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Study Of Paraelectric-Ferroelectric Phase Transitions In Lead(X) Barium(1-X) Titanium Oxide, Barium(X) Calcium(1-X) Titanium Oxide And Lead(X) Strontium(1-X) Titanium Oxide

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Study Of Paraelectric-Ferroelectric Phase Transitions In Lead(X) Barium(1-X) Titanium Oxide, Barium(X) Calcium(1-X) Titanium Oxide And Lead(X) Strontium(1-X) Titanium Oxide

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Content INFORMATION TO USERS This manuscript has been reproduced from the microfilm master. UMI films the text directly from the original or copy submitted. Thus, some thesis and dissertation copies are in typewriter face, while others may be from any type of computer printer. The quality of this reproduction is dependent upon the quality o f the copy submitted. Broken or indistinct print, colored or poor quality illustrations and photographs, print bleedthrough, substandard margins, and improper alignment can adversely affect reproduction. In the unlikely event that the author did not send UM I a com plete manuscript and there are missing pages, these will be noted. Also, if unauthorized copyright material had to be removed, a note will indicate the deletion. Oversize materials (e.g., maps, drawings, charts) are reproduced by sectioning the original, beginning at the upper left-hand com er and continuing from left to right in equal sections with small overlaps. Each original is also photographed in one exposure and is included in reduced form at the back of the book. Photographs included in the original manuscript have been reproduced xerographically in this copy. Higher quality 6" x 9" black and white photographic prints are available for any photographs or illustrations appearing in this copy for an additional charge. Contact UMI directly to order. A Bell & Howell Information Company 300 North Z eeb Road. Ann Arbor. M l 48106-1346 USA 313/761-4700 800/521-0600 STUDY OF PARAELECTRIC-FERROELECTRIC PHASE TRANSITIONS IN (PbxBai.x)Ti03 , (Bax Cai.x )Ti03 AND (Pbx Sri.x )Ti03 by Sudhakar Subrahmanyam A Dissertation Presented to the FACULTY OF THE GRADUATE SCHOOL UNIVERSITY OF SOUTHERN CALIFORNIA In Partial Fulfillment of the Requirements for the Degree DOCTOR OF PHILOSOPHY (Materials Science and Engineering) December 1994 Copyright 1994 Sudhakar Subrahmanyam UMI Number: 9601069 UMI Microform 9601069 Copyright 1995, by UMI Company. All rights reserved. This microform edition is protected against unauthorized copying under Title 17, United States Code. UMI 300 North Zeeb Road Ann Arbor, MI 48103 UNIVERSITY OF SO UTH ERN CALIFORNIA THE GRADUATE SCHOOL UNIVERSITY PARK LOS ANGELES, CALIFORNIA 90007 This dissertation, written by Sudhakar Subrahmanyam under the direction of h.% ?........ Dissertation Committee, and approved by all its members, has been presented to and accepted by The Graduate School, in partial fulfillment of re quirements for the degree of DOCTOR OF PHILOSOPHY Dean of Graduate Studies Qafe December 12, 1994 DISSERTATION COMMITTEE Chairperson ACKNOWLEDGEMENTS When I first started on my career as a graduate student in the United States, the tunnel in front of me seemed to be a long winding one, which held a lot of promise and complemented my desire to find the unicorn. The University of Southern California proved to be an ideal place to cultivate my talents and flair for research and there are several reasons which contributed to my intellectual stimulation for delving into the scientific world. I am greatly indebted to my advisor Dr. Edward Goo, who taught me the art of patience, orderliness and preparation while doing a Ph.D. Despite my several shortcomings initially, in terms of understanding the subject, formulating the problem, and the implementation of the work, he made it seem a lot easier by his attitude and confidence on my work. I appreciate all his guidance, understanding and patience which has in turn made me a better person equipped with a lot more skills and maturity to encounter the real world, than when I first started my graduate studies. Another person I would like to thank is Dr. Murray Gershenzon, who is my advisor in Electrical Engineering. He has given me the strength and courage during trying times, with his friendly smile and a genuine interest in my problems and welfare as a graduate student. Thanks are also due to Dr. Charles Sammis, Dr. Terence Langdon, Dr. Ronald Salovey and Dr. Daniel Rich for agreeing to be the members on my guidance and dissertation committees. I am grateful to Mr. Jack Worrall at the Center for Electron Microscopy and Microanalysis, for his help with the CEMMA equipment, and also to Ms. Mimi Nakata and Ms. Maria Santana at the Department of Materials Science and Engineering, for all their help and assistance given to me with genuine patience and friendliness during all these years. I would also like to express my thanks to my former roommates Dr. Sridhar Narayanan and Dr. K. Ramakrishnan and also my dear friend, Ms. Sheila Iyer for all their help, assistance and encouragement during the course of my graduate life. Last but not the least, my deepest gratitude goes to my parents, Varadarajan and Sita Subrahmanyam and my sister, Subhashini Srinath, for their unending love, support and encouragement and to whom this work is dedicated. Table of Contents Acknowledgements ..................................................................................................... ii List of Figures .......................................................................................................... viii List of Tables ............................................................................................................ xiii Abstract ..........................................................................................................................xiv Chapter 1 Introduction 1.1 Background .......................................................................................... 1 1.2 Perovskites ............................................................................................ 4 1.2.1 Simple Perovskites .................................................................... 4 1.2.2 Complex Perovskites ................................................................ 6 1.2.3 B-site Substitution .................................................................... 6 1.2.4 Ordering in Complex Perovskites ........................................... 7 1.3 Ferroelectrics ...................................................................................... 8 1.3.1 Definition and Basic Principles ................................................ 8 1.3.2 Ferroelectric Domains ............................................................. 8 1.3.3 Hysteresis ..................................................................................... 11 1.3.4 The Dielectric Curve .................................................................. 14 1.3.5 Diffuse Phase Transformations (DPTs) ..................................... 15 1.3.6 Relaxor Ferroelectrics ................................................................17 1.3.7 Microchemical R eg io n s................................................................18 1.4 Applications of Bulk Ferroelectrics .................................................. 20 1.5 Applications of Thin Film Ferroelectrics ...........................................21 iv 21 23 25 26 28 28 28 29 29 29 29 31 32 33 33 33 39 39 41 v Emphasis of the Present Study ........................................ Bibliography ......................................................................... Experimental Procedure Fabrication and Bulk Processing of Complex Perovskites X-ray Diffraction ................................................................ Transmission Electron Microscopy ................................. Scanning Electron Microscopy ........................................ Dielectric and Ferroelectric Properties .......................... 2.5.1 Dielectric Measurements ...................................... 2.5.2 Hysteresis Measurements ...................................... 2.5.3 Impedance Measurements ................................... 2.5.4 Resistivity Measurements ...................................... Bibliography ......................................................................... Study of (Pbl t Ba1 .J ( )TiC > 3 Structure and Properties of BaTi03 and PbTi03 .......... Structure and Properties of (PfyBaj.^TiOs .................... 3.2.1 Crystal Structure ...................................................... 3.2.2 Observation of Domain Structure .......................... 3.2.3 Dielectric and Ferroelectric Properties ................. 3.2.3.1 Ferroelectric Phase Transformations 3.2.3.2 Hysteresis Properties ........................ 3.2.3.3 Impedance Properties ....................................... 46 3.2.3.4 Resistivity ..........................................................49 3.3 Bibliography .............................................................................................52 Chapter 4 Study of (Ba^Cax.JTiOa 4.1 Structure and Properties of CaTi03 ...................................................53 4.2 Structure and Properties of (Bax Ca1 .x )T i03 ....................................... 53 4.2.1 Crystal Structure ....................................................................................53 4.2.2 Microstructure ........................................................................................ 56 4.2.2.1 Ferroelectric Domain Structure..... ............................................. 56 4.2.2.2 Ordered Structure ......................................................................60 4.2.2.3 Existence of a Secondary Phase ............................................. 62 4.2.2.4 Effect of Sintering Temperature on Grain Size .....................67 4.2.3 Dielectric and Ferroelectric Properties ..............................................67 4.2.3.1 Ferroelectric Phase Transformations .......................................67 4.2.3.2 Hysteresis ................................................................................... 72 4.2.3.3 Impedance Properties .............................................................. 72 4.2.3.4 Resistivity ................................................................................... 74 4.3 Bibliography .......................................................................................................77 Chapter 5 Study of (PbiSr^TiO;, 5.1 Structure and Properties of SrTi03 .....................................................79 vi 5.2 Structure and Properties of (Pbx Sr1 .x )T i03 ......................................... 80 5.2.1 Crystal Structure ................................................................................... 80 5.2.2 Ferroelectric Domain S tru ctu re............................................................80 5.2.3 Dielectric and Ferroelectric Properties .............................................. 85 5.2.3.1 Ferroelectric Phase Transformations ......................... 85 5.2.3.2 Impedance Properties ................................................... 85 5.2.3.3 Resistivity ........................................................................ 91 5.3 Bibliography..............................................................................................95 Chapter 6 Diffuseness Parameter and Microregion Size 6.1 Introduction ........................................................................................... 96 6.2 Estimation of the Diffuseness P a ra m e te r.............................................97 6.2.1 (Pbx Bai.x )T i03 ......................................................................................... 97 6.2.2 (Pbx Sr1 .x )Ti03 ....................................................................................... 100 6.2.3 (BaxCajJTiOa .................................................................................... 100 6.3 Quantitative Analysis of the Microregion Size .............................. 100 6.3.1 Estimation of the Microregion Size ............................................ 108 6.3.1.1 (Pbx Ba!.x )Ti03 .................................................................................... 108 6.3.1.2 (Pbx Sr1 .x )Ti03 ...................................................................................... 110 6.3.1.3 (Bax Ca!.x )Ti03 .................................................................................... 110 6.4 Bibliography........................................................................................... 112 Chapter 7 Conclusion ............................................................................................. 113 vii Fig. 1.1 Fig. 1.2 Fig. 1.3 Fig. 1.4 Fig 1.5 Fig 1.6 Fig 1.7 Fig 1.8 (a) (b) Fig. 2.1 Fig. 2.2 Fig. 3.1. Fig 3.2. List of Figures Perovskite unit cell composed of an oxygen octahedron .............. 2 Packing of the perovskite unit cell in terms of the tolerance factor, (a) t = 1, (b) t > 1, (c) t < 1 (after Goldschmidt). 7 ...............................5 Interrelationship of piezoelectrics and subgroups on the basis of internal crystal symmetry (after Haertling).2 1 ................................. 9 The crystal structure of BaTi03 . (a) The crystal is cubic above the Curie point, (b) The structure is tetragonal below the Curie point, with the Ba2 + ions and the Ti4 + ions displaced relative to the O2 ' ions (after Xu).2 3 ........................................................................................................10 Typical pattern of ferroelectric domains (after Merz).2 2 .................12 A typical hysteresis loop in ferroelectrics (after Xu).2 3 ................... 13 Permittivity of lead titanate as a function of temperature (after Shirane and Hoshino).2 4 .....................................................................................16 Characteristic features of a ferroelectric relaxor (after Cross).2 5 Dielectric dispersion in lead magnesium niobate (PMN)as a function of temperature and frequency................................................................ 19 Dielectric hysteresis in PMN as a function of temperature ............ 19 Sample geometry for the 0-26 diffractometer scans ........................27 Dielectric set up designed for high temperature measurements . 30 The variation of lattice parameters along the a and c-axis with composition for tetragonal (Pbx Bai-x )Ti03 ........................................ 34 Dark field micrograph taken (x — 0.2) with {110} type reflection from [111] zone axis showing the 90° domain walls oriented along the (101) plane. 180° domains can also be seen ....................................35 v i i i Fig. 3.3 (a) The two beam condition from the {110} type reflection in the [100] zone axis, showing spot splitting in the region of the 90° domains ....................................................................................... 37 Fig. 3.4. Fig. 3.5. Fig. 3.6. Fig. 3.7 Fig. 3.8 Fig. 3.9. Fig. 3.10. Fig. 3.11. Fig. 3.12. Fig. 4.1. Fig. 4.2. Fig. 4.3 (b) Dark-field of the same region ............................................... 37 SEM micrograph of (Pbft 2Baa8)Ti0 3 showing sub-micron grains 38 The variation of dielectric constant (at 10 kHz) with temperature for the (Pbx Ba!.x )T i03 system .................................................................... 40 The variation of Curie point with composition for the (Pbx Bal x )Ti03 system ..................................................................................................... 42 The variation of room temperature dielectric constant with composition (at 10 kHz) in (Pbx Ba!.x )T i03 ............................................................. 43 The variation of peak dielectric dielectric constant with composition (at 10 kHz) in (Pbx Ba!.x )Ti03 .................................................................... 44 Polarization vs electric field for (Pbo2 Bao8 )T i03 (Coercive field = 1.587 M V /m ).............................................. 45 The variation of phase lag (at 1 V) with frequency for the (Pbx Baj. x )Ti03 system ......................................................................................... 47 Bode plot showing the variation of impedance (at 1 V) with frequency for the (Pbx Ba!.x )T i03 system ............................................................. 48 The variation of resistivity (at 1 V) with composition for the (Pbx Baj. x )T i03 system ..................................................................................... 50 X-ray diffraction pattern showing a secondary phase (•) of Ca4 Ti3 O1 0 in (Ba0 .2 Ca0 .8 )TiO3 ............................................................................. 55 X-ray diffraction of (Bao.5 Ca0 .5)Ti03 showing peaks from both BaTi03 (X) and CaTi03 ( • ) due to the lack of a solid solution formation 57 Dark field micrograph taken (x = 0.9) with {110} type reflection from [100] zone axis showing the 90° domain walls oriented along the (101) plane ..................................................................................... 58 Fig. 4.4. (a) The two beam condition from the {110} type reflection in the [100] zone axis, showing spot splitting in the region of the 90° domains ................................................................................... 59 Fig. 4.5. Fig. 4.6 Fig. 4.7 Fig. 4.8. Fig. 4.9. Fig. 4.10. Fig. 4.11. Fig. 4.12. Fig. 4.13 Fig. 4.14. Fig. 4.15 (b) Dark-field of the same re g io n ................ 59 The structure of calcium titanate is a regular T i06 octahedra rotated with respect to their ideal perovskite positions (after Koopmans et a l.y ° ........................................................................................................61 The ordered unit cell shown with respect to the perovskite unit cell (after King et al.).9 ................................................................................ 63 Ordering with Ba/Ca atoms on alternating (a) {111} planes, (b) {100} planes, and (c) {110} planes (after King).1 1 ................................... 64 The <107> zone axis of the orthorhombic secondary phase of C a ^ O jo .................................................................................................65 EDS spectra from the region of non-perovskite reflections showing the absence of Ba peaks ..............................................................................66 Grain distribution in (Ba09Ca01)TiO3 (a) sintered at 1200 °C and (b) sintered at 1350 °C ..............................................................................68 The variation of dielectric constant (at 10 kHz) with temperature for the (Bax Ca!.x )Ti0 3 system for x = 0.9 and 0.8 ..................................69 The effect of sintering temperature on the dielectric curves for x)Ti03 ......................................................................................................71 A distinct hysteresis loop in the (Ba0gCa02)TiO3 composition confirming its ferroelectric nature (Scale : x-axis : 1 div = 0.5 MV/m; y-axis : 1 div = 2.5 mC/m2 ) ..........................................................................................73 The variation of phase lag with frequency for (Bax Ca!.x )T i03 at 1 V74 Bode plot showing the variation of impedance with frequency for (Bax Ca1 .)Ti03 (at 1 V) ......................................................................... 75 x Fig. 5.1. X-ray diffraction pattern showing a cubic structure in (Pbo4 Sro6)Ti03 81 Fig. 5.2. Fig. 5.3 Fig. 5.4 Fig 5.5 Fig 5.6 Fig. 5.7 Fig 5.8 Fig 5.9 Fig. 5.10 Fig. 5.11 Fig 6.1 Fig 6.2 Fig. 6.3. Fig. 6.4. X-ray diffraction pattern showing a tetragonal structure in (Pbo.5 Sro.j)Ti03 .....................................................................................82 The variation of c/a ratio with composition for (Pb„Sri.x )Ti03 . . . 83 Dark field micrograph taken from [100] zone axis showing the presence of 90° domain boundaries in (Pb0 . 5 SrftjTiO3 ) ............................... 84 The variation of dielectric constant (at 10 kHz) with temperature for the (Pbx Sr1 .x )T i03 system ................................................................ 86 The variation of Curie point with composition for the (Pb^ri.^TiOs system ..................................................................................................... 87 The variation of room temperature dielectric constant with composition (at 10kHz) in (Pb^r^T iO ;, ................................................................88 The variation of phase lag with frequency for (Pbx Sr1 .x )T i03 at IV 89 Bode plot showing the variation of impedance with frequency for (Pbx Sr1 .x )Ti03 at 1 V ..............................................................................90 Linear I-V plot of (Pb0 6Sr04)TiO3 showing a constant resistivity of 7.87 MQm ........................................................................................................92 Variation of resistivity with composition for (PbxSr^TiCXj . . . . 93 The variation of the exponent y with composition for (P fyB a^T iG ^ The variation of the diffuseness parameter, < 5 „ with composition for (Pbx Bai,)T i0 3 ....................................................................................... 99 The variation of the exponent y with composition for (PbxSri.x )T i03 ........................................................................................101 The variation of the diffuseness parameter, d„ with composition for (PbxSri.x )Ti03 ................................................................................... 102 X I Fig. 6.5. Determination of the exponent y for (a) (Bao9 Ca01)T i03 and (b) (Bao.8Cao.2)Ti03 ................................................................................... 103 Fig. 6.6. Determination of the diffuseness parameter < 5 X for (a) (Ba0 .9 Ca< ) 1 )TiO3 and (b) (Bao.8 Cao.2 )T i03 ..................................................................... 104 Fig. 6.7. Illustration of the width at half-maximum (WHM), A ..................107 Fig. 6.8. Theoretical and experimental variation of the width at half-maximum (A) for (Pbx Ba!.x )T i03 ....................................................................... 109 Fig. 6.9. Theoretical and experimental variation of the width at half-maximum (A) for (Pbx Sr1 .x )T i03 ....................................................................... I l l xii List of Tables Table 3.1 Physical and Electrical Properties of (PbJJa/.JTiOj ...................... 51 Table 4.1 Transformation Temperatures of (Bax Ca1 .1 )TiOs ............................. 70 Table 4.2 Physical and Electrical Properties of (BaJ .Ca;.J .)T i03 ...................... 76 Table 5.1 Physical and Electrical Properties of (Pb,Sr7 .x )Ti0 3 .........................94 x i i i ABSTRACT The crystal structure, microstructure and electrical properties of the A-site substituted titanates are investigated. The systems studied are (PbxBai^TiOij, (PbxSrj. x )Ti03 and (Bax Ca1 .x )Ti03 . The (Pbx Bai.x )Ti03 structure is determined to be tetragonal over the entire composition range (0.0 < x < 1.0). The system shows a prominent presence of strain- induced ferroelectric domain boundaries which decrease in density with increasing lead content. The Curie point increases with increasing Pb content while the maximum and room temperature values of the dielectric constant decrease linearly with increasing Pb content and are consistent with linearly interpolating the values for BaTi03 and PbTi03 . The (Pbx Sr1 .x )Ti03 remains cubic for x < 0.4 and becomes tetragonal for x > 0.4. In addition to the presence of strain-induced ferroelectric domains in the compositions with* > 0.4, the system has a Curie point above room temperature for these compositions. The (BaxCa^TiO;} is orthorhombic for (0.0 < x < 0.2) and is tetragonal for (0.8 < x < 1.0) but does not form a solid solution for (0.2 < x < 0.8). The strain- induced ferroelectric domains are seen for (0.8 < x < 1.0) and are absent for (0.0 ^ x < 0.2). The presence of a secondary phase, Ca4 Ti3 Oic in the Ca-rich region is confirmed by XRD and EDS peaks. The effect of sintering temperature on the grain size, maximum value of the dielectric constant and domain boundaries are investigated. Even though both (Pbx Ba!.x )Ti03 and (Pbx Sr1 _ x )TiC> 3 show diffuse phase transitions above room temperature, the diffuseness is most pronounced in the (Bax Ca1 .x )T i03 system which exhibits a diffuse phase transition (paraelectric to ferroelectric) above room temperature over the composition range 0.8 < x < 1.0 and a sharp transition from a tetragonal to an orthorhombic phase below room temperature. An empirical relation is used to estimate the diffuseness of the paraelectric- ferroelectric phase transitions in order to obtain a diffuseness parameter. It is observed that the diffuseness parameter, 6, attains a maximum around the mid composition range for both the (Pbx Bai_x )Ti03 and the (Pb^rj.^TiO^ In a very small region or microregion of the crystal, the compositions differ from the average composition, and is the cause of the diffuse phase transition. The size of the microregions is an important parameter that has not been experimentally measured. These microregions represent the minimum size for a ferroelectric nucleus in the paraelectric to ferroelectric transitions. A model has been used to determine the size of these microregions, by measuring the dielectric constant vs temperature over a range of compositions for a given solid solution. The diameter of the microregions is determined to lie between 20 A - 75 A for the three systems studied. None of the three systems studied showed any relaxor behavior. xv Chapter 1. Introduction 1.1 Background Perovskites are a group of ceramics with the general chemical formula A B03 where A is typically a divalent cation, located at the corner of a cube, B is typically a tetravalent cation, located at the center of the cube, and O is the oxygen anion, located at the center of each face of the cube, as shown in Fig. 1.1. The main reason for interest in this class of materials is because of their excellent dielectric and piezoelectric properties.1 ,2 In the early 1950’s, new compounds with the perovskite structure were formed by substituting more than one cation onto the A (or B) site.3 ,4 The new class of materials thus formed had the general formula A(B’1 .x B"x )0 3 or (AVx A"x )B0 3 , which were usually referred to as complex perovskites. These complex perovskites form the majority of the materials which are dielectric and piezoelectric in nature.5 The fundamental work in the field of ferroelectric materials has been concerned predominantly with single crystals of various groups of substances. But for industrial applications, only polycrystalline materials with perovskite structure (general formula : A B 03 ), especially displacive ferroelectrics like BaTi03 , and lead zirconate titanate (PZT) are important today for several reasons. Their production by conventional ceramic processing is relatively inexpensive, they are stable with respect to temperature and humidity and their dielectric and piezoelectric properties are excellent. 1 Fig. 1.1. Perovskite unit cell composed of an oxygen octahedron. 2 The optimum properties for individual applications can be obtained by crystals composed of two or three different cations on the A or B sites and in addition are doped with cations to maximize resistivity. Since the growing of a simple perovskite structure is relatively difficult and expensive, the attempt to grow complex perovskites will be much more complicated. Ferroelectric ceramics have found wide spread applications and are the focus of much research and development.6 Both capacitors and transducers frequently use ferroelectric materials in their construction and between them, constitute the bulk of the market. However, there are a number of more specialized and quite intriguing applications which rely upon the properties of ferroelectrics. Perhaps one of the simplest applications of ferroelectric ceramics comes from the direct use of temperature dependance of remanent polarization (PR ), the so called pyroelectric effect in ciystals and ceramics. The charge released on heating is such that a thin flake of the ferroelectric material can become an exceedingly sensitive broad-band infrared detector. There is also a considerable interest in perovskite materials because of their versatility of the structure to be formed with many different cations. In the late 1980’s, the discovery of superconductivity in layered perovskite crystals has resulted in increased research into the ordering and the electrical and microstructural properties of these crystals. 3 1.2 Perovskites The perovskite structure is essentially an octahedron of oxygen atoms, connected to the adjacent octahedra through the sharing of the corner atoms, as shown in Fig. 1.1. The packing efficiency of this structure can be characterized by a tolerance factor, t, which was first introduced by Goldschmidt in 19267 , which is defined as R a + R 0 = ty/2 ( R b + R 0 ) ( 1 ) where RA , RB and R0 are the ionic radii of the A, B, and O ions, respectively. The packing efficiency is directly related to the value of /, as shown in Fig. 1.2. The limits of stability for forming the perovskite structure is given by the empirical relation 0.8<r<1.0. For Fig. 1.2 (b) the limits of cation radii are given by a {AAo touch) = + F q) ( 2 ) and for Fig. 1.2 (c), a (BAo touch) ~ ^ (F g + R q) 1.2.1 Simple Perovskites Barium titanate, BaTi03 , is a widely used perovskite material which undergoes several phase transitions. Upon cooling through the Curie point, at 120 °C, the structure transforms from the cubic non-ferroelectric phase to a tetragonal ferroelectric phase. A further distortion occurs at the second transition point near 4 Fig. 1.2 Packing of the perovskite unit cell in terms of the tolerance factor (a) t = 1, (b) t > 1, (c) t < 1 (after Goldschmidt).7 10° C where the tetragonal phase transforms to an orthorhombic phase. This is marked by a small peak in dielectric constant, and a peak in electro-mechanical coupling coefficients. The third distortion occurs at -90° C where the orthorhombic phase transforms to a rhombohedral phase. The operation of barium titanate transducers over extended temperature ranges, including the second transition point, has been unsatisfactory. 1.2.2 Complex Perovskites Since most transducers operate near the 10° C range, it is desirable to develop a barium titanate ceramic which has a lower temperature for the second transition. This was the motivating factor which formed the basis for the advent of complex perovskites. The BaTi03 -SrTi03 system was the first complex perovskite system to be studied7 , where the Curie point was found to linearly decrease with increasing Sr content, along with the second and third transformation temperatures. Interests in complex perovskites grew as it became clear that they: (1) were relatively easy to process and sinter (2) had higher electromechanical coupling factors when compared to barium titanate (3) had high electrical resistivity, (4) had a wide range of dielectric constants (5) could be easily poled, (6) had relatively low dielectric loss and (7) formed solid solutions over a wide range of compositions, which allowed a wide range of properties to be obtained.8 6 1.2.3 B-Site Substitution Most of the research on complex perovskites have been done on B-site substituted systems. The lead zirconium titanate system Pb(Zr,Ti)03 system [PZT] is the most well known and widely studied of the B-site substituted systems.9 -1 0 The PZT system has a large piezoelectric modulus and a high electro-mechanical coupling coefficient for compositions which are close to the tetragonal-rhombohedral phase boundary. Complex perovskites have been prepared and studied with virtually every suitable cation on the B-site. 1.2.4. Ordering in Complex Perovskites In the early 1980’s, it was shown that some perovskite compounds with the general formula A(B’ x B"1 .x ) 0 3 were ordered with the two B-site cations. Pb(Sci/2 Nbi/2 ) 0 3 1 1 - u 1 3 and Pb(Sc1 /2 Ta1 /2 ) 0 3 1 4 -1 5 were found independently, to be ordered with an arrangement of the B-site cations. It was shown that the degree of ordering could be affected by the annealing temperature, which was confirmed by X- ray powder diffraction. Similar behavior was also observed in other systems like Pb(Mg1 /3 Nba3) 0 3 .1 6 But so far, there has been only one report on the ordering of complex perovskites with the composition (A*A"i.x)B03 .1 7 7 13 Ferroelectrics 13.1 Definition and Basic Principles Ferroelectricity was first discovered in Rochelle salt by Valasek, in 19201 8 . BaTi03 was the primary system which brought about further developments in ferroelectricity.1 9 ' 2 0 Structural symmetry considerations form the basis for ferroelectricity. All crystal systems can be classified into 32 different point groups as shown in Fig. 1.3.2 1 Of these 32 point groups, 20 are piezoelectric. Piezoelectric materials become polarized under stress. Of these 20 point groups, 10 develop a spontaneous polarization, thereby forming permanent dipoles in the structure. These structures are pyroelectric in nature, since this spontaneous polarization is a temperature function. A subgroup of these spontaneously polarized pyroelectrics are ferroelectrics. A ferroelectric is a material which is spontaneously polarized where the polarization direction can be changed by the application of an external electric field. Fig. 1.4 shows the crystal structure of BaTiO*2 2 BaTi03 has a cubic crystal structure above the Curie point of 120 °C, with the Ba2 + ions at the corners of the cube, the Ti4 + ions at the body centers and O2 - at the face centers, as shown in Fig. 1.4a. The structure is slightly distorted below the Curie point, where the Ba2 + and the Ti4 + ions are displaced relative to the O2 " ions resulting in a spontaneous polarization. 13.2 Ferroelectric Domains The direction of spontaneous polarization changes in the different regions of the ferroelectric crystal. These regions are called ferroelectric domains and 8 CENTROSYMMETRIC NONCENTROSYMMETRIC 32 SYMMETRY POINT GROUPS 20 PIEZOELECTRIC (POLARIZED UNDER STRESS) 10 PYROELECTRIC (SPONTANEOUSLY POLARIZED) SUBGROUP FERROELECTRIC (SPONTANEOUSLY POLARIZED, REVERSIBLE POLARIZATION) Fig. 1.3. Interrelationship of piezoelectrics and subgroups on the basis of internal crystal symmetry (after Haertling).2 1 9 4+ (a) (b) Fig. 1.4. The crystal structure of BaTi03 . (a) The crystal is cubic above the Curie point, (b) The structure is tetragonal below the Curie point, with the Ba2 + ions and the Ti4 + ions displaced relative to the O2 - ions (after Xu).2 3 10 are separated by domain walls. Similar to the ferromagnetic domains of iron, the electric polarization can be along any one of the six {100} directions. The sharp 45° lines in Fig. 1.5 are the 90° walls (boundaries between domains polarized at 90° to each other). The 180° walls (boundaries between anti-parallel polarized domains) cannot be seen very easily. However, by applying an external electric field or stress in the crystal, one can change the optical extinction position for parallel and anti parallel domains in opposite directions and thus make the two types of domains distinguishable in polarized light. The crystals prevent the formation of surface charges on the 90° walls by joining the head of the polarization of one domain with the tail of the polarization of the neighboring domain, forming a zig-zag head to tail arrangement (Fig. 1.5). A newly grown ferroelectric crystal always exhibits a polydomain structure. A crystal with a single domain can be obtained by applying an external electric field of sufficiently high strength. Also, the direction of spontaneous polarization can be reversed by applying a strong external electric field in the opposing direction. This process of dynamic domain reversal is known as domain switching. 133 Hysteresis The ferroelectric hysteresis loop is an important characteristic of all ferroelectric materials. When a ferroelectric material is subjected to an alternating field, the instantaneous relation between the polarization and the field or the charge and the potential, produces a hysteresis loop, as shown in Fig. I.6.2 3 When the applied electric field is small, the ferroelectric crystal exhibits normal dielectric 11 Fig. 1.5. Typical pattern of ferroelectric domains (after Merz).2 2 12 E_____ Fig. 1.6. A typical hysteresis loop in ferroelectrics (after Xu). 13 behavior, as no domain switching takes place. This is observed in segment O A As the applied electric field is gradually increased, the number of domains having a polarization opposite to the direction of the applied field are switched over to the direction of the field and the polarization increased rapidly (segment AB) until all the domains are aligned in the field direction (segment BC). In this state, the crystal is composed of a single domain. As the field is decreased, the polarization also decreases but retains a finite value at zero field. This is indicated by the point D. In this situation, a few of the domains remain aligned in the same direction as at point B, resulting in a remanent polarization, Pr The extrapolation of the linear segment BC of the curve to the polarization axis at E gives the spontaneous polarization, P,. When the direction of the applied field changes and reaches the coercive field strength E„ the remanent polarization vanishes. As the field is further increased in this direction, the dipoles become completely aligned along this direction. The cycle is completed when the field direction is reversed once again. 1.3.4 The Dielectric Curve The Curie point (T0 ) is another important feature of ferroelectrics. This is the temperature at which the phase transition from the paraelectric phase to the ferroelectric phase occurs when the temperature is decreased. This transition is accompanied by a small lattice distortion in the crystal, such that the ferroelectric phase symmetry is lower than the paraelectric phase symmetry. Changes in thermodynamic properties such as dielectric, elastic, optical and thermal are seen 14 near the Curie point. This is illustrated by the variation in the dielectric constant (k) of lead titanate2 4 , as a function of temperature (Fig. 1.7). Lead titanate is cubic (paraelectric phase) above 490 °C, which is the Curie point (T0 ). The structure becomes tetragonal below T0 (ferroelectric phase). The dielectric constant (k) reaches a maximum value near the Curie point. This phenomenon is referred to as "the dielectric anomaly".2 3 The temperature dependence of the dielectric constant above the Curie point may be given by the Curie-Weiss law where Tc is the Curie-Weiss temperature (which is in general different from the Curie point T0 ) and C is the Curie-Weiss constant. 1-3.5 Diffuse Phase Transformations (DPTs) The transition from the non-ferroelectric to a ferroelectric phase is generally a very sharp transition. A gradual or a diffuse phase transition is observed in complex perovskites.2 5 ' 2 6 It has been suggested that the reason for the diffuse characteristics of the normally sharp phase transitions is due to the statistical composition fluctuations which must occur if crystallographically equivalent sites are occupied randomly by different cations.2 7 2 8 The local variation in composition causes the transformation to occur over a range of temperatures. Therefore, the transition should become sharper as the degree of order increases since the compositional variations would decrease with increasing order of the cations. There has been 15 800 G O O 400 200 Fig. 1.7. Permittivity of lead titanate as a function of temperature (after Shirane and Hoshino).2 4 16 experimental evidence that show the sharpening of the transition with increasing order in the cation arrangement.1 2 ,1 4 13.6 Relaxor Ferroelectrics Many complex perovskites exhibit diffuse phase transformations. Relaxor ferroelectrics are a class of ferroelectrics that display diffuse phase transitions but in addition, have certain additional properties not seen in all materials that undergo DPTs. Relaxor behavior are a subset of diffuse phase transformations. Normal ferroelectrics have a sharp transition at the Curie point while relaxor ferroelectrics have a broad-diffuse transition about the Curie maxima Tm > x . Normal ferroelectrics have a weak frequency dependence as opposed to a strong frequency dependence of relaxor ferroelectrics. The remanent polarization is strong and weak for normal and relaxor ferroelectrics, respectively. Scattering of light is strongly anisotropic for normal ferroelectrics and is weak for relaxor ferroelectrics.2 9 There are two main theories that account for the large differences in behavior of these two classes of materials, namely normal and relaxor behavior.2 5 ,2 9 But neither of them have been verified experimentally nor generally accepted universally. One of the theories attributes the nature of the polarization mechanism in these two groups as essentially the reason for large differences in behavior. In normal ferroelectrics, there is a long range cooperative alignment of dipoles (or anti-dipole alignments) whereas in the relaxors, there is only short-range (« 100 A) cooperative alignment of dipoles forming thermally unstable polar micro-regions.2 9 The other 17 theory attributes the fluctuations in Curie point (leading to diffuse phase transitions) to the statistical compositional fluctuations which leads to an intimate mixing of the ferroelectric and paraelectric regions over a wide range of temperature.2 5 PbMgi/sNb^Os (PMN) is a typical relaxor ferroelectric (shown in Fig. 1.8). In the dielectric response (Fig. 1.8a) the weak field permittivity reaches a peak value « 20.000 typical for a ferroelectric perovskite near T0 but the dielectric maximum clearly does not mark a phase change into a ferroelectric form as the temperature of the maximum increases with frequency in a manner typical of a relaxor ferroelectric. The associated maximum in e (tan < 5 ) is also typical of a relaxor ferroelectric. Also, the hysteresis response slowly degenerates into non-linearity as the temperature increases, i.e., that the spontaneous polarization is not suddenly lost at the T0 but decays gradually to zero (Fig. 1.8b). 13.1 Microchemical Regions The general feature of all perovskite compounds is the existence of ions of different types in equivalent crystallographic positions. The assumption of statistical distribution of different ions in those positions explains the diffuseness of phase transitions by composition fluctuations. Kanzig3 0 concluded from X-ray measurements that the region near the phase transition from the paraelectric to the ferroelectric phase were divided into microregions in which the spontaneous polarization appeared or disappeared because of thermal fluctuations. These regions were termed as " Kanzig regions" and the 18 Pb (Mg|/3 Nb2/3)03 20i Strong dispersion in < ' ! ! > U 0 . 1 0 0. 8 0.6 0. 0 0 S tro n g dispersion in to n 8 160- 120- 80-40 0 40 80 " H y storetic Slow decoy of ferro electric c h a ra c te r ► J 3 a T in c re a s in g ■ Fig. 1.8. Characteristic features of a ferroelectric relaxor (after Cross).2 9 (a) Dielectric dispersion in lead magnesium niobate (PMN)as a function of temperature and frequency. (b) Dielectric hysteresis in PMN as a function of temperature. 19 spontaneous polarization in these regions were independent of the state of similar neighboring regions. Similar to Kanzig regions, one may define microchemical regions where the phase transition occurs at different temperatures due to chemical fluctuations. It should be noted that the diffuseness of phase transition can also result from macroscopical inhomogeneity of composition. 1.4 Applications of Bulk Ferroelectrics The applications of ferroelectric ceramics have been the focus of considerable interest in the recent years.3 1 3 2 Piezoelectric ceramics are used in ultrasonic transducers for underwater sonar and hydrophones3 3 , ignition devices, ceramic filters, microphone oscillators, pressure sensors and surface-acoustic wave (SAW) devices.5 '3 3 Thin, electroded piezoelectric plates are used as mechanical positioners and relays when the required movements are very small. One of the more recent successful applications for piezoelectric ceramics has been in the area of piezoelectric loud speakers, particularly tweeters. Compared with the conventional electrodynamic tweeter, the piezo tweeter is lighter, shallower in design, and more power efficient, more reliable, has better transient response, and is cost competitive. These desirable features make them ideally suited for high power audio applications, hi-fi stereo audio systems. Bulk ferroelectrics are used as dielectric materials for capacitors, electro-optic devices and pyroelectric detectors. Thin polished plates of PLZT, when used in conjunction with polarized light, make excellent wide aperture electronic shutters. Their advantages over competing technologies such as mechanical 20 shutters and liquid crystal (LC) light gates include : (1) faster response time, in the low-microsecond range; (2) less vibration; (3) lighter weight; (4) thinner profile; and (5) wider operating temperature range, from -40 °C to + 80 °C.2 1 1.5 Applications of Thin Film Ferroelectrics Most commercial applications involve bulk ferroelectrics but there has been much interest in thin film ferroelectrics in the research community. Recently, PZT and PLZT thin film perovskites have been developed for use in non-volatile random access memories.3 4 They are ideally suited for non-volatile RAM capacitors due to their large remanent polarization. PZT films have been the most widely developed and film thicknesses typically are in the range of 100-300 nm. Advantages of the ferroelectric memories are their non-volatility and high radiation hardness. Ferroelectric random access memories are used in video game cartridges as well as in applications using electrically erasable and programmable read only memories (EEPROMs). There is also considerable interest in high dielectric constant ferroelectric thin films for applications in dynamic random access memories (DRAMS). 1.6 Emphasis of the Present Study Substitution of other cations for Ti at the B site in BaTi03 and PbTi03 have been extensively studied and Pb(Zr,Ti)03 is an example of such a compound which is widely in use because of its excellent piezoelectric properties. There has 21 been very little work that has gone into the study of A-site substituted titanates. This study investigated the dielectric and microstructural characteristics of three A-site substituted titanates, namely ((Pbx Bai.x )Ti(>}, (Bax Cai.x )Ti03 and (Pbx Sri_x )T i03 . The crystal structure has been studied by X-ray diffraction. The microstructure investigations were done by transmission and scanning electron microscopy. The dielectric properties were studied by observing the ferroelectric phase transitions at high temperatures and low temperatures (in the case of (BaxCa^TiO;, and (PbxSrj. x )Ti03 ). Electrical characterization also included the impedance and resistivity characteristics of these materials. Finally, a mathematical model was developed to determine the size of the Kanzig regions which are responsible for the diffuse phase transformations in these systems. 22 1.7 Bibliography 1. F.S. Galasso, Structure. Properties and Preparation of Perovskite Compounds. pp. 20-25, Pergamon Press, Oxford (1969). 2. Franco Jona and G. Shirane, Ferroelectric Crystals, pp. 70-87, Pergamon Press, Oxford (1962). 3. Shoichiro Nomura and Shozo Sawada, J. Phys. Soc. Jpn., 6, 36 (1951). 4. G. A. Smolenskii, A.I. Agranoskaya, and N.N. Krainik, Doklady Akad. Nauk. S.S.S.R., 91, 55 (1953). 5. M.E. Lines and AM . Glass, Principles and Applications of Ferroelectrics and Related Materials, pp. 53, Clarendon Press, Oxford (1971). 6. L.E. Cross, Ceram. Bull., 63, 587 (1984). 7. D. F. Rushman and M. A. Strivens, Trans. Faraday Soc., 42 A, 231 (1946). 8. Kiyoshi Okazaki, Piezoelectricity, ed. G. W. Taylor, J. J. Gagnepain, T. R. Meeker, T. Nakamura, and N. A. Shuvalov, pp. 131, Gordon and Breach, New York (1985). 9. G. Shirane, K Suzuki, and A Takeda, J. Phys. Soc. Jpn., 7, 12 (1952). 10. G. Shirane, K. Suzuki, and A. Takeda, J. Phys. Soc. Jpn., 7, 333 (1952). 11. N. Setter, and L. E. Cross, J. Mater. ScL, 15, 2478 (1980). 12. N. Setter, and L. E. Cross, J. Appl. Phys., 51, 4356 (1980). 13. N. Setter, and L. E. Cross, Phys. Stat. Sol. A , 61, K71 (1980). 14. C. G. F. Stenger, A J. Burgraaf, Phys. Stat. Sol. A , 61, 653 (1980). 15. C. G. F. Stenger, A J. Burgraaf, J. Phys. Chem. Sol, 41, 25 (1980). 16. Jie Chen, Helen M. Chan, Martin P. Harmer, J. Am. Ceram. Soc., 72, 593 (1989). 17. Grace King Goo, Ph.D. Thesis, University of Southern California (1990). 18. J. Valasek, Phys. Rev. 15, 537, (1920). 23 19. B.M. Wul and I. M. Goldman, C.R. Acad. ScL USSR, 49, 177 (1945). 20. A Von Hippel and co-workers, N. D. R. C. Rep. No. 300, August 1944, cited in Tech. Rep. 51, MIT (1950). 21. G. H. Haertling, Piezoelectric and Electrooptic Ceramics, in Ceramic Materials for Electronics, ed. R.C. Buchanan, pp. 129, Marcel Dekker, Inc., New York (1991). 22. W. J. Merz, J. App. Phys., 25, 1346 (1954). 23. Y. Xu, Ferroelectric Materials and Their Applications. North-Holland, Amsteram (1991). 24. G. Shirane and S. Hoshino, J. Phys. Soc. Jpn., 6, 265 (1951). 25. D. Hennings, A Schnell and G. Simon, J. Am. Ceram. Soc., 65, 539 (1982). 26. G. A Smolenskii, J. Phys. Soc. Jpn., 28 Suppl., 26 (1970). 27. G. Shirane and K. Suzuki, J. Phys. Soc. Jpn., 6, 274 (1951). 28. G. Shirane and A Takeda, J. Phys. Soc. Jpn., 6, 329 (1951). 29. L. E. Cross, Ferroelectrics, 76, 241 (1987). 30. W. Kanzig, Helv. Phys. Acta 24 175 (1951). 31. A L Robinson, Science, 235, 531, (1987). 32. James F. Scott, Carlos A Paz de A aujo, Science, 246, 1400 (1989). 33. J. M. Herbert, Ferroelectric Transducers and Sensors, pp. 57, Gordon and Breach, New-York (1982). 34. J. M. Herbert, Ceramic Dielectric and Capacitors, pp. 125, Gordon and Breach, New-York (1985). 24 Chapter 2 Experimental Procedure 2.1 Fabrication and Bulk Processing of Complex Perovskites The three systems studied were (Pbx Bai.x )Ti0 3 , (Pb„Sri.x )T i03 (for compositions 0.0 < x < 1.0) and (Bax Ca1 .x )T i03 (for compositions 0.0 < x < 0.2 and 0.8 < x < 1.0). The compositions are based on the relative amounts of the oxides used in preparing the powder and are not the measured composition of the sintered material. The starting materials for each of the three system were as follows: (Pbx Ba1 .x )Ti03 : PbO (99.5%), T i02 (99.7%) and BaC03 (99.8%), (Pbx Sri.x )Ti03 : PbO (99.5%), T i02 (99.7%) and SrC03 (99.5%), and, (Bax Ca1 .x )Ti03 : BaC03 (99.8%), TiOz (99.7%) and CaC03 (99.8%). The powders were mixed together and ball milled with alumina balls in a polyethylene container for 5 hours and calcined in an alumina crucible at 850° C for 5 hours in air. They were again remilled for five hours and oven dried. Powders were then cold pressed at a pressure of 30,000 psi into 3 mm disks, one inch in diameter. The cold pressed samples were then sintered in a Lindberg furnace for five hours at 1350° C. For the (PbxBaj.^TiO;*, the sintering temperature was gradually lowered from 1350° C to 1250° C, as the lead content was increased. For the (BaxCa^TiOs system, only the compositions x = 0.1, 0.2, 0.5, 0.8 and 0.9 were prepared and sintered, as this system did not form a solid solution for 0.2 < x < 0.8. The starting materials used in this study had a relatively high impurity concentration as compared to those used for semiconductors. These impurity levels do not have a significant effect on the dielectric and piezoelectric properties of these 25 materials, because the band gap of these materials are quite large, which makes them behave as insulators. If the impurity content was low enough to prevent the formation of secondary phases, the dielectric and piezoelectric properties of these materials were unaffected. Similarly, there would be no effect on the mechanical properties of the resulting product as well as long as the impurity content is not large enough to form secondary phases either within the grains or at the grain boundaries. 2.2 X-ray Diffraction Since all the samples were polycrystalline and showed no preferred orientation, X-ray samples were obtained by cutting a thin slice of the as-sintered samples, and mechanically polishing the surface in a 0.3 fim alumina slurry to give a smooth finish. X-ray diffractometer scans were done using a Rigaku X-ray diffractometer which had a Nal scintillation detector attached with a pyrolitic graphite monochromator, at the Center for Electron Microscopy and Microanalysis (CEMMA) at USC. Measurements were done using Cu-Kct radiation from a rotating anode source operated under an accelerating voltage of 35 kV and a beam current of 50 mA. Diffractometer scans were obtained with scan speeds between 0.5 degrees/min and 5 degrees/min. Fig. 2.1 is a schematic of the sample geometry without the monochromator for the 6-26 diffractometer scans. Lattice parameters were determined from the X-ray scans, using the least square method given by Parrish and Wilson.1 26 Tube sh ield ■ocusmg :ircle Center of the focusing c ir c le Focus Rotation axis, of the goniometer Axis of the receivin g s l i t Divergence s l i t Receiving s l i t Scatter s l i t Divergence s o lle r s l i t Receiving s o lle r s l i t i Goniometer radius ‘(185 m m ) Take-off angle Level divergence angle Bragg angle Counter arm Counter Fig. 2.1. Sample geometry for the 0-20 diffractometer scans. 23 Transmission Electron Microscopy Transmission electron microscopy (TEM) samples were obtained by cutting the sintered samples into 3 mm disks with an ultrasonic drill. The disks were mechanically polished, dimpled and then ion-milled with argon ions at an accelerating voltage of 3 kV. Conventional TEM was performed on a Phillips EM420 microscope at accelerating voltage of 120 kV and using a double-tilt stage. Bright field and dark field micrographs were obtained to check the microstructure and for the presence of ferroelectric domains. Selected area diffraction was also done to determine if there was ordering in these systems at the atomic scale. 2.4 Scanning Electron Microscopy Samples were prepared by mechanically polishing the surface in a 0.3 fim alumina slurry and sputter depositing the as-sintered surface with a thin layer of gold in order to prevent charging. The grain size was measured by scanning electron microscopy on the as-sintered surface using a Cambridge 360 SEM. The grain size was determined using the circular intercept method.2 2.5 Dielectric and Ferroelectric Properties Samples for electrical measurements were prepared by mechanically polishing both the surfaces in a 0.3 fim alumina slurry. The two as-sintered surfaces of the samples were then vapor deposited with silver electrodes, using a Denton vacuum evaporator, to act as ohmic contacts. 28 2.5.1 Dielectric Measurements A dielectric apparatus was specifically designed and built with two plates of stainless steel (AU 304) which were supported by four alumina rods screwed to the plates. The center of the top plate had a screw attachment which could extend up to the bottom plate, which held the sample (Fig.2.2). This set up was specifically designed to study the high temperature dielectric properties of the bulk specimens. The whole setup was placed with the sample inside a Lindberg box furnace and external leads from the set up were connected to a Keithley 3322 LCZ meter for the measurements. The low temperature measurements in the case of (BaxCa^TiOs and (PbxSrj^TiOs samples were done by immersing the whole setup in a liquid nitrogen bath. 2.5.2 Hysteresis Measurements Hysteresis measurements were done at the Department of Materials Science and Engineering, Pennsylvania State University, using an automated Hewlett Packard system, based on the Sawyer-Tower circuit.3 2.53 Impedance Measurements Impedance measurements were carried out over a range between 1 Hz and 1 MHz at 0.5 V, IV and 2V using a Schlumberger network analyzer connected to the dielectric set up and a software package. 2.5.4 Resistivity Measurements Resistivity measurements were done at d.c.voltages between -2 V to + 2 V using an automated software package connected to the dielectric setup. 29 Stainless steel screw S ta in le ss ste e l p la te To LCZ m e te r A lum ina Rod T h erm o co u p le S ta in le ss ste e l p la te S am p le Fig. 2.2. Dielectric set up designed for high temperature measurements. 30 2.6 Bibliography 1. W. Parrish and A. J. C. Wilson, International Tables for X-Rav Crystallography.. 2, pp. 216, ed. John S. Kasper and Kathleen Lonsdale, The Kynoch Press, Birmingham, England (1959). 2. 1985 Annual Book of A STM Standards. ASTM, pp. 117-149 (1985). 3. C. B. Sawyer and C. H. Tower, Phys. Rev., 35, 269 (1930). 31 Chapter 3 Study of (PbrBa1 .x )Ti03 3.1 Structure and Properties of BaTiOj and PbTiOj Barium titanate is a widely used perovskite because of its high dielectric constant and excellent piezoelectric properties. Lead titanate is also a ferroelectric perovskite, with a relatively high Curie point of 490° C and large tetragonal distortion (c/a ratio ~ 1.064).1 Its small dielectric constant (er ~ 100) along the c-axis and large spontaneous polarization (P, = 75 fiC/cm2 )2 makes it an excellent candidate for piezoelectric transducers and infrared detectors. However, its large c/a ratio has limited its application due to the difficulty in fabricating a polycrystal. A solid solution exists between BaTi03 and PbTi03 3 '4 although very little is known about these compositions. In particular, the Pb2 + ions have been found to shift the Curie point higher in this solid solution. Factors which control dielectric and piezoelectric characteristics are as follows : heating conditions, compositional fluctuations, properties of raw materials, porosity, and the degree of abnormal grain growth. Maintaining a stoichiometric composition in the (Pbx Bai.x )T i03 system is constrained by the evaporation of lead. Hence, in order to prevent lead loss, the samples are sintered in a crucible covered with a lid and packed with powders of the same composition as the sample.5 The addition of lead titanate improves the piezoelectric properties of barium titanate.6 The (Pbx Ba7 .x )Ti03 is potentially an excellent system for dielectric and piezoelectric applications and not much research has been done in this system. 32 3.2 Structure and Properties of (Pi^Ba^JTiOj 3.2.1 Crystal Structure It has been reported previously7 that both BaTi03 and PbTi03 have a tetragonal structure at room temperature with da ratios of 1.029 and 1.061 respectively. In the present study, it has been verified that the crystal structure of (Pb^Ba^TiOj) remains tetragonal over the entire composition range 0 < x < 1.0. The indexed x-ray diffraction peaks and their corresponding 2-theta values were used to calculate the lattice parameters using the method given by Parish and Wilson8 . The lattice parameters a and c decreased and increased respectively with increasing lead content and was in agreement with linearly interpolating the a and c values for PbTi03 and BaTi03 (Fig. 3.1). The theoretical density increased with increasing lead content (Table 3.1). The experimental density (fia) was always greater than 85% of the theoretical density (prt). The cell volume (V = a2 c) did not show any significant trend over the range measured. X-ray diffraction and electron diffraction did not reveal any cation ordering. 3.2.2 Observation of Domain Structure Ferroelectric domains have been observed in all the compositions 0.0 < x < 1.0. Both 90° and 180° domain boundaries were seen [Fig. 3.2]. The 90° boundary walls lie on the {101} planes, and tend to be straight. These are the strain-induced domains whose boundaries are planar and lie on well-defined crystallographic planes. The boundaries between 180° domains do not lie on any crystallographic plane and 33 4.200 4.100 o U v 0 4 - ^ < v B 2 4.000 ®- f lj ru < D O 3.900 3.800 0.0 0.2 0.4 0.6 0.8 1.0 C o m p o sitio n (x) Fig. 3.1. The variation of lattice parameters along the a and c-axis with composition for tetragonal (Pbx Ba1_ x )Ti0 3 . D ark field micrograph taken (x = 0.2) with {110} type reflection from [111] zone axis showing the 90° domain walls oriented along the (101) plane. 180° domains can also be seen. are in general nonplanar9 . These domains are created by the random nature in which the direction of the polar axis may lie upon the nucleation of the ferroelectric phase. The energy of the 180° boundary walls is less sensitive to crystallographic orientation and hence, they are ’ wavy’ . The SADP of the <100> zone axis in the composition x = 0.2 shows spot splitting in the region of the 90° domains (Fig. 3.3 (a)). Fig. 3.3 (b) shows the dark field image for g = (Oil) close to the <100> zone axis region. The spot splitting is consistent with the presence of 90 ° domains. The domain boundaries were observed with less frequency with increasing lead content. This is a surprising result since the transformation strain increases with increasing Pb content. A possible explanation is that the grain size decreases with increasing lead content. Grain size measurements using the circular intercept method revealed the presence of sub-micron grains (Fig. 3.4) whose size decreased with increasing lead content for 0.0 < x < 0.4 and for 0.5 < x < 0.8. There have been many reports on the absence of strain-induced domains in ferroelectric ceramics. Yamaji et. al.1 0 have reported the absence of domains in fine grained Dy-doped BaTi03 and in samples with average grain size less that 0.75 p m. Demczyk et. al.1 1 reported the absence of domains in La-modified PbTi03 with grain size less than 0.3 pm. There is a minimum grain size for domain formation, since the energy of the domain boundary depends on the square of the grain diameter while the total strain energy is dependent on the cube of the grain diameter. The minimum grain size for domain formation is where the decrease in strain energy due to the 36 Fig. 3.3(a) (b) The two beam condition from g - (O il) in the [100] zone axis, showing spot splitting in the region of the 90° domains. Dark-field of the same region. 37 Fig. 3.4. SEM micrograph of (Pb0 .2 Bao.s)T i0 3 showing sub-micron grains. domain formation is equal to the increase in total domain boundary energy1 2 . During sintering, the individual cubic crystals are formed at high temperature. The high mechanical stresses that are set up due to the close contact of the neighboring grains are reduced by the formation of the 90° domain walls, when a densely sintered material passes the phase transition from the cubic to the tetragonal structure, on cooling. In BaTi03 ferroelectrics, there is a spontaneous strain 1% which accompanies the phase transition. At the transition, each grain stresses its neighbor within a ceramic which changes the elastic boundary conditions of each grain. These self-induced stresses affect the dielectric permittivity of the BaTi03 grains, which is especially significant in BaTi03 ceramics with grain sizes close to ~ 1.0/rm1 3 . In order to consider the relative importance of this effect, the temperature dependence of the dielectric permittivity at fixed frequencies should be considered, as this also accounts for the influence of both Km a x and the diffuseness with grain size in relaxor systems. 3.2.3 Dielectric and Ferroelectric Properties 3.23.1 Ferroelectric Phase Transformations The (PbJBa^TiOj system exhibits diffuse phase transition (Curie point) over the composition range 0.1 < x < 0.8 (Fig. 3.5). The compositions at x = 0.9 & 1.0 could not be studied as the samples proved to be extremely brittle, due to the large c/a ratio. It was observed that the Curie point varies linearly with composition (Fig. 39 Dielectric Constant (k) 12000 o o 10000 8000 6000 4000 0-2 0.3 0.4 0,5 2 0 0 0 0 100 200 300 400 600 T em perature ( °C) Fig. 3.5. The variation of dielectric constant (at 10 kHz) with temperature for the (Pbx Ba!.x )Ti0 3 system. 40 3.6). None of the samples exhibited any relaxor behavior since the Curie point did not vary with frequency. The nature of the dielectric curve varied with each sample. Some of the dielectric curves showed a shoulder which has been reported in other systems2 though it is not clear as to the cause of the shoulder formation. Because of the porosity, the dielectric loss was significant. It must be mentioned that the dielectric curves for the compositions x = 0.7 and 0.8 had a peculiar shape different from that for the other compositions. The room temperature values (Fig. 3.7) and the maximum values (Fig. 3.8) of the dielectric constant decreased with increasing lead content. The dielectric loss increased at lower frequencies, which resulted in higher values for the dielectric constant. The full width at half maximum (FWHM) of the peaks over the composition range studied showed no significant trend. This could be due to the local variations in grain size which have a considerable influence on the dielectric properties. Fine grained materials (as compared to coarse grained materials) have lower losses and a different hysteresis behavior1 3 . In fine-grained materials, a compressive stress in the c- direction and a tensile stress in the a- direction lead to an increase in the dielectric constant. 3.23.2 Hysteresis Properties The Ba-rich compositions showed the presence of distinct hysteresis loops (Fig. 3.9) at room temperature. The nature of the hysteresis loops became elliptical with 41 Curie Point (°C) 500 450 400 350 300 250 200 150 100 0.0 0.2 0.4 0.6 0.8 1.0 C om p osition (x) Fig. 3.6. The variation of Curie point with composition for the (PtvBai. x )Ti03 system. 42 Dielectric Constant (k) at RT 3000 2500 2000 1500 1000 500 0 0.0 0.2 0.4 0.0 0.8 1.0 C om position 'x' Fig. 3.7. The variation of room temperature dielectric constant with composition (at 10 kHz) in (PbyBa^TiOs. 43 Peak Dielectric Constant (Kmaz) 11000 9000 7000 5000 3000 1000 0.0 0.2 0.4 0.6 0.8 1.0 Com position 'x' Fig. 3.8. The variation of peak dielectric constant with composition (at 10 kHz) in (PbxBaj.JTiOa. 44 38.460 m C /m * .... -..n 1.587 M U /m — ----------------f i- .1 ............ —1 ---------------------------- - > < L ......" " Polarization vs electric field for (Pbo2Bao.8 )Ti0 3 (Coercive field 1.587 MV/m). increasing lead content which is consistent with the decreasing frequency of the domains at higher lead compositions. This could be due to the processing limitations in the material, resulting in porosity, leakage currents etc. 3.23J3 Impedance Properties The impedance measurements were carried out over a range of 1 Hz to 1000 kHz at 0.5 V, 1 V and 2 V. The measurements showed that the impedance values were identical at 0.5 V and 1 V but fluctuated rapidly at 2V. This could be due to the sample response and external noise at higher voltages. It was observed that for all the samples studied, the phase lag increased gradually with increasing frequency and reached 90° between 1 kHz and 20 kHz, which is the value for an ideal capacitor (Fig. 3.10). From the Bode plots, it is seen that all samples had a purely resistive region at low frequencies 1 kHz and were ideally capacitive above 1 kHz (Fig. 3.11). Also, BaTi03 had the smallest resistive region. This could be explained from the theory of parallel circuits for dielectrics which is used when the loss is significant1 4 . The impedance is given by I 'M ^ \Z \= ----------£------ (i+ M /y 2 )1 * where Z is the magnitude of the impedance, RP and CP are the absolute values of the resistance and capacitance in parallel and f l> is the angular frequency. At low frequencies, when (o is very small, Z « R P which is observed in the present set of ’ 46 150.0 120.0 60.0 30.0 0.0 2 10 F req u en c y (H z) Fig. 3.10. The variation of phase lag (at 1 V) with frequency for the (Pbx Bai. x )T i03 system. 47 Impedance (O hm s) 3.11. 10 108 0.7 0.5 106 0.8 4 10 10° 101 102 103 104 105 106 107 F req u en cy (H z) Bode plot showing the variation of impedance (at 1 V) with frequency for the (Pbx Ba1 .x )Ti03 system. results. At frequencies higher than 1 MHz, there was an error in the analyzer readings. 3.23.4 Resistivity The resistivity values were measured at d.c. voltages (-2 < V < 2) and it was found that the resistivity showed a maximum at jc = 0.5 (Fig. 3.12). 49 8.0E + 6 7.0E + 6 6 .0E + 6 a a 2 5.0E + 6 £ 4 .0E + 6 > a > • H J 3.0E + 6 K 2 .0E + 6 1.0E +6 O.OE+O Sh 0.0 0.2 0.4 0.6 0.8 1.0 C om p osition 'x' Fig. 3.12. The variation of resistivity (at 1 V) with composition for the (Pbx Ba!_ x )Ti03 system. 50 TABLE 3.1 Physical and Electrical Properties of (PbJ t Ba/.,)Ti03 Composition V 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 Molecular Weight (gins) 233.20 240.18 247.17 254.16 261.15 268.14 275.12 282.11 289.10 296.09 303.08 Sinter Temperature (°C) 1350 1350 1330 1310 1310 1300 1290 1280 1270 1270 1260 a(A) 3.999 3.984 3.977 3.970 3.967 3.939 3.938 3.922 3.929 3.906 3.892 c(A) 4.039 4.032 4.042 4.054 4.063 4.059 4.075 4.080 4.106 4.127 4.138 c/a 1.0100 1.0120 1.0163 1.0211 1.0241 1.0304 1.0347 1.0402 1.0450 1.0565 1.0632 Cell Volume (A)3 64.591 63.996 63.930 63.894 63.939 62.978 63.194 62.758 63.384 62964 62681 A>n(gm/cm3 ) 6.009 6.231 6.419 6.604 6.781 7.068 7.228 7.463 7.572 7.807 8.028 /^(gm /cm 1 ) 5.613 5.677 5.761 5.859 5.973 6.134 6.264 6.919 7.145 7.284 7385 p% 93.40 91.10 89.74 88.71 88.08 86.77 86.66 92.70 9435 93.29 94.48 Curie Point (°C) 120 164 211 259 299 340 372 403 421 - 495 Dielectric Constant (RT) 2800 1230 890 745 650 510 445 320 260 . . Dielectric Loss (Tan < 5 ) 0.003 0.005 0.006 0.010 0.017 0.024 0.045 0.073 0.086 - - Resistivity (p, MQm) - 1.60 1.72 2.22 4.51 7.02 2.95 0.65 0.19 - - Grain Size (pm) 0.8 0.65 0.55 0.45 0.3 0.6 0.55 0.4 0.2 - - 3 3 Bibliography 1. G. Shirane, R. Pepinsky, and B. Frazier, Acta Ctyst. 9, 131 (1956). 2. V. G. Gavrilyachenko, R.I. Spinko, M. A. Martynenko, and E. G. Fesenko, Sov. Phys. Solid State 12, 1203 (1970). 3. M. McQuarrie, /. Am. Ceram. Soc., 40 35 (1957). 4. T. Ikeda, J. Phys. Soc. Japan, 13 335 (1958). 5. K. H. Jo, E. S. Kim and K. H. Yoon, /. Mat. ScL, 29 1031 (1994). 6. D. A. Berlincourt and F. Kulcsar, J. Acoust. Soc. Am., 24, 709 (1952). 7. F. S. Galasso, "Perovskites and High T. Superconductors." pp. 18, Gordon and Breach Science Publishers, New York (1990). 8. W. Parish and A. J. C. Wilson, International Tables for X-rav Crystallography. Vol. 2; pp. 816-34. Edited by John S. Kasper and Kathleen Lonsdale, The Kynoch Press, Birmingham, England (1959). 9. B. Jaffee, R. Cook, and H. Jaffee, "Piezoelectric Ceramics." pp. 66-68, Academic Press, New York (1971). 10. A. Yamaji, Y. Enomoto, K. Kinoshita, and T. Murakami,/. Am. Ceram. Soc., 60, 97 (1977). 11. B. G. Demczyk, A. G. Khachaturyann and G. Thomas, Scr. Metall., 21, 967 (1987). 12. G. King and E. K. G oo,/. Am. Ceram. Soc., 73, 1534 (1990). 13. W. Kanzig, Helv. Phys. Acta, 24, 175 (1951). 14. R. C. Buchanan, " Ceramic Materials for Electronics" second ed., pp. 26-40 , Marcel Dekker Inc., New York (1991). 52 Chapter 4 Study of (Ba^Ca^JTiO, 4.1 Structure and Properties of CaTi03 Several previous investigations have been carried out on the structure and dielectric properties of Ca-doped barium titanate. In 1952, it was found that Ca addition to barium titanate caused only negligible changes in the Curie point.1 Ca- doped BaTi03 multilayer ceramic capacitors have been investigated for use with base metal electrodes, which can be sintered in a reducing atmosphere.2 It is speculated that the broadened Curie peak shifting is caused by the lattice distortion caused by replacing Ti with the larger Ca ion, acting in the same manner as a hydrostatic pressure.3 Calcium titanate is a perovskite-type material which is not ferroelectric at room temperature. CaTi03 is orthorhombic (a = 5.381 A, b = 7.645 A and c = 5.443 A) at room temperature with space group Pcmn.4 With increasing temperature in the range -200° C to 900° C changes in cell dimensions are such as to approximate more closely the cubic symmetry, but the structure is still orthorhombic at 1200° C.5 CaTi03 undergoes an orthorhombic to cubic phase transition at 1257° C.6 4.2 Structure and Properties of (Bax Ca1 .x )Ti03 4.2.1 Crystal Structure The compositions of the samples studied were (Ba^Ca/.JTiOj, where x varied from 0.0 to 0.2 and 0.8 to 1.0 in 0.1 increments. The composition at x = 0.5, i.e. 53 (Bao.5 Cao.5)Ti03 was also studied. The samples for x = 0.8 and x = 0.9 were sintered for 5 hours at two different temperatures, namely 1200oC and 1350 °C to study the effect of the sintering temperature on material properties. A solid solution for (BaxCai.x )Ti03 exists only in the composition range (0.0 < x < 0.2) and (0.8 < x < 1.0)7 although little is known about these compositions.8 It has been reported previously that BaTi03 is tetragonal (with a c/a ratio of 1.029) and CaTi03 is orthorhombic at room temperature.4 In the present study, it has been verified that the crystal structure of (Ba^Ca^TiOj) remains tetragonal over the composition range 0.8 < x < 1.0 and is orthorhombic over the composition range 0 < x < 0.2. The indexed x-ray diffraction peaks and their corresponding 2-theta values were used to calculate the lattice parameters using the method given by Parish and Wilson.9 The lattice parameters a and b increased with increasing barium content both in the orthorhombic and tetragonal regions while c decreased in the orthorhombic and increased in the tetragonal regions. The c/a ratio decreases with increasing barium content in the orthorhombic region. The cell volume (V = abc) increases with increasing barium content, both in the orthorhombic and the tetragonal compositions. Additional peaks were seen (which were non-perovskite type) in the x = 0.2 composition, due to a secondary phase (Fig. 4.1). This could be due to the fact that x = 0.2 is close to the boundary of complete miscibility and non-miscibility.7 Incomplete or inhomogeneous mixing of BaTi03 and CaTi03 close to the miscibility gap, resulting in the presence of traces of both BaTi03 and CaTi03 could be the reason for the formation of the secondary phase Ca4 Ti3 0 1 ( > . A more likely explanation 54 • M fl 9 o u 20 25. 30. 35. 40. 45. 50. 55. 60. 2 8 Fig. 4.1 X-ray diffraction pattern showing a secondary phase ( • ) of Ca4 Ti3 O1 0 in (Ba0. 2Cao.8)Ti0 3 . could be an incomplete reaction betwen BaTi03 and CaTi03 on calcination when preparing the powder. The presence of a secondary phase, Ca4 Ti3 O1 0 , was later confirmed by transmission electron microscopy. Also, X-ray diffraction did not reveal any cation ordering. X-ray diffraction of (BaojCaas^iOs showed the presence of peaks resulting from both BaTi03 and CaTi03 (Fig. 4.2), confirming the absence of solid solution formation at this composition. 4.2.2 Microstructure 4.2.2.1 Ferroelectric Domain Structure Ferroelectric domains have been observed in the compositions 0.8 < x < 1.0. 90° domain boundaries were prominently seen [Fig. 4.3]. The domain boundaries were observed with less frequency with increasing Ca-content. The 90° boundary walls lie on the {101} planes, and tend to be straight. These are the strain-induced domains whose boundaries are planar and lie on well-defined crystallographic planes. The SADP of the <100> zone axis from a sample with composition* = 0.8 shows spot splitting in the region of the 90° domains (Fig. 4.4 a). Fig. 4.4 b shows the dark field image for g = (011) close to the [100] zone axis region. The spot splitting is consistent with the presence of 90 ° domains. But these domain boundaries were observed only in the Ba-rich compositions. 56 Counts I ' CD O 20. 25. 30. 35. 40. 45. 50. 55. BO. B5. 70. 75. 80. 20 Fig. 4.2. X-ray diffraction of (Bao.5 Cao.5 )Ti03 showing peaks from both BaTiOj (X) and CaTi03 (•) due to the lack of a solid solution formation. Fig. 4.3 Dark field micrograph taken (x = 0.9) with {110} type reflection from [100] zone axis showing the 90° domain walls oriented along the (101) plane. O l 00 i The two beam condition from the {110} type reflection in the [100] zone axis, showing spot splitting the region of the 90° domains. Dark-field of the same region. 4.2.2.2 Ordered Structure In the Ca-rich compositions, namely x = 0.1 and 0.2, no domain boundaries were seen. Instead, the selected area diffraction patterns showed the presence of superlattice reflections along the three principal zone axis which were identical to those observed in (PbxCa^TiOa.1 0 The electron diffraction patterns for the [100] zone axis contained both the 1/2{100} superlattice reflections alone, and the 1/2(100} and 1/2(110} superlattice reflections together. These reflections were indexed in terms of the perovskite unit cell, unless stated otherwise. Similarly, the electron diffraction pattern for the [111] zone axis showed 1/2(110} superlattice reflections in all three directions, in two directions and in one direction only. This may be explained if the reflections arise from different variants. The [110] zone axis diffraction pattern showed the presence of 1/2(111} reflections alone, and also the 1/2(100} and 1/2(111} reflections together. The calcium titanate structure is a regular T i0 6 octahedra rotated with respect to their ideal perovskite positions as shown in Fig. 4.5.n This occurs primarily due to the small displacements of the calcium and oxygen atoms from their ideal lattice positions. The presence of superlattice reflections due to such displacements is revealed by TEM studies on CaTi03 . From the above results, a reciprocal lattice of the ordered structure similar to the one proposed by King et. al.1 0 can be obtained. The orientation relationship of the ordered (Ba-Ca) structure is [100]O Id e r e d j J [110]p e iO T r iU le , and [001]O Id e re d | ! [ 0 0 1 ] ^ ^ , with lattice parameters ao rd e re d = 21 % p e ro v ,k ite and c0 ld e re d = 60 Fig. 4.5. The structure of calcium titanate is a regular T i06 octahedra rotated with respect to their ideal perovskite positions (after Koopmans et al.).w 2cpemM te. The location of the superlattice reflections with respect to the fundamental perovskite reflections in a simple tetragonal reciprocal lattice, is outlined in Fig. 4.6. The ordered structure proposed by King etal.n explained the reflections seen in (Pbx Ca!.x )Ti0 3 close to * = 0.5 (Fig. 4.7). Similar ordering of barium and calcium atoms accounts for the presence of 1/2{111} superlattice reflections. Atomic shuffles or electrical ordering is responsible for the presence of 1/2{100} and 1/2{110} reflections. Atomic shuffles occur when a crystal transforms to a ferroelectric or antiferroelectric state, and this is also referred to as electrical ordering.1 2 As CaTi03 is antiferroelectric, atomic shuffles similar to that observed in pure CaTi03 is responsible for the presence of 1/2{110} and 1/2{100} superlattice reflections in (BaxCa^TiOu.1 2 This is further confirmed by the fact that both (Pbx Ca!.x )Ti03 1 2 and (Srx Ca!.x )T i03 1 2 also show superlattice reflections identical to (BaxCa^TiO* however, no superlattice reflections are seen in the (PbJBa^TiCV3 and (PbxSri.x )T i03 1 4 systems. 4.2.23 Existence of a Secondary Phase There were a few regions in the Ca-rich side which showed non-perovskite type reflections (Figs. 4.8). These reflections could be due to the presence of a secondary phase, Ca4 Ti3 Oj0 ls as indicated by the XRD peaks. This is supported by the fact that two major X-ray peaks of this phase (at © = 33° and 47°) corresponds to that seen in the present system. The EDS spectra from these regions (Fig. 4.9) do not show the presence of any Ba peak, which gives further evidence that these 62 ■ O Q > k_ 0 T3 k_ O O Q Be or Ca aordered Fig. 4.6 The ordered unit cell shown with respect to the perovskite unit cell (after King et al.).9 On M W v f T s & f T Fig. 4.7 Ordering with Ba/Ca atoms on alternating (a) {111} planes, (b) {100} planes, and (c) {110} planes (after King).1 1 . 64 Fig. 4.8. The <107> zone axis of the orthorhombic secondary phase of Ca/TisOio. li e n b ■ 5 O O C O M C O > 0 in Fig. 4.9. EDS spectra from the region of non-perovskite reflections showing the absence of Ba peaks. 66 regions may be a secondary phase of CaTiO^ The Ca4 Ti3 O1 0 phase is orthorhombic with a = 3.827 A, b = 27.15 A and c = 7.094 A. 4.2.2.4 Effect of Sintering Temperature on Grain Size Grain size measurements by SEM (Fig. 4.10) indicate that the grains were 15.0 fim for samples sintered at 1200 °C and increased with increasing sintering temperature. Also, it was seen that the domain boundaries were observed with increasing frequency as the sintering temperature was increased. This was true for both x = 0.9 and 0.8 compositions. 4.2.3 Dielectric and Ferroelectric Properties 4.23.1 Ferroelectric Phase Transformations The (BajCa^TiO j system exhibits a diffuse phase transition (Curie point) above room temperature over the composition range 0.8 < x < 1.0. (Fig. 4.11). Just as BaTi03 shows a paraelectric to ferroelectric transformation at 120 °C (Curie point) and another phase transformation from tetragonal to orthorhombic at 5 °C, it is seen that (Bax Ca1 .x )Ti03 shows two transformations, one diffuse transformation above room temperature and one sharp transformation below room temperature (Table 4.1). 67 15.0Hm i Fig. 4.10. Grain distribution in (Ba09Ca01)TiO3 (a) sintered at 1200 °C and (b) sintered at 1350 °C. 68 2500 2000 1500 m 0 o O u 0.9 -u y < u 1000 500 0.8 -125 100 175 -50 25 T e m p e ra tu re ( °C) Fig. 4.11. The variation of dielectric constant (at 10 kHz) with temperature for the (Bax Ca1 .x )T i03 system for x = 0.9 and 0.8. 69 Table 4.1 : Transformation Temperatures of (BOjCa^JTiOj (Ba.Ca.JTIOj Cubic to Tetragonal (Tt) (°C) Tetragonal to Orthorhombic (°C) x = 1.0 120 5 x = 0.9 143 15 x = 0.8 136 11 The addition of calcium to barium titanate shifts the Curie temperature beyond 120° C (that of BaTi03 ) and gives rise to diffuse phase transformations above room temperature1 6 . Since CaTi03 undergoes an orthorhombic to cubic phase transition at 1257° C6 , with increasing additions of CaTiO^ the temperatures at which the tetragonal to cubic or the orthorhombic to cubic transitions occur also increases. The sharpness of the tetragonal - orthorhombic transformation could be due to the effect of moisture while cooling. The dielectric loss increased at lower frequencies, resulting in higher values for the dielectric constant. It was observed that the dielectric curves for the samples that were sintered at 1350° C were sharper and higher than for those sintered at 1200 °C. The peak value of the dielectric constant was higher in the 1350 °C case, and the peaks were less diffuse (Fig. 4.12). It is well known that grain size has a pronounced effect on the dielectric properties.1 7 Effect of chemical purity, preparation procedure, initial particle size distribution of the powder, final grain size distribution, resistivity of the grains and the grain boundaries and the density of the ceramic etc. should be considered as external contributions to the dielectric anomaly. 70 Dielectric C onstant (k) Fig. 4.12. (a) (Ba0 9 Ca01)TiO3 1300 1200 1100 i 1000 1200 ‘C 900 1350 'C i 800 \ 700 600 0 50 100 160 200 Tem perature ( *C) The effect of sintering temperature on (b) (Ba0 S Caa2)TiO3 9 0 0 626 460 316 300 0 40 1 M 80 100 300 340 T r a p n e t e r e ( *C) dielectric curves for (BaxCa^yTiOj. 4.23.2 Hysteresis The composition at x = 0.8 is confirmed to be ferroelectric by the presence of a distinct hysteresis loop (Fig. 4.13) at room temperature. This composition had a coercive field of 0.732 MV/m and a spontaneous polarization of 6.587 f i d cm2 . This is comparable to that of BaTiO^ which has a spontaneous polarization of 26 //C/cm2 . 4.233 Impedance Properties Similar to the (Pbx Bax.x )T i03 system, the phase lag was closer to zero at lower frequencies only for the Ca-rich side (Fig. 4.14) and the samples were ideally capacitive between 1 kHz and 1 Mhz (Fig. 4.15). The x = 0.9 composition had a 90° phase lag over the largest frequency range while that with x = 0.1 had a 90° phase lag over the smallest frequency range. Table 4.2 gives a summary of the physical and electrical properties for the (Bax Cai.x )Ti03 system. 72 - ■ ■ I ' 1 | ' | > T T " T ~ T '-1 1 • ' 1 1 1 ' 6.587 m C /m 2 0.732 W/m f 1 I < > ............... 1 i 1 . 1 . it* . , \ , \ , | "'"T1 " 1 -r-| , j— r - - * — 1 — * J~. 1 * 1 • 1 • • 1 • i . 1 • ■ \p * “ " v • ■ " 1 f-j'-f- \ ■ ■ « ■ -t— i-t— » -t-« - ■ - 1 — * " ■ .... i... i * i . i . _ j . i . . i. .. i . i . Fig. 4.13 A distinct hysteresis loop in the (Baft8 Cao.2)Ti03 composition confirming its ferroelectric nature (Scale : x-axis : 1 div = 0.5 MV/m; y-axis : 1 div = 2.5 mC/m2 ). 73 0.0 O .JI o.i 0.2 0.9 - 100.0 10° 101 102 103 104 105 106 107 108 F r e q u e n c y (H z) Fig. 4.14. The variation of phase lag with frequency for (Bax Ca1 .x )T i03 at 1 V. 74 Im pedance ( | Z |) —x = 0.8 108 0.2 7 10 5 10 10° 101 102 103 104 105 106 107 108 F r e q u e n c y (Hz) Fig. 4.15 Bode plot showing the variation of impedance with frequency for (BaxCaj^TiOs at 1 V. 75 TABLE 4.II Physical and Electrical Properties of (Ba^Ca^TiOj Composition V 0 0.1 0.2 0.8 0.9 1.0 Molecular Weight (gins) 135.88 145.61 155.34 213.73 223.46 223.20 a(A) 5.381 5.456 5.470 3.973 3.991 3.999 b (k ) 7.645 7.668 7.680 3.973 3.991 3.999 c(A) 5.443 5.393 5.379 4.006 4.013 4.039 c/a 1.0115 0.9884 0.9833 1.0083 1.0055 1.0100 Cell Volume (A)3 223.912 225.624 225.969 63.233 63.919 64.591 Curie Point (°C) - - - 136 143 120 Dielectric Constant (Rl) 100 - - 400 1000 2800 Dielectric Loss (Tan < 3 ) 0.015 - - 0.015 0.009 0.005 Resistivity (p, MQm) - 3.37 M 0.94 M 1.64 M 7.87 M - 43 Bibliography 1. B. Jaffe, W. R. Cook, and H. Jaffe, " Piezoelectric Ceramics" , pp. 91, Academic Press, NY (1971). 2. W. J. Merz, Phys. Rev., 77, 52 (1950). 3. F. S. Galasso, "Structure, Properties and Preparation of Perovskite-Type Compounds", pp. 23, Pergamon Press, Oxford (1969). 4. H. F. Kay and P. C. Bailey, Acta Cryst. 10, 219 (1957). 5. D. A. Berlincourt and F. Kulesar, J. Acoust. Soc. Am. 37, 709 (1952) . 6. B. F. Naylor and O. A. Cook, J. Am. Chem. Soc., 68, 1003 (1946). 7. T. Ikeda, J. Phys. Soc. Japan 13, 335, (1958). 8. G. Durst, M. Grotenhuis, and A. G. Barkow,/. Am. Ceram. Soc. 33, 231 (1950). 9. W. Parrish and A. J. C. Wilson, in International Tables for X-ray Crystallography, Vol. 2, edited by J. S. Kasper and K. Lonsdale (The Kynoch Press, Birmingham, England (1959). 10. Grace King, Edward Goo, Takashi Yamamoto and Kiyoshi Okazaki, J. Am. Ceram. Soc. 71, 454 (1988). 11. H. G. A. Koopmans, G. M. H. Van De Velde and P. J. Gellings, Acta Cryst. C 39, 1323 (1983). 12. Grace King, Ph.D. Thesis, University of Southern California (1990). 13. S. Subrahmanyam, R. Ganesh and E. Goo, Ceram. Trans. 32, 139 (1992). 14. K. Ananth, R. Ganesh and E. Goo, Ceram. Trans. 32, 145 (1992). 15. Roth, J. Res. Natl. Bur. Stand. (U.S.) 61, 437 (1958). 77 16. P. S. R. Krishna, Dhananjai Pandey, V.S. Tiwari, R. Chakravarthy and B.A. Dasannacharya, Appl. Phys. Lett. 62, 231 (1993). 17. U. Kumar, S. F. Wang, S. Varanasi and J. P. Dougherty, in Proceedings of the 8th IEEE International Symposium on Applications o f Ferroelectrics. p. 55 (1992). 78 Chapter 5 Study of (Pb.Sr^TiOs 5.1 Structure and Properties of SrTi03 It is not certain if SrTi03 is ferroelectric at low temperatures. SrTi03 has a cubic structure above -163° C (a = 3.904 A).1 2 Below -163 °C, it transforms to a paraelectric phase which is thought to be isomorphous with high temperature tetragonal CaTi03 .2 There is no dielectric anomaly at -163° C, but a strong elastic anomaly is observed.3 The dielectric constant exactly follows the Curie-Weiss law below room temperature (with an extrapolated Curie-Weiss temperature of -238° C) and only starts to deviate in the range below -213° C.1 4 SrTi03 has a dielectric constant of 200 at room temperature.5 There are conflicting reports on the possibility of it being ferroelectric at very low temperatures, even though Granicher6 did report the observation of a hysteresis loop with a field of 300 V/cm at 4 K. The spontaneous polarization was reported to be 3 x 10"6 coulomb/cm2 and the remanent polarization was 1 x 10"6 coulomb/cm2 . Even though a solid solution exists between PbTi03 and SrTi03 and a distinct hysteresis loop has been observed in (Pb0 .4 Sro.6 )T i03 7 , very little is known about these compositions. The (PbxSr^TiOs is potentially an excellent system for dielectric and piezoelectric applications and not much research has been done in this system. 79 5.2 Structure and Properties of (Pbx Srlx)Ti03 5.2.1 Crystal Structure The compositions of the samples studied were (Pb,Sr7 .,TiOj), where x varied from 0.0 to 1.0 in 0.1 increments. It has been reported previously5 that PbTi03 and SrTi03 have a tetragonal and cubic structure, respectively at room temperature with c/a ratios of 1.061 and 1.000 respectively. In the present study, it has been verified that the crystal structure of (Pb,Sr7 .*TiOj) remains cubic over the composition range 0 < x s 0.4 (Fig. 5.1) and becomes tetragonal over composition range 0.4 < x < 1.0.s(Fig. 5.2) The indexed x-ray diffraction peaks and their corresponding 2-theta values were used to calculate the lattice parameters using the method given by Parish and Wilson.9 The lattice parameters a and c decreased and increased, respectively and the c/a ratio increased with increasing lead content for* > 0.4 (Fig. 5.3). The cell volume (V = abc) did not show any significant trend with changing lead content. 5.2.2 Observation of Domain Structure Ferroelectric domains have been observed in all the compositions 0.0 < * < 1.0. 90° domain boundaries were prominently seen (Fig. 5.4). The 90° boundary walls lie on the {101} planes, and tend to be straight. The orientation of these strain- induced domains are similar to that in the (Pbx Bai.x )T i03 system. It was seen that the strain-induced domains vanished at * < 0.4 which is consistent with the material not being ferroelectric at room temperatures for * < 0.4. 8 0 Counts o o CM I ° H \ <-p - n t- p 4 r r f l i i | / i*i i ■ * * A T r * ) 0 i i i 10. 2 0 . 30 6 0 . 70 4 0 . 5 0 . 2 0 Fig. 5.1. X-ray diffraction pattern showing a cubic structure in (Pbo.4Sr0 6 )TiO> BO 90 00 Counts CD CD CD m i rm rTT _ j'r m r P 'i 1 2 5 . 3 0 . o HTI 2 0 . 3 5 . 4 0 . 4 5 . 5 0 . 5 5 . 6 0 . 6 5 . 70 Fig. 5.2. X-ray diffraction pattern showing a tetragonal structure in (Pbo.5 Sro.s)TiO> 00 NO 202 c/a ratio 1.050 1.040 1.030 1.020 1.010 0.990 0 .0 0 .2 0 .4 0 .6 0 .8 1.0 Composition 'x' Fig. 5.3 The variation of c/a ratio with composition for (Pbx Sri.x )Ti03 . 83 Fig. 5.4 Dark field micrograph taken from [100] zone axis showing the presence of 90° domain boundaries in (Pb0 .5 Sro.5Ti0 3 ). C O 5.23 Dielectric and Ferroelectric Properties 5.23.1 Ferroelectric Phase Transformations The (PbjSry.^TiQj system exhibits diffuse phase transitions over the composition range 0.1 ^ x < 0.9 (Fig. 5.5). The discontinuity in the peak value of the dielectric constant occurs at x = 0.4 which is the composition at which the crystal symmetry changes from cubic (for x < 0.4) to tetragonal for x > 0.4 at room temperature. It was observed that the Curie point varies linearly with composition (Fig. 5.6). There was also a linear variation of the room temperature dielectric constant in this system (Fig. 5.7) None of the samples exhibited any relaxor behavior since the Curie point did not vary with frequency. The nature of the dielectric curve varied with each sample. Some of the dielectric curves showed a shoulder which has been reported in other systems2 though it is not clear as to the cause of the shoulder formation. 5.23.2 Impedance Properties Between 1 kHz and 1000 kHz, the impedance behavior is similar to that of the (Pbx Bai.x )T i03 system. But there was a steep drop in the phase lag for all samples less than 100 Hz and beyond 1 x 106 Hz, which is very different from the results obtained in the (Pbx Bai_x )Ti03 system. The phase lag variation is bow shaped instead of increasing with increasing frequency and reached 90° between 100 Hz and 1 MHz, which is the value for an ideal capacitor (Fig. 5.8) & (Fig. 5.9). 85 D ielectric C onstant (k) 8000 7000 6000 6000 4000 3000 2000 1000 0 -300 -200 -100 0 100 200 300 400 500 600 o T e m p e r a t u r e ( C) Fig. 5.5 The variation of dielectric constant (at 10 kHz) with temperature for the (Pbx Sr1 .x )Ti03 system. 0.7 0.0 0.9 ■ 86 Curie Point ( °C) 450 375 300 225 150 75 -75 150 1.0 0.8 0.6 0.2 0.4 0.0 C o m p o s itio n 'x' The variation of Curie point with composition for the (PbxSr^TiOa system. D ielectric Constant (at RT) 3 0 0 250 200 150 100 50 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 C om position 'x' Fig. 5.7 The variation of room temperature dielectric constant with composition (at 10 kHz) in (Pb^Sr^TiOj. 88 0.00 /— * V 00 a > a ) b o a ) 0.3 to c d J 0.7 0.6 0.6 - 100.00 10° 101 102 103 104 105 106 107 108 Frequency (Hz) Fig. 5.8 The variation of phase lag with frequency for (Pbx Sr1 .x )T i03 at 1 V. 89 10 10 0 0 s J C J o tsi < u o 0 ) -a a ) ft 0 0.2 0 .3 8 0.7 0.8 106 5 4 LlUlll 2 1 0 3 1 0 4 1 0 10 10 1 0 Frequency (Hz) Fig. 5.9 Bode plot showing the variation of impedance with frequency for (Pbx Sr1.x )Ti03 . 90 5.233 Resistivity The resistivity values measured at d.c. voltages (-2.0 < V < 2.0) showed linear plots (Fig. 5.10) indicating a constant resistivity value for each sample. It was seen that resistivity decreased with increasing Pb content up tox = 0.4 and then increased for x > 0.5. This could also have something to do with the transition region from a pure cubic to a tetragonal phase forx > 0.4 (Fig. 5.11). It is possible that at* = 0.4, there may be regions which could exist as both cubic and tetragonal phases, thereby giving a lower resistivity value. Table 5.1 gives a summary of the physical and electrical properties for the (PbxSrj.JTiOa system. 91 Amperes 3.00E-9 - 2.00E-9 - “ * $ S * ‘ < : 1.00E-9 - sta® 2 02E-28 1.DOE-9 3.00E-9 4.00E-9 2.0 1.0 0.0 1.0 2.0 volts Fig. 5.10 Linear I-V plot of (Pbo.6Sro.4)Ti0 3 showing a constant resistivity of 25.73 MQm 92 40.00 £ § 30.00 S -P > • H -P •s 20.00 © C 5 10.00 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 Composition 'x' Fig. 5.11 Variation of resistivity with composition for (PbxSr^TiOs. 93 TABLE 5.1 Physical and Electrical Properties of (PbT Sr/ r)Ti03 Composition V 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 Molecular Weight (gms) 183.52 195.50 207.43 219.40 231.35 243.30 255.26 267.21 279.17 291.13 303.10 a (A) 3.904 3.880 3.880 3.943 3.927 3.8% 3.882 3.903 3.864 3.837 3.892 c (A) 3.904 3.880 3.880 3.943 3.927 3.960 3.947 3.984 3.983 4.004 4.138 c/a 1.000 1.000 1.000 1.000 1.000 1.016 1.016 1.020 1.030 1.043 1.063 Density (Th.) 5.120 5.556 5.893 5.940 6.330 6.719 7.122 7.308 7.793 8.015 8.028 Density (Exp.) 4.812 5.333 5.598 5.405 5.697 6.315 6.766 6.665 7.405 7.790 7.779 Cell Volume (A)J 59.50 58.42 58.44 61.32 60.59 60.12 59.50 60.70 59.47 58.95 62.68 Curie Point (°C) -163 -145 -87 -24 16 120 211 283 323 389 495 Dielectric Constant (RT) 110 122 138 147 166 180 189 219 231 239 437 Dielectric Constant (Peak) - 2750 3100 3500 1950 3250 3975 5450 7675 7240 - Resistivity (p, MOm) 28.23 26.50 22.30 20.21 17.50 20.43 24.75 26.82 31.48 34.36 - S3 Bibliography 1. Muller, K. A., Helv. Phys. Acta 31, 173 (1958). 2. T. Mitsui and W. B. Westphal, Phys. Rev. 31, 1354 (1961). 3. W. H. Winter and O. Jakits, Bull. Am. Phys. Soc., 7, 438 (1962). 4. H. E. Weaver, J. Phys. Chem. Solids 1, 274 (1959). 5. F. S. Galasso, "Perovskites and High Tc Superconductors," pp. 18, Gordon and Breach Science Publishers, New York, (1990). 6 . H. Granicher, Helv. Phys. Acta, 29, 210 (1956). 7. C. R. Griffiths and R. Russell, Jr., J. Am. Ceram. Soc. 55, 110 (1972). 8 . K. Ananth, R. Ganesh and E. Goo, Ceram. Trans. 32, 145 (1992). 9. W. Parrish and A. J. C. Wilson, International Tables for X-ray Crystallography, Vol. 2; pp. 816-34. Edited by John S. Kasper and Kathleen Lonsdale, The Kynoch Press, Birmingham, England (1959). 95 Chapter 6 Diffuseness Parameter and Microregion Size 6.1 Introduction For diffuse phase transitions, the temperature dependant dielectric constant can be approximated to a Gaussian behavior1 ' 2 as where km a x is the maximum in the dielectric constant, Tc is the Curie-Weiss temperature and d is the diffuseness parameter. The above equation was expanded as a power series by Smolenskii1 , who, after neglecting the higher order terms, arrived at a semi-empirical power law relation to describe the temperature dependence of the dielectric constant for a relaxor dielectric at a fixed frequency which was given by : 1 1 (T - T f ( 2 ) where kx = dielectric constant, kx m a x = maximum dielectric constant, Tc = Curie point, and < 5 X = diffuseness parameter. 96 The modified form of the above equation was given as3 : I . - L n ^ i ( I * * ) ® ^ ^m tx 2b x where y is an empirical term which is equal to 1 for ideal Curie-Weiss law behavior and is equal to 2 for ideal relaxor behavior and has intermediate values for all other materials. In order to determine the diffuseness parameter d„ the exponent ywas obtained from the slope of ln[km iX /k -1] vs ln[T-TJ using a least square fit. The diffuseness parameter < 5 X was obtained from the slope of the plot of 1/k vs [T-Tc ]y , using a least square fit. 6.2 Estimation of the DifTuseness Parameter 6.2.1 (Pbx Ba1 .J t Ti03 It is seen that the exponent y increases with increasing Pb content and has a maximum around the mid-composition range and then decreases (Fig. 1). A similar trend was observed in the case of the diffuseness parameter, (Fig. 2) which is expected because, the system exhibits maximum diffuseness at x = 0.5 where largest fluctuation in composition is expected. Both y and < 5 X show a significant decrease in their values for x > 0.5. Since y is a purely empirical term, a value less than one is not unusual, even though y has been reported with values ranging between one and two. 97 Gamma (7) 2.00 1.80 1.60 1.40 1.20 1.00 0.80 0.60 0.0 0.2 0.4 0.6 0.8 1.0 Composition, V Fig. 6.1 The variation of the exponent y with composition for (Pbx Ba!.x )Ti03 . 98 Diffuseness Parameter (S') 6 0 0 500 400 300 200 100 0 0.0 0.2 0.4 0.6 0.8 1.0 Composition, 'x1 Fig. 6.2 The variation of the diffuseness parameter, 6„ with composition for (Pbx Ba1 .x )Ti03 . 99 6.2.2 (Pb.Sr^JTiOj Similar to the (P b x B a i-x )T i0 3 system, it is seen that the exponent y increases with increasing Pb content and has a maximum around the mid-composition range and then decreases (Fig. 3). A similar trend was observed in the case of the diffuseness parameter, < 5 „ (Fig. 4). 6.23 (Ba,Calx)Ti0 3 Since (Bax Ca1.x )Ti0 3 does not form a complete solid solution for (0.2 < x < 0.8), it was not possible to calculate y (Fig. 5) and < 3 (Fig. 6) for all the compositions, as the system was ferroelectric only for x > 0 .8 . 63 Quantitative Analysis of the Microregion Size The paraelectric to ferroelectric phase transition is generally a very sharp transition. A gradual or diffuse phase transition have been observed in complex perovskites1 '4 . It has been suggested that the statistical composition fluctuations which must occur in the submicron regions, if crystallographically equivalent sites are occupied randomly by different cations2 is the reason for the diffuse characteristics of the normally sharp transitions. The study of ordered complex perovskites is consistent with this model5 . Although the (AJBi-OTiO;} system forms a homogeneous solid solution in a macroscopic sense, there exists microregions which have compositions differing from the average composition, which results in a diffuse phase transition. 6 The size of these 100 Gamma 3 2 1 0 o.o 0.2 0.4 0.8 0.0 1.0 Composition 'x' Fig. 6.3. The variation of the exponent y with composition for (Pbx Sr1 .x )Ti03 . 101 Delta 1 . 0 0 0 0.800 — 0.600 0.400 — 0.200 — 0 . 0 0 0 [o]--------|c]--------Jo] [o]------- [o]--------jo] Composition ' x ' Fig. 6.4. The variation of the diffuseness parameter, d„ with composition for ( P b ^ J T iO * 102 ln(K m /K 0.00 ' 1.00 -2.00 • 6 .00 .0 0 1.3 3.6 4.3 2.1 2.6 ln lT - T(c)) M -3E+0 s a w * a 4E40 •7E+0 0 .0 0 0.76 1.60 2.26 3.00 4.60 ln(T-Tcl (a) (b) Fig. 6.5. Determination of the exponent y for (a) (Bao.9Cao.i)TiOj and (b) (BaogCa^TiOj. o U ) 1 0 4 2E-S IE-3 lE-3 IE-3 9E-4 0 1000 2000 8000 5000 4000 IT-T (e))'n 3E-3 2E-3 2B-3 2E-3 0 76 160 226 300 [T-TcKn (a) (b) Fig. 6.6. Determination of the diffuseness parameter dx for (a) (Ba0 9 Ca0 1 )TiO3 and (b) (Ba0 gCa0 2 )TiO3 microchemical regions represent the critical size that is needed to transform to a ferroelectric state on cooling through the Curie point. These microregions that have varying compositions have different local Curie points. Smolensky reported a quantitative analysis of the influence of composition fluctuations on diffuse phase transitions for solid solutions of two perovskite compounds. 1 The size of these microregions is an important parameter that has not been experimentally measured. These microregions represent the minimum size for a ferroelectric nucleus in the paraelectric to ferroelectric transitions and control the width of the transition range. By measuring the dielectric constant vs temperature curves over a range of compositions for a given solid solution, the size of the microregions may be determined. In a microregion consisting of n molecules of A’B 0 3 and A"B03 , in a solid solution of the form A V A 'i^O * where the A-site atoms are located in a polyhedra with 12-fold coordination and the B-site atoms occupy the octahedral positions, the probability of finding m molecules of A’B 0 3 in the absence of any ordering is given by P(m)=-p _ J „ — ex p [-^ g -] v/2itnx(1 -x) 2 * 0 -*) (4) where £ is the difference between the macroscopic and microscopic concentrations and is given by £ = q-x, where, q = m/n. At £ = 0, P(m) has a maximum. Hence, the value of £ at half the maximum is given by 105 exp[— ■ ]=- 2r(1 -a:) 2 (5) Solving for £ gives ( 6 ) *=±N jc(1 ~x)ln4 n The Curie point changes linearly with composition for small fluctuations in composition. Hence, £ = v(T-T0 ), where £ is the difference in the microscopic and macroscopic concentration, T and T 0 are the Curie points of the microscopic and macroscopic regions respectively, and v, is a constant of proportionality, which is the slope of the plot of Curie point as a function of composition. The number of microregions that have compositions statistically close to the mean composition, is a maximum. Hence, T0 is the temperature at which a maximum number of these microregions transform to the ferroelectric phase. Therefore, the width at half maximum (A) of the peak in the e vs T curve is given by (7) A =—\/x(1 -x)whereC=. v > ln4 n where x = composition, n = number of unit cells and A = the spread in the transition region (as shown in Fig. 7). 106 Dleleotrio Conatant (k) 3000 2000 1000 0 0 Fig. 6.7. Illustration of the width at half-maximum (WHM), A. — -A — * ! WHM t I i I i I i £ c ! i I l 75 150 225 300 375 450 T e m p e r a t u r e ( °C) 107 Eqn. 7 makes it possible to determine the size of the microregions by using the value of A obtained from the dielectric constant versus temperature curve for a particular frequency and composition. The size of the microregions is estimated by comparing the WHM (A) at different compositions with the above equation. 6 3 .1 Estimation of the Microregion Size 63.1.1 (Pb.Ba^JTiOj Fig. 8 gives a plot of the theoretically and experimentally obtained WHM with composition. The width at half maximum (WHM) of the e vs T peaks over the composition range studied showed a significant scatter. This scatter in data may be due to the small and varying grain size (which have a considerable influence on the dielectric properties). Fine grained materials (as compared to coarse grained materials) have lower losses and a different hysteresis behavior7 . In BaTi0 3 ferroelectrics, there is a spontaneous strain ~ 1% which accompanies the phase transition. At the transition, each grain stresses its neighbor within a ceramic which changes the elastic boundary conditions of each grain. These self-induced stresses affect the dielectric permittivity of the BaTi0 3 grains, which is especially significant in BaTi0 3 ceramics with grain sizes close to ~ 1.0 jwm 8 . In fine-grained materials, a compressive stress in the c- direction and a tensile stress in the a- direction lead to an increase in the dielectric constant. The value of n was found to lie between 135 and 450 which are the limiting curves for these compositions (Fig. 8). This is considerably less than that reported 108 W H M (A) Fig. 6.8. 75 n = 135 60 45 450 30 0.0 0.2 0.4 0.6 0.8 1.0 Com posHioa, V Theoretical and experimental variation of the width at half maximum (A) for (PbxBa^TiC^. 109 for BaTi03 1 . From these n values, the microregion diameter is estimated to lie between 40 A and 65 A, assuming an average cell volume of 64 A3 . 6.3.1.2 (Pb,Sr1 .JTi03 The width at half maximum increased with increasing Pb content and reached a maximum at x = 0.5 and decreased for x > 0.5. The size of the microregions is estimated by comparing the WHM (A) at different compositions with the above equation. Fig. 9 gives a plot of the theoretically and experimentally obtained WHM with composition. The value of n was found to lie between 100 and 500 which are the limiting curves for these compositions. From these n values, the microregion diameter is estimated to lie between 40 A and 60 A, assuming an average cell volume of 64 A3 for PbTi0 3 . 6.3.13 (Bax Calx)Ti03 Although the (Bax Ca1.x )T i0 3 system forms a homogeneous solid solution in a macroscopic sense (for 0 < x < 0 .2 , and 0 . 8 < x < 1 .0 ), there exists several ordered microregions which have calcium or barium compositions differing from the average, which may result in a diffuse phase transition. The size of the microregions is estimated by comparing the WHM (A) for the compositions x = 0.8, 0.9 and 1.0 with the above equation (Table 4.2). The value of n for* = 0.8 and 0.9 was found to be considerably less that reported for BaTiO* The microregion size is determined to be 15 A, assuming a average cell volume of 64 A3 . The results may be in error because of the ordering of the A-site cations. 110 WHM 80 100 70 0 0 60 40 30 20 10 0.0 0.2 0.4 0.8 0.6 1.0 Composition, 'x' Fig. 6.9. Theoretical and experimental variation of the width at half maximum (A) for (Pbx Sr1 _ x )Ti03 . I l l 6.4 Bibliography 1. G. A. Smolensky, J. Phys. Soc. Jpn., 28 (Suppl.), 26 (1970). 2. B. N. Rolov, Sov. Phys. Solid State, 6 , 1676 (1965). 3. K. Uchino and S. Nomura, Ferroelectr. Lett., 44, 55 (1982). 4. L. E. Cross, Ferroelectrics, 76, 241 (1987). 5. N. Setter and L. E. Cross, J. Mater. Sci, 15, 2478 (1980). 6 . W . Kanzig, Helv. Phys. Acta, 24, 175 (1951). 7. K. H. Hardtl, Feroelectrics, 12, 9 (1976). 8 . W . R. Buessem, L. E. Cross, and A. H. Goswami, J. Am. Ceram. Soc., 49, 33 (1966). 112 Chapter 7 CONCLUSION The crystal structure, microstructure and the electrical properties of A-site substituted titanates, namely (PbxBa^TiCX}, (Pbx Sri.x )T i0 3 and (Bax Ca 1.x )Ti0 3 were investigated. The crystal structure and microstructure properties were studied by X- ray diffraction, and transmission and scanning electron microscopy while the electrical properties were studied by impedance measurements, temperature dependant dielectric measurements and I-V measurements. Both (Pbx Ba1.x )T i0 3 and (Pb^rj. x )T i0 3 showed similar properties and trends, which can be summarized as follows: The crystal structure of (Pbx Baa .x )T i0 3 remained tetragonal over the entire composition range with the c/a ratio increasing with increasing value of x. (P b ,^ . x )T i0 3 remained cubic for x < 0.4 and became tetragonal for x > 0.4. with the c/a ratio increasing with increasing value of x in the tetragonal region. Strain-induced 90° ferroelectric domains were seen in the two systems and the density of these domains decreased with increasing lead content in (PbxBa^TiOs. The 90° domain boundary walls were found to lie on the {101} planes, and tended to be straight. Neither of the systems had an ordered structure. The domains were seen for only x > 0.4 in the (Pbx Sr1.x )Ti0 3 system. There was a linear variation of the Curie point with composition which increased with increasing lead content in both (Pbx Ba!.x )T i0 3 and (Pbx Sr1.x )TiO> Similarly, the room temperature values of the dielectric constant linearly decreased in (Pbx Bai.x )Ti0 3 and increased in (Pbx Sri.x )Ti0 3 with increasing Pb content and the results are consistent with linearly interpolating the values of the end members. 113 Neither of the systems exhibited any relaxor behavior. The phase lag decreased with increasing frequency and reached 90° (ideally capacitive) at 1000 Hz and the systems were found to be ideally capacitive between 1 kHz and 1 MHz. The resistivity reached a maximum of 7 M Qm at the mid composition range in (Pbx Ba1.x )T i0 3 and a minimum of 15 M Qm at x = 0.4 in ( P b ^ T i O j . The diffuseness parameter reached a maximum at the mid point of the composition range and the size of the microregions which were responsible for the diffuse phase transitions was determined to lie between 40 A and 65 A in (Pbx Ba!. x )Ti0 3 and between 40 A and 60 A in (PbxSr^TiOj. The (Bax Ca!.x )Ti0 3 system had an orthorhombic structure for (0.0 < x < 0.2) and became tetragonal for (0 . 8 < x < 1 .0 ) but did not form a solid solution for (0 . 2 < x < 0.8). Strain induced ferroelectric domains were prominently seen for (0.8 < x ^ 1 .0 ) and had the same orientation as in the (Pb!.x )Ti0 3 system and were absent for (0 . 0 < x < 0 .2 ). A secondary phase, Ca4Ti3O 1 0 was observed in the Ca-rich region which had an orthorhombic structure. An ordered structure existed in the Ca-rich region which was very similar to that observed in the (Pbx Ca!.x )T i0 3 system. Even though both (Pbx Ba1.x )Ti0 3 and (Pb^rj^TiO s show diffuse phase transitions above room temperature, the diffuseness is most pronounced in the (Bax Ca!.x )Ti0 3 system which exhibited a diffuse phase transition (paraelectric to ferroelectric) above room temperature over the composition range (0 . 8 < x < 1 .0 ) and a sharp transition from a tetragonal to orthorhombic phase below room 114 temperature. The composition at x = 0.8 showed a distinct hysteresis loop at room temperature, with a coercive field of 0.732 MV/m. The sintering temperature was found to have a pronounced effect on the grain size, the peak value of the dielectric constant and the domain boundaries which increased with increasing sintering temperature. This system also did not exhibit any relaxor behavior. Future work in the study of A-site substituted titanates should include the fabrication and investigation of these titanates with the incorporation of some dopants like Mn which will reduce the leakage currents and increase the insulating properties of these materials. Also, the effect of sintering temperatures over a wider range must be done to see if it influences the diffuseness of the transformations and can cause any relaxor behavior in these systems. Hot stage work is required on the (BaxCai- x )Ti0 3 system to verify the temperatures of appearance and disappearance of the super-lattice reflections. Finally, hysteresis properties and d 3 3 measurements should be done on all these systems to determine the magnitude of coercive field and the polarization phenomena. Also, investigations of the coupling coefficients in these systems, namely, Kt and KP would be useful for ultrasonic imaging and transducer applications with these systems. 115

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Creator Subrahmanyam, Sudhakar (author)

Core Title Study Of Paraelectric-Ferroelectric Phase Transitions In Lead(X) Barium(1-X) Titanium Oxide, Barium(X) Calcium(1-X) Titanium Oxide And Lead(X) Strontium(1-X) Titanium Oxide

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