Dielectric and Electromechanical Properties of
Barium and Zirconium Co-Doped Sodium Bismuth Titanate
by
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
© 2000 Massachusetts Institute of Technology. All rights reserved.
Signature of Author:
1
7
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_
·
Department of Materials Science and Engineering
August 4, 2000
Certified by: _
J
-
/'et-Ming Chiang
Kyocera Pr'fessor of Ceramics
Thesis Supervisor
Accepted by:
C
-
I Carl V. Thompson
Stavros Salapatas Professor of Materials Science & Engineering
Chairman, Departmental Committee on Graduate Students
INSTftE
MASSACHUSETTS
OF TECHNOLOGY
OCT 2 6 2004
LIBRARIES
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ARCHIVES
Dielectric and Electromechanical Properties of
Barium and Zirconium Co-Doped Sodium Bismuth Titanate
by
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 d33 of 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
1.1 Piezoelectricity, Electrostriction and Ferroelectricity
1.2 Relaxor Complex Perovskites-1.3 Lead-Based ElectromechanicalMaterials
1.4 Alternatives to Lead-Based ElectromechanicalMaterials
1.5 Research Objective.........................
13
................... 13
......................................
15
19
20
22
Chapter 2.
Experimental Procedure
..........................
2.1 PolycrystallinePowderPreparation
..
2.2 Single Crystal Growth.............................
2.3 Polycrystaland Single Crystal SamplePreparationfor Testing.
2.4
25
.
26
31
36...............
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 -----------------------2.4.4 Dielectric Characterization
39
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 -----------------------3.1 Composition,Phaseand Density Analysis---------------------------3.2 DielectricPropertiesof Polycrystalline(Ba+ Zr) Co-DopedNBT
61
51
51
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 Electromechanical
Propertiesof Polycrystalline(Ba + Zr) Co-DopedNBT..72
3.3.1 Room Temperature Electromechanical Properties of
Polycrystalline NBT-xBT-3NBZ
-------------------4
- 73
.
3.3.1.1 Predominantly Ferroelectric Actuation -----------------------------------75
82
3.3.1.2 Field-Forced Transition (PE-FE) --------------------------3.3.1.3 Predominantly
Electrostrictive
Actuation -----------------------------------94
3.3.2 Room Temperature Electromechanical Properties of
Polycrystalline
NBT-xBT-4NBZ -----------------------3.3.2.1 Predominantly
Electrostrictive
98
Actuation ------------------------------------
99
3.3.3 Pure Electrostriction in Highly Doped Polycrystalline
NBT-26BT-29NBZ
3.3.4 Phase Diagrams for the Ternary System:
104
------
106
.................
109
Na1/2Bi1 /2TiO3-BaTiO3-Nal/ 2Bi1 /2ZrO3 ...............................
-
3.3.5Temperature Dependence of Electrostriction
3.3.6 Comparison
of Electrostrictive
111
Properties ----------------------
Chapter 4.
113
Results II: Co-Doped Single Crystals......................
4.1
4.2
113
Single Crystal Growth by Self-Flux Method.............................
Composition and Phase Symmetry Analysis .116
4.3 DielectricPropertiesof (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
120
and Loss Tangent ......................
4.3.3 Comparison of the Dielectric Constant and Loss Temperature
Dependence in Single Crystals and Polycrystals .
4.3.4 Volger-Fulcher Analysis......................
4.3.5 Temperature Hysteresis in Dielectric Response .
4.4
122
..................
124
127
.......................
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
Appendix
141
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 .
Bibliography.
......................................................................
167....
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
Figure 2.3
Model 590 Tripod PolisherB South Bay Technology, Inc.-
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
35
37
....................
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
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
6
r
at 10 kHz for Polycrystalline Co-Doped NBT ........ 62
at 0.1, 1, 10, 100, 1000 kHz -----------------------------------------66
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
Figure 3.9
1 /Tm as a Function of Frequency with Volger-Fulcher Law Fit for
NBT-xBT-3NBZ
Figure 3.10
Figure 3.11
Figure 3.12
67
69
1 /Tm as a Function of Frequency with Volger-Fulcher Law Fit for
NBT-xBT-4NBZand NBT-26BT-29NBZ
70
Trend in Acutation and Polarization Character for 3 mol% Zr4+
with Increasing Ba2+ in Co-Doped NBT Polycrystals
74
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 ------------------------------------
Figure 3.15
Figure 3.16
Figure 3.17
Figure 3.18
Figure 3.19
Figure 3.20
77
Strain (Bipolar and Unipolar) Versus Field for FTPhase NBT-14BT-3NBZ
Polycrystal
-----------------------------------------
79
Polarization and Current Versus Field for FT Phase NBT-14BT-3NBZ
Polycrystal ------------------------------------
79
Resonance Analysis (Zero Bias) in Poled FTPhase NBT-14BT-3NBZ
Polycrystal with Disc Geometry ------------------------------------
80
Low Field Electrostrictive Strain (Bipolar) Versus Field for FFTRPhase
NBT-6BT-3NBZPolycrystal-------------------------
84
Low Field Polarization and Current Versus Field for FFTRPhase
NBT-6BT-3NBZ Polycrystal------------------------
84
Low Field Electrostrictive Properties d33 and Qn
1 of FFTRPhase
NBT-6BT-3NBZ Polycrystal -------------------------
85
Figure 3.21
Evolution of the Field-Forced Phase Transition with Increasing Field
in FFTRPhase 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
Low Field Polarization and Current Versus Field for FFTTPhase
NBT-12BT-3NBZPolycrystal -----------------------------------------
90
Low Field Electrostrictive Properties d33 and Qll Field for FFTT Phase
NBT-12BT-3NBZPolycrystal --------------------------------
91
Figure 3.24
Figure 3.25
7
Figure 3.26
Evolution of the Field-Forced Phase Transition with Increasing Field
92
for FFTT Phase NBT-12BT-3NBZ Polycrystal- -------------------------
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 PETPhase NBT-1OBT-3NBZ
Polycrystal-----------------------Figure 3.31
-
Electrostrictive Strain (Bipolar and Unipolar) Versus Field for PET
Phase NBT-8BT-3NBZPolycrystal.-.....................
Figure 3.32
Polarization and Current Versus Field for PETPhase NBT-8BT-3NBZ
Figure 3.33
Electrostrictive Properties d33 and Q,1 of PETPhase NBT-8BT-3NBZ
Polycrystal
-----------Polycrystal -..
Figure 3.34
Figure 3.35
Figure 3.36
Figure 3.37
Figure 3.38
97
97
........................................................
98
Electrostrictive Strain (Bipolar and Unipolar) Versus Field for PE
Phase NBT-xBT-4NBZPolycrystals-....................
100
Polarization and Current Versus Field for PE Phase NBT-xBT-4NBZ
Polycrystals
101
.
Predominantly Electrostrictive Bipolar Strain Versus Field for PE
Phase NBT-xBT-4NBZ Polycrystal Series ...............................................
102
Predominantly Electrostrictive Polarization Field for PE
Phase NBT-xBT-4NBZ Polycrystal Series--...............................
102
Electrostrictive Properties d33 and Qn
1 of PE Phase NBT-xBT-3NBZ
Polycrystals--
,,,,,,,,
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
Na 1 /2Bil/2TiO3-BaTiO3-Nal/ 2Bi,/ 2ZrO 3...........................
- .........................
Figure 3.41
96
103
107
Partial Phase Diagram at Room Temperature for Naj/2Bij/2TiO3-BaTiO3
at 3 mol% Nal/ 2Bi,/ 2ZrO3 -------------------------------------------------------------------- 108
Figure 3.42
Figure 3.43
Temperature Dependence of Actuation Behavior for Predominantly PE
Phase (Room Temperature) NBT-8BT-3NBZ
-...................
110
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/Tmas 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]-------------------------
Figure 4.15
133
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]-------------------------
Figure 4.19
137
Electrostrictive Properties d33 and Q,1 of PERPhase (Ba + Zr) Co-Doped
NBT Single Crystals Oriented [100]------------------------
138
9
Figure AIII.1
4 +0 )------------ 169
Illustration of the Ideal Cubic Perovskite Structure (A2+B
3
Figure AIII.2
Calculated Tolerance Factor Versus Dopant Fraction in NBT-Based
Solid Solutions with Known MPB Compositions --------------------
Figure AIII.3
171
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 YetMing 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 microposition-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,Electrostrictionand 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
- in simple oxides and 10-6 in oxide perovskites [11]. However, some
of 1011
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
Charter1
Chve
.
.
.
.
t.o
.Introduction
.
.
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
U
0
0.25
0
0.15
0.2
4")
Cu
0.1
:I.
r
'A
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)0 3 (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
.
.
.
.
.
.
.
Introduction
d.......
(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
1.3
Introduction
Lead-Based ElectromechanicalMaterials
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)O
3 (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-BasedElectromechanicalMaterials
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/2TiO
3 (KBT),
BaTiO3, CaTiO3, SrTiO3 , and PbTiO 3 [26-29]. Compared to lead perovskites, NBTbased 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 weight20
Chapter1
Introduction
based actuation applications [26]. The strain energy density emax
is a measure of
the device energy output per unit mass [21]:
e
emax
2
S max
8'
where, G is the elastic modulus of the actuator, Smax
is the maximum fieldinduced 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 edgedefined film-fed growth [30]. Flux grown NBT-BTcrystals 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-BTsingle 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°Cat 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 (micromacro) 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/2TiO
3BaTiO3-Na1 /2Bi,/2ZrO3 solid solution. The abbreviation NBT-xBT-yNBZwill be
used, where x and y represent mol% Ba and mol% Zr, respectively.
25
Chanter
Chavtr22E-rmnal
2.1
Exvzerimental Procedure
Prcdr
PolycrystallinePowderPreparation
High purity (>99 % purity), ultra-fine grain size (< 1 pm) starting powders
of Na 2CO3, Bi203, BaCO3, TiO2, and ZrO 2 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
Exerimental
Procedure
Procedure~~~
Exver~~Imental
Chavte~~~~~r
Table 2.1
Nominal Batch Compositions for (Ba + Zr) Co-Doped Polycrystals
(Na1/2Bi1/2)1_xBax(Ti_yZry)03
mole fraction
Ba2+(x)
mole4 fraction
Zr + (y)
p12
0.09
0.09
0.03
p13
0.11
0.05
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
Batch ID
mole2fraction
+
mole4fraction
Zr ()
Batch ID
p1
0.04
0.03
p2
0.06
p3
Ba
(x)
27
Exerimental Procedure
Charter
2
Chatr
EvmnaPocde
2
Na1 /2Bi1/ 2 ZrO 3
2
NBT2_
NBT
10
20
40
30
mol% BaTiO 3
BaTiO
,-
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
3
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 8000 C 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 10000 C. Batch p6 was calcined
twice: in air at 8000C for 3 hours and in air at 9500C for 6 hours with the same
29
Chapter
t 2
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 Na 2CO3 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
Batch
ID
mole fraction
Ba 2 ' (x)
mole fraction
Zr 4 + (y)
Self-Flux
Growth Schedule
R.T.-1350°C @ 100°/hr
S1
0.08
0.03
S2
0.08
0.03
hold 5 hours
1350C - 8000C @ 50 /hr
800°C - R.T. @ 50°/hr
s3
0.06
0.03
R.T.-*1350°C @ 100°/hr
hold 5 hours
s4
0.10
0.03
1260C -_ 1000C @ 1.5/hr
S5
0.10
0.03
1350°C - 12600C @ 100°/hr
hold 1 hour
1000°C - R.T. @ 50/hr
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
Chapter
Chae- 22-
Procedure
Exerimental
EermnPoceI
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
2
Chanter
Ch..tr
2...Pod
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
2.3
Experimental Procedure
Polycrystaland Single Crystal SamplePreparationfor 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
Exerimental
Procedure
ri
22
Chanter
Cha-
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 Xray 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
IFor 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, TiO 2, 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
Exerimental
Procedure
Prcde
ExeImn
Chanter
Chatr_ 22
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:
Ct
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
.. ...
C-h r..2...
.
Prnreduri-
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
5.0 Software (Microcal Software, Inc. ©1997)using the method of adjacent
averaging, in which the smoothed point i is the average of points in the interval:
[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
Exerimental
Procedure
i
Charter 2
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 1023
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:
Tm(f)
Eact
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
Pr
'-oeu
...-rm
Exerimental Procedure
Chanter 2
Photograph of BNC Connectors
HP4192A
L curr
Schematic of BNC Connectors
H urr
H pot
L pot
I
I
I
®(~
®.
I
I
A
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
efficiency:
k2
=
electrical energy input
mechanical energy output
45
Chapter 2
Experimental Procedure
Schematic of Sample Holder
... to high voltage...
........................................................................
...to ground....
......*...........................................
electroded
sample
"I
ml
J
I
f
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
..
.
spring loadea
j
ExperimentalProcedure
Chapter 2
Thickness-extensional coupling factor kt is calculated according to the following
equation:
tkt =J
f
2 a
tan z Aflr
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
co
C
a,
E
fa
Frequency--
E
/r
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]
(Controlling Dimension x Resonant Frequency)
N
=
afr
P
Frequency constant (circumferential) (Nc)
[Hz- m]
N = afa
(Controlling Dimension x Resonant Frequency)
47
Experimental Procedure
Chapter 2
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 fieldinduced d33 may be characterized.
for these samples.
48
Thus, d33 can be plotted as a function of field
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
m , Q is charge in C, and i is current in A - C/s. Thus,
2
P=
Pi dt
A
can be plotted against field to obtain what are often referred to "hysteresis
loops." For ferroelectric bipolar polarization loops, the coercive field Ecis
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:
S3
=
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,Phaseand 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, Sr3Ti 2O7, 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
Chanter .3
V.rI.
Results : Co-Do-ned
Polucrusals
P-'...
r
..-..
Ru
....-
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
ID
(Ba/Zr)
Na
Bi
Ba
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
(Na+Bi+Ba)/
(Ti+Zr)
* indicates composition was normalized to unity on the A-site
54
Symmetry
R = rhombohedral, T = tetragonal
Chapter 3
Chavr
PoirutCo-Doed
Results
Results I: Co-Doed Polucrustals
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 2TiO 3
(110)
(200)
(2
(100)
Rhombohedral i
(211)
(11) _
il
(111)
(10
~~~~~~I
(220) ( 2 0 2 )
(211)
,
i
I
(310
0 1)
I
p 1
Rhombohedral
0
Ii
I
)
Ietriao
I
1
l
ip 10
Tetragonal
t
ca
a)
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/2TiO
3 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
Polucrustals
Results I: Co-Doved
·
Y Y
F--"----
---
i
i
0o
i
C
0
m
I
Ii
i
0)
i
i
iI
O
z
0
a)
0o
C
Q
0
c5
I-H
Hr
-o
N
0-
I
m
z
o
m
7
00
0
II
C(
O.
6O
0)
CD
o
I
I
6
i
N
E
0
-c
I
H-
oc0)
a0
CY)
0c.
.C
O
-
60:
zCo
CD
Co
+
z
13
13,
N
o
i
o0
0
I
iI
E
II
I
i
O
I
II
O
0
,
I
()
E
C;I
m
o
I--
E
o
Loo
It
Cr4
-00
a)
Ln
,
0
CU
u,
,I-_
57
Chapter3
ChaJter
Results : Co-Doed Polucrustals
D
Results
3
d
ru.....
Na/ 2 Bi1/2 ZrO 3
'I,
MPB
.............
R = rhombohedral
T = tetragonal
11
I
I
TB234
NBT
10
20
40
30
mol% BaTiO3 -
BaTiO 3
*
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-BTsystem are
reported to be - 6 g/cm 3 [26]. Relatively low Zr4 + doping in the NBT-BTsystem
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/cm 3 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/cm 3 , 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/cm 3, 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
Results I: Co-Doped Polycrustals
Chapter 3
FEI/ Philips XL30 FEG ESEM of sintered and fracture surfaces for sample p6a.
Adobe Photoshop software (Adobe Systems, Inc. ©1998)was used to estimate
the pore fraction cross-section in sintered bodies to be less than 3%.
Minor Second Phase
(BaTi 2O 5 )
/
200 pm
100 pm
Fracture Surface
20 pm
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
3.2
Results I: Co-Doped Polycrystals
DielectricPropertiesof 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 - 1600for
less than 15% Zr4 + and decreasing to ~ 750 for the highly-doped NBT-26BT29NBZ 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
Results I: Co-Doed
Polucrustals
ResultsI:
Co-Doved
r Polu
r ss
Chapter
33
Chavter
a--1 bUU
0
OA
A
o8
a0
a
mol% Zr
+*
0· +
0-
1200
0k1
O~~~~~~~~~~~~~~~~~~~~
w
800
Ao
03
A4
X5
@6
07
+8
09
-10
*11
I
014
400
AL
X 30
10 kHz
'
.-
I
I
5
0
I
I
I
10
I
Il
15
I
I
I
20
,
25
mol% Ba
Figure 3.5
Room Temperature
A maximum in
62
Sr
Er
at 10 kHz for Polycrystalline Co-Doped NBT
occurs for compositions slightly to the tetragonal side of the MPB.
22
Chapter 3
Results I: Co-Do~ed Polycrstals
- -
14%
(
12%
10%
00
*A
CIO
r.
8%
CU
I.~
6%
mol% Zr
AO
03
A4
X5
*6
07
+8
09
-10
*11
]
4%
E114 0 22
X30
2%
10 kHz
' '
0%
''''''"`'''''
I I
0
I I
5
I
I
10
I
I
15
I
I
I
II
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 nonpolar 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 NBTbased 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-BTsystem [26, 33]. Overall, as Zr-concentration increases,
Tm decreases.
65
Chavter
3
I
Results I: Co-Doved
Polucrustals
·
Y Y
NBT-xBT-3NBZ
0.1 > 1 > 10 > 100 > 1000 kHz
Sr:
Heating Rate: 200°C/hr
tan : 0.1 < 1< 10 < 100 < 1000 kHz
0.25
5000
n'
0.2
4000
0.4
3000
0.3
0.1
2000
0.2
0.05
1000
0.1
u.t
4000
3000
0.15
2000
1000
o
C
b
C
0
o
50
100
150
200
250
300
350
50
100
150
6000
u.
n
500
300C
0.3
200C
0.2
1000
0.1
350
C
0.2
3000
2000
0.1
1000
0
300
0.1
1000
0
100
150
200
250
300
40 0
350
0.8
7000
0.7
6000
0.6
5000
0.5
4000
0.4 '
3000
0.3
2000
0.2
1000
0.1
0
400
f
v
50
100
150
200
250
300
Temperature(°C)
Figure 3.7
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
350
8000
Temperature(C)
Temperature
£o
2000
50
4000
250
0.2
0
0.3
200
0.4
x = 0.10
3000
0
400
5000
150
400
0.3
0.4
100
350
Temperature(C)
6000
50
300
4000
0.4
200 250 300
Temperature(C)
250
5000
0.5
400C
150
200
Temperature(C)
_
100
a
0
400
Temperature (°C)
50
£0
350
0
400
Chapter 3
Results I: Co-Doped Polvcrvstals
NBT-xBT-4NBZ
Heating Rate: 21<101001000C/hr
0.3
r: 1 > 10> 100>
1 000 kHz
tan 6: 1<10 < 100 < 1000 kHz
5000
0.5
4000
0.4
3000
0.3
2000 -
0.2
4000
0.2
3000
C
2000
C
0.1
1000
1000
0
50
100
150
200
250
300
350
0
400
x = 0.09
0
50
100
150
Temperature
(IC)
250
300
350
0
400
Temperature
(IC)
___----sns_
----
bUUU
200
0.1
U.4
4000
0.3
3000
sUUU
U.4
4000
0.3
3000
0.2
0.2
2000
2000
0.1
1000
0
50
100
150
200
250
300
350
0
400
0
50
Temperature
(IC)
100
150
200
250
300
350
0
400
Temperature
(IC)
1000 -
0.4
750 t-
0.3
500
0.2
250
Na0.39 Bi0.36Ba0.26Ti0.71 Zr0 .2 9
0.1
"',
0
50
0.1
1000
0
100
150
200
250
300
350
400
Temperature (IC)
Figure 3.8
Temperature and Frequency Dependence of Erand tan 6 for NBT-xBT4NBZ 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 0.05Hz approaches room
temperature, shifting as low as 370C for sample p23a. The calculated values of Tf
68
Results I: Co-Doped Polycrystals
Chapter 3
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
I
I
I
I
I
0_
x = 0.04
b
7.
b
0 Experimental Data
.............VF nonlinear fit
o
5Q
0
0
o,
x
x
E
E
lZ
6.
Relative Error of Fit: 0.2%
6
,
2
1
I
3
I
5
4
I
6
t
logf [Hz]
log f [Hz]
I
. = 0.08
C)
8_
x= 0.10
0.-,.
.
8
.
.
,
~~6
~,~~~'.
'.
E
x
O
Relative Error of Fit: 2%
Relative Error of Fit: 1%
I
2
1
I
4
3
I
5
I
6
1
2
3
log f [Hz]
I10
I
l
I
4
logf
I
~
7
3....
I
x = 0.12
I
x = 0.14
6
C)
o
o
xX
xE
E
t
Relative Error of Fit: 2%
1
I
2
5I
4I
I3
log f
[Hz]
Q
I
6
:7
6
II
--.
~0~~'
5
[Hz]
.,
5_
Relative Error of Fit: 1% ?
;
7
I24
I
3
I
4
log f
I
5
I
6
[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
NBT-xBT-4NBZ
I
I
O ExperimentalData
.............VF nonlinearfit
I
=0.09
10.0x
x = 0.07
o
10
o0.
b
O.
0,
O",%
"to
8
X
x
E
lZ:
'O
Relative Error of Fit: 2%
I
3
62
I
4
I
5
Relative Error of Fit: 2%
I
6
7
2
6
3
logf [Hz]
oE
10
I
I
I
I
5
4
log f [Hz]
I
I
I
I
x=0.12
0
I
6
I
x = 0.14
0~-·
o"
o
.
X
0
x
X
E
E
17
lZ
Relative Errorof Fit: 3%
1
2
3
4
Relative Error of Fit: 2%
5
6
77
4
L
log f [Hz]
2UOI
b
15
I
10
I
I
5
I
I
I
4
D
b
log f [Hz]
I
' .
Nao.
3 9Bio. 3 6 Bao. 2 6Tio.7 1
X
E
10_.,
1
Relative Error of Fit: 1%
2
I
3
I
4
I
5
I
6
7
log f [Hz]
Figure 3.10
1/Tmas a Function of Frequency with Vogel-Fulcher Law Fit
for NBT-xBT-4NBZ and NBT-26BT-29NBZ
70
ZrO 2 9
7
Chapter 3
Results I: o-Doped Polycrstals
Table 3.2
Volger-Fulcher Parameters for Co-Doped NBT Relaxor Polycrystals
Doping Level
Sample
mol%
ID
Zr
Calculated Parameters from Volger-
Extrapolation
Fulcher Fit
to 0.05 Hz
3
mol%
Bact x
3
10
(0C)
(eV)
Rel.
Logf
Error
(Hz)
(%)
Tm (C)
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
................................. ...............................................................................................................................................
.........................................
37
p23a
29
26
31.0
11
7.6
1
37
71
Charter
r 3
3
3.3
Results
: Co-Doed
Polucrustals
R
C
ElectromechanicalPropertiesof 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
c0
C0
LL
II
E
tO
Eu
0
II
Co
T-
\
II
cZ
6
O
L
4n
11
·
E
w
LL
E
t
a&
:
C-e
w
cL CY)
CY)
X
N
CO
co
-
LL
LL
0
-
*c0*
LC)
·-
C,
o
03
O
'CD
cs
o
0
-'
O
C
CD
Cu>
L- a)
O0r
co
N
m
0
Co
N
Z
CY)
L
0-
Co
't
0
Co
o
c
Co)
CY)
LO
..
z
0
U-
t
UL
C-
Z
-a
o0
o
E
o
Ln
E
N 0
0o
C) Co
cm
C\!
o
cu
L
Os
Cu°
C)
Co
03
o
CD
CY)
E-
o
0
-.
LL
CD
O
N
O
CO
L
O4
E
'.0
O
E
Co CO
.0)
Cu
6'I
1LL
o
cd
II
II
I
I
II
0
C)
l
II
E
11
_._._.....~
.
O
0
ra
E
Co
o
a)
cn
I
N
r
m
L
a)
1cX
oa
E
E
D
Co
CL
6
-0
C
xc
)
ct
mn 2
CL
T
x
U)
E
m~ 2
.m
cu
ao
C:
Lo
u?
LC
co
r~c
m
O
Cu
0>
II
a
N
$Y
E
.
N
(L
C
LL.
O
E
.<c-0
O >
to
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
coercive field Ec - 31 kV/cm and remnant polarization Pr N26pC/cm2 (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
-1
o0
0
-J
C:
0.015-
r- 0.0251
0.0201
0.010
-r
0.0151
C
0.010
t-
0.005
^ ^^'
0.000
rt-
0.005
O
,_J
0.030-
^ ^^-r It
fl
Jr'
U.UUU
._1
-20
20
0
-40
-20
0
40
0.20
0.05
C
m 0.04
-'
rC 0.15
-003
0.03
.
r-.
C:
C0 0.10
':3 0.02
tC
u) 0.01
·'C:
-- 0.05
o0.00
0.00
-50
-25
0
25
Field (kV/cm)
50
-jo
0.00
-60
-40
-20
0
20
Field (kV/cm)
Figure 3.12
Evolution of Bipolar Strain Response for Initially Poled FR Phase
NBT-4BT-3NBZ Polycrystal
76
20
Field (kV/cm)
Field (kV/cm)
40
60
Chapter 3
Chpter
Resuts I: Co-Doed Polucrustals
3
Result
Co-Dod·
P
'usa
NBT-4BT-3NBZ Polycrystal
0.10
0.08
Uo
0.06
C
0.04
0
0.02
_1
0.00
20
0
40
60
Field kV/cm
Figure 3.13
Strain (Unipolar) Versus Field for FRPhase NBT-4BT-3NBZ
Polycrystal
NBT-4BT-3NBZ Polycrystal
40
N
P_=26-----/cm
Pr
E
26 C/cm2
------7
15
10
0 20
O
r
o
0
E
5
C
a,
0i
CU
N -20
(
4
o -40
-10
At"I
- IJ
Q_
-80
-5
-40
0
Field (kV/cm)
40
80
-80
-40
0
40
80
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 /cm 2 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
n
..
n
U.5U
In
.
..
0.15
0
-
0.14 % at 49 kV/cm
0.25
.M
C
Co
0.20
0.10
.C
0.15
.0-
C
:I,
0
0.10
cJ)
0.05
C
-.0
J
0)
v,
0
-J
0_j n n0
0.05
d 3 3 = 310 pC/N
_j
-50
-25
0
25
0.00
50
0
Field (kV/cm)
10
20
30
40
50
Field (kV/cm)
Figure 3.15
Strain (Bipolar and Unipolar) Versus Field for FTPhase NBT-14BT-3NBZ
Polycrystal
NBT-14BT-3NBZ Polycrystal
40
0
20
20
10
E
aO
Co
-10
a -40
-20
-50
-25
0
25
Field (kV/cm)
50
-50
-25
0
25
50
Field (kV/cm)
Figure 3.16
Polarization and Current Versus Field for FT Phase NBT-14BT-3NBZ
Polycrystal
79
Polhcrwstals
Results I: Co-Doped
·
V V
Chavter 3
NBT-4BT-3NBZ Polycrystal
1500
_ .._
_.
-
0.3
0.25
1000
....... 0.2 ,-
.....
.......
500
0.15
*
0.1
0.05
0
1
10
100
1000
10000
Log Frequency (kHZ)
NBT-14BT-3NBZ Polycrystal
2500
2.00
2000
1.50
1500
1.00
Q)
D
1000
-- 0.50
500
oo
0
1
10
100
1000
Log Frequency (kHZ)
10000
kt Resonance Peak
1000
350
-.
900
300
OS250
C
a)
X
800
( 200
C
CU 150
700
I
a) 100
a)
E
-
kt:
600
E
50
0
500
E_
220
245
270
295
320
345
I
iIII1
1500
2000
Frequency (kHZ)
2500
3000
Frequency (kHZ)
Figure 3.17
Resonance Analyses (Zero Bias) in Poled FT Phase
Polycrystal with Disc Geometry
80
NBT-14BT-3NBZ
3500
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-BTin 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 Afis 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
i a-l,Results-ICo-DoedPl
J Polucrustsals
haer- 3
Table 3.3
Comparison of PiezoelectricProperties For Polycrystalline Materials
I
Nt
Np
(Hz m)
(Hz m)
310
2400
2985
378
- 0.51
125
1586
2975
na
- 0.34
300
2070
2170
900 - 1600
d33
kt
(pC/N)
NBT-4BT-3NBZ
NBT-14BT-3NBZ
Qm
170
0.45
--·
-
NBT-6BT
PZT-8
[26]
[34]
na = not available
kt estimated by the relation: k 33
k + k + kpk2 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-4BT3NBZ to - 950 C 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
is - 450 pC/N at 32 kV/cm and the electrostrictive coefficient Q11 is -1.8 x 10-2
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
Results
Polucrustals
.. P
i....
Results: Co-Doed
Co-De
Charter
Ch....r 33
NBT-6BT-3%NBZ Polycrystal
0.05 Hz, 1 MPa Prestress
v
0.14
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
Pmax =
40
28 pC/m
2
at 46 kV/cm
0.8
I-F-
0
C)
I
0.4
20
4-,
0
4-,
Co
N
----?
0
a)
0
)
!
g
0 -0.4
-20
a-r
-40
I
-50
I
-25
0
-0.8
25
Field (kV/cm)
50
1,
-50
I
I
-25
0
Field (kV/cm)
Figure 3.19
Low Field Polarization and Current Versus Field for FFTR Phase
NBT-6BT-3NBZ Polycrystal
84
25
50
Chapter 3
Results I: Co-Doped Polycrystals
NBT-6BT-3NBZ Polycrystal
,
I--^ r%
VUU
- .I
U. -IU
.
Max d33- 450 pC/N
at 32 kV/cm
z- 400
60 300
0.12
.c 0.08
'
200
100
n
C)
/
0
0.04
5 point smoothing filt(
i
10
i
20
I
30
Field (kV/cm)
I
n
LJ
40
0
0.03
0.06
0.09
p 2 (C 2 /m 4 )
Figure 3.20
Low Field Electrostrictive Properties d33 and Q11 of FFTR Phase
NBT-6BT-3NBZ Polycrystal
85
Results I: Co-Doped Polvcrustals
Chapter 3
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
Field (kV/cm)
60
Field (kV/cm)
0.25
-
0.3
0.2
.C
'
0.15
0.2
(n
.
0.1
'
0.1
0.05
-60
C
-
o
0
°
-30
0
Field (kV/cm)
30
0
60
0
30
Field (kV/cm)
60
0
30
Field (kV/cm)
60
0.3
0.3
c
Cu
U)
._i
0.2
.U
c'
0.1
Co
~6
0)
c
'O
c
0.2
0.1
a
C
0
0)
C
0,
-J
0
-J
0
-60
-30
0
Field (kV/cm)
30
0
60
0.3
z
0.3
2 0.2
.'
C
0
0.1
:
pC/N
0.1
.,C:
0 0
-j
0
-60
-30
0
Field (kV/cm)
30
60
0
30
Field (kV/cm)
60
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
Results : Co-Doed Polucrustals
Reslts
I
C
-De
P
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
Results : Co-Doed
i v Polucrstals
Charter
t- 33.eslt
Cha.
(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-BTsystem 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
40
N
0
O
10r
." I
'
-
20
1_1_I
_
0.5
0.0
Co
N
0-0.5
-20
m -40
I
II
I
-80
-40
I I I I
0
I I I I
40
Field (kV/cm)
' _i
80
.
- 1 .
-80
-z 40
0
Field (kV/cm)
Figure 3.22
High Field Polarization and Current Versus Field for FFRR Phase
NBT-6BT-3NBZ Polycrystal
88
40
30
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 fieldforced 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
electrostrictive coefficient Q11 is ~1.8 x 10-2 C2 /m4 . 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/cm 2 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
Results I: Co-Doved Polucrustals
Chapter 3
NBT-12BT-3NBZ Polycrystal
0.05 Hz, 1 MPa Prestress
0.1
0
0.08
._CU
0.06
L-
cn
0.04
0
._
0.02
-1W
.
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
21.5 pC/m 2 at 29 kV/cm
Pmax =
4
ou
I
i~~~~~~~~~~~~-
20
0E
cV
O
C:
0
.- '
CU
N
10
E
-'
0
C:
a)
O
-Jl
-3OU
0
L.
-10
0
-20
0._
I
2
I
r1
-40
1
.
-20
.
.
.
.
.
.
0
.
.
.
20
Field (kV/cm)
-2
i
-4
.
40
-40
-20
_1~~~~~~~~~~~~~~~~
0
Field (kV/cm)
Figure 3.24
Low Field Polarization and Current Versus Field for FFTT Phase
NBT-12BT-3NBZ Polycrystal
90
20
40
Chapter 3
Results I: Co-Doped Polvcrystals
NBT-12BT-3NBZ Polycrystal
500
z
0.1
Peak d33 460 pC/N
at 27 kV/cm
J 1~
400
0.08
it
O 300
0.06
_0
v,
200
oo
4 .
100
0.02
3 point smoothing filter
0
'I
0
I
10
0.04
,
I
20
Field (kV/cm)
I
30
0
0
0.02
2
0.04
0.06
4
p (C2/m )
Figure 3.25
Low Field Electrostrictive Properties d33 and Q 11 of FFTT Phase
NBT-12BT-3NBZ Polycrystal
91
Chavter 3
J
LnTt(
Roc1i41c
L-n'u
oc AiLi0"L11
b. fi, TULJTL-IU
lrnn
DM.
i
NBT-12BT-3NBZ
at 0.05 Hz, 1 MPa Prestress
Polycrystal
0.12
-0.12
·
0.08
·
0.08
'
0.04
c
0.04
C
C
I
I
I
I
I
1
I1
I
1
r
.
_,
35 -25 -15 -5 5
Field (kV/cm)
15
25
0
35 _j
0.2
'_
0
10
20
Field (kV/cm)
0
20
Field (kV/cm)
30
0.2
0.15
' 0.15
C-
o)
0.1
o
i 0.05
o
-40
-20
0
20
Field (kV/cm)
40
0
-a
0
0.2
0.25
.' 0.20
0) 0.15
0.15
0.1
0.10
0.05
. 0.05
0
O
40
U.OU
0.25
c
0.1
U)
-I
-55 -40 -25 -10 5 20
Field (kV/cm)
35
50
pC/N
0.00
0
15
30
Field (kV/cm)
45
_ 0.30
-0.25
C
0.20
.
·.i 0.15
;5 0.10
c) 0.05
C
0.00
.-
0.00
-60
-10
Field (kV/cm)
40
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
E
-0
O
45
12
30
8
15
E
0
C
r
0 -15
CU
0-
0
a,
._
N
4
L.
)
-30
-45
I
-60
-30
I
I
I
0
I
I
30
Field (kV/cm)
-4
-8
-12
I
60
-60
-30
0
30
60
Field (kV/cm)
Figure 3.27
High Field Polarization and Current Versus Field for FFTT Phase
NBT-12BT-3NBZ Polycrystal
93
33
Chapter
Chate
Results
Co-Doed Polucrustsals
oVut
Reut I::C-oe
3.3.1.3 Predominantly Electrostrictive Actuation
As the MPB is approached from NBT-12BT-3NBZ,a gradual decrease in
Sample
the degree of FE character, as well as a decrease in Tm(O.
0 5Hz),is observed.
0
NBT-8BT-3NBZ (Tm(O.0
5 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
coefficient Q11 is -1.9 x 10- 2 C 2 /m 4 .
94
Chapter 3
Results I: Co-Doped Polycrstals
NBT-1 OBT-3NBZ Polycrystal
at 0.05 Hz, 1 MPa Prestress
Bipolar Actuation
0.25
C
C
0.2
C,)
0.15
Unipolar Actuation
0.25
0.24 % at 53 kV/cm
0.2
C
0.15
C
V
75
C
.a
-S-
:~
0.1
I
~~I
0.1
0.05
.0
-j 0.05
0)
-j
:LI
0
-60
0
-10
40
Field (kV/cm)
25
0
50
Field (kV/cm)
Figure 3.28
Electrostrictive Strain (Bipolar and Unipolar) Versus Field for PET Phase NBT10BT-3NBZ Polycrystal
NBT-10BT-3NBZ Polycrystal
Pma = 36 pC/m2 at 49 kV/cm
40 F '
6
cN
E
0
0C-
20
E 2
0
-2
I
04.
0
LII-
-20
-40
O -4
! -
-60
,
. .
.
.
-30
0
30
Field (kV/cm)
.
-6
60
I
-60
I
T
rI
r
TIr
I
Ir
-30
0
30
Field (kV/cm)
60
Figure 3.29
Polarization and Current Versus Field for PET Phase NBT-10BT-3NBZ
Polycrystal
95
Results I: Co-Doed Polucrustals
Charter3
·
R
C
--
rt
--
NBT-10BT-3NBZ Polycrystal
~~~~~~~~~~~~UZ
duu
'
.Z
1
1.9 x 10 -2 C 2/m4
Q11
n
0.2
600
0.15
F
C 400
-C
200
'
Peakd33 - 725pC/N
(
/I
0.1
0.05-
at 32 kV/cm
=
0
25
Field (kV/cm)
50
0
I
I
--
0.05
I
0.1
0.15
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
Unipolar Actuation
0.16
-
0
C
C
.M
4-
at 0.05 Hz, 1 MPa Prestress
0.13 % at 44 kV/cm
: 0.12
0.12
.. _
U) 0.08
0.08
C
C'
.0 0.04
-J
:11
0)
0.00
C
o 0.00
-50
-25
0
25
Field (kV/cm)
50
0
15
30
Field (kV/cm)
45
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
O
4.00
20
E 2.00
-,
C
0
oN
0
C 0.00
-2.00
-20
° -4.00
C.
-.
-40
-6.00
-50
-25
0
25
Field (kV/cm)
50
-50
-25
0
25
Field (kV/cm)
50
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
500
0.20
Q1 - 1.4 x 102 C2/m4
0.15
z 400
300
to
- 0.10
-a 200
Peak d33 - 500 pC/N
at 29 kV/cm
100
(D 0.05
0.00
---
0
0
15
30
45
Field (kV/cm)
0
0.04
2
0.08
0.12
4
p (C2/m )
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-7BT4NBZ (Tm(0.0
800 C) and NBT-9BT-4NBZ (Tm(0 .05 Hz) -79 0C), which lie near MPB.
5 Hz)
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 3.343.38 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-FEphase boundary.
99
Chapter 3
Results
I: Co-Doved Polucrustals
·Y·l
NBT-xBT-4NBZ
Polycrystals
at 0.05 Hz, 1 MPa Prestress
x = 7 mol% Ba (R)
x = 7mol% Ba (R)
--
U.Z
0.25
0.2
-
Cr
unipolar
1 0.15
.
0.15
'a
0.1
-'
0.1
'
0.05
.0)
c
0A
-
0.2
C
n 0.05
0.2% max strain
._0)
0
-80
-40
0
40
Field (kV/cm)
S
80
40
Field (kV/cm)
0
80
x = 9 mol% Ba (T)
0.07
0.06
c0.05
0.04
(,-0.03
C
*0 0.02
0) 0.01
0
0
-J
-40
0.25
C
Cu
C
0)
C
0
-j
0
Field (kV/cm)
40
x = 12 mol% Ba (T)
0.2
0.15
Unipolar
0.1
0.2
C
0.15 -
0)
-20
20
Field (kV/cm)
60
x = 14 mol% Ba (T)
0.23°%max strain
0 l-
U
0
-
Unipolar
0.1
0.05
-j
_~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
0
.
o
-j
-20
20
Field (kV/cm)
0.21% 40.
max strain
.
r
i
Im
r
40
Field (kV/cm)
unipolar
:)
c
-60
_ _ _
c 0.15
0.2
0.1
i:
._
C
... .
x = 14 mol% Ba (T)
0.25
0.2
C
_
0.1
'O 0.05
0
-j
0.15
._
Co
_
C:
0
0.25
, _, ...... ,
unipolar
_ I
F
e0
0.05
-60
x = 12 mol% Ba (T)
1
n
U.ZD3
0.22% max strain
60
0.05
0.21% max strain
O
0
40
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-Dnned
V YV VI -Pnljcruijtal.
I V·II-
NBT-xBT-4NBZ Polycrystals
-
I
x= 7 mol% Ba
40
-I-
(R)
1.5
33 pC/cm2 max
P
o
1
20
C
o
=
-20
o
-40
-5
-1.5
-80
-40
0
40
Field (kV/cm)
80
-100
x =9 mol% Ba (T)
20
'
16 pC/cm2 max P
E
-50
0
50
Field (kV/cm)
100
x = 9 mol% Ba (T)
0.6
04
0.4
10
.o;
-
x 10
4
°_
-0.6
& -20
I
-
-40
-20
0
20
Field (kV/cm)
-0.6
40
-50
x=12 mol% Ba (T)
x
' 37 pC/cm max P
E 40
4
E -0-0
2
*0 -40
2
-60
-30
0
30
Field (kV/cm)
60
-80
x = 14 mol% Ba (T)
-25
0
25
Field (kV/cm)
50
12mol% Ba (T)
-40
0
40
Field (kV/cm)
80
x = 14 mol% Ba (T)
E 20 26 pC/cm max P
O-0.5
-2o
8
0 -30
-1
-60
-30
0
30
Field (kV/cm)
60
-80
-40
0
40
Field (kV/cm)
80
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
N
E0
20
O
10
o
-
0
CU
0
N
-10
M.
-20
0-
-30
0~
-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 = 7mol% Ba (R)
500
0.25
400
- 0.2
300
c0.15
200
0.1
100
0.05
Peak d33 425 pC/N
* t 45 kV/cm
*416l1
0
30
Field (kV/cm)
0
0
0
60
x=9
0.03
0.06
0.09
p2 (C2/m4 )
-
mol% Ba ((T)
400
0.06
300
o 0.04
" 200
.C_
f 0.02
100
0.12
. QO
, 2.1C2/m4
0
0
0
10
20
30
0
0.01
0.02
p2 (C2/m 4 )
Field (kV/cm)
0.03
x= 12 mol% Ba (T)
0.2
600
500
0.15
400
300
v,
.F
200
I=
,,*
100
Peak d33 - 580 pC/N
.-
0
0
at 35 kV/cm
10
0.1
Ql - 1.5 C2/m4
0.05
0
20
30
40
Field (kV/cm)
i.
0
50
q,
r
I
I
I
I
0.03 0.06 0.09
p2 (C2/m4 )
I
0.12
x = 14 mol% Ba (T)
U.Zs
800
0.2
600
*
#
4 ,
R 400
'
'O
200
Peak d33 - 780 pC/N
35 kV/cm
0
0
10
20
30
Field (kV/cm)
I
~~~~~~
0.1
C, 0.05
0
40
,, -
,
'- 0.15
e;
Q - 3.0C2/m4
0.02
0.04
0.06
P2 (C2/m 4 )
w
0
I
,
,
0.08
Figure 3.38
Electrostrictive Properties d 3 3 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
Hz)
extrapolated to 0.05 Hz for NBT-26BT-29NBZ lies around 37°C (Tm(O.05
370 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
1 Hz, 1 MPa prestress
Q.
O
C
.
80
60
C
40
0
c- 20
O
...
n
-60
-30
0
30
60
Field (kV/cm)
Cu
20
w7
15
1.5
10
1
5
E 0.5
0E
o-
0
N
-5
L-
O
Q.
-10
°-1
-15
-1.5
-20
~j
-L
-80
-40
0
Field (kV/cm)
40
80
_
-80
-50
-20
10
40
70
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/2TiO
3-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 60-100degrees 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 NBT12BT-3NBZmay be an example of this phenomenon, although there seems to be
an overprinting ferroelastic component in this system as well. Thus the micromacro region begins to appear in the NBT-BT-NBZsystem for AT - 600C.
106
Results
I: Co-D.ved
Co-Doed Polucrustals
Polurust...
Ru
-:
Chapter
33
t
Na1/ 2 Bi1/2 ZrO
3
Room Temperature Isotherm
/
.00
PER
'\I
PER*
PE
QP\
0
PER
0
*
,
3,
T
FFTT
FR
FE
0·
FT
I
Na1/ 2Bi 1/TiO
3
I
I
I
4
I
I
I
I
2
4
6
8
10
12
mol% BaTiO 3
14
BaTiO 3
-"
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
Na1/2 Bi1 /2 TiO3 - BaTiO3 -Na1 /2Bi1 /2ZrO 3
Based on room temperature XRD and actuation behavior at 0.05 Hz.
107
Charter
Char- 3
Results I: Co-Dov~ed
Polucrustals
v
-
200
3 mol% NBZ
175
4 mol% NBZ
o 150
a)
Q)
L
E
a,
F-
-As -
125
100
75
50
25
0
0
NBT
2
4
6
8
10
mole % BaTiO3
12
14
,-
16
BT
Figure 3.41
Partial Phase Diagram for Na1 /2 Bi1/ 2 TiO 3 -BaTiO 3 at 3 mol% Na 1 /2 Bi1/ 2 ZrO 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, NBT8BT-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
(extrapolated Tm(lHz)
-
880C) 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
Results
Results I:: Co-Doed
Co-Doped Polcr~stals
PoliVcrustals
33
Chanter
Chrrnter
.....
-
r
V
NBT-8BT-3NBZ Polycrystal
1200
E
Q
._
Cn
c~
L
Co:
._
-.-
rJ
0
1000
800
600
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
Charter
33.Results.
Cha...r
d
...-....
-Pl
-Jc....l..s
Results I Co-Dop~ed olucrustals
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 d 33 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
Results
Polycrvstsals
'
C
R l I: Co-Doed
33
Charter
Catr
0.25
0.2
-
.: 0.15
,._
co
0
-J
0.05
0
0
2C
40
Field (kV/cm)
60
80
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-FluxMethod
Single crystals of (Ba, Zr) co-doped NBT were grown by the flux method,
using Na20Oand Bi20 3 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
I
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
\I III
/I
('rxicfclsaltcnmnhnz9;_q)
'!P1
Reflected Light
Crossed Polarized Light
Side 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
4.2
Results II: Co-Doped Single Crystals
Compositionand PhaseSymmetry 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
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
(Na+Bi+Ba)/
* indicates composition was normalized to unity on the A-site
R = rhombohedral, T = tetragonal
117
Chapter 4
Results II: Co-Doped Single Crystals
4500
6000
Tetragonal
4000
5000
3500
(200)
4000
3000
e)
2500
3000
00o
o
2000
(002)
2000
1500
1000
1000
(001)
ov
(100)
,
20
,
30
500
r
-
I ._
40
50
-
I
,
60
70
,,
80
90
100
0o
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
DielectricPropertiesof (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-NBZcomposition 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
Results
I: Co-Doed Sinqle
Crystal
n
R--
Chantpr
al rev.. . 4L
- --
-
2000
_
_
_
_
10 kHZ
1500
X
1000
MPB
500
0
I
I
I
2
4
6
I
I
Il
8
'
10
12
14
I
I
12
14
mol % BaTiO 3
0.1
10 kHZ
0.08
O
4 -a
0.06
0.04
MPB
0.02
0
I
0
I
I
2
4
6
8
10
I
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
Results II: Co-DovedSingle Crustals
Chavter 4
NBT-xBT-4NBZ
rhombohedral [100]
Heating
0.1Rate:
> 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
8r
E
0.2
2000
increasing f
1000
tan 6
/
50
100
s4c:
.
0.1
150 200 250 300 350 400
Temperature (C)
s5b: 6 mol% Ba, 4 mol% Zr
6 mol% Ba, 4 mol% Zr
4UUU
U.Z0
3000
2000
0.2
3000
0.15
2000
0.1
1000
0.05
n
n
50
100
150
200
250
300
350
400
.U.ZL
0.2
//
- 0.15
-
-0.1
1000 -.
..
-
50 50
100 150100
200 250150
300 350
200
400
50
Figure 4.5
Temperature and Frequency Dependence of
Er
0.05
250
300
350
-
400
100 150 200 250 300 350 400
and tan 6 for Co-Doped
(Ba + Zr) NBT Rhombohedral Single Crystals Oriented [100]
121
Results
Sinvle Crystals
Chavrt II:
4 Co-Doed
-D
Cr
Charter4
NBT-xBT-4NBZ
Heating Rate: 200'C/hr
sla:
tetragonal [100]
Er: 1 > 10 > 100 > 1000 kHz
tan 6: 1< 10 < 100 < 1000 kHz
s4b: 9 mol% Ba, 4 mol% Zr
12 mol% Ba, 4 mol% Zr
bUUU
0.6
4000
bUUU
U.3
5000
0.25
0.2
increasing f
2000
0.15
tan 6000
I,~1000
9999~~~~~'
0 10~~
1
50
I1
I
I
I
100 150 200 250 300 350 400
Temperature
(°C)
0.1
0.05
00
0
50
100 150 200 250 300 350 400
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 44 hatr
Results I: Co-Doed Single Crustals
5000
Polycrystal (plOa):
Nao. 4 6 Bio. 4 4 Bao.
4000
1 2 Tio. 9 6 Zro. 0 4
Single Crystal [100] (sla):
'Nao.
4 7 Bio. 4 5
Ba
0
.12Tio.95Zro.04
3000
2000
leating
Rate: 200 0 C/hr
:r 1 > 10 > 100 > 1000 kHz
1000
an 6: 1 < 10 < 100 < 1000 kHz
0
50
100
150
200
250
Temperature
300
350
400
(C)
--
5
Single Crystal [100] (s4b):
45 Nao. 4 9Bio. 4 3 Bao.0 9 Tio. 9 7Zro. 0 4
5000
4
4000
35
Polycrystal (p9a):
Nao.5
0 B io.4 5 Ba o 9 Tio
0 96Zro 0 4
3
3000
25
2
2000
Heating Rate: 2000 C/hr
15
Cr:
10 > 100 > 1000 kHz
1
1000
05
tan6: 10 < 100 < 1000 kHz
0
50
100
150 200 250 300
Temperature
(C)
350
400
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 codoped (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
.............
VF nonlinear fit
x
t
E
4
log f
8
I
I
[Hz]
I
I
s4c: 6 mol% Ba. 4 mol% Zr
s2b: 5 mol% Ba. 4 mol% Zr
10
b
7
.
b
8
X
x
6
E
.
E
17
lZ
Relative Error of Fit: 1%
5
2
I
3
I
I
4
6
I
5
6
Relative Error of Fit: 1%
7
2
log f [Hz]
I
I
I
3
4
5
6
7
log f [Hz]
s5b: 6 mol% Ba. 4 mol% Zr-
s5a: 6 mol% Ba. 4 mol% Zr
10
10
b
O
0
x
I
o
8
1.),
8
x
E
E
17
t
6
2
3
4
5
log f [Hz]
6
Relative Error of Fit: 0.2%
6
2
3
4
5
,
6
7
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
Charter4
-- har
4
R
:
CD
d
Cts
bo
-
Co-Doped (Ba + Zr) Tetragonal Single Crystals
10
s4b: 9 mol% Ba. 4 mol% Zr
? 8
6--
8X
'Q
_
E
6
Relative Error of Fit: 3%
Relative Error of Fit: 2%
I4
3
2
12 mol% Ba. 4 mol% Zr
sla:
10
I
5
I
4
log f
I
6
[Hz]
4
2
7
I
3
I
5
4
o Experimental
Data
.............
VF nonlinear fit
logf
I
6
7
[Hz]
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
10--33
10
Sample
mol
mol
ID
% Zr
% Ba
Tf
(°C)
s2b
4
5
119
15
s2a
4
5
121
15
s4c
4
6
79
s5a
4
6
4
6
s5b
..................
............
s4b
sla
l
126
Eactx
(eV)
Logf
Log0
(Hz)
15~~~~
9.8
Rel.
Error
(%)
Tm (C)
1
126
8.5
2
129
10
7.6
1
85
93
2
6.4
0.7
94
94
2
6.4
0.2
96
...............
l......lllllllllll..................l...
4
9
81
11
7.6
2
4
12
86
11
7.2
3
87
93
l
MlPB
Chapter4
-Che-
4
Results II, Co-Doed Sinle Crustals
Result
I: -
C
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
Results
II: Co-Doved
Single
-- Crustals
-----
Chanter
V·"'Y'· 4-
-
I
200 0 C/hr
Heating & Cooling Rate:
s2b 5 mol% Ba,4 mol% Zr
s2a: 5 mol% Ba, 4 mol% Zr
4000
V.l
.
0.1
3000
3000
0.1
0.08
0.06
2000
0.04
1000
2000
0.05
X> > ;
,
1000
0.02
0
100
200
300
Temperature
400
50
250
150
45(iO
350
Temperature (C)
(C)
s4c: 6 mol% Ba, 4 mol% Zr 04
/ 0.35
4000I
0
0
500
0
0.3
0.25
0.2
3000I
I
2000I
s5a: 6 mol% Ba, 4 mol% Zr
---4000
ii
nJ
U.4
0.35
0.3
3000
0.25
0.2
2000
0.15
A1iE
0.1
1000
.i f"
c·· .,·"
I
0
0.05
0
150
5(
250
350
4450
c,~~~~~~~~~~~~~~~~~~~
1000
0.1
0.05
Iu
.
50
0
.
150
250
350
450
Temperature (°C)
Temperature (°C)
S ;5b: 6 mol% Ba, 4 mol% 2-T n,9
u.15
4000I
3000I
0.15
2000I
0.1
1000I
~
I.6,
Co
50
..
.
~~~11
O.O
_11
,
/,
II
250
150
U
450
350
Temperature (°C)
5000
s4b: 9 mol% Ba, 4 mol% Zr
6000
5000
1 10 /
400(
300
/
0.3
0.25
4000
0.2
: 0.15
3000
0.05
1000
T
1
sla: 12 mol% Ba, 4 mol% Zr
5000
1-
- --
0.3
0.25
0.2
0.15
2000
0.1
200
100(
n/
I
50
r
150
n
.
250
Temperature
350
(°C)
450
I
I
,
n
0
100
200
-
. -"
I
300
0.05
nAI._.,-
400
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
4.4
Results II: Co-Doped Single Crystals
ElectromechanicalPropertiesof (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 fieldinduced d33 than 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]
.M
C
L5
a
4CO
0)
C:
0
-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
C
0.2
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 Q11 lies 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 C 2m -4.
132
Chapter 4
Results II: Co-Doped Single Crystals
5U Pmax= 98 C/cm 2
'-_
a
· nn
0.8
i
'.. Uv
o UU
0 50
E
._
-0.4
E
0.2
0
0
'
-0.2
I!
N -50
*C
0,
i
r
0
O -0.4
- vv.n
-
I
I-
L-
-L.
I
/
I
.IV
U.v
-.n 8
-1;n
-50
-25
0
25
50
-50
-25
Field (kV/cm)
30
E
0
25
_ -__ . , .. i sla 1
i
P,
i
20
,_
O
0
i
0.5
i
i
i
i
E
C:
a
i
0
i
.N 10
0
) -0.5-
-0
-20
I
_,In -50
I
-25
I
I
0
I
50
bu
40
O
20
E
-A7.t
-50
I
I
-25
I
0
I
25
50
Field (kV/cm)
I60 _2
cAh
-- A7 ,,r"/,.m 2
D
rm
I
ch
-
1
--------
-_
--"'-1"1
0.5
E
.O
-
)4
-40
-60
o
C
N -20
.N_
-'
I
I
_1
25
Field (kV/cm)
NE
50
Field (kV/cm)
,
-50
I
-25
-0.5
O
-1
0
Field (kV/cm)
25
50
-50
-25
0
25
50
Field (kV/cm)
Figure 4.14
Polarization and Current Versus Field for PET Phase Co-Doped (Ba + Zr)
Single Crystals Oriented [100]
133
Results II: Co-Doped Single Crustals
Chapter 4
sla
2000
*.
Peak d33 - 2000 pC/N
0.25
0** 00
0.2
at 35 kV/cm
1500 -
c
*
CO 1000
0.15
0o.1
+* vS*+^+
500 -
(0
"r*
0.05
Q1 - 0.2
.,dA
x 102 C2/m 4
0
^\
v
,.
0
10
30
20
40
0
0.2
Field (kV/cm)
sld
1400
Peak d 33
1200
at 40 kV/cm
1000
c 800
1200 pC/N
*
-
200
*
0
0
*
**
0s
.//
0.15
0.1
*+*
.
10
1
0.2
*: *0
*
*
400
0.8
0.3
0.25
A
600
0.4
0.6
4
2
p2 (C /m )
0.05
0
30
20
-U
11- 4.3 x 10 ' C2/m4
._
.
0
40
e,'~
0.02
0.04
0.06
0.08
4
p2 (C2/m )
Field (kV/cm)
s4b
0.25
2000
0.2
1500
'-' 0.15
CO 1000
Co
0) 0.05
500
0
0
0
10
20
Field (kV/cm)
30
0
0.05
0.1
0.15
p2 (C 2 /m 4 )
0.2
0.25
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
II:
Resuls
Cr-stals
I Co-Doed
C-oved-- Sinlee Crustals
Results~-
Chanter 44
Chaner·
0.35
s4c (0.05
0.3
s5a (0.05
C
..
0.25
:5
c)
.0
=3
:110)
C:
0_j
s4d (0.05 Hz)
0.2
0.15
0.1
z)
0.05
n
-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
0
j 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
Results II: Co-Doped Sin le Crystals
Chapter 4
150
E
s2b
-
2
il
1.5
100
i
1
O
50
0.5
E
C
0
0
C
03
-50
-0.5
I
O
N
i
-1.
-100
i
-1.5
I
-2
-15n
-75
-50
-25
0
25
50
c
100
80 PR
60
40
20
iI
i
s4c
E
,
I
i
-0.5
I
I-
0
1
-100
-75 -50 -25
Ii
-1
I
-1.5
0
25
50
-75
75
-50
100
s5a
Pmax= 82 pC/cm2
80
0
25
50
75
15
1
60
(
,-
40
20
C
O
0
-20
N
-40
'-
-60
zE
<:Z
v
cC
I,,
L.
o0::
1.9 X 10 4
'K=
-80
Q_ -100
0.5
0
-0.5
-1
-1 .: :D
-75
-50
-25
0
25
50
-75
75
i
150
._A
100
C
0
....
-25
i
0
25
50
,
i~
75
Field (kV/cm)
s4d
I
N
0E
0o
,·
-50
Field (kV/cm)
0
-25
Field (kV/cm)
Field (kV/cm)
E
0
75
0
C
-40
Q/,
N
50
0.5
i
I
-60
OL
1.5
i
I
-20
N
25
Field (kV/cm)
0
0
0
75 -50 -25
75
Field (kV/cm)
oE0
i~~~~~~
1
0.8
0.6
< 0.4
E 0.2
:
0
C
50
,) -0.2
CU -50
N
-
cu-100
K=2x 10'
o
-0.8
-1
-150
-75
-0.4-
(0) -0.6
A
-50
-25
0
25
Field (kV/cm)
50
75
-75
-50
-25
0
25
50
75
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
600
Peak d33 - 540 pC/N
500
co,
at 50 kV/cm
. .
#f
-- -
g
.
.
..
.
_.
.
_
.
...
' /)"
0.05
1
10
20
30
40
50
60
0
0.5
Field (kV/cm)
s4c
1000
Peak d 3 3 - 835 pC/N *.
at 45 kV/cm
**.tS,
900
800
700
600
500
400
300
200
100
0
.
...
......
........
0.1 x 12C/
1
p 2 (C2/m 4 )
1.5
0.3
0.25
o
0.2
.
... ,t
0.15
0.05
0
0
10
20
30
40
50
60
0
0.2
s5a
1400
1200
0.6
0.4
p2 (C 2 /m 4 )
Field (kV/cm)
-- -
0.35
--- --
1000
0.25
0.2
600
·
0.15
400
'""
I,
°
200
0.1
0.5 x 102 C2/m 4
0.05
0O r
0
0
10
20
40
30
50
0
l
0.2
s4d
1000 -
0.6
0.8
0.25
930 )C/N
at 40 kV/cm
800
0.4
p 2 (C 2 /m 4 )
Field (kV/cm)
Peak d 33
z
I
I
0.3
CO 800
c
----.- _..- ._.....
... -. . .
....
0
0
-
.
0.1
W3
*s %*.
0
V
...
C._
100
co)
.
0.15
*0.
200
n
0.2
400
300
-
,\
U.zo
*.
0.2
600 -
*
-
400
0.15
0.1
On
**
200
0.05
tt...
0
0
0
10
20
30
40
Field (kV/cm)
50
0
0.2
0.4
0.6
p 2 (C 2 /m 4 )
0.8
1
Figure 4.19
Electrostrictive Properties d33 and Q 11 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, Pmax
and 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 leadoxides 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 Polycrystallineand Single Crystal Electrostriction
Peak d
Peak
Material
Longitudinal
P
x 102,
P
max
2
2
Strain, %
Single crystal [100]
(tetragonal)
045
NBT-12BT-4NBZ
Single crystal [100]
(rhombohedral)
(rhombohedral)
NBT-12BT-4NBZ
0.30
1180
82
0.5
0.24
780
37
3.0
0.11 (R.T.)
213
30
1.15
-
2.5
Polycrystal
(tetragonal)
NBT-14BT-4NBZ
Single crystal PMN
[111]1
[100]2
Polycrystal PMNT 3
Polycrystal PLZT4
-
-
0.16 (R.T.)
1100
0.12 (R.T.)
700
-
1030
2.5
2.12
8.8/65/35
BaTiO
3
PbTiO 3
PZN
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
11
8
2.4
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 leadbased systems. Predominantly electrostrictive polycrystal relaxors in the NBTBT-NBZsystem 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 Qmis lower for the NBT-
BT-NBZcompositions. 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 leadoxide 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
·
I t < 3 mm I
shape may be irregular
Permittivity & Dielectric Loss
Tangent
Temperature
- vs.
vs.
Temperature
* Strain and Polarization vs. Field
Thick-Plate
* Can be tested for resonance,
but ifit does show resonance,
the modes may not be
separable.
I----------
w
Permittivity & Dielectric Loss
1>10t; w>lOt
Tangent
|0.3< t < 3 mm
shape may be irregular, but side
surfaces must be I to faces
L
I t,.
,
nt-rIclL
- vs. Temperature
* Impedance vs. Frequency to
determine k, Nt
* Strain and Polarization vs. Field
t
1~~~~~~~~
w
> 2.5 t;
> 2.5 w
<3mm
Permittivity & Dielectric Loss
Tangent
-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, s 33 , S3 3 , d 33, g33,
t
,m
w
N,, /QY33, Y33
* 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
1> 5w;
w > lt;
Applicable Measurements
· Permittivity
& DielectricLoss
Tangent
- vs. Temperature
0.3 < t < 3 mm
* Impedance vs. Frequency to
determine k31, k3,, kt,
k 3 1-Plate
t
Y33, Y33, d3l,
*
w
d 31
31
, S,
N~ Nt
vs. Temperature
· Strain and Polarization vs. Field
* Permittivity & Dielectric Loss
a > lt
Tangent
0.3 < t < 3 mm
-
Disk
*
*polycrystalline
vs. Temperature
Impedance vs. Frequency to
determine kp, Np, N,
· Strain and Polarization vs. Field
samples only
X
a
(a = diameter)
145
Sample Testing Procedure
Appendix I
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.
Sputter Coater Settings:
c)
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
Avvendix
AvvendixII
Samle
Procedure
TestinY'Procedure
Samvle Testing,
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
* ElectricalQualityFactor(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 300 C 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 compositionT(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
-
f= fo exp
-act
B(Tmax -
Tmax
= temperature of the permittivity
maximum T(Fmax)
fo = attempt frequency
Eact= activation energy
kB= Boltzmann's constant
= 1.38 x 10-23 J/K
149
---cedu
---..' Procedure
. Samle
-..r- Testinv
..
Arr..e..Annendix
Use a non-linear fit (Origin graphing software) to the following
andfto determine the adjustable
equation with your data for Tmax
parameters,
Eact, f 0,
Tf:
Tm,(f) = T
Eact
-
c
kB inf
12. Pole the Sample (equipment in 13-4135)
a) Submerge the sample and a thermometer in a silicon oil bath.
then field cool (at a constant
b) Heat sample 20-300C above T(Emax),
field) to 300C.
c) Electric Field =
voltage
sample thickness
>E = V
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 Cris 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
v~~~~~
AppendixI
Sample TestinQ Procedure
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 (IEEEstandardnotation):
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 IEEEnotion of aCE)
vE may be approximated
for 0.2 < vE < 0.45 by:
a = [2.048+0.62(vE -0.30)]
v= 1psf
is the velocity of a
compressional wave in a slim bar normal to
where,
the poling axis (i.e. twice
constant (frl) of such a bar)
the frequency
151
Samvle
Testing
Procedure
-'
-----
Annendix
I
rr-·-------
--
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
r
I
t
A
I
a)
0C
a)
C
CU
O
ca)
E
_
<k
o
i
~~~~I
ma1
0E
17
-
-
. -
-
,
rl
- quLU' Yr
Frequency--
hN-
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
1
Resonance at lower frequencies due to I and w vibrational modes will]
likely be separable only if k3,-plate geometry requirements are met.
,I.
t
tkt (highest frequency resonance)
/
a
0
E
Frequency -
Calculated Constants (from kt resonance)
Frequency constant (thickness) N [Hz m
= tfr
(Controlling Dimension x Resonant Frequency)
153
Appendix I
o
SampleTesting Proceure
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)
O
a,
I
c-
~
"'"
[,
2
,.geometry.
I
(D
=1.
a)
a
i
P
N)
Frequency
-
3
= k Lta(
2fa
tan
2 fa
Calculated Constants (from Ik33 resonance/anti-resonance)
Elastic compliance at constant dielectric
displacement
s
Elastic compliance at constant electric field
s3 E
[m
2
1
SD
[m 2 /N]
/N]
4Pfa2t2
E
D
2
33
Modulus of Elasticity Y3, Y33 [N / m 2 = Pa]
1
(stress/strain)
SD
1
S33E
Piezoelectric strain coefficient dij [C/N =
m/V]
d33=k
T
(strain developed/applied field)
Piezoelectric voltage constant gij [Vm/N]
(open circuit field/applied stress)
Frequency constant (longitudinal) Na [Hz- m]
(Controlling Dimension x Resonant Frequency)
154
d33
9
0£3T
o033
Na = fa
Appendix I
Samvle Testine Procedure
Rod Extensional Coupling Factor, Transverse Excitation 'k 31 :
k3 -plate ( x w electrode) geometry
o
wk
a,
0
C
co
"0
E
CL
E
Frequency
'-
3
t1~
3
wkf - - k3I
.
VE
Wk~l
=31~~~
J1-ik~ VI-3
31
V
1-V
*applies to polycrystalline
samples only
Calculated Constants (from 'k31 resonance)
Elastic compliance at constant dielectric displacement
S
D
[m2/N]
,E
s1I= ( - k)11
(1k
D
Elastic compliance at constant electric field sE [m 2 /N]
Modulus of Elasticity Y,
YE [N/m
2
=
E
1
S
4fr 21 2
Pa]
(stress/strain)
Piezoelectric strain coefficient dij [C/N = m/V]
(strain developed/applied field)
1
D
E
d -'k
31
Piezoelectric voltage constant gij [Vm/ N]
(open circuit field/applied stress)
1
T E
31V
E033
d
g31
T
33
Frequency constant (transverse) N 1 [Hz m]
(Controlling Dimension x Resonant Frequency)
NI = If = wfr
155
Samvle
.... dur
Pr...... Procedure
S..r Testinv
Annendix
Ar""
A
Calculated Constants (from k 33 & k 3 l measurements)
Hydrostatic Conditions:
dh = d 33 + 2d31
dh [C/N]
2 d 33 + d 3
gg 33+ 2=
gh[Vm/N]
gh
+ 231 =
£03.IT
E
gh [Vm/N]
o Other electro-mechanical coupling coefficients:
Corresponding
to k3 -plate geometry (t x w electrode):
3
1
2
31
Corresponding to k3 -plate geometry (t x 1electrode):
3 -*--/,*, 1
E
E
where, A=
X
,
and B=
E E
c 11+ E m
Ne
13
s EE
**Note: s3 cannot be determined by resonance
:...............................................................................................................................................................
156
AppendixI
o
Sample Testinq Procedure
Planar Coupling Factorkp:
disk geometry *applies to polycrystalline samples only
where 'k 31 is known:
where
k 33 &
Ti1
k t are known:
k323tk2 + kp2+ kp2· k
kp zkI
k32
kP Vk l+'k
kt 2
2
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
AvvendixI
Ae
Samle Testing Procedure
a
I
. 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 (k 3 1-plates)
158
Avvendix
I
I·
Testinq
Samvle
_
__ 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
IZI and angle
(good for measuring the
sample resistance)
(versus)
equivalent
circuit: series
Variable
Frequency
* Can set a constant Bias
and/or Oscillation Level
(amplitude of AC signal) for
the frequency sweep.
* Can do a logarithmic or linear
IYIand angle
(good for measuring the
sample conductivity)
IZl: real &imaginary
equivalent
circuit: parallel
circuit: parallel
frequency sweep.
Temperature
equivalent
circuit:series
Temperature
+
Frequency
IYI: real &imaginary
equivalent
circuit: parallel
Frequency
+
· Oscillation Level = AC RMS
voltage
Oscillation Level
* Stores matrix of data for
Frequency
* Stores matrix of data for
frequency sweep and osc.
level sweep
L (inductance)
C (capacitance)
Can measure:
C/Q
C/D
C/[R/G]
+
Bias
frequency sweep and bias
sweep.
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
sample area
where, F = force measured with the load cell.
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
Ecmay 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=
i = dQ/dt
E+P =
i = current (A
o+ KE =
E
C/s)
i
Hysteresis Loop for
Polycrystalline Ferroelectric
Hysteresis Loop for a Classical
Ferroelectric Single Crystal
ID
50
Ps
S
U
U
E
0
0
N
CL.
cur
-U50
et 1. (1971)
0
50
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):
(133
0.12
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 ,
total area unllr' cIlr1 : [I
a
I(n
·r
e-
'E
-W
V)
o
162
Field
7
-i
Avvendix
d II
Samle
TestinQ,Procedure
Procedure
ml Testin
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 87.5wt% H 20
constituent.
3. Add a magnetic stirrer to the solution and place the beaker into the water
bath (750 C).
4. Cover the beaker with a glass dish in order to prevent excessive H 2 0
evaporation during the process. You may want to mark the initial level of the
H 2 0 solution so that you can subsequently refill with H 20 if there is
substantial evaporation.
5. Stir slowly (setting the stir plate on low speed) at 75C for 3 hours.
165
I
Annendix
[F!
Armendix--
Relative
vrah ...
ato Avroach
Toeac Factor
Reatv Tolerance
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)0 3 (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
Relative ToleranceFactorApproach...
Appendix III
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
Apendx
II
App-Ii-i II
RA +
Relative
ToleranceFactor Avroach
vrah. ...
eaieTlrneFco
Ro:
B-Site
O
*
+
m
r,~
(1/2, 1/2,
1/2)
O-sites (/2, ½,0); (2,
A-site (0,0,0)
0,
/2);
(0, 1/2, /2)
...
RA = A-site cation radius (avg.)
PR= PRitfP rnftinn rliie
{/ln \
Ro = Oxygen ion radius
Figure A111.1
Illustration of the Ideal Cubic Perovskite Structure (A2+B4 +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
Avvendix III
Alenil
I
Relative ToleranceFactorAvroach ...
Rltv
TlrneFcoAloah.
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 ToleranceFactor 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 endmember. 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 ToleranceFactor 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
NBT-KBT8*
A
(NaO
sBi
5 0.5) 0 94 Bao 6Ti0 3
NaO.
42 Ko.Bio.TiO 3
* NBT-PT14
(N ao.BiO.5) 0.86Pb
0 .14Ti 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 ToleranceFactor 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 FactorApproach...
NBT-XBT-3NBZ
Predicted Target for MPB: It = 0.9755 - 0.9775[
Peak (200) 2-Theta Range: 44.750 - 480
{Background & Ka2Subtracted; Filtered}
I
I
I
I -,
j
I
I
. 1.1,
.
1
11
I
1
I~ ~~ ~ ~ ~ ~ I I
~ 1 )~~~ III
l-TH·~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
I
I
I
I~~~~~~~~~~~~~~~~~~~~~~~~
. PA_
I
I
I
5
45
4
I
75
4725
475
I
In
I
I-I
I
S
I
U15155
Ih"I
uln
rsTI
111- I'll
I
11
.11,
.I-
.1
a
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 ToleranceFactorApproach...
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-PEboundary, which
this work has shown to be a zone of optimized properties in the relaxor NBT-BTNBZ composition system.
174
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