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Ferroelectric-Paraelectric Phase Transitions In The Lead(X) Calcium(1-X) Titanium Trioxide And The Lead(X) Barium(Y) Strontium(1-X-Y) Titanium Oxide Perovskite Systems

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Ferroelectric-Paraelectric Phase Transitions In The Lead(X) Calcium(1-X) Titanium Trioxide And The Lead(X) Barium(Y) Strontium(1-X-Y) Titanium Oxide Perovskite Systems

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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 of 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 UMI a complete 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 comer 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 FERROELECTRIC-PARAELECTRIC PHASE TRANSITIONS IN THE Pbx Ca1 .x T i03 AND THE PbJBaySr^TiOa PEROVSKITE SYSTEMS. BY RAMARATNAM GANESH 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) May 1995 Copyright 1995 Ramaratnam Ganesh UMI Number: 9601090 UMI Microform 9601090 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 SOUTHERN CALIFORNIA THE GRADUATE SCHOOL UNIVERSITY PARK LOS ANGELES, CALIFORNIA 90007 This dissertation, written by G anesh, R............................................... under the direction of his. 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 Date DISSERTATION COMMITTEE Chairperson ACKNOWLEDGEMENTS This work is dedicated to my parents. CONTENTS Acknowledgements ...................................................................................................... ii List of Figures ............................................................................................................. v List of Tables ................................................................................................................ ix Abstract ..............................................................................................................................x Chapter 1 INTRODUCTION 1.1 History of perovskites ............................................................. 1 1.2 Theory and nature of ferroelectricity ................................... 6 1.3 Applications of ferroelectrics .............................................. 13 1.4 Conclusions .................................................................................. 17 R eferen ces................................................................................... 19 Chapter 2 EXPERIMENTAL PROCEDURE 2.1 Powder preparation and processing ........................................21 2.2 Grain size measurements.............................................................23 2.3 X-ray studies ................................................................................24 2.4 TEM sample preparation techniques .......................................24 2.5 Electrical property measurements ............................................ 29 2.5.1 Dielectric measurements ............................................. 31 2.5.2 Hysteresis measurements ............................................. 31 R eferen ces................................................................................... 33 Chapter 3 STUDIES IN THE Pbx Cal x T i03 SYSTEM 3.1 Introduction .................................................................................. 35 3.2 Results and discussion ................................................................36 3.2.1 Grain size studies ......................................................... 36 3.2.2 Crystal structure analysis ............................................. 36 3.2.3 Dielectric studies ........................................................... 59 3.3 Mathematical modelling ............................................................. 66 3.4 Conclusions .................................................................................. 73 R eferen ces................................................................................... 75 iii Chapter 4 STUDIES IN THE Pbx Bay Sr1 .x y T i03 SYSTEM 4.1 Introduction ................................................................. 77 4.2 Studies in the Pbx B ao.5.x Sra5T i0 3 system ................................... 78 4.2.1 X-ray and grain size measurements ...........................78 4.2.2 Dielectric studies ........................................................... 84 4.2.3 TEM analysis ................................................................92 4.3 Studies in the Pbx Sr0 .s.x B ao.sT i03 system ................................... 96 4.3.1 X-ray and grain size measurements ......................... 100 4.3.2 TEM studies ............................................................. 100 4.3.3 Dielectric measurements ........................................ 104 4.4 Mathematical modelling of microfluctuations in composition ........................................................................ 104 4.5 Conclusions.................... ............................................................ 113 R eferen ces............................................................................... 114 Chapter 5 CONCLUSIONS AND FUTURE WORK 5.1 Summary .................................................................................. 116 5.2 Future w o r k ............................................................................. 117 R eferen ces............................................................................... 119 iv List of Figures Fig. 1.1. The perovskite structure .......................................................................... 2 Fig. 1.2. Multiple ion substitution in the perovskite lattice [5] ........................ 4 Fig. 1.3. Crystal structure of BaTi03 below the Curie point. The Ba2 + and Ti4 + ions are displaced relative to the O2 - ions [10].................................................... 9 Fig. 1.4. Schematic of the domain wall arrangement ...................................... 10 Fig. 1.5. A typical hysteresis loop observed in ferroelectric m a te ria ls 12 Fig. 1.6. Dielectric constant as a function of temperature at 1 khz. for the Bax Sri. x TiOa system [14] .................................................................................................... 14 Fig. 1.7. Trends in dielectric capacitors for DRAMS [17]............................... 16 Fig. 2.1. Schematic of a diffractometer .............................................................. 25 Fig. 2.2. Basic arrangement of a) grinding wheel b) turn table and c) specimen during dimpling ...................................................................................................... 27 Fig. 2.3. Sections of the sample after dimpling.................................................. 28 Fig. 2.4. Position of the sample with respect to the ion beam during milling 30 Fig. 2.5. Sawyer-Tower circuit [3], V and H represent the vertical and horizontal scales of the oscilloscope respectively................................................................ 32 Fig. 3.1. SEM micrograph showing the grain size and morphology of the Pb04Ca0 .6 TiO3 composition ................................................................................... 38 Fig. 3.2. Electron diffraction patterns for (a) [111] zone axis (b) [101] zone axis (c) [100] zone axis having both 1/2{110} and 1/2(100} reflections (d) [100] zone axis having 1/2(110} reflections .......................................................................... 39 Fig. 3.3. The ordered structure with respect to the perovskite unit cell .... 40 Fig. 3.4 T i0 6 octahedra tilted with respect to their ideal perovskite positions. The coordination number of the calcium atoms is reduced to eight due to the rotation [11] ............................................................................................................................ 42 Fig. 3.5. Electron diffraction pattern from the [110] zone axis of CaTi03 showing the presence of 1/2{111) reflections ................................................................... 43 Fig. 3.6. Electron Diffraction patterns from the [101] zone axis of the x=0.2 composition showing the presence of 1/2{110} reflections in addition to 1/2{100} and 1/2{111} reflections........................................................................................ 44 Fig. 3.7. X-ray diffraction pattern for Pb02Cao.8Ti03 indicating an orthorhombic unit c e l l ..................................................................................................................... 46 Fig.3.8. X-ray diffraction pattern for Pb0 .4C ao.6 T i0 3 showing the absence of peak sp littin g ..................................................................................................................... 48 Fig. 3.9. X-ray diffraction pattern for Pb0 7Ca0 3 TiO3 indicating a tetragonal unit cell ............................................................................................................................ 49 Fig. 3.10. Diffraction patterns from the [110] zone axis of Pbo.2Ca0 .8 T i0 3 showing the presence of 1/2{100}, 1/2{110} and 1/2{111} reflections at a) room temperature and b) at 950° C .............................................................................. 51 Fig. 3.11. Electron diffraction pattern from the [112] zone axis of the 0.3 composition at a) room temperature and b) 910° C. The 1/2{111} reflections are present but the 1/2{110} reflections are a b se n t................................................ 52 Fig. 3.12. Electron diffraction pattern from the [112] zone axis of the 0.5 composition at a) room temperature b) at 400°C and c) at 725°C .............. 53 Fig. 3.13. Theoretical electron diffraction patterns from a) [100] b) [010] c) [110] d) [101] and e) [111] zone axes. The radii of the circles are proportional to the intensity of the diffracted s p o ts ............................................................................ 57 Fig. 3.14. Disappearance of superlattice reflections along the main axes on tilting for a) [100] and b) [111] zone axes. The tilt axis is indicated by the arrows 58 Fig. 3.15. Dielectric constant at 1 KHz. as a function of temperature of Pbx Ca:. x T i0 3 for a) x=0.4 b) x=0.5 c) x=0.6 d) x=0.7 and e) x = 0 .8 ........................ 60 Fig. 3.16. Dielectric constant as a function of temperature and frequency for the 0.5 composition ...................................................................................................... 61 vi Fig. 3.17. A typical plot of the dielectric constant versus temperature. The width at half maximum (A) is also show n..................................................................... 71 Fig. 3.18. Curie point as a function of composition in the PbxCa^TiOa sy ste m ........................................................................................................................ 72 Fig. 3.19. Variation of A2 with composition for the PbxCai.xTiCX} system. The value of n calculated theoretically is also indicated..................................................... 74 Fig. 4.1. XRD patterns for the Pb0 .4Bao.iSro.5 T i0 3 com position................. 81 Fig. 4.2. XRD patterns for the Pb0 1Bao.4SrosT i0 3 com position................. 82 Fig. 4.3a) High resolution electron micrograph of a typical grain boundary region for the x=0.3 composition. 4.3b) The grain boundary at a lower m agnification..............................................................................................................83 Fig. 4.4. SEM micrograph showing the grain size and morphology for the Pbo.3 Bao.2 Sro.5Ti03 composition ............................................................................ 85 Fig. 4.5. Dielectric constant as a function of temperature at 100KHz.for a) x=0.0 b)x=0.1 c) x=0.2 d) x=0.3 and e) x=0.4 in the Pbx Bao.5.xSr0 .jTi03 system . . 86 Fig. 4.6. Dielectric constant at different frequencies for a) Pbo.3 Bao.2Sro.5 T i0 3 composition and b) Pba4Ba01Sr0 . 5TiO3 composition ......................................... 87 Fig. 4.7. Frequency dependence of the several contributions to the polarizability ........................................................................................................... 89 Fig. 4.8. Curie point as a function of composition for the PbxBa0 .5 .xS ro.5 T i0 3 sy stem ........................................................................................................................ 90 Fig. 4.9. Hysteresis loop for the Pbo.4Ba01Sra5T i0 3 composition ................... 91 Fig. 4.10. Variation of a) y and b ) < 5 as a function of composition for the Pbx Bao.5. xSr0 5 TiO3 system ...................................................................................................... 93 Fig. 4.11. Electron diffraction patterns from a) [111] b) [110] and c) [100] zone axes for the Pbx Bao.j.xSro.5Ti03 system ................................................................. 94 Fig. 4.12. Bright field image showing the presence of ferroelectric domains along the (011) planes for the x=0.3 composition....................................................... 95 vii Fig. 4.13. A schematic diagram of the domain wall arrangement for a) 10% difference in the c and a values and b) less than 0.5% difference in the c and a values ....................................................................................................................... 97 Fig. 4.14. Electron diffraction pattern from the [111] zone axes showing the absence of spot splitting........................................................................................ 98 Fig. 4.15. High resolution electron micrograph showing no perceptible variation in lattice spacing across the domain boundary. The approximate position of the domain boundary is indicated by the arrows marked d ................................. 99 Fig. 4.16. X-ray scans for different compositions in the Pbx S ro .5 _ x Bao.5Ti03 system. The arrows indicate the (200) p e a k s ................................................................ 101 Fig. 4.17. Bright field image showing the presence of 90° ferroelectric domains in the Pbo3 Sro.2 Ba0jT i03 composition................................................................ 103 Fig. 4.18. Dielectric constant as a function of temperature at lOKHz.for a) x=0.1 b) x=0.2 c) x=0.3 and d) x=0.4 in the PbxSros.xBaosTiO;} system ............. 105 Fig. 4.19. Dielectric constant at different frequencies for the Pbo.2 Sro.3 Bao.5 T i0 3 com position........................................................................................................... 106 Fig. 4.20. Hysteresis loop at room temperature for the Pbo.4Sr01Bao.sT i 0 3 com position........................................................................................................... 107 Fig. 4.21. P(m,n) as a function of < 5 3 and d2 for a) x=0.1, 0.4 b) x=0.2, 0.3 and c) x=0.25 in the Ax B0 .s.x C0 .sTiO3 system. A value of 500 was used for N for each of these p lo ts .............................................................................................................. 110 Fig. 4.22. A plot of the Curie point for different compositions for a ternary system. The condition x + y ^ l is contained within the p la n e ........................ 112 List of Tables Table 1.1. Important events in ferroelectricity..................................................... 7 Table 2.1. Percentage purity of the starting p o w d ers.................................. 22 Table 3.1. Dielectric and microstructural data for the Pbx Ca1 .x T i0 3 system . 37 Table 3.2. Atomic positions for the 0.1 and 0.2 compositions in the Pbx Cai.x T i0 3 sy stem ....................................................................................................................... 47 Table 3.3. The disappearance temperature for the 1/2{100}, 1/2{110} and 1/2{111} superlattice reflections.......................................................................... 54 Table 4.1. Properties of the Pbx Ba0 . 5.x Sr0 . 5TiO3 system ........................ 79 Table 4.2. Properties of the PbxSros.xBaosTiO;} system..................................... 102 ABSTRACT The paraelectric-ferroelectric phase transformations in the PbJ i Ca1 .x T i0 3 and the Pbx Bay Sri.x .y Ti0 3 systems are analyzed. Studies on the Pbx Bay Sr1 .x .y T i0 3 system were focussed on the Pbx Ba0 . 5 .x Sro.5Ti0 3 and the Pbx Sr0 . 5 .x Bao.5Ti0 3 compositions. X-ray studies indicate that both Pbx Ca!.x T i0 3 and Pbx Bay Sr1 _ x _ y T i0 3 form a solid solution in the entire composition range studied. Transmission electron microscopy studies combined with dielectric measurements reveal that lead and calcium atoms order on alternate {111} planes for the x>0.2 compositions, in the Pbx Cai.x T i0 3 system, but, the ordering is less than perfect. No structural ordering was observed in the PbxBaySri.x.yTiC^ system for the compositions studied. Dielectric constant as function of temperature was measured to study the paraelectric-ferroelectric phase transitions in these systems. Addition of calcium titanate was found to broaden the width of the ferroelectric- paraelectric transition region in the Pbx Ca!.x Ti0 3 system. Hysteresis measurements reveal that Pbx Ca!.x T i03 is ferroelectric at room temperature for the x>0.5 compositions. A similar behavior was observed for the x>0.2 compositions in Pbx Ba0 .5 .x Sro.5 T i0 3 and for the x>0.1 compositions in the Pbx Sr0 . 5.x Ba0 . 5TiO3 system. Diffuse phase transitions in solid solutions are primarily attributed to statistical fluctuations in compositions on a microscopic scale. The size of the ferroelectric nucleus determines the fluctuations in compositions and is of paramount importance in determining the nature of the paraelectric-ferroelectric phase transformation in solid solutions. A mathematical model based on probability distribution functions was used in this study to quantitatively establish the size of such fluctuations in composition for the Pbx Ca1 .x T i0 3 and the Pbx Bay Sr1.x . y Ti0 3 systems. The size of the ferroelectric nucleus was determined to be 15A for the Pbx Ca1 .x T i0 3 system and for the ternary system it was determined to be between 15-30A for Pbx Ba0 . 5.x Sr0 .5 TiO3 and between 10-20A for the Pbx Sr0 . 5.x Ba0 . 5TiO3 compositions. CHAPTER 1 INTRODUCTION 1.1 History of Perovskites Compounds with the general formula A B 03 usually have the perovskite structure. The atomic arrangement of the atoms with this type of structure is shown in Figure 1.1. This type of arrangement was first discovered for the mineral perovskite (CaTi03 ) where the Ca atoms occupy the corners of the cube, the titanium atoms the body center positions and the oxygen atoms the face center positions. This cubic structure has retained the name ’perovskite’, although CaTi03 was later discovered to be orthorhombic at room temperature by several independent workers [1,2]. During the last few decades it has been found that at room temperature very few perovskite-type oxides have the ideal cubic structure described above, but transform to the cubic structure at elevated temperatures. According to the geometric requirements of Goldschmidt [3], the perovskite structure can only be formed when the following condition is met: ra+ rb=\f2t(rb+r0 ) (1-1> Here, t is the tolerance factor and ra, rb and rQ are the ionic radii of the A, B and O ions in ABQ3 . The perovskite structure forms when the tolerance factor has the 1 aanum \_vygen Fig. 1.1 The perovskite structure. value 0.85<t<1.05 and the ratio of the ionic radii values are 0.41 <rb /r0<0.73 and ra /ro>0.73. In addition to the above mentioned requirements, the average valence of the A and B sites must add up to six [4]. Typically the A-site cation has a valence of +2 and the B-site cation has a valence of +4. After the discovery of ferroelectric properties of barium titanate in 1945, A B 03 compounds with the perovskite structure have been extensively studied. These studies resulted in the discovery of many new ferroelectric and piezoelectric materials. Active interest in this area led solid-state chemists to discover new ternary perovskite compounds. By the early 1950s it appeared all combinations of A and B atoms had been tried. It was during that time when Galasso et al. [6] found that new perovskite compounds could be prepared by introducing more than one element in the B position of the perovskite structure. A comprehensive survey of the possibilities of ion substitutions was published by Roy [5] who summarized all possible combinations of ion substitution in the perovskite structure as shown in Fig. 1.2. Because these compounds contained two different ions with different valence states, many combinations of elements and, therefore, the formation of many compounds were possible. Studies were conducted throughout the world and a large number of structural and property data on these compounds were generated. However, to date, most of the research has been centered on B-site substitutions and relatively lesser work has been done on A-site substitutions. Therefore, it is of significant scientific and technological interest to 3 B a,” N i” -N b,” Sr,” G a” -.\'b ” La,” M g” -T i” La,” L i” -Ta” K ,” M o” -T i” ' T P '’ Ag‘ K 1+ R b' K ” K ” R b' K ,“ ■La” -■La” ■ L a” “•L a” ■Nd” •Sm ” “ Nd” •L a” Ce‘ One large ion for B a two small ions for Ti 2 large ions for B a 2 or more ions for both B a an d T i K ” -La” Cr” -T a” K '- - N d ” Al” -N b” Ca” -Sr” Zr” -G e” K ” -B a” -La” N b” -T i” -Al” Sr” -L a” -N d” T i” -C r” -A l” G a” N b” C r” T a ” M g” W ” Z n” Cr” Two small ions for Ti (O H ),- L i1 ’'B a ” (O H ),- M g” K ” (O H ),- In ” B a” T i” 0 , ” F - f o r 0 ” I F ,- A l” F r Z n” A g” F ,- L i” B a” F r A l” -L i” K ,” (OH) - for 0 ” ( 0 H ;: - - F - L i” B a” M ixed ___F ,- - ( 0 H ) - M g” K 'J Anions F . - - Q - L i ” S r” F --C 1 ,- L i” B a” P artial F or S for 0 S” o.i-o.:• 0 * Ti-3a F - - 0 ” , T i” K ” Fig. 1.2. Multiple ion substitution in the perovskite lattice [5]. analyze the properties of A-site substituted perovskites and was the primary motivating factor for us undertake research in this area. The advent of thin-film processing technologies of perovskite type materials and their accelerated growth in the last few years has generated an immense interest in the possibility of integrating them with the existing silicon- based technologies that dominate the microelectronics industry. Perovskite thin films have good dielectric properties that make them ideal candidates for memory devices, however, lack of proper processing techniques had stymied their growth during the early 1980s. Fabrication of perovskite thin films present a major challenge, since many commercialy important materials are complex oxides. Advanced techniques such as laser ablation, sol-gel methods etc. are available now and therefore, processing of perovskite thin films has become easier and is being studied with the aim of replacing the existing Si02 and Si3 N4 dielectric films used in memory devices. Trends in thin-film processing technologies up to 1993 has been reviewed by K. Sreenivas [7]. Current research in perovskite thin films is primarily focussed on the following areas: a) Research and development of new processing technologies. b) Methods for accelerated testing and property measurements. c) The development of novel thin film devices using the functional properties of perovskites. The future for perovskite thin films is very promising and it will be interesting to 5 see if they replace the existing silicon-based thin films in the next few years to come. 1.2 Theory and Nature of Ferroelectricity Ferroelectrics have become increasingly important as materials for electronic devices. Substantial research and development has been devoted to these materials with the goal of achieving better properties. The most widely used ferroelectric occur in the perovskite family with the general formula ABOa. Ferroelectricity is a phenomenon discovered in Rochelle salt by Valasek in 1926 [8]. Since then these class of materials have found widespread applications in the electronic industry. The name ferroelectricity refers to certain magnetic analogies although it is somewhat misleading as there is no connection with iron (ferrum). In a study by Cross and Newnham [9] the evolution of ferroelectricity through the last few decades has been systematically listed. A brief summary of the history of ferroelectricity tracing back to the early 30s is listed in Table 1.1. Some of the characteristics of ferroelectrics are briefly summarized in this section. The polarization, P, is defined as the dipole moment per unit volume. Since, the polarization is strongly correlated with the crystal structure, the axis of polarization is along a specific crystal direction. A pyroelectric crystal exhibits a spontaneous polarization, Ps, in the absence of an external electric field and in a certain temperature range. A pyroelectric crystal is ferroelectric if the direction of P, can be changed by the application of an external electric field. 6 Table 1.1 Important events in ferroelectricity. 1920-1930 Rochelle salt period: discovery of ferroelectricity. 1930-1940 Thermodynamic and atomic models of ferroelectricity were studied. 1940-1950 Early barium titanate era: high dielectric constant capacitor materials. 1950-1960 Discovery of new ferroelectrics. 1960-1970 Analysis of soft modes and order parameters. 1970-1980 Discovery of ferroics, electro-optics and thermistors. 1980-1990 Age of ferroelectric packaging and integrated optics. 1990-2000 Age of miniaturization: thin film processing technologies. 7 Ferroelectricity disappears above a certain temperature called the Curie point (T0 ); above this temperature the crystal is in a paraelectric state. The term paraelectric is analogous to the term paramagnetism and is characterized by the absence of spontaneous polarization. In the ferroelectric state the center of the positive charge of the crystal does not coincide with the center of the negative charge. Fig. 1.3. [10] shows the crystal structure of BaTi03 . Above the Curie point, the crystal structure is cubic with the Ba2 + ions at the cube corners, 0 7 r ions at the face centers and Ti4 + ion at the body center. Below the Curie point, the structure is slightly deformed with the Ba2 + and the Ti4 + ions displaced relative to the O2 ' ions. The ions are at their equilibrium positions at which the free energy of the crystal is a minimum and the center of positive charge does not coincide with the center of negative charge, thereby creating a dipole directed from the center of the negative charges to the center of the positive charges. In general, uniform alignment of the spontaneous polarization occurs only occur in certain regions of a crystal, while in other regions the direction of polarization may be rotated by a certain amount from that direction. Such regions with uniform polarization are called ferroelectric domains and the interface between two domains is called the domain wall. Ferroelectric domains were first discovered in BaTi03 by B. Matthias and von Hippel in 1948 [11]. A schematic of the domain wall arrangement is shown in Fig. 1.4. Another important characteristic of a ferroelectric material is the hysteresis Fig. 1.3. Crystal structure of BaTi03 below the Curie point. The Ba2 + and the Ti4 4 - ions are displaced relative to the O2 ' ions [10], 9 Fig. 1.4. Schematic of the domain wall arrangement. 10 loop obtained when the polarization of the material is plotted as a function of the applied field. A ferroelectric hysteresis loop can be observed by means of a Sawyer-Tower circuit [12]. The details of the circuit and the measurement procedure is explained in the chapter on experimental methods. A typical ferroelectric hysteresis loop is shown in Fig. 1.5. The presence of a hysteresis loop on the application of an alternating electric field is usually used as a conclusive proof of the ferroelectric nature of the material. The dielectric constant is another important property of a ferroelectric material and is related to the polarization and the electric field as shown below: where, k is the dielectric constant, P is the polarization, E is the total field and e0 is the permitivitty of free space. The dielectric constant when plotted against temperature, shows a maximum on transition into the ferroelectric state and the temperature at which this occurs is known as the Curie point T0 . In the paraelectric, non-polar state, the changes of the dielectric constant with temperature can be described by the Curie-Weiss law [13] as shown below: 1.2 T-Tc 1.3 11 C l Fig. 1.5. A typical hysteresis loop observed in ferroelectric materials. where T is the temperature,Tc is the Curie-Weiss temperature, k is the dielectric constant, k« is the dielectric constant at temperatures »T C and C is a material constant. When T approaches Tc the dielectric constant attains a very high value. Therefore, by plotting the dielectric constant as a function of temperature it is possible to find out when the ferroelectric-paraelectric transition occurs and hence, determine the Curie point. A plot of the dielectric constant as a function of temperature for the barium strontium titanate system is shown in Fig. 1.6. [14]. In ferroelectrics, the value of Tc present in the Curie-Weiss relation is in general identical with the real temperature (T0 ) of phase transition from the polar to the non-polar state. When however, the value of Tc is determined on monocrystals of perovskite structure, its value is found to be about 10° below the actual transition temperature T0 [15]. In polycrystalline materials this difference becomes indistinct. 1.3 Applications of Ferroelectrics Ferroelectric ceramics with the perovskite structure are used in numerous electronic applications. Some of the major applications of ferroelectric ceramics with perovskite structure are discussed below. al Dielectric applications: The high dielectric constant and low dielectric loss make ferroelectric materials ideal for compact multilayer capacitors (MLCs). Ferroelectric hysteresis response is of interest in thin film non-volatile semiconductor memory [16]. High permitivitty films are used in high density DRAMs. With the down-scaling of devices sizes, the need for thin films with high 13 Fig. 1.6. Dielectric constant as a function of temperature at lKHz. for the Bax Srx x T i03 system [14]. dielectric constant to replace the already existing S i02 and S i ^ is growing. Fig. 1.7. shows the recent trends in capacitor dielectrics for DRAMs[17]. bl Piezoelectric and electrostrictive responses: Electrostriction is a material property where the application of an electric field produces a strain in the material. The effect of the electric field on the strain is quadratic. The induced strain is unchanged on reversing the applied electric field. Piezoelectricity is also a material property where the application of an electric field produces a strain in the material (and vice versa), but the effect is linear. Reversal of the field produces a reversal in induced strain. Piezoelectric and electrostrictive responses in ferroelectric compositions are of importance in transducers for converting electrical energy to mechanical energy and vice versa. The high piezoelectric constants of perovskites are made use of in efficient conversion of electric to mechanical response [18].The strong electrostrictive coupling is made use of in high precision position control and domain and phase switching with shape memory is used in polarization controlled actuation [19,20]. c) Pyroelectric systems: In pyroelectric materials there is a change in the spontaneous polarization as the temperature changes. Ferroelectricity is a subset of pyroelectricity in the sense that all ferroelectric materials are pyroelectric but the converse is not true. The pyroelectric effect in ferroelectrics is made use of in the detection of long wavelength infrared radiation, imaging systems for night vision and for thermal medical diagnosis [21,7]. 15 Si02 equivalent thickness (nm) 5 4 3 2 1 ^ 16M 6 4 M 2 5 6 M 1G 4 G DRAM (Mbit) S i3 N 4 # P r0dU C ti0n 3development A conference O target -t (BaSrJTiOs Fig. 1.7. Trends in dielectric capacitors for DRAMS [17]. d) Positive Temperature Coefficient of Resistance (PTCR): PTCR ceramics posses a rapidly increasing coefficient of resistance when heated above the Curie temperature and an almost constant temperature coefficient of resistance below the Curie temperature [22]. Recently, PbxSri.xTiOs PTCR ceramics having a large negative temperature coefficient of resistance below Tc in addition to PTCR characteristics above Tc have been reported [22,24]. PTCR ceramics are used to make various devices including temperature controllers, temperature detectors, electrical heating elements, degaussers for televisions, starters for larger power motors and motor protectors against overheating [10]. 1.4 Conclusions It is clearly seen from the earlier paragraphs that perovskite and related materials find widespread applications in the electronics industry. The basic focus of research in these materials has been to characterize them on the basis of their microstructure, dielectric properties etc. Therefore, the primary aim of undertaking the present research work was to study the dielectric and microstructural properties of the (Pb,Ca)Ti03 and the (Pb,Ba,Sr)Ti03 systems and establish a structure property correlation. The (Pb,Ca)Ti03 system was chosen because of the interest in the ordering behavior observed [25]. Most of the research work in this system has been concentrated on the lead rich compositions (Pb>50mol%) and no work has been done on the calcium rich compositions (Pb<50mol%). Also, the effect of 17 structural disorder on the ferroelectric-paraelectric phase transition is of significant scientific and technological importance and has never been studied for the (Pb,Ca)Ti03 system. A detailed study on the effect of ordering on the diffuseness of the ferroelectric-paraelectric phase transitions and a quantitative estimation of certain parameters associated with the diffuseness is presented in this work. This type of analysis is the first of its kind ever reported. Interest in the (Pb,Ba,Sr)Ti03 ternary system stems from the good dielectric characteristics exhibited by the (Ba,Sr)Ti03 system. It has been the object of extensive research to find some composition where the dielectric peak would spread out with a reasonably constant high value over the working temperature range. Since, these materials find potential application in devices where the working range is close to room temperature any additions that would increase the dielectric constant at room temperature and increase the diffuseness of the paraelectric-ferroelectric phase transition would be desirable. Because of its high Curie point and ferroelectric nature at room temperature, addition of lead titanate to (Ba,Sr)Ti03 would increase the dielectric constant at room temperature and the width of transition region. The present work aims to study the microstructure through X-ray diffraction and transmission electron microscopy investigations in the (Pb,Ba,Sr)Ti03 system and examine its dielectric properties. A theoretical model to quantitatively establish the effect of compositional fluctuations on the paraelectric-ferroelectric phase transition for a ternary system 18 is also presented. REFERENCES 1. H. D. Megaw, Proc. Phy. Soc., 58, 133 (1946). 2. H. F. Kay and P. C. Bailey, Acta. Cryst., 10, 219 (1957). 3. V. M. Goldschmidt, Zeits. Techn. Physic., 8, 251 (1927). 4. H. L. Yakel Jr., Acta. Cryst., 8, 394 (1955). 5. R. J. Roy, Am. Cer. Soc. 37, 581 (1954). 6. F. Galasso, L. Katz and R. Ward, J. Am. Chem. Soc., 81, 820 (1959). 7. Ferroelectric ceramics, edited by N. Setter and E. L. Colla 213 (1993). 8. J. Valasek, Phy. Rev. Bull. 24(5), 560 (1964). 9. L. E. Cross and R. E. Newnham, Ceramics and civilization-vol.III, edited by W. D. Kingery, The American Ceramic Society, Ohio, 289 (1987). 10. Y.Xu, Ferroelectric Materials and their applications, Elsevier Science, Holland (1991). 11. B. Matthias and A. von Hippel, Phy. Rev. 73, 1378 (1948). 12. C. B. Sawyer and C. H. Tower, Phy. Rev., 35, 269 (1930). 13. H. D. Megaw, Proc. Roy. Soc. Lon., 189, 261 (1947). 14. Landolt Bornstein Tables, Ferroelectric Oxide, 16a, Springer Verlag, Berlin (1981). 15. W. Kanzig, Ferroelectric and Antiferroelectric Materials, Solid State Physics, New York, 4, 1-199 (1957). 16. E. R. Myers and A. I. Kingon, Ferroelectric Thin Films, Materials Research Symposium Proceedings, San Francisco, 200 (1990). 17 A. Ishitani, P. Lesaicherre, S. Kamiyama, K. Ando and H. Watanabe, IEICE Trans. Elec., E76-C, 1564 (1993). 18. H. Jaffe and D. Berlincourt, Proc. IEEE, 53, 1372 (1965). 19. R. E. Aldrich, Ferroelectrics, 27, 19 (1980). 20. W. Y. Pan, T. R. Shrout and L. E. Cross, J. Matt. Sci. Lett., 8, 771 (1989). 21. R. W. Whatmore, J. M. Herbert and F. W. Ainger, Phy. Stat. Solidi, A61, 73 (1980). 22. O. Saburi, J. Phy. Soc. Jpn., 14, 1159 (1959). 23 Y. Hamata, J. Electr. Cer. Jpn., 5, 33 (1988). 24. C. Lee, N. Lin and C. Hu, J. Am. Cer. Soc., 77, 1340 (1994). 25. G. King, E. Goo, T. Yamamoto and K. Okazaki, J. Am. Cer. Soc., 71, 454 (1988). 20 CHAPTER 2 EXPERIMENTAL PROCEDURE 2.1 Powder Preparation and Processing Conventional powder processing techniques were employed to prepare the bulk powder. The purity of the powders used in this work is listed in Table 2.1 Stoichiometric amounts of powders to yield 25 grams of the final product were calculated using the following equations: xPbO + (l-x)CaC03 + T i02 — > Pbx Ca1 .x T i0 3 + (l-x)C 02 xPbO + yBaC03 + (l-x-y)SrC03 + TiOz --> Pbx Bay Sr1 .x .y T i0 3 + (l-x)C 02 The compositions of the samples that are listed in this work always refer to the relative amounts of the oxides used in preparing the powder and do not represent the measured composition of the sintered material. The weighed powders were then ball milled for five hours using alumina balls and deionized water. This was followed by vacuum filtration and oven drying of the filtrate residue. The dry powders were then ground using a mortar and pestle and calcined at 850° C for five to eight hours in a covered alumina crucible and using a Lindberg box furnace. Calcination removes the C 0 2 and aids in the formation of Pbx Cai.x T i0 3 and Pbx Bay Sr1 .x .y T i03 powders. The calcined powders were ball milled again for five hours and then dried to obtain a homogeneous distribution. The calcined powders were cold pressed in a hydraulic press at 35,000 psi 21 Table 2.1. Percentage purity of the starting powders. Powder % Purity C aC 03 99.5 PbO 99.5 T i0 2 99.7 B aC 03 99.6 SrC03 99.5 into cylindrical pellets 25mm in diameter and 3mm in thickness. The compacts were sintered at 1200° C for five hours in a covered alumina crucible loosely packed with powder of the same composition to minimize the lead loss due to evaporation. For the Pbx Cai.x T i0 3 system, polycrystalline samples with x>0.8 were not prepared as they disintegrated into powders on cooling through the Curie point. This is primarily due to the large c/a ratio (1.06) that results in high internal stresses as the crystal structure changes from cubic to tetragonal. Samples with compositions in increments of 10 mol% were prepared. 2.2 Grain Size Measurements The as-sintered samples were mechanically polished using disc polishers. Polishing papers of finer grit size were used as the specimen thickness progressively decreased. Final polishing was done using alumina emulsion (0.05/^m particulate size) as abrasive to obtain a smooth flat surface devoid of any scratches. Sample thus prepared were etched for five minutes in a solution containing 4.5% HF and 4.5% H N 03 . Grain size measurements were done on a Cambridge Model 360 Scanning Electron Microscope (SEM) equipped with a LaB6 filaments and at an accelerating voltage of 20KV. Ceramics in general are non-conductive and therefore, sample charging is a common problem when they are exposed to electron beam irradiation as in SEM studies. Therefore, to avoid beam drifting due to charging, the samples were sputter coated with gold- palladium alloy. The average grain size was calculated using the lineal intercept 23 method specified by ASTM standard E l 12-85 [1]. In this method, the grain size is determined by counting the number of grains intercepted by one or more straight lines sufficiently long enough to give fifty intercepts. The average grain size is then determined by dividing the total length of the test lines with the number of intercepts. 2.3 X-ray Studies Samples for X-ray studies were obtained by mechanically polishing the as- sintered samples till a flat, smooth surface was obtained. X-ray diffraction studies were done on a Rigaku diffractometer equipped with a Nal scintillation detector and operating at an accelerating voltage of 35KV and a beam current of 50mA. X-ray diffraction studies are done to detect the various crystalline phases that are present and determine the crystal structure and lattice parameters of those phases. The underlying principle of X-ray diffraction is Bragg’s law which is given by, «A=2Jsin0 where, n is the order of the reflection, X is the wavelength of the X-rays, d is the interplanar spacing and 6 is the scattering angle of the X-rays. Copper K* radiation with A=1.54A was used in the present study. A schematic diagram of the basic parts of a spectrometer is shown in Fig. 2.1 [2]. 2.4 TEM Sample Preparation Techniques Preparation of specimens for TEM studies is a complicated and 24 mtKlcnt-h?£u!; s:i:s line sourre diffractom eter axis ■ e m r in g slit tn rm tr.ter Fig. 2.1. Schematic of a diffractometer. 25 time consuming process. The most crucial aspect of specimen preparation involves the ability to prepare electron transparent sections with little distortion or transformation from the original bulk sample. TEM sample preparation is more of an "art". Although, specific procedures exist for preparing these specimens, the final result of producing a "good" TEM sample relies entirely on the skill of the person doing it and on his ability to wisely modify the standard procedures so as to yield the best result for his sample. This section briefly outlines the TEM specimen preparation techniques adapted in the present study. Circular disks of 3mm diameter were cut from the as-sintered sample using an ultrasonic drill. The disks were then mechanically thinned using the procedure outlined for SEM sample preparation. The thickness of the disks after mechanical polishing is approximately 100-15Q«m. The disks were then subject to mechanical dimpling where an accurately sized depression is cut on the surface of the specimen to reduce the time required for final thinning process. A grinding machine composed of a turntable and a grinding wheel in mutually perpendicular planes of rotation is used for this purpose. Fig. 2.2 shows the basic arrangement of a dimpler. A slurry of silicon carbide particles (3,«m particulate size) is used as an abrasive. A cross section of the sample after dimpling is shown in Fig. 2.3 The dimpled sample is then glued to a copper grid using M-bond. This is primarily done to increase the mechanical strength and enable easy handling of the sample. The final stage in specimen preparation involves a thinning procedure to 26 Fig. 2.2. Basic arrangement of a) grinding wheel b)turntable and c) specimen during dimpling. 27 Fig. 2.3. Sections of the sample after dimpling. generate electron transparent areas in the sample. This is usually achieved by ion milling of the sample. Ion milling is a low energy sputtering process used for TEM specimen preparation. In this process argon ions accelerated in a potential field of 5KV hit the surface of the specimen at a low angle of incidence and thinning occurs by removal of material due to ion bombardment. Fig. 2.4 shows the position of the sample with respect to the incident ion beam. A Gatan ion mill was used in this study. For hot-stage TEM studies, samples were prepared as described above however, epoxy burn off at high temperatures precluded the use of copper grids for mechanical support of the samples. This made preparation and handling of hot stage TEM specimen an extremely difficult and time consuming process. Room temperature TEM studies were done on a Phillips EM 420 electron microscope operating at an accelerating voltage of 120KV. High resolution TEM studies were done on an Akashi 002B electron microscope operating at 200KV. Hot stage TEM studies were done using a Jeol JEM 2000FX microscope operating at 200KV. A single tilt Gatan 628-0500 holder was used for hot stage studies. Due to limited tilting capability of the hot stage it was difficult to go to the exact zone axes conditions during high temperature electron diffraction studies. 2.5 Electrical Property Measurements Samples for electrical property measurements were prepared by 29 Probing Light / Ion Bean Ion ean Fig. 2.4. Position of the sample with respect to the ion beam during milling. 30 mechanically polishing the as sintered samples till a flat smooth surface was obtained. Silver electrodes were then vapor deposited on the sample using a Denton vacuum evaporator. 2.5.1 Dielectric Measurements The dielectric constant, k, is related to the capacitance by the following relation, c _ *e < A 2.2 d where C is the capacitance of the sample,eQ is the permitivitty of free space, A is the electrode area and d is the distance between the electrodes. By measuring the capacitance of the sample at different temperatures one can obtain the value of k at those temperatures. A Keithley 3322 LCZ meter was used to measure the capacitance of the sample at different frequencies and a Lindberg box furnace was used for changing the temperature of the sample. For below room temperature measurements the sample was place in a container with liquid nitrogen. The sample temperature was changed by allowing the liquid nitrogen to evaporate thereby, letting the sample reach room temperature slowly. 2.5.2 Hysteresis Measurements The most commonly accepted evidence of ferroelectricity is a hysteresis loop between the polarization (P) and applied field (E). The P-E display is obtained using a Sawyer-Tower circuit [3] as shown in Fig. 2.5. The basic principle 31 Sample AC Fig. 2.5. Sawyer-Tower circuit [3]. V and H represent the vertical and the horizontal scales of the oscilloscope respectively. 32 involves in relating the stored charge to the instantaneous voltage. A large capacitor is place in series with the sample and the voltage across it measures the charge stored on the test sample. This is displayed on the vertical scale of the oscilloscope. The applied voltage is displayed on the horizontal scale. In the case of paraelectric samples a straight line is obtained instead of hysteresis loop. The area of the loop represents the energy loss as heat and hence, to avoid sample overheating the experiment is usually run at low frequencies (60Hz.). In ferroelectrics there is a minimum field required before a hysteresis loop can be observed and is called the coercive field (Ec ). For perovskite materials Ec lies in the range of lKV/cm to 20KV/cm. This, therefore, necessitates the use of either high voltage power supplies or samples with smaller dimensions. A dielectric set up was designed for analyzing the hysteresis behavior of the samples studied in the present work. However, due to lack of high voltage power supply and dimensional limitations of the samples, the set up could be used only for samples with low coercive fields such as barium titanate and for thin films such as lead zirconate titanate. For the present studies hysteresis measurements were done on an automated Hewlett Packard system at the Materials Research Laboratory, Pennsylvania State University. REFERENCES 1. ASTM, Annual book of ASTM standards, 3.01 (1987). 33 2. B. D. Cullity, Elements of X-ray diffraction, Addison-Westerley, Massachusetts (1978). 3. C. B. Sawyer and C. H. Tower, Phy. Rev., 35, 269 (1930). 34 CHAPTER 3 STUDIES IN THE Pbx CalxTi03 SYSTEM. 3.1 Introduction The ferroelectric nature of the lead rich compositions in the Pbx Ca!.x T i03 system was discovered as early as 1956 [1]. A detailed study on the hysteresis behavior was reported in 1959 [2]. However, no work was done in this system for the next twenty years. It was only in early 1980s interest in this system was renewed after the discovery of large anisotropy in the piezoelectric coupling factors and high mechanical quality factors which are important for wide band ultrasonic transducers [3,4]. Since then numerous efforts have been directed towards obtaining improved dielectric and piezoelectric properties in these materials [5-8]. A detailed study on the crystal structure and defects in the lead rich compositions of the PbxCaj.xTiOs system was reported by King and co workers in late 1980s [9,10]. Most of the research done in this system has been concentrated on the lead rich compositions and no work has been done on the calcium rich compositions. Also, the ordering behavior observed in this system was not fully explained and the relationship between the ordering behavior and the dielectric properties was never analyzed. The present work is directed towards resolving some of the issues unexplained earlier and also present a detailed analysis of the crystal structure and dielectric properties of this system. 3.2 Results and Discussion 3.2.1 Grain Size Studies Grain size measurements done on the Pbx Ca!.x T i03 system did not reveal any specific trend as a function of composition. No grain boundary phases were seen. A typical grain size and morphology for the Pbo.4Ca0 .6 T i0 3 composition is shown in Fig. 3.1. The grain sizes for the other compositions studied are listed in Table 3.1. 3.2.2 Crystal Structure Analysis Earlier studies in the PbxCax.xTiOs system have revealed ordering of the lead and calcium atoms on alternate {111}* planes [9]. Presence of 1/2(111}, 1/2(110} and 1/2(111} superlattice reflections in electron diffraction were reported for compositions between 0.5 £ x < 0.61. TEM studies of the calcium rich compositions (0<x<0.5) also reveal the presence of these superlattice reflections. The electron diffraction patterns from the three principal zone axes for the 0.4 composition are shown in Fig. 3.2. An ordered structure was proposed by King et al. [9] to explain the reflections seen in Pbx Ca1 .x T i03 close to the x=0.5 composition. The orientation relationship between the ordered structure and the perovskite unit cell is shown in Fig.3.3 The lead and calcium atoms occupy crystallographically equivalent sites and ideal ordering occurs at the x=0.5 Unless otherwise stated, all reflections are indexed with respect to the perovskite unit cell. 36 Table 3.1. Dielectric and microstructural data for the P^Ca^TiO j system. Composition (x) Crystal Structure % Density c/a < 5 Y d(/tm) Tc (°C) K 0.1 Orthorhombic 93 - - - 3.4 - - 0.2 Orthorhombic 93 - - - 2.7 - - 0.3 Pseudocubic 95 *1 - - 3.0 - - 0.4 Pseudocubic 99 «1 1.5 0.6 3.2 13 1928 0.5 Tetragonal 97 1.003 12 1.34 3.5 29 3000 0.6 Tetragonal 98 1.015 9 1.31 2.4 158 6370 0.7 Tetragonal 98 1.04 7 1.25 2.3 254 7995 0.8 Tetragonal 98 1.045 5.5 1.20 2.9 334 9030 %Density: Experimental density, d: Grain size, T0 : Curie point and km : Dielectric constant at T0 and at lKAiz. Fig. 3.1. SEM micrograph showing the grain size and morphology of the Pbo.4Cao.6T i0 3 composition. 38 Fig. 3.2. Electron diffraction patterns for (a) [111] zone axis (b) [101] zone axis (c) [100] zone axis having both 1/2{110} and 1/2(100} reflections (d) [100] zone axis having 1/2(110} reflections. 39 perovskit ordered •a a O ■a Fig. 3.3. The ordered structure with respect to the perovskite unit cell. 40 composition. Ordering of lead and calcium atoms occurs on alternate {111} planes, thereby, changing the crystal structure to face centered cubic. The reciprocal lattice is therefore, body centered cubic resulting in the appearance of 1/2{111> reflections in electron diffraction. However, presence of 1/2{111} reflections in electron diffraction can also occur due to atomic displacements. Kay and Bailey [11] and Koopmans et al. [12] have shown that the structure of calcium titanate is a regular T i0 6 octahedra rotated with respect to their ideal perovskite positions as given in Fig. 3.4. This occurs primarily due to the small displacement of the calcium and oxygen atoms from their ideal lattice positions. TEM studies on CaTi03 reveal the presence of superlattice reflections due to such displacements as shown in Fig. 3.5. It is therefore, seen that the 1/2(111} superlattice reflections are not only a result of ordering but can also occur due to atomic shuffles. This needs to be taken into account to explain the presence of 1/2(111} superlattice reflections in compositions other than x=0.5 in the Pbx Caj. x T i0 3 system. Also, based on the ordered structure mentioned earlier one would expect the presence of 1/2(110} superlattice reflections in the <110> zone axis. However, no such reflections were seen in the <110> zone axis for the x>0.2 compositions. For the x=0.1 and 0.2 compositions weak 1/2(110} reflections were observed in the <110> zone axis as shown in Fig. 3.6. These reflections are similar to those observed in pure CaTi03 . X-ray studies reveal that the x=0.1 and 0.2 compositions have an orthorhombic structure with lattice parameters close to 41 Fig. 3.4. T i0 6 octahedra tilted with respect to their ideal perovskite positions. The coordination number of the calcium atoms is reduced to eight due to the rotation [11]- 42 Fig. 3.5. Electron diffraction pattern from the [110] zone axis of CaTi03 showing the presence of 1/2{111} reflections. 43 Fig. 3.6. Electron diffraction pattern from the [101] zone axis of the x=0.2 composition showing the presence of 1/2{110} reflections in addition to l/2{ 100} and 1/2{111} reflections. those of pure CaTi03 . The X-ray diffraction scan for the x=0.2 composition is shown in Fig. 3.7. Based on these observations it is concluded that Pbo.1 Caa9T i03 and Pbo.2 Caa8Ti03 have a crystal structure similar to pure CaTiO^ The superlattice reflections observed in these compositions are a result of atomic displacements similar to those observed in CaTi03 . The atom positions for the 0.1 and 0.2 compositions are listed in Table 3.2. X-ray studies on the 0.3 and 0.4 compositions reveal a crystal structure corresponding to cubic symmetry. No peak splitting was observed in the X-ray scan as shown in Fig. 3.8. However, TEM studies of these compositions reveal the presence of 1/2{111} reflections in only one direction in the < 111> zone axis as shown in Fig. 3.2a. This suggests a lack of three-fold symmetry along the < 111> direction and, therefore, indicating that the x=0.3 and x=0.4 compositions are not cubic at room temperature. This is not contradictory because, X-ray scans average over a greater area of the sample as compared to electron diffraction and therefore, the different variants give rise to a cubic pattern in X-ray. The x=0.3 and 0.4 compositions are therefore, pseudocubic with a c/a ratio close to unity. For the x>0.4 compositions the crystal structure exhibits tetragonal symmetry with increasing c/a ratio as the lead content increases. The X-ray diffraction scan for the 0.7 composition is shown in Fig. 3.9. The crystal structures of Pbo.iCa0 .9 T i0 3 and Pbo.2 Ca0 .8 T i0 3 have a lower symmetry as compared to the other compositions. Therefore, the presence of an extra screw axis or a glide plane due to higher 45 Counts O o o c u 'I' r i A ri 3 0 . 5 0 . 5 0 . 7 0 . 20 v r n ? i i i r 8 0 . 9 0 . TTt / iS T" 1 0 0 . Fig. 3.7. X-ray diffraction pattern for PboaCaogTiC^ indicating an orthorhombic unit cell. 46 Table 3.2. Atomic positions for the 0.1 and 0.2 compositions in the Pb^Ca^TiOj system. Four Pb/Ca atoms in: x,0,z; -x,l/2,-z; l/2+x,l/2,l/2-z; l/2-x,0,l/2+z; with x=0 and z=do. There is no ordering of Pb and Ca atoms and the site occupancy is random. Four Ti atoms in: 1/2,3/4,0; 0,3/4,1/2; 0,1/4,1/2; 1/2,1/4,0. Four O atoms in: l/2+x,0,z; l/2-x,l/2,-z; x,l/2,l/2-z; -x,0,l/2+z; with x=d! and z=d2 - Eight O atoms in: l/4-x,3/4-y,l/2-z; l/4-l-x,l/4+y,3/4-z; 3/4+x,l/4-y,3/4+z; 3/4-x,3/4+y,l/4+ z; 3/4+x,3/4+y,3/4+z; 3/4-x,l/4-y,l/4+z; l/4-x,l/4+y,l/4-z; l/4+x,3/4-y,3/4-z; with x = < 53 , y=d4 and z=d3 . < 5 j represents slight deviations from equilibrium positions. 47 o c u h- BO. 9 0 . 6 0 . 7 0 . 5 0 . 3 0 . 2 0 Fig. 3.8. X-ray diffraction pattern for Pbo.4Cao.6 T i03 showing the absence of peak splitting. 48 CD O CD O ? o O 3 0 . 5 0 . 60 70 90 Fig. 3.9. X-ray diffraction pattern for Pb0. 7Cao.3Ti0 3 indicating a tetragonal unit cell. 49 symmetry would account for the absence of 1/2{110} reflections in the <110> zone axes for the x>0.2 compositions. High temperature electron diffraction studies were carried out to determine the nature and origin of the superlattice reflections. Specimen warping due to lead loss at high temperatures and equipment limitations precluded hot stage TEM studies to be conducted for temperatures greater than 950° C. Also, a single tilt hot stage was used for this study and therefore, exact zone axes conditions could not be attained for electron diffraction patterns. This however, did not affect the results obtained from hot stage microscopy experiments. Selected area electron diffraction patterns at different temperatures for the 0.2, 0.3 and 0.5 compositions are shown in Fig. 3.10., Fig. 3.11. and Fig. 3.12. respectively. The results are listed in Table 3.3. It is seen that the 1/2{100} and the 1/2{110} superlattice reflections disappear at the same temperature whereas, the 1/2(111} reflections disappear at a higher temperature for the x>0.3 compositions. Also, dark field studies reveal that different regions light up on imaging with the 1/2(111} reflections as compared to imaging with 1/2(100} and the 1/2(110} reflections in these compositions [10]. These observations indicate that the 1/2(111} reflections are of a different origin as compared to the 1/2(100} and 1/2(110} reflections. Chemical ordering of lead and calcium atoms account for the presence of 1/2(111} superlattice reflections and atomic shuffles or electrical ordering is responsible for the presence of 1/2(100} and 1/2(110} 50 Fig. 3.10. Diffraction patterns from the [110] zone axis of Pb0 . 2 Ca0 8 TiO3 showing the presence of l/2{ 100}, 1/2{110} and 1/2(111} reflections at a) room temperature and b) at 950° C. Fig. 3.11. Electron diffraction pattern from the [112] zone axis of the 0.3 composition at a) room temperature and b) 910° C. The 1/2{111} reflections are present but the 1/2(110} reflections are absent. 52 @ U 'l C lA p Fig. 3.12. Electron diffraction patterns from the [112] zone axis of the 0.5 composition at a) room temperature b) 400° C and c) at 725° C. 53 Table 33. The disappearance temperature for the 1/2{100}, 1/2{110} and 1/2(111} superlattice reflections. X Disappearance of 1/2(100} and 1/2(110} Disappearance of 1/2(111} 0.1 >950°C >950° C 0.2 >950°C >950° C 0.3 910° C >950° C 0.4 750° C «930°C 0.5 400° C 725° C 0.6 <450°C 450° C 54 superlattice reflections in the x>0.3 compositions. Atomic shuffles similar to that observed in pure CaTi03 is believed to be responsible for the presence of 1/2{110} and 1/2{100} superlattice reflections in the Pbx Ca1 .x T i0 3 system. This is further corroborated by the evidence that BaxCa^TiOs and Srx Ca1 .x T i0 3 also show superlattice reflections identical to Pbx Ca1 .x T i0 3 , however, no superlattice reflections are seen for the Pbx Ba!.x T i0 3 and the PbxSr^TiOs systems [13,14]. It is also noticed that the temperature at which the superlattice reflections disappear increases with increasing CaTi03 additions. C aTi03 undergoes an orthorhombic to cubic phase transition at 1257° C [15]. Therefore, with increasing additions of CaTi03 the temperatures at which the tetragonal to cubic or the orthorhombic to cubic transitions occur also increases. Hence, the small atomic displacements that are present in the structure with lower symmetry are no longer present as the material becomes cubic. The 1/2(100} and the 1/2(110} reflections which arise due to such displacements, therefore, disappear as the material becomes cubic. For the x^0.3 compositions the 1/2(111} reflections, however, are a result of ordering of Pb and Ca atoms on alternate {111} planes and therefore, disappear at a different temperature. For the x=0.1 and 0.2 compositions the crystal structure is similar to pure CaTi03 and there is no ordering of Pb and Ca atoms. Hence, all the superlattice reflections disappear at the same temperature in these compositions. As mentioned earlier, if atomic displacements similar to CaTi03 is 55 assumed, then a presence of a glide plane would account for the disappearance of the 1/2{110} reflections in the <110> zone axes. Theoretical electron diffraction patterns were calculated using a program written at the University of Southern California, Los Angeles. When displacement of oxygen atoms similar to CaTi03 and ordering of lead and calcium atoms on alternate {111} planes were taken into account, it was found that the theoretical patterns were in good agreement with the experimentally observed patterns. The theoretical diffraction patterns from the different zone axes are shown in Fig. 3.13. In the experimental diffraction patterns the 1/2{110} superlattice reflections appear in the < 111> zone axes along the row through the origin because of double diffraction. This was confirmed by the disappearance of these reflections on tilting along the row through the origin as shown in Fig. 3.14. The superlattice reflections were weak in electron diffraction and absent in X-ray diffraction as shown in Fig. 3.8. Therefore, the order parameter and the exact atomic displacements could not be calculated. Based on the similarity between the experimental and theoretical patterns, it is concluded that addition of calcium titanate is highly influential in determining the ordering behavior in these systems. However, the exact amount of atomic displacements and the space group for the Pbx Ca1 .x T i0 3 system are still unclear. Sawaguchi and Charters [2] have reported that the polar anisotropy in Pbo.5Ca0 .sTi0 3 is due to the separation of a single phase into two phases as a 56 a b o O o O 0 O o O o o 0 0 o o 0 o 0 o 0 o 0 O o o 0 o o o o o o 0 O 0 O o o 100 001 o 0 • • O 0 o 0 o O 0 o o 0 o O o O 001 O O O O O D o o 0 ° • O o o 0 O °6° O o o o o o O o o o o 0 0 o 0 o 0 o o O O o o o o o o O o 0 o O 0 0 o o O o o o 0 c d « - ~ ~ _ o o o o o o o o C o o o o o o o 0 0 o o o o g o o o o o i o o 0 o o o o • o 0 o o 0 o O © o o o n o O O O o o $ o o o o o o Tto 0 O o • o 0 o o 0 o • o o ° 6 ° o 0 O o o O o o o 0 o 0 o o o o 0 o O o o o < t > o o O o O o o o o oil 0 o o O o o o o Tot o O © o o 0 o o O o o o 0 o o O o o 0 0 o o Fig. 3.13. Theoretical electron diffraction patterns from a) [100] b) [010] c) [110] d) [101] and e) [111] zone axes. The radii of the circles are proportional to the intensity of the diffracted spots. 57 Fig. 3.14. Disappearance of superlattice reflections along the main axes on tilting for a) [100] and b) [111] zone axes. The tilt axis is indicated by the arrows. result of aging. However, X-ray studies done on the x=0.5 composition did not reveal any such phase separation. Also, TEM studies did not reveal the presence of two phases close to the x=0.5 composition. In the absence of any phase separation, the polar anisotropy in Pb0sCao.sTi03 maybe a result of time dependent atomic displacements. 3.2.3 Dielectric Studies Dielectric constant as a function of temperature was measured for various compositions in the PbxCa^TiOj system. Plots of dielectric constant as a function of temperature for different compositions are shown in Fig. 3.15. It is seen that Pb04Ca0 6 TiO3 shows a transition from a paraelectric to ferroelectric state at 14° C. Below the 0.4 composition Pbx Ca!.x T i03 is paraelectric at -50° C. Due to experimental limitations temperatures below -50°C were not studied. In all these cases no shift in the maxima of the curves with change in frequency is seen as shown in Fig. 3.16. This indicates the absence of relaxor behavior in the Pbx Ca!_ x T i03 system. Relaxor behavior is typified by the spread in the Curie point as a function of frequency. Addition of calcium titanate to lead titanate broadens the width of the paraelectric-ferroelectric transition region but there is no relaxor behavior. Width of the transition region is largest close to the x=0.5 composition. The dielectric constant as a function of temperature approximates Gaussian behavior [16,17] as, 59 a b x ; o o 500 0 • o o o Twnpwatu* (C ) f l Tenpaiatiia (C ) 0 0 100 200 300 9000 6000 200 Temparatura (C ) Taffpatalna (C ) e 0 0 * 10' I u I 400 500 300 200 Fig. 3.15. Dielectric constant at lKHz. as a function of temperature of Pbx Caj x T i03 for a) x=0.4 b) x=0.5 c) x=0.6 d)x=0.7 and e)x=0.8. 60 Dielectric Constant 3 500 100 KHz 10 KHz 1 KHz 120 Hz. 2500 1500 500 -100 0 100 200 Tem perature (C) Fig. 3.16. Dielectric constant as a function of temperature and frequency for the 0.5 composition. 61 (T-Tf- k =k e 282 @.1) "■m ax * e km a x is the maximum in the dielectric constant, T0 is the Curie point and d is the Gaussian diffuseness. Smolensky [17] expanded the above equation as a power series and after neglecting the higher-order terms arrived at the power law relation as shown below, 1 1 n (r - r .) 2, < 3-2> k K«x 2«2 The above equation was modified by Uchino et al. [18] to give, M (3 ,) k *max 2 6 y is an empirical term and has a value of one for ideal Curie-Weiss behavior and a value of two for relaxor behavior. For other materials it falls between these two values. By plotting ln[(km /k)-l] as a function of ln[T-T0 ] it is possible to obtain the value of y. Using the value of y thus calculated in a plot of 1/k vs [T-TJ1 , it is possible to obtain the value of d. The values of d and y so obtained for different 62 compositions in the Pbx Ca1 .x TiC> 3 system are listed in Table 3.1. It is seen that the diffuseness parameter increases with increase in calcium content and is largest for the x=0.5 composition. A similar behavior is noted for the variation of y with composition, y has a value of 1.2 for the x=0.8 composition and gradually increases to 1.34 at the 50% composition. Below the 50% composition, both y and < 5 show a significant decrease in their values. Pb0 . 4Cao.6 Ti0 3 has y=0.6 and (5=1.5. A value below one for y has not been reported, but, since y is a purely empirical term such variations are not unusual. Diffuse phase transitions, in ceramics forming solid solutions, is attributed to statistical fluctuations in composition [17]. There are submicron regions in which the spontaneous polarization and composition are constant within each region but vary from one "microvolume" to the other [19]. The random or statistical fluctuations in composition becomes larger as the size of the microregion becomes smaller. These regions represent the size of the ferroelectric nucleus that is needed to transform to the ferroelectric state on cooling through the Curie point. Due to the dependence of the Curie temperature on composition, the microvolumes of differing composition have different local Curie temperatures. A Gaussian distribution of Curie temperatures of the microregions explains the diffuse phase transition observed. Ordering of atoms tend to minimize such fluctuations in compositions resulting in a sharp transition from the paraelectric to ferroelectric phase. Earlier studies on the lead scandium tantalate (PST) system have confirmed the effect of ordering on the paraelectric- 63 ferroelectric transition [20]. Ordered PST shows a sharp transition whereas, disordered PST has a broad ferroelectric-paraelectric phase transition. If a similar argument is extended for the Pbx Ca!.x T i0 3 system, then Pbo.5 Cao.5 T i0 3 should show the sharpest transition from the ferroelectric to the paraelectric phase because, ideal ordering in Pbx Cax .x T i0 3 should occur at the 0.5 composition. However, experimental studies reveal that Pbo.5 CaosT i0 3 shows the broadest transition.The ordering behavior reported earlier, therefore, does not sufficiently explain the paraelectric to ferroelectric transition observed in the Pbx Caj.x T i0 3 system. In the Pbx Ca!.x T i03 system no strain-induced domains are observed for x<0.6 compositions [10]. Therefore, when Pbo.5Ca0 .sTi03 is cooled through the Curie point, a polar axis develops along one of the original cubic axes and the crystal remains stressed in compression along the c axis and in tension along the a axis. For material under stress it has been observed that there is a broadening of the transition region. The dielectric constant as a function of temperature no longer shows a sharp transition but exhibits diffuse behavior when the material is stressed [21]. In the case of lead titanate, the c/a ratio is considerably high (1.06) so that preparation of polycrystalline samples is difficult as they disintegrate due to the high stresses involved during transition. With increasing additions of calcium titanate the c/a ratio, however, decreases. Therefore, the internal stresses are not very high to significantly account for the observed broadening of the transition region in Pbo.sCao.sTi03 and hence, is a result of compositional fluctuations. In perovskites of the type (A’ A")B03 or A(B’B")03 , large differences in the valence of the A’ and A" or B’ and B" atoms result in a very strong tendency for the material to order through electrostatic forces. The larger the difference in valence the higher the degree of ordering. In the case of PST, the difference in the valence of the B-site cations is 2, unlike Pbx Ca!.x T i03 where there is no difference in the valence of A-site cations. Therefore, there is a greater tendency for PST to order as compared to Pbx Ca!.x T i0 3 . The order parameter in Pbx Caj. x T i0 3 is believed to be small. The superlattice reflections were absent in X-ray data due to a high density of anti-phase boundaries, therefore, the order parameter could not be determined. If the order-disorder temperature is low, only localized or short range diffusion is allowed. In such a case, each Kanzig region orders but the chemical inhomogeneity remains and ordering is less than perfect. The ordering temperature in Pbx Caj.x T i0 3 was obtained by observing the disappearance of the 1/2{111} reflections and was determined to be 450° C for the x=0.6 composition. This is considerably lower than the ordering temperature of 1000° C observed in PST. Therefore, in Pbx Ca!.x T i0 3 , due to short range diffusion, each microregion orders but the chemical inhomogeneity remains resulting in a diffuse phase transition. In a macroscopic sense, Pbx Ca!.x T i0 3 forms a homogenous solid 65 solution however, in a microscopic sense, there exists a number of small ordered microregions having different lead or calcium concentration than the average resulting in a diffused phase transition. Maximum spread of these microvolumes occurs at 50% composition resulting in a relatively broader phase transition as we approach this composition. PST undergoes perfect ordering at 1000° C and therefore, undergoes a sharp phase transition on cooling through the Curie point. The diffuse phase transition can also be explained if there is no ordering of lead and calcium atoms contrary to the earlier reports. However, in the absence of ordering, the presence of 1/2^ 111} superlattice reflections in the <110> zone axis cannot be accounted for by pure atomic displacements. In addition, on heating the material to high temperatures the 1/2{110} and the 1/2{100} reflections disappear, whereas the 1/2{111} reflections are still present as listed in Table-3. At this temperature Pbx Cai.x T i0 3 has an ideal cubic crystal structure and therefore, atomic shuffles cannot account for the presence of the 1/2{111} reflections. Hence, ordering behavior of the type explained earlier is necessary to account for the presence of these reflections. However, the ordering is less than perfect and chemical inhomogeneity remains resulting in the broadening of the dielectric curves for the x=0.5 composition. 3.3 Mathematical Modelling The diffuse ness behavior in solid solutions is primarily attributed to compositional fluctuations on a microscopic scale. Each of these microregions 66 have a different composition and hence, different Curie points for the onset of ferroelectricity. A general feature of materials exhibiting diffuse phase transitions is the random occupation of ions of different types in crystallographically equivalent positions. Ordering of atoms tend to minimize such fluctuation in compositions resulting in a sharp transition from the paraelectric phase to the ferroelectric phase on cooling through the Curie point. A mathematical treatment on the effect of statistical fluctuations in composition on the diffuseness of the paraelectric-ferroelectric phase transition for a solid solution of two compounds with perovskite structure was reported by Smolensky [17]. However, most of the research work in this area has been qualitative in nature and no experimentally evaluated results have been reported. The size of the microregions regions is a critical parameter that controls the width of the transition range and is of paramount importance in ferroelectrics with diffuse phase transitions. In this study, a quantitative model to experimentally determine the size of the microfluctuations in compositions is presented. Consider a solid solution of the form AVVVx BOi j . The A-site atoms are located in a polyhedra with 12-fold coordination and the B-site atoms occupy the octahedral positions. In a microregion consisting of n molecules of A’B 0 3 and A"B03 the probability of finding m molecules of A’B 0 3 in the absence of ordering of any sort is given by, 67 Each of the events that occur within the microregion is independent and is not affected by the events in other microregions. For large n we can use the De Moivre-Laplace theorem [23] shown below to modify the above equation. We have, x m (1 xYn'm ) = ____ -_____e 2 (3*5) m\(n-m)\ v/2rc/u(1 -x) Where z is given by, tn-nx s s . Z = ■ (3.6) \/nx(1 -x) Therefore the probability, P(m) is given by, P ( m ) = . j A . . = e x p [- ] (3.7) \/2tc«jc(1 -x) ~x) The microscopic concentration, q, is given by q=m/n and £=q-x gives the amount by which the microscopic concentration differs from macroscopic concentration. From the above equation it is seen that the maxima in the probability curves 68 occurs at |= 0 , therefore, the value of £ at half the maximum value is given by, e x p [- ^ h ' - i (X8) Solving for £, we have x(1-x) ln4 (3.9) rt The negative value of £ in the above equation is neglected as the curve is symmetrical about the maxima. For small fluctuations in composition the change in the Curie point is assumed to vary linearly with concentration change. Therefore, £=f(T-T0 ) where, f is a proportionality constant, T is the Curie point of the microregion and T0 is the macroscopic Curie point. Statistically the number of microregions that have compositions close to the mean composition is a maximum. Hence, T0 represents the temperature at which maximum number of these microregions undergo a transformation into a ferroelectric phase. In other words, at TO J microregions corresponding to £=0 transform into the ferroelectric state from the paraelectric state. Therefore, the spread in the transition region (A) with respect to temperature for a curve centered at T0 is given by, 69 A = _1 jc(1 -x) ln4 = /N " (3.10) The above equations are valid for temperatures greater than the Curie temperature and A represents the width of the transition region above the Curie point and at half the maximum value of the dielectric constant at a given frequency. A typical plot of the dielectric constant versus temperature curve for a diffuse phase transition is shown in Fig. 3.17. The value of A is indicated on the curve. From the above equation it is possible to measure the size of the microregions by using the value of A calculated from the dielectric constant versus temperature curve for a particular composition and frequency. The value of f in such a case may be obtained by interpolating the Curie points of the given composition with the Curie points of the pure compositions. However, to minimize the errors involved, the following procedure is adopted. Experimentally calculated values of A are plotted as a function composition. The value of f is obtained from a plot of T0 as a function of x for a range of compositions as shown in Fig. 3.18. The value of f, thus calculated, is incorporated in equation 3.10 and the value of n varied to obtain a best fit with the experimentally calculated values of A. Curve fitting is done by plotting A2 as a function of composition to yield a 70 Dielectric Constant (k) Temperature (° C) Fig. 3.17. A typical plot of the dielectric constant versus temperature. The width at half maximum (A) is also shown. 71 Curie P o in t 50 0 y = +846x1 -351. var.691. max dev 42 9 400 300 200 100 25 75 50 1.00 Composition 'x) Fig. 3.18. Curie point as a function of composition in the Pbx Ca1 .x T i0 3 system. 72 parabolic curve as shown in Fig. 3.19. The value of n was found to 35. Assuming a cell size of approximately 64A3 , the size of the microregions is found to be approximately 15A. 3.4. Conclusions Dielectric and microstructural results in the Pbx Ca1 .x T i0 3 system are reported. At room temperature, Pbx Ca!.x T i0 3 is orthorhombic for x=0.1 and x=0.2 compositions, pseudocubic for x=0.3 and x=0.4 compositions and tetragonal for other compositions. Addition of calcium titanate to lead titanate is responsible for the observed ordering behavior in the Pbx Ca1 .x T i0 3 system. Hot stage microscopy combined with dielectric studies reveal that ordering of Pb and Ca atoms occur on alternate {111} planes for 0.3<x<0.61 compositions but, the ordering is less than perfect. Dielectric studies reveal that addition of calcium titanate to lead titanate broadens the transition region and lowers the Curie point. The diffuseness exponent y, has a value of 1.2 for x=0.8 and reaches a maximum value of 1.34 at x=0.5. Pb0 .4 Ca0 4 TiO3 has a Curie point below room temperature at 14° C. A mathematical model to quantitatively establish the size of microfluctuations in composition was developed and the size of such microregions was calculated to be approximately 15A. 73 2500 2000 n=3 Experimental 1000 500 0 5 4 6 7 .8 Composition (x) Fig. 3.19. Variation of A2 with composition for the Pbx Ca1 .x T i0 3 system. The value of n calculated theoretically is also indicated. 74 REFERENCES 1. E. Sawaguchi, T. Mitsuma and Z. Ishii, J. Phy. Soc. Jpn., 11, 1298 (1956). 2. E. Sawaguchi and M. L. Charters, J. Am. Cer. Soc., 42, 157 (1959). 3. Y. Yamashita, K. Yokoyama and H. Honda, Jpn. J. App. Phy., 20 (Suppl.), 183 (1981). 4. Y. Yamashita, S. Yoshida and T. Takahashi, Jpn. J. App. Phy., 22 (Suppl.), 40 (1983). 5. S. H. Chavan and U. N. Kulkarni, Ind. J. Pure and App. Phy., 23, 523 (1985). 6. T. Yamamoto, H. Igarashi and K. Okazaki, Cer. Intl., 11, 75 (1985). 7. T. Yamamoto, M. Saho, K. Okazaki and E. Goo, Jpn. J. App. Phy., 26 (Suppl. 2), 57 (1987). 8. A. Tsuzuki, H. Murakami, K. Kani, K. Watari and Y. Torii, J. Mat. Sci. Lett., 10, 125 (1991). 9. G. King, E. Goo, T. Yamamoto and K. Okazaki, J. Am. Cer. Soc., 71, 454 (1988). 10. G. King and E. Goo, J. Am. Cer. Soc., 73, 1534 (1990). 11. H. F. Kay and P. C. Bailey, Acta Cryst., 10, 219 (1957). 12. H. G. A. Koopmans, G. M. H. Van De Velde and P. C. Gellings, Acta Cryst., C39, 1329 (1983). 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). 75 15. B. F. Naylor and O. A. Cook, J. Am. Chem. Soc., 42, 68, 1003 (1946). 16. B. N. Rolov, Sov. Phy. Solid State, 6, 1676 (1965). 17. G. A Smolensky, J. Phy. Soc. Jpn., 28 (Suppl.), 26 (1970). 18. K. Uchino and S. Nomura, Ferroelectr. Lett., 44, 55 (1982). 19. W. Kanzig, Helv. Phy. Acta, 24, 175 (1951). 20. N. Setter and L. E. Cross, J. Mat. Sci., 15, 2478 (1980). 22. N. Setter and L. E. Cross, Phy. Stat. Solidi, 61, K71 (1980). 23. E. Kreyszig, Advanced Engineering Mathematics, Wiley Eastern Limited, New York (1972). 76 CHAPTER 4 STUDIES IN THE Pbx Sry Ba1 .x .y Ti03 SYSTEM 4.1 Introduction The dielectric and piezoelectric properties of barium titanate have been extensively studied for the past fifty years. Several modified forms of barium titanate have been used as ceramic dielectrics for high permittivity applications [1-5]. Pure barium titanate undergoes a paraelectric-ferroelectric phase transition at 120° C, which is accompanied by a sharp rise in the dielectric permitivitty (— 10,000). Additions such as strontium or lead are usually employed to raise or lower the Curie point for particular applications and to reduce the temperature dependence of the dielectric constant. Barium titanate and strontium titanate are known to form solid solutions with each other at all compositions because of their identical crystal structure and comparable ionic radii of Ba2 + and Sr2 + ions [6-7]. Variation of strontium titanate composition offers good control over many of the desired dielectric characteristics and therefore, has been extensively studied [8-10]. BaxSr^TiOs is ferroelectric at room temperature for the barium rich compositions and has a Curie temperature of -37° C for the x=0.5 composition. It has been the object of extensive research to find some composition where the dielectric peak would spread out with a reasonably constant high value over the working temperature range. Since, these 77 materials find potential application in devices where the working range is close to room temperature any additions that would increase the dielectric constant at room temperature and increase the diffuseness of the paraelectric-ferroelectric phase transition would be desirable. Lead titanate has a tetragonal crystal structure with a fairly high c/a ratio of 1.06 and is ferroelectric at room temperature. The transition to the ferroelectric tetragonal phase from the cubic paraelectric phase occurs at 490° C. Therefore, addition of PbTi03 to Ba0 . 5Sro.5Ti0 3 would change the dielectric constant at room temperature and at the same time increase the width of the paraelectric-ferroelectric transition region as statistically greater fluctuations in composition is possible. No prior work has been done in the (Pb,Ba,Sr)Ti03 ternary system and, therefore, it is of scientific and technological interest to examine its dielectric and microstructural behavior. The present work aims to study the microstructure of Pbx Ba0 . 5 .x Sr0 .sTiO3 and Pbx Sr0 j.x Ba0 .5 TiO3 through X-ray diffraction and transmission electron microscopy investigations and make correlations to the dielectric properties. A theoretical model to quantitatively estimate the size of microregions with compositional fluctuations that affect the ferroelectric-paraelectric transitions is also presented. 4.2 Studies in the Pbx Baas.x Sr0 - sTiO3 System 4.2.1 X-ray and Grain Size Measurements X-ray studies done at room temperature reveal that the material is cubic for x=0, 0.1 and 0.2 compositions and tetragonal for other compositions. The 78 Table 4.1. Properties of the PbxBaos.xSrosTiOs system. X Lattice Parameter (A) Crystal Structure Grain Size (/im) %p tand Ec (Kv/cm) Pr(ftC/cm2 ) 0.0 a =3.947 Cubic 4.3 98 0.07 - - 0.1 a=3.951 Cubic 4.3 96 0.10 - - 0.2 a=3.952 Cubic 4.4 98 0.07 - - 0.3 a=3.941 c=3.950 Tetragonal 4.2 98 0.06 1.96 0.57 0.4 a=3.932 c=3.953 Tetragonal 4.3 95 0.12 3.98 0.31 0.5 a=3.896 c=3.961 Tetragonal 4.1 91 0.10 7.00 0.70 %p gives the percentage theoretical density and tan<5 values are at room temperature and at 1 Khz. Ec and Pr are the coercive field and remnant polarization respectively. results are shown in Table 4.1. The x-ray scan for the Pb0 .,iBaftlSrojTiC)3 composition is shown in Fig. 4.1. The cubic structure was determined by the lack of peak splitting in the spectra. For the x=0 and 0.1 compositions additional Ka 2 peaks were seen at higher angles as shown in Fig.4.2. Co-existence of a ferroelectric tetragonal phase and a paraelectric cubic phase have been reported for the x=0.76 and 0.715 compositions in the Bax Sr1 .x T i03 system [8]. This is believed to be due to the preferential diffusion of Sr2 + ions into BaTi03 . In order to check if a similar behavior exists in the present system the (200) reflections from the x-ray scan were analyzed. In the event of co-existing phases, these reflections would consist of a doublet corresponding to the tetragonal symmetry and a singlet corresponding to the cubic symmetry. The line intensities are strong enough to allow any appreciable differences to be observed. Our analysis did not reveal the co-existence of two or more phases for any given composition. However, segregation of an amorphous phase or a secondary phase not observable in x-ray scans can be detected by electron microscopy techniques [11]. High resolution TEM studies were done to check for the presence of any grain boundary phase. Fig. 4.3. shows the high resolution TEM picture of a typical grain boundary region for the x=0.3 composition. The grain boundaries are devoid of any secondary phases. Similar microstructure was noted for other compositions as well. Therefore, it is concluded that Pbx Ba05 .x SrasTiO3 forms a solid solution in the entire composition range. COUNTS 3 ’ rrffVr p T 1 pp r y w r n' |~ H ri' i1 rp rr r1 1 rpn riT i T iT |iT M 1 1 ■ i ■ p prPT 1 1 < i' i ■ i ■ i 'jr 2 0 . 2 5 . 3 0 . 3 5 . 4 0 . 4 5 . 5 0 . 5 5 . 5 0 . 5 5 . 7 0 . 7 5 . 2 0 Fig. 4.1. XRD patterns for the Pbo.4BaaiSro.5Ti0 3 composition. 81 D - o > or © td w o -U » - ! p l/i H O u > O O 3 1 3 O O 3 00 N ) Intensity (Counts) ■ v } 4000 => Ka Ka Fig. 4.3. a) High resolution electron micrograph of a typical grain boundary region for the x=0.3 composition, b) The grain boundary at a lower magnification. 83 The grain size was measured using the intercept method specified by ASTM Standard E112 [12]. Fig. 4.4. shows the grain size and morphology for the Pb0 .3Bao.2Sro.sTi03 sample. The average grain size for different compositions studied is given in Table 4.1. No specific trend is noticed in the grain size with change in composition. 4.2.2 Dielectric Studies The dielectric constant (k) as a function of temperature was measured for various compositions in the Pbx Baos.x Sro.sT i03 ternary system and is shown in Fig. 4.5. A plot of the dielectric constant curves at different frequencies for the x=0.3 and 0.4 compositions is shown in Fig. 4.6. No shift is observed in the maxima of the dielectric curves at different frequencies indicating the absence of relaxor behavior in this system. However, for the x=0.4 composition it is seen that above the Curie point there is a spread in the k values at different frequencies. This is unusual because, ideally at frequencies below 107 hz. the total polarizability is a sum of the ionic, electronic and dipolar polarizabilities and all of them are active within the frequency range studied. The total polarizability, a, is expressed as a = a e+ a t+ a d (4-1) where, « e is the electronic polarizability, a j is the ionic polarizability and ad is the orientational or dipolar polarizability. a d is of importance in liquids and gases where the dipoles are free to rotate on the application of a field. The variation 84 Fig. 4.4. SEM micrograph showing the Pb0. 3Bao.2Sr0 5 Ti0 3 composition. Dielectric Constant Oielectric C onstant § 1.00x10* 2 o 0.75x10* S 9 2 050x10* O •80 -60 T em p e ratu re (C) 8000 6000 2000 •so 50 6000 4000 2000 0 • 1 0 0 0 too Tem perature (C) T em p eratu re (C) 1500 c < 8 < s > c o C J o ■ c T 5 9 1200 a > a 200 2500 2000 1500 150 200 •50 Tem perature (C) T em perature (C) Fig. 4.5. Dielectric constant as a function of temperature at lOOKHz. for a) x=0.0 b) x=0.1 c) x=0.2 d) x=0.3 and e) x=0.4 in the PbxBaos.^ro^TiC^ system. 86 4 0 0 0 3 5 0 0 a 3 0 0 0 m e o C J • 5 2 5 0 0 o o a 2000 1500 1000 200 100 -100 0 T e m p e r a tu r e (C ) 2 5 0 0 2000 c 1500 C O c O u o 1000 o a 50 0 150 200 50 100 0 T e m p e r a tu r e (C ) Fig. 4.6. Dielectric constant at different frequencies for a) Pb03Bao2Sro.5 T i0 3 composition and b) Pbo.4Ba01Sro.5 Ti0 3 composition. 87 of the total polarizability with frequency is shown in Fig. 4.7. As the frequency is increased a d shows a relaxation approximately at 10uHz. and a e and a -, show relaxation effects which lie in the infrared region of 101 6 Hz. and 101 3 Hz. respectively. Therefore, within the frequency range studied the k values should have nearly identical values at different frequencies unlike that observed for the x=0.4 composition. However, often in solid solutions space-charge polarization due to the poor insulating quality of the grain boundaries can lead to dielectric relaxation up to 106 Hz. This is a possible reason for the dielectric relaxation observed in the x=0.4 composition. The Curie point increases with increasing additions of lead as shown in Fig. 4.8. and the dielectric maxima decreases as the lead content increases. This is expected as PbTi03 has a higher Curie point and a lower dielectric maxima as compared to BaTi03 . For the x=0.2 composition the paraelectric-ferroelectric transition occurs at 14.5 °C and has a room temperature dielectric constant of approximately 5000. For the x>0.2 compositions the material is ferroelectric at room temperature. Hysteresis measurements at room temperature confirm the ferroelectric nature of these compositions. A typical hysteresis loop for the x=0.4 composition is shown in Fig. 4.9. and the coercive field and remnant polarization for the compositions studied are listed in Table 4.1. The dielectric constant, k, as a function of temperature can be written as [13] 88 Total polarizability (real part) UHFto microwaves Ultra violet Infrared " T ------- X a e le c tro n ic Frequency Fig. 4.7. Frequency dependence of the several contributions to the polarizability. 89 150 100 50 0 0 .2 .3 4 5 Composition (x) Fig. 4.8. Curie point as a function of composition for the Pbx Ba0 .5 .x Sro.5Ti03 system. 90 1 1 1 1 X X X Fig. 4.9. Hysteresis loop for the Pb0 .4 Ba0 1Sr0 5 TiO 3 composition. where km a x is the maximum in the dielectric constant, T0 is the Curie point and d is the diffuseness parameter, y is an empirical term having a value of one for ideal Curie-Weiss behavior and between one and two for diffuse behavior. A plot of y and d as a function of composition for the Pbx Bao.5.x Sr0 5Ti0 3 system is shown in Fig. 4.10. Except for the 0.1 composition, both y and d increase with increasing lead content. The higher y value for the 0.1 composition may be a result of processing inhomogeneity. 4.2.3 TEM Analysis Selected area electron diffraction patterns from the three principal zone axes for the PbxBaoj.xSrosTiC^ system are shown in Fig. 4.11. Electron diffraction studies did not reveal the presence of any secondary phases confirming that Pbx Bao.5 .x Sro5 Ti0 3 forms a complete solid solution in the composition range studied. Presence of transformation domains was evidenced for the x=0.3, 0.4 and 0.5 compositions as shown in Fig. 4.12. These are 90° ferroelectric domains where the direction of the polar axis remains unchanged within each domain but is rotated 90° from domain to domain. The polarization vector assumes a "head-tail" arrangement to maintain charge neutrality at the domain wall. A schematic of the 0.0 O .t 0 2 0.3 0.1 X Fig. 4.10. Variation of a) y and b) < 3 as a function of composition for the PbxBaoj. x Sr0 5 TiO3 system. 93 a . " T . u m • ' © 'S V c D 'O 'o X o y o ) Fig. 4.11. Electron diffraction patterns from a) [111] b) [110] and c) [100] zone axes for the Pbx Ba0 5_ x Sr0 5TiO3 system. 94 Fig.4.12. Bright field image showing the presence of ferroelectric domains along the (001) planes for the x=0.3 composition. 95 domain wall arrangement is shown in Fig. 4.13. The transformation domains are formed when the cubic paraelectric phase transforms to the tetragonal ferroelectric phase. The domain boundaries are planar and lie on well defined crystallographic planes. In the Pbx Ba0 .s.x Sro.5Ti03 system the domain boundaries lie along the {011} planes. Electron diffraction patterns from a region consisting of 90° domains for the x=0.3 composition is shown in Fig. 4.14. No spot splitting was seen even for higher index planes. In the case of Pbo.3 Bao.2 Sro.5Ti03 the c/a ratio is 1.005 and therefore, it is difficult to see the effect of 90° rotation in the diffraction patterns. High resolution TEM studies were done to observe if any difference in the arrangement of the atoms were visible across the domain boundaries. No perceptible difference in the arrangement of the atoms was noticed as shown in Fig. 4.15. even though the 90° domains were visible at low magnifications. This is not unusual as there is only a 0.5% difference between the a and c values making it difficult to observe the change in the high resolution image or observe the spot splitting in the diffraction patterns. The effect of the c/a ratio on the atom positions across the twin domain is shown in Fig. 4.13. 4.3 Studies in the Pbx Sras.x BaasTi03 System The earlier studies have been focussed on analyzing the properties of the (Pb,Ba,Sr)Ti03 system with the SrTi03 composition fixed at 0.5. In this section analysis of microstructural and dielectric properties in the Pbx Sr0.5.x Bao.5 T i 0 3 system is presented. 96 b Fig. 4.13. A schematic diagram of the domain wall arrangement for a) 10% difference in the c and a values and b) less than 0.5% difference in the c and a values. 97 fltl'D •* Fig. 4.14. Electron diffraction pattern from the [111] zone axis showing the absence of spot splitting. 98 %*«*%<*♦%** %• •* « % « •« * » « •% * /% 4.2 s r ~ r - '° ,att/ce ’.? * ? U U r'dary £ T ‘ng awoss :: ‘•,e« ron . __________ *S “ "ifcdX r" = appro e an^ ° Perce 'Ktiiah Ptibfe varjati ‘ * * * * $ £ 4.3.1 X-ray and Grain Size Measurements X-ray studies reveal that Pbx Sr0j.x Ba0 .sTiO3 is cubic for the x=0.1 composition and tetragonal for the other compositions. X-ray scans at room temperature for this system are shown in Fig. 4.16. It is clearly seen that the (200) peaks split as the lead content increases indicating an increase in the c/a ratio. This trend is expected as PbTi03 has a tetragonal structure with high c/a ratio and SrTi03 is cubic at room temperature. The results are shown in Table 4.2. Analysis of the (200) peaks reveal that there are no secondary phases present in this system. Therefore, it is concluded that the PbxSrosJBaosTiO;, system forms a solid solution in the entire composition range. Grain size measurements on this system did not reveal any specific trend with change in composition. The average grain size for the different compositions studied are listed in Table 4.2. 4.3.2. TEM Studies Electron diffraction studies did not reveal the presence of any secondary phases confirming that Pbx Sr0 . 5 .x Ba0 .sTiO3 forms a complete solid solution in the composition range studied. The electron diffraction patterns from the [100], [110] and the [111] zone axes were similar to the electron diffraction patterns obtained for the Pbx Ba0s.x Sra5TiO3 system as shown in Fig. 4.11. Presence of 90° ferroelectric domains oriented along the (011) planes were evidenced for the x=0.2, 0.3 0.4 and 0.5 compositions. Fig. 4.17 shows the presence of transformation domains in the x=0.3 composition. 100 COUNTS 0.4 z e . o a ct I ■ . W i,h t p :o a ^ x = 0.3 ,A \ ' T Liw* . ' _ r x = 0.2 , ? 1 0 A .A ( • - > • - F * a . € » - * a n T ?.0 3 » ^ x = 0.1 ^ r \ z,c/ Fig. 4.16. X-ray scans for different compositions in the Pbx Sro.5 .x Bao.5Ti0 3 system. The arrows indicate the (200) peaks. 101 Table 4.2 Properties of the Pbx Sr05.x Bao.5Ti03 system. X a (A) c (A) T0 (°C) %p Grain Size (mdi) Ec (Kv/cm) Pr (uC/cm2 ) 0.1 3.93 3.93 -8 97 4.25 - - 0.2 3.95 3.98 101 99 4.20 6.3 0.9 0.3 3.96 4.01 171 97 4.10 20 5.0 0.4 3.96 4.04 250 97 4.11 29 0.8 102 Fig. 4.17. Bright field image showing the presence of 90° ferroelectric domains in the Pb0 3 Sro.2 Ba0sTi0 3 composition. 103 4.3.3 Dielectric Measurements The dielectric constant versus temperature curves at lKHz. for the Pb^ro j. x Ba0 .sTiO3 system are shown in Fig. 4.18. It is seen that addition of PbTi03 increases the Curie point and decreases the dielectric maxima. This expected as PbTi03 has a higher Curie point (490° C) and a lower dielectric maxima (1000) as compared to Ba0 .sSr0 S TiO3 . A plot of the dielectric constant at different frequencies for the x=0.2 composition is shown in Fig. 4.19. The dielectric curves peak at the same temperature for all the frequencies studied indicating the absence of relaxor behavior. However as in the Pbx Bao.5.*Sro.5Ti03 system, there is a slight spread in the dielectric curves at temperatures above the Curie point. As mentioned earlier this is believed to be due to the space charge polarization which occurs as a result of poor insulating quality of the grain boundaries. Hysteresis measurements at room temperature confirm the ferroelectric nature of the x>0.2 compositions. A typical hysteresis loop for the x=0.3 composition is shown in Fig. 4.20. The results are tabulated in Table 4.2. 4.4. Mathematical Modelling of Microfluctuations in Composition A mathematical treatment on the effect of compositional fluctuations on the diffuseness of the paraelectric-ferroelectric phase transition for a solid solution of two compounds with perovskite structure was reported by Smolensky [14]. Attempts to extrapolate these results to different binary systems have been made, however, no report exists on analyzing the diffuseness behavior for the ternary 104 601*0 2000 0 •100 0 0 50 0 100 150 200 0 ') to o 0 200 300 100 Fig. 4.18. Dielectric constant as a function of temperature at lOKHz. for a) x=0.1 b) x=0.2 c) x=0.3 and d) x=.4 in the Pbx Sr0 .5 .x Bao.5Ti03 system. 105 Dielectric Constant 6000 5 0 0 0 — 4 0 0 0 — 3 0 0 0 — 2 0 0 0 — 1000 — 0 L 0 a) 120 Hz. b) 1 KHz. c) 10 KHz. d) 100 Khz. X. a 5 0 10 0 15 0 2 0 0 Tem perature (C) Fig. 4.19. Dielectric constant at different frequencies for the Pb0. 2Sro.3Bao.5Ti0 3 composition. , . , — 1 • T r .,— - Ec=29 KV/cm : - Pr= 0.8^ C/cm2 o . : i i * i ' » •" 1 ’ T - ' l 1 • y . i . i . i . i . i— ... i . i . i . i . E . 1 . 1 ^— 1 — ■ — t- - L .. . . 1 . —1 ---- _ i. .. . 1 . Fig. 4.20. Hysteresis loop at room temperature for the Pb0 .4 Sro.1 Bao.5Ti03 composition. 107 systems. A mathematical model for analyzing the effect of microfluctuations in composition on the ferroelectric-paraelectric transitions for a binary system was explained in the earlier chapter. An attempt to extend the analysis to a ternary system is presented here. In the binary case the probability distribution was directly related to the De Moivre-Laplace theorem as given in equations 3.4 and 3.5. In the ternary case, introduction of another variable complicates the probability distribution function and therefore, necessitates certain approximations to be made to arrive at the desired result. Consider a ternary system of the type Ax By C1 .x ^,Ti03 . The macroscopic compositions of A, B and C are therefore, x, y and 1-x-y respectively. In a microvolume containing a total of N molecules of (A,B,C)Ti03 , the probability, P(m,n), of finding m molecules of A Ti03 and n molecules of BTi03 is given by, P(m,n) = — - x "y "(1 -x-y)®-*-* (4.3) /7 J l« I(iv — m— /z )I Where N!=N(N-l)(N-2)....3.2.1. Using Stirling’s approximation for large N we have N\ = V ^ J V )(-)" (4-4) e 108 Using this approximation in the earlier equation we have 2ny/nm(N-m-n)n "m (4.5) If a = m/N and /?=n/N represent the composition of the microvolume we have If a-x=d1 and p-y=d2 , then < 5 j and d2 represent the deviations of the microscopic composition from the macroscopic composition. For a given N we can plot P(m,n) as function of these deviations to identify how the diffuseness varies with fluctuations in composition for a ternary system. Plots of P(m,n) as a function of < ? ! and d2 for a given N for the Ax B0. 5 .x Co5Ti0 3 system are shown in Fig. 4.21. It is seen that the diffuseness is maximum for the x=0.25 composition and the curves are symmetric about < 5 12=0. These plots are similar to plots obtained for the binary systems [14]. In order to correlate the diffuseness seen in P(m,n) with the diffuseness of the dielectric curves it is necessary to obtain the width at half maximum (WHM) from the above equations. It is clearly seen from Fig. 4.21. that P(m,n) is maximum when both c 5 j and d2 are zero. Therefore, substituting a=x and j3=y in equation 4.6 we have (4.6) 2 ir iV V a P (1 -a -p )a J V “ Pwp(1 - a - p ) w(1- “- p> P{m,n) = (4.7) 2TiAVaP(1-a-P) 109 Fig. 4.21. P(m,n) as a function of dj and d2 for a) x=0.1, 0.4 b) x=0.2, 0.3 and c) x=0.25 in the Ax B05.x C0 5 TiO3 system. A value of 500 was used for N for each of these plots. 110 Therefore the value at half maximum is given by T max (m ,n ) = ^ (4 -8) 2 4TclV^aP(1 - a - P ) Substituting this in equation 4.6 we have x N«y W { U x _y)N(Ua-fi) _ ± a VapA/p(i _ a _p)M 1-a-p) " 2 For small fluctuations in composition we assume that the Curie point varies linearly with composition. Therefore, for a < 5 x or a < 5 y change in composition, the macroscopic Curie point, T0 , of the ternary Ax By C1 .x ^Ti03 is given by T0= Ta x+ Tb y+ Tc ( 1 -x-y), where, Ta , Tb and Tc are the Curie points of A Ti03 , BTi03 and CTi03 respectively. This equation generates a plane in three dimensional space as shown in Fig. 4.22. and the condition x + y < l generates a prism within this space. The gradient of T0 (VT0 ) is given by V r c = i Z k f + - H k j ( 4. 10) dx dy where i and j are the unit vectors along the x and y directions respectively. Mathematically, dTJdx and dTJdy represent the change in the value of Tc as we change x and y respectively by small amounts. As in the binary case if we have a- 111 Fig. 4.22. A plot of the Curie point for different compositions for a ternary system. The condition x+y<l is contained within the plane. 112 x=f(T-T0 ) and j3-y=g(T-TQ ), where f and g are proportionality constants, then lli=STYJdx and l/g=dTJdy [15]. If T-T0=A then, a-x=A/(dTJdx) and /9- y-A/(dTJdy). If we substitute these values in equation 4.9 then, A represents the width at half maximum with respect to T and is experimentally obtained from the dielectric constant versus temperature curves. Using the experimentally calculated value of A in equation 4.9, we can obtain the value of N and hence, the size of the microregions. Using Ta, Tb and Tc as 490°C, 120° C and -265° C respectively and a cell volume of 64A3 , the size of the microregions for the Pbx Bao.s-xSr0 . 5Ti0 3 system was estimated to lie in the range of 15-30A and in the range of 10-20A for the Pbx Sr0. 5 .,( Bao.5Ti0 3 system. It should be noted that the above treatment does not include the effect of internal stress on the spread of the transition region. The model also assumes perfect processing to allow perfect statistical mixing which may not be true in practice. However, the significance of the model is that it enables quantitative estimation of the microregions which is very important in the analysis of the diffuse nature of the ferroelectric-paraelectric phase transitions. 4.5. Conclusions Microstructure and dielectric studies in the Pbx Ba0 S .x Sr0 5TiO3 and the Pbx Sr0 . 5 .x Ba0 5 TiO3 system have been analyzed. Studies reveal that Pbx Ba05. x Sr0 .sTiO3 forms a solid solution in the entire composition range and is cubic for the x=0, 0.1 and 0.2 composition and tetragonal for the other compositions studied. Pbx Sr05.x Ba0 5 TiO3 also forms a solid solution and is cubic for the x=0.1 113 composition and tetragonal for x>0.1 compositions. The c/a ratio increases with increasing lead content for both the systems studied. Dielectric studies reveal that Pbx Ba0 .s-x S ro . 5Ti0 3 js ferroelectric for the x>0.2 compositions and has a broad paraelectric-ferroelectric transition region. Pbx Sro.s.x Bao.5Ti0 3 is ferroelectric at room temperature for the x>0.2 compositions. No shift in the dielectric maxima with frequency was observed for both the systems. However, a spread in the k values as function of frequency was observed. A mathematical model to quantitatively estimate the size of the microregions for a ternary system is presented and the size was determined to lie in the range of 15-30A for the PbxBao.s.xSro.sTiOa system and in the range of 10-20A for the Pbx Sr0 . 5 .x Bao.5Ti0 3 system. TEM studies revealed the presence of transformation twins lying along the {011} planes for both systems studied. REFERENCES 1. V. C. Sanvordenker, J. Am. Cer. Soc., 50, 261 (1967). 2. T. Nomura and T. Yamaguchi, Am. Cer. Soc. Bull., 59, 453 (1980). 3. W. Y. Howng and C. McCutcheon, Am. Cer. Soc. Bull., 62, 231 (1983). 4. N. M. Molokhia, M. A Issa and N. A Nasser, J. Am. Cer. Soc., 67, 289 (1984). 5. U. Syamaprasad, R. K. Galgali and B. C. Mohanty, J. Am. Cer. Soc., 70, C147 (1987). 6. D. Kolar, M. Trotelj and Z. Stadler, J. Am. Cer. Soc., 65, 470 (1982). 114 7. A. Basmajian and R. S. de Vries, J. Am. Cer. Soc., 40, 373 (1957). 8. D. Barb, E. Barbulescu and A. Barbulescu, Phys. Stat. Solidi A, 74, 79 (1982). 9. E. N. Bunting, G. R. Shelton and A. S. Creamer, J. Res. Natl. Bur. Std., 38, 337 (1947). 10. L. Benguigui and K. Bethe, J. App. Phy., 47, 2787 (1976). 11. D. R. Clarke and G. Thomas, J. Am. Cer. Soc., 60 491 (1977). 12. 1985 Annual Book of ASTM Standards, ASTM, 117 (1985). 13. K. Uchino and S. Nomura, Ferrolect. Lett., 44, 55 (1982). 14. G. A. Smolensky, J. Phy. Soc. Jpn., 28 (Suppl.), 26 (1970). 15. B. N. Rolov, Sov. Phy-Solid-State, 6, 1676 (1965). 115 CHAPTER 5 CONCLUSIONS AND FUTURE WORK 5.1 Summary The dielectric properties and microstructural data for the Pbx Ca 1.) f Ti0 3 and Pbx Bay Sr1 .x . y T i0 3 systems are reported. X-ray studies on Pbx Ca!.x T i0 3 reveal that this system is orthorhombic for the 0.1 and 0.2 compositions, pseudocubic for the 0.3 and 0.4 compositions and tetragonal for the x>0.4 compositions. Presence of 1/2{100}, 1/2{110} and 1/2{111} superlattice reflections were detected for the x<0.61 compositions. However, dielectric analysis combined with hot stage TEM studies reveal that ordering of Pb and Ca atoms occur on alternate {111} planes only for the 0.3<x<0.61 compositions. The 0.1 and 0.2 compositions are orthorhombic with atomic displacements similar to pure CaTi03 . A mathematical analysis to quantitatively determine the size of microfluctuations in composition was developed and the size of such microregions was found to be 15A for the Pbx Ca1 .x T i0 3 system. In the Pbx Bay Sr1 .x . y T i0 3 system, studies were conducted for the Pbx Ba05. x Sr0 .sTiO3 and the Pbx Sr0 .j.x Ba0 .jTiO3 compositions. X-ray and TEM studies reveal that both Pbx Ba0 5 _ x Sr0 .sTiO3 and Pbx Sr0 . 5.x Ba0 .5 TiO3 form a solid solution in the entire composition range. Pbx Ba0 .s.xSra5TiO3 is cubic for the x<0.2 compositions and tetragonal for the other compositions. Pbx Sr0 .5 .x Bao.5 T i03 is cubic for the x<0.1 116 compositions and tetragonal for the other compositions. Dielectric studies did not reveal any relaxor behavior in these systems, however, addition of PbTi03 to Ba0 . 5Sro.sTi0 3 is found to broaden the width of the ferroelectric-paraelectric transition region. The ferroelectric nature of the compositions studied were confirmed by hysteresis measurements; As in the binary case, a mathematical model to experimentally determine the size of microfluctuations in compositions was presented. The size of the microregions was determined to be between 15- 30A for Pbx Ba0 .s.,< Sro.5Ti03 and between 10-20A for the Pbx Sr05.x Bao.5 T i0 3 system. TEM studies did not reveal any superlattice reflections, thereby corroborating the evidence that CaTi03 is responsible for the ordering behavior observed in these systems. Presence of transformation twins oriented along the {011} planes were observed for both the ternary systems studied. 5.2 Future Work The processing procedure in the present study consisted of slow speed ball milling of stoichiometric powders. However, the limitation of this type of processing is that long ball milling times are necessary to obtain good statistical mixing. High speed milling combined with specialized dispersion techniques are often employed these days to avoid processing inhomogeneities and reduce the time involved. A similar procedure needs to be adopted for future processing of the refractory oxides. The exact amount of atomic displacements that give rise to the 117 orthorhombic structure and the space group for the Pbx Ca1 .x T i0 3 system are still unclear. In order to determine the magnitude of the atomic displacements and hence the space group, it is necessary to find out the relative intensities of the superlattice peaks. Since these peaks are absent in x-ray scans it is a difficult task to find out the nature of the atomic displacements. Neutron diffraction studies similar to those done on CaTi03 and C aZ r03 [1] may be a possible solution to find out the relative intensities of the superlattice peaks. Recently the atomic displacements in the Pbx Ca1 .x Z r0 3 system was calculated using the X-ray powder Rietvelt analysis [2]. A similar study could be extended for the Pbx Ca1 .x T i03 system to determine its space group. Also, as mentioned in chapter-1 thin film perovskites are becoming increasingly important as compared to the bulk materials, and therefore, it would be of scientific and technological interest to examine the dielectric and microstructural properties of Pbx Ca!.x T i0 3 thin films. The first step in this direction has been already made by Yamaka et al. who have studied the ferroelectric and pyroelectric properties of c-axis oriented Pbx Cai.x T i03 thin films grown by rf magnetron sputtering [3]. The future of thin film Pbx Caj. x T i0 3 appears promising. Sawaguchi and Charters [4] have reported that the polar anisotropy in Pbo.5C a0.5 T i 0 3 is due to time dependent phase separation. However, our studies did not reveal any secondary phases in these compositions. Long term annealing at high temperatures followed by quenching and immediate T E M studies would 118 help in identifying the presence of any time dependent phase separations. The studies on the Pbx Bay Sr1.x .y Ti0 3 system have been focussed only on few compositions, and therefore, it is necessary to extend the analysis to other compositions as well to fully understand the dielectric and microstructural behavior in these systems. Dopant additions such as manganese help in reducing the dielectric loss, and therefore, should be incorporated in the compositions studied. REFERENCES 1. H. J. A. Koopmans, G. M. H. van de Velde and P. J. Gellings, Acta. Cryst., 39, 1323 (1983). 2. J. Kato, M. Fuji, H. Kagata and K. Nishimoto, Jpn. J. App. Phy., 32, 4356 (1993). 3. E. Yamaka, H. Watanabe, H. Kimura, H. Kanaya and H. Ohkuma, J. Vac. Sci. Tech. A, 6, 2921 (1988). 4. E. Sawaguchi and M. L. Charters, J. Am. Cer. Soc., 42, 157 (1959). 119

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Creator Ganesh, Ramaratnam (author)

Core Title Ferroelectric-Paraelectric Phase Transitions In The Lead(X) Calcium(1-X) Titanium Trioxide And The Lead(X) Barium(Y) Strontium(1-X-Y) Titanium Oxide Perovskite Systems

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Advisor Goo, Edward (committee chair), Mansfeld, Florian (committee member), Sammis, Charles G. (committee member)

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