Characterization, Modeling, and Energy Harvesting of Phase Transformations in Ferroelectric ...

224 Pages·2015·9.98 MB·English

UCLA
UCLA Electronic Theses and Dissertations
Title
Characterization, Modeling, and Energy Harvesting of Phase Transformations in Ferroelectric
Materials
Permalink
https://escholarship.org/uc/item/6dq5z3jn
Author
Dong, Wen
Publication Date
2015

Peer reviewed|Thesis/dissertation
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University of California
UNIVERSITY OF CALIFORNIA
LOS ANGELES

Characterization, Modeling, and Energy Harvesting of
Phase Transformations in Ferroelectric Materials

A dissertation submitted in partial satisfaction
of the requirements for the degree of
Doctor of Philosophy in Mechanical Engineering

By

Wenda Dong

2015
© Copyright by
Wenda Dong
2015
ABSTRACT OF THE DISSERTATION
Characterization, Modeling, and Energy Harvesting of
Phase Transformations in Ferroelectric Materials
By
Wenda Dong
Doctor of Philosophy in Mechanical Engineering
University of California, Los Angeles, 2015
Professor Christopher S. Lynch, Chair

Solid state phase transformations can be induced through mechanical, electrical, and thermal
loading in ferroelectric materials that are compositionally close to morphotropic phase
boundaries. Large changes in strain, polarization, compliance, permittivity, and coupling
properties are typically observed across the phase transformation regions and are phenomena of
interest for energy harvesting and transduction applications where increased coupling behavior is
desired.
This work characterized and modeled solid state phase transformations in ferroelectric
materials and assessed the potential of phase transforming materials for energy harvesting
applications. Two types of phase transformations were studied. The first type was ferroelectric
rhombohedral to ferroelectric orthorhombic observed in lead indium niobate lead magnesium
niobate lead titanate (PIN-PMN-PT) and driven by deviatoric stress, temperature, and electric
field. The second type of phase transformation is ferroelectric to antiferroelectric observed in
lead zirconate titanate (PZT) and driven by pressure, temperature, and electric field.
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Experimental characterizations of the phase transformations were conducted in both PIN-PMN-
PT and PZT in order to understand the thermodynamic characteristics of the phase
transformations and map out the phase stability of both materials. The ferroelectric materials
were characterized under combinations of stress, electric field, and temperature.
Material models of phase transforming materials were developed using a thermodynamic
based variant switching technique and thermodynamic observations of the phase transformations.
These models replicate the phase transformation behavior of PIN-PMN-PT and PZT under
mechanical and electrical loading conditions. The switching model worked in conjunction with
linear piezoelectric equations as ferroelectric/ferroelastic constitutive equations within a finite
element framework that solved the mechanical and electrical field equations. This paves the way
for future modeling work of devices that incorporate phase transforming ferroelectrics.
Studies on the energy harvesting capabilities of PIN-PMN-PT were conducted to gauge
its potential as an energy harvesting material. Using the phase stability data collected in the
characterization studies, an ideal energy harvesting cycle was designed and explored to ascertain
the maximum energy harvesting density per cycle. The energy harvesting characteristics under
non-ideal sinusoidal stress and constant electric load impedance were also investigated. Energy
harvesting performance due to changes in loading frequency and electrical load impedance was
reported.

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The dissertation of Wenda Dong is approved.

Gregory P. Carman
Laurent Pilon
Ertugrul Taciroglu
Christopher S. Lynch, Committee Chair

University of California, Los Angeles
2015
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TABLE OF CONTENTS

1. Introduction ..............................................................................................................................1
1.1. Motivation ...........................................................................................................................1
1.2. Background .........................................................................................................................5
1.2.1. History of 95/5 PZT .................................................................................................5
1.2.2. History of [011] Cut and Poled Single Crystal Relaxor Ferroelectrics ...................9
1.2.3. History of Micromechanics Modeling ...................................................................14
1.2.4. History of Phase Field Modeling ...........................................................................17
1.2.5. History of Energy Harvesting ................................................................................19
1.3. Contributions ....................................................................................................................21
1.4. Dissertation Overview ......................................................................................................22

2. Pressure, Temperature, and Electric Field Dependence of Phase Transformations in Nb
Modified 95/5 Lead Zirconate Titanate ...............................................................................27
2.1. Experimental Approach ....................................................................................................28
2.1.1. Specimen Preparation ............................................................................................28
2.1.2. Experimental Arrangement ....................................................................................29
2.1.3. Experimental Methodology ...................................................................................31
2.2. Results ...............................................................................................................................32
2.3. Discussion .........................................................................................................................36
2.4. Concluding Remarks ........................................................................................................47

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3. Characterization of FER – FEO Phase Transformation in PIN-PMN-PT ........................49
3.1. Experimental Arrangement ...............................................................................................51
3.1.1. Materials and Specimen Preparation .....................................................................51
3.1.2. Experimental Procedure .........................................................................................52
3.2. Experimental Results and Discussion ...............................................................................55
3.3. Concluding Remarks ........................................................................................................65

4. Ideal Energy Harvesting Cycle using a Phase Transformation in Ferroelectric PIN-
PMN-PT Relaxor Single Crystals .........................................................................................66
4.1. Ideal Energy Harvesting Cycle .........................................................................................68
4.2. Experimental Arrangement ...............................................................................................73
4.2.1. Materials and Specimen Preparation .....................................................................73
4.2.2. Experimental Procedure .........................................................................................74
4.3. Experimental Results ........................................................................................................76
4.4. Discussion .........................................................................................................................81
4.5. Conclusions .......................................................................................................................82

5. Frequency and Electric Load Impedance Effects on Energy Harvesting Using Phase
Transforming PIN-PMN-PT Single Crystal ........................................................................84
5.1. Non-Ideal Energy Harvesting Cycle .................................................................................85
5.2. Experimental Arrangement ...............................................................................................89
5.2.1. Materials and Specimen Preparation .....................................................................89
5.2.2. Experimental Arrangement ....................................................................................90
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5.3. Experimental Results ........................................................................................................92
5.4. Discussion .......................................................................................................................104
5.5. Conclusions .....................................................................................................................113

6. Micromechanics Model of Solid State Ferroelectric Phase Transformations ................115
6.1. Constitutive Relations .....................................................................................................117
6.2. Boundary Value Problems and Finite Element Formulation ..........................................120
6.3. Micromechanics Switching Criteria ...............................................................................123
6.4. Results and Discussion ...................................................................................................133
6.4.1. Model of 95/5-2Nb PZT ......................................................................................133
6.4.2. Model of Near MPB FER PIN-PMN-PT ..............................................................139
6.5. Conclusions .....................................................................................................................143

7. A Finite Element Based Phase Field Model for Ferroelectric Domain Evolution .........145
7.1. Material Model ...............................................................................................................147
7.1.1. Time-Dependent Ginzburg-Landau .....................................................................147
7.1.2. Finite Elements ....................................................................................................148
7.1.3. Constitutive Relation ...........................................................................................152
7.2. Implementation ...............................................................................................................161
7.3. Results and Discussion ...................................................................................................163
7.4. Conclusions .....................................................................................................................168

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8. Conclusions ...........................................................................................................................171
8.1. Summary of Results ........................................................................................................172
8.2. Contributions ..................................................................................................................175
8.3. Future Work ....................................................................................................................176

A Variant Transformation Equations....................................................................................179
A.1 Phase/Variants Transformation Matrices .......................................................................179
A.1.1 Tetragonal ..............................................................................................................179
A.1.2 Rhombohedral .......................................................................................................180
A.1.3 Orthorhombic ........................................................................................................182
A.2 Grain Randomization in Ceramic Materials ...................................................................186

B 95/5-2Nb PZT Phase Transformation Supplementary Data ...........................................188

C PIN-PMN-PT Phase Transformation Energy Harvesting Supplementary Data ...........191
C.1 Idealized Energy Harvesting Cycle ................................................................................191
C.2 Non-Idealized Energy Harvesting Cycle ........................................................................193

References ...................................................................................................................................197

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