Investigation of Piezoelectric Softening Mechanisms in Lead Zirconate Titanate Using Diffraction and Property Measurements

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Investigation of Piezoelectric Softening Mechanisms in Lead Zirconate Titanate Using Diffraction and Property Measurements
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Seshadri, Shruti B.
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Doctorate ( Ph.D.)
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University of Florida
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Materials Science and Engineering
Committee Chair:
Jones, Jacob L.
Committee Members:
Hummel, R. E
Andrew, Jennifer
Hess, Henry
Nishida, Toshikazu

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diffraction -- lead -- piezoelectric -- softening -- titanate -- zirconate
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Abstract:
Lead zirconate titanate (PZT) is a well-known piezoelectric ceramic of commercial and scientific importance. Typically, PZT is used in its doped form as doping allows its properties to be tailored for specific applications. Donor doping turns PZT into a "soft" ferroelectric.One of the characteristics of soft ferroelectrics is an increase in their longitudinal piezoelectric coefficient. Softening is currently attributed to an increase in the concentration of lead vacancies and the associated effect on the behavior of ferroelectric domain walls. However, the exact mechanism by which donor doping enhances the longitudinal piezoelectric coefficient is still not understood. In this work, the crystallographic response of donor-doped PZT is studied in situ during the application of electric fields in order to deduce the strain mechanisms which contribute to ferroelectric softening. X-ray diffraction from a synchrotron source is employed for this investigation. It was found that the use of different donor dopants results in distinctive, characteristic strain mechanisms that soften PZT. Sm and Nd aid in the softening of PZT solely by enhancing 90° domain wall mobility. However, La and Nb doping results in a material with coexisting ferroelectric phases. It was further found that Nb doping results in at least two additional strain mechanisms including interphase boundary motion and alarge strain in the (200) rhombohedral lattice plane. As piezoelectrics are also used in high temperature applications, the temperature dependence of the piezoelectric coefficient in soft doped PZT was also investigated. It was found that Sm doping leads to a high temperature (˜ 300°C)piezoelectric coefficient that is substantially greater than that found in La and Nb-doped PZT. In some cases, the coefficient in Sm-doped PZT is greater than that of La and Nd-doped PZT by a factor of two. Conventionally, the largest piezoelectric coefficient values are obtained in soft doped PZT by using a Zr:Ti ratio close to the morphotropic phase boundary (MPB). It is shown that in Sm-doped PZT, enhanced high temperature piezoelectric coefficients can also be obtained at compositions far from the MPB due to the presence of a mixed tetragonal and cubic phase. The mixed phase is hypothesized to enable a larger extrinsic piezoelectric response in Sm doped PZT due to enhanced strain accommodation in the coexisting polymorphic phases.  In summary, it is presented that dopants yield signature,qualitative softening mechanisms, contributing differently to high piezoelectricity in PZT. The results suggest that in contrast to prior-held assumptions, an increase in Pb vacancies is not a necessary criterion for softening.
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Thesis (Ph.D.)--University of Florida, 2012.
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Adviser: Jones, Jacob L.
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by Shruti B. Seshadri.

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1 INVESTIGATION OF PIEZOELECTRIC SOFTENING MECHANISMS IN LEAD ZIRCONATE TITANATE USING DIFFRACTION AND PROPERTY MEASUREMENTS By SHRUTI B. SESHADRI A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY UNIVERSITY OF FLORIDA 2012

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2 2012 Shruti B. Seshadri

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3 To my family

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4 ACKNOWLEDGMENTS I am very grateful t o my adviser, Prof. Jacob Jones, for giving me the opportunity to do this work and for guiding me through my PhD. I thank Prof. Henry Hess for his guidance through my MS studies. I owe both Prof. Jones and Prof. Hess an intellectual debt for equipping me w ith the skills necessary to be a researcher. My approach to scientific problems is influenced by them to a great degree. I thank my committee members, Prof. Jennifer Andrew, Prof. Henry Hess, Prof. Rolf Hummel, and Prof. Toshikazu Nishid a for their suppor t and interest in my work. Many thanks to the wonderful people in the academic advising office: Martha McDonald, Meisha Wade, Doris Harlow and Jennifer Horton for their help. During my PhD, I had the opportunity to collaborate with Prof. Dragan Damjanovic from the Laboratory of Ceramics, Institute of Materials, Swiss Federal Institute of Technology EPFL, Prof. Pam Thomas from the Department of Physics, University of Warwick, Dr. Andrew Studer from the Bragg Institute, Australian Nuclear Science and Techn ology Organisation (ANSTO), and Prof. Juan Nino from the Department of Materials Science and Engineering, University of Florida. I thank Prof. Damjanovic for allowing me to spend three weeks doing experiments in his laboratory. I am also grateful for the p atience with which he was always willing to discuss my data and ferroelectrics with me at a time when I was new to the field. I thank Prof. Thomas for the excellent, stimulating discussions on interpreting crystallographic data. I am thankful to Dr. Studer for showing me how to play with neutrons and for all the expertise he provided during the neutron diffraction experiments at ANSTO. Special thanks to Prof. Nino for giving me full access to his laboratory and above all, for never turning me away when I ha d questions or wanted to discuss ideas.

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5 I am thankful to Prof. Moudgil for the excellence with which he taught the Interfacial Phenomena courses. I also thank him for the enthusiasm he showed in my work and for taking the time and effort to mentor me. I a m much obliged to Gautam Kini for encouraging me to apply to the Materials Science and Engineering program at the University of Florida and to Elena Aksel for encouraging me to join Prof. Jones' research group. I thank the organizers of the 12 th National School on Neutron and X ray scattering for the great introduction to the powerful characterization technique of diffraction. I wish to express my utmost gratitude to Rajnish Sinha for helpful discussions on a variety of subjects. I also thank Sonalika Goy al, Satyajit Phadke, Christopher Turner, Luping Li, Donald Moore, Hyuksu Han and Roberto Esquivel for discussions and equipment help. I am grateful for the chance to have worked with the following undergraduate students: Michelle Nolan, Bruna Bregadiolli, Cassandra llano, Alexandra Henriques, Natasha Woodruff, David Lynch and Krystal Acosta. This work would not have progressed as quickly without them. Michelle also measured the temperature laboratory in the Technische Universitt Darmstadt. Special thanks to her for sticking with me from beginning to end. For their friendship, counsel, support, knowledge and for being incredible lab mates, I thank the members of the JJones gr oup: Abhijit, Anderson, Jenny, Goknur Dipankar, Krishna, Akito, Tedi Marie, Sungwook, Bas, Elena, Giovanni, Brienne,

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6 Tarielle, Jared, Chris Dosch, Lyndsey, Katherine, Clay, Michelle, Bruna, Ali, Natasha, David, Krystal, Michael, Peishi, Henry, Claudia, Dan iel, Zach, Humby, Isaac, Patrick and Zhi. I especially thank Krishna for his guidance during my graduation semester, Dipankar for the discussions that made graduate school that much more awesome and Jenny for reviewing my dissertation, and help with the Ri etveld refinements presented in this work. I deeply appreciate the support of my friends. I cannot thank my family enough for always doing everything possible to encourage and support me. I acknowledge the Bragg Institute at the Australian Nuclear Science and Technology Organisation (ANSTO) for providing neutron diffraction facilities through program proposal number PP911. Use of the Advanced Photon Source at Argonne National Laboratory was supported by the U. S. Department of Energy, Office of Science, Off ice of Basic Energy Sciences, under Contract No. DE AC02 06CH11357 and DOE under contract no. W 31 109 ENG 38. I thank Dr. Yang Ren and Dr. Guy Jennings for their help with the usage of beamlines 11 ID C and Dr. Matthew Suchomel for his help with the usage of beamline 11 BM. I gratefully acknowledge the following funding sources: Tatachem Golden Jubilee Foundation Trust for the funds to travel to the USA from India to start graduate school; M.K.Tata Trust for the funds to cover my expenditures in the first month of graduate school; The National Science Foundation (NSF) award numbers DMR 0746902 and OISE 0755170 for the stipend and travel funds that enabled this work.

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7 TABLE OF CONTENTS page ACKNOWLEDGMENTS ................................ ................................ ................................ .. 4 LIST OF TABLES ................................ ................................ ................................ ............ 9 LIST OF FIGURES ................................ ................................ ................................ ........ 10 LIST OF ABBREVIATIONS ................................ ................................ ........................... 12 ABSTRACT ................................ ................................ ................................ ................... 13 CHAPTER 1 INT RODUCTION ................................ ................................ ................................ .... 15 1.1 Motivation and Problem Statement ................................ ................................ ... 15 1.2 Piezoelectric ity ................................ ................................ ................................ .. 16 1.3 Dielectric Permittivity ................................ ................................ ......................... 17 1.4 Ferroelectricity and Ferroelectric Domain Structure ................................ .......... 17 1.5 Polycrystalline Ferroelectrics ................................ ................................ ............ 21 1.6 Lead Zirconate Titanate ................................ ................................ .................... 22 1.7 Intrinsic and Extrinsic Contributions to the Piezoelectric Response .................. 24 1.8 Morphotropic Phase Boundary and Enhanced Piezoelectric Response ........... 24 1.8.1 Increased Ease of Polarization Reorientation during Poling ............. 25 1.8.2 Displacement of Domain Walls and Phase Boundaries, and their Contribution to Electro Mechanical Properties ................................ ........ 26 1.8.3 Role of the Monoclinic Phase and Polarization Rotation ................... 28 1.9 Hard and Soft PZT ................................ ................................ ............................ 29 1.10 Organization of the Dissertation ................................ ................................ ...... 30 2 EXPERIMENTAL METHODS ................................ ................................ ................. 39 2.1 Synthesis of PZT Based Cerami cs ................................ ................................ ... 39 2.2 Temperature Dependent Dielectric Property Measurements ............................ 40 2.3 Temperature Dependent Piezoelectric Property Measurements ...................... 40 2.4 Characterization of Electric Field induced Structural Changes using High Energy X ray Diffraction from a Synchrotron Source ................................ ........... 41 2.4.1 Experimental Setup ................................ ................................ ................. 41 2.4.2 Binning of Diffraction Data ................................ ................................ ....... 42 2.5 Characterization of Temperature Dependent Structural Changes using High Resolution XRD from a Synchrotron Source ................................ ....................... 42 3 A STRUCTURAL INSIGHT INTO THE SOFTENING MECHANISMS IN LEAD ZIRCONATE TITANATE ................................ ................................ ......................... 49

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8 3.1 Softening in Donor Substituted PZT ................................ ................................ .. 49 3.2 Experimenta l ................................ ................................ ................................ ..... 50 3.2.1 Sample Preparation ................................ ................................ ................. 50 3.2.2 Diffraction Measurements ................................ ................................ ........ 51 3.2.3 Coercive Field and Piezoelectric Coefficient Measurements ................... 52 3.3 Results ................................ ................................ ................................ .............. 52 3.4 Discussion ................................ ................................ ................................ ........ 56 3.4.1 90 Domain Wall Motion ................................ ................................ .......... 57 3.4.2 Coexistence of mixed ferroelectric phases ................................ .............. 57 3.4.3 Interphase Boundary Motion During Subcoercive Electric Field Application ................................ ................................ ................................ ..... 58 3.4.4 Strain in the Rhombohedral (200) Lattice Plane ................................ ...... 58 3.5 Conclusions ................................ ................................ ................................ ...... 59 4 COOPERATIVE STRAIN ACCOMMODATION AND HIGH temperature PIEZOELECTRIC coefficients IN Soft DOPED PZT ................................ ............... 70 4.1 High Piezoelectric Coefficients in PZT ................................ .............................. 70 4.2 Experimental ................................ ................................ ................................ ..... 71 4.2 Variation of Piezoelectric and Dielectric Properties as a Functio n of Temperature in Sm, La and Nb doped PZT ................................ ......................... 72 4.3 Temperature Dependent Structural Changes in Sm, La and Nb doped PZT .... 74 4.4 Discussion ................................ ................................ ................................ ........ 76 4.5 Conclusions ................................ ................................ ................................ ...... 82 5 SUMMARY ................................ ................................ ................................ ............. 94 6 FUTURE WORK ................................ ................................ ................................ ..... 97 6.1 Measurement of the Temperature Dependent Crystallographic Response During the In Situ Application of Electric Fields ................................ ................... 97 6.2 Frequency Dependence of the Piezoelectric Response ................................ ... 97 6.3 Effect of Dopant Homogeneity ................................ ................................ .......... 98 6.4 Measurements on Undoped PZT Compositi ons ................................ ............... 98 6.5 Effect of the Ionic Radius of the Dopant on the Ferroelectric Paraelectric Phase Transition ................................ ................................ ................................ .. 98 APPENDIX: DETERMINATION OF THE CONTRIBUTION OF 90 DOMAIN WALL MOTION TO LONGITUDINAL STRAIN ................................ ................................ .. 99 LIST OF REFERENCES ................................ ................................ ............................. 106 BIOGRAPHICAL SKETCH ................................ ................................ .......................... 114

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9 LIST OF TABLES Table pa ge 3 1 Lattice parameters, phases present and coercive fields of the various doped PZT 50:50 compositions. ................................ ................................ .................... 62 3 2 Strai n mechanisms in soft doped PZT 50:50 compositions. ............................... 63 4 1 Summary of Rietveld refinement results. ................................ ............................ 89 4 2 Ratio of the slopes of the linear fits to the left and right regions of inverse susceptibility at the point of divergence. ................................ ............................. 93

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10 LIST OF FIGURES Figure page 1 3 Illustratio n of a) 180 and b) 90 domains and domain wall regions in a ferroelectric tetragonal perovskite. ................................ ................................ ...... 33 2 1 Processing steps for PbZr 1 Ti x O 3 based ceramic synthesis. ............................. 44 2 2 Schematic diagram of the measurement apparatus used to determine the in situ temperature dependent longitudinal relative permittivity. ............................. 45 2 4 Experi mental arrangement for time resolved high energy X ray diffraction.. ...... 47 2 5 Schematic of a 2D diffraction image showing the Debye Scherrer ring as measured when a) no electric field is b) an e lectric field is applied to the sample. ................................ ................................ ................................ ............... 48 3 1 Diffraction patterns showing the (002) and (200) reflections of 2 at. % Sm, Nd, La and Nb doped PZT 50:50 before the application of an electric f ield. ....... 61 3 2 Time resolved diffraction patterns measured in situ during the application of the first strong bipolar electric field ................................ ................................ .... 64 3 3 Time resolved diffraction patterns measured in situ during the application of the third strong bipo lar electric field ................................ ................................ ... 65 3 4 Selected region of the diffraction patterns showing the {002} type reflections of a) Sm b) Nd c) La and d) Nb doped PZT 50:50 before and after poling. ........ 66 3 5 Time resolved diffraction patterns measured in situ d uring the application of weak subcoercive electric fields ................................ ................................ ........ 67 3 6 Selected region of the diffraction pattern showing the {002} type reflections for a) Sm b) Nd c) La and d) Nb doped PZT 50:50. ................................ ............ 68 3 7 Gaussian fits to the {002} reflections in Nb doped PZT ................................ ..... 69 4 1 Variation of d 33 r 33 as a function of temperature for various PZT compositions. ................................ ................................ ................................ ...... 84 4 2 Behavior of d 33 as a function of temperature during the first, second and third thermal cycles for 2 at% Sm PZT 50:50. ................................ ............................ 85 4 3 Selected regions of high resolution synchrotron XRD patterns showing the (002) and (200) type reflections for Sm, La and Nb doped PZT 50 :50. .............. 86 4 4 Magnified view of the (002) and (200) tetragonal reflections of Sm, La and Nb doped PZT 50:50 at 332 C. ................................ ................................ .......... 87

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11 4 5 Rietv eld refinements of 2 at % Sm doped PZT 50:50 fit to a cubic model (332 C, 360 C, 500 C), tetragonal model (250 C, 290 C, 308 C, 332 C) and a mixed phase model consisting of the tetragonal P 4 mm and cubic Pm m phases (308 C, 332 C). ................................ ................................ ...................... 88 4 6 Variation of the dielectric loss tangent as a function of temperature for various PZT compositions. ................................ ................................ ................. 90 4 7 Inverse dielectric susceptibility as a function of temperature for 2 at% Sm, La and Nb doped PZT 50:50. ................................ ................................ .................. 91 4 8 Linear fits to the a) left, and b) right linear regions at the point of divergence of inverse susceptibility plotted for 2 at% Sm, La and Nb PZT 50:50. ................ 92 A 1 002 two subcoercive electric field amplitudes. ................................ ......................... 104 A 2 002 nt modeled values and the symbols represent experimentally measured data ................... 105

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12 LIST OF ABBREVIATION S EDS Energy dispersive spectroscopy LCR Inductor, capacitor, resistor LGD Landau Ginzburg Devonshire MPB Morphotropic phase boundary PZT Lead zirconate titanate SEM Scanning electron microscopy TEM Transmission electron microscopy XRD X ray diffraction YSZ Yitria stabilized zirconia

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13 Abstract of Dissertation Presented to the Graduate School of the University of Florida in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy INVESTIGATION OF PIEZOELECTRIC SOFTENING MECHANISMS IN LEAD ZIRCONATE TITANATE USING DIFFRACTION AND PROPERTY MEASUREMENTS By Shruti B. Seshadri December 2012 Cha ir: Jacob L. Jones Major: Materials Science and Engineering Lead zirconate titanate (PZT) is a well known piezoelectric ceramic of commercial and scientific importance. Typically, PZT is used in its doped form as doping allows its properties to be tailore d for specific applications. Donor doping turns PZT into a "soft" ferroelectric. One of the characteristics of soft ferroelectrics is an increase in their longitudinal piezoelectric coefficient. Softening is currently attributed to an increase in the conce ntration of lead vacancies and the associated effect on the behavior of ferroelectric domain walls. However, the exact mechanism by which donor doping enhances the longitudinal piezoelectric coefficient is still not understood. In this work, the crystallo graphic response of donor doped PZT is studied in situ during the application of electric fields in order to deduce the strain mechanisms which contribute to ferroelectric softening. X ray diffraction from a synchrotron source is employed for this investig ation. It was found that the use of different donor dopants results in distinctive, characteristic strain mechanisms that soften PZT. Sm and Nd aid in the softening of PZT solely by enhancing 90 domain wall mobility. However, La and Nb doping results in a material with coexisting ferroelectric phases. It was further found

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14 that Nb doping results in at least two additional strain mechanisms including interphase boundary motion and a large strain in the (200) rhombohedral lattice plane. As piezoelectrics are also used in high temperature applications, the temperature dependence of the piezoelectric coefficient in soft doped PZT was also investigated. It was found that C) piezoelectric coefficient that is substantia lly greater than that found in La and Nb doped PZT. In some cases, the coefficient in Sm doped PZT is greater than that of La and Nd doped PZT by a factor of two. Conventionally, the largest piezoelectric coefficient values are obtained in soft doped PZT b y using a Zr:Ti ratio close to the morphotropic phase boundary (MPB). It is shown that in Sm doped PZT, enhanced high temperature piezoelectric coefficients can also be obtained at compositions far from the MPB due to the presence of a mixed tetragonal and cubic phase. The mixed phase is hypothesized to enable a larger extrinsic piezoelectric response in Sm doped PZT due to enhance d strain accommodation in the coexisting polymorphic phases. In summary, it is presented that dopants yield signature, qualitati ve softening mechanisms, contributing differently to high piezoelectricity in PZT. The results suggest that in contrast to prior held assumptions, an increase in Pb vacancies is not a necessary criterion for softening.

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15 CHAPTER 1 INTRODUCTION 1.1 Motivat ion and Problem Statement PZT is a piezoelectric material of commercial and scientific interest as it has very high piezoelectric coefficients. These high piezoelectric properties are obtained by the addition of soft dopants to PZT. Even though the widespr ead commercial application of soft doped PZT has made it one of the most studied ferroelectric systems, the mechanism by which softening occurs in PZT is not understood. This is because changes in the lattice and domain response of PZT due to the addition of soft dopants have not been measured in situ during the application of electric fields. Therefore, the first objective of this work is to use X ray diffraction from a synchrotron source to study the crystallographic structure of various soft doped PZT co mpositions. In addition, the structural response of these compositions during the in situ application of electric fields is measured. The response of the various compositions is compared. From these experimental studies, the structural origin of softening mechanisms in PZT is deduced. The piezoelectric coefficient of soft PZT is temperature dependent. 1 The second objective of this work is to establish temperature dependent structure property relationships for select soft doped PZT materials. High resolutio n XRD from a synchrotron source is used for the structural studies. These studies are carried out across a range of Zr:Ti ratios in order to separate the MPB effects from other possible variables. Temperature dependent piezoelectric and dielectric properti es are measured from room temperature to above the Curie temperature. This analysis also provides information regarding the dopant dependent paraelectric ferroelectric phase transition characteristics in PZT.

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16 1.2 Piezoelectricity Piezoelectricity is a mat erials property, wherein the electric charge developed on the surface of the material is linearly coupled to the mechanical stress applied on it (Eq. 1 1). 2 Conversely, an applied electric field produces a linearly proportional strain in these materials (E q. 1 2). Piezoelectric materials thus convert electrical energy into mechanical energy and vice versa. (1 1) (1 2) In Eq. 1 1 and 1 2, D i is the electric displacement (Cm 2 ) vector, E i is the electric field vector (Vm 1 ), S ij is the strain ten sor, T ij is the stress tensor (Nm 2 ) and d ijk and d' ijk are the piezoelectric charge or strain coefficient tensors. d ijk and d' ijk are third rank tensors and the components of this tensor are referred to as the piezoelectric coefficients. The units for the se coefficients are CN 1 and mV 1 respectively. Thermodynamic considerations show that d ijk = d' ijk namely the coefficient that connects the field and strain is equal to the one that connects stress and polarization. The electrical response to mechanical stimulation is the direct piezoelectric effect (Eq. 1 1) and the mechanical response to electrical stimulation is referred to as the converse piezoelectric effect (Eq. 1 2). A non centrosymmetric crystal structure is a necessary criterion for expression o f piezoelectricity. Lead zirconate titanate (PbZr 1 x Ti x O 3 or PZT), the material investigated in this dissertation, is an example of an inorganic piezoelectric material.

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17 1.3 Dielectric Permittivity Dielectric permittivity 2,3,4 is a measure of the ability of a material to be polarized by an electric field. The polarization P i (Cm 2 ) that is induced in an insulating polarizable material (a dielectric) by an applied electric field vector E j (Vm 1 ) is given by: (1 3) ij (Fm 1 ) is a second rank tensor known as dielectric susceptibility of a material. Relation 1 3 is valid only for linea r materials or in the linear range for nonlinear materials. The total surface charge density that is induced in the material by the applied field is given by the dielectric displacement vector, D i (Cm 2 ): (1 4) o is a scalar quantity that equals 8.854 10 12 Fm 1 It is the dielectric permittivity of a vacuum. Eq. 1 4 can also be presented as: (1 5) ij is the dielectric permittivity of the material. The relative dielectric permittivity, or r,ij is: (1 6) 1.4 Ferroelectricity and Ferroelectric Domain Structure Some piezoelectric materials, such as PZT, are ferroelectric in nature. This means that each unit cell of the material has a spontaneous polarization or dipole moment. The direction of the polar axis in ferroelectric materials can be reversed by the application of an electric field. The new direction of the polar axis is maintained upon the removal of the field.

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18 PZT, like many other ferroelectric materials, transforms into a ferroelectric state from a high temperature paraelectric (non polar) phase. Upon cooling, PZT undergoes a phase transition into a polar structure. The temperature at which this pha se transition occurs is called the Curie temperature. The phase transition occurs by a small displacement of some ions from their centrosymmetric positions or by some other ordering process that creates a net dipole moment. Near the Curie temperature, the crystalline lattice is dielectrically compliant and can be polarized strongly by small electric fields. Therefore, the permittivity of PZT reaches a maximum at the Curie temperature as illustrated in Figure 1 1. This dielectric compliance of the lattice ar ound the Curie temperature makes dielectric properties temperature dependent across a large span of temperatures. This is one reason why other materials properties such as the piezoelectric coefficient can also be temperature dependent. The spontaneous po larization in a ferroelectric crystal is usually not aligned along the same direction throughout the entire crystal. PZT adopts the perovskite crystal structure as shown in Figure 1 2. PZT with a Zr:Ti ratio of 52:48, i.e. PbZr 0.52 Ti 0.48 O 3 transforms from a non ferroelectric (paraelectric) cubic phase to a ferroelectric tetragonal phase at its Curie temperature of 386 C. 5 Perovskite crystals have the general formula ABO 3 where the valence of the A site and B site cations can vary from +1 to +3 and +3 to +6 respectively. As shown in Figure 1 2, the perovskite structure may be viewed as consisting of a BO 6 octahedra surrounded by A cations. Most of the ferroelectric materials that are of practical application have perovskite structures and many are solid solu tions of lead titanate, PbTiO 3 and lead zirconate, PbZrO 3 The spontaneous polarization direction in tetragonal PZT lies along the c T axis of the

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19 tetragonal unit cell and the crystal distortion is usually described in terms of shifts of the O and Ti ions r elative to Pb. 4,6,7 In the ferroelectric phase, the crystal is spontaneously strained with a T C < c T where a T and a C are the a axes of the tetragonal and cubic unit cell, respectively. The six directions (including positive and negative orientations) along the three a C axes of the cubic unit cell are equivalent. When the crystal is cooled thro ugh the Curie temperature, the probability that the spontaneous polarization may arise along any one of the a C axes directions is equal. The direction along which the polarization will develop depends on the local and global electrical and mechanical bound ary conditions imposed on the material. Once these domains are formed, regions of the crystal with uniformly oriented spontaneous polarization directions are called ferroelectric domains. The region between two domains is the domain wall as illustrated in Figure 1 3. The walls which separate domains with oppositely oriented polarization directions are called 180 walls and those which separate regions with mutually perpendicular polarization directions are called 90 walls (Figure 1 3). 4,7 The driving forc e for the formation of 180 domain walls is the depolarizing field (E d ) that arises due to the onset of the spontaneous polarization (P S ) at the Curie temperature. 8 E d oriented in the opposite direction to P S as shown in Figure 1 4. E d develops whenever th ere is a non homogenous distribution of P S Non homogenous distribution of P S can occur due to a reduction in the polarization near the surface of the ferroelectric (polarization is zero surrounding the ferroelectric material and non zero within) or due t o a change in the direction of polarization at grain boundaries. E d may be very strong (of the order of MVm 1 ) rendering the single domain state of the ferroelectric

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20 unfavorable. 4,7,8 The electrostatic energy associated with the depolarizing field may be m inimized if i) the ferroelectric splits into domains with oppositely oriented polarization (Figure 1 4), or ii) the depolarizing charge is compensated for by electrical conduction through the crystal or by charges from the material surrounding (such as fro m the atmosphere or the electric circuit to which the material is connected).As shown in Figure 1 4 the PZT splits into 90 domains due to the influence of mechanical stresses when a part of its crystal is mechanically compressed along the (100) cubic dire ction as it is cooled through the Curie temperature. To minimize the elastic energy, the long c T axis of the tetragonal cell will develop perpendicular to the stress. In the unstressed section of the crystal, polarization may remain parallel to the direct ion of the stress (short a T axis perpendicular to the stress). The domain walls in PZT may therefore separate regions in which polarization orientation is antiparallel (180 walls) or perpendicular (90 walls) to each other. Both 90 and 180 walls may r educe the effects of depolarizing electric fields. However, only the formation of 90 walls minimizes the elastic energy. A combination of electric and elastic boundary conditions to which a crystal is subjected as it is cooled through the ferroelectric ph ase transition temperature usually leads to a complex domain structure with many 90 and 180 walls. Domain walls which differ in orientation to the spontaneous polarization vector are called ferroelectric domain walls and those which differ in orientation to the spontaneous strain are called ferroelastic domain walls. In PZT, 180 walls are purely ferroelectric because they differ only in the orientation of the polarization vector. 90

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21 walls are both ferroelectric and ferroelastic as they differ both in or ientation of the polarization vector and the spontaneous strain. The types of domain walls that can occur in a ferroelectric crystal depend on the symmetry of both the non ferroelectric and ferroelectric phases of the crystal. 9 In the rhombohedral phase of PZT, the direction of the polarization develops along the body diagonals ( 111 direction) of the paraelectric cubic unit cell. This allows 8 possible directions of the spontaneous polarization with 180 71 and 109 domain walls. Criteria which may be u sed to derive possible types of domain walls in a ferroelectric material have been derived by Fousek and Janovec. 9 Observations made using transmission electron microscopy show that domain walls are on the order of 1 10 nm. 8 1.5 Polycrystalline Ferroelect rics Due to the complex set of elastic and electric boundary conditions at each grain, ferroelectric grains in polycrystalline ceramics are always split into many domains as shown in Figure 1 5. If the direction of the spontaneous polarization throughout t he material is random or distributed in such a way as to lead to zero net polarization, the piezoelectric effects of individual domains will cancel and this material is not piezoelectric at the macroscopic length scale. Polycrystalline ferroelectric materi als may be brought into a polar state by applying a strong electric field (1 10 kV mm 1 ) often at elevated temperatures. This process, termed poling, cannot orient grains but can reorient domains within individual grains in the direction of the applied field. A poled polycrystalline ferroelectric exhibits piezoelectric properties, even if many domain walls remain (Figure 1 5). The measured polarization after the removal of the field (at zero field) is called remnant polarization, P R The maximum remnant polarization, (P R ) max achievable in a

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22 polycrystalline material depends on the availabl e domain states. In a ferroelectric which exhibits only 180 domain walls the maximum remnant polarization in the polycrystalline state is 0 25 P S In a tetragonal ferroelectric with 6 available domain states(P R ) max = 0.83 P S In a rhombohedral ferroelectr ic with 8 possible domain states, (P R ) max = 0 87 P S In an orthorhombic ferroelectric with 12 possible domain states, (P R ) max = 0 91 P S 10 These ideal values assume reorientation of all domains along available directions dictated by the poling field. The a ctual polarization is in fact always lower, as many domains cannot be reoriented due to a complex set of internal stresses and electric fields in grains and because some domains switch back after the poling field is removed. In materials with non 180 doma in walls, the poling process changes the sample dimensions, because reorientation of non 180 domains involves reorientation of the spontaneous strain (see Figures 1 3 and 1 4). 1.6 Lead Zirconate Titanate Lead zirconate, PbZrO 3 is antiferroelectric (and not piezoelectric). 8 Lead titanate (PbTiO 3 ) is of limited interest as a piezoelectric material since it is difficult to pole and has a large thermal expansion anisotropy of the tetragonal phase which causes mechanical fracture during cooling from the sinte ring temperature. 11 However, the solid solution of these two compositions, lead zirconate titanate, Pb(Zr 1 x Ti x )O 3 or PZT, exhibits outstanding piezoelectric properties. Its widespread use in industry, science, medicine, transportation, communications and information technologies has also made PZT one of the most studied ferroelectrics. 11,12,13,14 Despite this, many aspects of the high piezoelectric response in PZT remain unclear. Perhaps nothing attests better to the complex nature of PZT than the fact tha t approximately 60 years after its discovery (Shirane et al. 1952 15 ) and numerous in depth studies (e.g. Jaffe et al. 1971 16 )

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23 modifications of the composition temperature phase diagram of this ternary system are still being proposed (Noheda et al. 1999 17 ) In fact, n ew er questions are still being raised about the origins of the large piezoelectric response in this and related ferroelectric materials. 18 Lead zirconate and lead titanate are mutually soluble in all proportions. The first phase diagram of Pb(Z r 1 x Ti x )O 3 was derived by Sawaguchi 19 in 1953 showing the most prominent feature of the system, the compositionally driven structural transformation from the tetragonal ( P 4 mm ) to the rhombohedral phase ( R 3 m ) at x 0 47 at room temperature. This work was foll owed by the discovery of a large piezoelectric response in compositions close to this phase boundary by Jaffe et al. 20 in 1954. The composition temperature phase diagram of Sawaguchi was refined by Jaffe and coworkers in 1971. 16 A significant modification of the Jaffe et al. phase diagram was proposed by Noheda et al. 17 They proposed that a monoclinic phases separates the tetragonal and rhombohedral regions. The nature of this phase is still a subject of debate and much study. The phase diagram proposed by Jaffe et al. with the modification made by Noheda et al. are shown in Figure 1 6. In this work, PZT compositions are abbreviated by 100(1 x): 100 x PZT where100(1 x): 100 x indicates in percent the Zr:Ti ratio in the solid solution. Zr and Ti are randomly dist ributed over B sites of the perovskite structure AB O 3 (see Figure 1 2). For example, PZT 50:50 is used to denote a PZT composition with the chemical formula PbZr 0.5 Ti 0.5 O 3

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24 1.7 Intrinsic and Extrinsic Contributions to the Piezoelectric Response The piezoel ectric properties of polycrystalline ferroelectric ceramics are generally dependent on both intrinsic and extrinsic mechanisms. 5 Intrinsic contributions are the result of lattice strain due to the displacement of the cations. Changes in polarization of the unit cell are accompanied by a change in the unit cell volume. Intrinsic contributions in typical PZT compositions total less than 50% at room temperature. 21 The remaining contributions to the piezoelectric effect are extrinsic in nature and arise due to domain wall displacement, defect dipoles, interphase boundary motion, and intergranular interactions. 22 Extrinsic mechanisms are thermally activated processes that can be frozen out at low temperatures. 21 Figure 1 7 shows the intrinsic and extrinsic mechan isms that contribute to the piezoelectric coefficient. 1.8 Morphotropic Phase Boundary and Enhanced Piezoelectric Response A striking feature of the PZT phase diagram is the nearly temperature independent boundary between tetragonal and rhombohedral (mono clinic) phases, 16 ). The composition of the MPB is approximately PZT 52:48 at room temperature. The MPB is considered the most interesting composition from the technological application point of view as the piezoelectric coefficients, electromechanical coupling coefficients, dielectric permittivity and rem nant polarization measured on ceramic samples reach a peak in the region of the MPB (Figure 1 8). The origin of the enhanced dielectric, elastic, and piezoelectric properties of PZT at the MPB has been investigated in detail by many authors and is still a topic of avid

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25 interest. 23 Several mechanisms have been proposed to explain the enhanced piezoelectric properties of PZT at the MPB. Presently, there is no consensus in literature on this problem. The disagreement could be a mere question of the quality of samples examined by different authors but also a consequence of the scale on which the material is examined. Recent studies 24 suggest that local tetragonal and rhombohedral nanostructure of PZT in the MPB region may appear to X ray diffraction as monoclin ic. It is suggested that the high properties in the MPB region are then at least in part related to the high mobility of these nanodomains. The facilitated rotation of polarization (as evidenced by high transverse permittivity) is accomplished through easy reorientation of the nanodomains. Sections 1.8.1 1.8.3 outline the main points of the different proposed mechanisms. 18 1.8.1 Increased Ease of Polarization Reorientation during Poling The tetragonal phase has 6 possible orientations of polarization (alon g the pseudo cubic 100 directions), while in the rhombohedral phase, polarization can orient along 8 possible 111 directions. At the MPB, the tetragonal and rhombohedral phases can coexist 23 because the free energy barrier between them are very low and switching between the phases can be accomplished by external fields (e.g., by a poling field). Therefore, in effect, polarization within each grain of a tetragonal and rhombohedral mixed phase material has effectively 14 directions along which it can orient. Better poling r esults in larger piezoelectric properties. 16,23 It has been shown experimentally that remnant polarization in PZT has a maximum near the MPB. 16 Recent results suggest that the MPB region contains a monoclinic phase. 17 If this is the case, the number of av ailable orientations for polarization would be further increased as polarization can adopt 24 orientations in a monoclinic phase.

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26 1.8.2 Displacement of Domain Walls and Phase Boundaries, and their Contribution to Electro Mechanical Properties Displacemen t of domain walls and phase boundaries and their resulting contribution to the electro mechanical properties is enhanced at the MPB. 10,23 This argument is related to that presented in Section 1.8.1 but, here specifically relates to operation under subcoerc ive electric fields. With multiple domain states available in the MPB region, the energy barrier between different states should be relatively small, facilitating displacement of domain walls even by relatively weak driving fields. Similarly, the boundary between crystalline phases with degenerate energies should be easily displaced. It is known that displacement of domain walls can greatly enhance the piezoelectric and dielectric properties of ferroelectric ceramics. 25 Experimental results clearly show tha t domain wall contributions in PZT indeed increase as the MPB is approached. 26 Jones at al. 27 have shown that the displacement of phase boundaries participate in the enhanced response. Intrinsic properties of PZT crystals at the MPB region are high. Due to the historical unavailability of PZT single crystals of MPB composition, information on the intrinsic (lattice) properties of PZT is almost exclusively available through theoretical calculations, based on the phenomenological Landau Ginzburg Devonshire (L GD) approach, 28 and more recently, ab initio calculations. 29,30 Using a thermodynamics based LGD approach, it was shown qualitatively that the dielectric permittivity perpendicular to the polarization direction (transverse permittivity) diverges as the MPB is approached from both the tetragonal and rhombohedral sides, while the permittivity along the polar axis (longitudinal permittivity) exhibits a comparatively weaker divergence. 31 The reason that the transverse permittivity diverges as the tetragonal

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27 rho mbohedral phase transition is approached can be understood intuitively in the following way: in the tetragonal phase, polarization is oriented along the [001] pseudo cubic direction, while in the rhombohedral phase it develops along the [111] pseudo cubic axis. In the phase transition region, the crystal dielectrically softens along directions dictated by the symmetry of the incipient crystal structure. 32 Thus, on the tetragonal side of the MPB, the crystal dielectrically softens in such a way as to anticip ate the new direction of the polarization along the [111] pseudo cubic axis in the rhombohedral phase. This means that the longitudinal permittivity will increase much more than the transverse permittivity. A similar effect will occur on the rhombohedral s ide. This result was confirmed in a quantitative study, 28 and later extended 33 to derive general conditions for the appearance of an MPB. The maximum in piezoelectric properties is thus a direct consequence of the anomaly in the permittivity. Since diverge nce at the MPB is stronger for the transverse than for the longitudinal component of the permittivity, the shear piezoelectric coefficient will be enhanced more strongly in all phases than the longitudinal coefficient. 28 This means that the propensity of c rystals for polarization rotation is enhanced at the MPB. The anomalous behavior of monodomain single crystals at the MPB is reflected in ceramics through averaging of the properties over all grains and domain orientations. The ceramic samples thus exhibit a maximum of the properties at MPB, which are essentially the intrinsic, single crystal properties. Improved poling of ceramics at the MPB and facilitated domain wall displacement in ceramics add to this intrinsic mechanism. However, internal stresses in

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28 ceramics, interactions among grains and domains, and local texture affect the overall intrinsic as well as extrinsic response of ceramics and should not be neglected. 34,35 1.8.3 Role of the Monoclinic Phase and Polarization Rotation After the proposal of t he monoclinic phase in PZT, 17 many attempts have been made to explain MPB behavior in PZT and other ferroelectrics by enhanced piezoelectric response within this phase. It was indicated in the previous sections that the propensity of PZT crystals for polar ization rotation is augmented as the MPB is approached. The field induced polarization rotation is thought to take place within the monoclinic mirror planes (Davis et al. 2006; Fu and Cohen 2000). 36,37 It is believed that if the monoclinic phase in d eed exi sts, it facilitates the polarization rotation and hence produces a high dielectric and piezoelectric response. However, it should be noted that the propensity of a crystal for polarization rotation is determined not by the crystal structure itself but by t he value of the transverse permittivity (see section 1.7.2). Thus, LGD calculations which include the monoclinic phase suggest that property enhancement is largest at the boundary between monoclinic and tetragonal or monoclinic and rhombohedral phases, not within the monoclinic phase itself. 38 This also agrees with results of phenomenological simulations. 39 The enhancement of the properties associated with the presence of a monoclinic phase is thus likely related to pre transitional phenomena. One such exam ple of pre transitional phenomena is Curie Weiss behavior of permittivity in the cubic phase of ferroelectric material. If polarization changes direction at the MPB (e.g., tetragonal rhombohedral), the transverse permittivity will increase in both phases a round the MPB and enhance propensity of the material for polarization rotation. However, the mechanisms of enhancement of

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29 properties via divergence of the transverse permittivity are not qualitatively different, irrespective of the presence of a monoclinic phase 40 1.9 Hard and Soft PZT In ceramic processing terminology, chemical substituents of concentrations less than 5 atomic % are referred to as "dopants". 11,41 This terminology is adopted throughout this dissertation. PZT ceramics are rarely used in th eir undoped state. Commercially available samples are synthesized with chemical additives to adjust their properties for specific applications. It was discovered that addition of donor dopants leads to materials with increased resistivity, decreased ageing higher piezoelectric coefficients, higher losses, lower mechanical quality factor, and low coercive field; these materials are known as 16 Typical donor or soft dopants are Nb +5 substituting for the B site (denoted as or Vink notation) or La +3 substituting for the A site ( ). A plausible charge compensation scheme due to the introduction of the aliovalent soft dopant Nb, is shown in Eq. 1 7. (1 7) The addition of acceptor dopants leads to materials with lower permittivity, lower dielectric loss, lower resistivity, high mechanical quality factor, and more difficult poling and depoling. 16 Fe +2 substituting for the B site ( or ). A plausible charge compensation scheme due to the introduction of the aliovalent hard do pant Fe is shown in Eq. 1 8. (1 8)

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30 The mechanisms of hardening are relatively well understood, 31,42 while many interpre tations of softening are not well understood. 10,43 1.10 Organization of the Dissertation Chapter 2 provides a detailed description of the experimental methods used in this dissertation. The conditions used for the solid state processing of bulk PZT ceramic s are given. The measurement of temperature dependent dielectric and piezoelectric properties and the methodology used for structural characterization using high resolution and high energy XRD from a synchrotron source are also described. In Chapter 3, the structural changes that occur in four donor doped PZT compositions are examined in situ during the application of both large and subcoercive electric fields. High energy X rays from a synchrotron source are used for this purpose. These studies provide ins ight into the softening mechanisms in donor doped PZT. In Chapter 4, the temperature dependent piezoelectric and dielectric response of various donor doped PZT compositions are studied. The temperature dependent structural changes that occur in these mater ials are also measured using high resolution XRD from a synchrotron source. These measurements are used to provide an explanation for the origin of the anomalously high piezoelectric coefficient values shown in some compositions. Chapter 5 provides a summa ry of the dissertation. Chapter 6 proposes future work that can be carried out in the investigation of strain mechanisms that contribute towards softening. Appendix A presents method to calculate the contribution of 90 domain wall motion to longitudinal strain using a time resolved diffraction pattern taken at only one angle (parallel to the electric field) with respect to the electric field.

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31 Figure 1 1 Schematic diagram showing the changes in permittivity that occur in a ferroelectric material with temperature. The permittivity curve represents data measured in a PZT ceramic. The arrows show the possible directions of spontaneous polarization (in two dimensions). The unit cell is represented by a square in the cubic phase, and a rectangle in the tet ragonal phase. Adapted without permission from D. Damjanovic, "Ferroelectric, Dielectric and Piezoelectric Properties of Ferroelectric Thin Films and Ceramics," (Page 1279, Figure 3) Rep. Prog. Phys., 61 [9] 1267 324 (1998)

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32 Figure 1 2 The perovsk ite crystal structure of PZT in its paraelectric cubic (left), ferroelectric tetragonal (center) and rhombohedral (right) states. The ferroelectric state of PZT adopts a rhombohedral crystal structure when less than approximately 47% of the B site is occup ied by Ti. When greater than 47% of the B site atoms are occupied by Ti, PZT adopts a tetragonal crystal structure in its ferroelectric state R eprinted without permission from G. Bertotti and I. D. Mayergoyz, The Science of Hysteresis. (Page 346 Figure 4. 4) Academic Press, Oxford, UK, 2006.

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33 Figure 1 3. Illustration of a) 180, and b) 90 domains and domain wall regions in a ferroelectric tetragonal perovskite The schematic changes in polarization across the domain wall are shown for a 180 wall i n a). The tetragonal distortion in b) is exaggerated. Reprinted without permission from D. Damjanovic, "Ferroelectric, Dielectric and Piezoelectric Properties of Ferroelectric Thin Films and Ceramics," (Page 1281, Figure 5) Rep. Prog. Phys., 61 [9] 1267 32 4 (1998).

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34 Figure 1 4. Schematic illustrating the formation of 180 and 90 ferroelectric domain walls in a ferroelectric te tragonal perovskite such as PZT. The deformation of the crystal in the domain wall region due to the formation of 90 walls i s exaggerated for the sake of clarity. Symbols are explained in the text. Reprinted without permission from N. Setter, ABC of Piezoelectricity (Page 5, Figure 1.1) EPFL, Lausanne, Switzerland, 2002.

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35 Figure 1 5. A polycrystalline ferroelectric w ith random orientation of grains before and after poling (reprinted from Cross). Many domain walls are present in the poled material, however the net remnant polarization is nonzero. Reprinted without permission from D. Damjanovic, "Ferroelectric, Dielectr ic and Piezoelectric Properties of Ferroelectric Thin Films and Ceramics," (Page 1283, Figure 7) Rep. Prog. Phys., 61 [9] 1267 324 (1998).

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36 Figure 1 6. Revised PZT phase diagram proposed by Noheda et al. Data from Jaffe et al. are represented by o pen circles. The monoclinic region is shaded with diagonal lines. Horizontal lines are superimposed in the region of tetragonal monoclinic phase coexistence. For x = 0.45, the solid symbols represent the limits of the tetragonal rhombohedral coexistence re gion Reprinted without permission from B. Noheda, D. E. Cox, G. Shirane, R. Guo, B. Jones, and L. E. Cross, "Stability of the Monoclinic Phase in the Ferroelectric Perovskite PbZr 1 x Ti x O 3 ," (Page 014103 7, Figure 6) Phys. Rev. B, 63 [1] 014103 (2000).

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37 Figure 1 7. (a) Intrinsic contributions due to lattice strain and extrinsic contributions from (b) the motion of 180 domain walls, (c) the motion of a 90 domain wall (c) interphase boundary motion and (d) intergranular interaction during the app lication of an electric field E. The dashed lines represent the configurations before the application of the external electric field (d) is reprinted without permission from A. Pramanick, D. Damjanovic, J. E. Daniels, J. C. Nino, and J. L. Jones, "Origins of Electro Mechanical Coupling in Polycrystalline Ferroelectrics during Subcoercive Electrical Loading," (Page 295 Figure 1) J. Am. Ceram. Soc., 94 [2] 293 309 (2011).

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38 Figure 1 8. Piezoelectric coefficients of PZT ceramics as a function of com position in the vicinity of the morphotropic phase boundary Reprinted without permission from B. Jaffe, W. Cook, and H. Jaffe, Piezoelectric Ceramics. (Page 143 Figure 7.9 (b)) Academic Press, San Diego, USA, 1971.

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39 CHAPTER 2 EXPERIMENTAL METHODS 2.1 S ynthesis of PZT Based Ceramics Polycrystalline PbZr 1 x Ti x O 3 ceramics are used in the present work. The ceramics were synthesized using a solid state processing technique. 44 A two step reaction was used. The first reaction step, given in Eq. 2 1 was common for all the compositions synthesized. For A site don or dopants given by the general formula A 2 O 3 the second reaction step is given by Eq. 2 2. For B site dopants given by the general formula B 2 O 5 the second reaction step is given by Eq. 2 3 and 2 4 when charge is compensated by B and A site vacancies resp ectively. (1 x)ZrO 2 + xTiO 2 1 x Ti x O 2 (2 1) (1 1.5y)PbO + 0.5A 2 O 3 + Zr 1 x Ti x O 2 1 1.5y A y Zr 1 x Ti x O 3 (2 2) PbO + 0.5yB 2 O 5 + (1 1.25y) Zr 1 x Ti x O 2 1 x Ti x ) 1 1.25y B y O 3 (2 3) (1 0.5y)PbO + 0.5yB 2 O 5 + (1 y) Zr 1 x Ti x O 2 (1 0.5y) (Zr 1 x Ti x ) (1 y) B y O 3 (2 4) Steps used in th e synthesis are shown in Figure 2 1. Ball milling was carried out in ethanol, using spherical yitria stabilized zirconia (YSZ) media, 3 mm in diameter. The calcination conditions for the first reaction step was 1300 C, for 4 h using a ramp rate of 4 C/min. 2 mol% above the stoichiometric quantity of PbO was used to compensate for lead volatilization in the second reaction step. 16 The calcination conditions for reactions 1 2 and 1 3 is 950 C for 3 h using a ramp rate of 4 C/min. Both uniaxial and isostatic p ressing were used to form dense ceramics. A PbTiO 3 powder bed was prepared using x=1 in Eq. 1 1. A single reaction step proved sufficient for this purpose. Sintering of the green body was carried out in the bed of PbTiO 3 .The sintering conditions used were 1200 C for 2 h using a ramp rate of 4 C /min

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40 2.2 Temperature Dependent Dielectric Property Measurements r,33 ) was measured in situ as a function of increasing temperature using an apparatus based on an Inductance (L), Capacitance (C), Resistance (R) ( LCR) meter. The sample was suspended from platinum shea thed gold leads in a quartz reactor tube using platinum electrodes. The reactor was then placed in a tube furnace. A calibrated thermocouple was used to r,33 was measured using an LCR meter upon heating the sample from room temper ature to approximately 600 C at a ramp rate of 2C/min. The measurements were made at a frequency of 1 kHz. A schematic diagram of the experimental setup is shown in Figure 2 2. 2.3 Temperature Dependent Piezoelectric Property Measurements The temperature dependent converse longitudinal piezoelectric coefficient (d 33 ) was measured in situ as a function of increasing temperature using an apparatus based on Doppler vibrometry 45,46 shown schematically in Figure 2 3. Poled samples were placed in a furnace with two thermocouples to cross check the uniformity of temperature around the sample. The laser from the vibrometer (Politec sensor head OFV 505 and front end VDD E 600) was coupled to the sample surface through a pinhole in the center of a porous alumina lid used for thermal insulation. Displacements induced in the sample due to the converse piezoelectric effect were determined by the Doppler effect with a precision of 1 pm, 47,48 although the actual resolution is limited by background noise at >10 pm. A sinu soidal AC voltage of 10 V at a frequency of 1 kHz was used as an input signal. Data were obtained upon heating from room temperature to approximately 400 C, using a ramp rate of 2C/min.

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41 2.4 Characterization of Electric Field induced Structural Changes us ing High Energy X ray Diffraction from a Synchrotron Source The electric field induced structural response of piezoelectric PZT can be characterized using diffraction. 49 X rays from a synchrotron source were chosen for this study as they have higher flux w hen compared to laboratory X rays. High flux is essential for this work as subtle structural changes that occur in the material as a response to the applied electric field are measured. Due to a large penetration depth, high energy X rays also enable great er sampling volume and less surface sensitivity than laboratory X rays. 2.4.1 Experimental Setup High energy X ray diffraction experiments were carried out on beamline 11 ID C at the Advanced Photon Source, Argonne National Laboratory. A monochromatic bea m of energy 114 keV and size 500 m 500 m was used. A ceria powder pattern was measured in order to calibrate the distance and orientation of the detector relative to the sample and beam. Diffraction patterns were collected using forward scattering geom etry (transmission mode) on a Perkin Elmer amorphous silicon area detector placed approximately 2.2 m from the sample. A schematic of the measurement setup is shown in Figure 2 4. In situ measurements were recorded during the application of an electric fie ld. Sub coercive electric field cycling measurements utilized stroboscopic data acquisition procedures. 50 Figure 2 5 illustrates the differences between a diffraction pattern taken with and without electric field loading of the sample. Time resolved diffra ction images were collected during cyclic actuation of the sample. The stroboscopic data acquisition process was achieved by the following process. An electric field signal was applied across the sample using a function generator (FLUKE

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42 PM5193) and a high voltage amplifier (TREK 10/10B). A delay generator was simultaneously triggered by this signal and applied a set delay. This delayed signal was then used to trigger a detector frame, the length of which provided the time resolution of the experiments. A nu mber of detector frames were then summed together to produce a single image, and the delay signal was adjusted. In this way, large area detector images are collected as a function of time that can be represented in a single electric field cycle. 51 2.4.2 Bi nning of Diffraction Data The 2 D images from the area detector were initially analyzed using the software Fit2D Ver.12.077. The beam center and tilt were refined for each pattern with respect to a standard diffraction pattern of CeO 2 (standard reference m aterial 674b from National Institute of Standards and Technology), recorded under identical collection settings. The Debye Scherrer diffraction rings from the sample were segmented into azimuthal sectors of 15 width. The pattern within each azimuthal sect grains with their hkl poles approximately parallel t field (within 5). 51 2.5 Characterization of Temperature Dependent Structural Changes using High Resolution XRD from a Synchrotron Source In order to capture the subtle temperature dependent structural differences wit hin various soft doped polycrystalline PZT ceramics, accurate structural information is critical. Hence, high resolution powder diffraction patterns were measured at beamline 11 BM 52 at the Advanced Photon Source, Argonne National Laboratory. A

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43 monochromat ic X 20 mm diameter quartz capillary and spun at 60 Hz. The samples were heated from room temperature to 500 C at a ramp rate of 2C/min using a Cyberstar hot gas blower. XRD patterns were measured for 30 min at six distinct temperatures in the following order: 500C, 360C, 332C, 308C, 290C and 250C. Data from this series of measurements were analyzed using the Rietveld refinement program GSAS.

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44 Figure 2 1 Processing steps for PbZr 1 Ti x O 3 based ceramic synthesis.

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45 Figure 2 2. Schematic diagram of the measurement apparatus used to determine the in situ temperature dependent longitudinal relative permittivity.

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46 Figure 2 3. Schematic of the measurement apparatus used to deter mine the in situ temperature dependent converse longitudinal piezoelectric coefficient Reprinted from T. Leist, J. Chen, W. Jo, E. Aulbach, J. Suffner, and J. Rdel, "Temperature Dependence of the Piezoelectric Coefficient in BiMeO 3 PbTiO 3 (Me = Fe, Sc, ( Mg 1/2 Ti 1/2 )) Ceramics," (Page 712, Figure 1) J. Am. Ceram. Soc., 95 [2] 711 5 (2012).

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47 Figure 2 4. Experimental arrangement for time resolved high energy X ray diffraction. The X ray beam penetrates the sample simultaneous to the application of an electric field. The 2D diffraction image shows the Debye Scherrer rings.

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48 Figure 2 5. Schematic of a 2D diffraction image showing the Debye Scherrer ring as measured when a) no electric field is b) an electric field is applied to the sample. The distortion of the Debye Scherrer ring in b) is exaggerated. hkl peaks obtained after integrating the azimuthal sector 0 for 2 at% Sm doped 50:50 PZT when c) no electric field is applied d) an electric field is applied to the sample. e) (111) and (002) hkl peaks of Sm PZT as measured with and without the application of an electric field. The blue difference pattern emphasizes the change in d spacing of the (111) plane and interchange in intensities between the (002) and (200) planes that takes place upon the application of an electric field.

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49 CHAPTER 3 A STRUCTURAL INSIGHT INTO THE SOFTENING M ECHANISMS IN LEAD ZIRCONATE TITANATE 3.1 Softening in Donor Substituted PZT Lead zirconate titanate (PbZr 1 x Ti x O 3 or PZT) based ceramics are extens ively used in science, medicine, and several industries such as transportation, communications and information technologies. 11,12,18,53,54,55,56 Typically, commercial PZT ceramics are compositionally modified with small amounts of chemical additives in ord er to improve, optimize or tailor their properties for specific applications. 18,57 When a substituent whose valence is higher than the host ion (donor dopant) is used, PZT becomes a "soft" ferroelectric. A characteristic of soft ferroelectric ceramics is a n increase in the longitudinal piezoelectric coefficient (d 33 ). 4,7,16 Softening has been associated with an increase in Pb vacancies that arise to charge compensate for aliovalent donor doping 58,59 and their interaction with domain walls. Despite the wides pread use of soft PZT, the structural origin of the variation in d 33 brought about by donor doping remains unknown due to a lack of in situ characterization of the crystallographic structural response. The exact mechanism by which softening occurs is there fore still uncertain. 60,61,62 Until now, it has been thought that there is no qualitative difference in the mechanism by which different dopants generate softening. 18 For example, regardless of whether Nd +3 or La +3 is substituted for Pb +2 on the A site, it is thought that the softening of the PZT material (and the corresponding increase in d 33 ), is brought about by the same qualitative mechanism that is associated with an increase in Pb vacancies. In this study, we use high energy X rays from a synchrotron source to study the structural response of soft PZT to the application of electric fields. The structural changes occurring during the application of both strong (greater than

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50 coercive) and weak (subcoercive) electric fields is measured in situ on four dif ferent soft doped PZT materials. It is shown that dopants can have different qualitative mechanisms by which they generate softening and high d 33 From these measurements, distinct qualitative softening mechanisms are correlated to different quantitative d 33 values. 3.2 Experimental 3.2.1 Sample Preparation 2 at% of four donor dopants, Sm +3 Nd +3 La +3 (A site substituents) and Nb +5 (B site substituent) were used to dope PZT 50:50. Stoichiometric quantities of the reactants were chosen such that charge com pensation for the A site substituents was by Pb vacancies as given in Eq. 3 1. (3 1) The chemical reaction used for A site substitution is given in Eq. 2 2. The chemical formula of the resultant A site substituted PZT 50:50 compositions were Pb 0.97 Sm 0.02 Zr 0.5 Ti 0.5 O 3 Pb 0.97 Nd 0.02 Zr 0.5 Ti 0.5 O 3 and Pb 0.97 La 0.02 Zr 0.5 Ti 0.5 O 3 Two types of Nb doped PZT 50:50 compositions were synthesized. One composition was synthesized as per the chemical reaction given in Eq. 2 3. Charge compensation for the B site dopant was by Zr and Ti vacancies as per Eq. 3 2. This composition is referred to as Zr or Ti vacancy compensated Nb doped PZT 50:50. (3 2) The chemical formula of the resultant B site substituted PZT 50:50 compositions was PbZr 0.485 Ti 0.485 Nb 0.02 O 3

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51 Another type of B site substituted PZT 50:50, where charge compensation due to doping was by Pb vacancies as per Eq. 3 3 was also synthesized. The chemical reaction used for the synthesis of this composition is given in Eq. 2 4. This composition is refer red to as Pb vacancy compensated Nb doped PZT 50:50. (3 3) The chemical formula of the resultant B site substituted PZT 50:50 compositions was Pb 0.99 Zr 0.49 Ti 0.49 Nb 0.02 O 3. D isc shaped pellets, 10 mm in diameter and 1 mm in thickness, of all compositions were prepared using the conventional solid state synthesis and sintering techniques described in Section 2.1. The samples were electroded with silver paste and used for the co ercive field and piezoelectric coefficient measurements. Samples of dimensions 6 mm 1 mm 1 mm were sliced from other disc shaped pellets. The samples were annealed at 600C for 3 h using a ramp rate of 4C/min. The samples were then electroded with sil ver paste for use in the diffraction experiments. For Nb doped PZT, diffraction experiments were performed only on the Pb vacancy compensated composition. 3.2.2 Diffraction Measurements High energy X ray diffraction experiments were carried out on beamlin e 11 ID C at the Advanced Photon Source, Argonne National Laboratory using a monochromatic beam of energy 114 keV and size 500 m 500 m. A ceria powder pattern was measured in order to calibrate the distance and orientation of the detector relative to t he sample and beam. Diffraction patterns were collected using forward scattering geometry (transmission mode) on a Perkin Elmer amorphous silicon area detector placed

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52 approximately 2.2 m from the sample. In situ measurements were recorded during the applic ation of an electric field. Electric fields were applied cyclically to the samples utilizing the stroboscopic data acquisition 50 technique described in Section 2.4.1. For these stroboscopic measurements, the electric field was synchronized with the detecto r electronics and the material response to 20 repetitive electric field cycles were summed at particular time periods relative to the waveform. The angle between the electric field This value is approximately 1.5 for the (002) reflection. In polycrystalline ferroelectric materials, planes at these angles to the electric field direction behave equivalently to those parallel to the electric field. 22,63 3.2.3 Coercive Field and Piezo electric Coefficient Measurements The coercive field of the samples was determined from the polarization response of the materials to an applied bipolar electric field of triangular waveform and frequency 1 Hz. Polarization was measured using a 15 F capac itor in a Sawyer Tower circuit. The Berlincourt d 33 of the samples was measured after the diffraction experiments. 3.3 Results The coercive fields of the Sm, Nd, La and Nb doped PZT compositions, were found to be 2.68, 2.40, 2.41 and 2.04 kV/mm, respectiv ely when measured at a frequency of 1 Hz These PZT compositions were subject ed to strong electric fields of amplitude 1.3 times coercive fields for 5 min during diffraction measure ments. Berlincourt d 33 values of the compositions as measured after the dif fraction experiments were found to be 77, 149, 109 and 202 pC/N for Sm, Nd, La and Nb doped PZT, respectively.

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53 The effect of the substitution scheme on the piezoelectric coefficients were also evaluated. The Pb vacancy and Zr or Ti compensated Nb doped PZ T were poled by the application of strong electric fields of amplitude equal to their coercive field for 5 min The Berlincourt d 33 values of the Pb vacancy and Zr or Ti compensated Nb doped PZT after poling were found to be 1205 pC/N and 13416 pC/N respe ctively. A selected region of the diffraction pattern of the unpoled samples is shown in Figure 3 1. Table 3 1 shows the unit cell parameters and c/a ratios of the doped PZT compositions. In order to orient the domains in the material, a strong bipolar electric field of triangular waveform with a frequency of 0.05 Hz and amplitude equal to approximately 1.3 times the coercive field of material was applied to each of the doped compositions. Three such triangular waveforms were applied. In situ diffraction was performed to capture the structural response of the material to the application of strong fields. The structural changes occurring during the application of strong electric fields become more apparent with the application of each subsequent waveform. Figures 3 2 and 3 3 show portions of the diffraction pattern collected with the scattering vector parallel to the electric field direction during the application of the first and third electric field cycle, respectively. The diffraction patterns show how t he nature of the (002) type diffraction peaks change as a function of time in response to the triangular, bipolar electric field waveform applied during the poling cycle. In the case of the Sm and Nd doped PZT materials an intensity interchange occurs betw een the tetragonal (002) and (200) peaks when the electric field changes sign. This can be the result of a change in the volume fraction of the ferroelectric

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54 domains that is brought about by 90 domain wall motion. 63 The La and Nb compositions also show an intensity interchange between the tetragonal (002) and (200) reflections. In the case of the La and Nb doped PZT compositions, an additional peak is observed between the (002) and (200) tetragonal reflections. This can be interpreted to be due to the pres ence of the rhombohedral phase in addition to the tetragonal phase. Further, an electric field induced phase transformation of the tetragonal phase to the rhombohedral phase is observed in Nb doped PZT. A positive d.c. electric field of magnitude 1.3 time s the coercive field of the material was applied to each of the four differently doped PZT compositions for 5 min in order to further strengthen the domain alignment in the positive electric field direction. Diffraction patterns of the samples were measure d after the application of the d.c. field. The {002} type reflections of these patterns are shown in Figure 3 4 and compared to the patterns from the unpoled (initial) condition. A difference plot highlighting the changes that emerged in each of the doped PZT materials due to the application of strong electric fields is also shown in FIgure 3 4. The interchange in the tetragonal (002) and (200) intensities observed in all samples shows that the fraction of 001(c axis) type domains grew at the expense of the 100(a axis) type domain due to 90 domain wall motion. Subsequently, unipolar square electric fields of frequency 0.02 Hz and subcoercive amplitudes equal to approximately 0.7 times the 1 Hz coercive field of the materials were applied and diffraction da ta were measured using the stroboscopic approach. 22,63 The contour plots in Figures 3 5 (a), (b), (c) and (d) show the changes occurring in the {002} diffraction peaks as a function of time during the application of

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55 these subcoercive electric fields. The l ine plots in Figure 3 6 show the difference in the structure between the zero field and positive subcoercive field state. For all the samples, no change is observed in the {002} reflections during the first 25 s of the waveform as the electric field amplit ude is zero during this portion of the waveform. After the electric field is applied, the intensity of the tetragonal (002) reflection increases and there is a corresponding decrease in the intensity of the (200) reflection in all four differently doped ma terials. The change in intensities between the positive and zero polarity of the electric field implies that there is motion of the 90 walls separating these domains. In the case of the La doped sample, there is no change in the volume fraction of the rho mbohedral phase between the zero and positive polarity states of the subcoercive electric field. The rhombohedral phase fraction of the Nb doped sample increases during the positive polarity state of the subcoercive electric field. This is indicative of in terphase boundary motion during the application of subcoercive electric fields in Nb doped PZT. Notably, interphase boundary motion in Nd doped PZT 50:50 occurs during both strong and weak field conditions. Peak center positions were obtained by curve fit ting to a Gaussian triplet as shown in Figure 3 positive state of the electric field is indicative of a large strain in the (200)R lattice plane 4. (3 4) In Eq. 3 4, d 0 and d 1 are the d spacing of the (200) R lattice plane during the off and positive polarity of t he subcoercive electric field respectively. The electric field induced

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56 strain coefficient in the rhombohedral peak (d 33,(200)R ) can then be calculated as per Eq. 3 5. (3 5) E o is the amplitude of the subcoercive field. In Nb doped PZT, d 33,(200)R is found to be 950 22 pm/V. 3.4 Discussion As the d 33 values of the Pb vacancy and Zr or Ti compensated Nb doped PZT were found to be 1205 pC/N and 13416 pC/N respectively, there is no statistically significant difference in the d 33 values resulting from these two different substitution schemes Thus, the data suggests that Pb vacancies are not a necessary criterion for softening in PZT. The {002} reflections of the four unpoled PZT compositions show that various soft dopants have distinctive influences on c and a axis distortion and phase. These structural parameters, coupled with interaction among grains and domain s, local texture and internal stresses in ceramics, affect the overall intrinsic and extrinsic strain response in piezoelectric ceramics. 34,35 The four soft doped PZT based ceramics showed Berlincourt d 33 values that varied from 77 pC/N (in Sm doped PZT) t o 202 pC/N (in Nb doped PZT). In situ diffraction experiments during the application of strong and weak subcoercive electric fields show that the differently doped materials display four distinctive strain mechanisms which are outlined in Sections 3.4.1 to 3.4.4. A summary of the strain mechanisms displayed by the dopants in given in Table 3 2.

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57 3.4.1 90 Domain Wall Motion The intensity interchange between the tetragonal (002) and (200) peaks was used to infer the motion of 90 domain walls. Sm, Nd, La and Nb doped PZT all show 90 domain reorientation during both strong and weak electric field cycling. 90 domain wall motion leads to a change in the volume fraction of the c(001) type domains. This effect is known to increase the extrinsic strain response a nd hence results in materials with higher d 33 22,51 which is characteristic of soft ferroelectrics. 3.4.2 Coexistence of mixed ferroelectric phases In the La and Nb doped compositions, two ferroelectric phases coexist. In the Nb doped composition, an elect ric field dependent interphase boundary motion between the ferroelectric tetragonal phase to the ferroelectric rhombohedral phase was observed. This was evidenced by the appearance of a (200) rhombohedral peak together with a corresponding decrease in the intensity of the {200} tetragonal peaks. Diffraction patterns recorded after the application of electric fields show that the rhombohedral phase formed during the application of strong electric fields, remains in the material when the electric field is rem oved after poling. Some differences were observed in the rhombohedral phases of the La and Nb doped samples. Under strong bipolar electric field amplitudes, a volume fraction of the tetragonal material is transformed to the rhombohedral phase in Nb doped P ZT, whereas the volume fraction of the rhombohedral phase remains roughly the same even under strong bipolar electrical field loading in La doped PZT. This indicates that Nb doped PZT may be closer in proximity to the rhombohedral tetragonal MPB as the ene rgy barrier for the phase transition is smaller in the case of the Nb doped material. As Nb is a B site substituent and the compensation for aliovalent doping in Nb doped PZT was by Zr and

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58 Ti vacancies, the Nb doped PZT composition could be closer to the M PB than the La doped composition. 3.4.3 Interphase Boundary Motion During Subcoercive Electric Field Application The volume fraction of the tetragonal and rhombohedral phases remains constant during subcoercive cycling in La doped PZT. This suggests that the weak electric fields applied during this experiment are insufficient to overcome the phase transition energy barrier present in this material. On the other hand, the volume fraction of the rhombohedral phase increases during the positive polarity of th e subcoercive electric field waveform in Nb doped PZT. This indicates that the interphase boundary between the tetragonal and rhombohedral phases moves during subcoercive electric field cycling in Nb doped PZT. It has been hypothesized 21,27,64,65,66 and al so directly demonstrated 27 that interphase boundary contributes to an increase in piezoelectric coefficients. The present results further demonstrate a measureable contribution of interphase boundary motion to the piezoelectric coefficients in ceramics 3 .4.4 Strain in the Rhombohedral (200) Lattice Plane There is a sizeable shift in the (200) R peak of Nb doped PZT which is indicative of the large strain in the rhombohedral (200) lattice plane in Nb doped PZT. This equates to a high d 33,(200)R of 950 pm/V. As large strain coefficients of individual lattice planes contribute to the total strain response of the material, the high d 33,(200)R contributes to an increase in the piezoelectric coefficient of Nb doped PZT. It has been previously shown that the (00l) planes of the rhombohedral phase strain significantly more than other planes. For example, Du et al. 67 demonstrated that the piezoelectric coefficients are orientation dependent in PZT through phenomenological calculation. As a result of this orientation dependence, they suggest that the effective d 33 can be

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59 enhanced by a factor of 4 when the [001] orientation is favored in epitaxial thin films. The rhombohedral phase of Pb(Mg 1/3 Nb 2/3 )O 3 PbTiO 3 (PMN PT), Pb(Zn 1/3 Nb 2/3 )O 3 PbTiO 3 (PZN PT), Pb(Sc 1/2 Nb 1/2 )O 3 P bTiO 3 (PSN PT) and Pb(Yb 1/2 Nb 1/2 )O 3 PbTiO 3 (PYbN PT) single crystals have also been shown to have high piezoelectric coefficients when measured along the <001> direction even though <111> is the polar direction. 68,69,70 The (200) R peak in La doped PZT does not strain under the application of an electric field. Hence, d 33,(200)R in La doped PZT is zero. Thus, there is no contribution from d 33,(200)R to the piezoelectric coefficient in La doped PZT. 3.5 Conclusions In contrast to prior held assumptions, the r esults suggest that an increase in Pb vacancies is not a necessary criterion for softening. While different soft dopants are known to increase the piezoelectric coefficient, this work has uniquely shown that these different dopants do so by activating dist inctive strain mechanisms. The present work alternatively suggests that the value of piezoelectric coefficient depends on the number and magnitude of the strain mechanisms in play. Nb doped PZT exhibits all four strain mechanisms and, as a result, Nb dope d PZT has the highest d 33 (202 pC/N). Although Nd doping gives rise only to one strain mechanism (90 domain wall motion) it has the next highest d 33 (149 pC/N). It is suggested that this is because the magnitude of 90 domain wall motion that occurs in Nd doped PZT is large relative to the other doped compositions. La doped PZT exhibits two strain mechanisms (90 domain wall motion and the coexistence of ferroelectric phases). It has the third highest d 33 (109 pC/N). Sm doped PZT exhibits only 90 domain w all motion. It is suggested that the extent of 90 domain wall motion in Sm

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60 doped PZT is lesser than that in Nd doped PZT. Sm doped PZT has the lowest d 33 (77 pC/N).

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61 Figure 3 1. Diffraction patterns showing the (002) and (200) reflections of 2 at. % Sm, Nd, La and Nb doped PZT 50:50 before the application of an electric field.

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62 Table 3 1. Lattice parameters, phases present and coercive fields of the various doped PZT 50:50 compositions. The c lattice parameter is not calculated for La doped PZT 50:50 as the (200) T peak is not sufficiently resolved. Dopant c () a () c/a phase E c (kV/mm) Sm 4.138(0.005) 4.033(0.005) 1.026(0.001) P 4 mm 2.68 Nd 4.138(0.003) 4.035(0.003) 1.026(0.001) P 4 mm 2.40 La 4.036(0.007) P 4 mm R 3 m 2.41 Nb 4.126(0. 006) 4.043(0.009) 1.021(0.003) P 4 mm R 3 m 2.04

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63 Table 3 2. Strain mechanisms in soft doped PZT 50:50 compositions. The checks and crosses denote the strain mechanisms present and absent respectively. Sm (d 33 = 77 pC/N) Nd (d 33 = 149 pC/N) La (d 33 = 109 pC/N) Nb (d 33 = 202 pC/N) 90 domain wall motion Coexistence of ferroelectric phases Interphase boundary motion Strain in (200) R

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64 Figure 3 2. Time resolved diffraction patterns measured in situ during the app lication of the first strong bipolar electric field of triangular waveform, frequency 0.05 Hz and amplitude equal to 1.3 times the coercive field (E c ) to a) Sm b) Nd c) La and d) Nb doped PZT 50:50. Intensity interchange between the tetragonal (002) and (2 00) diffraction peaks due to a change in volume fraction of 90 domains can be observed in a), b), c) and d). Additionally, the appearance of the rhombohedral (200) peak between the tetragonal (002) and (200) peaks is observed in d).

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65 Figure 3 3 T ime resolved diffraction patterns measured in situ during the application of the third strong bipolar electric field of triangular waveform, frequency 0.05 Hz and amplitude equal to 1.3 times the coercive field (E c ) to a) Sm b) Nd c) La and d) Nb doped PZT 50:50. Intensity interchange between the tetragonal (002) and (200) diffraction peaks due to a change in volume fraction of 90 domains can be observed in a), b), c) and d). Additionally, the appearance of the rhombohedral (200) peak between the tetragona l (002) and (200) peaks is observed in d).

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66 Figure 3 4. Selected region of the diffraction patterns showing the {002} type reflections of a) Sm b) Nd c) La and d) Nb doped PZT 50:50 before and after poling.

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67 Figure 3 5. Time resolved diffra ction patterns measured in situ during the application of weak subcoercive electric fields of square waveform, frequency 0.02 Hz and amplitude equal to 0.7 times the coercive field (E c ) to a) Sm b) Nd c) La and d) Nb doped PZT 50:50. Intensity interchange between the tetragonal (002) and (200) diffraction peaks due to an increase in volume fraction of 90 domains during the positive polarity of the electric field can be observed in a), b), c) and d). Additionally, an increase in intensity of the rhombohedra l (200) peak is observed in d) during the positive polarity of the electric field. The dashed line on the diffraction contour plots indicate the time at which the amplitude of the electric field changes. The arrows on the plot of the electric field wavefor m also correspond to this time.

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68 Figure 3 6. Selected region of the diffraction pattern showing the {002} type reflections for a) Sm b) Nd c) La and d) Nb doped PZT 50:50. The behavior of the {002} type reflections when no electric field is appli ed on the doped PZT compositions is compared to its behavior during the application of a weak, unipolar square electric field waveform of positive polarity, frequency 0.02 Hz and amplitude equal to 0.7E c (subcoercive).

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69 Figure 3 7. Gaussian fits to the {002} reflections in Nb doped PZT. The (002) R reflection R during the application of a weak, subcoercive electric field of positive polarity. Cyclic, unipolar square waveforms were used for this meas urement.

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70 CHAPTER 4 COOPERATIVE STRAIN A CCOMMODATION AND HIG H TEMPERATURE PIEZOELECTRIC COEFFI CIENTS IN SOFT DOPED PZT It is well established that the value of the piezoelectric coefficient reaches a maximum around the morphotropic phase boundary. 16 A s outlined in section 1.7.1 several mechanisms have been proposed to explain the enhanced piezoelectric coefficient of PZT at the MPB. In this work, results are shown in the classic PZT system that evidence unexpectedly high piezoelectric coefficient value s at elevated temperatures for Zr:Ti ratios far away from the MPB. Specifically, it is shown that incorporation of 2 at% Sm into the crystal structure of PZT alters its ferroelectric to paraelectric phase transition character and gives rise to high tempera ture piezoelectric coefficients up to 915 pm/V, values that are approximately twice those measured in other donor substitution schemes (e.g., 477 pm/V for Nb and 435 pm/V for La). High resolution X ray diffraction from a synchrotron source is used to study the structural changes that occur during the ferroelectric to paraelectric phase transitions of doped PZT. These results show that the cubic phase begins to form approximately 50C below the Curie temperature in Sm doped PZT, whereas Nb, the cubic phase f orms at the Curie temperature in and La doped PZT. The effect of thermal cycling on the temperature dependent piezoelectric coefficients of these doped PZT compositions is also studied, and provides insight into the nature of the origin of the effect. 4.1 High Piezoelectric Coefficients in PZT A piezoelectric material is one that generates a voltage in response to a mechanical strain and vice versa. This electromechanical coupling effect makes piezoelectric materials the pervasive electroactive material us ed in the transducer industry. 11 The solid solution of lead zirconate titanate (PZT), PbZr (1 x) Ti x O 3 15,71 has

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71 been the most commonly used commercial piezoelectric material for the last 50 years due to the high piezoelectric coefficients. 11,72 A large body of work has been aimed at understanding the origin of the high piezoelectric response in PZT. It is generally accepted that high piezoelectric properties are obtained in PZT by donor doping 16,41,62 and by using a Zr:Ti ratio in the region of the morphotro pic phase boundary (MPB). 16,73 In the present work, the effect of three donor dopants on the temperature dependent piezoelectric coefficient of tetragonal PZT is studied. The dopants studied are Sm and La (A site dopants), and Nb (B site dopant). These do pants are known as donor dopants and yield a ferroelectric behavior classified as "soft" as described in Section 1.9. We show that, unlike the other dopants studied, Sm alters the ferroelectric tetragonal to paraelectric cubic phase transition characterist ics in PZT. It also gives rise to a piezoelectric coefficient approximately double that of La and Nb doped PZT. 4.2 Experimental PZT 50:50, PZT 45:55, and PZT 40:60 compositions were doped with either 2 atomic percent of Sm, La or Nb. The chemical formulae of the doped materials are Pb 0.97 Sm 0.02 Zr 0.5 Ti 0.5 O 3 Pb 0.97 Sm 0.02 Zr 0.45 Ti 0.55 O 3 Pb 0.97 Sm 0.02 Zr 0.4 Ti 0.6 O 3 Pb 0.97 La 0.02 Zr 0.5 Ti 0.5 O 3 Pb 0.97 La 0.02 Zr 0.45 Ti 0.55 O 3 Pb 0.97 La 0.02 Zr0 .4 Ti 0.6 O 3 PbZr 0.485 Ti 0.485 Nb 0.02 O 3 PbZr 0.439 Ti 0.536 Nb 0.02 O 3 and PbZr 0.385 Ti 0 .585 Nb 0.02 O 3 Disc shaped pellets, with 10 mm diameter and 1.5 mm thickness, of all the compositions were produced using the conventional solid state synthesis techniques outlined in section 2.1. Silver paste was applied to the flat surfaces as electrodes, and the samples were then fired at 550C for 30 min. The samples were electrically poled to saturation by applying an electric field just below the breakdown field of the material. The poled disc samples were used for both d 33 r,33 measurements. All samples were aged for

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72 at least one week at room temperature prior to the measurements in order to mitigate the potential effects of initial aging on ferroelectric behavior. 74 The temperature dependant d 33 was measured using a custom built apparatus based on Doppler vibrometry. 45,46 A sinusoidal voltage of 10 V at a frequency of 1 kHz r,33 was measured by an LCR meter using a small input voltage of frequency 1 kHz. This is a typical frequency at which piezoelectrics are used for several applications suc h as actuation, transduction and vibration control.{Mokr, during both the d 33 r,33 measurements. For the high resolution XRD measurements, the sintered disc shaped pell ets were crushed into a fine powder. The powder was annealed at 600C for 3 h in a closed alumina crucible to alleviate residual intragranular stresses. High resolution XRD patterns were measured on beamline 11 BM of the Advanced Photon Source at Argonne N ational Laboratory. A monochromatic X ray beam with a wavelength of powders were packed into a 0.3 mm diameter quartz capillary and spun at 60 Hz about the axis of the capillary to increase powder averaging. The samples were heated from room temperature to 500C at a ramp rate of 2C/min. XRD patterns were measured for 30 min at six fixed temperatures on cooling in the following order: 500C, 360C, 332C, 308C, 290C and 250C. 4.2 Variation of Piezoelectric and Dielectric Properties as a Function of Temperature in Sm, La and Nb doped PZT The measurements of d 33 r,33 in all compositions as a function of temperature are shown in Figure 4 1. For all Zr:Ti ratios, the d 33 of the Sm, La and Nb doped

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73 behavior of the Sm doped composition s differs greatly from that of the La and Nb doped compositions. In the La and Nb doped compositions, the increase in d 33 with 33 is reached. The Sm doped compositions show a stronger tem perature dependence of d 33 250C until the maximum d 33 value is reached than that demonstrated by the La and Nb doped compositions. For each respective Zr:Ti ratio, the maximum d 33 observed in Sm modified PZT is roughly twice that observed in either the La or the Nb modified materials. The effects of thermal history on this behavior were also explored. Heating the PZT compositions from room temperature to depoling temperature is referred to here as a thermal cycle. After thermal cycling, Sm doped PZ T 50:50 was again poled to saturation and its d 33 behavior as a function of temperature determined for a second time. As shown in Figure 4 2, the maximum d 33 observed during the second thermal cycle. However, it is still higher than the maximum d 33 observed in La doped PZT 50:50 (435 pm/V) and Nb doped PZT 50:50 (475 pm/V) d uring the first thermal cycle. After the completion of the second thermal cycle, Sm doped PZT 50:50 was poled to saturation for a third time and its d 33 behavior as a function of temperature was again measured. The maximum d 33 observed during the third the rmal cycle is 438 pm/V. The maximum d 33 during the first thermal cycle. This value is still higher than the maximum d 33 observed in

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74 La doped PZT 50:50 and is approximately equal to the maximum d 33 observed in Nb doped PZT 50:50 during the first thermal cycle. 4.3 Temperature Dependent Structural Changes in Sm, La and Nb doped PZT To obtain an insight into the structural changes taking place in the materials as a function of temperature, high resolution synchrotron XR D patterns of the Sm, La and Nb doped PZT 50:50 were measured at 500C, 360C, 332C, 308C, 290C and 250C. A selected region of the XRD patterns containing the (002) and (200) reflections of the materials are shown in Figure 4 3. With increasing tempera ture, the (002) and (200) reflections of the ferroelectric tetragonal phase become closer together and finally merge into a single (002) reflection above the Curie temperature. 16 At 332C, some extra intensity is observed between the (002) and (200) reflec tions in the Sm doped composition. This is highlighted using a magnified view in Figure 4 4. The data presented in Figure 4 4 suggests that a single tetragonal phase insufficiently describes the diffraction pattern of Sm doped PZT 50:50 at 332C due to th e presence of an additional polymorph. In addition to the tetragonal phase, the other phases that have been previously observed in the PZT phase diagram are rhombohedral, monoclinic and cubic. 73 From the phase diagram, it can be seen that for PZT 50:50 the rhombohedral phase becomes less favorable at high temperatures. This reduces the probability that the second polymorph detected at 332C is rhombohedral. It is also unlikely that the second polymorph is monoclinic because the symmetry of ferroelastic crys tal structures tend to increase with increasing temperature. As the extra intensity at 332C appears between the (002) and (200) peaks and the rhombohedral and monoclinic phases have been eliminated as unlikely, the extra intensity may

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75 suggest the presenc e of a cubic phase in addition to the tetragonal phase. The implications of a coexisting cubic phase are further explored in Section 4.4. In order to quantify the phase fraction of the cubic phase present in Pb 0.97 Sm 0.02 Ti 0.5 Zr 0.5 O 3 at 332C, crystallogra phic refinement of the diffraction patterns was undertaken using the Rietveld refinement program GSAS. 76 In all the refinements, 12 background parameters in the shifted Chebyschev model were used. A combination of profile functions 3 and 4 were utilized. P rofile function 4 includes the Stephens model for asymmetry 77 which was used to model the asymmetric peak shapes particularly in the refinements using the tetragonal space gr zero, scale factor, lattice parameters, atomic positions in the tetragonal phase, and isotropic displacement parameters. For all refinements, Zr and Ti were constrained to the same atomic position and displacement pa rameter. In addition, Sm and Pb were both constrained to the (0,0,0) atomic position, and the same isotropic displacement parameter. Sections of the measured and modeled diffraction pattern resulting from the final refined values of Pb 0.97 Sm 0.02 Ti 0.5 Zr 0.5 O 3 to a mixed phase model consisting of both the tetragonal P 4 mm and cubic Pm m phases at 332C are shown in Figure 4 5. Using the phase fraction calculation described by Hill et al. 78 it was found that the phase fraction of the cubic phase in Pb 0.97 Sm 0.02 Ti 0.5 Zr 0.5 O 3 at 332C is 31%. A summary of the refinement results is available in Table 4 1. At 250C and 290C, the diffraction patterns were successfully modeled using a single tetragonal phase. The diffraction patterns recorded at 308C and 332C were modeled using different combinations of cubic and tetragonal phases as the asymmetry in the 002 and 200 reflections indicated the presence of a mixed phase. The diffraction

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76 patterns collected at 360C and 500C were modeled using a cub ic phase as no peak splitting was observed in the {00 l } type reflections. 4.4 Discussion Sm doping results in high temperature piezoelectric coefficients that are extremely large. At temperatures above 250C, the d 33 of Sm doped PZT shows a stronger tempe rature dependence than the d 33 of La and Nb doped PZT. The maximum d 33 observed in the Sm doped PZT compositions is approximately double that obtained by the other donor dopants, La and Nb. Previous explanations for the origin of very high piezoelectric co efficients at room temperature include: i) the existence of a lower symmetry monoclinic Cm phase 17 or the presence of monoclinic symmetry within microdomains 24 and ii) the presence of ferroelectric nanodomains. 79 However, these effects are present in PZT m 50%) between the tetragonal and rhombohedral phases. As Sm doping gives rise to extremely high d 33 values in PZT materials across a range of Zr:Ti ratios from 50:50 to 40:60, it is unlikely that MPB re lated phenomena can fully account for the origin of the anomalously high d 33 observed in the Sm PZT compositions. The temperature dependence of d 33 the maximum d 33 value is reached is greater in all the PZT comp ositions in this study than in the commercial composition used in the work done by Anton et al. 47 Once the values of d 33 begin to drop, the rate of its decay is also greater in the PZT compositions used in this work. The d 33 decays from its maximum value t o zero over a temperature C in the commercial composition used by Anton et al. 47 In the present work, the decay takes place over a temperature range of approximately 3 C to 15 C and resembles the decay shown by BiNaTiO 3 in Anton et. al's work. 47 Less temperature

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77 dependence in d 33 during depoling has been associated with the existence of additional domain structures such as low symmetry nanopolar domains in PZT. 79 However, in the present work, the PZT compositions closer to the MPB (PZT 50:50) d o not show a less rapid decay in temperature dependent d 33 during depoling when compared to the compositions further away from the MPB (PZT 45:55 and PZT 40:60). This indicates that the presence of nanodomain structures may not be a sufficient explanation for the temperature dependent depoling behavior. The contributions to piezoelectric and dielectric properties of polycrystalline ferroelectrics can be divided into two categories: intrinsic and extrinsic. The intrinsic response of a material is due to lat tice and ionic displacements in the ferroelectric crystal and originates from the piezoelectric and dielectric responses of single domains. The extrinsic contributions to the material response are attributed to the presence of defect dipole, domain walls a nd other crystalline effects not associated with a perfect crystal. 5,80 The total response of the material is determined by both the intrinsic and extrinsic responses. The intrinsic d 33 r,33 are related through the coefficient of electrostriction (Q 11 ) and spontaneous polarization (P s ) as per Eq. 4 1. 2 d 33 r33 Q 11 P s (4 1) A peak in the d 33 r,33 for all the compositions. This implies that, for all the PZT compositions, the increase in d 33 with r,33 Also, the maximum r,33 in the Sm r,33 values of the La and Nb doped compositions across all the Zr to Ti ratios. From this, it may be inferred that the rapid increase in the temperature dependent d 33 of the Sm doped

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78 r,33 values increasing more rapidly with temperature relative to the La and Nb modified compositions. Th e possibility that the valence of Sm changes from +3 to +2 at high temperatures is now considered. Sm +3 is a donor dopant. In its +2 state, Sm is an isovalent dopant. A major effect of isovalent doping is enhancement in permittivity. 81 No atypical enhancem doping compensates for p type conductivity usually assumed for PZT materials. 82 As a consequence, if the valence of Sm changes from +3 to +2, it should result in an increase in conductivi ty and dielectric loss tangent. Figure 4 6 shows the dielectric loss tangent as a function of temperature for Sm, La and Nb doped PZT. No increase in loss tangent that would indicate the presence of Sm +2 is observed. Furthermore, Sm +2 is unstable. 83 Thus, it is unlikely that the valence of Sm changes from +3 to +2 at high temperatures. Extrinsic effects due to 90 domain wall motion are known contribute to enhanced piezoelectric coefficients at room temperature 22 and have been shown to contribute up to 70% of d 33 in PZT. 22,51 They are now considered as a possible explanation for the behavior of the high temperature d 33 in Sm doped PZT. Tetragonal PZT has two types of domain walls: 180 and 90 walls. It has been shown that the major extrinsic contribution t o the piezoelectric coefficient under weak external driving fields, such as those applied during the measurement of d 33 is from the motion of 90 domain walls. Due to the considerably steeper free energy wells, 180 walls can be considered as idle under we ak fields and are therefore not able to induce sizeable changes in piezoelectric properties. 1 When the temperature increases, the energy

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79 available for 90 domain wall motion increases exponentially according to the Arrhenius equation. As a result, it is po ssible that 90 domain wall motion increases rapidly at With increasing temperature, the c/a ratio of PZT has been known to decrease. 16 This change in the structure may also facilitate domain wall mobilit y. As domain wall motion in the tetragonal ferroelectric phase causes strain in the material, the strain could also increase rapidly with temperature. Given that d 33 is the strain in the material due to an applied voltage, it can also increase in the same manner. This strong temperature dependence of d 33 is present until Sm doped PZT depoles at temperatures close to the Curie temperature. The lower maximum d 33 value observed with each subsequent thermal cycle in Figure 4 2 further suggests that the origin o f the high temperature dependant d 33 values observed in Sm doped PZT is extrinsic in nature. High piezoelectric coefficients have also been attributed to the coexistence of multiple phases. 84 The high coefficients in mixed phase materials have been associa ted with mechanisms such as interphase boundary motion 27 (the motion of the interface between the phases) and the concept that materials containing multiple polymorphs can better accommodate strain by allowing for more overall deformation strain in polycry stalline aggregates. 14,85 Interphase boundary motion has been shown to be frequency dependent. 27 It is unlikely to play a significant role in the kHz frequency range at which the piezoelectric coefficients were measured in this study. Thus, 90 domain wall motion is the m ost likely extrinsic contribution to the piezoelectric coefficient. From the high resolution XRD results in the present measurements, it is seen that the tetragonal and cubic phases coexist in Sm doped PZT at temperatures approaching the

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80 ph ase transition. The coexistence of the polymorphs in the Sm doped PZT compositions enable them to have a larger capacity to enhance the strain from an increase in 90 domain wall mobility. As La and Nb doping do not result in a mixed phase material at high temperatures, the extent of 90 domain wall motion and the resulting strain is restricted. Consequently, temperature dependant d 33 in La and Nb doped PZT does not increase as rapidly as observed in Sm doped PZT. The crystallochemical reasons why the phas e transition behavior of Sm PZT may be different from that of Nb and La doped PZT are now considered. In an ideal cubic perovskite, the ionic radius of the A site atom, r A is 1.49 The ionic radius of La is 1.36 86 only 5% smaller than the ideal. Howe ver, the ionic radius of Sm is 1.24 86 which is 35% smaller than the ideal A site radius. The ideal radius of the B site atom in the ideal cubic perovskite structure, r B is 0.605 The ionic radius of Nb is 21% smaller than this. 86 When a dopant atom r eplaces a host atom of a different size, it induces strain. This strain is known as internal strain or chemical pressure. As the ionic radius of Sm deviates most from the ideal values, the Sm doped PZT compositions can be considered to have the most chemic al pressure. This is relevant because PZT undergoes a phase transition from the tetragonal phase to the cubic phase with an increase in pressure. 87,88 Ahart et al. 14 suggest that the chemical pressure created due to doping varies monotonically with the pre ssure needed for phase transformation. For example, Zeches et al. 89 report the observation of strain induced phase transformation in BiFeO 3 perovskites. Chemical pressure driven phase transformation has been shown through first principle calculations in ot her materials systems as well. 90 The large magnitude of chemical pressure caused by Sm doping may cause the characteristics of

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81 the tetragonal ferroelectric to cubic paraelectric phase transition to change and allow for the formation of a mixed tetragonal a nd cubic phase over a defined temperature range. The homogeneity of the distribution of the dopant in the PZT solid solution may also play a role in the magnitude of chemical pressure generated due to the mismatch in the ionic radii of the host and dopant atom. Moreover, it may affect the presence of two coexisting polymorphs. For cubic and tetragonal phases to coexist, the phase transition is required to be of the first order. The order of the phase transition can be determined from the variation of inver se susceptibility as a function of temperature by calculation of the slopes of the inverse susceptibility curve in the linear region at the point of divergence. For a first order phase transition, the absolute value of the ratio of the slopes of the right and left regions is 0.25. The variation of inverse dielectric susceptibility as a function of temperature is shown in Figure 4 7, for Sm, La and Nb doped PZT 50:50. The left and right linear regions at the point of divergence are plotted in Figure 4 8. The ratio of the slopes is given in Table 4 2, where it was found to be approximately 0.5 for all the doped PZT 50:50 compositions. This indicates that the phase transition is second order. The Gibbs free energy function used to compute the order of the phase transition is given in Eq. 4 2. (4 2) is the change in Gibb's free energy, is dielectric susceptibility, T is temperature, is Curie temperature, P is polarization and is a constant. However, Eq. 4 2 does not take into account chemical pressure and 90 domain wall motion.

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82 Phenomenological calculations have shown that when extrinsic effects such as domain wall motion are taken into consideration, the nature of the ferroelectric to paraelectric phase transition in PZT is of the first order. 91 These results suggest that cooperative strain accommodation between the tetragonal and cubic polymorphs of Sm doped PZT gives rise to the strong temperature dependence in its piezoelectric coefficient. This puts forward yet another mechanism that can be exploited to obtain large piezoelectric coefficients in the PZT system. Sm doped PZT exhibits cooperative strain accommodation and as a result, has piezoelectric coefficients that are two times greater than that of La and Nb doped PZT 4.5 Conclusions The behavior of d 33 as a function of temperature was studied for Sm, La and Nb doped PZT across a range of Zr:Ti ratios in order to understand the impact of chemical substitution on the high temperature piezoelectric coefficients of dono r doped PZT. It was found that Sm results in high temperature piezoelectric coefficients that are twice those obtained by doping with La and Nb across all the Zr:Ti ratios studied. It is shown r33 and MPB related effects cannot account for the anomalous behavior demonstrated by the Sm doped PZT compositions. A theory to explain the origin of the high d 33 values of Sm doped PZT is proposed. It is suggested that Sm doping gives rise to the most internal strain or chemical pressure in PZT as, relative to La and Nb, the ionic radius of Sm deviates most from the ideal value for a cubic perovskite. This large internal stress in Sm changes the ferroelectric to paraelectric phase transitions characteristics in Sm doped PZT and allows for a mixed tet ragonal and cubic phase to form at temperatures below the Curie temperature. Due to the presence of the mixed phase, Sm doped PZT compositions have higher strain accommodation capacities

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83 compared to their La and Nb counterparts. With increasing temperature the energy available for 90 domain wall motion increases exponentially for all the PZT compositions. However, the Sm doped PZT compositions have a larger capacity to accommodate strain from an increase in 90 domain wall mobility. Hence, the Sm doped co mpositions have high temperature piezoelectric coefficients that are roughly twice those obtained by doping with La and Nb. Thermal cycling studies further reinforce that the origin of the high d 33 in Sm doped PZT is extrinsic in nature.

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84 Figure 4 1. Variation of d 33 r 33 as a function of temperature for various PZT compositions.

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85 Figure 4 2. Behavior of d 33 as a function of temperature during the first, second and third thermal cycles for 2 at% Sm PZT 50:50.

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86 Figure 4 3. Selected regions of hig h resolution synchrotron XRD patterns showing the (002) and (200) type reflections for Sm, La and Nb doped PZT 50:50.

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87 Figure 4 4. Magnified view of the (002) and (200) tetragonal reflections of Sm, La and Nb doped PZT 50:50 at 332 C. The extra refl ection not belonging to the tetragonal phase in Sm doped PZT is highlighted in pink.

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88 Figure 4 5. Rietveld refinements of 2 at % Sm doped PZT 50:50 fit to a cubic model (332 C, 360 C, 500 C), tetragonal model (250 C, 290 C, 308 C, 332 C) and a mixed phase model consisting of the tetragonal P 4 mm and cubic Pm m phases (308 C, 332 C).

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89 Table 4 1. Summary of Rietveld refinement results. The standard deviations for phase fraction are of the order of 0.1%. Temperature ( C) Space group Phase fractio n a ( ) c ( ) Criteria of fit 250 P 4 mm 100% 4.054075(24) 4.095974(32) R p = 9.00% R wp = 11.20% Chi 2 =2.804 290 P 4 mm 100% 4.058846(20) 4.086615(26) R p = 8.43% R wp = 10.25% Chi 2 = 2.388 308 P 4 mm Pm m 71% 29% 4.060155(15) 4.067567(23) 4.083100(21) R p = 5.40% R wp = 6.65% Chi 2 = 1.005 332 P 4 mm Pm m 69% 31% 4.065098(15) 4.067787(22) 4.073675(34) R p = 5.70% R wp = 7.11% Chi 2 = 1.176 360 Pm m 100% 4.067774(12) R p = 8.64% R wp = 10.54% Chi 2 = 2.648 500 Pm m 100% 4.072079(10) R p = 7.59% R wp = 8.8% Chi 2 = 1.1901

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90 Figure 4 6. Variation of the dielectric loss tangent as a function of temperature for various PZT compositions.

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91 Figure 4 7. Inverse dielectric susceptibility as a function of temperature for 2 at% Sm, La and Nb doped PZT 50 :50.

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92 Figure 4 8. Linear fits to the a) left, and b) right linear regions at the point of divergence of inverse susceptibility plotted for 2 at% Sm, La and Nb PZT 50:50.

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93 Table 4 2. Ratio of the slopes of the linear fits to the left and right regions of inverse susceptibility at the point of divergence. Material m R / m L 2 at % Sm doped PZT 50:50 0.5 2 at % La doped PZT 50:50 0.5 2 at % Nb doped PZT 50:50 0.6

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94 CHAPTER 5 SUMMARY In this work, new structural insight into the p iezoelectric properties of PZT based ceramics was gained using synchrotron X ray diffraction. It was found that the soft dopants Sm, Nd, La and Nb have unique or signature effects on the strain mechanisms contributing to the extrinsic piezoelectric respon se of PZT. All the doped PZT 50:50 compositions show 90 domain reorientation during the application of both large and subcoercive electric fields. Only La and Nb doped PZT 50:50 PZT show the presence of a mixed tetragonal and rhombohedral phase. Under wea k electric fields, the interphase boundary between the tetragonal and rhombohedral phases moves in Nb doped PZT and shows no response in La doped PZT. The rhombohedral (200) lattice plane in Nb doped PZT exhibits very large strains. The corresponding plane in the La doped composition shows no strain response to electric fields. Thus far, there has been no definitive information regarding how doping increases the piezoelectric coefficient in PZT. This work shows that different dopants soften PZT via distinc tive mechanisms and that the value of the piezoelectric coefficient achieved through chemical substitution depends on the magnitude and number of strain mechanisms that are accessible to the doped material. The effect of doping schemes on the temperature dependent piezoelectric response was also examined. Sm results in high temperature piezoelectric coefficients that are roughly twice those obtained by doping with La and Nb across all the Zr:Ti ratios studied. It was found that the ferroelectric paraelectr ic phase transformation characteristics of PZT based ceramics are influenced by doping. At temperatures

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95 approaching the Curie temperature, Sm doped PZT 50:50 is composed of a mixed tetragonal and cubic phase whereas La and Nb doped PZT are composed of a si ngle tetragonal phase. It is hypothesized that the origin of the large piezoelectric coefficient values shown by Sm doped PZT at high temperatures is extrinsic in nature. Due to the presence of the mixed phase, Sm doped PZT compositions possess higher stra in accommodation capacities when compared to the La and Nb compositions. With increasing temperature, the energy available for 90 domain wall motion increases for all the PZT compositions. However, the Sm doped PZT compositions have a larger capacity to e nhance the strain from an increase in 90 domain wall mobility. Hence, the Sm doped compositions have high temperature piezoelectric coefficients that are approximately twice those obtained by doping with La and Nb. PZT has been extensively studied in the past in order to understand the origin of its electromechanical properties. The insight into strain mechanisms developed in this work contributes to the understanding of the enhanced piezoelectric properties of soft doped PZT materials. PZT ceramics are extensively used in several industries. In recent years, considerable research has been undertaken towards the development of new generations of Pb based and Pb free materials with higher electromechanical properties. The understanding of specific strain m echanisms that have been studied in this dissertation can be exploited in order to facilitate these advancements. By adjusting the composition of the piezoelectric material, an attempt can be made to induce whichever strain mechanisms are required for the purpose of obtaining the optimal longitudinal piezoelectric coefficients in various materials systems. Three of the strain

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96 mechanisms (90 domain wall motion, coexistence of mixed ferroelectric phases and interphase boundary motion) are enhanced close to t he MPB. The strain capability of the rhombohedral (200) plane may not be affected by the proximity to an MPB. Strain enhancements due to the coexistence of a mixed phase (only one of the phases needs to be ferroelectric) can be used to enhance the piezoele ctric coefficient in systems that are not proximate to a MPB. Thus, this work contributes towards the understanding of the process by which the piezoelectric coefficient is enhanced by softening.

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97 CHAPTER 6 FUTURE WORK The results presented in the presen t dissertation reveal new insight into electric field induced and temperature dependent strain mechanisms of ferroelectric compositions. Several future areas of study are natural extensions of the present work. These new possible directions of research wil l enable a better understanding of the strain mechanisms that contribute to softening in donor doped PZT These research directions are presented in Sections 6.1 6.5. 6.1 Measurement of the Temperature Dependent Crystallographic Response During the In Sit u Application of Electric Fields In the present work, the crystallographic structure of the Sm, La and Nb doped PZT 50:50 was studied at 6 fixed temperatures. In order to obtain a better understanding of the temperature dependent strain mechanisms in this material, it would be of interest to study the temperature dependent crystallographic response of these compositions during the in situ application of an electric field. If these measurements were carried out across temperatures ranging from room temperatu re to temperatures above T c the effect of the various soft dopants on the depoling behavior of the PZT compositions can also be studied. 6.2 Frequency Dependence of the Piezoelectric Response The strain mechanisms observed is this study are frequency de pendent. It would be beneficial to compare the frequency dependence of the macroscopic polarization, strain, relative permittivity and longitudinal piezoelectric coefficient to the frequency dependence of the strain mechanisms observed using diffraction.

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98 6.3 Effect of Dopant Homogeneity As a relatively small percent of the A or B site atoms are dopant atoms (2%), it is possible that the dopants are not homogeneously distributed throughout the PZT solid solution. Dopant homogeneity may affect the phase tran sformations observed in this work. Namely, the likely strain driven phase transformation in Sm doped PZT at high temperatures described in Section 4 and the electric field driven phase transformation in Nb doped PZT described in Sections 3.4.2 and 3.4.3. I t would be valuable to study dopant distribution in the PZT compositions using EDS mapping in a TEM or SEM. The effects of processing time, processing temperature and annealing conditions on dopant homogeneity can also be studied. 6.4 Measurements on Undo ped PZT Compositions It would be beneficial to repeat all the measurements done in this work and suggested for the future work with an undoped PZT composition in order to better compare the effect of soft doping on the strain mechanisms in undoped PZT. 6. 5 Effect of the Ionic Radius of the Dopant on the Ferroelectric Paraelectric Phase Transition Results discussed in Chapter 4 suggest that the internal strain due the mismatch between the ionic radii of the dopant, Sm and the host, Pb provides an additiona l driving force for the ferroelectric tetragonal to paraelectric cubic phase transformation in Sm doped PZT. It would be valuable to ascertain if there are other dopants that can similarly cause the cubic phase to coexist with the tetragonal phase below th e Curie temperature. Nd doping on the A site is an option that can be explored in this regard.

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99 APPENDIX DETERMINATION OF THE CONTRIBUTION OF 90 DOMAIN WALL MOTION TO LONGITUDINAL STRAIN When a poled polycrystalline material is subjected to subcoercive electric field cycles, 90 domain walls in grains of all orientations respond to the applied electric field. The total longitudinal strain in the material due to all the 90 domain wall motion is obtained by projecting the anisotropic strains of all the cr ystalline orientations to the longitudinal direction and performing a weighted summation of the projected strains as described in Pramanick et al. 42 The experimental data needed for the determination of the overall contribution of 90 domain walls to the m acroscopic longitudinal strain are time resolved diffraction patterns measured at all angles with respect to the electric field direction. Here, a more efficient method of data measurement that requires a time resolved diffraction pattern to be taken at on ly one angle (parallel to the electric field) with respect to the electric field is developed based on known behaviors of domain wall motion. 90 o domain wall motion results in a conservative interchange in symmetry dependent reflections. The fraction of c axis domains that are oriented in a specific sample direction can be calculated from the {002} diffracted intensities by using the equation 63 (A 1) where I ijk is the integrated intensity of the (002) and (200) peaks in both the state of interest and the unpoled state. During the electric field c ycling, the fraction of c axis

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100 domains that are re 002 is expressed relative to the maximum and minimum values through, 63 (A 2) where + 002 and 002 are the volume fraction of 002 domains oriented in a particular direction during the positive and negative electric field cycles respectively. As a random distribution of ferroelectric domains contains 1/3 of the 002 domain orientation, the multiple of a random distribution, f, of 002 domains is given by, 63 (A 3) f 42 For the purposes of determining d 33,90 42 From known behaviors of domain wall motion, 42,63,100 it was determined that t he following for 0 < < (A 4) for < < (A 5) 002 0.The relation b 002 is as given in equation (A 3). Equations (A 1) to (A 5), together with a time 002 as a function of as modeled by equations (A 4) and (A 5). As can be seen from Figure A 1, equations (A 4) and (A 5) adequately d 002

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101 orientation space enclosing all possible c axis directions of domains within the range of G = (A 6) Integrating f across all possible orientations gives 92 Z = (A 7) (A 8) When Z is axisymmetric, equation ( A 8) reduces to, (A 9) Considering that 9 ) further reduces to (A 10) For an unpoled sample, i.e., a sample with a random distribution of domains, for all (A 11) Using (A 11) in (A 10) gives, (A 12) Integrating equation (A 12) gives, (A 13) Equating the right hand side (RHS) of equation (A 10) to the RHS of equation (A 13) gives,

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102 (A 14) As the total volume of domains is a constant, any function 14). To check the validity of using equations (A 4) and (A 5 (A 4 ) and (A 5 A 14) If the evaluation of the i ntegral on the left hand side (LHS) of (A 14 ) yields 1, then (A 4) and (A 5 ) follow conservation of domain volumes. Substituting for f in (A 14 ) using equations (A 4 ) and (A 5 ) gives, (A 15) Integrating equation (A 15 ) gives, (A 16) Simplifying (A 16 ) gives the LHS of (A 14 ) to be 1. As the LHS of (A 14 ) equals the RHS of (A 14 (A 4 )and (A 5 ), these equations are valid models to 002 (A 4)) and (A 5) and is shown in Figure A 2. The extent of 90 domain switching that occurs ca n be quantified and used to determine the longitudinal strain in the material 90 according to the equation 42 (A 17) erence between the initial and final the 002 domains in a poled sample subjected to the positive polarity of a subcoercive

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103 bipolar electric field cycle. Let f MRD of 002 domains in a poled sample subjected to the negative polarity of a subcoercive bipolar electric field. Then, (A 18) Using (A 4 )and (A 5 )to substitu (A 18) gives, (A 19) = A + A (A 20) Integrating equation (A 19) and substituting for A+ and A using (A 20) gives, (A 21) Equation (A 90 from a single time resolved diffraction pattern 002 was obtained from the integrated (002) and (200) peak intensities as per equations (A 1) and (A 002 were also numerically integrated according to Equation (A 16) and as described in Pramanick et al., 93 this value equals that obtained by using equation (A 20), providing additional validity to equation (A 20).

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104 Figure A 1. 002 at two subcoercive electric field amplitudes.

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105 Figure. A 2. 002 values and the symbols represent experimentally measured data

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106 LIST OF REFERENCES 1 Q. M. Zhang, H. Wang, N. Kim, and L. E. Cross, "Direct Evaluation of Domain Wall and Intrinsic Contributions to the Dielectric and Piezoelectric Response and Their Temperature Dependence on Lead Zi rconate Titanate Ceramics," J. Appl. Phys., 75 454 9 (1994). 2 N. Setter, ABC of Piezoelectricity EPFL, Lausanne, Switzerland, 2002. 3 M. W. Barsoum, Fundamentals of Ceramics Taylor and Francis Group, New York, USA, 2003. 4 D. Damjanovic, "Ferroelectric Dielectric and Piezoelectric Properties of Ferroelectric Thin Films and Ceramics," Rep. Prog. Phys., 61 [9] 1267 324 (1998). 5 C. A. Randall, N. Kim, J. P. Kucera, W. Cao, and T. R. Shrout, "Intrinsic and Extrinsic Size Effects in Fine Grained Morphotro pic Phase Boundary Lead Zirconate Titanate Ceramics," J. Am. Ceram. Soc., 81 [3] 677 88 (1998). 6 R. J. Nelmes and W. F. Kuhs, "The Crystal Structure of Tetragonal PbTiO 3 at Room Temperature and at 700 K," Solid State Comm., 54 [8] 721 3 (1985). 7 G. Ber totti and I. D. Mayergoyz, The Science of Hysteresis. Academic Press, Oxford, UK, 2006. 8 M. E. Lines and A. M. Glass, Principles and Applications of Ferroelectrics and Related Materials Oxford University Press, Oxford, UK, 2001. 9 J. Fousek and V. Janove c, "The Orientation of Domain Walls in Twinned Ferroelectric Crystals," J. Appl. Phys., 40 [1] 135 42 (1969). 10 L. E. Cross, "Ferroelectric Ceramics: Tailoring Properties for Specific Applications," in Ferroelectric Ceramics: Tutorial Reviews, Theory, Pr ocessing, and Applications Birkhuser, University of California, USA, 1 86 (1993). 11 G. H. Haertling, "Ferroelectric Ceramics: History and Technology," J. Am. Ceram. Soc., 82 [4] 797 818 (1999). 12 J. F. Scott, "Applications of Modern Ferroelectrics," Science, 315 954 9 (2007). 13 D. Damjanovic and R. Newnham, "Electrostrictive and Piezoelectric Materials for Actuator Applications," J. Intel. Mat. Syst. Str., 3 [2] 190 208 (1992). 14 M. Ahart, M. Somayazulu, R. E. Cohen, P. Ganesh, P. Dera, H. k. Mao, R. J. Hemley, Y. Ren, P. Liermann, and Z. Wu, "Origin of Morphotropic Phase Boundaries in Ferroelectrics," Nature, 451 545 8 (2008).

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114 BIOGRAPHICAL SKETCH Shruti Banavara Seshadri earned a Bachelor of Engineering degree in Chemical Engineering from Rashtreeya Vidyalaya College of Engineering and MS and PhD degrees in Materials Science and Engineering from the University of Florida. Prior to starting her PhD work, Shruti studied the kinesin microtubule self assembly system with Prof. Henry Hess at the University of Florida. She also researched the synthesis of gold nanoparticles and the quantification of order in nanoparticle arrays with Pr of. Venugopal Santhanam at the Indian Institute of Science. She was the 2009 USA winner of the talk "Lessons from nature: making materials by self assembly". Shruti won t he Alec Courtelis Award in 2012 for academic excellence and contributions to the Department of Materials Science and Engineering. The scientific publications that have influenced Shruti the most are The Origin of Species by Charles Darwin and A. Raj, A. va n Oudenaarden, "Nature, Nurture, or Chance: Stochastic Gene Expression and Its Consequences," Cell, 135 [ 2 ] 216 226.2008.