoichiometric ratios of 0/987 and Fig.5.3. Percentage theoretical density vs. Nd 2 O 3 mol% for Nd/Zr doped BT sintered at C for 90 minutes xii

14 Fig.5.4. SEM images of polished surfaces of (a) 0.15, (b) 0.3, (c) 0.6 and (d) 1 mol% Nd 2 O 3 doped BT sintered at C for 90 minutes Fig.5.5. SEM images of polished cross-section for (a) 0.15, (b) 2, (c) 4 mol% of ZrO 2 doped BT sintered at C for 90 minutes (d) Variation of relative density with ZrO 2 content for specimens sintered at C for 90 minutes Fig.5.6. SEM images for the secondary phase development of 0.6 mol% Nd 2 O 3 / (a) 1 (b) 2 (c) 3 mol% ZrO 2 doped BT sintered at C for 90 minutes..64 Fig.5.7. Low angle XRD spectrum for (a) Nd (b) Nd/Zr doped BT sintered at C for 90 minutes Fig.5.8. (a) Slow (b) fast sintering profiles employed to compare the effect of densification.66 Fig.5.9. SEM images of polished cross-sections corresponding to the (a) slow (b) fast sintering profiles for pure BT sintered at C for 90 minutes.. 67 Fig SEM images of polished cross-section for pure BT (Ba/Ti = 0.987) sintered at (a) C, (b) C, (c) C for 90 minutes 68 Fig.5.11.Relative density vs. sintering temperature for pure BT (Ba/Ti = 0.987) sintered for 90 minutes Fig TGA and DTA plots obtained for (a) Pure BT (Ba/Ti=0.987), (b) 0.15mol% Nd 2 O 3, 0.15 mol% ZrO 2 doped BT.69 Fig SEM images of polished BT cross-sections for the doping composition of 0.6 mol% Nd 2 O 3, 1 mol% ZrO 2, pressed at (a) 10,000 psi (b) 12,000 psi, (c) 14,000 psi (d) 16,000 psi Fig SEM images of polished cross-sections of BT at the doping composition of 0.6 mol% Nd 2 O 3, 1 mol% ZrO 2 and PVA concentrations (a) 1 wt% (b) 2 wt% (c) 3 wt% pressed at 14,000 psi and sintered at C for 90 minutes.. 71 Fig (a) Relative density (b) Porosity variation withy applied pressure for different binder contents for 0.6 mol% Nd 2 O 3, 1 mol% ZrO 2 doped BT sintered at C for 90 minutes Fig Temperature dependence of the dielectric constant with applied pressure for (a) 1wt% PVA (b) 3wt% PVA and (c) Loss vs. temperature for 1wt%, 3wt% PVA at 10,000 and 16,000 psi for 0.6 mol% Nd 2 O 3, 1 mol% ZrO 2 doped BT sintered at C for 90 minutes...72 Fig (a) Variation of the room temperature dielectric constant (b) dielectric loss (measured at 1 khz) of BT with the Nd 2 O 3 doping concentration xiii

15 Fig Dielectric constant, loss vs. temperature curves for (a) Nd (b) Nd/Zr doped BT samples sintered at C for 90 minutes..77 Fig Curie temperature vs. Nd 2 O 3 doping concentration for BT specimens sintered at C for 90 minutes 78 Fig SEM images of thermally etched (a) pure BT, (b) 0.3, (c) 0.6 and (d) 1 mol % of Nd 2 O 3 doped BT sintered at C for 90 minutes Fig AFM micrographs indicating the etch depth for 0.3 mol% Nd 2 O 3 doped BT sintered at C for 90 minutes 80 Fig Comparison of SEM images of surface and the interior of 0.3 mol% Nd 2 doped BT sintered at C for 90 minutes followed by chemical etching.81 Fig Resistivity vs. Nd 2 O 3 doping concentration for Nd/Zr doped BT sintered at C for 90 minutes Fig (a) The measurement technique adopted for cross sectional resistivity Measurement (b) Cross-sectional view of the specimen indicating the thin oxidized surface region Fig Resistivity vs. cross-sectional position for Nd 2 O 3 doped BT samples sintered at C for 90 minutes Fig XRD peaks of (400) plane on the surface and the interior of 0.7 mol% Nd 2 O 3 / 1 mol% ZrO 2 doped BaTiO 3 sintered at C for 90 minutes Fig Tetragonality ratio vs. Nd 2 O 3 doping concentration for specimens sintered at C, 90 minutes...86 Fig (a) Effect of peak broadening and merging with increased Nd 2 O 3 composition (b) Tetragonality variation across the thickness for Nd 2 O 3 doped BT samples sintered at C for 90 minutes Fig Schematic representation of the cross-sectional positions used to obtain the SIMS atomic mass spectrum..89 Fig SIMS atomic mass spectrum obtained for different cross-sectional position indicating 144Nd + and Ti 2 O 3 + peaks.91 Fig Plot of dielectric constant and loss vs. temperature for 0.2 mol% Nd 2 O 3 doped BT sintered at C for 90 minutes...93 Fig Dielectric response vs. (a) temperature (b) anneal time at C, for 0.2 mol% Nd 2 O 3 doped BT sintered at C for 90 minutes xiv

16 Fig Comparison of the dielectric response for 0.3 mol% Nd 2 O 3 doped BT sintered at C for 90 min with 0.2 mol% Nd 2 O 3 doped BT sintered at C for 90 min and annealed at C for 2hrs..96 Fig Variation of resistivity for 0.2 mol% Nd 2 O 3 doped BT sintered at C for 90 min and annealed at C..96 Fig Optical micrographs of 0.2 mol% Nd 2 O 3 doped BT sintered at C for 90 min and annealed for different time periods (In hours) Fig Oxidized layer thickness vs. annealed time for 0.2 mol% Nd 2 O 3 doped BT sintered at C for 90 min..98 Fig Oxygen diffusion coefficients vs. annealed time for 0.2 mol% Nd 2 O 3 doped BT sintered at C for 90 min Fig EDS analysis for the oxygen and Nd atomic concentration as a function of Cross sectional position for 0.2 mol% Nd 2 O 3 doped BT sintered at C for 90 min and annealed for 2 and 4hrs Fig SEM micrographs of the surface and the interior region of chemically etched 0.2 mol% Nd 2 O 3 doped BT samples sintered at C for 90 min and annealed for 0 to 16 hrs Fig Grain size vs. anneal time in 0.2 mol% Nd 2 O 3 doped BT samples sintered at C for 90 min Fig (a) Temperature (b) frequency variation of the dielectric constant (c) corresponding Cole-Cole plot for pure BT sintered at C for 90 minutes 105 Fig Imaginary permittivity vs. frequency for (a) Nd 2 O 3 doped BT and (b) 0.6 mol% Nd 2 O 3 /0-3 mol% ZrO 2 doped BT sintered at C for 90 minutes Fig (a) Cole-Cole plots (b) frequency vs. dielectric response for mol% Nd 2 O 3 / 1 mol% ZrO 2 doped BT sintered at C for 90 minutes, indicating difference in relaxation response with increased Nd 2 O 3 composition Fig Cole-cole plots for (a) 0.6 mol% Nd 2 O 3 / mol% ZrO 2 (b) 1 mol% ZrO 2 / 0.6- mol% Nd 2 O 3 doped BT sintered at C for 90 minutes. 108 Fig SEM cross-sectional image of a 0.7Nd/1Zr doped BT sintered at C for 90 minutes Fig (a) (b) Comparison of the frequency variation of dielectric constant, dielectric loss, Cole-Cole plots of a 0.6 mol % Nd 2 O 3 and 1.0 mol% ZrO 2 doped BT pellet before and after removal of the oxidized surface region xv

17 Fig Surface oxidized layer thickness vs. ZrO 2 concentration for Nd/Zr doped BT sintered at C for 90minutes..113 Fig EDS area mapping for (a) Zr and (b) Nd in a Nd/Zr doped BT sample sintered at C for 90 minutes 114 Fig Comparison of surface and the interior oxygen atomic concentrate ons (a) Nd 2 O 3 doped BT (b) 0.6 mol% Nd 2 O 3 / ZrO 2 doped BT, sintered at C for 90 minutes Fig ε vs. Nd 2 O 3 doping concentration for 0 to 3 mol% ZrO 2 and varying concentrations of Nd 2 O 3 doped BT pellets sintered at C for 90 minutes..120 Fig Dielectric constant, loss vs. temperature curves for 1 mol% of ZrO 2 and mol% of Nd 2 O 3 doped BT samples sintered at C for 90 minutes. 120 Fig Curie temperature vs. Nd 2 O 3 concentration for specimens sintered at C for 90 minutes Fig Resistivity vs. Nd 2 O 3 concentration for Nd/Zr doped BT sintered at C for 90 minutes Fig Resistivity vs. ZrO 2 content for Nd doped BT sintered at C for 90 minutes 123 Fig Tetragonality variation across the thickness for mol% of Nd 2 O 3 and 1 mol% ZrO 2 doped BT samples sintered at C for 90 minutes Fig (a) Tetragonality variation across the thickness (b) Optical microscopic cross- section (c) TEM image of the core-shell structure for 0.7 mol% of Nd 2 O 3 and 1 mol% ZrO 2 doped BT samples sintered at C for 90 minutes..126 Chapter 6 Fig.6.1. (a) Equivalent circuit constituted of series connected circuit elements representing each region in the BL structure (b) SBL/ GBBL structure (c) schematic diagram showing two adjacent grains..129 Fig.6.2. Schematic illustration of the brick layer model incorporated into combined GBBL/SBL structure. 132 Chapter 7 Fig.7.1. (a) Variation of the room temperature dielectric constant measured at 1 khz (b) Normalized oxygen atomic concentration for Nd 2 O 3 doped BT sintered at C for 90 min xvi

18 Fig.7.2. (a) Resistivity and c/a ratio vs. cross-sectional position (b) Corresponding Cole-Cole plot for 0.5 mol% of Nd 2 O 3 doped BT samples sintered at C for 90 minutes sintered at C for 90 minutes Fig.7.3. Optical micrographs of 0.2 mol% Nd 2 O 3 doped BT sintered at C for 90min (a) As-sintered (b) Annealed for 4hrs showing A- reduced semiconducting, B- diffuse gradient and C- oxidized outer regions.139 Fig.7.4. SEM micrographs for (a) surface (b) Interior for 0.2 mol% of Nd 2 O 3 doped BT sintered at C and annealed for 4hrs 141 Fig.7.5. Schematic representation of the induced BL morphology of Nd 2 O 3 doped BT specimen..142 Fig.7.6. Variation of the room temperature dielectric constant/ loss measured at 1 khz for Nd 2 O 3 doped BT sintered at C for 90 min Fig.7.7. Imaginary permittivity vs. frequency for (a) Nd 2 O 3 doped BT and (b) 0.6 mol% Nd 2 O 3 /0-3 mol% ZrO 2 doped BT sintered at C for 90 minutes xvii

19 CHAPTER 1 Introduction Ferroelectric BaTiO 3 (BT), is one of the most extensively studied and widely used ceramic materials. Its superiority as a dielectric for multilayer ceramic capacitors (MLCC) and other electronic devices applications such as PTCR (positive temperature coefficient of resistivity) sensors, piezoelectric transducers, ferroelectric thin-film memories are well known [1-4]. The microstructure and defects that govern the electrical properties of BT ceramics can be favorably controlled by donor / acceptor doping of the A and/or B sites of the ABO 3 peroskite structure [1, 3, 5-10]. The ferroelectric transition and Curie temperature (T c ), electrical conductivity, dielectric constant, breakdown voltage and the temperature stability of BT materials can also be adjusted by incorporation of suitable additives which produce combined barrier layer/ core-shell structures [11-15]. Barrier Layer Capacitors (BLC) have been developed to achieve the stable high dielectric constants at room temperature needed for the miniaturization of capacitors components. Typically, BLCs consist of reduced and oxidized regions of BT compositions distributed across the solid sample. The semiconducting and insulating regions of the BLCs are obtained by controlling the sintering atmosphere to develop a reduced inner region and oxidize outer the region to form an insulating layer. There are two categories of BLCs namely, Grain Boundary Barrier Layer Capacitors (GBBLC) and Surface Barrier Layer Capacitors (SBLC). GBBLCs are made by forming a thin insulating layer along the grain boundaries surrounding the semiconducting grains. Generally, SBLCs are fabricated via a two-step sintering process in particular by creating a semiconducting body by sintering the ceramic in a reducing atmosphere, followed by re-oxidization of the outer layer in an oxidizing atmosphere [13, 16-19]. BT 1

20 ceramics possessing both, GBBLs and SBLCs enable fine tuning of the capacitor properties. However, their fabrication is a challenge owing complex morphology which is highly sensitive to physical and chemical parameters. Kahn et al [17] was the first to observe barrier layer (BL) structures in BT ceramics. Subsequently Buchanan et al noted that introduction of isovalent cations into the B site of BT perovskite structure, significantly influenced the temperature dependence of the dielectric constant. A common B-site dopant such as Zr 4+ generally causes a linear decrease in the Curie temperature (T c ), in addition to the widely known core-shell formation [20, 21]. Besides, it has been found that with increasing ZrO 2 doping, the ferroelectric to paraelectric phase transition becomes increasingly second order [22]. Combined with BLC ceramics, core shell grain structures have been studied by Buchanan et al for developing dielectric materials with superior thermostatic properties and high break down voltages [20]. The perovskite ABO 3 structure of BT (A = Ba, B = Ti) admits doping at both A and B sites, depending on the valence and radius of the substituting ions [3]. A recognized fact is that after addition of small concentrations of trivalent rare earth (TRE) ions, insulating BT becomes semiconducting, whereas at higher doping concentrations the material reverts to an insulating phase. This semiconducting-insulating transition is the basis for the development of GBBLC ceramics. To explain the semiconducting-insulating transition, several hypotheses have been proposed. These include the presence of insulating phases at higher dopant concentrations, dopant segregation, donor compensation variations, and also changes in the compensation mechanism at the insulating-semiconducting transition [1, 2, 23]. The extensive literature [3, 4, 7, 9, 12, 24-31] on doping of BT with TRE ions indicate the complexity of the defect chemistry of trivalent doping of BT. The properties of the doped material strongly depends on the nature of the TRE ion, its concentration, Ba/Ti ratio, oxygen partial pressure during sintering, and other 2

21 sintering conditions [25, 27, 31-33]. Because of the wide range of variations and combinations permitted, studies on TRE doping of BT initiated many decades ago continues to date. More recently it has been found that TRE ions, along with acceptors such as Mn, Ca on Ti sites, improve the reliability and enhance the lifetime of MLCCs [19, 34, 35]. However, in many cases the doping mechanism and defect chemistry of TRE ion substitution into BT lattice remains poorly understood and/or controversial [36-38]. Under defined sintering conditions, each TRE dopant imparts unique property characteristics, dictated mainly, but not exclusively, by the ionic radius which decides the site occupancy. TREs of larger ionic radius at the beginning of the rare earth series (La, Ce) enter into the A site, whereas those of smaller ionic radii at the end of the series (Yb, Lu) occupy the B site. Elements in the middle of the rare earth series (notably elements from Sm to Er) show amphoteric behavior and can reside on either Ba or Ti site of the BT lattice, suggesting the possibility of a reversible flip of the site occupation [27, 31, 37]. Of the TREs dopants, Nd is special because its ionic radius lies almost midway between Ba and Ti. In particular, due to its extraordinarily high dielectric constant in Nd 2 O 3 doped BT at appropriate doping concentrations and the PTCR effect, the doping mechanism of Nd in BT has been debated and warrant further investigations. An in-depth study of defects, microstructure, surface chemistry and electrical conductivity is essential, in order to analyze and fully understand the behavior of complex BL structured materials, notably dielectrics for capacitor applications. The frequency dependent dielectric relaxation spectroscopy measurements can be employed to analyze and mathematically model the controllability of the above properties for energy storage device applications. This can be accomplished on the basis of Debye and/or Maxwell Wagner type relaxation theories along with the equivalent circuits and brick layer model approximations. A BL structure consisting of a 3

22 semiconducting region intercalated between near-insulating materials (SBL structure), can be described using the MW two-layer condenser model and further the output can be incorporated into the ideal relaxation response known as the Debye relaxation behavior where GBBL type structural features are taken into consideration [39]. Under action of an AC field, frequency dispersion or dielectric relaxation originates from a number of different polarization mechanisms such as ionic, dipolar, atomic and electronic. The presence of any dielectric relaxation (Debye, Maxwell Wagner or other) gives important clues to the possible polarization mechanisms that occur on a microscopic scale. Each relaxation process may be characterized by a relaxation time (τ), which describes the decay of the polarization with time in a periodic field [40-43]. The brick layer model helps to simplify the geometry of the grain and the grain boundary microstructure and provides a means of incorporating the material properties (i.e., dielectric constants, resistivities) as well as the dimensions of the grains and grain boundaries into the theory. As indicated the kinetics of doping and compensation mechanisms originating from rare earth dopants such as Nd is not fully understood. Hence it is important to develop theoretical models for the systems, to assess the dielectric properties and to interpret relaxation measurements. The effect of oxygen diffusion and the SBL structure development in doped BT ceramics are interrelated. The oxygen partial pressure during sintering has been shown to play an important role in controlling the trivalent carrier mobility, but needs further mechanistic understanding. The rate of oxidation of grains from the surface to the interior and the growth of the oxidized surface layers during sintering can be determined by the diffusion coefficient of O 2. Fick s laws and diffusion reaction equations can be used to estimate the oxygen diffusion coefficient. 4

23 In this work BT ceramics doped with Nd 2 O 3 and also co-doped with ZrO 2 was prepared using high purity BaTiO 3, Nd(NO) 3 and ZrO 2 as precursors materials. Doping concentrations and sintering conditions were widely varied and the resulting materials duly characterized. Dielectric relaxation experiments enabled identification of dopant concentrations and sintering conditions, yielding high static dielectric constant at minimal loss and satisfactory break-down voltages. Relaxation data were analyzed and interpreted in terms of a mathematical model, which takes into account the GBBL and SBL structure of the specimens. Further, the oxygen diffusion mechanisms leading to formation of the BL structures were studied and the related diffusion coefficients were calculated from the data. An important result of this investigation is the development of a low loss, high dielectric constant material, which excellent potential for applications in capacitor systems for electronics and energy storage uses. 5

24 CHAPTER 2 Background and Literature Review 2.1 Ferroelectric Barium Titanate The most extensively studied ferroelectric material; barium titanate continues its dominance as a basic material for dielectric capacitor applications. This section describes the properties of barium titanate, and how these properties can be modified by varying the doping and processing parameters. As trivalent rare earth dopants play a crucial role in modulating electronic properties and the structural morphology of barium titanate ceramic, literature on this area will be extensively reviewed. The previous work on aliovalent doping of barium titanate carried out at the Department of Materials Science, University of Cincinnati is also discussed and the importance of barrier layers in enhancing the dielectric properties of the barium titante ceramic, is emphasized Crystalline Structure and Phase Transitions The property of a material which allows the maintenance of a permanent electric field via macroscopic alignment of domains with net dipole moments is referred to as ferroelectricity. The phenomenon was first described by J. Valasek in 1921, while investigating the dielectric properties of Rochelle salt (NaKC 4 H 4 O 6.4H 2 O). However, the most commonly used ferroelectric material BaTiO 3 (BT), was observed to be ferroelectric in 1944 by A. von Hippel [44, 45]. Due to the unusually high dielectric constant and ferroelectric properties, BT is widely used in the manufacture of electronic components such as multilayer capacitors (MLCs), piezoelectric transducers, thermistors and a variety of other electro-optic devices. 6

25 Barium Titanate has a cubic perovskite structure [2, 16, 20]. This structure is considered as a FCC derivative in which, larger Ba 2+ cations and O 2- together form a FCC lattice while the smaller Ti 4+ cations occupy the octahedral interstitial sites in the FCC array. The corner positions of the cubic structure formed by Ba 2+ are termed A-sites and the center positions occupied by Ti 4+, inside the oxygen octahedra the B-sites. These concepts are illustrated in Fig (a) (b) Ba 2+ O 2- Ti 4+ Fig.2.1 (a) Cubic Perovskite BT structure (b) Tetragonal BT structure below the Curie temperature (T C ) In the BT structure, although the Ti-O bond is mainly ionic, it also contains a significant covalent component. If this bond was purely ionic, then the electrostatic forces would keep the Ti 4+ ion at the centre position of the structure. However, due to the covalent component, it produces an asymmetry in the octahedral TiO 8-6 cage as illustrated in Fig 1(b). Consequently, the Ti 4+ ion can become displaced towards the minimum energy position inside the oxygen cage under an applied external force or thermal fluctuation. The magnitude and direction of this movement are controlled by ionic forces and lattice vibrations of the O 2- ion respectively [13, 44]. Furthermore, in BT, the energy of the octahedral TiO 8-6 cage decreases in transforming from the cubic to the tetragonal structure. In this tetragonal state, the charge center of positive atoms (Ti 4+ ) in the TiO 8-6 octahedral cage, no longer coincides with the charge center of negative 7

26 atoms (effect of O 2- ). This gives rise to a net dipole moment per unit cell leading to a dipolar structure with the formation of domains and development of spontaneous polarization within the BT lattice. On decreasing the temperature below ~125 0 C, BT undergoes a transition to the tetragonal phase in which the cubic unit cell of the perovskite structure elongates along the c-axis with associated slight contraction along the a-axis, leading to a ratio of c/a = [7, 13]. A result of this phase transition and Ti 4+ ion displacement is the development of a net dipole moment and the onset of spontaneous polarization. The critical temperature at which the spontaneous polarization takes place is termed as the Curie temperature (T c ), below which all ferroelectric materials are polar. Above T c, the material reverts to the cubic non-polar state. When the temperature is gradually decreased below the Curie point, the cubic BT structure displays three dielectric anomalies associated with the phase transitions around 125 o C, 5 o C and -90 o C [46, 47]. Between 125 o C - 5 o C the cubic structure elongates along the c-axis and produces a tetragonal structure. This structure transforms into an orthorhombic form around 5 o C to -90 o C via elongation through the face diagonal. When cooled below -90 o C BT transforms to the rhombohedral form by elongating along the body diagonal of the orthorhombic structure. These structural accommodations are indicated in Fig 2.2. <111> Polarized Rhombohedral <110> Polarized Othorhombic <100> Polarized Tetragonal Non polar Cubic -90 o C 5 o C 125 o C Fig. 2.2 Phases of BaTiO 3 indicating the directions of polarization [13] 8

27 The alternations of the structure of BT result in a change of direction of the spoanteneous polarization with decreasing temperature. Six energitically equivalent directions of strain and polarization occur during the cubic to tetragonal phase transition (Fig. 2.3a) [13,47]. The regions of constant polarization within the tetragonal structure are known as ferroelectric domains. Domains typically are separated by 90 0 or domain boundaries (Fig. 2.3b). (a) Tetragonal (b) Cubic Tetragonal Fig. 2.3 (a) Six polarization/strain directions of Tetragonal structured BT. (b) Schematic diagram showing the separation of phase boundaries and domain structure [49] These boundaries can be nucleated or moved by an applied electric field (ferroelectric switching) or stress (ferroelastic switching). In ferroelectric switching, the polarization vector aligns with the direction of the electric field, whereas in ferroelastic switching, the direction of polarization aligns parallel to the tensile stress and perpendicular to the compressive stress [49] Capacitance and Dielectric Properties The dielectric constant or relative dielectric permittivity (ε r ) is a material property that determines the degree of electric polarization in response to an applied electric field [44]. Moreover, the dielectric properties are the result of short range displacement of charge carriers, under an applied electric field. Due to this charge displacement, energy is stored inside the material. Therefore, the capacitance can be understood as the ability to store the displaced 9

28 charges inside the material, when a potential field is applied [13, 44]. Consider two parallel plate capacitors as shown in Fig 2.4 separated by a vacuum with a distance of h and subjected to an electric field of E. From Gauss s Law it follows, 2.1 Where, σ and ε 0 are charge density and permittivity of free space respectively. h +σ -σ h + V - Fig. 2.4 (a) Circuit representation of a parallel plate capacitor (b) Charge separation under an applied electric field [49] The potential ( V) between the plates of capacitor (Fig 2.4b) is given by, Where, ds is the displacement increment of the plates. 2.2 Eqns. 2.1 and 2.2 gives; 2.3 When a dielectric material is inserted between the two parallel plates of the capacitor, an additional charge density (σ p ) of opposite sign will be created due to the polarization (Fig.2.5). Therefore, the eqn. 2.1 can be re-written for a dielectric material as follows; 10

29 2.4 h +σ T -σ T P -σ P +σ P + V - Fig. 2.5 Schematic representation of parallel plate capacitor with a dielectric medium When an electric field E is applied, bound charges in the dielectric material marginally separate creating a local dipole moment per unit volume (P). The electric displacement field (electric flux density) D is defined as; 2.5 Generally, polarization is proportional to the electric field and it is expressed as; 2.6 Where, χ e is the electric susceptibility. From eqns. 2.5 and 2.6 it follows that; 2.7 Electric displacement D is also the magnitude of charge per unite area of capacitor plate given by, 2.8 Therefore, in a parallel plate capacitor with a dielectric medium, the capacitance C is related to susceptibility through the expression given below. Where,

30 Combining above equations, capacitance (C) can be expressed as; 2.11 Although, dielectrics are generally insulators, they possess non-negligible resistivities that contribute to electrical properties, especially when alternating electric fields are applied. In this situation the effect of electrical conductivity is incorporated into a complex permittivity ε r defined as, 2.12 The response of a dielectric material to an external field generally depends on the frequency of the field. Therefore, the permittivity is a complex function of the frequency ω of the applied electric field, i.e., ε ε(ω) and the time varying electric displacement is written as ; 2.13 The dielectric constant of a medium under a static electric field is described by the low frequency limit of permittivity, the so called static permittivity ε s defined as, 2.14 The high frequency limit, the complex permittivity is commonly referred to as ε. In general, ε r depends on temperature and in most materials to a lesser extent on the applied pressure. The parameters, ε r and ε r cannot vary independently with frequency since these variations are connected through the Kramers Krönig relation which states that, a drop in ε r with increasing frequency is necessarily associated with a peak in ε r. Due to non-negligible electrical conductivity of the dielectric medium, capacitors dissipate energy when an alternating electric field is applied and the power dissipation W given by;

31 Where, f is the frequency and E is the magnitude of the applied electric field. The complex permittivity, (ε) is often pictured in a plot of ε vs. ε and power dissipation is written as, 2.16 where; 2.17 tan δ is referred to as the loss tangent [50]. Even good dielectrics have measurable electrical conductivities. For a low loss material, σ/(ωε) << 1, whereas for a good conductor σ/(ωε) >> 1. Electrical conductivity of the dielectric that contributes to loss can originate from both mobile electrons and ions. However, under normal conditions the electronic conductivity of a dielectric is low in comparison to its ionic conductivity. Ionic conductivity mainly depends on ions peculiar to dielectric substance, however, the extrinsic impurity ions in the material also contributes to the ionic conductivity. The possibility of ion movement within a crystal is closely associated with the crystal defects and the resulting migration of vacancies, which leads to migration of the charge through the entire crystal. A perfect dielectric is a material that has no conductivity, hence exhibiting only a displacement current. Therefore, it stores and releases electrical energy as if it were an ideal capacitor. Modern semiconductor integrated circuits require low voltage capacitors capable of storing a significant amount of electrical energy in a minimum volume. In the development of these passive electronic components, ceramic multilayer capacitors (CMC) play an important role due to relatively low loss, high volumetric capacitance efficiency, good temperature stability and low self-inductance. The dielectric properties of CMC systems have been greatly improved during the past few decades and further enhancement of their characteristics can be expected [18, 19, 13

32 22]. The common high dielectric constant ceramic materials used for CMC are based on BT [18, 19, 51]. However, pure BT is not qualified for direct use because it exhibits a significant change in dielectric constant near phase transition temperature. For practical capacitor formulations, BT must be physically and chemically modified. This can be affected by controlling the grain size and/or by the creation of doped regions of isovalent or aliovalent cations, which forms a grain core and a grain shell. These structures transform the sharp, high temperature Curie peak of BT into an elevated and flattened permittivity profile [13, 46, 47, 50, 52]. Furthermore, the core-shell structures leads to development microscopic barrier layers that greatly influence the dielectric properties. A ferroelectric material can lose its spontaneous polarization and becomes paraelectric at temperatures above the Curie temperature (T c ). This process involves a phase transition from tetragonal to cubic in the crystal structure as discussed in section (Fig 2.6). According to the Curie-Weiss Law, below T c the relative dielectric constant can be written as follows [13,44] Tetragonal Cubic 0.08 Dielectric Constant Rhombo hedral Orthorho mbic Loss Tangent (tan δ) (ε ) Temperature ( 0 C) 0 Fig. 2.6 Phase transformation around the Curie temperature for a typical BT sample [44] 14

33 2.18 where, C 0 is a material specific parameter referred to as the Curie Constant, T 0 is the Curie-Weiss temperature and T c is Curie temperature. Many classic ferroelectric materials obey Curie Weiss behavior in the paraelectric state and for undoped BT, T 0 is typically ~ C, much lower than T c (for BT, T c ~ C) [2, 45, 53]. Relaxor type materials show deviations in the (T c -T 0 ) value. The degree of deviation, (T c -T 0 ), indicates the order of the transition; (T c -T 0 ) > 0 indicates a first order transition with a sharp dε /dt profiles close to T c, whereas a second order transitions shows a broad ε max peak with (T c -T 0 ) = 0. The ferroelectric/paraelectric phase transition in BT under heating is considered to be first order Semiconduction in BT Pure BT is an insulator with a large energy gap (~3.05eV) and a high resistivity (10 10 Ω.cm) at room temperature. Semiconductive behavior can be induced into BT by generating O 2- vacancies via atmospheric reduction or by donor doping (with trivalent or pentavalent cations) [2, 8] For small concentration of dopants ( mol %), the n-type conductivity occurs by the valancy transformation of the Ti 4+ ion which produces a polaron [55]

34 Fig. 2.7 Mobility of a polaron inside a crystal lattice [54] A polaron is a quasiparticle consisting of a charge and its associated polarization field. When an electron in a BT crystal slowly moves within the lattice, it interacts with lattice ions and will permanently be surrounded by lattice polarization. This defect condition acts as a potential well that hinders the charge movements, thus decreasing the electron mobility. Furthermore, the polaron is characterized by its self-energy ΔE, an effective mass m* and by its characteristic response to external electric and magnetic fields. The effective mass of a polaron is rather large and is estimated to be ~ 20m 0, where, m 0 is the mass of a free electron. The mobility of a polaron (Fig. 2.7) in the BT lattice was found to be 0.65 cm 2 /V.sec above the Curie temperature and below the Curie temperature, the mobility diverges due to lattice distortions [23, 54]. According to Preis et al. [56], cation vacancies and electrons give rise to the n-type conduction when there is a negligible concentration of oxygen vacancies in the system [57]. At higher concentration of dopants, the conductivity occurs by the formation of cation vacancies. In general, the conductivity increases with increase in dopant concentration up to a critical concentration (corresponding to a resistivity minimum) before transforming into an insulating state [3]. 16

35 2.1.4 Site Substitution Site Substitution Mechanisms for Trivalent Rare Earth (TRE) Dopant Ions The Goldschmid tolerance factor t for a peroveskite structure defined as; 2.23 where, r i are the ionic radii (i=a, B, O), is an important parameter that determines the site substitution of TRE ions in BT [4, 32, 37, 38]. By substituting the ionic radii of O, Ti, Ba and Nd i.e., r o = r (O 2- VI) = 0.14 nm, r (Ti 4+ VI) = nm and r (Ba 2+ XII) = 0.161nm, r (Nd 3+ VI) = nm using Shannon s compilation, and assuming that the local strain is similar in both sites, the tolerance factors obtained are t A = for A site and t B =0.893 for B-site (Fig. 2.8). It is expected that if the incorporation of an ion into one site results in a tolerance factor much closer to unity than the incorporation into the other site, then the first one would be preferred over the second. However, as t A ~ t B in the case of Nd 3+, the Goldschmid tolerance factor argument does not provide conclusive information regarding the substitution site of Nd 3+. Fig.2.8 Nearest neighbors of a trivalent dopant (a) in A-site (b) in B-site [55] 17

36 According to D. W. Hahn et al [3] and Y. Yuan et al [58], who summarized several studies, the ions from the beginning of the rare earth series (La 3+, Ce 3+ ) are incorporated exclusively into the A site of the BT structure (Fig. 2.8a), whereas the smaller ions from the end of the series (Lu 3+, Yb 3+ ) enter the BT structure at the B-site (Fig.2.8b). The ions from the middle of the rare earth series show amphoteric behavior, which means that, the ions could occupy both the cationic lattice sites in the BT structure [37, 38]. Therefore, generally there are three different models proposed for site occupancy in TRE cations in BT. The A- site model suggests that these dopants act as donors and induce electronic compensation [22, 59] while the B-site model suggests that the dopants act as acceptors and improve reliability by reducing the bulk diffusion of oxygen vacancies through strain and electric field interactions [4, 6, 7, 31, 37]. In the double substitution model, selfcompensation has been proposed as the substitution mechanism, dependent on Ba/Ti ratio and the oxygen partial pressure during the firing [8, 24, 27, 51, 60]. Additionally, Randall et al have studied the double substitution of TRE cations in BT and substantiated the idea by providing evidence based on X-ray diffraction (XRD), atomistic simulations, conductivity measurements, luminescence and electron paramagnetic resonance (EPR). In order to understand the influence of the site occupancy ratio, Randall et al [38] considers the following reaction for a TRE cation substituting into the BT lattice at A and B sites; Equations (2.24 and 2.25) can be written in the form,

37 and law of mass action yields the relation, 2.27 where, M is a trivalent cation and the above equation holds only during the sintering and when there is sufficient ionic mobility to establish near equilibrium conditions. Since the charge difference of trivalent ion is 1 for both sites, the author further suggests that the ionic size will be the main factor influencing the rate constant of the substitution reaction. Large ions will tend to occupy the A- sites (large K) and small ions will tend to occupy the B- sites (K approaches zero) [61]. Equation 2.27 suggests that the TRE ion site occupancy on BT depends on the Ba/Ti ratio of the material. Another set of equations can be developed by taking the Schottky barrier reaction into consideration as follows; 2.28 Here, the corresponding mass action relation can be written as below, where K x is the reaction constant of the equation If the Ba rich phase is considered; The corresponding mass action relation takes the form; Where, Ky is the rate constant of the reaction. Therefore, the ratio of 2.29 and 2.31 leads to the following relation; 2.32 When the proportionality of the reaction constants is considered, it follows;

38 Equation 2.33 indicates that the site occupancy in BT depends on the oxygen partial pressures. According to this postulation, the lattice expands with TRE ion on the B-Site and shrinks with TRE on the A-site [55]. However, the lattice shrinkage also occurs via differences in solubility as well [18]. As a consequence, the band of amphotericity in Fig. 2.9 should be pushed toward larger ionic radii for air fired samples [55]. Fig. 2.9 Plot of atomic number vs. ioni radii for lanthanide 3 + ions, using XRD data [55] Furthermore, based on XRD measurements for different TRE cations, Randall et al suggest that for ionic radii > nm, the dopants occupy B-site and the compensation is mainly via oxygen vacancies. For ionic radii falling between nm and nm, the dopants are amphoteric and finally, for ionic radii < nm, the A site substitution is prominent and the compensation is electronic [31, 55]. Substitution mechanism of Nd 3+ into BT is still controversial and the literature supports contradictory ideas. Some authors suggest that Nd 3+ solely substitute into Ba 2+ Site [7, 8, 37, 38], 20

39 while the other authors propose a double substitution mechanism [24, 60]. Furthermore, Nd 3+ could not easily be assigned to a particular site using Electron Paramagnetic Resonance (EPR) method or X-Ray Diffraction (XRD) measurements alone [62]. The studies conducted by L. Zhang et al and A. R. West et al concludes that the substitution mechanism of Nd 3+ and BT is clearly different from that of La-doped BT, where La 3+ substitutes onto the Ba 2+ site with concomitant creation of Ti 4+ vacancies [22, 59, 63]. These authors argue that the ionic radius of Nd 3+, nm is almost exactly midway between those of Ti 4+ and Ba 2+ but La 3+, nm is slightly larger [64]. Thus, Nd 3+ could substitute into the Ti 4+ sites as well, whereas La substitutes exclusively into the Ba 2+ site [65, 66]. Although ionic radii can be used to predict ion substitution behavior in a crystalline structure, one cannot rely on it alone [55]. Amphoteric substitution is further determined by the solubility of the rare earth material [3, 67]. However, diffusion mechanisms of trivalent cations within the BL structure are still to be understood. Site Substitution of Zr 4+ in Barium Titanate Addition of ZrO 2 is known to have beneficial effects on microstructural refinement, aging and dielectric properties of BT. Generally Zr 4+ substitutes into the Ti 4+ site of the BT structure because of its small ionic radii (Zr 4+ IV) = nm [64], compared to Ba and Ti [20, 61]. Buchanan et al has found that Zr 4+ reside primarily in the grain boundary forming a core-shell biphasic structure due to the low diffusivity of Zr 4+ ions when sintered < 1320 C. Furthermore, their results indicate a grain growth inhibition and suppression of the T c along with a reduction in the c/a ratio of lattice parameters giving a pseudocubic structure with higher internal stresses and a decrease in the spontaneous polarization [20, 21, 61, 68, 69, 70]. The core-shell structure formation in Zr doped BT observed Buchanan et al [61] and the subsequent work on co-doping 21

40 of TRE doped BT with Zr has profound implications on modulating dielectric properties of BT via combined grain boundary and surface barrier layer formation. 2.2 Core Shell Structures and Barrier Layers (BLs) in Doped BT Work conducted under this project and number literature reports indicate that core-shell structured doped barium titanate ceramic exhibits favorable dielectric characteristics owing to formation of grain boundary and surface barrier layer structures. This section reviews previous work in this area of research including mathematical modeling useful for gaining insight into a complex problem of utmost importance for development of barium titanate based dielectric ceramics for electronic and energy storage applications Core Shell Structure Core shell grains in BT ceramics consists of cores of pure BT grains surrounded by a shells of modified BT as shown in Fig. 2.10(a-c) [11, 16, 20, 21]. Generally, the shell is in a paraelectric state whereas, the core remains ferroelectric. In these structures, the dopant concentration varies from the core towards shell and a T c distribution can be observed due to the existence of the compositional gradients (Fig 2.10b,c) of additives and the increase of the volume fraction of ferroelectric domains in the high gradient regions [11, 20, 16, 21]. The dielectric constant of the core-shell BT will mainly depends, therefore, on the grain and domain sizes, interfacial effects, distribution of Curie points, internal stress and on the inhomogeneous chemical composition state [16, 20, 21]. An earlier study has shown that, the core-shell grain morphology can be conveniently achieved by doping BT with 1-3 mol% of ZrO 2. Buchanan et al [20] observed that Zr 4+ diffuses into BT lattice by replacing Ti 4+ at the unit cell to facilitate this 22

41 morphology. They also showed that the larger Zr 4+ ion can cause an increase in the unit cell dimensions and in the lattice parameters. Due to above reasons, a volume expansion mismatch in the microstructure could induce stresses into the material [7, 16, 61]. The internal stresses originating from the core-shell grain structure generally leads to a flattened permittivity response (Fig 2.11) readily noticeable in Zr doped BT [61]. (a) (b) (c) Fig.2.10 (a) TEM image of a core-shell structure of Nb 2 O 5 doped BaTiO 3 [11] (b) TEM analysis of Zr distribution inside a typical core-shell grain [21] (c) Experimental Ba, Ti, Zr concentration profiles [69] 23

42 BaTiO 3 BaTiO 3 +2wt% ZrO 2 Dielectric Constant Temperature ( 0 C) Fig 2.11 Dielectric response of pure BT and BT doped with Zr sintered at C for 2hrs. [69] Barrier Layer Capacitors (BLC) The interest in BLCs ascended from the possibility of getting high permittivity capacitive layers on reduced BT. Depending on the location where the barrier layer is formed, BLCs can be classified into Grain Boundary Barrier Layer Capacitors (GBBLC) and Surface Barrier Layer Capacitors (SBLC). The dielectric properties of these BLCs significantly depend upon the thickness of the barrier layer and microstructure of the semiconducting body. In GBBLCs the semiconducting grains are typically surrounded by a thin insulating layer formed around the grain boundary. This insulating layer is obtained by premixing or diffusing an oxide material after sintering into the BT ceramic and/or by annealing. As previously noted, the SBLCs consist of a semiconducting layer intermediate between two thin insulating layers. In order to produce a SBLC, the ceramic is initially sintered in a reducing atmosphere to obtain the semiconducting body as well as to prevent the electrodes form oxidation. Then by re-oxidization, an insulating layer is formed at the surface of the ceramic [16]. 24

43 In a ferroelectric material, a BL can be developed at the grain and grain boundary junction, creating a Schottky barrier effect (Fig 2.12). When T T C the energetic electrons in the conduction band (CB) of the material will tunnel into the valence band (VB), searching for lower empty energy levels. This effect produces a negative charge flow at the junction. Additionally, in BT, a BL can be created owing to the resistivity anomaly connected with different interface layers. The resistivity of doped BT ceramic increases sharply when it is heated above T c as acceptor states at the interface, create a space charge region. Then, according to the Poission s relation, the barrier height (φ B ) is given by; 2.34 GB / Insulating region Grain / SC region GB / Insulating region Depletion Layer + + Fig Formation of Schottky Barrier 25

44 where, e is the electron charge, n D is the dopant concentration and d represent the thickness of the barrier region. The barrier height mainly depends on T c and below T c it determines the direction of spontaneous polarization and ferroelectric domain orientations. The BLs are not only non-linear in resistance, but additionally exhibits a capacitance variation in parallel with the resistance. Usually these capacitance variations are associated with a high dielectric constant and high breakdown voltages [23] Combined Core Shell Barrier Layer Capacitors The combined effect of doping ZrO 2 and Nd 2 O 3 into BT and the formation of BLCs has been studied by Buchanan et al [16] who found that this novel system possess compositions of high dielectric constant (ε r = 20000), high breakdown voltage (> 800V/mm), enhanced temperature stability and high strain response. Fig.2.13 below shows an ideal model of a coreshell BL structure and its equivalent circuit. Until recently, this structure has been identified as a layer of reduced titanate ceramic sandwiched between oxidized titanate ceramic. However, these structures does not contain an abrupt transition from a conductive to an insulating phase, but rather a diffused gradient transition, gradually turning the conducting reduced region into an insulating oxidized region, maintaining the core shell structured grains as shown in Fig The core shell structure itself can be considered as a GBBL structure (Fig.2.14) while the macroscopic structure of diffused oxidized and reduced regions can be approximated to a SBL structure. Current research indicates that the BL morphology can be achieved by simply doping the BT with trivalent additives such as Nd 2 O 3 creating a complex structure of semiconducting but still ferroelectric grain core region giving a GBBL structure. These structures provide not 26

45 Electrode Oxidized Direction of Oxidation Reduced Oxidized Fig BL core-shell structure and the equivalent circuit [16] only substantially higher dielectric constants but also unique relaxation behaviors. These features can be beneficially modulated by the level of Zr addition and/or by controlled heat treatment. Therefore, the mathematical techniques adopted for modeling these structures are quite complex. Further research is thus needed for a better understanding of this complex morphology, compensation mechanisms and resulting dielectric properties of this system. Therefore, the purpose of this study is to understand the mechanism of enhancement of the dielectric properties of these co-doped BT systems and to correlate them to structural properties, in order to utilize these materials in modern integrated electronics and possibly energy storage systems. 27

46 Fig A schematic representation of Core-shell development in doped BT 2.3 Polarization and Dielectric Relaxation Mechanisms in Doped BT Microscopic processes that lead to bulk electric polarization and material properties favorable for development of a high dielectric constant low loss material can be elucidated by measurement of the real and imaginary components of the dielectric constant as a function of the frequency of the applied electric field. This technique generally referred to as dielectric relaxation spectroscopy. This section describes experimental techniques for such dielectric spectroscopy as well as the mathematical analysis used for extracting physical information from the measurements. Physical information related to the development of barrier layer structures and indications of how the ceramic should be processed in order to optimize the dielectric properties can be ascertained from the above measurements and analysis of data in the context of theoretical models. 28

47 2.3.1 Dielectric Polarization Analysis of dielectric properties as a function of frequency referred to as dielectric relaxation spectroscopy reflects the collective response of microscopic polarization processes under an external electrical field. It is a useful technique to study defects, microstructure, surface chemistry and electrical conductivity for materials, notably dielectrics for capacitor applications. Under an applied alternating electric field, frequency dispersion or dielectric relaxation originates from a number of different polarization techniques, namely, electronic, atomic, orientational and ionic polarization (Fig. 2.15). The electronic and ionic polarizations are caused by displacement of the electrons within the atom/ or molecule, while the orientational Dipolar Ionic Atomic Electronic Frequency (Hz) Fig Dielectric permittivity spectrum of a material [71] polarization is associated with the molecules having a permanent dipole moment. Unbalanced sharing of electrons by atoms of a molecule leads to a permanent dipole moment. In absence of an external electric field, these moments are oriented randomly such that no net polarization is 29

48 developed in the material. Under an external electric field, the dipoles rotate to align with the electric field causing orientation polarization. Ionic polarization consists of ionic conductivity and interfacial or space charge polarization. At low frequencies ionic conduction is predominant and it mainly introduces losses into the system. Space charge polarization occurs when more than one material component is present and when the charge carriers become trapped at the interfaces of these heterogeneous systems. Thus, the piling up of space charge in a volume, or of surface charges at an interface, incorporates large scale field patterns that greatly affect the overall polarizability of the material [72, 73]. All the polarization mechanisms can only be operated at a certain frequency and beyond that frequency limit; the polarization mechanism disappears due to the inertia of the moving entities involved. Furthermore, the dielectric loss factor (tan δ = ε"/ε ) will correspondingly peak at each critical frequency as shown in Fig The contribution of the spring-like forces in electronic and ionic polarization leads to the disappearance of polarization by the absorption at resonance and at certain frequencies of the order Hz, Hz respectively. For orientational polarization, the disappearance is accompanied by several steps of relaxation at frequencies between Hz. As discussed on section 2.1.2, the dependence of the complex dielectric constant ε(ω) = ε 1 (ω) + iε 2 (ω) on the frequency ω of an alternating field is called the dispersion of the dielectric constant. The nature of the dispersion is determined by response of the polarization as a function of time. If this process is a relaxation, (Figure 2.16a) the dispersion will have the shape shown in Figure 2.16b. Usually, the amplitude of polarization of a dielectric (P) is very small in comparison to the magnitude of polarization of a dielectric in a static field (i.e. ε 1 1 and ε 2 0). Thus, as the frequency increases, ε 1 changes from ε to 1. The greatest change in ε 1 occurs precisely at frequencies where the ε 2 passes through its maximum. This kind of a momentary 30

49 delay of the dielectric dispersion is defined as relaxational dispersion, and is associated with a relaxation time (τ). Therefore, each relaxation process may be characterized by a relaxation time which describes the decay of its polarization with time in a periodic field [74]. P ε(ω) ε ε 1 P 0 1 ε 2 0 τ t 1/τ ω Fig (a) Polarization of a dielectric as a function of time, t (b) Relaxational dispersion of dielectric constant ε(ω), corresponding P(t) in (a) [75]. So far, this discussion has been confined to the dielectric polarization which arises under the influence of an external electric field. In pyroelectric materials, the polarization occurs without the presence of an external electric field. Further, in piezoelectrics, polarization arises from deformation of the crystal and that changes the structural properties of the crystal lattice. Ferroelectrics are considered to be a sub-category of pyroelectrics. The variation of spontaneous polarization with external conditions such as temperature (P=0 at T>T C and P 0 at T<T C for E=0), electric field is observed only in ferroelectrics, which is a sub-category of pyroelectrics (Fig 2.17). The ferroelectrics characteristically show very high values of dielectric constants, strong non-linear dependence of polarization on electric field, and domain structure. 31

50 P Rhomboh edral Monoclinic Tetragonal T C1 T C2 T C3 T Fig Polarization as a function of temperature for BT Dielectric Relaxation Dielectric relaxation is the result of a movement of dipoles or electric charges due to a changing electric field in the frequency range of Hz. This mechanism is a relatively slow process when compared with electronic transitions or molecular vibrations which have frequencies above Hz. When an alternating electric field is applied to a dielectric medium, it produces a delay in molecular polarization. Therefore, the dielectric relaxation can be further considered as the momentary delay/ lag in the dielectric constant of a material. The maximum polarization corresponding to the highest observable dielectric constant can be realized in a material, only when sufficient time is allowed for the applied electric field to attain equilibrium conditions by the proper orientation of the dipoles. If the time permits to attain the equilibrium conditions, then the observed dielectric constant is the static dielectric constant (ε s ). If the polarization is measured immediately after the field is applied, (without allowing time for dipole orientation), then the instantaneous dielectric constant, ε, is observed. The relaxation time occurs in between these extremes and it is given by [60, 72, 73]; 32

51 2.35 The relaxation is often described in terms of permittivity as a function of frequency, which can be described by using the Debye equations. In addition to Debye relaxation, the existence of interfacial effects such as diffused barrier layers within the dielectric material or blocking layers at the electrodes causes trapping of charge carriers. These interfacial layers give rise to conducting regions, classified under the Maxwell Wagner effects. These effects are generally associated with the frequency dependent loss characteristics. Cole Cole relaxation and Havriliak Negami relaxation are some derivatives of the classical Debye relaxation which could apply for other types of materials such as polymers. Mainly polarization associated with Debye and Maxwell Wagner relaxation are seen in doped BT systems. Debye Relaxation Named after Peter Debye, this relaxation is considered to be the dielectric relaxation response of an ideal, non-interacting population of dipoles to an alternating external electric field. Further, when orientational polarization is present, this is the dominant polarization mechanism observed. In Debye relaxation involving a single relaxation time τ, the variation of ε r with angular frequency ω is expressed as; 2.36 Where, ε s and ε are static dielectric constant and the instantaneous dielectric constant respectively. The real and imaginary parts of the above equation can be separated as follows; and

52 A Cole-Cole plot can be generated if ε is plotted against ε as shown in Fig (a) C (b) ε" ω=1/τ ωrc = 1 Fig.2 The equivale corresponding system R ε ε' ε s Fig.2.18 The equivalent electrical circuit and the corresponding Cole-Cole plot for a Debye system This plot is typically a semicircle if the Debye conditions are obeyed. In this case the relaxation peak can be observed at ωτ =1 and τ follows an Arrhenius relation and the activation energy dominates the width of the relaxation peak. Fig.2.18a illustrates the equivalent circuit for the Debye type system. The electrical impedance of this circuit (Z) can be obtained by introducing the angular frequency ω of the sinusoidal signal as follows: 2.38 where, C is the capacitance of the Debye system. The diameter of the Cole-Cole plot typically corresponds to the resistance R of the equivalent circuit and therefore the angular frequency at the apex equals to 1/ RC [60, 76, 77]. Thus, (1) can be re-written as;

53 While the Debye dispersion describes the re-orientation of dipoles within a medium, there is a second category of dielectric dispersion (Maxwell Wagner) that occurs at the interface between two unlike dielectric materials/ electrodes as discussed at the beginning of this section. In such structures, charge carriers are usually blocked at inner dielectric boundary layers, leading to a separation of charges which in turn give rise to an additional contribution to the polarization [72]. Maxwell Wagner Relaxation The combined GBBL and SBL structures observed in Nd and Zr doped BT system deviates considerably from the ideal relaxation conditions due to the complexity of the system. Therefore, it is worth studying alternative relaxation mechanisms, which accounts for deviations from the ideal behavior. Maxwell Wagner type condenser consists of two layers of materials with different conductivities and permittivities. In such a structure, charge carriers are usually blocked at inner dielectric boundary layers, leading to a separation of charges which in turn giving rise to an additional contribution to the polarization [72]. Further, MW polarization effect can be considered as a combination of conductivity term and Debye term (Fig. 2.19) and can be effectively used to model the combined GBBL and SBL effects observed in Nd/ Zr doped BT ceramic capacitive structures. Additionally, analysis of the imaginary permittivity of these systems can be used to distinguish Debye relaxation from Maxwell Wagner behavior. In particular ε 0 as ω 0 in a Debye system, whereas in a Maxwell Wagner system ε under similar conditions [78, 79]. The presence of any dielectric relaxation (Debye, Maxwell Wagner or other) gives important clues as to the possible polarization mechanisms that occur on a 35

54 microscopic scale. The Maxwell Wagner relaxation has been discussed extensively first by Maxwell and later by Wagner in 19 th century. Due to the blocked charges at the BL boundaries, Maxwell Wagner relaxation is usually associated with materials possessing extremely high dielectric constants and relaxation times. This concept can be further expressed as a double layer resistor capacitor (RC) arrangement (Fig. 2.20), which provides the simplest model for describing an inhomogeneous structure. Fig.2.19 Maxwell Wagner and Debye Models [72, 78] In the double layer arrangement, each dielectric layer is characterized by its permittivity ε 1, ε 2 and their conductivities σ 1, σ 2. For the double layer system, the real part of the complex permittivity is the same as in the Debye relaxation (eqn. 2.37), however, the imaginary part 36

55 modifies as follows by taking the total thickness (d), thickness of each layers (d 1, d 2 ) into consideration. C 1 C 2 R 1 R 2 Fig.2.20 The equivalent electrical circuit for a two-layer system Where, And the corresponding relaxation time as; 2.43 The above discussion explains how dielectric relaxations measurements can be used to extract information about microscopic processes that occur in a dielectric medium subjected to an alternating electric field. This information is valuable in efforts to modulate dielectric properties in a combined GBBL and SBL structured diffused systems in order to predict and control the process variables such as thickness of the each layer. 37

56 2.3.3 The Effective Medium Theory and Brick Layer Model As discussed in the previous section, the impedance of an ideal capacitor system corresponding to the equivalent circuit shown in Fig. 2.18a is expressed by the eqn As observed in the same section, this circuit gives rise to semi-circular arc in the complex impedance plane. This is the basis of equivalent circuit analysis of impedance spectra, however in real situations impedance plots are more complex and the equivalent circuit needs to be modified arbitrarily incorporating additional capacitances and/or resistances to the circuit. A disadvantage of the equivalent circuit approach is absence of a clear connection between equivalent circuit and the microstructural physics of the system. An approach different to equivalent-circuit impedance analysis which resolves this problem to some extent will be to use of effective media theories and/or the Brick Layer Model (BLM). Effective medium theories express the gross physical properties of a mixture of two or more materials in terms of the properties of the individual components. The first effective media equations were generated for a dilute dispersion of spheres in a matrix by Clark Maxwell. Under dilute conditions; the effective media equations for electrical conductivity reduce to the form given below Where σ m, σ c and σ i are the complex conductivities of the composite, the more conducting component and the less conducting component respectively and f is the volume fraction of the dispersed phase. Since the complex conductivity and dielectric constant are related by σ = iωε 0 ε r, 38

57 the effective media equation above can be written in terms of the complex permittivities as follows: 2.45 The Maxwell-Wagner (MW) effective medium equation (i.e. Maxwell Garnet) basically describes the properties of a matrix driven composite structure. The microstructure corresponding to the MW model is shown in Fig.2.21a. This microstructure consists of core-shell spheres where the core region is mainly conducting compared to the shell region. However, the ideal microstructure shown in Fig. 2.21a does not occur in practice. Figure 2.21b shows a matrix driven microstructure of a ceramic composite material where the insulating grain boundaries can be considered as the shell region and the conducting grain interior can be considered as the core region [80, 81, 82]. Cole-Cole plots corresponding to this type of a microstructure usually consist of two arcs in complex impedance plane as shown in Fig. 2.21c. The complex permittivity for the MW microstructure can be obtained from; and 2.46 The BLM assumes that the material is constituted of cubic conducting bricks surrounded by insulating layers as shown in Fig This simple geometry enables expression of the effective dielectric constant and the resistivity of the medium in terms of values of the 39

58 corresponding parameters for material in the cubic bricks and the lateral layers and their dimensions. (a) (b) (c) ε" Fig (a) MW Microstructure consisting of a large array of conducting spheres (white) surrounded by a less conducting material (black). The volume ratio of the interior to the exterior remains constant for all the coated spheres. (b) An SEM micrograph showing the microstructure of a Yitria stabilized Zirconia ceramic. (c) Corresponding Cole-Cole diagram for the system [83]. ε' Generally, the cubic bricks represent the conducting grains and insulating grain boundaries, the lateral layers. The gross impedance feature of conducting grain/ insulating grain boundary system is satisfactorily described by BLM. However, recent work has shown that the details of impedance behavior depend on the shape of the grains [83]. 40

59 Conducting Grain Insulating Grain Boundary Fig Schematic representation of the ideal Brick Layer Model The combined GBBL and SBL structures observed in Nd/Zr doped BT system deviate considerably from the ideal conditions discussed above due to the complexity of the system. Therefore, it is worth studying alternative relaxation mechanisms, which accounts for deviations from the ideal behavior. Many Maxwell- Garnett type effective medium theories have been used to estimate ε r of two component medium [82]. However, the estimations based on these models are not reliable when the volume fractions of the two phases are comparable. Further, no satisfactory method has been found to incorporate an irregular shape into an effective medium theory. A useful guideline is the Weiner s upper and lower bounds ε U and ε L for the ε r of two phase system with individual dielectric constants ε 1 and ε 2 and volume fractions f 1 and f 2 given by [84]: and 2.47 Expressions in 2.47 indicate, under favorable circumstance ε r comparable to that of the component with highest permittivity may be achieved. If pure homogeneous materials of giant ε r and very high resistivity and temperature stability are available, composite systems would be unnecessary. In the absence of such materials multiphase systems seem to be a good option for achieving the high dielectric constant at relatively low loss. 41

60 2.4 Oxygen Diffusion in Doped BT Experimental investigations performed on oxygen transport in doped BT confirm the rapid diffusion of oxygen through the grain boundaries [34]. In most dielectric ceramics, space charge regions such as pores or diffused areas are often found at the grain boundaries. In these regions, the concentration of the mobile charge carriers are either enhanced or depleted. If the mobile charge carriers are negative, the positively charged oxygen vacancy concentration inside space charge layers along the grain boundaries may be enhanced. Thus, one can expect fast oxygen diffusion along grain boundaries accompanied with space charge regions. Furthermore, many [62] studies on oxygen diffusion in BT ceramics reports that the grain boundary diffusion of oxygen in donor doped BT is extremely fast at temperatures C Kinetics of Diffusion Fick s law; As in any diffusion process, the diffusion of oxygen in BT is basically governed by the 2.48 Where J, D, c and x are is the diffusion flux, diffusion coefficient, concentration of the diffusing species and the diffused distance respectively. Fick s law leads to the following differential equation. or 2.49 Solution to eqn subject to initial and boundary conditions yields, the spatio- temporal variation of the diffusing substance. A useful solution of the 1-D diffusion equation is an 42

61 instantaneous concentration released at time t =0, here the subsequent space time dependence of concentration is given by; 2.50 The above equation indicates that the width of the diffusion profile in time t is ~ 2 ( Dt ) and the result can used to estimate the diffusion coefficient of oxygen in a pellet of BT during sintering, provided oxygen concentration in the pellet is measurable. Oxygen sensors and mass spectroscopy using oxygen isotopes have used to assess the oxygen concentration. Frequently in doped materials oxidation is associated with a color change, giving ready means estimating the diffusion coefficient. Oxygen entering the system could also be consumed in reaction with BT or dopants in this situation, the variation of the diffusing oxygen concentration could be on basis of a reaction diffusion equation of the form, 2.51 Where, U is function of the oxygen concentration. In first approximation U(c) can be taken as a linear function. The diffusion coefficient of oxygen in BT is highly sensitive to the temperature, generally the varies with temperature as D T ~ D 0 Exp (- E/kT), where E, k and T are the activation energy, Boltzmann constant and absolute temperature respectively. Sintering of BT ceramics is a complex processes with the involvement of temperature gradients lasting for finite durations of time. Consequently, the dielectric properties of sintered BT pellet, depends on the temperature profile during sintering and therefore, mathematical modeling of this process is exceedingly complex. 43

62 2.4.2 Oxygen Diffusion and Dopant Solubility in BT The diffusion of oxygen into doped BT leads to the formation of cation vacancies as shown in the eqn given below The types of cation vacancies created during the oxidation of donor doped BT has not been fully elucidated and theoretically understood. Some authors propose [37] the creation of V Ba during atmospheric sintering and in contradiction formation of V Ti was suggested to be a more thermodynamically stable process by many other authors [85]. On basis of the arguments of the latter authors, one can assume that Ti rich phases could be created at the grain boundaries. The corresponding mass action relationship for the eqn determines the activity of TiO 2 during the atmospheric sintering process, which can be expressed as, 2.53 where, [V Ti ], [e] and p(o 2 ) are concentration of Ti vacancies, concentration of electrons and oxygen partial pressure respectively. It follows from equations 2.24 and 2.25, that oxygen vacancies in donor doped BT creates low oxygen partial pressures via the following reaction, with a corresponding mass action reaction given by, The dependence of oxygen partial pressure on diffusion coefficient is shown in Fig for BT doped with Mn and Y. This plot reveals an increase of the dopant diffusion coefficient with the 44

63 increase of the oxygen partial pressure. Further, the effect of increased sintering temperature on the dopant diffusion coefficient is also shown in the same figure [62, 86]. Pries et al [56] have suggested that the criterion that determines the rate of fast diffusion of oxygen along grain boundaries is the difference between the grain boundary and bulk diffusion coefficients. According the literature [87], the grain boundary diffusion coefficient should be at most 10 orders of magnitude greater than the bulk diffusion coefficient, in order to satisfy the requirement. The bulk vacancy diffusion of Ti in doped BT is 10 orders of magnitude less than the oxygen vacancy diffusion coefficient (10-5 m 2 s -1 at C) observed in the grain boundaries. Therefore, the oxidation kinetics of BT can be interpreted as fast diffusion of oxygen through grain boundaries via highly mobile oxygen vacancies and counter diffusion of cation vacancies from the grain boundaries into the grain [62]. Fig Chemical diffusion coefficient of doped BT with Y as a function of p(o2) for different temperatures [56].. 45

64 The solubility of donor elements in BT lattice is typically high and can exceed 10 at%. However, as discussed above the oxygen partial pressure also plays a major role in the solubility of dopants in BT [34]. According to the phase diagram shown below in Fig using EPMA data [65], it has been found that the solubility limit of Nd 2 O 3 in BT at C and atmospheric sintering is around 0.3 mol%. Above that solubility limit of both Nd 2 O 3 and Nd 2 TiO 5 phases have been detected. The occurrence of the latter phase is due to loss of small amounts of BaO [65]. These observations could be varied and shifted into elevated concentrations with the increasing oxygen partial pressures in the system. Controlled and differential oxidation of doped BT ceramics is essential for development of high dielectric constant, low loss BT ceramics for capacitor application. Consequently, a detailed understanding of oxygen and dopant diffusion in BT is essential. The above discussion provides the necessary background information collected from an extensive study of literature reports Temperature ( 0 C) 1400 Cubic BaTiO 3 ss BaTiO 3 ss + Nd 2 O mol% Fig.2.24 Phase diagram of BaTiO 3 solid solution [65] 46

65 CHAPTER 3 Motivation and Objective Capacitors can release stored energy quite rapidly and are much more reversible compared to the best batteries. Unlike a battery, a capacitor stores energy in the dielectric medium without chemical changes. Some modern super capacitor systems have the capability of storing energy up to seven times greater than a regular capacitors and these structures can be adopted effectively in hybrid and electric vehicles which provides much greater acceleration, faster steering of rockets and spacecrafts and in new generation laser driving systems. There are also many other uses of these devices in electronic systems and consumer electronic devices. However, solid-state dielectric capacitors of the above capability are not yet available. Currently the available supercapacitors are electrochemical double layer systems. The energy stored in electrochemical double layer capacitors are limited by the charging voltage, which cannot exceed the decomposition potential of the electrolyte. Furthermore, miniaturization of electronics requires high energy density dielectric capacitors. The development of dielectric solid-state materials with energy storage capabilities similar to supercapacitors is difficult and challenging and further there are no fundamental physical constraints ruling out the possibility of inventing high energy density solid-state dielectric capacitors. The best currently available dielectric capacitors are based on ceramics of high dielectric constants. The morphology of the surface and the grain boundary structure depend on dopants and processing techniques and it plays a key role in determining the dielectric properties of the ceramic. The classical dielectric material, BT continues to be promising for development of high energy density solid-state dielectric capacitors. Controlled doping and thermal processing of BT 47

66 is a known produce that enhances the dielectric constant. If the energy loss is also minimized, such materials would be valuable in capacitor applications. Trivalent rare earth doping is extensively studied in order to modulate the dielectric properties of BT. Previous work in this area, suggests that Nd doped BT possess promising attributes, which can be adopted for development of high energy density capacitors. Therefore, this study aims to conduct an in-depth investigation to determining the factors yielding high effective dielectric constant, low loss and high break down voltage in newly developed BL structured, Nd doped BT ceramics, so that they could be adopted in high energy density capacitor systems. The fine tuning of physical properties in these materials will be investigated on the basis of dopant concentration and solubility variations, combined doping of aliovalent substituent such as Zr, sintering time/ temperature and annealing dependence. The physical mechanisms governing the dielectric properties of above mentioned systems will be understood mainly by dielectric measurements and impedance spectroscopy, measurement of electrical resistvities, morphological and chemical characterization and evaluation of oxygen diffusion coefficients. The experimental data will be analyzed, elucidating relaxation mechanisms in relation to the morphological structure and diffused chemical gradients observed in the newly developed BL structures. Information gathered is interpreted in terms a mathematical model developed for understanding BL dielectric ceramics. The scope of work covered in this thesis is as follows: 1. The physical characteristics of Nd and Nd/ Zr doped BT structures are explored in depth to understand the mechanism of dopant diffusion and the formation of combined GBBL and SBL morphologies under one step sintering and annealing procedures. 48

67 2. The GBBL and SBL effects in Nd/ Zr doped BT structures are mathematically analyzed in terms of equivalent circuits, relaxation mechanisms and a model based on the brick-layer approximation of the barrier layer structure is developed and correlated to the experimental results. 3. The site substitution mechanism of Nd 3+ in BT are investigated as far as possible with view to clearing up the controversy in literature and to utilize the favorable BT doping attributes of Nd to develop high dielectric constant and low loss dielectric ceramics. The work conducted on processing, characterization and analysis based on mathematical models of Nd and the combined Nd/ Zr doped BL structures of BT could pave way towards fabrication of tunable capacitors for electronic miniaturization and energy storage capabilities. The study has also should generated fundamental knowledge pertaining to BL structures in doped BT ceramics 49

68 CHAPTER 4 Experimental 4.1 Sample Preparation The materials used in this study were 99.99% purity BaTiO 3 (Ticon-HPB, Ferro Corp.) with a stoichiometric excess of Ti (Ba/Ti = 0.987) and the average particle size 1.23 µm. The dopants, (0-1 mol%) Nd 2 O 3 and (1-3 mol%) ZrO 2, in forms of neodymium nitrate hexahydrate Nd(NO 3 ) 3.6H 2 O and unstabilized ZrO 2 (Aldrich Chemical Corp.) were dissolved in a solvent mixture of 40 vol% de-ionized water and 60 vol % isopropyl alcohol (IPA) and the ph was adjusted to 7 by adding NH 4 OH. Additionally, 1wt% Menhadden fish oil was introduced to the slurry as a dispersant and the batch was ball milled for 12 hours using ZrO 2 balls weighing 650g. The oxide content of Nd(NO 3 ) 3.6H 2 O was estimated gravimetrically after pyrolysis of the solid at 550 o C. Next a binder / lubricant mixture of 3 wt% Polyvinial Alcohol (PVA) and Carbowax (1 wt%) were added into the medium and ball milled for an additional 1.5 hrs (Fig. 4.1). After the milling process, the slurry was spray dried using a Buchi 190 Mini Sprayer system with the following controlling parameters; inlet temperature C, outlet temperature C, Aspirator 12; air flow 675 ml/min. A measured amount of (1.5g) the fine powder collected from this process was uniaxially pressed at 14,000 psi in a ½ die, into discs of diameter 0.22 cm. All the measurements were repeated for four samples each from different batches for repeatability. Fig 4.1 Flow Chart for processing doped BT ceramics 50

69 4.2 Sintering and Heat Treatment All samples were fired on ZrO 2 setters in air at sintering temperature ranging C C for 15 to 120 minutes. During sintering, a heating rate of 10 0 C/min was adapted from room temperature to C and binder/nitrate burnout was allowed for 30 minutes. From C to C or C, a heating rate of 3 0 C/min was maintained. After sintering, the samples were furnace cooled into room temperatures. Some of the specimens sintered at C, were annealed at C for 2 to 32 hours to study the effect of annealing. 4.3 Density Measurement The sintered specimens were lightly polished with 600 grit SiC powder in order to measure the sample dimensions such as the diameter (d) and thickness (t) geometrically. The dimensional measurements were carried out using a Vernier caliper with the resolution of 25.5 µm. After measuring the weight (w) of these samples using a microbalance with resolution, the geometrical density (ρ g ) was calculated using the following equation: 4.1 The theoretical density (ρ t ) for Nd/Zr doped BT was calculated using the mixing rule as follows: 4.2 Where, ρ Zr, ρ Nd, ρ BT and V Zr, V Nd, V BT are the densities and the volume fractions of ZrO 2, Nd 2 O 3, BT respectively. Therefore, finally the percentage theoretical density of the specimens was calculated as;

70 4.4 Dielectric and Electrical Measurements Dielectric Measurement Aluminum electrodes were evaporated onto the surfaces of the sintered pellets as ohmic contacts for the dielectric, impedance and resistance measurements. The resistance of the electroded surface was maintained below 0.3 Ω. Computer Keithley A LCZ Meter Power Supply Metal Cover Furnace Sample Thermocouple Fig 4.2 Schematic of the setup for measuring the temperature dependent dielectric constant 52

71 Temperature dependence of the capacitance and the loss tangent was measured over a range of 25 0 C C, using HP 4276A, Hewlett Packard LCZ meter at 1, 10 and 20 khz. Fig. 4.2 shows a schematic representation of the setup used to perform the above measurement. As illustrated in the figure, the samples were placed inside a shielded chamber and a spacer was placed in between the probe tip and the sample surface to produce an even electric field across the sample. Data necessary for computation of capacitance and loss tangent were recorded while heating the specimen in a chamber at a rate of 3 0 C/minute. For specimens having Curie points below room temperatures, the sample container was cooled by surrounding it with a liquid nitrogen bath. The observed capacitance values and the dimensional measurements of the specimen were used to calculate the relative dielectric constant (ε r ) at a given temperature and frequency using the following equation: 4.4 Where, C, ε 0, A and t are capacitance, permittivity of free space, area and thickness of the specimen respectively. The loss tangent (tanδ) of the specimen was measured directly using the LZC meter Impedance Measurement Room temperature impedance measurements were carried out using a HP 4194A impedance analyzer from 100 Hz to 40 MHz with an output voltage of 8 Vrms. As represented in Fig. 4.3, the specimen was placed in a shielded sample holder connected to the automatic 53

72 impedance analyzer. Before performing the impedance measurements, the setup was calibrated at zero open and zero short positions. Top contact (shielded silver wire) Low Potential Cu Lead Sample High Potential Mica Substrate Fig 4.3 Schematic setup of the sample holder to measure the frequency dependent dielectric constant Resistivity Measurement In order to measure the resistance of the pallets, a Quad Tech 1865 Megohmmeter was adopted. Additionally, to measure the resistivity variations of the pellets across the thickness, samples were mechanically thinned with 600grit SiC in order to obtain plane parallel surfaces followed by Al sputter evaporation for Ohmic contacts and the average resistance was determined using the d.c two probe measurement. By using the dimensional measurements obtained during the density measurement step discussed in section 4.3, the resistivity (ρ) of the specimen was calculated using the following equation: 4.5 Where, R, A and t are the corresponding resistance, surface area and thickness of the specimen. 54

73 4.5 Microstructural Measurements X-Ray Diffraction The lattice parameters, cell volumes and the availability of phases of Nd/ Zr doped BT ceramics were determined by XRD (Philips X Pert Diffractormeter) with respect to Cu Kα, at a scanning speed of 2 0 /min in steps of over the range of 2θ = The internal stress development and the pseudo cubic structural formation within the BL structure was analyzed by X-Ray line broadening effect of <400> planes obtained at higher angles (2θ= ) Optical Microscopy The cross sections of the sintered and annealed specimens were analyzed using a light microscope with digital camera (Nikon Eclipse E600). The accompanied software was used to record the oxidized layer thicknesses within the specimen cross-sections using the effect of interfacial contrast obtained in the light microscopy. The same microscopy was used to estimate the quality of the surface polishing before SEM analysis of the specimen cross-sections Scanning Electron Microscopy (SEM) For SEM and EDS (Energy Dispersive Spectroscopy) analysis, a Philips environmental SEM accompanied with a field emission gun was used. The samples were cut using a diamond blade and mounted on epoxy resin. The cross-sections of the mounted specimens were initially polished with grit SiC and fine polished using diamond paste ranging from 6µm- 0.25µm. After polishing, the samples were ultrasonically cleaned using Alconox solution followed by a DI water and IPA. Just after removing the sample from IPA solution, it was blow 55

74 dried to minimize the drying marks on the polished surface. For grain boundary, domain and grain size distribution analysis, the specimen cross sections were removed from the epoxy mount by dipping in an acetone bath for 24hrs and picking out the polished sample cross section from the swollen/ soften epoxy material, followed by thermal or chemical etching. The thermal etching was performed at C for 1 minute and the chemical etching was carried out by dipping the samples in a 5 vol% HCl, 5 vol% HNO 3, 1 vol% HF, DI water solution for 30 seconds followed by several steps of rinsing with DI water and IPA. Before inserting the samples into the SEM chamber, the polished sections were coated with Au-Pd to alleviate charging during observation. The main features investigated using SEM were the grain size distribution, distribution of second phases and porosity. EDS measurements enabled determination of elements in the grains and grain boundaries and their variations with the processing conditions Secondary Ion Mass Spectroscopy (SIMS) Time of Flight secondary ion mass spectrometry (ION-ToF SIMS) was employed in this study, in order to ascertain the spatial variation of the elemental compositions. The sample preparation for SIMS analysis was also carried by the same procedure as for SEM discussed in section Gallium (Ga) ions were used as the primary ion beam to remove a 1 µm X 1 µm mono layer from the surface of the specimen (Fig. 4.4). The particles removed from the specimen surface are accelerated into a "flight tube" and their mass is determined by measuring the exact time at which they reach the detector (i.e. Time of Flight). Here the ToF-SIMS was employed in order to determine the atomic masses in the surface of 0.3 mol% Nd 2 O 3 doped BaTiO 3 samples. 56

75 Fig. 4.4 Schematic of the mass analyzer in SIMS Atomic Force Microscopy (AFM) AFM analysis (Dimension 3100, Veeco AFM was used with Si 3 N 4 coated Cr and Au tip, Spring constant 0.32 N/m and Resonance Freq 56 khz) was carried out for thermally etched sample cross sections prepared similar to the technique discussed in the section In order to analyze the ferroelectric domains of the specimen, it was glued into the scanner head of the AFM using silver paste and a voltage of 2-6 V were applied in between the AFM tip and the scanner head (Fig. 4.5). Fig. 4.5 Setup for domain observation using AFM 57

76 A 2-10 µm square region of the specimen was analyzed for domain observations. This measurement was performed at tapping mode (probe tip in contact with the sample), while a DC bias is applied between the tip and the sample, with a zero band gap. 58

77 5.1 Densification and Microstructure CHAPTER 5 Results and Discussion The dielectric behavior of BT ceramics strongly depends on its microstructural features such as grain size and density distributions. The effect of density in BL pellets prepared under different conditions and their dielectric properties were studied mainly in terms of pore formation during the densification process. An effort was made to minimize the porosity via ZrO 2 substitution, sintering profile variation, binder content and applied pressure changes. The optimized process obtained from this study was adopted as the standard method of sample preparation. Fig.5.1 shows the relative density and room temperature dielectric constant vs. sintering temperature variations for stoichiometric compositions of Ba/Ti= and A higher relative density with a particle size of 0.33 µm was observed in Ba/Ti =1.003 samples compared to Ba/Ti= samples where the average particle size was 0.38 µm. Furthermore, as the decrease of Ba/Ti ratio, the dielectric constant of the material increased significantly (notably if the sintering temperature was higher i.e., ~ C) indicating that an excess of Ti provides more Jahan Teller active Ti 3+ sites, creating more oxygen ion vacancies [34]. The low angle X- ray diffraction patterns for the BT powders of stoichiometric ratios and are shown in Fig.5.2. Both patterns indicate that the materials are purely tetragonal with additional tetragonal peaks visible in powders with Ba/Ti stoichiometric ratio of Considering the fact that the high dielectric constants are obtained for Ti rich compositions, porosity minimization was studied for the BT powders of stoichiometric composition corresponding to Ba/Ti =

78 (a) (b) Fig. 5.1 (a) % Relative density (b) room temperature dielectric constant vs. sintering temperature variations for BT powders with stoichiometric compositions and

79 Fig.5.2 Low angle XRD spectrum for BT powders with stoichiometric ratios of 0/987 and Effect of Dopant Composition Fig.5.3 indicates the changes in bulk density compared to the % theoretical density with increasing Nd 2 O 3 concentrations for specimens sintered at C for 90 minutes. It is clear that the density decreases with the increasing Nd 2 O 3 content [40] and this trend is more evident in SEM images for Nd doped BT samples as depicted in Fig.5.4. Furthermore, according to Fig.5.3, increase in ZrO 2 from 1-3 mol% rapidly increased the bulk density from ~ 68% to 95% of the theoretical density for 1 mol% Nd 2 O 3 doped BT samples. This observation clearly indicates the improvements in densification on ZrO 2 addition into Nd doped BT structures [61]. Additionally, when BT is doped with a lower concentration of Zr, higher densification was accompanied with a low level of pore formation (Fig.5.5). 61

80 Fig.5.3 Percentage theoretical density vs. Nd 2 O 3 mol% for Nd/Zr doped BT sintered at C for 90 minutes (a) (b) (c) (d) Fig.5.4 SEM images of polished surfaces of (a) 0.15, (b) 0.3, (c) 0.6 and (d) 1 mol% Nd 2 O 3 doped BT sintered at C for 90 minutes 62

81 (a) (b) (c) (c) (d) (d) Fig. 5.5 SEM images of polished cross-section for (a) 0.15, (b) 2, (c) 4 mol% of ZrO 2 doped BT sintered at C for 90 minutes (d) Variation of relative density with ZrO 2 content for specimens sintered at C for 90 minutes Development of a secondary phase was observed in ZrO 2 doped BT samples with relatively high concentration starting from 1-3 mol%. The SEM images shown in Fig. 5.6, clearly indicate this phenomenon for 0.6 mol% Nd 2 O 3 and for 1, 2, 3 mol% ZrO 2 doped BT samples. 63

82 This observation was further analyzed using low angle XRD. Fig.5.7 shows the low angle XRD spectrum for mol% Nd 2 O 3 doped BT and 0.6 mol% Nd 2 O 3 /1-3 mol% ZrO 2 doped BT systems. According to Fig.5.7a, XRD analysis does not reveal any secondary phases of Nd or BT other than the BT tetragonal phase. This could be either due to the complete solubility of Nd 2 O 3 in BT over this compositional range, or be the result of the undetectable of impurity levels of the dopant additions. A small amount of secondary phase Ba 6 (Ti 1-x Zr x ) 17 O 40, was detected on increasing the ZrO 2 content up to 3 mol% as shown in Fig.5.7b [68]. Therefore, definitively the solubility limit of ZrO 2 in BT is below 3 mol% for the sintering conditions used. Further, the same figure indicates that addition of ZrO 2 into the system eliminates the tetragonalily via transformation to a pseudocubic structure. However, the secondary phases observed in Fig.5.6 for 0.6 mol% Nd 2 O 3 / 2 mol% ZrO 2 doped BT were not evident in the XRD profiles. (b) (c) (c) Fig.5.6 SEM images for the secondary phase development of 0.6 mol% Nd 2 O 3 / (a) 1 (b) 2 (c) 3 mol% ZrO 2 doped BT sintered at C for 90 minutes 64

83 (a) (b) Tetragonal BaTiO 3 Monoclinic Ba 6 (Ti 1- x Zr x ) 17 O 40 Fig.5.7 Low angle XRD spectrum for (a) Nd (b) Nd/Zr doped BT sintered at C for 90 minutes 65

84 5.1.2 Effect of Sintering Profile and Temperature Sintering Profile: In order to analyze the effect of sintering rate on porosity, BT samples of stoichiometry Ba/Ti = were sintered according to the profiles shown in Fig.5.8. In both cases, similar rates of increase in temperature were preserved until the binder burnout temperature and beyond that point, two separate profiles were maintained. Samples fired under the slow sintering profile (Fig.5.8a) had a relative density of 92.17% whereas the density of samples sintered under the fast sintering profile (Fig.5.8b) was 98.12%. The SEM images of the samples corresponding to Fig.5.8a and b are presented in Fig.5.9 (a) and (b) respectively. As seen, the picture corresponding to profile of Fig.5.8a is crowded with small elongated pore structures and scattered patches indicative of secondary phases (marked with arrowheads). However, in the second picture (Fig.5.9b) corresponding to the sintering profile 5.8b, the elongated pore structures has been reduced with a merging of secondary phases into larger islands. Branching into these islands suggest a fast growth of the secondary phase. The large pores in these samples seem to originate from formation of O 2 gas bubbles during the sintering process. (a) (b) Temperature ( 0 C) C/ min 5 0 C/ min 90 mins Time (minutes) Temperature ( 0 C) mins 10 0 C/ min 5 0 C/ min 3 0 C/ min Time (mins) Fig 5.8 (a) Slow (b) fast sintering profiles employed to compare the effect of densification 66

85 (a) (b) Fig 5.9 SEM images of polished cross-sections corresponding to the (a) slow (b) fast sintering profiles for pure BT sintered at C for 90 minutes Sintering Temperature: Effect of sintering temperature on pore formation in pure BT samples are shown in SEM pictures of Fig Here the samples were fired according to the sintering profile indicated in Fig.5.8b. Although proper densification of the ceramic begins around C and reaches the maximum at C (Fig.5.11), open pores were also observed for samples sintered at C indicating that pore formation occurs before the densification. Additionally, the darker areas corresponding to secondary phases observed in the SEM images, excluding the pores were further analyzed using EDS. The results indicate that these regions are relatively rich in TiO 2 and ~15% higher than the other regions. These results suggest that diffusion of Ti and O into the BT structure occurs before the densification is completed. Furthermore, secondary phase structures similar to 1-3 mol% ZrO2 doped systems were detected in pure BT (Ba/Ti = 0.987), suggesting that this effect is not only due to dopant addition. 67

86 (a) (b) (c) Fig 5.10 SEM images of polished cross-section for pure BT (Ba/Ti = 0.987) sintered at (a) C, (b) C, (c) C for 90 minutes Fig 5.11 Relative density vs. sintering temperature for pure BT (Ba/Ti = 0.987) sintered for 90 minutes. TGA and DTA obtained for pure BT (Ba/Ti=0.987) and 0.15 mol% Nd, 0.15 mol% Zr doped BT (Fig.5.12a, b) indicates that in pure BT, a high temperature weight loss occurs around C which is compatible with the observed porosity in SEM images illustrated in Fig However, corresponding to this weight loss, there is no peak observed in the DTA curve. Similar 68

87 weight loss was not seen in Nd/Zr doped samples in agreement with improved densification and low porosity for samples doped with smaller concentrations as discussed in section (a) Delta Temperature (µv) Temperature ( 0 C) (b) Weight Change (%) Delta Temperature Weight Change (%) Temperature ( 0 C) Fig 5.12 TGA and DTA plots obtained for (a) Pure BT (Ba/Ti=0.987), (b) 0.15mol% Nd 2 O 3, 0.15 mol% ZrO 2 doped BT 69

88 5.1.3 Effect of Binder Content and Applied Pressure The SEM images shown in Fig indicate the variations in surface morphology for the 0.6 mol% Nd 2 O 3, 1 mol% ZrO 2 doped BT samples as a function of applied pressure. On comparison of the micrographs, it is not evident that the applied pressure has a direct effect in maximizing the achievable green density of the specimens. Fig compares the specimen green density variation for different binder (Polyvinyl Alcohol-PVA) contents, at constant applied pressure of 14,000 psi. When the PVA content increased from 1wt% to 3wt%, a reduction in the specimen density was clearly noticeable. Fig 5.15 and 5.16 compare the combined effect of binder content and applied pressure on increasing the specimen density up to maximum attainable levels. (a) (b) (c) (d) Fig 5.13 SEM images of polished BT cross-sections for the doping composition of 0.6 mol% Nd 2 O 3, 1 mol% ZrO 2, pressed at (a) 10,000 psi(b) 12,000 psi, (c) 14,000 psi (d) 16,000 psi 0 70

89 (a) (b) (c) Fig 5.14 SEM images of polished cross-sections of BT at the doping composition of 0.6 mol% Nd 2 O 3, 1 mol% ZrO 2 and PVA concentrations (a) 1 wt% (b) 2 wt% (c) 3 wt% pressed at 14,000 psi and sintered at C for 90 minutes (a) (b) 71

90 (a) (b) (c) Fig 5.16 Temperature dependence of the dielectric constant with applied pressure for (a) 1wt% PVA (b) 3wt% PVA and (c) Loss vs. temperature for 1wt%, 3wt% PVA at 10,000 and 16,000 psi for 0.6 mol% Nd 2 O 3, 1 mol% ZrO 2 doped BT sintered at C for 90 minutes The observed variation of the dielectric constant (Fig.5.16 ) with applied pressure in 0.6 mol% Nd 2 O 3, 1 mol% ZrO 2 doped BT samples sintered at C for 90 minutes, indicates that 3wt% of PVA binder, improves the dielectric constant, but increases the dielectric loss (~0.07) compared to the 1wt% of PVA added samples (~0.05). Increase in the interfacial polarization in between the dielectric material and the porous regions leads to Maxwell Wagner type loss behavior [88, 89]. Furthermore, regardless of the composition, the dielectric constant varies with the applied pressure and the binder content. As Fig.5.16 indicates, dielectric constant varies with 72

91 the applied pressure and the binder content in a rather complex manner. A maximum room temperature dielectric constant of ε r = was obtained for 3wt% of PVA added specimens subjected to a pressure of 14,000 psi. Due to the more sensitive density variation dependence with the dopant composition as discussed in section 5.1.1, the overall investigation was carried out with 3wt% PVA binder content and 14,000 psi applied pressure for purpose of attaining high dielectric responses Summary Although density is a readily measurable parameter, its variation with doping composition, pressure applied to the green pellets and sintering temperature profile gives important clues regarding microstructure, doping compensation mechanisms and dielectric behavior. Interrelated effects determining the density are too complex for quantitative explanation, but the gross qualitative understanding gained is useful for optimization of the dielectric properties. The effect of porosity on dielectric behavior was analyzed in greater detail. High porosity lead to loss as previously observed, but the present work shed more light on dependence of the porosity on processing parameters, suggesting that the porosity mediated loss is of Maxwell Wagner type, originating at the interfaces. 73

92 5.2 Characteristics of Structural Inhomogeneities Compositional Dependence Fig.5.17a shows a plot of ε vs. Nd 2 O 3 doping concentration for BT pellets sintered at C for 90 minutes. Two peaks in ε r (~10 6 and 10 4 ) were found to occur at dopant concentrations of 0.12 mol% and 0.43 mol% (expressed as Nd 2 O 3 mol %). When Nd 2 O 3 doping concentration is increased from 0 to 0.15 mol%, the color of the specimens gradually changes from yellowish brown to dark gray/ blue, indicating the presence of Ti 3+ ions originating from the Jahn Teller active electronic compensation as shown in the same figure. The first maxima at the low doping concentrations of Nd 2 O 3 (0-0.3 mol% for Nd doped BT system) corresponds to the electronically compensated high dielectric constant phase leading to Maxwell Wagner (MW) dielectric relaxation. When the Nd 2 O 3 doping concentration is increased from 0.3 to 1 mol%, the color of the specimen changes from light gray to white, indicating transition into ionic compensation. It appears that transition to full ionic compensation [22, 59, 63] occurs at an Nd 2 O 3 doping concentration > ~ 0.9 mol %. The region of intermediate concentration ( mol%) where the specimens are light gray/ blue, could be identified as the Barrier Layer (BL) region where a diffused phase of compositional gradient referred to the surface barrier layer ( SBL) co-exists with the grain boundary barrier layer (GBBL) structures formed as a result of grain boundary oxidation [90-95]. Most significant feature of this plot is the second maximum falling within the doping range 0.3 to 0.5 mol% of Nd 2 O 3, not previously reported in studies on TRE doped BT systems corresponding to combined Maxwell Wagner and Debye behavior which provides significantly high room temperature dielectric constants (ε r = 30,000) coupled with relatively low losses (tanδ= 0.02). This region was further identified as the Barrier Layer (BL) region where a diffused 74

93 oxidized phase co-existing with a compositional gradient (SBL) accompanied with Grain Boundary Barrier Layer (GBBL) formation, leading to combined dielectric relaxation. The standard pattern of variation for a typical TRE dopant is depicted by the dotted line in Fig. 5.17a. When the Nd 2 O 3 doping concentration exceeds 0.3 to 1 mol%, the color of the specimen changes from light gray to white, indicative of a transition to a phase compensated via different mechanisms. It appears that transition to pure ionic compensation corresponding to Debye relaxation occurs at Nd 2 O 3 dopant concentration> ~ 0.6 mol%. Electron probe microanalysis (EPMA) experiments have shown that the solid solubility limit of Nd 2 O 3 in BT at C is around 0.3 mol% [65], where a sudden decrease in the dielectric constant occurs, as shown in Fig.5.17a. Therefore, a local minimum at 0.3 mol% originates as a result of the saturation of the solid solubility limit of Nd 2 O 3 in BT at C, a dependent on atmospheric oxygen partial pressure [96, 97]. This observation strongly suggests that by fine tuning of the dopant concentration and processing conditions, the dielectric properties may be further improved to a level suitable for energy storage applications [98]. The loss characteristics in Nd 2 O 3 doped BT system lies within the range and rapidly decreases with the increase of the dielectric constant showing a peak around 0.3 mol% of Nd 2 O 3 as shown in Fig.5.17b. The temperature dependence of dielectric properties for mol% of Nd 2 O 3 modified BT sintered at C for 90 minutes and measured at 1 khz are shown in Fig As shown in this figure, with increasing Nd 2 O 3 concentration, the Curie peak gets suppressed, decreasing the dielectric constant. It can be further seen that the dielectric constant of Nd doped BT system increases up to 0.5 mol% of Nd 2 O 3 and decreases on further increase of the doping concentration due to the changes in the charge compensation mechanism as discussed earlier in this section. 75

94 (a) Room Temperature Dielectric Constant Electronic High - r 106 High loss 1.2 V b < 6kV/cm BL High 20,000 r Relatively low loss 0.1 V b > 9kV/cm Ionic Low 2000 r Low loss 0.02 V b > 10kV/cm (b) Fig.5.17 (a) Variation of the room temperature dielectric constant (b) dielectric loss (measured at 1 khz) of BT with the Nd 2 O 3 doping concentration 76

95 Fig.5.18 Dielectric constant, loss vs. temperature curves for (a) Nd (b) Nd/Zr doped BT samples sintered at C for 90 minutes The Curie temperature vs. Nd 2 O 3 concentration is plotted in Fig It can be observed that the Curie temperature has shifted down from ~130 0 C to 90 0 C on increasing the Nd 2 O 3 concentration form 0-1 mol%. The Curie temperature is affected by many factors such as chemical composition, particle size, tetragonality, oxygen vacancy concentration and internal stress [10, 11, 46, 99, 100]. A shift in T c could occur due to the internal stresses caused by structural changes as well as the existence of core- shell structures [58]. 77

96 BL Region Fig.5.19 Curie temperature vs. Nd 2 O 3 doping concentration for BT specimens sintered at C for 90 minutes Other than the dielectric characteristics, dopant compositions also influence the grain size distribution in BT. Fig.5.20 shows thermally etched cross-sections of the Nd 2 O 3 doped BT samples. From Fig.5.20 and Table 5.1, it is clearly evident that with the increasing Nd 2 O 3 concentration the grain growth is inhibited, as previously reported [24]. Figures 5.20a-5.20c also show distinct and wide ranging orientation of ferroelectric domains, indicative of the multigrain orientation in Nd 2 O 3 doped BT samples. Table 5.1 further provides a comparison of average grain sizes distribution for the Nd/ Zr doped BT samples, near the surface as well as in the interior region. From the table, it is apparent that Nd 2 O 3 addition to BT reduces the grain size near the surface region of the pellet, unlike in the case of pure and 1 mol% of ZrO 2 doped BT samples. This observation is not fully understood and needs further investigation, but is likely due to a change in unit cell parameters as a result of fluctuations in Nd 3+ site substitution. 78

97 (a) (b) (c) (d) Fig.5.20 SEM images of thermally etched (a) pure BT, (b) 0.3, (c) 0.6 and (d) 1 mol % of Nd 2 O 3 doped BT sintered at C for 90 minutes Table 5.1 Average grain sizes for specimens sintered at C for 90 minutes 79

98 However, it can be concluded that, both Zr, and Nd enriched at the grain boundaries restrain abnormal grain growth during sintering [4, 7]. The groove patterns observed in Fig.5.20 were further analyzed using AFM in order to confirm that they originate precisely from domain orientations. The analysis was basically carried out using 0.3 mol% Nd 2 O 3 dopde BT sintered at C for 90 minutes followed by thermal etching. Fig 5.21 shows the AFM images of these specimens and the measurements indicate that the average depth of the thermal groove is ~ 25 nm, and the average distance between two groove lines is approximately µm. Literature indicates that for pure BT, the average distance between 2 domains is between 1-10 µm [3]. Therefore, it is most likely that the groove patterns on the grain surfaces are either domain patterns or twin plains (twin coupled domain structure) [4, 6]. Usually, twin walls are planar defects that separate domains with uniform, but different, strain or polarization. The physical and microstructural properties such as wall thickness of the twin plains are strongly related to their domain patterns and dielectric properties [3]. Thus, the groove lines still signify the domain orientations even if it does represent the planar defects. Fig.5.21 AFM micrographs indicating the etch depth for 0.3 mol% Nd 2 O 3 doped BT sintered at C for 90 minutes 80

99 Pellets of BT doped with 0.3 mol% of Nd 2 O 3, sintered at C for 90 minutes and chemically etched in HCl, HNO 3, HF and water solution for 30 seconds were used to analyze the morphology of the BL composition as indicated in the Fig.5.22 SEM images. As seen in these images, the difference in selective etching over the surface and the interior of the specimen cross-sections give a clear indication of the differences in the etching rates of surface and the interior regions of the samples. According to literature, etching rate perpendicular to the dipole direction [7, 11, 101]. It also provides clear information regarding the direction of polarization in the surface and the interior region. Therefore, the grains or portions of grains that reveals flat surfaces after chemical etching can be identified as c-domains and those on the surfaces which are sharper can be considered as a-domains [ ]. This reveals that the interior region of the sample is c-domain rich while the surface region of the sample is a-domain abundant. Interior Surface Fig.5.22 Comparison of SEM images of surface and the interior of 0.3 mol% Nd 2 O 3 doped BT sintered at C for 90 minutes followed by chemical etching 81

100 5.2.2 Variation of Resistivity Resistivity vs. Nd 2 O 3 doping concentration for Nd doped BT is plotted in Fig The figure indicates a sudden drop in resistivity around mol% of Nd 2 O 3 due to strong electronic compensation. Beyond this composition, the resistivity again increases, however some fluctuation can be seen for the compositions corresponding to the BL region as marked in Fig The bulk resistivity change in the BL region can be associated with the concentration of active BT donors, and possibly due to oxygen or cation vacancies [99]. BL Region Fig.5.23 Resistivity vs. Nd 2 O 3 doping concentration for Nd/Zr doped BT sintered at C for 90 minutes The resistivity across the thicknesses of Nd 2 O 3 doped BT pellets were measured using the measurement technique as illustrated in Fig For each measurement, the specimen was carefully polished on both surfaces in order to remove equal amount of material. 82

101 (a) 0.2 mm Al Electrode 0.2 mm Polishing along the direction of thickness (b) Polishing direction Specimen Fig.5.24 (a) The measurement technique adopted for cross sectional resistivity measurement (b) Cross-sectional view of the specimen indicating the thin oxidized surface region Subsequent to polishing and cleaning, aluminum was evaporated onto the polished surface to secure ohmic contacts. The measured resistivity values across the cross-section for Nd 2 O 3 doped BT sintered at C for 90 minutes are plotted in Fig It is clear that the formation of a BL region occurs above the doping concentration of 0.15 mol% Nd 2 O 3. On increasing the Nd 2 O 3 content from mol%, the low resistive region becomes narrower due to the surface insulation via oxidation. The advantage of an insulating layer is the lowering of the dielectric loss while maintaining a high dielectric constant. However, beyond an optimal thickness of the oxidized surface region, the dielectric constant drops due to increasing dominance of the insulation layer. In this experiment the average resistivity ρ calculated from d.c two probe measurements using the formula;

102 R = ρ (T 2δ )/πr 2, where R = measured resistance, t = thickness of the pellet, δ = thickness scraped from each face of the pellet. Fig.5.25 Resistivity vs. cross-sectional position for Nd 2 O 3 doped BT samples sintered at C for 90 minutes X-Ray Diffraction Analysis Diffraction analysis was carried out on high angle (004), (400) peaks to determine the lattice parameters of the unit cells on the surface as well as towards the interior of the pellets (Fig.5.24). The intensities of (004) and (400) peaks of 0.7 mol% Nd 2 O 3 /1 mol% ZrO 2 doped BT in Fig.5.26 has reversed, likely due to the compressive residual stresses parallel to the surface encountered during the grinding process, conducted in order to reach the interior of the sample 84

103 [106]. Other than the reversing of the tetragonal peaks, the accompanied peak shift in Fig could cause by the development of internal stresses during the BL formation. Fig.5.26 XRD peaks of (400) plane on the surface and the interior of 0.7 mol% Nd 2 O 3 / 1 mol% ZrO 2 doped BaTiO 3 sintered at C for 90 minutes Stoichiometric ratio calculations of tetragonality (c/a) were performed utilizing Cohen s lest squares determination [6, 107, 108]. The c/a ratio is plotted against Nd 2 O 3 concentration in Fig It is seen that within the Nd 2 O 3 concentrations 0 and 0.3 and beyond 0.5 mol% the slope of the curve becomes less steep compared to that within the range mol%, the later range implicates the BL region. 85

104 BL Fig.5.27 Tetragonality ratio vs. Nd 2 O 3 doping concentration for specimens sintered at C, 90 minutes Fig. 5.28a illustrates the high angle (004), (400) XRD peaks for mol% of Nd 2 O 3 doped BT. As observed, increase in dopant concentration has significantly depressed the tetragonality of BT, transforming it into a more pseudo cubic type structure. As discussed above, the effect of peak broadening and merging is an indication of internal stress development. Fig.5.28b illustrates the variation of the c/a ratio for the same specimens, Fig. 5.28a across the thickness (Fig. 5.28a). In samples of BT doped with 0.5, 0.7 mol % Nd 2 O 3, the c/a ratio increases towards the interior suggesting the presence of a higher fraction of the tetragonal phase BT in the reduced middle region. Clearly, the tetragonality is lowest in a region that coincides with the SBL. Oxygen ion vacancies that generate Jahan Teller active Ti 3+, promotes formation of the tetragonal phase of BT in the interior and high oxygen partial pressure eliminate this effect from 86

105 the surface region [76]. The asymmetries of these plots are clearly reminiscent of the oxygen diffusion profile. During sintering, oxygen diffuses rather slowly from the under-side of the pellet compared to the upper-side, and it follows that the rate of decrease of the c/a correlates with the oxygen partial pressure during sintering. However, it is clear that 0.15 mol% Nd 2 O 3 modified BT specimen does not show any c/a ratio changes, due to the non-existence of the SBL. Further, a minor change in c/a ratio was determined for 0.3 mol% of Nd 2 O 3 doped BT samples. By this observation it can be considered that 0.3 mol% Nd 2 O 3 corresponds to the initial Nd 2 O 3 composition, giving the first direct indications of general BL structural characteristics. The values of c/a and cell volume calculated for the BL specimens using high angle XRD data are shown in Table 5.2. Noticeably cell volume is lesser and c/a ratio is higher in the interior compared to the surface region suggestive of a difference in the lattice strains in the two regions. (a) (400) (004) 87

106 (b) Fig.5.28 (a) Effect of peak broadening and merging with increased Nd 2 O 3 composition (b) Tetragonality variation across the thickness for Nd 2 O 3 doped BT samples sintered at C for 90 minutes Table 5.2 Variations in unite cell parameters with different Nd/Zr concentrations for BT samples sintered at C, 90 minutes 88

107 5.2.4 Analysis of the Valence State of Ti within the BL Structure Time of Flight (ToF) SIMS was employed in order to determine the atomic mass spectroscopy of 0.3 mol% Nd 2 O 3 doped BaTiO 3 cross-sections. The selection of the specific Nd 2 O 3 composition was determined as the lowest dopant composition, where the BL region is readily noticeable under the visual inspection of the specimen cross-sections. The four positions of the sample cross-section used in the analysis are shown in Fig Fig 5.29 Schematic representation of the cross-sectional positions used to obtain the SIMS atomic mass spectrum The mass spectrum for each position shown in Fig is indicated in Fig A significant difference in the shape of the 144Nd + peak in the surface and the interior region of the specimen was observed. In the interior region, this peak split in to two maxima suggesting presence of Ti x+ ions. The recognition of the valance state of Ti (i.e. the value of x) was determined considering the isotopic abundance of the Ti metal as represented in Table 2. As indicated in Table 5.3, Ti(48) is the most abundant Ti isotope in nature [109]. Similarly most abundant oxygen isotope is O(16) with an atomic number of amu [64] and a percentage abundance of % [109]. This leads to Ti 2 O 3 = [64] amu, which is in agreement with, 89

108 Table 5.3 Isotopes of Ti, atomic number and the abundance Isotope Atomic Number Abundance (%) Ti (46) Ti (47) Ti (48) the atomic mass number of the extra peak observed in sample interior. Therefore, the valence state of the Ti x+ ion was determined to be x=3 (Ti 3+ ). Thus, as revealed in Fig. 5.30, the additional peak observed in the interior region of the specimen clearly indicates the presence of the Ti 3+ ions in the reduced interior region [110]. As discussed in previous sections, the bluish interior region of the sample indicates presence of Jhan-Teller active Ti 3+ ions. Further, SIMS mass spectrum analysis the absence of Ti 3+ ion, (Ti 2 O + 3 ) in the oxidized region indicates the variation of poloron conduction across the BL cross-section. As indicated in Fig and Table 5.4, the maximum number of counts for 144Nd + appears to drop over the oxidized surface region of the 0.3 mol% of Nd 2 O 3 doped BT pellet cross-section. This does not fully represent the overall compositional gradient of Nd 3+ ions along the BL cross section, but specifically tracks the 144Nd + concentration throughout the crosssection. In order to track the Nd 3+ BL gradient, EDS analysis was carried out as described in the following section. 90

109 0.2 cm 0.8 cm 1.2 cm 2.0 cm Fig 5.30 SIMS atomic mass spectrum obtained for different cross-sectional positions indicating 144Nd + and Ti 2 O 3 + peaks 91

110 Table 5.4 Maximum peak intensities determined for 144Nd + and Ti 2 O 3 + in SIMS atomic mass spectru Cross-Sectional Position (cm) Maximum Intensity (Counts) Nd 3+ Ti Effect of Annealing Experiments were carried out in order to understand the possibility of inducing BL configuration in specimens which does not generate a natural BL in between the Nd 2 O 3 dopant concentrations of 0.2 to 0.3 mol%. The results discussed below are based on Nd 2 O 3 dopant composition of 0.2 mol%, initially sintered at C. Fig indicates the variation of dielectric constant and the loss parameters with the increasing temperature for 0.2 mol% Nd 2 O 3 doped BT sintered at C for 90 minutes. A dielectric constant of ε r = 44x10 4 was archived with a loss tangent of 0.68 at room temperature. Fig. 5.32a, b illustrates the dielectric response with temperature for the same specimen annealed for 2, 4, 16 and 32hrs at C. By comparing Fig and Fig. 5.32, it is evident that dielectric constant degrades (ε r = 44x10 4 to 3000) with increasing annealing time and reducing the dielectric loss from 0.63 to 0.06 due to the generation of oxidized surface BL via annealing. The development of oxidiced surface BL structure was further analyzed in this section and also has been compared with 0.3 mol% Nd 2 O 3 doped BT specimens sintered at C for 90 minutes consisting non-annealed BL morphology. 92

111 Fig Plot of dielectric constant and loss vs. temperature for 0.2 mol% Nd 2 O 3 doped BT sintered at C for 90 minutes (a) 93

112 (b) 94

113 Fig Dielectric response vs. (a) temperature (b) anneal time at C, for 0.2 mol% Nd 2 O 3 doped BT sintered at C for 90 minutes Fig compares the dielectric response of 0.3 mol% Nd 2 O 3 doped BT sintered at C for 90 minutes with 0.2 mol% Nd 2 O 3 doped BT sintered at C for 90 minutes and annealed at C for 2hrs. Although the pattern of dielectric constant variation is similar in both cases, the loss tangent deviates widely, displaying a lower loss in the former sample. Fig shows the resistivity variation for the specimen with the annealing time. For 0.2 mol% Nd 2 O 3 doped BT annealed at 2hrs, a resistivity of ~0.04 x 10 9 Ω.cm achieved, whereas for 0.3 mol% Nd 2 O 3 doped BT, the resistivity was ~1.2 x 10 9 Ω.cm, showing the sensitivity of resistivity to dopant concentration. 95

114 Fig Comparison of the dielectric response for 0.3 mol% Nd 2 O 3 doped BT sintered at C for 90 min with 0.2 mol% Nd 2 O 3 doped BT sintered at C for 90 min and annealed at C for 2hrs Fig Variation of resistivity for 0.2 mol% Nd 2 O 3 doped BT sintered at C for 90 min and annealed at C 96

115 In order to calculate the oxygen diffusion coefficient of the annealed specimens, the thickness of the oxidized surface region was measured using an optical microscope. Fig shows the optical micrographs for 0.2 mol% Nd 2 O 3 doped BT annealed for different time periods. The oxidized layer thickness measured (Fig. 5.36) and the diffusion coefficient was calculated using the equation 5.2 below (Fig and Table. 5.5). 5.2 Where, <x>, t and D are the mean diffusion length, time and diffusion coefficient respectively. The derivation of the equation (2) will be discussed in the next chapter. A highest diffusion coefficient was seen for the samples annealed for 2hrs and 4hrs. The data obtained from this measurement is in agreement with the EDS analysis for the oxygen concentration (atomic %) of sample interiors, where more oxygen was detected in the interiors of samples annealed for 2hrs and 4hrs (Fig. 5.38). When the samples are annealed for different durations, the amount of liquid phase created over the grain boundaries changes [27, ]. A higher liquid phase component will be created in the samples that are annealed for longer durations and this could hinder the mass transport resulting from decreased oxygen vacancies and possibly corresponding to a slower oxygen diffusion rate. As illustrated in Fig. 5.38, the concentration of Nd in the interior region of the sample decreases with increased annealing time (concentration of Nd in the edge region increases with the annealed time). When the surface regions of the samples are more oxidized, Nd tend to move towards the region where a high oxygen concentration is available, due to the increased solubility of Nd 3+ in BT lattice at higher oxygen partial pressures [3]. Therefore, the remaining amount of Nd 2 O 3 in the interior region of the sample is ~0.15mol% (semiconducting) and at the surfaces, it exceeds 0.2 mol%. 97

116 hrss 2 hrs 4 hrs 16 hrs 32 hrs Fig Optical micrographs of 0.2 mol% Nd 2 O 3 doped BT sintered at C for 90 min and annealed for different time periods (In hours) Fig Oxidized layer thickness vs. annealed time for 0.2 mol% Nd 2 O 3 doped BT sintered at C for 90 min Fig Oxygen diffusion coefficients vs. annealed time for 0.2 mol% Nd 2 O 3 doped BT sintered at C for 90 min Table 5.5 Oxidized layer thickness measured and the calculated diffusion coefficient for 0.2 mol% Nd 2 O 3 doped BT sintered at C for 90 min and annealed for different time periods Annealed Time (hrs) Oxidized Layer Thickness (mm) 98 Diffusion Coefficient (m 2 /s) x x x x 10-14

117 Fig EDS analysis for the oxygen and Nd atomic concentration as a function of cross sectional position for 0.2 mol% Nd 2 O 3 doped BT sintered at C for 90 min and annealed for 0 to 32hrs 99

118 SEM micrographs in Fig 5.39 for chemically etched 0.2 mol% Nd 2 O 3 doped BT samples annealed from 0 to 16 hrs reveal that the chemical composition of the samples over the interior and the surface regions are different for annealed specimens. Surface region of the samples are preferentially etched compared to the interior regions of the annealed samples. The preferential etching could occur due to 2 reasons, (1) etching over a certain crystallographic direction (2) etching due to the chemical composition [4]. Both these factors could be affecting the system, as explained in Fig Clearly, EDS data confirms the difference in chemical composition over the interior and the surface region. Furthermore, SEM analysis reveals an increase grain growth with the anneal time and the average grain size towards the middle region of the sample is larger than the oxidized region (Table 5.6 and Fig The difference of grain sizes in the surface and interior regions increase with anneal time (Fig. 5.39), indicating Nd 3+ diffusion towards the surface where high oxygen partial pressure is high. Although the grain growth over the interior region increases with annealed time, the grain growth in the surface region remains extremely low. This indicates that the Nd 3+ diffused from interior region of the sample to the surface due to higher oxygen partial pressure, may be accumulating at the grain boundaries near the surface region. Since Nd 3+ is a well-known grain growth inhibitor, if all Nd 3+ diffused from the interior regions (in 2hrs- 32hrs annealed samples), resides in BT lattice, then it follows that the slope of the surface grain size distribution should be the same as the slope of the interior region of the grain sizes distribution (Fig. 5.40) which does not appear to be the reason. Therefore, it is possible that along with a high concentration of Nd substituting in to the BT lattice over the surface region, a fairly considerable portion is segregating at the grain boundaries. 100

119 Middle Regions Edge Regions 0 hrs Middle region grain growth 0 hrs 4 hrs 4 hrs hrs hrs the interior region of chemically etched 0.2 mol% Fig SEM micrographs of the surface and 0 Nd2O3 doped BT samples sintered at 1320 C for 90 min and annealed for 0 to 16 hrs 101

120 Table 5.6 Variation of the grain size over the surface and the interior region in 0.2 mol% Nd 2 O 3 doped BT samples sintered at C for 90 min and annealed for 0 to 16 hrs Annealed Time (hrs) Middle Grain Size (µm) Edge Grain Size (µm) Fig Grain size vs. anneal time in 0.2 mol% Nd 2 O 3 doped BT samples sintered at C for 90 min Summary Experiments suggest that compositional variation and heat treatment directly impact the surface BL formation in Nd 2 O 3 doped BT ceramics, while variation of Nd 2 O 3 concentration in between 0.3 to 0.6 mol% delivers a spontaneous SBL composition after sintering at C. Sintering accompanied heat treatment for the Nd 2 O 3 compositions below 0.3 mol% also induce a 102

121 SBL region. By comparing the SIMS and EDS analysis conducted for SBL specimens, it is clear that Nd +3 is abandoned in the regions where oxygen concentration is higher. Again the concentration of Jahan Teller active Ti 3+ ions, increases in the reduced interior region of the samples, when the Nd concentration is fairly low (i.e., compared to the oxidized surface region). Solubility variation of Nd attributed to the changes in oxygen partial pressure seems to be the force driving the structural gradients. Further, X-ray diffraction analysis and measurement of resistivity across the BL crosssection indicates a gradient distribution of internal stresses as well as a variation of the conductivity of the specimen. Similarly, SEM analysis suggests a variation of grain size over the interior and the surface region of the BL specimens, once again confirming the residual stress development and Nd compositional variation through the cross-section. Further, the difference in chemical composition over the surface and the interior of the BL pellets seems to be a result of preferential chemical etching generated. 103

122 5.3 Dielectric Characteristics in Core-shell/ BL Structures Dielectric and Relaxation Properties of Pure BT The temperature variation of dielectric constant measured at 1 khz for pure BT sintered at C for 90 minutes is shown in Fig (a). As seen in the figure, above the Curie point (~130 0 C), a structural transformation from tetragonal to cubic phase occurs along with spontaneous polarization. Fig.5.41 (b), (c) represents the frequency variation of dielectric parameters at room temperature for the same specimen. These figures clearly indicate a single dipolar relaxation (drop in the dielectric response) near 10 8 Hz, which represents a single semicircular arc in the corresponding Cole-Cole plot, Fig (d). Further as seen in Fig (b), below 10 8 Hz, the dielectric constant is almost a constant. (a) (b) 104

123 (c) Fig.5 41 (a) Temperature (b) frequency variation of the dielectric constant (c) corresponding Cole-Cole plot for pure BT sintered at C for 90 minutes Therefore, the impedance response for pure BT confirms that the single phase composition of the structure with no GBBL or diffused phase SBL formation Dielectric and Relaxation Properties of Nd/ Zr Doped BT As discussed in section (Fig. 2.19), the imaginary permittivity vs. frequency for Nd 2 O 3 doped BT and 0.6 mol% Nd 2 O 3 /0-3 mol% ZrO 2 doped BT were plotted in Fig5.42. By comparing the shapes of standard plots shown in Fig. 2.19, it appears that a low concentration of Nd 2 O 3 incorporation into the system creates Maxwell Wagner (MW) polarization behavior and when the Nd 2 O 3 concentration is increased, the system transforms into the original Debye type behavior (Fig.5.42a). By introducing 0-3 mol% of ZrO 2 into 0.6 mol% Nd 2 O 3 doped system; it has been observed that the MW behavior is maintained (Fig. 5.42b). Further, it is important to notice that the pure MW behavior (without the Debye term) observed in 0.15 mol% Nd 2 O 3 doped BT specimens is exactly similar to the shape of the curve obtained for 0.6 mol% Nd 2 O 3 /1mol% ZrO 2 composition. 105

124 (a) (b) Imaginary Permittivity (ε ) Imaginary Permittivity (ε ) Frequency (Hz) Fig.5.42 Imaginary permittivity vs. frequency for (a) Nd 2 O 3 doped BT and (b) 0.6 mol% Nd 2 O 3 /0-3 mol% ZrO 2 doped BT sintered at C for 90 minutes 106 Frequency (Hz)

125 Therefore, the observed enhancement of the dielectric constant in 0.6 mol% Nd 2 O 3 /1 mol% ZrO 2 doped BT system is attributed to the increased interfacial polarization created by the enhanced carrier mobility in the BL structure. The Cole- Cole plots in Fig.5.43 indicate the presence of above responses with three semicircular arcs corresponding to the core boundaries, grain cores and the outer oxidized SBL region. In the specimen where only 0.6 mol% Nd 2 O 3 is added, a single semicircular arc can be seen due to the absence of core-shell structures. However, Fig.5.44 shows that by increasing Nd 2 O 3 content, keeping ZrO 2 concentration constant at 1 mol%, three semicircular arcs appear as in Fig This indicates the formation of the diffused SBL region as well as the partitioning of Nd 2 O 3 at the grain boundaries with increased dopant concentrations. Above observations clearly confirms multiple relaxation mechanisms (MW/ Debye) governing the combined GBBL/ SBL structure in Nd and Nd/Zr doped BT. Multiple relaxation mechanisms indicate presence of several polarization mechanisms contributing to dielectric loss [114, 115]. Furthermore, materials exhibiting this property lead to an unbounded increase in ε with increasing ε, indicative of the extremely high dielectric constant. Therefore, it is reasonable to expect a Cole-Cole plot with a single arc enclosing a smaller area (indicating low dielectric constant) for a low loss dielectric material such as pure BT as discussed in section However, the unique characteristic of the materials with combined GBBL/SBL compositions is relatively low loss, even at extremely high dielectric constants. 107

126 Fig.5.43 (a) Cole-Cole plots (b) frequency vs. dielectric response for mol% Nd 2 O 3 / 1 mol% ZrO 2 doped BT sintered at C for 90 minutes, indicating difference in relaxation response with increased Nd 2 O 3 composition Fig.5.44 Cole-cole plots for (a) 0.6 mol% Nd 2 O 3 / mol% ZrO 2 (b) 1 mol% ZrO 2 / mol% Nd 2 O 3 doped BT sintered at C for 90 minutes 108

127 5.3.3 Relaxation Behavior of the Oxidized and the Reduced Regions of the SBL Structure Fig shows the diffused interface separating the oxidized surface region and the reduced interior in 0.7 mol% of Nd 2 O 3 and 1 mol% ZrO 2 doped BT sintered at C for 90 minutes. Attempts have been made to observe the variation of dielectric relaxation properties of the bulk specimen vs. the reduced sample interior for a specimen of above dopant concentration. The dielectric parameters of 0.7 mol% Nd 2 O 3 and 1 mol% of ZrO 2 doped BT pellet before and after removal of the oxidized outer layers are compared in Fig A decrease in the dielectric constant and a dramatic increase of the loss are seen in the latter specimen where the oxidized surface region is removed by polishing off 0.4 mm thickness using 600 grid SiC powder (Fig 5.46b). The Cole-Cole plot for the sample with oxidized barrier layers has large and small semicircular arcs corresponding to different relaxation mechanisms. Two semicircular arcs are clearly discernable and there is also evidence for a third semi-circle. Further, two shoulders in dielectric constant vs. frequency curve is observed around 10 3 and 10 6 Hz indicative of switching Oxidized Reduced Fig.5.45 SEM cross-sectional image of a 0.7Nd/1Zr doped BT sintered at C for 90 minutes 109

128 (a) (b) Fig.5.46 Comparison of the frequency variation of dielectric constant, dielectric loss, Cole- Cole plots of a 0.6 mol % Nd 2 O 3 and 1.0 mol% ZrO 2 doped BT pellet (a) before and (b) after removal of the oxidized surface region [92] into different relation mechanisms, possibly corresponding to the core boundaries, grain cores and the outer oxidized SBL regions. Additionally, the plot of dielectric loss vs. frequency for a bulk sample shown, again indicate three peaks confirming the existences of three relaxation processes as discussed above. In the Cole-Cole plot of the sample without the oxidized SBL ( Fig. 5.46b ), an unbounded increase in ε with increasing ε is an indication of the involvement of an reduced interior region as discussed in section

129 5.3.4 Summary The dielectric relaxation mechanisms of BT doped with Nd 2 O 3 and ZrO 2 indicate that the grain and grain boundary structure and formation of barrier layers lead to rather complex dielectric properties. Mechanisms involved can be satisfactorily explained on the basis of Cole- Cole analysis, separating relaxation into two well known schemes- Debye and Maxwell Wagner. The doping compositions and sintering conditions that leads to above relaxation mechanisms has been identified. The important result is identification of doping compositions and sintering conditions leading to high dielectric constant at relatively low loss. 111

130 5.4 Effect of Oxidation and Dopant Site Substitution in BL Formation Oxidation As discussed in section 2.4.1, a simplified version of eqn can be used to estimate the diffusion coefficient of oxygen in BT during sintering, provided oxygen concentration in the pellet is measurable. Further, the diffusion coefficient of O 2 determines the rate of oxidation of grains from the surface to the interior and the growth of the oxidized surface layer during sintering. As shown in appendix 1, by simplification of eqn and using the boundary conditions, the diffusion coefficient (D) can be related to the thickness of the oxidized surface layer (mean width of the O 2 diffusion profile, <x>), and the sintering time (t) as follows; < x >= 4Dt π 5.3 Fig indicates the variation of the oxidized surface layer thickness measurement with increasing Nd 2 O 3 and ZrO 2 concentrations. From the figure, it is evident that up to 0.7 mol% of ZrO 2 addition, the oxidized surface layer thickness is independent of Nd 2 O 3 concentration. Above 0.7 mol% of ZrO 2 addition, Zr gradually segregates at the grain boundaries providing a GBBL structure, increasing the solubility of Nd in Zr enriched grain boundary region. Therefore, with the increase Nd 2 O 3 concentration, more Nd tends to move towards the Zr rich grain boundary, hindering the oxygen diffusion from the surface region [116]. Clearly this effect has a potential of obtaining a lower oxidized layer thickness for high Nd 2 O 3 concentrations for the BT specimens doped with ZrO 2 concentrations < 0.7 mol%. Table 5.7 shows the observed variations for the oxidized layer thickness and the corresponding oxygen diffusion coefficients calculated from equation (1) for 0.6 mol% Nd 2 O 3 /1-3 mol% ZrO 2 doped BT and 1 mol% Nd 2 O 3 /1-3 mol% 112

131 ZrO 2 doped BT systems. In both structures, the oxidized layer thickness x, increases with the dopant concentration of ZrO 2. Fig Surface oxidized layer thickness vs. ZrO 2 concentration for Nd/Zr doped BT sintered at C for 90minutes. Table 5.7 Measured oxidized layer thicknesses and diffusion coefficients calculated using Eqn. 9(6) Composition Nd 2 O 3 /ZrO 2 Oxidized Layer Thickness (mm) Diffusion Coefficient (m 2 /s) 0.6 / x / x / x / x / x / x Oxygen diffusion coefficient of pure BT is ~ m 2 /s However, the value of x for 1 mol% Nd 2 O 3 /1-3 mol% ZrO 2 doped BT system is lower than that for the 0.6 mol% Nd 2 O 3 /1-3 mol% ZrO 2 doped BT system. As discussed above, 113

132 increased partitioning of Nd into the ZrO 2 phase and blocking of the oxygen diffusion along the grain boundaries is a likely reason for this observation. From Fig and Table 5.7, it is clear that ZrO 2 addition into the Nd 2 O 3 doped BT system enhances the oxygen diffusion into the material, increasing the surface oxidized layer thickness. Further, it is known that the oxygen diffusion is faster in ZrO 2 (29 at% at high temperatures [85]) compared to Nd 2 O 3 (~3 at% [30]), thus grain boundary segregation of ZrO 2 promotes oxygen diffusion along the grain paths. EDS area map shown in Fig.5.48a indicates a clear grain boundary segregation of ZrO 2. Furthermore, it appears that up to a limited amount, Nd 2 O 3 also segregate along the grain boundaries, due to the increased solubility of Nd in the ZrO 2 phase (Fig.48b) [4, 8, 97]. (a) (b) Fig.5.48 EDS area mapping for (a) Zr and (b) Nd in a Nd/Zr doped BT sample sintered at C for 90 minutes EDS data for percentage normalized oxygen atomic concentration (i.e. O/Ba+Ti at%) corresponding to the surface and the interior region of Nd and Zr modified BT samples are compared in table 5.8 and the plotted data are illustrated in Fig

133 Table 5.8 Oxidation changes in Nd and Nd/Zr doped BT specimens sintered at C for 90 minutes Surface Nd 2 O 3 mol% ZrO 2 mol% O at% (Ba at% +Ti at%) Interior O at% (Ba at% +Ti at%) Comments Non BL Non BL BL BL Non BL BL BL BL (a) (b) Fig.5.49 Comparison of surface and the interior oxygen atomic concentrations (a) Nd 2 O 3 doped BT (b) 0.6 mol% Nd 2 O 3 / ZrO 2 doped BT, sintered at C for 90 minutes 115

134 Figure 5.49 (b), confirms the increase of oxygen diffusion when the ZrO 2 concentration is increased in Nd 2 O 3 doped BT (as observed in Table 5.7 and Fig 5.47 from oxidized layer thickness measurements). However, as illustrated in Fig. 5.49(a), an increase of Nd 2 O 3 concentration in BT without ZrO 2 introduction, the system behaves differently compared to the Nd/Zr doped BT system. Oxygen diffusion in Nd 2 O 3 doped BT, corresponds to the variation of dielectric parameters with Nd 2 O 3 concentration as discussed in section Further, in section 5.2.1, the variation of dielectric parameters for 0.3 mol% of Nd 2 O 3 doped BT was extensively discussed in terms of solid solubility limit of Nd 2 O 3 in BT at atmospheric oxygen partial pressures. From Fig (a), it is clearly evident that the oxygen diffusion in BT reaches a minimum, at the point where solid solubility limit of Nd 2 O 3 in BT is achieved, indicating controlled oxygen diffusion around the limit of Nd 2 O 3 saturation in BT. Beyond the saturated region of solid solubility, oxygen diffusion in Nd 2 O 3 doped BT ramps up, minimizing the difference in oxygen concentration on the surface and the interior of the specimen (i.e. increased mobility of O 2- ions). This observation clearly emphasize the importance of controlled diffusion of oxygen near the BL region of Nd 2 O 3 doped BT sintered at atmospheric conditions Dopant Substitution Of the TRE ions, the radius of Nd 3+ is almost midway between that of Ba 2+ and Ti 4+ and Nd 3+ is the TRE of largest ionic radius which is known to demonstrate amphoteric behavior ( possibility of occupying either A or B sites ). Because of the relatively larger ionic radius, the insertion of Nd 3+ into the Ti 4+ site would, markedly distort the BT lattice. Consequently, the kinetic influence of site occupancy of amphoteric TRE ions would be easily noticeable in Nd doped BT as changes in tetragonality and cell volume. However, as the A site is the most 116

135 probable site for Nd 3+ of substitution, the free energy change (ΔG) in the flip of Nd 3+ from A to B is quite large, consequently, B site substitution will be observable only at high [O 2 ]. With the addition of Zr 4+, which only occupies Ti 4+ sites [20, 21], more of the Nd 3+ should be forced into the Ba 2+ sites. However, an earlier report claims that Nd 3+ has a 10% possibility of substituting into the Ti 4+ -Site [100]. The Goldschmid tolerance factor for the perovskite is defined as [4, 27, 100]: 5.4 (where, t is tolerance factor and r, is the ionic radii,i = A, B, O) provides, a better understanding of the site substitution of TRE ions. Assuming that the local strain is similar in both Ba 2+ and Ti 4+ sites, it is expected that if the incorporation into one site results in a tolerance factor much closer to unity than the incorporation into the other site, the ion would prefer occupation of the latter site [27, 117, 118]. Table 5.9 indicates calculations of the tolerance factor (t) carried out from three different standard ionic radii databases. Results is contrary to the assumption that Nd 3+ exclusively occupies B site (i.e. t A ~t B ). Therefore, as supported by the experimental data and calculations, behavior of Nd 3+ in diffused BL system can be well explained by the oxygen partial pressure dependent solubility variations. 117

136 Table 5.9 Calculation of the tolerance factor for Nd 3+ substitution [64, 119, 120] Ionic Radii (nm) Ionic State Shannon s Database Chemical Database Materials Reference Book O 2- VI Ba 2+ XII Ti 4+ VI Nd 3+ VI t A t B Summary Studies described in the above section clearly indicate importance of oxygen diffusion processes in site substitution mechanisms of TRE ions such as Nd 3+ in BT, leading to modulation of electronic properties and morphological structure of the ceramic. ZrO 2 segregating at the grain boundaries was found to enhance oxygen diffusion along the grain boundaries, greatly influencing the substitution mechanism of Nd. The complexity of the process is evident because some Nd accumulating in the grain boundaries together with ZrO 2, affects the oxygen diffusion rates. Analysis of data in the context of the Goldschmidt Tolerance Factor for ABO 3 structures suggest that Nd occupies only A-site and oxygen diffusion greatly depends on the region where the solid solubility limit of Nd in BT is accomplished. 118

137 5.5 Effect of Zr in Core-Shell BL Development Dielectric and Electrical Property Variation In Fig. 5.50, the plot of ε vs. Nd 2 O 3 doping concentration for 1 to 3 mol% ZrO 2 and varying concentrations of Nd 2 O 3 doped BT pellets sintered at C for 90 minutes is overlaid on dielectric property variation observed in Fig for only Nd 2 O 3 doped BT system. As observed in Fig for Nd 2 O 3 doped BT system, the patterns of the plots has not changed and they are similar regardless of ZrO 2 incorporation but followed by shifts in the peak positions. Generally, TRE oxides are more soluble in ZrO 2 than BT (solubility of trivalent rare earth oxides is at most few 3at% in BT and exceeds 10 at% ZrO 2 [30]). Therefore, this shift can be attributed to the changes in solubility and the saturation limits of Nd with the increased amounts of ZrO 2 addition. The dielectric loss drops further by ZrO 2 addition in the Nd doped BT system due to the higher degree of grain boundary insulation compared to only Nd 2 O 3 doped BT system. Further, from Fig it can be observed that an extraordinarily high dielectric constant occurs at 0.7 mol% Nd 2 O 3 /1 mol% ZrO 2 composition (room temperature dielectric constant ε r ~ 55000). However, enhancement in dielectric constant is generally associated with high dielectric loss ~ 0.07 at room temperature as revealed in the dielectric loss spectrum. Fig.5.51 shows that, with 1 mol% of ZrO 2 addition, the Curie peak gets suppressed and broadened compared to Nd 2 O 3 doped BT system. Presumably this is a result of excessive core-shell formation. The occurrence of broad permittivity maxima is commonly detected in BT solid solutions. The broadness of the peak is mainly affected by the nature of the diffuse phase and the internal stress [65, 99, 121, 122]. Besides, the broadened dielectric peaks are an indication of relaxaor type behavior [78]. Therefore, combining Fig and 5.52 ZrO 2 codoping is indeed a 119

138 Fig ε vs. Nd 2 O 3 doping concentration for 0 to 3 mol% ZrO 2 and varying concentrations of Nd 2 O 3 doped BT pellets sintered at C for 90 minutes Fig 5.51 Dielectric constant, loss vs. temperature curves for 1 mol% of ZrO 2 and mol% of Nd 2 O 3 doped BT samples sintered at C for 90 minutes 120

139 sound strategy, in addition to fattening of Curie peak and reduction of loss, there is a clear signature for enhancement of dielectric constant and reduction of loss [123]. Fig compares the variation of Curie temperature vs. Nd 2 O 3 concentration for 0 and 1 mol% of ZrO2 doped BT sintered at C for 90 minutes. It can be observed that the addition of 1 mol% ZrO 2 into the Nd 2 O 3 modified BT system shifts Curie peak further into lower temperatures. Fig.5.52 Curie temperature vs. Nd 2 O 3 concentration for specimens sintered at C for 90 minutes 121

140 In addition to the discussion in section (Fig. 5.23), resistivity vs. Nd 2 O 3 concentration for 1 mol% of ZrO 2 doped BT is plotted in Fig The figure indicate that the addition of ZrO 2 indeed enhance the BL properties in Nd 2 O 3 doped BT system. Additionally, in order to analyze the effect of ZrO 2 concentration at a fixed Nd 2 O 3 (0.6 mol%) concentration, the resistivity vs. ZrO 2 content (1 mol%) was plotted in Fig 5.54 for comparison. From this experiment, it is clear that the minimum resistivity values were obtained when 1 mol% of ZrO 2 is introduced into the Nd 2 O 3 doped BT system. Clearly this is a consequence of increased grain boundary insulation along with the core- shell formation. Further, Fig 5.54 does not show evidence of resistivity variation in the form of two separated maxima for different ZrO 2 dopant compositions, providing no indication of SBL generation due to increased concentrations of ZrO 2 addition. BL BL Fig.5.53 Resistivity vs. Nd 2 O 3 concentration for Nd/Zr doped BT sintered at C for 90 minutes 122

141 Fig.5.54 Resistivity vs. ZrO 2 content for Nd doped BT sintered at C for 90 minutes Variation of Structural Properties Variation of tetragonality is more evident in ZrO 2 doped BT with fixed Nd 2 O 3 concentration (Fig. 5.55) compared to Nd 2 O 3 doped BT system discussed in section 5.2, Fig Although it is clear that Nd incorporation into BT lattice alter the tetragonal BT structure into psedocubic, the Nd doped BT structure is further affected by internal stress development due to grain boundary insulation generated by core-shell formation via ZrO 2 addition. Further from Fig. 5.55, it is seen that the c/a ratio increases from face of the pellet towards the interior but the plot is asymmetric, i.e., the decrease of the c/a towards the exterior is more prominent near the face of pellet exposed to the atmosphere during sintering. The structure and the asymmetry of the plot are clearly reminiscent of the increased oxygen diffusion profile due to ZrO 2 addition. During sintering oxygen diffuses relatively slowly from the under-side of the pellet compared to the upper-side, and it follows that the rate of decrease of the c/a correlates with the oxygen partial pressure during sintering, i.e., c/a ratio is lower (higher) in regions where [O 2 ] is higher (lower). 123

142 Bottom surface Side facing pellet Top surface Side facing atmosphere Fig Tetragonality variation across the thickness for mol% of Nd 2 O 3 and 1 mol% ZrO 2 doped BT samples sintered at C for 90 minutes Fig.5.56(a) shows the combined BL configuration and variation of the c/a ratio calculated using wide angle XRD spectrum across the thickness of 0.7 mol% Nd 2 O 3 and 1 mol% ZrO 2 doped BT pellet. As discussed earlier, the c/a inflection indicates a high stress condition along those interfaces which contributes to higher polarization in the sample. The c/a profiles are also consistent with oxygen ion vacancies and active Ti 3+ being generated in the interior through the Jahan Teller effect. An optical micrograph of the same specimen is shown in Fig. 5.56(b). From the image, the diffused BL configuration in 0.7 mol% Nd 2 O 3 and 1 mol% ZrO 2 doped BT system is evident. A TEM specimen corresponding to above composition prepared by L. Zhou [124], (Department of Materials Science and Engineering, University of Cincinnati, OH) was further 124

143 analyzed for extended microstructural configuration (Fig.5.56c). Additionally, the cell parameters calculated using the wide angle XRD analysis is indicated in Table The fine variation of cell volumes over the interior and the surface of the specimen are evident due to the internal strain development. The figures clearly indicate the expected core-shell grain formation in 0.7 mol% Nd 2 O 3 and 1 mol% ZrO 2 doped BT system due to ZrO 2 addition. The emerges from the results of the measurements described above provide that when the BT pellets are pressed with Nd 2 O 3 and ZrO 2 dopant precursors followed by sintering, Nd diffuses into the grains, doping the BT, while ZrO 2 at the grain boundaries undergoes also limited diffusion [125, 126] into the BT, forming a core-shell structure. (a) BL BL Surface Interior Surface 125

144 (b) (c) (c) Fig (a) Tetragonality variation across the thickness (b) Optical microscopic cross-section (c) TEM image of the core-shell structure for 0.7 mol% of Nd 2 O 3 and 1 mol% ZrO 2 doped BT samples sintered at C for 90 minutes Table 5.10 Cell parameters calculated using XRD analysis for 0.7 mol% of Nd 2 O 3 1 mol% ZrO 2 doped BT sintered at C for 90 minutes Cell Parameter Surface Interior a(å) c(å) c/a Cell volume (Å 3 )

145 5.5.3 Summary The above discussion clearly indicates that co-doping of ZrO 2 has a profound effect on modulating the dielectric properties in Nd 2 O 3 doped BT BL configuration due to the increased dissolution of oxygen in ZrO 2 enriched grain boundaries. Thus, ZrO 2 influences the morphology of the ceramic as well as the electronic properties. Increased internal oxygen concentrations determine Nd 2 O 3 compensation mechanism. The net effect of all these influences of ZrO 2, when optimized enables synthesis of BT ceramic of favorable dielectric properties accompanied with combined GBBL and SBL configurations. 127

146 CHAPTER 6 Mathematical Model 6.1 Model Description As discussed in section 2.3.2, the complex impedance of a Debye system consisting of single resistor and a capacitor is given by: 6.1 The combined core-shell BL, Nd 2 O 3 and ZrO 2 modified BT system was analyzed on the basis of Debye theory and the equivalent circuit illustrated in Fig.6.1(a). The cores and diffused core boundaries (for the simplicity, the contribution of the diffused gradient of the SBL is also included to the core boundary term) in the middle portion of the pellet have capacitances (C c, C cb ) and resistances (R c, R cb ) as indicate in Fig.6.1 and the two fully oxidized insulating layers have a capacitance C b and a resistance R b. Using equation 6.1, the impedance of the circuit can be written as; 6.2 The first and the last terms of 6.2 are the contributions to Z * from the two oxidized layers and the two middle terms represents contributions from grain cores and core boundaries / diffused SBL in the partially or un-oxidized middle portion of the pellet [40, 92, ]. By definition, the complex impedance can be written as, Therefore, by splitting the real and imaginary part of equation 6.2, 128

147 (a) c b c cb c c c b R b R cb R c R b (b) d b Oxidized Diffused BL D Reduced Interior (c) Core (d c ) Core boundary (d cb ) Fig.6.1 (a) Equivalent circuit constituted of series connected circuit elements representing each region in the BL structure (b) SBL/ GBBL structure (c) schematic diagram showing two adjacent grains 129

148 R Z ' = c R + cb 2R + b 1+ (iωr c C c ) 2 1+ (ωr cb C cb ) 2 1+ (ωr b C b ) From equations 6.3 and 6.4, it is evident that there are three characteristic relaxation times in this system originating from grain cores, core boundaries/ SBL and the oxidized surfaces as written below:,, By re-writing the complex permittivity in the following form; 6.5 where, (as in Debye type relaxation) 6.6 and, 6.7 Where, τ relaxation time, ε s static dielectric const, ε - dielectric constant at infinity C 0 = ε 0 A/D (A- area, D- sample thickness) and, R 1, R 2 are the resistance of the two dielectric components as discussed in MW theory. Substitution of 6.6 and 6.7 in equation 6.5 yield, 6.8 Since Ohmic conductivity (σ ) is,

149 equation 6.8 can be re- written as, 6.10 The equations derived above can be applied into the GBBL/SBL system by using 6.2, 6.5 and 6.10 to obtain the static dielectric constant and the dielectric constant at infinite frequency as follows ; ε = C 0 C c C cb C b 6.11 ε s = R 2 cc c + R 2 cb C cb + 2R 2 b C b C 0 R c + R cb + 2R b [ ] By definition, the basic components of brick layer model (Fig. 6.2) consists of grain boundaries (gb) and grains (g). Therefore, the corresponding grain boundary resistivity can be derived from the same model as follows: 6.13 Where, ρ gb grain boundary resistivity, δ gb grain boundary thickness, d g grain thickness. Further, grin boundary capacitance in brick layer model is given by: 6.14 In Nd 2 O 3 or ZrO 2 modified GBBL/SBL system, there exist a macroscopic surface barrier layer other than the interior core and core boundary regions. Further, one can assume that the material constituent in the core boundary region is almost similar to the grain boundary, which is a dc insulator. Since the core is conducting in this structure the resistance is negligible compared to 131

150 d b d cb d c D Fig.6.2 Schematic illustration of the brick layer model incorporated into combined GBBL/SBL structure the core boundary and the surface barrier. Thus, for the GBBL/SBL system, eqns and 6.14 can be modified as follows: and, By substituting 6.15, 6.16, 6.17, 6.18 in 6.12 static dielectric constant is obtained, i.e.,

151 Since both the core boundary and the surface barrier are highly oxidized, it is reasonable to that assume the properties are similar, i.e. ρ cb = ρ b and ε cb = ε b. Accordingly, equation 6.19 simplifies to, 6.20 where d b, d c, d cb, D are the surface barrier thickness, core diameter, core boundary thickness, thickness of the bulk sample and ε b is the dielectric constant of the oxidized SBL or the GBBL region respectively. When d b is negligible, following approximations are obtained, i.e., GBBL contribution of the dielectric constant = 6.21 Neglecting the core shell contribution, we obtain; SBL contribution to the dielectric constant (neglecting core-shell contribution) = Above equations help to gain an quantitative understanding of the dielectric properties of the BT ceramic in terms of geometry and physical properties of grains and grain boundaries. 6.2 Summary Relating dielectric and other electronic properties of combined GBBL/SBL BT ceramic to its unique morphology in quantitative terms is exceedingly challenging. A simplification that admits approximate representation of the characteristics is the Brick Layer Model. Additionally, Maxwell Wagner (MW) modified Dabye relaxation theory combining into the Brick Layer model provide further simplification into the developed model. 133

152 The above analysis indicated that gross dielectric properties and relaxation phenomenon are reasonably well accounted by the Brick Layer model and MW-Debye relaxation theories. In reality the variation of the grins sizes, grain shape and grain boundary thickness have detectable influence on the dielectric properties of GBBL/SBL BT ceramics. The model discussed in this section readily accommodates the experimental observations made in Nd 2 O 3 / ZrO 2 doped BT structures with SBL/GBBL properties. 134

153 CHAPTER 7 Summary Discussion The main focus of this research has been to determine the effectiveness of Nd 2 O 3 in modifying the dielectric properties of BT via formation of surface and grain boundary BLs. Compositions and processing conditions necessary to enhance the static dielectric constant, while maintaining a relatively low loss was examined to gain an in-depth understanding of physical mechanisms involved. The significant experimental findings are: (1) identification and characterization of diffused barrier layer configurations in Nd 2 O 3 doped BT (2) induced BL formation under heat treatment (3) modulation of the BL structure via ZrO 2 incorporation. Data analysis and theoretical interpretations in terms of mathematical models enabled elucidation of optimum conditions needed for developing BT ceramic materials for capacitors and possible high energy storage systems. 7.1 Barrier Layer Phenomenon The extensive experiments conducted revealed that the BL formation in Nd 2 O 3 doped BT ceramics is indeed a complex phenomenon involving dopant concentration, oxygen partial pressure and details of the heat treatment procedure. Dopant solubility variations and multiple charge compensation mechanisms leads to different dielectric relaxation mechanisms were further understood and optimized on basis of mathematical models. A significant finding not previously reported in studies on trivalent rare earth doped BT systems, is the observation of a second maximum in dielectric constant falling within the dopant range of mol% Nd 2 O

154 As illustrated in Fig. 7.1, the dielectric constant at 0.3 mol% Nd 2 O 3 corresponds to a situation of minimum oxygen diffusion into the material, indicating that, at concentrations < 0.3 mol%, the Nd 2 O 3 solid solubility is only moderately controlled by the oxygen partial pressure, but influenced mainly by electronic compensation. Beyond that limit the solid solubility of Nd 2 O 3 is mainly driven by the partial pressure of oxygen with enhanced oxygen diffusion into the material. However, beyond 0.6 mol% the ionic compensation mechanism take over electronic compensation owing to increased oxygen diffusion. Fig 7.1 (b) further illustrates the variation of oxygen concentration on the surface and the interior of the BL specimen. The figure clearly indicate that the oxygen diffusion in BT reaches a minimum at the point where solid solubility limit of Nd 2 O 3 in BT is achieved, indicating controlled oxygen diffusion around the limit of Nd 2 O 3 saturation in BT. Beyond saturation, the oxygen diffusion is strongly increased by the mobility of O 2- ions. Assessment of oxygen and Nd 2 O 3 concentrations over the surface and the interior region for different mol% of Nd 2 O 3 suggests oxygen enhanced fast ion diffusion of Nd in BT generating SBL structures at concentration levels falling within the range 0.3 to 0.6 mol% Nd 2 O 3. Apart from the dopant concentration effects described above, BL specimens doped with Nd 2 O 3 within the region of mol% indicate, inherent variations in resistivity and dielectric relaxation mechanisms (Fig. 7.2) compared to other Nd 2 O 3 doped BT non-bl 136

155 (a) 10 6 Room Temperature Dielectric Constant Electronic BL Ionic (b) Fig.7.1 (a) Variation of the room temperature dielectric constant measured at 1 khz (b) Normalized oxygen atomic concentration for Nd 2 O 3 doped BT sintered at C for 90 min 137

156 configurations. Multiple relaxation mechanisms are evident as more than one semicircular arcs are seen in Cole-Cole plots (Fig 7.2b). These findings points to the conclusion that the BL phenomena in Nd 2 O 3 doped BT structures can be adopted in capacitive systems for energy storage applications. (a) BL BL Surface Interior Surface (b) Fig.7.2 (a) Resistivity and c/a ratio vs. cross-sectional position (b) Corresponding Cole-Cole plot for 0.5 mol% of Nd 2 O 3 doped BT samples sintered at C for 90 minutes sintered at C for 90 minutes 138

157 7.2 Induced BL Phenomenon by Annealing Another important finding of this study is the induced formation of an oxidized SBL by annealing (>4hrs) in doped (dopant composition~ mol% Nd 2 O 3 ), specimens as shown in Fig 7.3 (a) and (b). As discussed in section 7.1, under atmospheric sintering conditions, there is no evidence for BL formation within the doping range mol% Nd 2 O 3. Concentration variations of O 2-, Nd 3+ and Ti 3+, derived from EDS and SIMS analysis, are also shown in figure 7.3b, where it can be observed that the Nd 3+ concentration increases across the specimen from the interior to the surface, coincident with the [O 2 ] gradient across this region. This observation indicates an increased solubility of Nd 3+ in BT lattice in regions of higher oxygen partial pressures. The solubility migration; the driving force for the Nd 3+ concentration gradient from the interior to the sample surface increases with annealing time, altering the characteristics of SBL. At higher Nd concentrations (> 0.2 mol% Nd 2 O 3 ), the SBL develops almost spontaneously without annealing. (a) (b) O 2- Nd 3+ Ti Concentration (mol%) A B C Fig. 7.3 Optical micrographs of 0.2 mol% Nd 2 O 3 doped BT sintered at C for 90min (a) As-sintered (b) Annealed for 4hrs showing A- reduced semiconducting, B- diffuse gradient and C- oxidized outer regions 139