Barium and Zirconium Co-Doped Sodium Bismuth Titanate

Dielectric and Electromechanical Properties of Barium and Zirconium Co-Doped Sodium Bismuth Titanate

Sossity A. Sheets

A.B. Earth Sciences, Dartmouth College, 1995 M.S. Earth Sciences, Dartmouth College, 1997

SUBMITTED TO THE DEPARTMENT OF MATERIALS SCIENCE AND ENGINEERING IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF

MASTER OF SCIENCE IN MATERIALS SCIENCE AND ENGINEERING AT THE MASSACHUSETTS INSTITUTE OF TECHNOLOGY

SEPTEMBER 2000

Signature of Author: 1 7 _· · · _ · Department of Materials Science and Engineering August 4, 2000

Certified by: _ J- /'et-Ming Chiang Kyocera Pr'fessor of Ceramics Thesis Supervisor

C Accepted by: - I Carl V. Thompson Stavros Salapatas Professor of Materials Science & Engineering Chairman, Departmental Committee on Graduate Students

MASSACHUSETTSINSTftE OF TECHNOLOGY I

OCT 2 6 2004 ARCHIVES

LIBRARIES

Dielectric and Electromechanical Properties of Barium and Zirconium Co-Doped Sodium Bismuth Titanate

Sossity A. Sheets

Submitted to the Department of Materials Science and Engineering on August 4, 2000 in Partial Fulfillment of the Requirements for the Degree of Master of Science in Materials Science and Engineering

ABSTRACT

Compositional exploration was conducted within the alkaline bismuth titanate system by doping on the A- and B- sites with Ba'2 and Zr'4, respectively. Results on the phase, dielectric and electromechanical properties of single crystals and polycrystals for this new family of relaxor perovskite ferroelectrics are presented. The actuation and polarization characteristics in this system were found to be highly sensitive (within 2 mol%) to cation doping levels, and tailored compositions successfully isolated predominantly electrostrictive actuation at room temperature. Ultra-high room temperature electrostriction was observed in co-doped (Ba + Zr) NBT polycrystals (NBT-14BT-4NBZ)and <100> single crystals (NBT-12BT-4NBZ),up to 0.24% and 0.45% strain, respectively, with negligible hysteresis at 0.05 Hz. Polycrystals with d33of up to 780 pC/N and single crystals with d33 up to 2000 pC/N were measured. The low frequency actuation properties in the NBT-BT-NBZcompositions surpass highest reported values of strain and d33 for polycrystalline PMN and PLZT and single crystal PMN conventional lead electrostrictors. Predominantly ferroelectric room temperature unipolar actuation in polycrystalline NBT-14BT-3NBZat 0.05 Hz was observed to be linear and non-hysteretic, reaching up to 0.14% strain and d33 of 310 pC/N at 60 kV/cm. These low frequency properties match the reported strain and d33 values for conventional PZT-8, PMNT, and PZT-5a hard ferroelectrics and are more than double the reported values for polycrystalline NBT-BT (d33 = 125 pC/N). Electrostrictive and ferroelectric compositions in the NBT-BT-NBZsystem show the highest actuation strain and d33 reported to date in any polycrystalline, lead-free composition.

Thesis Supervisor: Yet-Ming Chiang Title: Kyocera Professor of Ceramics

3 Table of Contents

Chapter 1. Introduction 13 1.1 Piezoelectricity, Electrostriction and Ferroelectricity ...... 13 . 1.2 Relaxor Complex Perovskites-- ...... 15 1.3 Lead-Based Electromechanical Materials 19 1.4 Alternatives to Lead-Based Electromechanical Materials 20 1.5 Research Objective...... 22

Chapter 2. Experimental Procedure ...... 25 2.1 PolycrystallinePowder Preparation .. 26 2.2 Single Crystal Growth...... 31 2.3 Polycrystaland Single Crystal SamplePreparation for Testing. . 36...... 2.4 Polycrystal and Single Crystal Sample Characterization ...... 38 2.4.1 Crystal Symmetry Determination by X-ray Diffraction ------38 2.4.2 Composition Analysis by Electron Microprobe------38 2.4.3 Sample Electroding ------39 2.4.4 Dielectric Characterization by Impedance Analysis ...... 40 2.4.5Electromechanical Characterization by Impedance Analysis ...... 45 2.4.6Electromechanical Characterization Under Field 48

Chapter 3. Results I: Co-Doped Polycrystals ------51 3.1 Composition,Phase and Density Analysis------51 3.2 DielectricProperties of Polycrystalline(Ba + Zr) Co-DopedNBT 61 3.2.1 Room Temperature Dielectric Constant and Loss Tangent ------61 3.2.2 Temperature Dependence of Dielectric Constant and Loss Tangent ------64 3.2.3 Volger-Fulcher Anaysis------68 3.3 ElectromechanicalProperties of Polycrystalline(Ba + Zr) Co-DopedNBT. .72 3.3.1 Room Temperature Electromechanical Properties of Polycrystalline NBT-xBT-3NBZ------73 4 3.3.1.1 Predominantly Ferroelectric Actuation ------75 3.3.1.2 Field-Forced Transition (PE-FE) ------82 3.3.1.3 Predominantly Electrostrictive Actuation ------94 3.3.2 Room Temperature Electromechanical Properties of Polycrystalline NBT-xBT-4NBZ ------98 3.3.2.1 Predominantly Electrostrictive Actuation ------99 3.3.3 Pure Electrostriction in Highly Doped Polycrystalline NBT-26BT-29NBZ 104 3.3.4 Phase Diagrams for the Ternary System: Na1/2Bi1/2TiO3-BaTiO3-Nal/2Bi1 /2ZrO3 ...... ------106 3.3.5 Temperature Dependence of Electrostriction ...... 109 3.3.6 Comparison of Electrostrictive Properties ------111

Chapter 4. Results II: Co-Doped Single Crystals ...... 113 4.1 Single Crystal Growth by Self-Flux Method...... 113 4.2 Composition and Phase Symmetry Analysis .116 4.3 DielectricProperties of (Ba + Zr) Co-DopedNBT Single Crystals. . 118 4.3.1 Room Temperature Dielectric Constant and Loss Tangent ...... 118 4.3.2 Temperature Dependence of Dielectric Constant and Loss Tangent ...... 120 4.3.3 Comparison of the Dielectric Constant and Loss Temperature Dependence in Single Crystals and Polycrystals . 122...... 4.3.4 Volger-Fulcher Analysis...... 124 4.3.5 Temperature Hysteresis in Dielectric Response . 127...... 4.4 Electromechanical Properties of (Ba + Zr) Co-Doped NBT Single Crystals....129 4.4.1 Room Temperature Electrostrictive Properties of Tetragonal Phase Co-Doped NBT Single Crystals . 129...... 4.4.2 Room Temperature Electrostrictive Properties of Rhombohedral Phase Co-Doped NBT Single Crystals . 135...... 4.4.3 Comparison of Electrostriction -...... 139

Chapter 5. Conclusions 141 Appendix I. Sample Testing Procedure .143 Appendix II. Procedure for Preparation of 5% PVA-H20 Solution-...... 165 Appendix III. Relative Tolerance Factor Approach to Perovskite Structure Prediction . 167....

Bibliography...... 175

5 List of Figures

Figure 1.1 Typical Temperature Dependence of Permittivity and Dielecrtic Loss in Relaxor Ferroelectrics 16 Figure 1.2 Typical Dielectric and Polarization Behavior in Relaxor Ferroelectrics-17

Figure 2.1 Ternary Plot of Nominal Polycrystalline Powder Batch Compositions ----28

Figure 2.2 Set-Up For In-Situ Melting Observation ...... 35 Figure 2.3 Model 590 Tripod PolisherB South Bay Technology, Inc.- 37...... Figure 2.4 Polished (Ba + Zr) Co-Doped NBT Samples Prepared For Testing ------37 Figure 2.5 High Temperature Sample Holder for Impedance Measurements ------43 Figure 2.6 High Temperature Sample Holder for Impedance Measurements, continued (BNC Connectors)------44 Figure 2.7 Poling Set-Up ------46 Figure 2.8 Schematic Illustrating Resonance and Antiresonance Peaks ------47

Figure 3.1 X-ray Diffraction Patterns for Selected Single Phase Perovskite Powders 56 Figure 3.2 Trend in Degree of Tetragonality for 3 mol% Zr4 ' with Increasing Ba2+ Concentration in Co-Doped NBT Polycrystals 57

Figure 3.3 Phase Diagram for (Ba + Zr) Co-Doped NBT ------58 Figure 3.4 ESEM Images of As-Sintered and Fracture Surfaces of Sintered Polycrystals ------60

Figure 3.5 Room Temperature r at 10 kHz for Polycrystalline Co-Doped NBT ...... 62 Figure 3.6 Room Temperature tan 6 at 10 kHz for Polycrystalline Co-Doped NBT.- 63

Figure 3.7 Temperature and Frequency Dependence of Fr and tan 6 in NBT-xBT-3NBZ at 0.1, 1, 10, 100, 1000 kHz ------66

6 Figure 3.8 Temperature and Frequency Dependence of Fr and tan 6 in NBT-xBT-4NBZ and NBT-26BT-29NBZ at 0.1, 1, 10, 100, 1000 kHz 67

Figure 3.9 1 /Tm as a Function of Frequency with Volger-Fulcher Law Fit for NBT-xBT-3NBZ 69

Figure 3.10 1 /Tm as a Function of Frequency with Volger-Fulcher Law Fit for NBT-xBT-4NBZand NBT-26BT-29NBZ 70 Figure 3.11 Trend in Acutation and Polarization Character for 3 mol% Zr4+ with Increasing Ba2+ in Co-Doped NBT Polycrystals 74 Figure 3.12 Evolution of Bipolar Strain Response in Intially Poled FR Phase NBT-4BT-3NBZPolycrystal ------76 Figure 3.13 Strain (Unipolar) Versus Field for FRNBT-4BT-3NBZ Polycrystal ------77 Figure 3.14 Polarization and Current Versus Field for FRPhase NBT-4BT-3NBZPolycrystal ------77 Figure 3.15 Strain (Bipolar and Unipolar) Versus Field for FTPhase NBT-14BT-3NBZ Polycrystal------79

Figure 3.16 Polarization and Current Versus Field for FT Phase NBT-14BT-3NBZ Polycrystal ------79 Figure 3.17 Resonance Analysis (Zero Bias) in Poled FTPhase NBT-14BT-3NBZ Polycrystal with Disc Geometry ------80 Figure 3.18 Low Field Electrostrictive Strain (Bipolar) Versus Field for FFTRPhase NBT-6BT-3NBZPolycrystal ------84 Figure 3.19 Low Field Polarization and Current Versus Field for FFTRPhase NBT-6BT-3NBZ Polycrystal------84

Figure 3.20 Low Field Electrostrictive Properties d33 and Qn1 of FFTR Phase NBT-6BT-3NBZ Polycrystal ------85 Figure 3.21 Evolution of the Field-Forced Phase Transition with Increasing Field in FFTR Phase Co-Doped NBT-6BT-3NBZ Polycrystal ------86 Figure 3.22 High Field Polarization and Current Versus Field for FFTRPhase NBT-6BT-3NBZPolycrystal -88 Figure 3.23 Low Field Electrostrictive Strain (Bipolar) Versus Field for FFTTPhase NBT-12BT-3NBZPolycrystal ------90 Figure 3.24 Low Field Polarization and Current Versus Field for FFTTPhase NBT-12BT-3NBZPolycrystal ------90

Figure 3.25 Low Field Electrostrictive Properties d33 and Qll Field for FFTT Phase NBT-12BT-3NBZPolycrystal ------91

7 Figure 3.26 Evolution of the Field-Forced Phase Transition with Increasing Field for FFTT Phase NBT-12BT-3NBZ Polycrystal------92 Figure 3.27 High Field Polarization and Current Versus Field for FFTTPhase NBT-12BT-3NBZ Polycrystal------93 Figure 3.28 Electrostrictive Strain (Bipolar and Unipolar) Versus Field for PET Phase NBT-1OBT-3NBZPolycrystal ...... 95 Figure 3.29 Polarization and Current Versus Field for PETPhase NBT-1OBT-3NBZ Polycrystal ------95

Figure 3.30 Electrostrictive Properties d33 and Q1, of PET Phase NBT-1OBT-3NBZ Polycrystal------96 Figure 3.31 Electrostrictive Strain (Bipolar and Unipolar) Versus Field for PET Phase NBT-8BT-3NBZPolycrystal .-...... 97 Figure 3.32 Polarization and Current Versus Field for PETPhase NBT-8BT-3NBZ Polycrystal------97

Figure 3.33 Electrostrictive Properties d33 and Q,1 of PET Phase NBT-8BT-3NBZ Polycrystal -...... 98 Figure 3.34 Electrostrictive Strain (Bipolar and Unipolar) Versus Field for PE Phase NBT-xBT-4NBZPolycrystals -...... 100 . Figure 3.35 Polarization and Current Versus Field for PE Phase NBT-xBT-4NBZ Polycrystals 101 Figure 3.36 Predominantly Electrostrictive Bipolar Strain Versus Field for PE Phase NBT-xBT-4NBZ Polycrystal Series ...... 102

Figure 3.37 Predominantly Electrostrictive Polarization Field for PE Phase NBT-xBT-4NBZ Polycrystal Series--...... 102

Figure 3.38 Electrostrictive Properties d33 and Qn1 of PE Phase NBT-xBT-3NBZ Polycrystals-- ,,,,,,,, 103 Figure 3.39 Actuation, Polarization and Current Versus Field for pure PE Phase NBT-26BT-29NBZ Polycrystal -...... ,,,,,,,,,,,,,,,,,,,,,,,,105 Figure 3.40 Partial Phase Diagram at Room Temperature for the Ternary System Na1 /2Bil/2TiO3-BaTiO3-Nal/ 2Bi,/ 2ZrO 3-...... 107

Figure 3.41 Partial Phase Diagram at Room Temperature for Naj/2Bij/2TiO3-BaTiO3 at 3 mol% Nal/ 2Bi,/ 2ZrO3 ------108 Figure 3.42 Temperature Dependence of Actuation Behavior for Predominantly PE Phase (Room Temperature) NBT-8BT-3NBZ-...... 110 . Figure 3.43 Comparison of Room Temperature Electrostriction in Co-Doped Polycrystalline NBT to Polycrystalline PMN-15 (TRS Ceramics) ...... 112

8 Figure 4.1 As-Grown Crystal Batches of (Ba, Zr) Co-Doped NBT ------114 Figure 4.2 Optical Microfeatures of (Ba + Zr) Co-Doped NBT Single Crystals ------115

Figure 4.3 X-Ray Diffraction of (Ba + Zr) Co-Doped NBT [100] Oriented Single Crystals of Tetragonal and Rhombohedral Symmetry ------118

Figure 4.4 Room Temperature Cr and tan 6 Versus Ba2+ Concentraion for (4 mol% Zr) Co-Doped NBT Single Crystals Oriented [100] ...... 119

Figure 4.5 Temperature and Frequency Dependence of Cr and tan 6 for (Ba + Zr) Co-Doped NBT Rhombohedral Single Crystals Oriented [100] ------121

Figure 4.6 Temperature and Frequency Dependence of r and tan 6 for (Ba + Zr) Co-Doped NBT Tetragonal Single Crystals Oriented [100] ...... 122 Figure 4.7 Comparison of Temperature and Frequency Dependence of £r and tan 6 for (Ba + Zr) Co-Doped NBT Tetragonal Single Crystals ...... 123

Figure 4.8 1 / Tm as Function of Frequency with Volgel-Fulcher Law Fit for Rhombohedral Phase (Ba + Zr) Co-Doped NBT Single Crystals ------125 Figure 4.9 1/Tm as Function of Frequency with Volgel-Fulcher Law Fit for Tetragonal Phase (Ba + Zr) Co-Doped NBT Single Crystals ------126 Figure 4.10 Temperature Hysteresis in Dielectric Response at 10 kHz for (Ba + Zr) Co-Doped NBT Single Crystals Oriented [100]------128 Figure 4.11 Strain Versus Field for Predominantly Electrostrictive Tetragonal Phase (Ba + Zr) Co-Doped NBT Single Crystals Oriented [100]------. 130 Figure 4.12 Comparison of Predominantly Electrostrictive Actuation in Tetragonal Crystal [100] and Polycrystalline NBT-12BT-4NBZ------130 Figure 4.13 Comparison of Predominantly Electrostrictive Actuation in Tetragonal Crystal [100] and Polycrystalline NBT-9BT-4NBZ------131 Figure 4.14 Polarization and Current Versus Field for PETPhase (Ba + Zr) Co-Doped NBT Single Crystals Oriented [100]------133

Figure 4.15 Electrostrictive Properties d33 and Qj1 of PETPhase (Ba + Zr) Co-Doped NBT Single Crystals Oriented [100]------134 Figure 4.16 Strain Versus Field for Predominantly Electrostrictive Rhombohedral Phase (Ba + Zr) Co-Doped NBT Single Crystals Oriented [100]------136 Figure 4.17 Comparison of Predominantly Electrostrictive Actuation in Rhombohedral Crystal [100] and Polycrystalline NBT-7BT-4NBZ------136 Figure 4.18 Polarization and Current Versus Field for PER(Ba + Zr) Co-Doped NBT Single Crystals Oriented [100]------137

Figure 4.19 Electrostrictive Properties d33and Q,1 of PERPhase (Ba + Zr) Co-Doped NBT Single Crystals Oriented [100]------138 9 4 Figure AIII.1 Illustration of the Ideal Cubic Perovskite Structure (A2+B+03)------169 Figure AIII.2 Calculated Tolerance Factor Versus Dopant Fraction in NBT-Based Solid Solutions with Known MPB Compositions ------171 Figure AIII.3 Calculated Tolerance Factor for Compositions NBT-xBT-3NBTwith Target Relative Tolerance Factor for NBT-Based Systems ------173

10 List of Tables

Table 2.1 Nominal Batch Compositions for (Ba + Zr) Co-Doped Polycrystals ------27 Table 2.2 Nominal Batch Compositions for (Ba + Zr) Co-Doped Single Crystals with Growth Schedule 33

Table 2.3 Calculated Frequency Constants (from kt and kp resonance) ------47

Table 3.1 Composition (EPMA) and Phase (XRD)for Co-Doped Polycrystals ------54 Table 3.2 Volger-Fulcher Parameters for Co-Doped NBT Relaxor Polycrystals ------71 Table 3.3 Comparison of Piezoelelctric Properties for Polycrystalline Materials----- 82

Table 4.1 Composition (EPMA) and Phase (XRD)for Co-Doped Single Crystals.-.. 117

Table 4.2 Volger-Fulcher Parameters for Co-Doped NBT [100] Relaxor Crystals ---- 126 Table 4.3 Comparison of Polycrystalline and Single Crystal Electrostriction------140

Table AI.1 Summary of Sample Geometry Requirements 144

11 Acknowledgements

Financial support for this project was generously provided by the Office of Naval Research (ONR) contract #N00014-97-0989and the Defense Advanced Research Project Agency (DARPA) Single Crystal Fiber Composite (SCFC) Program under Air Force Office of Scientific Research (AFOSR) Prime Cooperative Agreement # F49620-99-2-0332. I wish to thank the many people who offered their time, support and friendship to me during my studies at MIT. My thesis advisor, Professor Yet- Ming Chiang, thank you for your guidance and enthusiasm in research. Toni Centorino, who is incredibly knowledgeable in the ways of MIT, thank you for keeping things organized and on schedule. I would like to thank Dr. Naoki Ohashi and Andrey Soukhojak for their many insightful discussions and experimental assistance; it has been a pleasure working with you. I wish also to thank Neel Chatterjee for EPMA and Haifeng Wang for ESEM experimental assistance. Greg Farrey, who was a great colleague and even greater friend, thank you for helping make the heavy things bearable. I would especially like to thank my family for the encouragement, love and support, which you have always given in abundance, and Justin, thank you for the love and strength you give me.

12 Chapter 1

Introduction

The electromechanical properties of relaxor ferroelectric materials have many useful actuator applications, making them the key components in transducers, electroacoustic transformers, signal-processing devices, and ultrasonic miniature motors [1-4]. Electrostrictive relaxor materials have been utilized in multilayer actuators developed for high precision micro- position-controllers, optical-path control systems, and low frequency sonar transducers [4-8]. An active field of research exists for the development of new actuator materials and optimization of properties for numerous applications.

1.1 Piezoelectricity,Electrostriction and Ferroelectricity

Piezoelectricity is an electromechanical coupling phenomenon occurring in non-centrosymmetric crystalline materials. A piezoelectric crystal will develop an electrical charge in response to an applied mechanical stress (direct effect). Conversely electrical energy can be converted into mechanical energy

13 Chapter 1 Introduction through the reorientation of dipoles, which deforms the crystal lattice (converse effect). The piezoelectric effect is linear (first order), producing a strain proportional to the electric field with the displacement directionally dependent on the sign of the applied field [9].

Electrostriction is a quadratic (second order) effect in which strain is independent of direction* and proportional to the square of the electric field.

This phenomenon is present in all materials, and is the only electromechanical response observed in centrosymmetric crystals, for which no polar properties exist [10]. The electrostrictive effect is usually very weak with strain on the order of 1011- in simple oxides and 10-6 in oxide perovskites [11]. However, some perovskites with high dielectric constants (indicating a high degree of polarizability) can exhibit large electrostrictive electromechanical coupling, with strains on the order of 10-3 [5, 6]. High-strain electrostrictors are the preferred materials for high precision controller actuator applications, for they have negligible hysteresis (i.e.no shift of the initial zero position) and do not require electric poling to preferentially orient dipoles or domains.

Ferroelectricity arises in non-centrosymmetric crystal systems for which it is possible to have one or more polar axes, giving rise to a spontaneous polarization. In ferroelectric materials, this polarization is reversible, meaning that the individual domain states may be reoriented under an applied electric

14 Chapter1 Introduction field. The field at which domain switching occurs is known as the coercive field

Ec. This reversible polarization, however, generally occurs with large hysteresis.

Upon the application of a uni-directional electric field, the material becomes poled. As the field is then reduced, a certain concentration of dipole moments retain, or "remember," their field-induced orientation as it is energetically unfavorable to return to their original state. The portion of dipoles that remain aligned down to zero field is termed remnant polarization P,. Application of an oppositely directed field -Ecis thus required to drive the polarization back to zero. In their reversible polar state, ferroelectrics exhibit piezoelectric and electrostriction effects, however, in most ferroelectric actuation, the piezoelectric effect dominates over the weak electrostrictive response.

1.2 Relaxor Complex Perovskites

Relaxor behavior has been studied extensively in lead-based complex perovskite systems [4, 12-15]. Relaxor ferroelectrics are distinguished from

"normal" ferroelectrics by the presence of certain key characteristics. The most distinctive characteristic is a diffuse and frequency-dependent maximum in dielectric permittivity (Tm)and dielectric loss tan 6 with temperature (Fig. 1.1).

The temperature of the permittivity and loss maxima increases with increasing

Electrostriction may be directionally dependent for crystals with anisotropic elastic constants.

15 Charter Introduction Chve 1 ...... t.o frequency. Below the maximum, c and tan 6 exhibit large frequency dispersion, with c decreasing and tan 6 increasing for increasing frequency. For temperatures above the maximum, frequency dispersion is negligible.

0.4 0.35 C 0.3

0 0.25 U :I. 0 0.2 r 0.15 0 'A 4") Cu 0.1 C 0.05 0

Temperature (K)

Figure 1.1 Typical Temperature Dependence of Permittivity and Dielectric Loss in Relaxor Ferroelectrics Frequency dispersion of permittivity and loss maxima shown in PMN, a typical B-site relaxor ferroelectric. Figure taken from Lin et al. [16].

For the B-site cubic complex perovskite relaxor, Pb(Mg/3Nb2/3)03 (PMN), it is observed that Tmdoes not represent a macroscopic phase transition between ferroelectric and electrostrictive states. Rather, Pr exhibits a gradual decay as temperature increases with the temperature of depolarization Td occurring well below Tm (Fig. 1.2) [14, 15].

The characteristic relaxor dielectric behavior in B-site complex perovskites

16 CharterI Chavr 1 ...... Introductiond......

(such as PMN) is attributed to the presence of ordered nanodomains with short correlation length. These nanodomains form as the disordered B-site structure induces A-site displacement (APb+2), giving rise to nanoscale compositional fluctuations [13-15].

Td Tm

T (C) -*

Figure 1.2 Typical Dielectric and Polarization Behavior in Relaxor Ferroelectrics Schematic of polarization ( · · ) and relative dielectric constant (-) curves for PMN as a function of temperature. The behavior is divided into three regions. Dielectric constant shows broad-diffuse maximum at Tm above which, behavior is electrostrictive (I). At temperatures below the thermal depolarization threshold Td, macro polarization develops and ferroelectric behavior is observed (III). The ferroelectric-electrostrictive transition is not sharp, but rather a gradational decrease in remnant polarization is observed with zero P occurring before Tm is reached. This leads to a region (II) of mixed behavior. (Figure adapted from Shrout and Fielding [4])

17 ChapterI Introduction

Shrout and Fielding [4] classify lead-based relaxors into three groups, based on their polarization behavior (Fig. 1.2): (I) electrostrictive (II) micro-macro

(III) macro-polar. Group I relaxor compositions are electrostrictive with Tmnear room temperature and generally have exceptionally high dielectric constants (r

> 20,000)[4]. Group III compositions lie at temperatures below the depolarization threshold Td and develop macro domains and remnant polarization, displaying ferroelectric behavior similar to standard PZTs [4].

As temperature is increased above Td a gradual, rather than sharp, decrease in Pr is observed, giving rise to the "micro-macro" behavior region.

Group II relaxor compositions generally have lower dielectric constants and lie between Tmand Tdat room temperature. They show mixed behavior, coupling electrostrictive and piezoelectric properties in which local polarization exists on a micro-scale. Under an applied electric field, it is possible to develop macro domains.

This gradual transition from ferroelectric (FE) to paraelectric (PE) behavior with intermediate mixed character has been well documented in PMN [17]. For

Group II compositions, strains with minimal hysteresis can generally be obtained only for lower frequencies (< 1 Hz) [4]. However, the temperature range of the micro-macro region AT = Tm-Tdcan be quite broad, allowing a large temperature stability range of operation.

18 Chapter1 Introduction

1.3 Lead-Based Electromechanical Materials

To date, lead-oxide-based perovskite polycrystalline ceramics have been used almost exclusively in electromechanical device applications due to their high actuation strain (~ 0.1 - 0.2%) and high electromechanical coupling efficiencies (k33 - 0.7%) [18]. Lead zirconate titanate (PZT) is the leading piezoelectric polycrystalline perovskite in commercial use [3, 19], however a large number of lead-based ferroelectric and relaxor-ferroelectric compositions have been developed for use in a variety of niche applications [14].

Polycrystalline PMN and (Pb1 3x,2Lax)(ZryTi-y)O3 (PLZT), relaxor perovskites, with strains approaching 0.1%, are currently the leading materials in electrostrictive actuator applications [6, 7, 20]. Recently developed single crystals of lead perovskites Pb(Zn1 /3Nb2/3)O3-PbTiO 3 (PZNT) and PMNT displaying ultra-high strain - 1.7%, d33 - 2500 pC/N and k33 - 0.9 [21] has ignited interest in the growth and investigation of single crystal compositions as higher performance alternatives to polycrystals in some applications.

There are, however, certain drawbacks to the use of lead-based piezoelectric materials, which include processing difficulties and environmental concerns. Extra steps must be taken in lead-oxide polycrystal preparation to minimize the amount of second phase cubic pyrochlore, which is easily stabilized in most lead-based polycrystalline materials and is detrimental to

19 ChapterI Introduction performance [22]. The main lead compositions of interest do not melt congruently, making it difficult or impossible to employ high precision crystal growth by such commonly used methods as Czochralski, Bridgman, or zone melting techniques, for which crystals solidify directly from the melt. High Pb2' volatility at elevated temperatures makes composition difficult to control and poses a serious health threat during processing. The neurotoxicity, kidney toxicity and the damaging effects of lead on reproductive health, leading to sterility have long been recognized. Most recently, lead exposure has been linked to the development of Alzheimer's disease [23]. However, lead in the environment from consumer products and processing waste poses the greatest threat to the developing nervous system in young children. Overexposure to lead is known to cause decreased intelligence, reading disabilities, and motor skill deficits in children [24].

1.4 Alternatives to Lead-Based ElectromechanicalMaterials

Polycrystalline properties of the A-site relaxor, Na1 /2Bij/2TiO 3 (NBT), a rhombohedral ferroelectric perovskite first described by Smolenskii in 1961 [25], have been studied in solid solution with end members K1/2Bij/2TiO3 (KBT),

BaTiO3, CaTiO3, SrTiO3, and PbTiO 3 [26-29]. Compared to lead perovskites, NBT- based perovskites have a higher elastic modulus (110 GPa vs. 70 GPa) and lower density (6 g/cm 3 versus -8 g / cm3), making them favorable for weight-

20 Chapter1 Introduction based actuation applications [26]. The strain energy density emaxis a measure of the device energy output per unit mass [21]:

e 2 e S max max 8' where, G is the elastic modulus of the actuator, Smaxis the maximum field- induced strain, and p is the actuator density. However, the electromechanical properties in these NBT-based solid solutions have not yet sufficiently matched the levels achieved by commercial lead-based perovskites. The highest polycrystalline performance has been reported in the NBT-BaTiO3 (NBT-BT) system, near the rhombohedral/ tetragonal morphotropic phase boundary

(MPB), with d33 ~125 pC/N and k33 - 0.55 observed for NBT-6%BT [26].

Investigations into the growth of lead-free single crystals in the NBT-BT system have shown that near MPB compositions are congruently melting and can be easily grown by the flux method and as single crystal fibers by edge- defined film-fed growth [30]. Flux grown NBT-BT crystals show piezoelectric properties that are comparable to, or exceed, those of commercial polycrystalline

PZT with strains up to 0.85% and d33 ~ 650 pC/N. [30, 31]. A variety of actuation characteristics have been observed in NBT-BT single crystals depending on composition and phase, ranging from ferroelectric to anti-ferroelectric coupled with a large electrostrictive component [31, 32]. Temperature of the permittivity

21 Chapter 1 Introduction maximum Tmranges from 1000C to 200°C,depending on the concentration of

BaTiO 3 [33].

1.5 Research Objective

The objective of this research was to conduct compositional exploration within the sodium bismuth titanate system, identifying compositions with a range of lowered Tm,in order to fully characterize the trend in actuation character in the micro-macro (Group II) region (Fig. 1.2).

Increased doping of BaTiO3 beyond the 6%BT-MPBcomposition continues to stabilize the ferroelectric tetragonal phase [33]. This thesis will show that through simultaneous doping on the A- and B-sites in NBT with Ba2+and Zr4+, respectively, rhombohedral and tetragonal non-ferroelectric phases can be stabilized for higher concentrations of Ba2' (up to 26 mol% Ba2 ). Relaxor properties are enhanced by the introduction of greater A-site disorder accompanying high-level Ba2' doping.

A- and B-site doping in polycrystalline samples succeeded in lowering the temperature of the permittivity maximum to - 60°C at 1kHz, isolating purely electrostrictive actuation (Group I). The highest polycrystalline actuation strain, however, occurs for a set of compositions that lie within the Group II (micro- macro) region, showing mixed actuation behavior. Predominantly electrostrictive strains > 0.2% were measured with minimal hysteresis at 0.05 Hz

22 ChapterI Introduction and d33 > 700 pC/ N at 25 kV / cm, surpassing the maximum reported properties for conventional PMN and PLZT at 1 Hz. Single crystals of the same composition, phase, and electrostrictive actuation character show up to 0.45% strain and maximum d33 ~ 2000 pC/N at 35 kV/cm. Predominantly ferroelectric polycrystalline compositions with d33 - 310 pC/N show actuation properties highly competitive with commercial PZT-8 (d33 - 300 pC/N [34]).

The following chapters will illustrate the experimental procedure for sample preparation and testing (Chapter 2), present dielectric and electromechanical results for a range of compositions in polycrystalline and single crystal samples (Chapters 3 and 4), and in conclusion, summarize and discuss the results (Chapter 5).

23 24 Chapter 2

Experimental Procedure

Through ionic polarizability and ionic radii considerations based on a novel method of applying the relativetolerance factor to predict the MPB in an unknown system (described in Appendix III), a set of stoichiometric compositions (Na1/ 2Bi1/ 2)1,,Ba(TilyZry)O3 were identified and prepared for which

Ba2' and Zr4+ substitute on the A- and B-sites, respectively. X-ray, dielectric, and electromechanical characterization of polycrystals and single crystals was performed in order to enhance current understanding of phase stability, A-site relaxor nature and range of actuation behavior in the sodium bismuth titanate system.

This composition system will herein be referred to as a Na1 /2Bij/2TiO3-

BaTiO3-Na1 /2Bi,/2ZrO3 solid solution. The abbreviation NBT-xBT-yNBZwill be used, where x and y represent mol% Ba and mol% Zr, respectively.

25 ChanterChavtr 2E-rmnal2 Exvzerimental PrcdrProcedure

2.1 PolycrystallinePowder Preparation

High purity (>99 % purity), ultra-fine grain size (< 1 pm) starting powders of Na2CO3, Bi203, BaCO3, TiO2, and ZrO2 were mixed in 15, 20, or 25 g sized batches according to the intended nominal stoichiometric composition (Table 2.1 and Fig. 2.1). Powder batches are designated "p#," where each number represents a separate powder batch. When referencing characterized samples, lowercase letters following the batch number represent the individual samples that were prepared and tested from that particular batch.

26 Charter 2 Chavte~~~~~r Exver~~ImentalExerimental Procedure~~~Procedure

Table 2.1 Nominal Batch Compositions for (Ba + Zr) Co-Doped Polycrystals

(Na1/2Bi1/2)1_xBax(Ti_yZry)03

mole fraction mole fraction mole fraction mole4 fraction Batch ID Ba2 + (x) Zr4 () Batch ID Ba2+(x) Zr + (y)

p1 0.04 0.03 p12 0.09 0.09

p2 0.06 0.03 p13 0.11 0.05

p3 0.08 0.03 p14 0.09 0.07

p4 0.10 0.03 p1 5 0.13 0.11

p5 0.12 0.03 p16 0.12 0.08

p6 0.12 0.03 p17 0.10 0.06

p7 0.14 0.03 p18 0.12 0.07

p8 0.07 0.04 p1 9 0.11 0.07

p9 0.09 0.04 p20 0.10 0.10

p10 0.12 0.04 p21 0.15 0.14

p11 0.14 0.04 p22 0.20 0.22

p23 0.25 0.30

27 Exerimental Procedure CharterChatr 2 EvmnaPocde

Na1 /2Bi1/2 ZrO 3

NBT2_ 2

NBT 10 20 30 40 BaTiO 3

mol% BaTiO 3 ,-

Figure 2.1 Ternary Plot of Nominal Polycrystalline Powder Batch Compositions The numbers plotted on this diagram represent the batch identification number with the preface "p" not included. See Table 2.1 for a list of nominal batch compositions.

28 Chapter 2 Experimental Procedure

The mixed powders were formed into slurries of a "creamy" consistency by the addition of ethanol was added (15 - 20 ml for 20 g batch, - 45 ml for 100 g crystal growth batch). Slurries were ball-milled with cylindrical (1 /4"-radius ended) zirconia media on a roller mill for 15 - 20 hours. After milling, slurries were rinsed with ethanol into a glass dish and set in a hood to dry under a heat lamp ( 12 hours). Once dried, the soft, yellowish precursor powders were ground with a zirconia mortar and pestle, transferred to a covered alumina crucible and calcined in air at 800°Cfor 3 hours. A Thermolyne 47900 series box furnace was used for the first calcination, set to heat at a rate of 100°C/hr and cool, unpowered, to room temperature. After the first calcination, the now ivory-colored powders were highly agglomerated, but easily crumbled. After grinding vigorously with a zirconia mortar and pestle, the powders were calcined a second time in air at 10000C for 20 hours. A Thermolyne 46100 series high temperature furnace was used for this second calcination, heating to 10000C and cooling to 8000C at 100°C/hr. Cooling below 8000C proceeded at an unpowered rate to room temperature. After the second calcination, powders were white and highly agglomerated, but soft. They easily crumbled when ground in a zirconia mortar. X-ray powder diffraction confirmed single-phase perovskite with minor second phase (< 1 vol%).

Only one powder batch was not calcined at 10000C. Batch p6 was calcined twice: in air at 8000C for 3 hours and in air at 9500C for 6 hours with the same

29 Chaptert 2 Exerimenal Procedure heating and cooling rates described above. The calcined precursor powders are not completely single phase. X-ray powder diffraction confirmed that pressed samples became single phase with minor second phase (- 5 vol%) during the sintering process. All other samples were prepared from single phase powders.

Dense polycrystalline samples were prepared for dielectric and electromechanical characterization from each of the powder batches listed in

Table 2.1. Between 0.8 and 1 g of powder was weighed out and ground in a zirconia mortar. The calcined powders were highly agglomerated, which is detrimental to good flow and packing during pressing. Also, the ball milling process results in an inhomogeneous particle size distribution consisting of irregularly shaped grains with angular edges. Such particles have non-ideal packing geometries that lead to pore stabilization during sintering [35].

To promote dense packing, grains were coated with a polymer binder, polyvinyl alcohol, before pressing. Approximately 5-6 drops of PVA-H20 binder solutiont was added to the ground powders, just enough to coat all the grains.

The binder was mixed thoroughly into the powder with a pestle and the resulting paste was allowed to dry, grinding occasionally until a hardened, granular consistency was achieved. The coated powder was then pressed through a 500 m mesh nylon screen. This produced evenly sized granules that flowed smoothly and packed densely. The coated granules were poured into a

30 Chapter 2 Experimental Procedure

1/2" die that had been lubricated with a thin layer of oleic acid. Samples were pressed by slowly increasing pressure, holding 1 minute every 30 MPa until a maximum of - 100 MPa was reached. The maximum pressure was held for 5 minutes before releasing. Pressing resulted in a highly consolidated green body with disc geometry. The disc edges were sanded with 15pm-grit silicon carbide paper in order to remove edge contamination from the steel die. Green body discs were placed on a layer of platinum foil within an alumina dish. The dish was fitted with an alumina lid with a hole in the center, in order to allow efficient lubricant and binder burnout yet minimize bismuth loss during sintering. Discs were sintered in air at 12000C for 4 hours in a Thermolyne 46100 series high temperature furnace with a heating rate of 1000 /hr to maximum temperature and a controlled cooling rate of 1000 /hr to 8000C. The sintered discs were approximately 10 mm in diameter with thickness between 1-2 mm and were near-full density (> 95%).

2.2 Single Crystal Growth

Single crystals of co-doped (Ba + Zr) NBT were grown by the self-flux method. High purity (>99 % purity) starting powders of Na2CO3, Bi203, BaCO3,

TiO2, and ZrO2 were mixed in 100 g sized batches according to the intended nominal stoichiometric composition (Table 2.2) with the addition of a self-flux

t The procedure for preparation of the PVA-H20 solution is described in Appendix II 31 Chapter 2 Experimental Procedure composed of 20 wt% excess each of Na2CO3 and Bi203. Table 2.2 lists the nominal compositions and conditions for flux growth batches that produced viable crystals for testing. The number following "s" represents a separate crystal batch. When referencing characterized samples, lowercase letters following the batch number represent the individual samples that were prepared from that crystal batch.

Powder preparation followed the same procedure through the first calcination at 800°C as described in Section 2.1 for polycrystalline samples. After the first calcination, powders were ground in a zirconia mortar and transferred to a 100 ml-capacity, covered, platinum crucible. The platinum crucible was fitted inside a larger, covered alumina crucible. The powders were held for 5 hours at 13500C, and cooled according to various schedules (Table 2.2) that typically yielded intergrown crystals set within solidified flux. Weight loss was less than 1% for all crystal growths, indicating that bismuth loss due to volatilization was not significant. Crystals were mechanically separated from the crucible and the flux. Intergrown crystals would be separated either with a Well diamond wire saw or broken apart with the application of pressure.

32 Chapter 2 Experimental Procedure

Table 2.2 Nominal Batch Compositions for (Ba + Zr) Co-Doped Single Crystals with Growth Schedule

(Nal/2Bil/2)1x-Bax(TilyZry)03

mole fraction mole fraction Self-Flux Growth Schedule BatchID Ba 2 ' (x) Zr4 + (y)

R.T.-1350°C @ 100°/hr S1 0.08 0.03 hold 5 hours 1350C - 8000C @ 50/hr 800°C - R.T. @ 50°/hr

S2 0.08 0.03 R.T.-*1350°C @ 100°/hr s3 0.06 0.03 hold 5 hours 1350°C - 12600C @ 100°/hr hold 1 hour s4 0.10 0.03 1260C -_ 1000C @ 1.5/hr 1000°C - R.T. @ 50/hr S5 0.10 0.03

The introduction of zirconia resulted in difficulty achieving high quality crystals by the flux method. Attempted growths with 10 mol% Zr4+ and 12 mol%

Ba2+ yielded numerous, but small, inclusion-bearing crystals (<1 mm on a side).

Few crystals of a quality and size meeting the requirements for testing could be extracted from the batch. The greatest success in achieving crystals viable for characterization occurred for nominal doping of 3 mol% Zr with 6, 8, and 10 mol% Ba2+. Flux grown co-doped crystals tend to grow with pseudo-cubic habit, however, highly planar as-grown 001}faces were rare. Back reflection Polaroid photography with a laue diffraction camera using a Philips 2KW sealed tube x-

33 ChapterChae- 22- EermnPoceIExerimental Procedure ray generator was not successful in orienting crystals, for diffraction spots were unresolvable. This may be due to internal inhomogeneities and distortion, which can cause a "smearing" of the spots [36]. Therefore, samples for testing could be prepared only from the small number of crystals with as-grown planar {001} faces. The pseudo-cubic {001}orientation of these crystals was confirmed by with diffraction experiments using a Rigaku 18kW rotating anode x-ray generator (copper anode), normally used for powder x-ray diffraction.

In-situ observation of the melting behavior of calcined powders and single crystals from previously grown batches was conducted in order to determine the appropriate soaking temperature (Fig. 2.2). When heated at 7.5°C/min from room temperature, co-doped single crystals and calcined powders (including flux) melting catastrophically 1265 ~ 1274°C. This observation suggests that addition of 20 wt% excess flux does not significantly lower the melting temperature. However, the flux likely serves to enhance diffusivity in the melt and thus contributes to crystal growth. Based on in-situ melting observations, a soaking temperature of 1260°Cwas chosen. Subsequent growths employing this soaking temperature resulted in improved crystal yield and quality, although micro-inclusions and internal strain were present within even the best-quality crystals as evidenced through optical microscope observations.

Table 2.2 lists the nominal compositions and conditions for flux growth batches that produced viable crystals for testing. The number following "s"

34 Ch..trChanter 2...Pod2 Exerimental Procedure represents a separate crystal batch. When referencing characterized samples, lowercase letters following the batch number represent the individual samples that were prepared from that crystal batch.

i ace thermocoupleJ

atinum pan ntains sample

a stand

Figure 2.2 Set-Up For In-Situ Melting Observation In-situ observation of the melting behavior for crystal and precursor powder was conducted to determine an appropriate soaking temperature for self-flux crystal growths. The sample was contained in a platinum pan - 0.5 cm diameter and was positioned no farther than 2 cm from the furnace thermocouple.

35 Chapter 2 Experimental Procedure

2.3 Polycrystaland Single Crystal SamplePreparation for Testing

The same procedure for sample preparation and testing was followed for polycrystals and single crystals. Single crystals were oriented to at least one

{001}face and cut into rectangular plates using a Well diamond wire saw.

Sintered polycrystalline bodies were either cut into rectangular plates or left whole as discs. Samples were mounted with crystal bond on a South Bay

Technologytripod holder (Fig. 2.3) and parallel, planar sides were polished using diamond abrasive film from 30plm-to 1,lm-grit (Fig. 2.4). Polished single crystal plates averaged approximately 2.5 mm x 1.5 mm, with no sample exceeding 5 mm on a side. Thickness averaged 0.7 - 0.8 mm with no sample exceeding 2 mm.

Polycrystal plates averaged approximately 7 mm x 3 mm, disc geometry averaged ~ 10 mm in diameter, and thickness did not exceed 2 mm after polishing. Samples were ultrasonically cleaned in three acetone baths followed by three methanol baths. Touch up cleaning when necessary was performed by wiping sample surfaces with a cotton-tipped applicator soaked in either methanol or ethanol.

36 Chapter2 Exerimental Procedure Top view

Figure 2.3 Model 590 Tripod Polisher® South Bay Technology, Inc. Polycrystalline and single crystal samples were mounted on tripod polisher to maintain parallel, planar sides. Leg lengths are adjustable with micrometer allowing control of sample thickness. This figure shows a mounted single crystal with plate geometry.

Polycrystalline Plate Polycrystalline Disc Single Crystal Plate

Figure 2.4 Polished (Ba + Zr) Co-Doped NBT Samples Prepared for Testing Parallel, planar sides polished down to a final diamond grit size of l1pm. Single crystals (C) are transparent with an amber-colored tint.

37 Chanter 2 Exerimental Procedure Cha- 2 ri

2.4 Polycrystaland Single Crystal SampleCharacterization

A detailed manual outlining the testing procedure followed in this work is included as Appendix I.

2.4.1 Crystal Symmetry Determination by X-ray Diffraction

The symmetry phase of the perovskite structure was determined from X- ray diffraction with a Rigaku 18kWatt rotating anode x-ray generator (copper anode). Continuous, standard 20 - 0 reflected scans were performed between 10

- 100° 20 at a maximum power of 60 kV and 300 mA using 1° diffraction and scattering slits and a 0.15 cm receiving slit. The tetragonal structure phase was distinguished from rhombohedral where splitting of the (100)*peak was detected, indicating inequality among symmetry axes lengths (a = b • c).

Structural phase analysis was performed on precursor polycrystalline powders, the surface of sintered polycrystalline discs, and single crystal {001}faces. The perovskite structure was confirmed in single crystals by x-ray diffraction of crystals ground to powder in a zirconia mortar.

2.4.2 Composition Analysis by Electron Microprobe

Quantitative analysis of polycrystal and single crystal compositions were performed with the JEOL JXA-733Electron Probe Microanalyzer (EPMA). Clean

I For simplicity, the Miller indices of the high temperature cubic phase is used to identify crystal planes in the rhombohedral and tetragonal phases.

38 Chapter 2 Experimental Procedure samples were sputter coated with carbon before being loaded into the EPMA to prevent charging. The samples were analyzed for elements Na, Bi, Ba, Ti, and Zr using the following standards: NaAlSi308 , Bi4Ge301 2, BaSO4, TiO2, ZrSiO4. One set of samples was also analyzed for Hf using pure element as standard in order to assess the degree of hafnium contamination from the zirconia starting powders. Hafnium contamination was determined negligible in all samples tested. The current (10nA), voltage (15 kV) and take-off angle (400)were kept constant during the measurements. Oxygen was not analyzed. No oxygen vacancies were assumed and compositions were normalized to 3 mole fraction of oxygen.

2.4.3 Sample Electroding

Prior to dielectric and electromechanical measurements, clean sample

surfaces were electroded. Gold electrode was sputtered for 300 seconds at 40 mA

and 0.08 mbar Ar pressure on single crystal surfaces with a Pelco SC-7 Auto

Sputter coater. The distance between the sample and gold target was

approximately 40 mm. Scotch tape was used ensure that the side surfaces of the

plate remained free of electrode. Polycrystalline samples were prepared with

silver electrode that was painted on the surfaces in the form of a colloidal paste.

The electrode on both polycrystalline and single crystal samples was annealed in

air at 4750C for 1 hour in order to bond the electrode to the surface. Annealing at

39 ChanterChatr_ 2 ExeImnExerimental PrcdeProcedure a temperature above that at which any testing would be carried out also minimized the chance that the electrode undergo a significant change in response to temperature (such as volatization of solvents in the case of the colloidal silver paste) that might affect the measurement.

2.4.4 Dielectric Characterization by Impedance Analysis

Capacitance C, dielectric loss tangent tan 6 and admittance Y were measured in poled and unpoled samples with a Hewlet Packard 4192A impedance analyzer. Measurements with the HP 4192A impedance analyzer and

Omega tube furnace were computer automated with Testpoint ISPEC 2000 software (programmed by Dr. Naoki Ohashi, visiting scholar, M.I.T.).

Room temperature C and tan 6 were measured under zero bias in unpoled samples as frequency was increased logarithmically. Relative dielectric constant

Er(real component) was calculated from capacitance by the following equation:

r E where, Er = -°T3= relative dielectric constant at constant stress T=0, t = sample thickness (distance between electrodes) in m, A = area of the electroded face in m 2, G0= permittivity of vacuum (8.854 x10 -1 2 F/m).

Computer automated measurements sampled C and tan 6 under zero bias every 60 seconds at frequencies of 0.1, 1, 10, 100 and 1000 kHz as the sample was

40 Charter2 EX1npimp71ta7J Prnreduri- C-h r..2...... rn..vvv v heated at 200°/hr in air to 4500C. The sample temperature, furnace set temperature, start time, and finish time of each measurement were also recorded.

Each sampling at the set of 6 frequencies took approximately 20 seconds.

Temperature dependence of the permittivity and loss in single crystals were measured for heating and cooling (at the same rate), for which temperature hysteresis of the permittivity and loss were detected. Polycrystalline samples showed negligible temperature hysteresis, thus only heating measurements were performed.

The sample holder used for temperature dependent measurements consists of a 4-wire coaxial cable configuration. The holder was designed and built by Dr. Naoki Ohashi, visiting scholar at M.I.T. A picture and schematic of the sample holder is shown in Figures 2.5 and 2.6. Samples were fastened between the measurement probes of the holder with colloidal silver paste.

Tmwas determined for each frequency from the minimum in second derivative of the smoothed data. Raw data was smoothed with Microcal Origin

[i-(n-1)/2, i+(n-1)/2] where, n is the specified number of points used to calculate the averaged point

(i.e. the degree of smoothing). Typical degrees of smoothing used here ranged from n = 5 to n = 7.

41 Charter 2 Exerimentali Procedure Ch..er 2 For relaxors, the frequency (J) dispersion of the permittivity maxima can be described by the Volgel-Fulcher(VF) law of finite freezing temperature:

fkB (T. - Tf )E

where, Tf is the static freezing temperature (f- 0) in Kelvin, fo is the attempt

frequency (s-l), Eactis the activation energy, kBis Boltzmann's constant (1.38 x 10-

23 J/ K). A general nonlinear fit was applied to the curves of Tmversus frequency

using Mathcad 2000 Professional software (MathSoft, Inc. 1999) to determine

the adjustable parameters Eact,f, Tf for:

Eact Tm(f) Eact kB lfo

42 Chapter 2 ExperimentalPocedure

:. _i "_~ _Tube Furnace

HP 4192A Sample Holder

EquipmentSet-up Close-up of Sample in Holder Schematic of Sample Holder

Sample Thermocouple

...... out to temperature moniter...

...... BNC Connectors ...out to HP4192A...

Close-up c

cinlsr I Ai I IUIG &. High Temperature Sample Holder for Impedance Measurements Sample holder was designed and built by Dr. N. Ohashi, Visiting Scholar, M.I.T.

43 ...Chanter-rm '-oeu 2 Exerimental PrProcedure

Photograph of BNC Connectors

HP4192A Schematic of BNC Connectors L curr L pot H pot H urr I

I I I I

®(~ ®.

Coaxial Cables A & B can connect either to L/L OR H/H in any order but NOT L/H.

. . . , _ . ·, . (C or D)-Hpot, (C or D)-Hcurr

An Incorrect Configuration: A-Lcurr, B-Hpot, C-Lpot, D-Hcurr

Figure 2.6 High Temperature Sample Holder for Impedance Measurements, continued (BNC Connectors) Sample holder was designed and built by Dr. N. Ohashi, Visiting Scholar, M.I.T.

44 Chapter 2 Experimental Procedure

2.4.5 Electromechanical Characterization by Impedance Analysis

Poling of polycrystalline and single crystal samples was attempted by constant field cooling from 2000C to room temperature at a field between 20 - 25 kV/cm. Samples were submerged in a silicone oil bath (to prevent arcing) that was heated to 2000C then allowed to cool while dc voltage was applied by a Trek

Model 10/40 high voltage amplifier with a Wavetek function generator. Figure

2.7 illustrates the poling set-up and sample holder.

After poling room temperature C and tan 6 versus frequency with logarithmic steps in the range 100 Hz to 13 MHz were measured with HP4192A impedance analyzer. A decrease in dielectric constant compared to the unpoled measurement and the appearance of resonance is an indication that the sample was poled. Most samples in this study did not pole, for they are predominantly electrostrictive.

Two samples of predominantly ferroelectric behavior were successfully poled and coupling coefficients kt and k31 were calculated from measurements of admittance Y versus frequency (where, impedance Z = 1/ Y) measurements performed under zero bias with the HP4192A impedance analyzer. The electromechanical coupling factor k is a measure of the electromechanical energy

electrical energy input efficiency: k2 = mechanical energy output

45 Chapter 2 Experimental Procedure

Schematic of Sample Holder

... to high voltage......

...to ground...... *......

electroded f "I ml J I . sample spring. .loadea j alumina tube with slit cut to hold clip

Figure 2.7 Poling Set-Up Sample holder was designed and built by G. Farrey, M.S., M.I.T.

46 Chapter 2 ExperimentalProcedure

Thickness-extensional coupling factor kt is calculated according to the following equation:

tkt =J f tan z Aflr 2 a n2 f, where f is the resonance frequency, fa is the antiresonance frequency (Fig.

2.8) and Af=fa -f. Table 2.3 lists the constants which may be calculated us from k, and kp.

t t a) .r C co a, E E /r fa Frequency-- Frequency--

Figure 2.8 Schematic Illustrating Resonance and Antiresonance Peaks

Table 2.3 Calculated Frequency Constants (from kt and kp resonance) Frequency constant (thickness) N [Hz m] N = tf (Controlling Dimension x Resonant Frequency)

Frequency constant (planar) (Np) [Hz. m] N = afr (Controlling Dimension x Resonant Frequency) P Frequency constant (circumferential) (Nc) [Hz- m] N = afa (Controlling Dimension x Resonant Frequency)

47 Chapter 2 Experimental Procedure

2.4.6 Electromechanical Characterization Under Field

Electric-field induced elongation and current was measured for 0.05,

1, and 20 Hz ac fields and 1 MPa prestress using a laser interferometer apparatus with automated data collection software, Trek high voltage amplifier, Wavetek function generator. The sample holder which was capable of applying varying compressive loads to the sample was designed and built by A. Soukhojak and G. Maskaly, M.I.T. Unipolar field induced elongation was measured for the same set of frequencies with an applied dc bias. Strain was calculated according to the following equation:

strain: S =- xo where, x = the distance between electroded faces Ax = x - xO and S is positive for sample extension.

The piezoelectric strain coefficient d33 (in m/V C/N) was measured directly as the slope of the strain vs. field at saturation (i.e. non-hysteretic portion) for ferroelectric behavior. Predominantly electrostrictive actuation does not directly exhibit piezoelectric properties such as d33, however the field- induced d33 may be characterized. Thus, d33 can be plotted as a function of field for these samples.

48 Chapter 2 Experimental Procedure

The effect of varying prestress on actuation was tested up to 32 MPa on single crystals and 5 MPa on polycrystals and shown to be negligible. Samples were actuated under 1MPa prestress for consistency.

Polarization (surface charge density) versus field was derived by numerically integrating the current versus field and dividing by the electroded surface area. This can be understood from the following relations: P = Q/A and i = dQ/dt, or Q = i. dt where P is polarization in C/m 2, A is electroded area in

m2 , Q is charge in C, and i is current in A - C/s. Thus,

Pi dt P = A can be plotted against field to obtain what are often referred to "hysteresis loops." For ferroelectric bipolar polarization loops, the coercive field Ec is determined as the field at which polarization is zero. For the case of pure, unsaturated electrostriction, polarization plots as a line (no hysteresis) against field. The dielectric susceptibility K is defined as: P = CoKE (SI units).

Dielectric susceptibility can be determined from the slope of polarization versus field divided by Co.

Electrostrictive strain can be described with the following equation:

S 3 = Q iP3

49 Chapter 2 Experimental Procedure where, Q,, is the electrostrictive coefficient and can be determined from the slope of strain versus the square of polarization.

50 Chapter 3

Results I: Co-Doped Polycrystals

Compositional, phase, dielectric, and electromechanical data measured for polycrystalline samples will be presented and discussed in this chapter. These results show that (Ba, Zr) co-doped NBT compositions are a promising alternative to the conventional lead-oxide based polycrystalline perovskites, such as electrostrictive PMN and PLZT electrostrictors and ferroelectric PZT-8, PMNT,

PZT-5a for device applications.

3.1 Composition,Phase and Density Analysis

EPMA composition analyses of polycrystalline samples show that the intending doping levels of Ba2' and Zr4 ' were achieved in nearly all of the samples (Table 3.1). Two samples, pl2a and p20a, are off by 0.01 mole fraction from the intended level. Composition analyses reported in Table 3.1 were measured on the primary phase only. Minor second phase, which was present in all of the samples, was able to be distinguished with back-scattered electron

51 Chapter 3 Results I: Co-Doped Polycrystals imaging and was carefully avoided. The reported compositions of atomic mole fraction were calculated assuming valences of Na", Bi3', Ba2', Ti4+, Zr4+ and normalized to 3 02- per formula unit. Based on counting statistics, the Ti, Na, Bi,

Zr concentrations are given with 1-2% accuracy, and Ba concentrations are given accurate to 5%. The A-site cations Na+1and Bi+3 were assumed to be substituted by Ba2' in equal parts. However, composition analyses show Ba does not replace

Na and Bi uniformly. Thus, the ratios of Na/Bi are not strictly controlled by the solid-state process used (refer to Section 2.1).

X-ray diffraction within the range 20-90° 20 confirmed that all samples were nearly single phase perovskite (Fig 3.1). X-ray patterns show negligible to minor second phase. Second phase content increases for higher zirconia doping levels above 20 mol% Zr, but remains < 5 vol%. Using back scattered electron imaging and composition analysis, only one second phase was identified in each sample. EPMA analysis of the second phase in samples doped < 14 mol% Zr identified barium titanium oxide (BaTi2O5) . For samples with > 14 mol% Zr, the second phase was identified as ZrO2 using EPMA analysis.

When normalized to 3 oxygen per unit formula, the compositions are nearly stoichiometric with slight A-site excess (ranging 0 - 0.09 ± 0.02 mole fraction). A-site excess in the perovskite crystal structure may be incorporated through Ruddlesden-Popper (RP) stacking faults, as seen in the extensively studied class of layered perovskites of the general form, LnlxAxMnO3, where Ln

52 Chapter 3 Results I: o-Doped Polyccstals is a lanthanide and A is an alkaline earth cation [37]. RP stacking faults have recently been demonstrated in SrTiO3 ceramics [38], in which A-site excess is incorporated through the insertion of individual SrO layers between perovskite units. The resulting defect oxide compositions Sr2TiO4, Sr3Ti2O7, and Sr4Ti3010 are reported [38]. The presence of a small concentration of such RP insertion layers causes the overall perovskite to composition to become slightly A-site rich.

However, given the presence of B-site cation-rich second phases, BaTi205 and ZrO2, the most likely interpretation is that the perovskite structure contains oxygen and B-site vacancies. Thus, it is assumed here that non-idealities in ABO3 perovskite stoichiometry are the result of either A-site or B-site (and oxygen) vacancies. For A-site rich compositions, cation mole fractions in Table 3.1 were normalized to unity on the A-site and reflect the level of B-site and oxygen vacancies. B-site rich compositions were normalized to unity on the B-site and reflect A-site and oxygen vacancies. The composition analyses suggest that the majority of the samples are B-site deficient with oxygen vacancies. Three samples, p3a, p7a and p8a show slight A-sight deficiencies. However, these samples are stoichiometric within error limits of the analysis.

53 ChanterV.rI. .3 ....- RuResults : ..-..Co-Do-nedr P-'...Polucrusals

Table 3.1 Composition (EPMA) and Phase (XRD) for Co-Doped Polycrystals

compositions given in mole fraction (normalized to unity on B-site except where indicated by *) Sample Nominal (Na+Bi+Ba)/ ID (Ba/Zr) Na Bi Ba (Ti+Zr) Symmetry pla 4/3 0.52 0.44 0.04 0.93 0.03 2.88 1.04 R

p2a 6/3 0.50 0.44 0.06 0.92 0.03 2.86 1.05 R

p3a 8/3 0.48 0.44 0.08 0.97 0.03 2.97 0.99* T

p4a 10/3 0.47 0.43 0.10 0.95 0.03 2.94 1.02 T

p5a 12/3 0.47 0.42 0.11 0.91 0.03 2.86 1.06 T

p6a 12/3 0.47 0.42 0.12 0.94 0.03 2.91 1.03 T

p6b 12/3 0.48 0.41 0.12 0.97 0.03 2.97 1.00 T

p7a 14/3 0.45 0.41 0.14 0.97 0.03 2.97 0.99* T

p8a 7/4 0.47 0.45 0.07 0.96 0.04 2.97 0.98* R

p9a 9/4 0.48 0.43 0.09 0.92 0.04 2.88 1.04 T

p10a 12/4 0.45 0.43 0.12 0.94 0.04 2.94 1.02 T p1la 14/4 0.46 0.41 0.14 0.93 0.04 2.91 1.03 T p12a 9/9 0.49 0.43 0.09 0.88 0.08 2.86 1.05 R

p13a 11/5 0.48 0.41 0.11 0.91 0.05 2.88 1.04 T

p14a 9/7 0.48 0.44 0.09 0.90 0.07 2.91 1.03 R

p15a 13/11 0.44 0.43 0.12 0.84 0.10 2.83 1.06 T

p16a 12/8 0.46 0.42 0.12 0.88 0.08 2.88 1.04 T

p17a 6/10 0.48 0.42 0.10 0.92 0.06 2.94 1.02 T

p18a 12/7 0.47 0.42 0.11 0.89 0.07 2.86 1.05 T

p19a 11/7 0.48 0.42 0.10 0.85 0.06 2.75 1.09 T

p20a 10/10 0.47 0.43 0.10 0.86 0.09 2.86 1.06 R

p21a 15/14 0.45 0.41 0.14 0.80 0.13 2.86 1.07 T

p22a 20/22 0.42 0.38 0.20 0.76 0.22 2.94 1.02 T

p23a 25/30 0.39 0.36 0.26 0.70 0.29 2.97 1.02 T

* indicates composition was normalized to unity on the A-site R = rhombohedral, T = tetragonal

54 Chapter 3 Chavr Results I: Co-Doed PoirutPolucrustals -

The symmetry of the perovskite phase for each sample as determined by powder x-ray diffraction is listed in Table 3.1 and showed excellent agreement with the structure predictions using the relative tolerance factor method (see

Appendix III). A systematic composition exploration with polycrystalline powder batches was successful in locating the rhombohedral (R)/ tetragonal (T) morphotropic phase boundary (MPB) to within 2 mol% Ba at a constant Zr level up to - 10 mol% Zr. Figure 3.2 illustrates the trend in (200) peak for 3 mol% Zr

and varying Ba content from 4- 14 mol%. The rhombohedral pseudocubic {100} peaks are unsplit, since the crystallographic axes are of equal length. Figure 3.2 illustrates the increase in degree of (200) peak splitting as the Ba content is

increased, indicating an increase in the degree of tetragonality, c/a, from 0.011 at

8 mol% Ba to 0.014 at 14 mol% Ba. The ternary diagram in Figure 3.3 plots phase

symmetry versus composition, based on x-ray diffraction analyses.

55 Chapter 3 Results I: Co-Doped Polycrstals

Simulated Pattern: Na11 2Bi11 2TiO3 Rhombohedral i

(110) (200)

(100) (2 (211) (11) _ (10(111) il (211) (220) (2 0 2 ) (310 0 1 ) ~~~~~~I i , I I

p 1 Rhombohedral 1

0 Ii I ) IetriaoI l

ip 10 Tetragonal

a)ca 4-C:

20 30 40 50 60 70 80 100 2-Theta

Figure 3.1 X-ray Diffraction Patterns for Selected Single Phase Perovskite Powders

Simulation of the x-ray pattern for rhombohedral perovskite Na1 /2Bil/2TiO3 used Jade (Jade, Inc., 1999) x-ray analysis software. The profile was generated based on x-ray data reported by Chang-lin et al. [39] as a Cauchy profile assuming a crystallite size of 1000 nm and includes Ka2. The undoped rhombohedral perovskite simulated profile is compared with single phase powder batches of co-doped NBT.

56 Chapter 3 Results I: Co-Doved· PolucrustalsY Y

i iF- -" ------i 0C o m 0 I Ii i 0) i i Ii O 0 z a)

o E 0- C 0 0 c50Q -c II C(O.

H O I-H- CD 0) r 6 I o N-o I 0- I i 6 N m I H- z o o CY) 0)c a0

- 00 O .Cc.0 m 60: Co7 CD Coz + 13 z 13, N o i

I o0 i E 0 I III i O I

II O 0

I ,

()

C;IE m o a) -00 o Loo Ln I-- , 0 Cr4It CU E u, ,I-_ 57 ChapterChaJter 3 Results : Co-DoedD d Polucrustalsru.....

Na/ 2 Bi1/2 ZrO 3

'I,

MPB ......

R = rhombohedral

T = tetragonal 11 I I

TB234

NBT 10 20 30 40 BaTiO 3

mol% BaTiO3 - *

Figure 3.3 Phase Diagram for (Ba + Zr) Co-Doped NBT Based on 1001 splitting in powder x-ray diffraction analyses of polycrystalline samples. The morphotropic phase boundary (MPB) between rhombohedral and tetragonal symmetry phases has been mapped for a portion of the field (up to 10 mol% Zr). Refer to Table 3.1 for sample identifications.

58 Chapter 3 Results I: Co-Doped Polycrystals

The density of sintered polycrystalline discs was investigated by means of dimensional measurements and electron microscopy (estimating the fraction of pore area in a cross-sectional view). Densities in the NBT-BT system are reported to be - 6 g/cm3 [26]. Relatively low Zr4+ doping in the NBT-BT system is not expected to cause a large deviation in density. In order to gauge the sintered density of polycrystalline samples, they were cut and polished into rectangular parallelepiped geometry. The sample volume was calculated from measurements of length, width and height (thickness). The sample weight was then divided by the calculated volume. Polycrystal densities ranged from 5.5 -

6.1 g/cm3 for the range of doping levels. Co-doped single crystals of similar composition and prepared in the same way showed densities in the range of 5.7 -

6.2 g/cm3, suggesting that the polycrystals are sintered to near full density. As will be discussed in chapter four, the crystal quality of single crystal samples was not perfect and microinclusions were present in most samples, which may cause density to be slightly underestimated. However, samples of the best quality with negligible inhomogeneities at a microscopic scale were measured to have densities of 5.7 - 5.8 g/cm3, suggesting that the sintered samples are at least >

95% dense.

Further confirmation of polycrystalline sample densities was achieved with electron microscopy of freshly fractured faces and estimation of total pore area in the cross-sectional view. Figure 3.4 shows images taken with an

59 Chapter 3 Results I: Co-Doped Polycrustals

FEI/ Philips XL30 FEG ESEM of sintered and fracture surfaces for sample p6a.

Minor Second Phase (BaTi 2O5)

200 pm 20 pm 100 pm Fracture Surface Sintered Surface

Figure 3.4 ESEM Images of As-Sintered and Fracture Surfaces of Sintered Polycrystal Sintered surfaces of sample p6a show grains with cubic habit. Image analysis of fracture surfaces show porosity < 3%.

60 Chapter 3 Results I: Co-Doped Polycrystals

3.2 DielectricProperties of Polycrystalline(Ba + Zr) Co-DopedNBT

3.2.1 Room Temperature Dielectric Constant and Loss Tangent

The room temperature dielectric constant in the solid solution NBT-BT reaches a maximum value of -1600 at 10 kHz for the MPB composition (6 mol%

BT) in polycrystalline samples [26], which is more than doubles the Fr of undoped NBT (-350). Room temperature dielectric constant in the NBT-BT-NBZ system is similar to that found in NBT-BTwith sr ranging from 1200 - 1600 for less than 15% Zr4+ and decreasing to ~ 750 for the highly-doped NBT-26BT-

29NBZ sample (Fig. 3.5). The maximum room temperature dielectric constant of

1.56 x 103 at 10 kHz was measured for NBT-1OBT-3NBZ, which lies slightly to the

tetragonal side of the MPB.

Room temperature dielectric loss in the co-doped systems is lowest for

NBT-4BT-3NBZ, tan 6 = 0.0453 at 10 kHz. Magnitude of loss increases generally

for increasing doping on both A- and B-sites, reaching a maximum of tan 6 =

0.1301 at 10 kHz for NBT-26BT-29NBZ. For a constant level of Zr4 + doping of 3

mol%, increasing tan 6 with Ba2' content begins to level off to a value of - 0.08 to

the tetragonal side of the MPB (Fig. 3.6).

61 ChapterChavter3 ResultsI:Results I: Co-DovedCo-Doedr PoluPolucrustals r ss

a--- 1 bUU 0 OA A o8 mol% Zr 0 + a a * Ao 0· + 03 1200 0- A4 X5

O~~~~~~~~~~~~~~~~~~~~ 0k1 @6 07

w 800 +8 09

I -10 *11

014 22 400 A L X 30

10 kHz ' -. I I I I I I Il I I I , 0 5 10 15 20 25

mol% Ba

Figure 3.5

Room Temperature Er at 10 kHz for Polycrystalline Co-Doped NBT A maximum in Sr occurs for compositions slightly to the tetragonal side of the MPB.

62 Chapter 3 Results I: Co-Do~ed Polycrstals

14% - -

( mol% Zr 12% AO 03

10% A4 X5 00 CIO *A *6 07 r. 8% CU I.~ +8 09

6% ] -10 *11

4% E114 0 22

X30 2% 10 kHz ' ' ''''''"`''''' ' 0% I I I I I I I I I I I II 0 5 10 15 20 25

mol% Ba

Figure 3.6 Room Temperature tan 6 at 10 kHz for Polycrystalline Co-Doped NBT Minimum loss occurs for NBT-4BT-3NBZ,and increases with increasing cation doping. The Zr 3 mol% series shows the magnitude of loss begins to level out on the tetragonal side of the MPB.

63 Chapter 3 Results I: Co-Doped Polycrystals

3.2.2 Temperature Dependence of Dielectric Constant and Loss Tangent

Investigations into the temperature dependence of phase stability in NBT have reported a "peculiar" phase transition behavior within the region of diffuse phase transition (DPT) [40]. NBT single crystals undergo a complex set of ferroelectric phase transitions and also non-polar ferroelastic phase transitions, which are related to shifts in octahedral tilt [41]. Above 540°C,NBT exists in the cubic, paraelectric phase. Upon cooling, it undergoes a transformation to a non- polar tetragonal symmetry phase around 3200C and the permittivity goes through a maximum. A non-polar tetragonal - rhombohedral transformation occurs around 2600C. NBT then passes through an anti-ferroelectric (AFE) phase field before the room-temperature stable, rhombohedral ferroelectric (FE) phase transformation is reached at approximately 2000C. This latter transformation is manifested as a local maximum in permittivity, which is defined here as Tm.

Doping with BaTiO3 has been shown to shift the temperature of the FE-AFE transition downward to -150°C in polycrystals [26] and closer to -1000C in single crystals [33].

Doping simultaneously on the A- and B-sites in NBT by the method described in Appendix III enabled further manipulation of the temperature of this transition. This systematic composition exploration in polycrystalline samples shows that Tmcan be shifted as low as 60°C in the highly doped

64 Chapter 3 Results I: Co-Doped Polycrystals sample p23a. This research has shown that composition tailoring can be used to successfully isolate either predominately electrostrictive or ferroelectric behavior at room temperature. The data presented here and in Section 3.3 will focus mainly on the series of 3 and 4 mol% Zr doped compositions, which showed the most interesting actuation properties.

Figures 3.7 and 3.8 show the temperature dependence of dielectric constant and loss for 3, 4 and 30 mol% Zr with varying Ba concentrations. The general features typical of relaxor behavior (refer to Fig. 1.1) are observed in all the samples, such as the diffuse, frequency dependent maximum in Crand tan 6.

The dielectric behavior reflects the complex phase transitions particular to NBT- based systems with the appearance of a second diffuse, non-frequency dispersive permittivity maximum, related to non-polar transitions at higher temperatures

(>200 0C).

For the set of compositions presented in Figures 3.7 and 3.8, Tmranges from 1300C - 600C at 1 kHz. At constant Zr-concentration, Tmdecreases as the

MPB is approached from either phase field. This behavior has also been observed in the NBT-BT system [26, 33]. Overall, as Zr-concentration increases,

Tm decreases.

65 ChavterI 3 Results I: Co-Doved· PolucrustalsY Y

NBT-xBT-3NBZ

Sr: 0.1 > 1 > 10 > 100 > 1000 kHz Heating Rate: 200°C/hr tan : 0.1 < 1< 10 < 100 < 1000 kHz

n' 0.25 5000 u.t 4000 0.2 4000 0.4

3000 0.15 3000 0.3 o b £0 C C 2000 a 0.1 2000 0.2

1000 0.05 1000 0.1

o 0 0 50 100 150 200 250 300 350 400 50 100 150 200 250 300 350 400 Temperature (°C) Temperature(C)

_ n 6000 0.4 u. x = 0.10 500 5000 0.5 0.3 400C 4000 0.4

300C 3000 0.2 £o 0.3 C 2000 200C 0.2 0.1 1000 1000 0.1 0 0 0 50 100 150 200 250 300 350 400 50 100 150 200 250 300 350 400 Temperature(C) Temperature(C)

6000 0.4 8000 0.8 7000 0.7 5000 0.3 6000 0.6 4000 5000 0.5 3000 0.2 4000 0.4 ' 3000 0.3 2000 0.1 2000 0.2 1000 1000 0.1

0 0 vf 0 50 100 150 200 250 300 350 400 50 100 150 200 250 300 350 400 Temperature(C) Temperature(°C)

Figure 3.7

Temperature and Frequency Dependence of -r and tan 8 in NBT-xBT-3NBZ at 0.1, 1, 10, 100, 1000 kHz Tmdecreases as the MPB is approached from the phase fields on either side.

66 Chapter 3 Results I: Co-Doped Polvcrvstals

NBT-xBT-4NBZ

r: 1 > 10> 100> 1 000 kHz Heating Rate: 21<101001000C/hr tan 6: 1<10 < 100 < 1000 kHz

0.3 5000 0.5 4000 4000 0.4

3000 0.2 3000 0.3 C C 2000 2000 - 0.2 0.1 1000 1000 x = 0.09 0.1

0 0 0 0 50 100 150 200 250 300 350 400 50 100 150 200 250 300 350 400 Temperature(IC) Temperature(IC)

---- ___----sns_ bUUU U.4 sUUU U.4

4000 4000 0.3 0.3

3000 3000 0.2 0.2 2000 2000

0.1 0.1 1000 1000

0 0 0 0 50 100 150 200 250 300 350 400 50 100 150 200 250 300 350 400 Temperature(IC) Temperature(IC)

1000 - 0.4

750 t- 0.3

500 0.2 Na0.39Bi0.36Ba0.26Ti0.71Zr0 .29

250 "', 0.1

0 0 50 100 150 200 250 300 350 400 Temperature (IC)

Figure 3.8 Temperature and Frequency Dependence of Erand tan 6 for NBT-xBT- 4NBZ and NBT-26BT-29NBZ at 1, 10, 100, 1000 kHz Tm decreases as the MPB is approached from the phase fields on either side and to nearly room temperature at 1 kHz for 26 Ba/29 Zr (mol %).

67 Chapter 3 Results I: Co-Doed PolycL-stals

3.2.3 Volger-Fulcher Analysis

For relaxors, the frequency dispersion of Tmdoes not follow an

Arrehenius-type, or Debye relaxation, dependence. The frequency-dependent Tm will reach a static freezing temperature Tf as f- 0. This relaxor behavior is best described by the Volger-Fulcher (VF) law of finite freezing temperatures:

f fkB(T. - )Tf where, Tf is the static freezing temperature (f- 0) in Kelvin, f is the attempt frequency (s-1),Eact is the activation energy, kBis Boltzmann's constant (1.38 x 10-23

J/K). Figures 3.9 and 3.10 show that the experimental data for 1/Tm versus logf in co-doped NBT polycrystalline samples is in good agreement with the VF curve

(relative error < 3%).

Electromechanical testing of samples was performed at frequencies of

0.05, 1 and 20 Hz. Using the parameters determined from the VF curve fits, Tm may be extrapolated to low frequency. Table 3.2 lists the parameters, Tf, Eact and fo, calculated from the Volger-Fulcher fit, and the extrapolated value of Tmat 0.05

Hz. Corresponding to the observed Tmbehavior, the calculated Tf and Tmat 0.05

Hz also decrease as the MPB is approached from either phase field. For MPB compositions and highly doped compositions, Tmat 0.05 Hz approaches room temperature, shifting as low as 370C for sample p23a. The calculated values of Tf

68 Chapter 3 Results I: Co-Doped Polycrystals can be used to determine the phase diagram for the solid solution NBT-BT-NBZ, which is discussed in Section 3.3.4 (see Fig. 3.41).

NBT-xBT-3NBZ 0 Experimental Data ...... VF nonlinear fit

I I I I I 0_ x = 0.04 7. b b o 5Q 0 0 o, x x E E 6. lZ Relative Error of Fit: 0.2%

6 , I I I 1 2 3 4 5 6 log f [Hz] t log f [Hz] I . = 0.08 0.-,. x= 0.10 . 8 . . 8 _ , C) ~~6 ~,~~~'. E '. x O Relative Error of Fit: 1% Relative Error of Fit: 2% I I I I 1 2 3 4 5 6 1 2 3 4 5 6 :7 log f [Hz] logf [Hz]

I 10 l I I I 7 ~ 3.... I II I --. x = 0.14 ~0~~' x = 0.12 6

C) o o .,

xX 5 _ E x E t Relative Error of Fit: 2% Q Relative Error of Fit: 1% ? I I3 4I 5I I ; I 4 I I I I 1 2 6 7 2 3 4 5 6 log f [Hz] log f [Hz]

Figure 3.9 1/Tm as a Function of Frequency with Vogel-Fulcher Law Fit for NBT-xBT-3NBZ 69 Chapter 3 Results I: Co-Doved Polucrustals

O ExperimentalData NBT-xBT-4NBZ ...... VF nonlinearfit

I I I o x = 0.07 10.0x = 0.09 10 o0. b O.

0, O",%"to 8 X x E 'O lZ: Relative Error of Fit: 2% Relative Error of Fit: 2% I I I I 6 I I 62 3 4 5 6 7 2 3 4 5 6 7 o E log f [Hz] log f [Hz]

10 I I I I I I I I 0 x=0.12 x = 0.14

0~-· o o" . X 0 X x E E 17 lZ Relative Error of Fit: 3% Relative Error of Fit: 2%

4 I I I I 1 2 3 4 5 6 77 L 5 4 D b log f [Hz] log f [Hz]

2UOI I I I

b 15 10 ' . Nao. 39Bio. 3 6Bao. 2 6Tio.7 1 ZrO29

X E 10_., 1 Relative Error of Fit: 1% I I I I 2 3 4 5 6 7 log f [Hz]

Figure 3.10 1/Tm as a Function of Frequency with Vogel-Fulcher Law Fit for NBT-xBT-4NBZ and NBT-26BT-29NBZ

70 Chapter 3 Results I: o-Doped Polycrstals

Table 3.2 Volger-Fulcher Parameters for Co-Doped NBT Relaxor Polycrystals Doping Level Calculated Parameters from Volger- Extrapolation Fulcher Fit to 0.05 Hz Sample mol% mol% 3 Rel. ID Zr Bact x 3 10 Logf Error Tm (C) (0C) (eV) (Hz) (%)

pla 3 4 115.8 5.9 7.8 0.2 119

p2a 3 6 89.9 8.4 7.3 0.7 95

p3a 3 8 81.3 9.5 7.3 1 87

p4a 3 10 83.4 11.0 7.1 2 90

p5a 3 12 86.8 10.0 7.0 2 93

p7a 3 14 122.4 9.8 7.1 1 128 ...... p8a 4 7 74.6 9.3 7.5 2 80

p9a 4 9 74.0 8.8 7.5 2 79

p1Oa 4 12 89.0 11 7.4 3 95

p11a 4 14 93.5 10 7.0 2 100 ...... 3 7 p23a 29 26 31.0 11 7.6 1 37

71 Charterr 3 RResults : CCo-Doed Polucrustals

3.3 ElectromechanicalProperties of Polycrystalline (Ba + Zr) Co-DopedNBT

The data presented in Section 3.2 demonstrate that controlled doping in

NBT-BT-NBZpolycrystalline compositions shifts Tmdownward, such that at room temperature these compositions lie within the "micro-macro" relaxor behavior region (refer to Section 1.2). This section will present low frequency, actuation data illustrating this mixed actuation behavior.

The distance a particular composition lies from its Tmat room temperature

(RT) may be considered in terms of AT (AT=Tm - RT). Electrostriction dominates the room temperature response for those compositions with low AT. As AT increases, the FE component increases until a PE -FE field forced transition is possible and continues to increases until the FE component dominates actuation behavior in compositions with the largest AT. While compositions will be classified according to the dominant character, nearly all compositions studied here exhibit a mixed response, with significant electrostrictive contributions overprinting the ferroelectric component, and in some compositions, dominating the actuation character. An additional feature of the micro-macro region described in the literature [4] is that non-hysteretic strain loops can only be achieved below 1 Hz. Correspondingly, predominantly electrostrictive co-doped

(Ba + Zr) NBT compositions are non-hysteretic only at lower frequencies, such as

0.05 Hz.

72 Chapter 3 Results I: Co-Doped Polycrystals

3.3.1 Room Temperature Electromechanical Properties of Polycrystalline NBT-xBT-3NBZ

Figure 3.11 provides an introductory summary to the trends in actuation and polarization observed in the system (Na1 /2Bil/2)1.xBax(Tio.97Zro.03) that will be

discussed in this section. Corresponding to the decrease in Tm(O.05 Hz) as the MPB is approached, actuation and polarization character is seen to shift from predominantly FE character far into the rhombohedral and tetragonal phase fields, through a field-forced phase transition to predominantly PE character, with the magnitude of FE contribution gradually decreasing as the MPB is approached at - 8 mol% Ba. Each of these predominant behavior regions, PE,

PE-FE and FE will be discussed in following sections.

73 Chapter 3 Results I: Co-Doped Policrustals

N E II E E u c0 tO 0 C0 I I 6 Co I I LL \ T- O cZ 4nL11 · E w -' CO LL t E a& : w C-e cL CY) CY) X N - C,0 LC) *c0* ·- CO 03 o co O LL - 'CD LL cs

o Cu> CD 0 L- a) co N O0r Co m0

N Z CY) 0 't - Co)c Co 0-L Co o LO CY)

.. z 0 U- E E Z -a t o 03Co Ln E- o C- UL 0 CD 0oN o cm C\! - CY) C) Co o Os o0 cu o0Cu° C) L -. LL CD ONO CO L O4 E E I I '.0 CuO O Co o 0 II 0> CO I I .0)Cu I I LL1 6 'I cd C)

II E 11 l LoC: . _._._.....~ u?

O L -0 L 0 D C C o a) - ra N E . E .< E a) Co cor~c C cn I 1- CL 6 c-0 Co N O L- mr cX m L. O > o xc) N to a CL x U) .mm~ 2 cu a - E E ct $Y L) E mn 2 T ao (L 0

74 Charter 3 Results I: Co-Doved Polvcrustals

3.3.1.1 Predominantly Ferroelectric Actuation

At room temperature, samples prepared from batches pl and p7 (doped with 4 and 14 mol% Ba, respectively) display butterfly strain loops and hysteretic polarization loops typical of ferroelectric response under applied field. These

samples represent compositions lying farthest into the rhombohedral (4 mol%

Ba) and tetragonal (14 mol% Ba) phase fields. Their strain loops exhibit large hysteresis at 1 Hz compared to lower frequencies, a characteristic described for

actuation in the micro-macro region.

Figure 3.12 shows the evolution of strain under an increasing ac field for

samples prepared from batch pl (4 mol% Ba). Initially poled rhombohedral plb

actuated under ac field shows initial signs of depoling around - 26 kV/cm. A

maximum bipolar field induced strain of 0.17% at 49 kV/ cm and 0.05 Hz was

achieved in sample pla. The unipolar strain is highly linear with low hysteresis

at 0.05 Hz (Fig. 3.13). Calculated from the slope of the unipolar strain driven to a

maximum strain of 0.08% at 47 kV/cm, d33 = 170 pC/N. Thus, the d33 of the

rhombohedral ferroelectric NBT-4BT-3NBZexceeds the highest values reported

for polycrystalline NBT-BT,for which d33= 125 pC/N [26]. The maximum

saturated polarization at ac fields of 47 kV/ cm reaches 37 C / cm2 with a

2 coercive field Ec - 31 kV/cm and remnant polarization Pr N26pC/cm (Fig. 3.14).

Pr is slightly higher than the observed Pr 20 pC/cm2 in NBT-BT.

75 Chater 3 Results I: Co-Doved Polucrustals

NBT-4BT-3ZR Polycrystal at 0.05 Hz, 1 MPa prestress - --- 0.020- 0 0.030- -1 o0 0.0251 0.015- r- 0 0.0201 -JC: 0.010 -r 0.0151 r- t- C 0.010 0.005 0.005 O ^ ^^- t- ^ ^^' r It ,_J U.UUUJr' fl ._1 0.000 -20 0 20 -40 -20 0 20 40 Field (kV/cm) Field (kV/cm)

0.05 0.20 C m 0.04 rC 0.15 -0030.03 . C:r-. C0 0.10 ' 0.02 :3 tC

u) 0.01 C: 0.00o ·'-- 0.05 0.00 -jo 0.00 -'-50 -25 0 25 50 -60 -40 -20 0 20 40 60 Field (kV/cm) Field (kV/cm)

Figure 3.12 Evolution of Bipolar Strain Response for Initially Poled FR Phase NBT-4BT-3NBZ Polycrystal

76 Chapter 3 Chpter 3 ResultResuts I: Co-Dod·Co-Doed PPolucrustals 'usa

NBT-4BT-3NBZ Polycrystal

0.10

0.08

Uo 0.06 C 0 0.04 0.02

_1 0.00 0 20 40 60 Field kV/cm

Figure 3.13 Strain (Unipolar) Versus Field for FR Phase NBT-4BT-3NBZ Polycrystal

NBT-4BT-3NBZ Polycrystal

40 P_=26-----/cm ------15 N Pr 26 C/cm2 7 E 10 0 20 O E 5 r 0 C 0i o a, CU -5 N -20 ( -10 4 o -40 At"I Q_ - IJ -80 -40 0 40 80 -80 -40 0 40 80 Field (kV/cm) Field (kV/cm)

Figure 3.14 Polarization and Current Versus Field for FR Phase NBT-4BT-3NBZ Polycrystal

77 Chapter 3 Results I: Co-Doped Polycrystals

The current versus ac field plotted in Figure 3.14 exhibits the characteristic FE current peaks separated by - 2E,.

Initially poled tetragonal sample p7b (14 mol% Ba) actuated under ac field showed qualitatively similar characteristics to those seen for sample plb in

Figure 3.12, however, initial signs of depoling occurred at a much lower field of -

10-13kV/cm. It also achieved a greater maximum bipolar and unipolar strain of

0.28% and 0.14% (0.05 Hz), respectively for the same fields (Fig. 3.15). The unipolar strain is highly linear with negligible hysteresis at 0.05 Hz, and d33- 310 pC/N. Thus, the tetragonal ferroelectric NBT-14BT-3NBZshows properties at low frequency that match the highest values reported for polycrystalline PZT-8 with d33- 300 pC/N [34]. The maximum saturated polarization at ac fields of 37 kV / cm reaches 49 IC /cm2 with a low coercive field of Ec - 14.5 kV / cm and remnant polarization of Pr - 21IC/cm 2 (Fig. 3.16).

Both samples plb and p7b (disc geometry) were field cooled from 200°C to room temperature under a constant field of 20 kV/cm, and low-field actuation data shows that both samples were poled. Sample plb showed - 15% decrease in dielectric constant upon poling, however, under zero bias, only small, spurious resonances were detected. Sample p7b exhibited negligible decrease in dielectric constant (- 3% decrease), however it was possible to separate the kt resonance peak from the spurious resonances (Fig. 3.17).

78 Chapter 3 Results I: Co-Doped Polycrstals

NBT-14BT-3NBZ Polycrystal at 0.05 Hz, 1 MPa prestress

. .. U.5UIn n n .. 0 0.15 - 0.14 % at 49 kV/cm 0.25 Co C.M 0.20 0.10 0.15 .C .0- :I,C 0.10 cJ) 0.05 -.0CJ 0 0.05 v,00) d33 = 310 pC/N -J0_j n n0 _j 0.00 -50 -25 0 25 50 0 10 20 30 40 50 Field (kV/cm) Field (kV/cm)

Figure 3.15 Strain (Bipolar and Unipolar) Versus Field for FT Phase NBT-14BT-3NBZ Polycrystal

NBT-14BT-3NBZ Polycrystal

40 20

0 20 10 E

aO Co -10

a -40 -20 -50 -25 0 25 50 -50 -25 0 25 50 Field (kV/cm) Field (kV/cm)

Figure 3.16 Polarization and Current Versus Field for FT Phase NBT-14BT-3NBZ Polycrystal

79 Chavter 3 Results I: Co-Doped· PolhcrwstalsV V

NBT-4BT-3NBZ Polycrystal 1500 _._ .._ - 0.3 0.25 1000 ...... 0.2 ,- ...... 0.15

500 * 0.1 0.05

0 1 10 100 1000 10000 Log Frequency (kHZ)

NBT-14BT-3NBZ Polycrystal

2500 2.00

2000 1.50

1500 Q) 1.00 D 1000 0.50 500 o o 0 1 10 100 1000 10000 Log Frequency (kHZ)

kt Resonance Peak 1000 350 - 300 kt: -. 900 -- - OS250 ( 200 a)C 800 C X 700 CU 150 I a) a) 100 I E 600 E 50 500 0 iIII1 E _ 220 245 270 295 320 345 1500 2000 2500 3000 3500 Frequency (kHZ) Frequency (kHZ)

Figure 3.17 Resonance Analyses (Zero Bias) in Poled FT Phase NBT-14BT-3NBZ Polycrystal with Disc Geometry

80 Chapter 3 Results I: Co-Doped Polycrystals

Electromechanical coupling coefficients and piezoelectric constants calculated for sample p7b are compared to those for PZT-8 and NBT-BT in Table 3.3. The measured properties of kt - 0.45 and d33 - 310 pC/N for NBT-14B-3Zare highly competitive with the current commercially available hard piezoelectric material,

PZT-8. The mechanical quality factor Qmfor NBT-14B-3Zis lower than PZT-8

(378 compared to 900 - 1600). Qmis a measure of the ratio of strain in phase with stress to strain out of phase with stress and is related to the sharpness of the resonance frequency (i.e. small Af is characteristic of sharp resonance). Materials with low Qn lose more energy (in the form of heat) due to mechanical damping

[9].

The numerous spurious resonances present in these samples may be caused by inhomogeneities in the sample (compositional, density, grain size distribution, etc.) or deviations in sample geometry from an ideal rectangular parallelepiped. Thus, the true values of the piezoelectric constants have not likely been reached. The property measurements provided here have identified

NBT-14B-3Zas a potential alternative to PZT-8 in commercial applications, and thus is a composition deserving further study.

81 Chavter 3 Results I: Co-Dop~ed Polucrustsals haer- 3 J ,Results-ICo-DoedPli a-l-

Table 3.3 Comparison of PiezoelectricProperties For Polycrystalline Materials

kt d33 N t Np Qm (pC/N) (Hz m) (Hz m)

NBT-4BT-3NBZ 170

NBT-14BT-3NBZ 0.45 310 2400 2985 378

- ---· NBT-6BT [26] - 0.51 125 1586 2975 na

PZT-8 [34] - 0.34 300 2070 2170 900 - 1600

na = not available 2 kt estimated by the relation: k 33 k + k + kpk t

3.3.1.2 Field-Forced Transition (PE-FE)

As the MPB is approached from the both the ferroelectric rhombohedral

(FR)and the ferroelectric tetragonal (FT)phase fields, a phase transition to predominantly electrostrictive actuation (PE) occurs. Samples that lie very close to the PE-- FE boundary undergo a field-forced transition (FFT)from PE response at low fields to FE at high fields. This behavior has been observed in rhombohedral NBT-6BT-3NBZ (FFTR)and tetragonal NBT-12BT-3NBZ (FFTT).

NBT doped with 6 mol% Ba and 3 mol% Zr lies near the MPB in the rhombohedral phase field. As the MPB is approached from far in the

82 Chapter 3 Results I: Co-Doped Polvcrystals rhombohedral phase field, Tmdrops from > 119°C for ferroelectric NBT-4BT-

3NBZ to - 950C in NBT-6BT-3NBZ at 0.05 Hz (Table 3.2). Low-field actuation is predominantly electrostrictive with negligible hysteresis at 0.05 Hz. Sample p2b reaches a maximum of 0.13 % electrostrictive strain at 46 kV/ cm before the field forced transition is initiated (Fig. 3.18). The polarization is linear and slightly hysteretic with a maximum of 28uC/ cm2 at 46 kV/ cm, where it begins to show signs of saturation (Fig 3.19). The current loop is a slightly distorted circle, with peaks at zero field showing only slight separation (Fig 3.19). Electrostrictive properties at low field are shown in Figure 3.20. The field induced maximum d33

-2 is - 450 pC/N at 32 kV/cm and the electrostrictive coefficient Q11is -1.8 x 10

C2 /m4 .

At fields higher than 46 kV/ cm in sample p2b, a field-forced phase transition occurs with increased hysteresis due to initiation of domain wall motion (ferroelectric and/or ferroelastic) and nearly infinite slope in strain/field at 50 kV/cm. Figure 3.21 shows the evolution of this field-forced phase transition in bipolar and unipolar longitudinal strain. Maximum bipolar strain reaches 0.28% at 60 kV/cm and unipolar strain reaches 0.31% at 73 kV/cm, however each shows significant hysteresis.

83 CharterCh....r 3 Results : Co-DeCo-Doed.. PPolucrustals i....

NBT-6BT-3%NBZ Polycrystal 0.05 Hz, 1 MPa Prestress 0.14

v 0.12 *· 0.1 n 0.08 c 0.06 * 0.04 - 0.02 0 -50 -25 0 25 50 Field (kV/cm) Figure 3.18 Low Field Electrostrictive Strain (Bipolar) Versus Field for FFTR Phase NBT-6BT-3NBZ Polycrystal

NBT-6BR-3NBZ Polycrystal

2 Pmax = 28 pC/m at 46 kV/cm 40 0.8 I-F- I ----? 20 0.4 C)0

4-, 0 0 0 a) ! ) 4-, g NCo -20 0 -0.4 a-r -40 I I -0.8 1, I I -50 -25 0 25 50 -50 -25 0 25 50 Field (kV/cm) Field (kV/cm)

Figure 3.19 Low Field Polarization and Current Versus Field for FFTR Phase NBT-6BT-3NBZ Polycrystal

84 Chapter 3 Results I: Co-Doped Polycrystals

NBT-6BT-3NBZ Polycrystal

I--^ r%, . - .I VUU Max d33- 450 pC/N U. -IU at 32 kV/cm - 400 z 0.12 6 0 300 .c 0.08 ' 200 C) 100 0.04 / 5 point smoothing filt( i i I I n LJn 0 10 20 30 40 0 0.03 0.06 0.09 Field (kV/cm) p2 (C2/m 4 )

Figure 3.20

Low Field Electrostrictive Properties d33 and Q11 of FFTR Phase NBT-6BT-3NBZ Polycrystal

85 Chapter 3 Results I: Co-Doped Polvcrustals

NBT-6BT-3NBZ Polycrystal

0.2

C 0.15

U) 0.1 0.05 Hz, 1 MPa Prestress C .5 0.05 C 0 0 -j -60 -30 0 30 60 Field (kV/cm) Field (kV/cm) 0.25 0.3 - 0.2 .C 0.15 ' 0.2 (n . 0.1 ' 0.1 0.05 - ° 0 o 0 -60 -30 0 30 60 0 30 60 Field (kV/cm) Field (kV/cm)

0.3 0.3 C c Cu 0.2 ._iU) 0.2 .U

c' Coc 0.1 0.1 ~60)c 'Oa C 0,C0)0 0 -J 0 -J 0 -60 -30 0 30 60 0 30 60 Field (kV/cm) Field (kV/cm) 0.3 z 0.3

2 0.2 pC/N .' 0.1 : 0.1

.,C: C 0 0 -j0 0 -60 -30 0 30 60 0 30 60 Field (kV/cm) Field (kV/cm)

Figure 3.21 Evolution of the Field-Forced Phase Transition with Increasing Field in FFTR Phase Co-Doped NBT-6BT-3NBZ Polycrystal

86 Chapter 3 Chapte#3 ResltsResults I : CCo-Doed -De PPolucrustals Jcsa

As high fields ( 70 kV/cm) are approached and time held under high field increases, the transition to FE phase continues to develop. Hysteresis becomes clamped for increasingly larger field ranges (45 -70 kV/ cm is the maximum range measured) giving a linear unipolar piezoelectric response with d33 190 pC/N. The strain under bipolar and unipolar fields is very high for a polycrystalline material. However, due to the large hysteresis associated with the field-forced transition this strain is not likely to be useful in most device applications.

In the system NBT-BT,an AFE phase field located between the FE and PE fields has been identified [26, 33]. The high field strain actuation character observed in this material may be compared to that displayed by well-studied

AFE materials, such as lead zirconate titanate stannate (PLZTS) [42, 43].

However, the characteristic AFE response in polarization under ac field is a

"pinched loop," for which the high field FE polarization loop clamps to Pr = 0 and zero field, where electrostriction dominates. The distinctive current loop shows two sets of peaks at high field, both offset from zero. The high field polarization loop for this sample, NBT-6BT-3NBZremains highly linear

(predominantly electrostrictive) with no obvious pinching in the center (Fig.

3.22). The shape of the high field current loop is also similar to the low field response. At zero field, the saturated electrostrictive component is reflected with two (positive and negative) current peaks, with negligible separation. To the left

87 CharterCha.t- 3.eslt3 Results : Co-Doedi v Polucrstals

(negative current) and right (positive current) of zero field, there are what may be a second set of unresolved peaks. These are related to the ferroelectric component. An additional set of current peaks, related to an AFE component, are not apparent. Thus, no conclusive evidence has been found here for the presence of an AFE phase at room temperature. Thus, it is concluded that additional doping of the NBT-BT system with zirconia pinches out the small AFE field. The character of the actuation loop can be the result of a FE-PE transition and may also include non-polar ferroelastic transitions, contributing to the observed hysteresis but not to the polarization.

NBT-6BT-3NBZ Polycrystal

Pmax = 36 p C/m2 at 57 kV/cm _ 1_1_I 40 ' 10r." I

N 20 - 0.5 0 O 0.0

Co N -20 0-0.5

I . m -40 I II I I I I I I I I ' _i - 1 . -80 -40 0 40 80 -80 -z40 0 40 30 Field (kV/cm) Field (kV/cm)

Figure 3.22 High Field Polarization and Current Versus Field for FFRR Phase NBT-6BT-3NBZ Polycrystal

88 Chapter 3 Results I: Co-Doped Polycrystals

Approaching the MPB from the FTfield, samples doped with 12 mol% Ba,

3 mol% Zr lie very near the PE/FE boundary and also undergo an field-forced phase transition. NBT-12BT-3NBZdisplays a slightly stronger FE component than NBT-6BT-3NBZas evidenced in the shape of the high field polarization loop

(Fig 3.27). Maximum electrostrictive strain is 0.09% at 29 kV/ cm before the field- forced transition is initiated around 30 - 35 kV/cm (Fig. 3.23). Even at low field, where the response is predominantly electrostrictive, the polarization loop has a higher remnant polarization (- 7 vs. 3 C / cm2) than NBT-6BT-3NBZand the saturation peaks in current display greater separation, indicating a significant FE component (Fig. 3.24). Electrostrictive properties at low field are shown in

Figure 3.25. The field induced maximum d33 is -460 pC/N at 32 kV/cm and the

-2 2 4 electrostrictive coefficient Q11 is ~1.8 x 10 C /m . A similar evolution from PE actuation with no hysteresis to a highly hysteretic strain loop which eventually clamps down to a linear piezoelectric response is seen for the FFTTphase, as shown in Figure 3.26. The high-field polarization (Pmax- 41 C/cm2 at 55 kV/cm) for NBT-12BT-3NBZ also does not show a pinched AFE loop, but shows a mix of electrostrictive and ferroelectric responses (Fig. 3.27). The high-field current clearly shows the mix of responses. Electrostrictive peaks are aligned near zero field, and the FE contribution, off-center, is less resolved but is easily observed.

89 Chapter 3 Results I: Co-Doved Polucrustals

NBT-12BT-3NBZ Polycrystal

0.05 Hz, 1 MPa Prestress 0.1

0 0.08 ._CU

L- 0.06

cn -1-W 0.04

._0 0.02 .0 n -40 -20 0 20 40 Field (kV/cm) Figure 3.23 Low Field Electrostrictive Strain (Bipolar) Versus Field for FFTT Phase NBT- 12BT-3NBZ Polycrystal

NBT-12BT-3NBZ Polycrystal

Pmax = 21.5 pC/m2 at 29 kV/cm ou 4 I i~~~~~~~~~~~~- 20 I 2 cV 0E 10 E

O -' C: 0 C: 0 0 a) .- ' L. CU -10 N 0 -2 -20

0 I i _1~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ ._O -3OU-Jl r1 1 ...... -4 -40 -20 0 20 40 -40 -20 0 20 40 Field (kV/cm) Field (kV/cm)

Figure 3.24 Low Field Polarization and Current Versus Field for FFTT Phase NBT-12BT-3NBZ Polycrystal

90 Chapter 3 Results I: Co-Doped Polvcrystals

NBT-12BT-3NBZ Polycrystal

500 0.1 Peak d33 460 pC/N at 27 kV/cm J 1~ z 400 0.08 O 300 it 0.06 _0 v, 200 - 0.04 oo 100 4 . 0.02 3 point smoothing filter 0 'I I , I I 0 0 10 20 30 0 0.02 0.04 0.06 Field (kV/cm) p2 (C2/m 4 )

Figure 3.25

Low Field Electrostrictive Properties d33 and Q11 of FFTT Phase NBT-12BT-3NBZ Polycrystal

91 Chavter 3 Roc1i41c. r TULJ-L-n'uJ L-nTt( i oc AiLi0"L11 b fi, TL-IUlrnn DM.

NBT-12BT-3NBZ Polycrystal at 0.05 Hz, 1 MPa Prestress

0.12 -0.12

C C · 0.08 · 0.08

I I I I I I 1I1 1 ' 0.04 c 0.04 .

_, _j0 35 -25 -15 -5 5 15 25 35 0 10 20 30 Field (kV/cm) Field (kV/cm) 0.2 0.2

'_ 0.15 ' 0.15 C- o) 0.1 U) 0.1

o i 0.05

o 0 -a0 -40 -20 0 20 40 0 20 40 Field (kV/cm) Field (kV/cm) 0.25 U.OU 0.2 0.25 .' 0.20 0.15 0) 0.15 c 0.1 0.10 pC/N 0.05 . 0.05 0.00 O 0 -I -55 -40 -25 -10 5 20 35 50 0 15 30 45 Field (kV/cm) Field (kV/cm) _ 0.30 -0.25 C . 0.20 ·.i 0.15 ;5 0.10 c) 0.05 C 0.00 .- 0.00 -60 -10 40 Field (kV/cm)

Figure 3.26 Evolution of the Field-Forced Phase Transition with Increasing Field in FFTT Phase NBT-12BT-3NBZ Polycrystal

92 Chapter 3 Rsults I: Co-Dop~edPolycrstals

NBT-12BT-3NBZ Polycrystal

Pmax= 41 pC/m 2 at 55 kV/cm 45 12

30 8 E -0 15 4 O E 0 C 0 . _ ra, 0 -15 L. -4 ) N -30 -8 CU -45 I I I I I I I -12 0- -60 -30 0 30 60 -60 -30 0 30 60

Field (kV/cm) Field (kV/cm)

Figure 3.27 High Field Polarization and Current Versus Field for FFTT Phase NBT-12BT-3NBZ Polycrystal

93 ChapterChate 3 ReutResults I::C-oe Co-Doed PolucrustsalsoVut 3.3.1.3 Predominantly Electrostrictive Actuation

As the MPB is approached from NBT-12BT-3NBZ,a gradual decrease in the degree of FE character, as well as a decrease in Tm(O.0 5Hz),is observed. Sample

0 NBT-8BT-3NBZ (Tm(O.05 Hz) - 87 C), of near-MPB composition, shows the purest electrostrictive response for the 3 mol% Zr set of compositions. NBT-1OBT-

3NBZ is predominately electrostrictive, but shows a slightly higher degree of ferroelectric contribution as it lies close to the PE-FE boundary. These compositions reflect the shifting downward of the electrostrictive phase field to near-room temperature at the MPB.

NBT-1OBT-3NBZreaches a maximum of 0.24 % bipolar strain at 53 kV/cm and 0.21% unipolar strain at 53 kV/cm (Fig. 3.28). The unipolar strain curve is parabolic (as opposed to the linear piezoelectric response), showing the same response as the bipolar loop. The polarization is linear and slightly hysteretic with a maximum of 36C / cm2 at 49 kV / cm where it begins to show signs of saturation (Fig 3.29). The current loop shows predominately electrostrictive peaks centered at zero field with some distortion from unresolved ferroelectric contribution (Fig 3.29). Electrostrictive properties are shown in Figure 3.30. The field induced maximum d33 is -725 pC/N at 32 kV/cm and the electrostrictive

- 2 4 coefficient Q11is -1.9 x 10 2 C /m .

94 Chapter 3 Results I: Co-Doped Polycrstals

NBT-1 OBT-3NBZ Polycrystal at 0.05 Hz, 1 MPa Prestress

Bipolar Actuation Unipolar Actuation 0.25 0.25 0.24 % at 53 kV/cm C 0.2 0.2 C C

C,) 0.15 VC 0.15 75 .aC 0.1 :~ ~~I I 0.1 -S- 0.05 .0-j 0.05 0) :LI -j 0 0 -60 -10 40 0 25 50 Field (kV/cm) Field (kV/cm)

Figure 3.28 Electrostrictive Strain (Bipolar and Unipolar) Versus Field for PET Phase NBT- 10BT-3NBZ Polycrystal

NBT-10BT-3NBZ Polycrystal

Pma = 36 pC/m2 at 49 kV/cm 40 F ' 6 cN E 0 20 0C- E 2 0 I -2 -20 04. L-0 O -4 II- ! - -40 , . . . . . -6 I I T rI r TIrI Ir -60 -30 0 30 60 -60 -30 0 30 60 Field (kV/cm) Field (kV/cm)

Figure 3.29 Polarization and Current Versus Field for PET Phase NBT-10BT-3NBZ Polycrystal

95 Results I: Co-Doed Polucrustals CharterC 3 R · -- rt --

NBT-10BT-3NBZ Polycrystal

1 duu ~~~~~~~~~~~~UZ .Z Q11n 1.9 x 10 -2 C2/m4 ' 600 0.2

C 400 F 0.15 -C 0.1 /I 200 ' Peakd 33 - 725pC/N ( 0.05- at 32 kV/cm

= I I -- I

0 25 50 0 0.05 0.1 0.15 Field (kV/cm) p2 (C2/m 4)

Figure 3.30

Electrostrictive Properties d33 and Q11 of PET Phase NBT-10BT-3NBZ Polycrystal

NBT-8BT-3NBZreaches a maximum of 0.15 % bipolar strain at 49 kV/ cm and 0.13% unipolar strain at 44 kV/cm (Fig. 3.31). The unipolar strain curve is parabolic, reaching a maximum strain of 0.13% at 44 kV/ cm. The polarization is linear and slightly hysteretic with a maximum of 33 pC / cm2 at 49 kV / cm where it begins to show signs of saturation (Fig 3.32). The current loop shows predominately electrostrictive peaks centered at zero field. A small FE component can still be observed (Fig 3.32). Electrostrictive properties are shown in Figure 3.33. The field induced maximum d33 is -500 pC/N at 32 kV/cm and the electrostrictive coefficient Q11 is -1.4 x 10-2 C2 /m4 .

96 Chapter 3 Results I: Co-Doped Polycrstals

NBT-8BT-3NBZ Polycrystal at 0.05 Hz, 1 MPa Prestress

Unipolar Actuation 0.16 - 0 C : 0.12 0.13 % at 44 kV/cm C 0.12 .. _ .M U) 0.08 0.08 4- C C' .0 0.04 -J :110) C 0.00 o 0.00 -50 -25 0 25 50 0 15 30 45 Field (kV/cm) Field (kV/cm)

Figure 3.31 Electrostrictive Strain (Bipolar and Unipolar) Versus Field for PET Phase NBT-8BT-3NBZ Polycrystal

NBT-8BT-3NBZ Polycrystal

Pmax= 33 pC/m2 at 49 kV/cm 40 6.00 NE E 4.00 O 20 E 2.00 -, C 0 C 0.00 0 o -2.00 N -20 C. ° -4.00 -. -40 -6.00 -50 -25 0 25 50 -50 -25 0 25 50 Field (kV/cm) Field (kV/cm)

Figure 3.32 Polarization and Current Versus Field for PET Phase NBT-8BT-3NBZ Polycrystal

97 Chapter 3 Resuls I: Co-Doped Polygnstals

NBT-8BT-3NBZ Polycrystal

600 0.20 4 500 Q1 - 1.4 x 102 C2/m - 0.15 z 400 300 to - 0.10 -a 200 (D 0.05 100 Peak d33 - 500 pC/N at 29 kV/cm 0 0.00--- 0 15 30 45 0 0.04 0.08 0.12 Field (kV/cm) p2 (C2/m 4 )

Figure 3.33

Electrostrictive Properties d33 and Q11of PET Phase NBT-8BT-3NBZ Polycrystal

3.3.2 Room Temperature Electromechanical Properties of Polycrystalline NBT-xBT-4NBZ

Increasing the doping level of Zr4 from 3 to 4 mol% lowers Tmat 0.05 Hz nearly 100C near the MPB. A systematic compositional study of constant 4 mol%

Zr shows that for increasing 7- 14 mol% Ba2+, actuation was predominantly electrostrictive with a small FE component. Predominantly FE actuation was not isolated in the range of Ba2+ concentration studied for the 4 mol% Zr series.

98 Chapter 3 Results I: Co-Doped Polycrustals

3.3.2.1 Predominantly Electrostrictive Actuation

All samples with 4 mol% Zr are classified as predominantly electrostrictive. Actuation behavior is most purely electrostrictive for NBT-7BT-

0 0 4NBZ (Tm(0.05 Hz) 80 C) and NBT-9BT-4NBZ (Tm(0 .05 Hz) -79 C), which lie near MPB.

Compared to NBT-8BT-3NBZ (Tm(0 0. 5 Hz) -87°C), electrostriction is also more pure in these two compositions, for they display less hysteresis in strain and polarization loops at 0.05 Hz. However, a small FE component is still present and can be detected as a distortion in the predominantly electrostrictive response of the current loop. As Ba2' concentration increases farther into the tetragonal phase field, compositions NBT-12BT-4NBZand NBT-14BT-4NBZshow an increasing FE component in polarization and actuation. The actuation character of NBT-14BT-4NBZ is similar to that of NBT-1OBT-3NBZ, suggesting that it lies very close to the PE-FE boundary. Thus, it is speculated that increasing Ba2' >

14 mol% in this system may isolate predominantly FE actuation. Figures 3.34 -

3.38 summarize longitudinal strain, polarization, and electrostrictive properties for this set of compositions. As is expected, as the contribution of the FE component increases the dielectric susceptibility K (proportional to slope of P vs.

E curve) increases, suggesting that predominantly electrostrictive materials with high polarizations may be engineered through controlled doping of compositions that lie close to the PE-FE phase boundary.

99 Chapter 3 Results·Y·l I: Co-Doved Polucrustals

NBT-xBT-4NBZ Polycrystals at 0.05 Hz, 1 MPa Prestress

-- x = 7mol% Ba (R) x = 7 mol% Ba (R) U.Z 0.25 unipolar - - 0.2 0.2 Cr 1 0.15 . 0.15

'a 0.1 -' 0.1 .- C ' 0.05 n 0.05 0) ._0) 0.2% max strain c 0 0 A S -80 -40 0 40 80 0 40 80 Field (kV/cm) Field (kV/cm)

x = 9 mol% Ba (T) 0.07 0.06 c- 0.05 0.04 (,-0.03 C *0 0.02 0) 0.01 0 0 -J -40 0 40 Field (kV/cm)

x = 12 mol% Ba (T) x = 12 mol% n 1 Ba (T) 0.25 U.ZD3 0.22% max strain , _, ...... , _ _ ... . _ _ _ _~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ _ I 0.2 F unipolar C 0.2

Cu 0.15 Unipolar C 0.15 - e0 0.1 C 0) 0.1 0) C: C 0.05 'O 0.05 0 0.21% 40.max .strain l- r i Im r 0 0 0 U -j -j -60 -20 20 60 0 40 Field (kV/cm) Field (kV/cm)

x = 14 mol% Ba (T) x = 14 mol% Ba (T) 0.25 - 0.25 0.23°%max strain unipolar 0.2 0.15 Unipolar 0.15 Co._ c 0.2 C 0.1 :) 0.1 ._ i: 0.05 . 0.05 C c 0.21% max strain o O -j 0 -j -60 -20 20 60 0 40 Field (kV/cm) Field (kV/cm)

Figure 3.34 Electrostrictive Strain (Bipolar and Unipolar) Versus Field for PE Phase NBT-xBT-4NBZ Polycrystals

100 Chavter 3 Res.ults__,,,,,, ,.: Cn-DnnedV YV VI -Pnljcruijtal.I V· - II-

NBT-xBT-4NBZ Polycrystals - I -I- 40 x= 7 mol% Ba (R) 1.5 33 pC/cm2 maxP 1 o 20

Co = -20 -5

o -40 -1.5 -80 -40 0 40 80 -100 -50 0 50 100 Field (kV/cm) Field (kV/cm)

x =9 mol% Ba (T) x = 9 mol% Ba (T) 20 - ' 0.6 16 pC/cm2 max P 04 E 0.4 10

.o; - x 10 4 °_ -0.6

& -20 - I -0.6 -40 -20 0 20 40 -50 -25 0 25 50 Field (kV/cm) Field (kV/cm)

x=12 mol% Ba (T) x 12mol% Ba (T) ' 37 pC/cm max P E 40 4

E -0-0-2 *0 -40 2

-60 -30 0 30 60 -80 -40 0 40 80 Field (kV/cm) Field (kV/cm)

x = 14 mol% Ba (T) x = 14 mol% Ba (T) E 20 26 pC/cm max P O-0.5

-2o 8 0 -30 -1 -60 -30 0 30 60 -80 -40 0 40 80 Field (kV/cm) Field (kV/cm)

Figure 3.35 Polarization and Current Versus Field for PE Phase NBT-xBT-4NBZ Polycrystals

101 Charter 3 Results I: Co-Doved Polucrustals

NBT-xBT-4NBZ Polycrystals

0.05 Hz, 1 MPa prestress 0o r-

c- ..J

-.- -80 -60 -40 -20 0 20 40 60 80 Field (kV/cm)

Figure 3.36 Predominantly Electrostrictive Bipolar Strain Versus Field for PE Phase NBT-xBT-4NBZ Polycrystal Series

40 30 EN0 20 o O- 10 0 -10 CU N0 -20 0~M. 0- -30 -40 -80 -40 0 40 80

Figure 3.37 Predominantly Electrostrictive Polarization Versus Field for PE Phase NBT-xBT-4NBZ Polycrystal Series

102 Chapter 3 Results I: Co-Doped Polycrystals

NBT-xBT-4NBZ Polycrystals

x = 7 mol% Ba (R) 500 0.25 400 - 0.2 300 c0.15 200 0.1 100 0.05 *416l1 Peak d33 425 pC/N * t 45 kV/cm 0 0 0 30 60 0 0.03 0.06 0.09 0.12 Field (kV/cm) p2 (C2/m4) x=9 mol% Ba ((T) 400 0.06

300 o 0.04 " 200 .C_ f 0.02 100 . QO, 2.1C 2/m4 0 0 0 10 20 30 0 0.01 -0.02 0.03 2 2 4 Field (kV/cm) p (C /m ) x= 12 mol% Ba (T) 600 0.2 500 0.15 400 300 0.1 v,.F 200 I= 0.05 Ql - 1.5 C2/m4 100 ,,* Peak d33 - 580 pC/N .- at 35 kV/cm 0 0 i. q, r I I I I I 0 10 20 30 40 0 0.03 0.06 0.09 0.12 50 2 4 Field (kV/cm) p (C2/m ) x = 14 mol% Ba (T) U.Zs 800 0.2 , ,, - I 600 * # 4 , '- 0.15 ~~~~~~ R 400 'O ' 0.1 e; Q - 3.0C 2/m4 200 C, 0.05 Peak d33 - 780 pC/N 35 kV/cm 0 0 w I , , 0 10 20 30 40 0 0.02 0.04 0.06 0.08 2 2 4 Field (kV/cm) P (C /m )

Figure 3.38

Electrostrictive Properties d33 and Q11 of PE Phase NBT-xBT-4NBZ Polycrystals

103 Chapter 3 Results I: Co-Doped Polycrystals

3.3.3 Pure Electrostriction in Highly Doped Polycrystalline NBT-26BT-29NBZ

High level Highly Ba2+ and Zr4' doping pushes compositions farther into the paraelectric phase field at room temperature. Table 3.2 shows that Tm

0 extrapolated to 0.05 Hz for NBT-26BT-29NBZ lies around 37°C (Tm(O.05Hz) 37 C), suggesting that room temperature actuation occurs within ~ 100C of the permittivity maximum. Correspondingly, sample p23a shows pure electrostrictive actuation behavior. No hysteresis is seen at 1 Hz (rather than 0.05

Hz), similar to the behavior observed for the Group I electrostrictor, PMN, at room temperature. However the achievable strain (0.01%)is much lower than that observed in PMN and the previously discussed co-doped NBT compositions. The polarization loop is highly linear with negligible hysteresis and the current loop is a nearly undistorted circle, consistent with pure electrostriction (Fig. 3.39).

104 Chapter 3 Results I: Co-Doped Polycrustals

E 100 Q. 1 Hz, 1 MPa prestress . O 80 C 60 C 40

c-0 20 n ...O -60 -30 0 30 60 Field (kV/cm)

20 w7

15 1.5

10 1

5 E 0.5 Cu 0 0 oE- N -5 L- -10 O °-1 Q. -15 -1.5 _ -20 -L~j -80 -40 0 40 80 -80 -50 -20 10 40 70 Field (kV/cm) Field (kV/cm)

Figure 3.39 Actuation, Polarization and Current Versus Electric Field for pure PE Phase NBT-26BT-29NBZ Polycrystal

105 Chapter 3 Results I: Co-Doped Polycrystals

3.3.4 Phase Diagrams for the Ternary System: Naj/2Bi /2TiO 3-BaTiO 3- Naj/2Bi /2ZrO 3

Figure 3.40 shows the room temperature isotherm for the ternary system

Na1 /2Bil/2TiO3-BaTiO3-Nal/ 2Bil/2ZrO3 based on the predominant actuation characteristic at 0.05 Hz. Ferroelectric rhombohedral, ferroelectric tetragonal, paraelectric rhombohedral, paraelectric tetragonal and field force phase transition regions are identified.

The temperature of the permittivity maxima at the zero frequency limit Tf may be used to plot the (frequency independent) phase boundary dependence on temperature. Figure 3.41 plots T versus mol % BaTiO3 for constant NBZ of 3 and

4 mol%. The phase boundaries suggested by T are 60-100 degrees above room temperature, suggesting that all the compositions studied here should be ferroelectric at room temperature. However, it has been observed in relaxor materials that the permittivity maximum does not represent a macroscopic phase change, for the depolarization temperature Tdis reached on heating before Tm

(see Section 1.2) [4]. Thus, local domains may be present, but macro domains may only be induced under applied field. The FFT behavior identified in NBT-

12BT-3NBZmay be an example of this phenomenon, although there seems to be an overprinting ferroelastic component in this system as well. Thus the micro- macro region begins to appear in the NBT-BT-NBZsystem for AT - 600C.

106 Chaptert 3 RuResults -:I: Co-D.vedCo-Doed Polurust...Polucrustals

Na1/2 Bi1/2 ZrO 3

Room Temperature Isotherm

.00

PER '\I PER* Q- PE

0 PER

3, T 0· FE FR FFTT FT

I I I 4 I I I I Na1/ 2Bi1/TiO 3 14 2 4 6 8 10 12 BaTiO3

mol% BaTiO3 -"

FR= (Predominantly) Ferroelectric Rhombohedral Phase FT = (Predominantly) Ferroelectric Tetragonal Phase FFTR = Field Forced Transition, Rhombohedral Phase FFTT = Field Forced Transition, Tetragonal Phase PER = (Predominantly) Electrostrictive Rhombohedral Phase PET = (Predominantly) Electrostrictive Tetragonal Phase 0 Characterized Composiiton

Figure 3.40 Partial Phase Diagram at Room Temperature for the Ternary System Na1/2Bi1/2TiO3 - BaTiO3-Na1 /2Bi1 /2ZrO3 Based on room temperature XRD and actuation behavior at 0.05 Hz.

107 CharterChar- 3 Results I: Co-Dov~ed- Polucrustals v

200 3 mol% NBZ 175 4 mol% NBZ o 150 -As - a) Q) 125 L 100 E 75 a, F- 50 25 0 0 2 4 6 8 10 12 14 16 NBT BT mole % BaTiO3 ,-

Figure 3.41

Partial Phase Diagram for Na1 /2Bi1/2TiO3 -BaTiO 3 at 3 mol% Na 1/2Bi1/ 2ZrO 3. Temperature of phase boundaries are based on Volger-Fulcher parameter Tf, where the permittivity maximum temperature Tm-Tf as f-0. Note that in relaxor materials, Tm or Tf does not necessarily represent a macroscopic phase transition (see Section 1.2).

108 Chapter 3 Results I: Co-Doped Polycrystals

Figure 3.41 shows that increasing Zr4+ doping levels begins to slightly depress Tm,corresponding to the stronger electrostrictive component to actuation observed in the NBT-xBT-4NBZcomposition series.

3.3.5 Temperature Dependence of Electrostriction

Figure 3.42 shows the trend in actuation as temperature is increased from room temperature above Tmfor predominantly electrostrictive, near-MPB, NBT-

8BT-3NBZ. At room temperature the actuation is predominately electrostrictive but highly hysteretic at 1 Hz, indicating the influence of the ferroelectric (and likely ferroelastic) component. Increasing the temperature above Tm

0 (extrapolated Tm(lHz) - 88 C) to 950and 1000C, the hysteresis decreases significantly as the sample passes farther into the pure PE phase (Group I) region. In this sample, as the electrostrictive component is further isolated, strain is slightly improved (increases by ~ 15%), suggesting that this family of compositions is characterized by an ultra-high electrostriction actuation component, similar to the B-site lead-oxide relaxors, PMN and PLZT.

109 - 3V Chanter..... r Chrrnter 3 Results I:: Co-DopedCo-Doed PoliVcrustalsPolcr~stals

NBT-8BT-3NBZ Polycrystal

1200

E Q 1000 ._

Cn 800

c~Co:L ._ 600

-.- rJ 0 400 -J 200

0 -50 -30 -10 10 30 50 Field (kV/cm)

Figure 3.42 Temperature Dependence of Actuation Behavior for Predominately PE Phase (Room Temperature) NBT-8BT-3NBZ

110 CharterCha...r3.Results.3 Results I Co-Dop~ed...-....d olucrustals-Pl-Jc....l..s 3.3.6 Comparison of Electrostrictive Properties

Figure 3.43 shows unipolar strain for the electrostrictive co-doped NBT polycrystalline compositions plotted with a PMN standard (PMN-15, TRS

Ceramics, State College, PA 16801). With higher saturation breakdown fields than PMN, co-doped NBT samples actuate at up to twice the strain as PMN and attain comparable d33 at high field (> 25 kV / cm) and 0.05 Hz. PMN reaches saturation at - 15 kV/cm, while the co-doped NBTs do not show signs of saturation until much higher fields, around 50 kV/cm. NBT-7BT-4NBZdoes not show signs of saturation even at fields approaching 70 kV/cm. The co-doped

NBTs show properties that are highly competitive with the conventional PMNs, especially for low-frequency applications, such as micro-positioning systems.

111 CatrCharter 3 RResults l I: CCo-Doed Polycrvstsals'

0.25

0.2

- .: 0.15

._, co

0 -J 0.05

0 2C 40 60 80 Field (kV/cm)

Figure 3.43 Comparison of Room -Temperature Electrostriction in Co-Doped Polycrystalline NBT to Polycrystalline PMN-15 (TRS Ceramics)

112

74 Chapter 4

Results II: Co-Doped Single Crystals

Compositional, phase, dielectric, and electromechanical data measured for single crystal samples will be presented and discussed in this chapter. These results show that (Ba, Zr) co-doped NBT single crystal compositions are a promising alternative to the conventional lead-oxide based polycrystalline and single crystal electrostrictive actuators.

4.1 Single Crystal Growth by Self-Flux Method

Single crystals of (Ba, Zr) co-doped NBT were grown by the flux method, using Na20Oand Bi203 as a self-flux. The crystal growth procedure is detailed in

Chapter 2. Figure 4.1 shows examples of as-grown crystal batches in platinum growth crucibles. Crystals show pseudo-cubic growth habit with (100) faces.

The largest crystals form up to ~ 2 cm on a side, however the crystal quality of the large crystals is generally poor, with many internal inhomogeneities including inclusions, cracks, and twin boundaries causing them

113 Chapter 4 Results II: Co-Doped Single Crystals

Figure 4.1 As-Grown Crystal Batches of (Ba, Zr) Co-Doped NBT to be nearly opaque. The large crystals usually split into smaller pieces due to their internal defects. Smaller crystals (2 - 5 mm on a side) are usually transparent, with markedly fewer inclusions and no internal cracks. Figure 4.2 shows some representative optical micrographs of polished crystal samples before testing. A low concentration of micro inclusions were present in all of the samples tested. Internal strain fields associated with defects such as inclusions could be detected in nearly all the crystals under crossed polarized light (Fig.

4.2). The intrinsic properties of the single crystal materials have not likely been realized, for crystal growth in this compositional system has yet to be optimized.

Ferroelastic domains have been identified in tetragonal phase samples.

They are identified as ferroelastic as opposed to ferroelectric domains because these crystals do not pole upon field cooling from 2000C to room temperature at

25 kV /cm. Correspondingly, they display predominantly electrostrictive

114 Chater...... --. 4- Results II: Co-Doped Single CrUstals actuation and polarization characteristics, which will be discussed in following sections.

plane of inclusions with surrounding strain field (bright) Phnmhrnhrnl ('rxicfclsaltcnmnhnz9;_q) \I III /I

'!P1

Reflected Light Side Light Crossed Polarized Light Tetragonal Crystal (sample sla)

Reflected Light

Crossed Polarized/Light

Ferroelastic domains from cubic --> tetragonal transition E C C Nu

Figure 4.2 Optical Microfeatures of (Ba + Zr) Co-Doped NBT Single Crystals

115 Chapter 4 Results II: Co-Doped Single Crystals

4.2 Compositionand Phase Symmetry Analysis

EPMA composition analyses (with the same accuracies as reported in

Section 3.1) of single crystal samples show that the exact nominal doping levels

of Ba2' and Zr4' were not reached in any of the crystals (Table 4.1). This is a typical result of the flux growth technique. As crystals nucleate out of the melt, the composition of the remaining melt is slightly altered. Crystallization occurs from a melt that is continually changing composition. Thus, it is common that each batch results in several crystals showing a range of compositions. Table 4.1 shows that crystal growth generally incorporated less Ba2' than the nominally mixed composition. Incorporation of Ba2' may be dependent upon cooling rate, as the fastest cooled growth (5°C/hr vs. 1.5°C/hr) incorporated up to 4 mol% greater Ba2' than the nominal composition. The cation Zr4' was incorporated at an apparently preferred amount of 4 mol% over the nominal 3 mol%. Nearly all of the crystals show an A-site cation excess. This may be explained by B-site nonstoichiometry or the presence of RP stacking faults in the perovskite structure, which was discussed in Section 3.1.

The symmetry of the perovskite phase, as determined by powder x-ray diffraction, for each sample is also listed in Table 4.1. Scans within the range 20-

90020 of single crystal faces and ground crystal powders confirmed that samples were single phase perovskite. Rhombohedral or tetragonal symmetry of

116 Charter4 Results II: Co-Doped Single Crustals ...... - oriented single crystals was determined by the presence (T) or absence (R) of pseudocubic (hOO)peak splitting. Figure 4.3. illustrates examples of x-ray diffraction scans for (hOO)oriented single crystals of rhombohedral and tetragonal symmetry. The identified phases for single crystal samples agree with the phase diagram constructed from polycrystalline sample compositions.

Table 4.1 Composition (EPMA) and Phase (XRD) for Co-Doped Single Crystals

compositions given in mole fraction (normalized to unity on B-site except where indicated by *) Sample Nominal (Na+Bi+Ba)/ ID (Ba/Zr) Na Bi Ba Ti Zr 0 (Ti+Zr) Symmetry sla 8/3 0.45 0.43 0.12 0.91 0.04 2.88 1.05 T slb 8/3 0.47 0.43 0.10 0.90 0.04 2.86 1.06 T s2a 8/3 0.50 0.45 0.05 0.94 0.04 2.94 1.02 R s2b 8/3 0.49 0.46 0.05 0.96 0.04 2.97 0.99* R s2c 8/3 0.49 0.45 0.06 0.95 0.04 2.94 1.01 R s4b 10/3 0.49 0.43 0.09 0.96 0.04 2.97 1.00 T

s4c 10/3 0.50 0.45 0.06 0.96 0.04 2.97 1.00 R s4d 10/3 0.49 0.44 0.07 0.94 0.04 2.94 1.02 R s5a 10/3 0.49 0.46 0.06 0.96 0.04 2.97 1.00 R s5b 10/3 0.50 0.44 0.06 0.89 0.04 2.80 1.08 R

* indicates composition was normalized to unity on the A-site R = rhombohedral, T = tetragonal

117 Chapter 4 Results II: Co-Doped Single Crystals

6000 4500 Tetragonal 4000 5000 3500 (200) 4000 3000 e) 2500 3000 o 2000 0o 0 2000 (002) 1500 1000 1000 (100) (001) 500 - I ._ o , , r - I , , , v 0o 20 30 40 50 60 70 80 90 100 20 30 40 50 60 70 80 90 100 Angle 2-Theta Angle 2-Theta

Figure 4.3 X-Ray Diffraction of (Ba + Zr) Co-Doped NBT [100] Oriented Single Crystals of Tetragonal and Rhombohedral Symmetry

4.3 DielectricProperties of (Ba + Zr) Co-DopedNBT Single Crystals

4.3.1 Room Temperature Dielectric Constant and Loss Tangent

Room temperature dielectric constants Er for single crystals in the NBT-

BT-NBZ composition system are on the order of 103and loss tangents range from

0.04 to ~ 0.08 for the 100-1000 kHz measurement range. Figure 4.4 shows a slight

trend toward maximization of the room temperature dielectric constant at the

MPB. The composition dependence is less clear for dielectric loss tangent.

118 Chantpr. 4L Results I: Co-Doed Sinqle Crystal -al-- rev .. - R-- n

_ _ 2000 _ _ 10 kHZ

1500

X 1000

MPB 500

I I I I I Il '

0 2 4 6 8 10 12 1 4

mol % BaTiO 3

0.1 10 kHZ 0.08

O 0.06

4-a 0.04 MPB 0.02

0 I I I I I I 0 2 4 6 8 10 12 14

mol % BaTiO 3

Figure 4.4 Room Temperature r and tan 5 Versus Ba2 + Concentration for Co-Doped (4 mol% Zr) NBT Single Crystals Oriented [100]

119 Chavter 4 Results II: Co-DovedSingle Crustals

NBT-xBT-4NBZ rhombohedral [100]

Heating0.1Rate: > 1200: > 10 > 100 > 1000 kHz Heating Rate: 200°C/hr tan 6: 0.1 < 1< 10 < 100 < 1000 kHz

s2b: 5 mol% Ba, 4 mol% Zr 0.3 3000 E8r 0.2 2000 increasing f tan 6 1000 / . 0.1

50 100 150 200 250 300 350 400 Temperature (C)

s4c: 6 mol% Ba, 4 mol% Zr s5b: 6 mol% Ba, 4 mol% Zr 4UUU U.Z0 .U.ZL

0.2 3000 0.2 3000 0.15 2000 // - 0.15 2000 0.1 - -0.1 1000 1000 -. .. 0.05 0.05

n n - - 50 50100 150100 200 250150 300 350200 400 250 300 350 400 50 100 150 200 250 300 350 400 50 100 150 200 250 300 350 400

Figure 4.5 Temperature and Frequency Dependence of Er and tan 6 for Co-Doped (Ba + Zr) NBT Rhombohedral Single Crystals Oriented [100]

121 Charter4 ChavrResultst II:4 Co-Doed-D Sinvle CrCrystals

NBT-xBT-4NBZ tetragonal [100]

Heating Rate: 200'C/hr Er: 1 > 10 > 100 > 1000 kHz tan 6: 1< 10 < 100 < 1000 kHz

sla: 12 mol% Ba, 4 mol% Zr s4b: 9 mol% Ba, 4 mol% Zr bUUU bUUU U.3 4000 0.6 5000 0.25 0.2 0.15 2000 increasing f tan 6000 0.1 9999~~~~~'I,~1000 0.05 0 10~~1 I1 I I I 00 0 50 100 150 200 250 300 350 400 50 100 150 200 250 300 350 400 Temperature (°C) Temperature (°C)

Figure 4.6 Temperature and Frequency Dependence of Er and tan 6 for Co-Doped (Ba + Zr) NBT Tetragonal Single Crystals Oriented [100]

4.3.3 Comparison of the Dielectric Constant and Loss Temperature Dependence in Single Crystals and Polycrystals

The overall shape of the dielectric constant and loss against temperature curve for single crystals correspond well with that of polycrystals of nearly the sample composition (same doping level of Ba2' and Zr4"), again, suggesting that the crystals also show relaxor behavior. The overall difference in magnitude of the permittivity and Tm(Figure 4.7) is likely due to anisotropy in the tetragonal crystal.

122 Chater 4 hatr Results I: Co-Doed Single Crustals

5000 Polycrystal (plOa):

Nao. 46Bio. 44 Bao. 12Tio.96Zro. 04 4000 Single Crystal [100] (sla):

'Nao. 4 7 Bio. 4 5 Ba 0 .12Tio.95Zro.04 3000

2000 leating Rate: 200 0 C/hr

1000 :r 1 > 10 > 100 > 1000 kHz

an 6: 1 < 10 < 100 < 1000 kHz 0 50 100 150 200 250 300 350 400 Temperature (C) -- 5 Single Crystal [100] (s4b):

5000 45 Nao. 4 9Bio. 43 Bao.0 9 Tio.97Zro. 04 4 Polycrystal (p9a): 4000 35 Nao.50 B io.4 5Ba o 9Tio0 96Zro 0 4 3 3000 25

2 2000 Heating Rate: 2000 C/hr 15 Cr: 10 > 100 > 1000 kHz 1000 1 05 tan6: 10 < 100 < 1000 kHz 0 50 100 150 200 250 300 350 400 Temperature (C)

Figure 4.7 Comparison of Temperature and Frequency Dependence of r and tan 6 for Co-Doped (Ba + Zr) NBT Tetragonal Single Crystals and Polycrystals

123 Chapter 4 Results I1: C-Doped Single Cystals

4.3.4 Volger-Fulcher Analysis

The Volger-Fulcher (VF) analysis was applied to single crystals of co- doped (Ba + Zr) NBT (see Section 3.2.3 for a discussion). Single crystal experimental data fits well to the VF equation, with relative errors ranging 0.7 -

3 % (Figs. 4.8 and 4.9). Table 4.2 lists the Volger-Fulcher Parameters calculated from the curve-fit equations. Tf shows some scatter for crystals with the same levels of Ba2' and Zr4' . This may be due to compositional differences between the samples in the other cation (Nal+, Bi3+, and Ti4+) levels as well as internal defects and inhomogeneities, which can enhance anisotropy and interfere with phase transitions, for example, by inhibiting domain wall motion.

In general, the crystals show the same trend in Tf with composition as the polycrystals, Tf decreasing as the MPB is approached from either the rhombohedral or tetragonal phase fields. Crystal sla (12 mol% Ba, 4 mol% Zr) shows remarkable agreement in Tf with its polycrystalline compositional counterpart plOa (860C 2 versus 890C ± 3). This suggests that the properties in this system are reproducible and strongly dependent on composition.

124 Chapter 4 Results II: Co-Doped Single Crstals

Co-Doped (Ba + Zr) Rhombohedral Single Crystals

b 0

b O Experimental Data x ...... VF nonlinear fit tE 4

log f [Hz]

8 I I I I s2b: 5 mol% Ba. 4 mol% Zr s4c: 6 mol% Ba. 4 mol% Zr 10

7 b .

b 8 X x E 6 E . lZ 17 Relative Error of Fit: 1% 6 Relative Error of Fit: 1% 5 I I I I 2 3 4 5 6 7 I I I I 2 3 4 5 6 7 log f [Hz] log f [Hz]

s5a: 6 mol% Ba. 4 mol% Zr s5b: 6 mol% Ba. 4 mol% Zr-

10 10 O b 1.), 0 o x 8 8 E x E 17 t Relative Error of Fit: 0.2% ,

6 6 2 3 4 5 6 2 3 4 5 6 7 log f [Hz] log f [Hz]

Figure 4.8 1/Tm as a Function of Frequency with Vogel-Fulcher Law Fit for Rhombohedral Phase Co-Doped (Ba+Zr) NBT Single Crystals

125 Results I: Co-Doed Sinqle Crstals Charter-- har 4 R : CD d Cts

Co-Doped (Ba + Zr) Tetragonal Single Crystals 10 s4b: -9 mol% Ba. 4 mol% Zr bo10 sla: 12 mol% Ba. 4 mol% Zr ? 8 8X

6-- 'Q _ E 6

Relative Error of Fit: 2% Relative Error of Fit: 3% 4I I I I 4 I I I 2 3 4 5 6 7 2 3 4 5 6 7 log f [Hz] o ExperimentalData logf [Hz] ...... VF nonlinear fit

Figure 4.9 1/Tm as a Function of Frequency with Vogel-Fulcher Law Fit for Tetragonal Phase Co-Doped (Ba+Zr) NBT Single Crystals

Table 4.2 Volger-Fulcher Parameters for Co-Doped NBT [100] Relaxor Crystals Doping Level Calculated Parameters from Extrapolation Volger-Fulcher Fit to 0.05 Hz Sample mol mol 10-3 Logf Rel. Tf Eactx 10-3 Log0 Error ID % Zr % Ba Tm (C) (°C) (eV) (Hz) (%) 15~~~~ s2b 4 5 119 15 9.8 1 126

s2a 4 5 121 15 8.5 2 129

s4c 4 6 79 10 7.6 1 85

s5a 4 6 93 2 6.4 0.7 94

s5b 4 6 94 2 6.4 0.2 96 ...... l...... lllllllllll...... l...... MlPB s4b 4 9 81 11 7.6 2 87

sla 4 12 86 11 7.2 3 93

l l

126 Chapter-Che- 4 ResultResults II, Co-DoedI: - Sinle CCrustals

4.3.5 Temperature Hysteresis in Dielectric Response

Significant temperature hysteresis in permittivity and dielectric loss tangent occurs in the region of the diffuse maxima (Fig. 4.10) for single crystals that is not observed in polycrystals. This may be related to anisotropy and/or internal inhomogeneities present in the single crystals that is not a factor in their isotropic polycrystalline counterparts. Crystal sla, which showed the closest correlation in dielectric response and Tf with the polycrystal of similar composition plOa, also displays the least temperature hysteresis. Crystal sla also exhibited the highest strain and d33. Thus, it is expected that its behavior should match the character of the polycrystalline response more closely and show

optimized actuation performance in crystals with minimal temperature hysteresis in dielectric properties. However, this crystal also shows the greatest hysteresis in dielectric loss at temperatures above the permittivity maxima. This,

again, may be due to internal defects that have increased contribution to loss at higher temperatures, suggesting that the response this crystal exhibited may still

not be optimized for the composition and orientation.

Crystals s5a and s4b show increasing permittivity above the second

maxima. This is likely due to the development of space-charge polarization

across the electrode [40].

127 Chanter 4 Results II: Co-Doved Single Crustals ----- - -- - V·"'Y'·I - Heating & Cooling Rate: 2000 C/hr s2a: 5 mol% Ba, 4 mol% Zr s2b 5 mol% Ba,4 mol% Zr 4000 V.l .

0.1 3000 3000 0.08 0.1 2000 2000 0.06

0.04 1000 , 0.05X > > ; 1000 0.02

0 0 0 0 100 200 300 400 500 50 150 250 350 45(iO Temperature (C) Temperature (C)

s4c: 6 mol% Ba, 4 mol% Zr 0 ---- s5a: 6 mol% Ba, 4 mol% Zr nJ 4 4000 ii U.4 4000I / 0.35 0.35 0.3 3000 0.3 3000I 0.25 0.25 0.2 2000 0.2 2000I IA1iE 0.15 0.1 1000 c,~~~~~~~~~~~~~~~~~~~ 0.1 1000 f" .i 0.05 0.05 c·· .,·" . . 0 I 0 Iu 0 5( 150 250 350 4450 50 150 250 350 450 Temperature (°C) Temperature (°C)

S;5b: 6 mol% Ba, 4 mol% 2-T n,9 4000I u.15

3000I 0.15

2000I 0.1

1000I I.6, ~ _11 /,~~~11 O.O

C o .. . , II U 50 150 250 350 450 Temperature (°C)

s4b: 9 mol% Ba, 4 mol% Zr 5000 sla: 12 mol% Ba, 4 mol% Zr 6000 0.3 50001- - - - T10 .3 0.25 5000 0.25 4000 0.2 400( 1 - 0.2 3000 0.15 300 10 / / : 0.15 2000 200 0.1 1000 I I 0.05 100( 0.05

n/ r . n n , - . -" I nAI._.,- I 50 150 250 350 450 0 100 200 300 400 Temperature (°C) Temperature (C)

Figure 4.10 Temperature Hysteresis in Dielectric Response at 10 kHz for Co-Doped (Ba + Zr) NBT Single Crystals Oriented [100]

128 Chapter 4 Results II: Co-Doped Single Crystals

4.4 ElectromechanicalProperties of (Ba + Zr) Co-DopedNBT Single Crystals

All crystal compositions studied here, with 4 mol% Zr, show predominantly electrostrictive actuation and polarization behavior at room temperature, similar to the behavior seen in the 4 mol% Zr polycrystalline series.

However, the single crystals achieve much higher actuation strain and field- induced d33than their polycrystalline counterparts.

4.4.1 Room Temperature Electrostrictive Properties of Tetragonal Phase Co-Doped NBT Single Crystals

Figure 4.11 summarizes the observed longitudinal strain versus field properties for tetragonal phase single crystals. Stain hysteresis loops are predominately electrostrictive in character but show hysteresis at 1 Hz.

Hysteresis becomes negligible at 0.05 Hz, as observed in the polycrystalline samples. Unipolar actuation is also parabolic against field (as opposed to the linear piezoelectric response), further supporting their electrostrictive classification. Crystal sla exhibited the maximum electrostrictive strain observed in this system of 0.45%, which is approximately twice the strain achieved (0.21%) in its polycrystalline compositional counterpart (Fig. 4.12). Crystal s4b showed more than quadruple the actuation strain achieved in the polycrystal of similar composition with a maximum longitudinal strain of 0.26% versus 0.06% at the same field (Fig. 4.13).

129 Chapter4 Results II: Co-Doved Single Crustals

0.5 0.45 - 0.4 c 0.35 ' 0.3 / 0.25 * 0.2 .: 0.15 o 0.1 j 0.05 0 -70 -45 -20 5 30 55 Field (kV/cm)

Figure 4.11 Strain Versus Field for Predominantly Electrostrictive Tetragonal Phase Co-Doped (Ba + Zr) NBT Single Crystals Oriented [100]

C.M

L5 a CO4-

0) 0C: -Iz)

v -70 -45 -20 5 30 55 Field (kV/cm)

Figure 4.12 Comparison of Predominantly Electrostrictive Actuation in Tetragonal Single Crystal [100] and Polycrystalline NBT-12BT-4NBZ

130 Chapter 4 Results II: Co-Doped Single Crystals

0.3

0.25

0 0.2

C 0.15

0.1 .C

o 0.05

0 -70 -45 -20 5 30 55 Field (kV/cm)

Figure 4.13 Comparison of Predominantly Electrostrictive Actuation in Tetragonal Single Crystal [100] and Polycrystalline NBT-9BT-4NBZ

131 Chapter 4 Results II: Co-Doped Single Crstals

Polarization and current loops are shown in Figure 4.14 for tetragonal phase co-doped single crystals. The polarization loops are quite linear with low hysteresis. The slight ferroelectric component is visible as a distortion in the predominantly circular current loops and is especially distinct for crystal s4b.

The polarization loop of crystal s4b compared to its polycrystalline counterpart p9a, qualitatively shows a greater FE component. This likely accounts for the exceptionally large increase (approximately by a factor of 4) in actuation exhibited by the crystal s4b compared to polycrystal p9a.

The ultra-high maximum polarization observed in crystal sla (also seen in certain rhombohedral crystals to be discussed in the next section) suggests that this material may have useful electro-optical applications. Leakage current does not appear to be a significant contributing factor to the high polarization values due to the nearly spherical current loops and low hysteresis in the polarization loops. However, more work is necessary to validate this data, as this ultra-high polarization is unique to this composition system.

Field induced d33 in NBT-BT-NBZ single crystals also far surpasses the polycrystalline compositions, reaching 2000 pC/N. The electrostrictive coefficient Q11lies in the same range as the polycrystals with values around 2-4 x

10-2 C2m-4. An exception occurs for the crystals with exceptionally high polarizations and large electrostriction, which correspondingly have Q11 on the order of 10- 3 C2m-4.

132 Chapter 4 Results II: Co-Doped Single Crystals

= 2 5U Pmax 98 C/cm a 0.8 i

'-_ · nn '.. Uv E UU o -0.4 0 50 E 0.2 - 0 iI! ._ 0 0 r ' -0.2 N -50 *C O -0.4 - .n vv I- I - / I 0, L- -L. I .-IV U.v -1;n -.n 8 -50 -25 0 25 50 -50 -25 0 25 50 Field (kV/cm) Field (kV/cm)

30 _ -__ . , .. i sla 1 i P, i E 20 i i ,_ 0.5 i O 0 i E i C: a 0 i .N 10 i

) -0.5- I 0 -0 -20

_,In - I I I I I _1 I I I I I -50 -25 0 25 50 -50 -25 0 25 50 Field (kV/cm) Field (kV/cm)

2 -- bu -A7.t I60 _ 2 cAh 1 A7 ,,r"/,.m --------"'-1"1 rmD -- I -ch-_ NE 40 E 0.5 O 20

E o .O C N -20 .N_ - -0.5 -' -40 )4 O

-60 , I -1 -50 -25 0 25 50 -50 -25 0 25 50 Field (kV/cm) Field (kV/cm)

Figure 4.14 Polarization and Current Versus Field for PET Phase Co-Doped (Ba + Zr) Single Crystals Oriented [100]

133 Chapter 4 Results II: Co-Doped Single Crustals

sla 0.25 2000 Peak d33 - 2000 pC/N *. at 35 kV/cm 0.2 0** 00 1500 - 0.15 * c CO 1000 0o.1 (0 +* vS*+^+ "r* 500 - 0.05 4 .,dA Q1 - 0.2 x 102 C2/m

,.^\ v 0 0 10 20 30 40 0 0.2 0.4 0.6 0.8 1 Field (kV/cm) p2 (C2 /m 4 ) sld 0.3 1400 Peak d33 - 1200 pC/N 0.25 1200 at 40 kV/cm 0s 1000 0.2 *: *0 .// c 800 A 0.15 600 * 0.1 400 * *+* ** . 0.05 200 * e,'~ 11- 4.3 x 10 ' C2/m4 * -U 0 ._ 0 . 0 *10 20 30 40 0 0.02 0.04 0.06 0.08 Field (kV/cm) p2 (C2/m 4)

s4b 0.25 2000 0.2 1500 '-' 0.15

CO 1000 Co 500 0) 0.05

0 0 0 10 20 30 0 0.05 0.1 0.15 0.2 0.25 Field (kV/cm) p2 (C2 /m 4 )

Figure 4.15

Electrostrictive Properties d33 and Q11 of PET Phase Co-Doped (Ba + Zr) NBT Single Crystals Oriented [100]

134 Chapter 4 Results II: Co-Doped Single Crystals

4.4.2 Room Temperature Electrostrictive Properties of Rhombohedral Phase Co-Doped NBT Single Crystals

Figure 4.16 summarizes the observed longitudinal strain versus field properties for rhombohedral phase single crystals. Stain hysteresis loops are predominately electrostrictive in character and also show negligible hysteresis at

0.05 Hz and parabolic unipolar actuation. Actuation strains range from -0.2% to

-0.3% in these crystals.

Crystal s4d (NBT-7BT-4NBZ)does not show significantly greater ultimately achievable strain compared to its polycrystalline compositional counterpart (0.23% versus 0.21%),however, the single crystal shows about twice the strain at 50 kV/cm as the polycrystal. Additionally, the single crystal shows no signs of saturation around 50 kV/cm, while the polycrystalline counterpart has already begun to saturate at similar fields (Fig. 4.17). Thus, the field induced d33 is much higher at - 930 pC/N versus - 425 pC/N (Fig. 4.19). Polarization is highly linear with little hysteresis and reaches up to 131pC/cm -2 (sample s2b), and the corresponding Qj1 values are an order of magnitude lower than the polycrystalline samples. The maximum field-induced d33 for rhombohedral crystals is - 1180pC/N at 40 kV/cm, still nearly double that of the polycrystalline counterparts.

135 Chaner·Chanter 4 Results~-Resuls III: C-ovedCo-Doed -- Sinlee Cr-stalsCrustals

0.35 s4c (0.05 0.3 s5a (0.05 0.25 C.. :5 c) 0.2 s4d (0.05 Hz)

0.15 .0 :11-0)=3 C: 0.1 0 z) _j 0.05

-70 -45 -20 5 30 55 Field (kV/cm) Figure 4.16 Strain Versus Field in Predominately Electrostrictive Rhombohedral Phase Co-Doped (Ba + Zr) NBT Single Crystals Oriented [100]

0.25

0.2 C

O0 0.15 c-

·' 0.1

j0 0.05

0 -75 -50 -25 0 25 50 75 Field (kV/cm) Figure 4.17 Comparison of Predominately Electrostrictive Actuation in Rhombohedral Single Crystal [100] and Polycrystalline NBT-7BT-4NBZ

136 Chapter 4 Results II: Co-Doped Sin le Crystals

- 150 s2b 2 1.5 il E 100 O 1 i 50 E 0.5 C 0 0 C 03 -0.5 -50 I NO . i -1 i -100 -1.5 I i~~~~~~ -15n -2 -75 -50 -25 0 25 50 75 75 -50 -25 0 25 50 75 Field (kV/cm) Field (kV/cm)

100 1.5 , iI s4c 80 PR i E o0 60 i 40 I 0.5 20 i c I E I 0 0 0 -20 C i -0.5 -40 N I- I -60 -1 Ii Q/, 0 OL I -100 1 -1.5 -75 -50 -25 0 25 50 75 -75 -50 -25 0 25 50 75 Field (kV/cm) Field (kV/cm) 100 2 s5a 15 N 80 Pmax= 82 pC/cm 1 0E 60 ( 40 0.5 ,- 20 <:Z zE C 0 v 0 O -20 c-C -0.5 N -40 I,,L. '- -60 4 0:: -1 -80 'K= 1.9 X 10 o Q_ -100 -1 .: :D i ,· .... i , i~ -75 -50 -25 0 25 50 75 -75 -50 -25 0 25 50 75 Field (kV/cm) Field (kV/cm) 150._A I s4d 1 N 0.8 E 100 0 0.6 0 50 < 0.4 o E 0.2 C 0 : 0 0 C ,) -0.2 CU -50 N - -0.4- (0) -0.6 cu-100 A o K=2x 10' -0.8 -150 -1 -75 -50 -25 0 25 50 75 -75 -50 -25 0 25 50 75 Field (kV/cm) Field (kV/cm)

Figure 4.18 Polarization and Current Versus Field for PER Co-Doped (Ba + Zr) NBT Single Crystals Oriented [100]

137 Chapter 4 Results II: Co-Doped Single Crystals

...... s2b ,\ n g . . .. . _. . _ ...... 600 U.zo ------.- _..- ._...... - . . Peak d33 - 540 pC/N *. 500 at 50 kV/cm . . #f 0.2 400 co, *0. 0.15 C- - 300 ._ 0.1 200 *s %*. W3

100 0.05 ' /)" 1 0.1 x 12C/

0 0 0 10 20 30 40 50 60 0 0.5 1 1.5 2 4 Field (kV/cm) p (C2/m )

1000 s4c 0.3 900 Peak d3 3 - 835 pC/N *. 800 at 45 kV/cm **.tS, 0.25 700 o 0.2 co) 600 V 500 0.15 400 . 300 t 200 ... , 0.05 100 0 0 0 10 20 30 40 50 60 0 0.2 0.4 0.6 2 2 4 Field (kV/cm) p (C /m ) s5a 1400 0.35 ------z I 1200 0.3 I

1000 0.25 I, CO 800 ° 0.2 - 600 · 0.15 400 '"" 0.1 200 0.05 0.5 x 102 C2/m 4

0 0O r l 0 10 20 30 40 50 0 0.2 0.4 0.6 0.8 Field (kV/cm) p 2 (C2/m 4)

1000 - s4d 0.25 Peak d33 - 930 )C/N 800 at 40 kV/cm 0.2

600 - 0.15 c * - 400 0.1 ** On 200 0.05 tt... 0 0 0 10 20 30 40 50 0 0.2 0.4 0.6 0.8 1 2 2 4 Field (kV/cm) p (C /m )

Figure 4.19

Electrostrictive Properties d33 and Q11 of PER Phase Co-Doped (Ba + Zr) NBT Single Crystals Oriented [100]

138 Chapter 4 Results I: Co-DopedSingle Crstals

4.4.3 Comparison of Electrostriction

Table 4.3 lists the properties of co-doped (Ba + Zr) NBT polycrystals and single crystals compared to the conventional lead-based electrostrictive materials. The material data show that this new NBT-BT-NBZfamily of relaxor electrostrictors are highly competitive in peak strain, Pmaxand d33, with the commercial lead relaxors PMNs, PMNTs and PLZTs. Although, as seen in Table

4.3, values of Q11 for polycrystalline NBT-BT-NBZcompositions and the lead- oxides are similar, the NBT-BT-NBZexhibit larger strain due to much higher induced polarizations. This can be seen to a much greater extent in the single crystals with very low Q11 (- 10-3).The highest actuation for tetragonal and rhombohedral crystals is observed in crystals that exhibit ultra-high induced polarization (80 - 100 C/cm2).

139 Chanter...--.- 4 Results II: Co-Doped Single Crustals

Table 4.3 Comparison of Polycrystalline and Single Crystal Electrostriction

Peak Peak d P x 102, Material Longitudinal P max 2 2 Strain, %

Single crystal [100] (tetragonal) 045 NBT-12BT-4NBZ Single crystal [100] (rhombohedral) 0.30 1180 82 0.5 NBT-12BT-4NBZ Polycrystal (tetragonal) 0.24 780 37 3.0 NBT-14BT-4NBZ Single crystal PMN [111]1 0.11 (R.T.) 213 30 1.15 [100]2 - - - 2.5

Polycrystal PMNT 3 0.16 (R.T.) 1100 2.5 0.12 (R.T.) 700 Polycrystal PLZT4 - 1030 2.12 8.8/65/35

BaTiO 3 11 PbTiO 3 8 PZN 2.4 1. S.G. Lee et al., Appl.Phys.Lett., 74 [7] 1030 (1999) 2. K. Uchino et al., J.Appl.Phys., 51 [2] 142 (1980) 3. www.TRSCeramics.com 4. Z.Y. Meng et al., J.Am.Ceram.Soc., 68 (8) 459 (1985)

140 Chapter 5

Conclusions

This research has developed a new family of Ba + Zr co-doped NBT relaxor ferroelectrics that may be compositionally tailored to shift the predominantly electrostrictive actuation phase to room temperature.

Single phase perovskite polycrystals were prepared through easy, conventional solid state processing techniques without the difficulties in cation volatilization and second phase pyrochlore stabilization common in the lead- based systems. Predominantly electrostrictive polycrystal relaxors in the NBT-

BT-NBZ system exhibit d33 properties that surpass the d33 previously reported for

NBT-BT [26] polycrystalline compositions by about a factor of six (780 vs. 125 pC/N), and are the highest reported lead-free polycrystalline actuators to date.

Peak actuation of the NBT-BT-NBZsurpasses even the conventional PMNs and

PLZTs [44, 45] (0.24% vs. 0.12-0.16%).

141 Chapter 5 Conclusions

Single crystals of [100] orientation in the NBT-BT-NBZcomposition family show exceedingly high electrostrictive strain, surpassing single crystal PMN [22,

46] by a factor of four. The [100] single crystals also show promising properties for electro-optical applications with ultra-high polarizations of - 100 uC/cm2 achieved at high fields (> 50 kV/cm).

Predominantly ferroelectric polycrystalline NBT-14BT-4NBZexhibit d33 -

310 pC/N making them competitive with PZT-8, PMNT and PZT 5a [34] at low frequencies (- 0.05 Hz). The mechanical quality factor Qm is lower for the NBT-

BT-NBZ compositions. However, this may be significantly improved with optimized processing conditions.

In conclusion, several key compositions have been identified in which the measurements to date show that actuation properties such as strain and d33 are highly comparable, at low frequencies, with values for the conventional lead- oxide piezoelectric and electrostrictive perovskites that currently dominate actuator device applications. These compositions deserve the attention of future investigations for full characterization. Further processing optimization may realize even higher properties than observed here. Continued exploration into this new composition system is also warranted, as the data presented here suggest that high actuation will be found for compositions lying along the

PET-FET phase boundary, and this boundary has yet to be fully explored.

142 Appendix I

Sample Testing Procedure

1. Photograph the "as-grown" crystal batch i.e. for flux growth, photograph the crystal batch in the crucible before excavation. 2. Determine the crystal orientation We are most interested in the (001) and (111) faces. a) Ideally, orient the crystal using Laue camera. b) Or, analyze the clean, as-grown crystal face with the powder x-ray diffractometer (Rigaku rotating anode x-ray generator with copper anode. Note: the best patterns are taken off of the clean as-grown crystal face; if the face has been cut or polished, the peaks are usually indiscernible, due to surface damage. 3. Cut and polish the sample* according to the required sample dimensions for the desired tests (equipment in 13-4011) Steps that refer to "sample," include both single crystal and polycrystalline samples See Table 1

4. Clean the prepared sample Several washes with acetone, then several washes with ethanol (or methanol) in the ultrasonic cleaner.

5. Measurement 1: Prepared Sample Dimensions a) Measure and record: (i) Length, width, thickness I x w x t (ii) Mass m (iii) Density p (if necessary; use Archimedes method) 143 Avvendix I Samvle Testinc Procedure

Table Al.1. Summary of Sample Geometry Requirements

indicates electroded surface

Sample Geometry Requirements Applicable Measurements

t < 3 mm · Permittivity & Dielectric Loss I t < 3 mm I Tangent shape may be irregular - vs.Temperature Temperature * Strain and Polarization vs. Field

Thick-Plate * Can be tested for resonance, but if it does show resonance, the modes may not be I------separable. w

Permittivity & Dielectric Loss 1>10t; w>lOt Tangent |0.3< t < 3 mm - vs. Temperature shape may be irregular, but side * Impedance vs. Frequency to surfaces must be I to faces determine k, Nt L I ,t,. nt-rIclL * Strain and Polarization vs. Field

t 1~~~~~~~~ w

Permittivity & Dielectric Loss > 2.5 t; > 2.5 w Tangent <3 mm -vs.Temperature *Note: Bar geometry is not ideal for capacitance measurements, so be aware that precision will be lower for these measurements. Bar /· Impedance vs. Frequency to D E determine k33, s33 , S3 3 , d33, g33,

t , m N,, /QY33, Y33

w * d33 vs. Temperature * Strain and Polarization vs. Field

144 AvvendixI Samnle Tesing Procedure

Table Al.1. Summary of Sample Geometry Requirements, continued

Sample Geometry Requirements Applicable Measurements

w > lt; 1> 5w; · Permittivity& DielectricLoss Tangent 0.3 < t < 3 mm - vs. Temperature * Impedance vs. Frequency to determine k31, k3,, kt, , S, k3 1-Plate t Y33, Y33, d3l, 31 N~ Nt

* d 31 vs. Temperature w · Strain and Polarization vs. Field

* Permittivity & Dielectric Loss a > lt Tangent 0.3 < t < 3 mm - vs. Temperature

Disk * Impedance vs. Frequency to determine kp, Np, N,

*polycrystalline · Strain and Polarization vs. Field samples only X

a (a = diameter)

145 Appendix I Sample Testing Procedure

6. Photograph the prepared sample a) Use the low-power (1 to 7) microscope to photograph the sample in: i. Reflected light (i.e.unpolarized light from above sample) ii. Side light (unpolarized) iii. Transmitted light (unpolarized and polarized, if different from unpolarized) iv. Cross-polarized transmitted light at different rotation angles about the optical axis b) Use the high-power microscope (objectives: 10 to 100) to photograph in plane-polarized and cross-polarized light c) Some Features of Interest: Quality of sample preparation (i.e. polished surface, shape) Crystal quality (presence or absence of internal defects) Defects: inclusions, cracks, internal inhomogeneities, boundaries, etc. Presence or absence of domains Internal stresses manifested as interference colors in cross-polarized light

7. Electrode the prepared sample a) Use the Pelco SC-7 Auto Sputter Coater to sputter gold electrode onto the appropriate, clean sample surfaces (see Table 1). b) The sides that are to remain free of electrode must be covered. Use scotch tape to cover them or coat them with Elmer's glue. c) Sputter Coater Settings: i. Argon cylinder regulator valve pressure: 0.3 bar (5 psi) ii. Argon pressure in chamber: 0.08 mbar iii. Sputtering current: 40 mA iv. Target to table distance: - 40 mm v. Pump vacuum to at least 0.05 mbar before initiating the coating cycle vi. Sputter coat sample for 5 minutes (300 s) on each side d) Refer to operation manual, located beside the sputter coater, for instructions on how to check and change settings.

146 AppendixI Sample Testing Procedure

8. Electrode Removal a) When the electrode must be removed after testing, or for any other reason in the meantime, try any of these techniques: i. Alternate between baths in the ultrasonic cleaner and gentle rubbing with cotton-tip applicator (use solvent of choice: acetone, ethanol, methanol, D.I. water, etc.) ii. Scratch off the electrode with a razor blade, being careful not to scratch the polished sample surface. iii. Where no other technique works, polish the electrode off with 1 gm abrasive.

9. Anneal the Electrode a) Anneal the electrode for better adhesion on the sample surface at either: (one or the other may be more appropriate, where volatilitization is a concern) i.3000C for 1 hour in air ii.400°Cfor 30 minutes in air

10. Measurement 2: Room Temperature Permittivity & Dielectric Loss Tangent Sample Geometries: all a) Hewlet Packard 4192A Impedance Analyzer. b) Measure R.T. (20-23°C)capacitance C and tan 6 at least for 1 kHz, 10 kHz, 100 kHz. You may also choose to do a log sweep over a large range of frequencies using the Testpoint ISPEC 2000 software programmed by Dr. Naoki Ohashi. Note: tan 6 may be referred to as the "dielectric loss tangent" or the "dissipation factor." It is denoted D in measurements with the HP analyzer. However, we will not use D for tan 6 in this document in order to avoid confusion with dielectric displacement D.

147 AvvendixAvvendix I SamvleSamle TestinY'Testing,Procedure Analysis of datafrom this measurementprovides: · Relative Dielectric Constant (Permittivity) Ct Ar or Notes: = £3 for our testing set-up where, £3T= relative dielectric constant at constant stress T = 0 t = sample thickness in m A = area of the electroded face in m2 permittivity of vacuum: 0 = 8.854 10-12F/m

* ElectricalQuality Factor(Qe) (at 1 kHz):

1 tan S

11. Measurement 3: Permittivity and Dielectric Loss Tangent versus Temperature at Different Frequencies a) Sample Geometries:thick plate (actually, any samples that are thick enough, t > 0.5 mm, to keep the electrodes from shorting and small enough to fit within the holding tube with inner diameter of 5 mm) b) Use Hewlet Packard 4192A Impedance Analyzer and the Omega Box Furnace (equipment is in 13-4096). This measurement is computer automated with Testpoint ISPEC 2000 software, programmed by Dr. Naoki Ohashi. c) Record capacitance C and tan 6 at least every 5 degrees within the range of 300C to 600°C at 0.1, 1, 10, 100, and 1000 kHz on both heating and cooling (upper temperature limit may vary based on your sample's behavior). Use the same rate for heating and cooling, in the range of 200C/hour.

148 Appendix I Sample Testing Procedure

Analysis of datafrom this measurementprovides: r vs. Temperature profile for a set of frequencies o The temperatures of phase transitions, in the case of broad maxima, the temperature of the permittivity maximum T(-max). Determine the transition temperatures using a Cauchy profile fit. From these temperatures, it is possible to build a composition- T(cmax)-frequency map.

o A measure of permittivity temperature hysteresis for each dT dt o A characterization of relaxor behavior: how does your sample compare to the classical relaxor behavior (diffuse, frequency (f)- dependent permittivity maxima)?

Illustration of classical relaxor frequency dispersion of permittivity maximum:

Temperature (C) -

The frequency () dispersion of the permittivity maxima can be described by the Vogel-Fulcher(VF) law of finite freezing temperature:

Tf = static freezing temperature (f-> 0)

E- Tmax= temperature of the permittivity f= fo exp -act maximum T(Fmax) B(Tmax - fo = attempt frequency Eact= activation energy kB = Boltzmann's constant = 1.38 x 10-23 J/K

149 ArAnnendixr..e..- .. . Samle-..r- Testinv---..' ---Procedurecedu Use a non-linear fit (Origin graphing software) to the following equation with your data for Tmaxandfto determine the adjustable parameters, Eact, f 0, Tf:

Eact Tm, (f) = T - c kB inf

12. Pole the Sample (equipment in 13-4135) a) Submerge the sample and a thermometer in a silicon oil bath. b) Heat sample 20-300C above T(Emax),then field cool (at a constant field) to 300C.

c) Electric Field = voltage > E = V sample thickness t d) Ideally, pole at a field about twice the coercive field. Where the coercive field is not known, try 2 kV/ mm. e) For samples that are difficult to pole, try increasing the field as the sample cools. Increase the field proportional to T- T where, T = temperature; To= temperature when the field is turned on, approximately 20-300C above T(cmax)

13. Measurement 4:

Room Temperature r after poling a) Has it decreased compared to the pre-poled value? By how much? b) The amount of decrease in Cr is a gauge of the degree of poling. If your samples shows little or no decrease, you may want to try to pole again, varying the field cooling conditions. Note: if your sample is predominantly electrostrictive, it will not pole; also, due to defects and other intrinsic characteristics, not all samples will be able to be poled to the same degree.

150 AppendixI Sample TestinQ Procedurev~~~~~ 14. Measurement 5: Resonance Measurement: Impedance versus Frequency

a) Sample Geometries: bar, k31-plate, kt-plate, disk b) Hewlet Packard 4192A Impedance Analyzer. This measurement is computer automated with Testpoint ISPEC 2000 software, programmed by Dr. Naoki Ohashi (equipment is in 13-4096). c) Example parameters for initial check for resonance: log sweep in the full range of frequencies. Where peaks are detected, examine at finer step intervals. Note: sample thickness must be greater than 0.3 mm so that the resonance peaks remain within the frequency range of the HP 4192A.

Analysis of datafrom this measurement provides: The electro-mechanical coupling factor: k Definitions (IEEEstandard notation): k= electrical energy input mechanical energy output

Zm= the minimum impedance p = density (kg /m 3) vE= Poisson's Ratio at constant electric field (*this notation is the only deviation from IEEE notion of aCE)

vE may be approximated for 0.2 < vE < 0.45 by:

a = [2.048+0.62(vE -0.30)]

where, v= 1psf is the velocity of a compressional wave in a slim bar normal to the poling axis (i.e. twice the frequency constant (frl) of such a bar)

151 --Annendixrr-·------I -'Samvle - ---Testing--- Procedure

fr = resonance freq. (zero susceptance); fa = antiresonance freq. (zero reactance)

fm = frequency of maximum impedance; fn = frequency of minimum impedance fl = the lower critical frequency, maximum admittance in a lossless resistor, which is equivalent to: fs = the frequency of maximum conductance for a real (lossy) sample

f2 = the upper critical frequency, maximum impedance in a lossless resistor, which is equivalent to: fp = the frequency of maximum resistance for a real (lossy) sample * For our resonators, we will assume that it is sufficient to use a measured value Offm orfr directly forf, and a measured value offn orfa directly for f2.

For simplicity, we will hereafter usefr (=fs =f) andfa (=fp =f2)

Af=fa-fr

fr,o A r I I a) ta) 0 C C CU c-O a) E 0- _ E i ~~~~Ima1

o Mechanical Quality Factor Qm at 1 kHz: also called the Damping Factor, it describes the mechanical losses. Qmis dependent on the mode of vibration:

fa 2zfr IZm C(fa2 fr )

152 Appendix I Sample Testing Procedure

o Thickness-Extensional Coupling Factor 'k or 'k33: kt-plate and k3 -plate ( x w electrode) geometries

Resonance at lower frequencies due to I and w vibrational modes will] likely be separable only if k3,-plate geometry requirements are met. 1 ,I.

tkt (highest frequency resonance) t / a 0 E

Frequency -

Calculated Constants (from kt resonance)

Frequency constant (thickness) N [Hz m = tfr (Controlling Dimension x Resonant Frequency)

153 Appendix I SampleTesting Proceure

o Rod Extensional Coupling Factor, Longitudinal Excitation 'k 3 3 : bar (w x t electrode) geometry

k33 (lowest frequency resonance)

/ ResonancEe at higher frequencie;s due to t and w vibrational modes will not likely be sieparable for bar a) a,O I ~ "'" [, ,.geometry. c- I 2 (D a)a=1. P i N) Frequency -

3 = k Lta( tan 2fa 2 fa

Calculated Constants (from Ik33 resonance/anti-resonance)

Elastic compliance at constant dielectric SD 1 displacement s [m 2 /N] 4Pfa2t2

Elastic compliance at constant electric field E D 2 s3E [m /N] 3 3 2

Modulus of Elasticity Y3, Y33 [N / m 2 = Pa] 1 1 (stress/strain) SD S33E

Piezoelectric strain coefficient dij [C/N = m/V] d33=k T (strain developed/applied field)

Piezoelectric voltage constant gij [Vm/N] d33 (open circuit field/applied stress) 9 0£3T o033

Frequency constant (longitudinal) Na [Hz- m] Na = fa (Controlling Dimension x Resonant Frequency)

154 Appendix I Samvle Testine Procedure

o Rod Extensional Coupling Factor, Transverse Excitation 'k31 : k3 -plate ( x w electrode) geometry wk

0a, C co "0 CLE E

Frequency '-

t1~

3 wkf - - k3I . VE *applies to polycrystalline Wk~l=31~~~ J1-ik~31 VI-3V 1-V samples only

Calculated Constants (from 'k31 resonance)

Elastic compliance at constant dielectric displacement D (1k ,E S D [m2/N] s1I= ( - k)11

Elastic compliance at constant electric field sE [m 2 /N] E 1 S 4fr 21 2

Modulus of Elasticity Y, YE [N/m 2 = Pa] 1 1 (stress/strain) D E

Piezoelectric strain coefficient dij [C/N = m/V] d -'k T E (strain developed/applied field) 31 31V E033 Piezoelectric voltage constant gij [Vm/ N] d (open circuit field/applied stress) g31 T 33

Frequency constant (transverse) N1 [Hz m] (Controlling Dimension x Resonant Frequency) NI = If = wfr

155 Annendix Samvle Testinv Procedure Ar"A " S..r ...... Pr-.... dur

Calculated Constants (from k33 & k 3l measurements) Hydrostatic Conditions:

dh [C/N] dh = d33 + 2d31

+ 2d 33 + d 3 gh[Vm/N]gg 33 2= gh [Vm/N] gh + 231 = E£03 .IT

o Other electro-mechanical coupling coefficients:

Corresponding to k3 -plate geometry (t x w electrode):

3 1

Corresponding to k3 -plate geometry (t x 1 electrode):

3 -*--/,*, 1

E E

where, A= X , and B= 13 NeEc 11 E + E m s EE **Note: s3 cannot be determined by resonance :......

156 AppendixI Sample Testinq Procedure

o Planar Coupling Factorkp: disk geometry *applies to polycrystalline samples only

where 'k31 is known: Ti1

· where k 33 & k t are known: k323tk2 + kp2+ kp2 k kp zkI k32 kt 2 2 kP Vk l+'k t

Calculated Constants (from kp resonance/anti-resonance) Frequency constant (planar) (Np) [Hz m] N = af (Controlling Dimension x Resonant Frequency) Frequency constant (circumferential) (No) [Hz. m] N = aa (Controlling Dimension x Resonant Frequency)

157 Samle Testing Procedure AvvendixAe II a . T

o Other electromechanical coupling coefficients *applies to polycrystalline samples only

Corresponding to bar geometry (t x w electrode):

3 k I k -A31 A is defined on page 12

15. Measurement 6: Resonance Measurement: Impedance versus Frequency with Temperature

a) Sample Geometries: bar, k31-plate b) Hewlet Packard 4192A Impedance Analyzer and the Omega Box Furnace. This measurement is computer automated with Testpoint ISPEC 2000 software, programmed by Dr. Naoki Ohashi. Analysis of data from this measurement provides:

· d33 vs. Temperature profile (bars)

· d31 vs. Temperature profile (k3 1-plates)

158 AvvendixI· I Samvle_ Testinq__ Procedure

16. Measurement 7: Other Electrical Measurements with HP 4192A a) Sample Geometries: bar, k3l-plate, kt-plate, disk b) Hewlet Packard 4192A Impedance Analyzer and the Omega Box Furnace. These measurements are computer automated with Testpoint ISPEC 2000 software, programmed by Dr. Naoki Ohashi. c) You can choose from a number of combinations:

Function (versus) Variable

IZI and angle equivalent Frequency * Can set a constant Bias (good for measuring the circuit: series and/or Oscillation Level sample resistance) (amplitude of AC signal) for the frequency sweep. * Can do a logarithmic or linear IYIand angle equivalent frequency sweep. circuit: parallel (good for measuring the circuit: parallel sample conductivity) Temperature

IZl: real &imaginary equivalent Temperature circuit:series + Frequency

IYI: real &imaginary equivalent Frequency · Oscillation Level = AC RMS circuit: parallel + voltage Oscillation Level * Stores matrix of data for frequency sweep and osc. level sweep

L (inductance)

C (capacitance) Can measure: Frequency * Stores matrix of data for + frequency sweep and bias C/Q Bias sweep. C/D C/[R/G]

159 Appendix I Sample Testing Procedure

17. Measurement 8: Strain versus Field a) Sample Geometries: all b) Laser interferometer strain testing system (in 37-372 - AMSL Laboratory). You will need to sign up to reserve: PiezoPark (the computer), the Optics Bench, the Trek Amplifier, and Function Generator. c) Set the amount of pre-stress applied to the sample to 1 MPa: amp areaF where, F = force measured with the load cell. sample area d) Record elongation (m), voltage and current to a matlab file: *.mat. e) Measure elongation versus field: i. for a wide range of frequencies (0.01 Hz - 100 Hz) ii. for different levels of pre-stress (up to 100 MPa)

iii. Make unipolar plots with E applied along P r (check the direction at low fields by observing the elongation response from a positive field). iv. Make bipolar plots, however note that going above coercive field Ec may de-pole the sample. Analysis of datafrom this measurementprovides:

· Achievable total strain (versus field)

strain: = Ax where, x = the distance between electroded faces

x0 Ax = x - x0 and S is positive for sample extension

· Effect of Pre-Stress Levels * Coercive Field (Ec) · Polarization versus Field o Integrate the current in time and divide by the sample area. Note: Although we actually measure dielectric displacement D when we integrate the current, for our samples K/c 1, thus D P and we will hereafter refer to polarization without subtracting the negligible term c0E.

160 Appendix I Sample Testing Procedure

K = susceptibility P= Q/A P = polarization, equal to surface charge density (C/m2) Q = charge (C) A = sample area (m2) D = E + P = o+ KE = E i = dQ/dt i = current (A C/s)

i Hysteresis Loop for Hysteresis Loop for a Classical Polycrystalline Ferroelectric Ferroelectric Single Crystal ID 50 Ps

S U U

E 0 0

CL.

cur -U50 0 50 et 1. (1971) Field (kV/cm) Pr = remnant polarization

Ps = spontaneous polarization (obtained by extrapolating from the linear high-field response back to zero field)

Ps is somewhat higher than Pr in polycrystals, but Ps, Pr in classical ferroelectric single crystals

161 Appendix I Sample Testinq Procedure

* d33

o Notes on measuring d33 from strain vs. field plots:

i. Only measure d33 at full saturation (where there is no hysteresis):

0.12 (133 0.10 0.08 .5 0.06

0.04 I 0.02 0 -50 4 ft 50 Field(kV/cm)

Coercive Field E, determined as the field at the onset of the highest clnno in t-rninxrC fioll

ii. If the sample is inherently hysteretic, report d33 + hysteresis:

hysteresis = areaofstrain loop: E , 7 total area unllr' cIlr1 : [I -i a e- I- -W'E (n·r V)

o Field

162 Avvendixd I Samleml TestinTestinQ, Procedure

18. Measurement 9: Composition Analysis a) JEOL Electron Microprobe. b) Remove electrode (see step 8). Samples will have to be carbon coated prior to analysis.

19. Measurement 10: Further Microscopic Analysis a) TEM & STEM, located in the CMSE Electron Microscope Facility (Rm. 13-1012)http: / / prism.mit.edu / b) For this analysis, the sample must be polished to 50-80 gm, then argon ion milled. **Thisanalysis should be saved until all other possible characterization measurements have been completed. c) TEM: used to analyze crystallographic structure and observe nanoscale features, noting whether these features are periodic and commensurate with the single cell perovskite lattice. For example, in NBT we observe both superlattice reflections with periodicity of two times the single cell perovskite lattice and also 3.4 nm wavelength modulations. d) STEM:used to construct nano-scale composition maps.

163 164 Appendix II

Procedure For Preparation of 5% PVA-H2 0 Solution

1. Start a hot water bath by placing a secondary container (glass dish) partially filled with tap water on hot plate (with magnetic stirring feature). Add a thermometer and maintain the bath temperature at 75C.

2. Of the desired total mass, weigh into a beaker: 5 wt% PVA (polyvinyl alcohol, hydrolyzed) and 7.5 wt% glycerol. Allow the glycerol to completely

wet the PVA powder before continuing to add the remaining 87.5 wt% H20 constituent.

3. Add a magnetic stirrer to the solution and place the beaker into the water bath (750C).

4. Cover the beaker with a glass dish in order to prevent excessive H20 evaporation during the process. You may want to mark the initial level of the

H20 solution so that you can subsequently refill with H20 if there is substantial evaporation.

5. Stir slowly (setting the stir plate on low speed) at 75C for 3 hours.

165 Armendix--Annendix [F!I RelativeReatv ToleranceToeac Factorato Avroachvrah ...

6. Watch the solution closely for at least the first 30 minutes. If a PVA film, or "skin" forms on the surface of the solution or around the edges of the beaker, use a glass stir rod to break up the film until the solution appears homogeneous.

7. Check the solution every 30 minutes or so until 3 hours have passed. The solution should be clear with no film residue.

8. Allow the homogeneous, clear solution to cool.

9. Pour the PVA-solution into a plastic container, seal and store in a relatively cool location. The solution should stay fresh for at least a month. As the solution ages, check for evidence of mold before using. This is a sign that you should mix a fresh batch.

166 Appendix III

Relative Tolerance Factor Approach to Perovskite Structure Prediction

The optimization of piezoelectric properties at compositions near the

morphotropic phase boundary MPB between rhombohedral and tetragonal

perovskite symmetry has been observed in many ferroelectric perovskite solid

solutions including the Pb(Ti,Zr)03 (PZT) and Na1/Bij/2TiO3-BaTiO3 (NBT-BT)

systems [9, 47]. Within one compositional system, piezoelectric properties may

also be enhanced with the addition of dopants with higher ionic polarizabilities,

aliovalent charges to induce vacancies, ionic size differences to manipulate

structural distortion, etc. However, the ability to predict the phase of a particular

composition and, correspondingly, where the MPB lies, is largely inhibited by

lack of detailed phase diagrams for many of these composition systems.

167 Appendix III Relative ToleranceFactor Approach...

A novel method has been developed which applies the Goldschmidt tolerance factor as a relative guide in systems with known MPB compositions to successfully predict the phase and, thus, the location of the MPB in new systems.

Goldschmidt Tolerance Factor

The ideal cubic (1:1)perovskite structure (ABO3) is composed of atoms in the following positions: A-site cation in (0 0 0); B-site cation in ( 1/2 ); oxygen anion in(/2 ½/20), (/2 0 ½/2),(0 /2 /2)(Fig. AIII.1). The A and B cations have coordination numbers (CN) of 12 and 6, respectively. The classic relation by

Goldschmidt called the tolerancefactor(t) defines the allowable limits of distortions in interatomic distance if the perovskite structure is to be maintained[48]. It is defined as

t= (RA + RO )

x2(R B + RO) where, RAis the average A-site cation radius, RBis the average B-site cation radius, and ROis the oxygen anion radius. Deviations from t=l1represent distortions from the ideal cubic perovskite structure. The stability range is approximately 0.75 < t < 1.06, with ferroelectric behavior generally associated with t > 1 [49].

168 ApendxApp-Ii-i II RelativeeaieTlrneFco Tolerance Factor Avroachvrah. ...

RA + Ro:

B-Site (1/2, 1/2, 1/2) O O-sites (/2, ½,0); (2, 0, /2); (0, 1/2, /2) + m * A-site (0,0,0) r,~ ... RA = A-site cation radius (avg.) PR = PRitfP rnftinn rliie {/ln \ Ro = Oxygen ion radius

Figure A111.1 4 Illustration of the Ideal Cubic Perovskite Structure (A2+B +0 3) The cubic perovskite structure may be considered as a Cubic close packed arrangement of A and O ions, with B ions filling the interstitial positions

Limitations to the Goldschmidt Tolerance Factor

The tolerance factor, thus, should be a useful guide for structure prediction of ABO3 perovskites. However, this relation is based on a simplified atomic model, assuming purely ionic bonds and rigid-sphere ions. It has been shown that even ideal cubic perovskites show some degree of cation and anion interpenetration, with overlap constituting approximately 2-3% of the ionic radius sum [50]. Also, some degree of error is present in any table of calculated ionic radii due to the fact that the effective ionic radius is not constant between all crystals. The ionic radii data set for all possible coordination numbers is incomplete for certain ions. For example, the CN 12 radius of Bi3+ is not available in even the most recent tables [49]. There are additional complications with

169 AvvendixAlenil IIII RltvRelative TlrneFcoAloah.Tolerance Factor Avroach ... attempts to apply this relation to the more complicated solid solutions of the complex perovskites, such as Naj/2Bij/2TiO3-BaTiO3 in which more than one or more cations occupy the A- and/ or B-sites.

Due to these physical limitations, the absolute value of t calculated for various perovskites will vary greatly and cannot be used reliably as a predictor of structure or phase. For example, while the tolerance factor predicts ferroelectric phase for t > 1, the calculated tolerance factor (using a value for the

Bi3' ionic radius extrapolated from CN8 data [49] to an estimated value for

CN12) for ferroelectric phase NBT-BT is 0.9698, which is less than unity.

The Relative Tolerance Factor to Predict Structure in Complex Perovskite Systems

In this research, it was recognized that the relativetolerance factor is a useful guide to predicting structure for novel doping of an end-member where the MPB is known for one or more other solid solutions with that particular end- member. The use of a relative tolerance factor eliminates the error associated with the calculated ionic radii, which is especially useful in the NBT-based systems which assume an additional absolute error due to the lack of data for

CN12 Bi3' . Figure AIII.2 shows that for NBT in solid solution with four different end-member cases, the tolerance factor calculated for the known MPB composition in each of these systems is nearly the same value (0.976± 0.001).

170

__ ___II__ Appendix III Relative Tolerance Factor Approach...

0.985 - 0.984 0.983 0.982 0.981

4 0.980 " 0.979 -8 0.978 L[ 0.977 { 0.976 2 0.975 O 0.974 1- 0.973 0.972 0.971 - 0.970 - 0 .969- ] , I , I , I , I , I , I , I , I , I , I , I 0.04 0.05 0.06 0.07 0.08 0.09 0.10 0.11 0.12 0.13 0.14 0.15 0.16 Fraction of Dopant in NBT

-+ * Indicates MPB composition-range

* NBT-BT6 (NaOsBi5 0.5)0 94 Bao 6Ti03 A NBT-KBT8* NaO.42Ko.Bio.TiO3

* NBT-PT14 (N ao.BiO.5)0.86Pb0 1. 4Ti 03

* N BT-PTBT9 (Nao.5Bio 5)0.91(Pbo.5Bao5)o.oTiO 3 * The biphasic region in this system is reported within a range of KBT dopant fraction of 0.08 < x < 0.3. However, d33 and kp are maximized in ceramic compositions of NBT-KBT8.

Figure A111.2 Calculated Tolerance Factor Versus Dopant Fraction in NBT-Based Solid Solutions with Known MPB Compositions The tolerance factor of the MPB composition for each of the systems lies within a narrow range of t = 0.9755 - 0.9775. MPB data reported in sources: [26, 28, 51, 52]

171 Appendix III Relative Tolerance Factor Approach...

Thus, it was hypothesized that the MPB composition could be estimated for a new solid solution with NBT by tailoring the dopant levels for tolerance factors within the range observed in Figure AIII.2 of t = 0.9755 - 0.9775. For t << 0.9755, where the average ionic radii of the B-site is expanded (from the

MPB ratio) relative to the A-site, rhombohedral structure is predicted.

Conversely, for t >> 0.9755-0.9775, where the average ionic radii of the A-site is expanded (from the MPB ratio) relative to the B-site, tetragonal structure is predicted.

This method of complex perovskite structure prediction through the application of a relative tolerance factor is shown by this work to be successful in targeting the MPB for the new relaxor family of compositions NBT-BT-NBZup to at least 26 mol% Ba and 29 mol% Zr, as confirmed by XRD analyses. An example of the relative tolerance factor prediction applied to a constant doping level of 3 mol% Zr is shown in Figure AIII.3. As Ba2 ' is systematically increased from 4 to 14 mol%, the relative tolerance factor method predicts that the MPB should fall near 8 mol% Ba. XRD analysis and determination of perovskite phase by the pseudo-cubic (hOO)peak splitting corresponds closely to the prediction.

172 Appendix III Relative Tolerance Factor Approach...

NBT-XBT-3NBZ Predicted Target for MPB: It = 0.9755 - 0.9775[ Peak (200) 2-Theta Range: 44.750 - 480 {Background & Ka2 Subtracted; Filtered}

I I I I - ,

j I

I . 1.1, . 1 11 1 I l-TH·~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ I I~ I ~~ ~ ~ ~ ~ I I I ~ 1 )~~~ I~~~~~~~~~~~~~~~~~~~~~~~~~rmIII

. PA_

I I

I 5 45 4 75 4725 475 I I I I-I In

S I

U15155 uln rsTI 111- I'll .11, .1 a I Ih"I I 11 .I- 1-

Figure A111.3 Calculated Tolerance Factor for Compositions NBT-xBT-3NBZ with Target Relative Tolerance Factor for NBT-Based Systems Comparing calculated tolerance factors to the relative MPB tolerance factor for NBT-based systems allows prediction of phase in the system NBT-BT-NBZfor which the phase diagram is unknown.

173 Appendix III Relative ToleranceFactor Approach...

This method is a useful tool the prediction of MPB compositions, especially in those systems where properties are optimized along the MPB. It may also prove useful for future investigations of the FE-PE boundary, which this work has shown to be a zone of optimized properties in the relaxor NBT-BT-

NBZ composition system.

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