Polar Dielectrics and Their Applications [Reprint 2019 ed.] 9780520315334

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P O L A R DIELECTRICS A N D THEIR A P P L I C A T I O N S

POLAR DIELECTRICS AND THEIR APPLICATIONS JACK C. BURFOOT and GEORGE W. TAYLOR

University of California Press Berkeley and Los Angeles

University of California Press Berkeley and Los Angeles, California ISBN:

0-520-03749-9

Library of Congress Catalog Card Number:

78-62835

Copyright © 1979 by Jack C. Burfoot and George W. Taylor Printed in Great Britain

Contents

Acknowledgements

¡x

1 INTRODUCTION PART 1: BASIC PROPERTIES 2 PREPARATION OF POLAR MATERIALS 2.1 2.2 2.3 2.4 2.5

Growth of Single Crystals Ceramic Fabrication Thin Film Fabrication Fabrication of Polar Glasses Post-fabrication Procedures

1 11 13 15 20 23 27 29

3 ELECTRICAL AND RELATED PROPERTIES 3.1 Small Signal Electrical Properties 3.2 Large Signal Electrical Properties 3.3 Conductivity EfTects

34 34 37 50

4 OPTICAL AND RELATED PROPERTIES 4.1 Refractive Index and Birefringence 4.2 Optical Dispersion

54 54 57

vi

4.3 4.4 4.5 4.6 4.7 4.8 4.9 4.10

CONTENTS

Thermo-optic Behaviour Elasto-optic Effect Electro-optic Characteristics Non-linear Optical Effects Photo-refractive Effect Light Scattering Effects Absorption Photoluminescence, Electroluminescence and Luminescence

5 MECHANICAL PROPERTIES 5.1 Introduction 5.2 Elasticities and Piezoelectric Coefficients 5.3 Measurement 5.4 Mechanisms of Mechanical Loss 5.5 Effects of Applying Mechanical Stress 5.6 Mechanical Properties of Improper and Ferroelastic Materials 5.7 Surface Waves 5.8 Effects of the Composition Variable

58 59 59 62 64 66 66 67 70 70 72 79 84 87 92 93 94

6 THERMAL PROPERTIES 6.1 Introduction 6.2 Thermal Parameters 6.3 Thermal-Electrical Parameters 6.4 Thermal-Mechanical Parameters

100 100 102 108 110

7 THE TRANSITION 7.1 Anomalies and the Classical Model 7.2 Transitions 7.3 The Lattice Vibration Viewpoint 7.4 Antiferroelectrics 7.5 Nomenclature 7.6 Non-linearity

116 116 124 128 134 142 145

8 SYMMETRY 8.1 Symmetry Groups 8.2 Symmetry of Materials 8.3 Symmetry of Sites 8.4 Magnetic Symmetries

153 153 156 162 162

9 FERROELECTRIC MATERIALS 9.1 Selection of Data 9.2 Transition and Space Groups

165 165 166

CONTENTS

Vii

10 SPECTROSCOPY 10.1 Introduction 10.2 Characterisation of Spectra 10.3 Spectroscopy 10.4 Interpretation of Spectra 10.5 Fluctuations 10.6 Central Peak, and Other Aspects of Fluctuations 10.7 Appendix

171 171 172 175 179 183 184 188

11 MODES O F LATTICE VIBRATION 11.1 Dielectric Parameters 11.2 Lattice Vibrations 11.3 Anharmonicity 11.4 Improper Ferroelectrics 11.5 Order-Disorder and Pseudospin Mechanisms

192 192 200 204 211 215

12 DOMAINS AND SWITCHING 12.1 Introduction 12.2 Methods of Observing Domains 12.3 The Depolarisation Problem 12.4 Depolarisation in Static Domains 12.5 Static Domain Wall Structure 12.6 Static Domain Configurations 12.7 Dynamics of Domain Movements 12.8 Ideal Insulator Characteristics 12.9 Wall Velocity 12.10 Physical Properties and Wall Effects 12.11 Compensation 12.12 Surface Effects

227 227 229 231 236 238 239 241 244 246 248 248 249

PART II:

APPLICATIONS

255

13 APPLICATIONS—SOME BASIC CONSIDERATIONS 13.1 Introduction 13.2 Memories and Displays 13.3 Methods of Addressing 13.4 Basic Limitation of Polar Materials

257 257 261 268 280

14 APPLICATIONS INVOLVING S W I T C H I N G — S I M P L E OPERATION 14.1 Matrix Addressed Memory 14.2 Shift Register 14.3 Transcharger 14.4 Devices Based on Self Reversal Effect

288 289 290 291 293

viii

CONTENTS

15 APPLICATIONS INVOLVING SWITCHING—COMPLEX OPERATION 15.1 Ferroelectric-Piezoelectric Devices 15.2 Ferroelectric-Optic Devices 15.3 TANDEL

296 296 302 326

16 APPLICATIONS INVOLVING SWITCHING — COMPLEX STRUCTURE 16.1 Ferroelectric-Electroluminescent Devices 16.2 Ferroelectric-Photoconductor Devices 16.3 Ferroelectric-Semiconductor Devices

336 336 341 351

17 NON-SWITCHING APPLICATIONS 17.1 Capacitors 17.2 PTC Thermistors 17.3 Artificial Gems 17.4 Electro-optic Applications 17.5 Non-linear Optic Applications 17.6 Photo-refractive Applications 17.7 Pyroelectric Applications 17.8 Piezoelectric Applications 17.9 Elasto-optic Applications

359 360 363 365 366 373 377 381 386 397

18 LIQUID CRYSTALS 18.1 Materials 18.2 Electro-optic Effects 18.3 Electro-optic Applications

403 403 407 411

18.4 Thermo-optic Effects and Applications

427

Bibliography

431

Author Index Subject Index

435 444

Acknowledgements

We have sought the permissions of authors and publishers to use their diagrams or data. We trust that we have made due and full acknowledgement, and we apologise for any accidental omissions. The acknowledgement is usually in the form of a reference number, directing attention to the references at the end of the chapter. We would like to express our thanks to a number of colleagues, rather too numerous to name, for their critical improvements; to C. E. Land and A. Miller for their patient reading and reviewing; to R. V. Latham for a reading of the whole manuscript; to R. V. Peacock for help with the diagrams; and to our families for their patience and help.

Introduction

Dielectric materials can be divided into 32 crystal classes or point groups. In all of these classes a polarisation or dipole moment can be induced by a n applied electric field. Twenty of the 32 classes are piezoelectric and they have the property that a polarisation can also be induced by an applied mechanical stress. Half of the piezoelectric classes of materials, i.e. ten of the original dielectric classes, exhibit the very important property that a finite and permanent value of polarisation, known as spontaneous polarisation, exists in the absence of an applied electric field or stress. Such dielectrics are termed polar materials and are the principal subject matter of this book. The spontaneous polarisation of a polar material results from an inherent asymmetry within the basic crystal cell. This asymmetry gives rise to ionic a n d / o r electronic forces that create elemental dipole moments. Because of cooperative effects the dipole moments add to give a finite and permanent polarisation. The spontaneous polarisation of a polar material cannot be measured directly with an electrometer, since charge compensation rapidly occurs within the crystal. For the same reason, the short circuiting together of electrodes on opposite surfaces of a polar material does not destroy the spontaneous polarisation. By comparison, in non-polar dielectric materials, the induced polarisation can be measured with an electrometer and can be destroyed by shorting the surface electrodes. A classical method of detecting spontaneous polarisation is to subject the

2

INTRODUCTION

polar material to a change in temperature. An increase or decrease in temperature alters the ionic and electronic forces within the basic crystal cell, and the extent of thermal disorganisation, which results in a change in the values of the dipole moments of the polar material. If the change in temperature is fast enough, then there is not time for charge compensation of the dipoles to occur. The net result is that a detectable current, termed the pyroelectric current, will flow out of electrodes placed on opposite surfaces of a polar material. Since all polar materials can, in theory, exhibit pyroelectricity, the adjectives polar and pyroelectric have been used synonymously by some authors. In practice, pyroelectric effects have only been measured in about a hundred out of a multitude of polar materials. The probable reason for this is the difficulties of measurement together with the lack of interest, until recently, in the pyroelectric effect. The pyroelectric coefficients of the materials that have been measured vary greatly in magnitude 1 . They range from 17 000/iC m - 2 K " 1 for barium titanate, BaTi0 3 , near its transition 1 temperature down to 0 002 /iC m~ 2 for animal bone. As we have seen, a polar material is a dielectric material which possesses a spontaneous polarisation. In certain polar materials, the direction of the spontaneous polarisation can be changed by a suitably applied electric field, subsequently removed. In most of these materials the change is a 180° reversal of the direction of the polar axis, but in some materials the polar axis is reoriented by less than 180°.2 Polar materials whose direction of spontaneous polarisation can be changed by an applied electric field are known as ferroelectrics or occasionally as Seignette-electrics. The term ferroelectric is derived from the analogy with ferromagnetic materials in that both types of materials possess domains, exhibit hysteresis loops and show Curie-Weiss behaviour near their phase transition temperatures. The hysteresis loop of a ferroelectric is obtained by plotting polarisation (P) against applied electric field (£), while in a ferromagnetic it is achieved by plotting magnetisation (B) against the applied magnetic field (//). The term Seignette-electric is derived from the name of the chemist who originally prepared Rochelle salt in the 17th century. This material was subsequently identified by Valasek 3 in 1921 as possessing a field reversible spontaneous polarisation. The study of the general classification of polar materials stretches back into antiquity 1 with the detailed qualitative work commencing in the 18th Century 4 . While the study of the ferroelectric subgroup of polar materials began just over 50 years ago with Valasek's work on Rochelle salt, it has since then grown at an exponential rate. This is shown in figure 1.1, which gives the number of papers on ferroelectricity published each year. Other manifestations of this growth are the holding every three or four years of an international t Strictly speaking, a ferroelectric hysteresis loop is a plot of dielectric displacement (D) versus P where D = P + t0E. In practice, for most ferroelectric materials, the product of t 0 , the permittivite of free space, and £ is very much smaller than P; hence D is essentially equal to P.

3

INTRODUCTION

Y

Figure 1.1 Number of research papers, N, on ferroelectrics and antiferroelectrics published in each year. The dashed line corresponds to N = exp{0.14

1921)}

Y is the year. Books on ferroelectrics published in each year are also shown. The one marked with asterisks represent a version translated into another language (from Ref. 11, Vol. 9) meeting 5 , a regional European meeting 6 , an IEEE Applications Conference 7 and national meetings in the USSR 8 and other countries 9 . There is an international journal Ferroelectrics10 devoted to the subject, the publication of which has increased from, initially one volume per year in 1970, to three volumes per year in 1976. Almost 700 ferroelectric pure compounds and solid solutions have been identified at this date 1 1 . The reversible spontaneous polarisations in these materials range from 5 x 105 ftC m ~ 2 for lithium tantalate, L i T a 0 3 , down to 1.7 x 1 0 3 / i C m ~ 2 for gadolinium molybdate, Gd2(Mo04)3. Major sources of bibliographic information on polar materials include the Landolt-Bornstein series 11 , Lang's Source Book of Pyroelectricity 1 and his annual literature Guide to Pyroelectricity 12 , Toyoda's continuing Bibliography of Ferroelectrics 13 , an annually published Digest of Literature on Dielectrics 14 and two O.R.N.L. Ferroelectric Literature Indexes 15 . Though ferroelectrics are only a sub-group of polar materials, they include the most significant polar materials, both from a basic viewpoint and from an applications viewpoint. Many of the ferroelectrics possess some of the most interesting piezoelectric, thermal, optical and electrical properties of all the dielectric materials. Polar materials, in particular the ferroelectrics, can exhibit a large degree of non-linearity in their electrical, optical and piezoelectric properties. Through-

4

INTRODUCTION

out this book the three adjectives polar, ferroelectric and non-linear are used somewhat interchangeably. However, as much as possible, we have striven to use the most suitable term in each instance. Like life itself, the writing of this book has been both pleasure and pain. The pleasure has stemmed from the satisfaction of covering, in an age of scientific specialisation, a subject as broad as polar materials. The chemist, the crystallographer, the ceramicist, the physicist and the mechanical and electrical engineer all have a vital interest in polar materials. The interest covers the gamut from theory through experiment to application. The pain has been the challenge of writing within a reasonable number of pages a meaningful book for a diverse readership. In a rapidly growing field there is always the necessity to be quite selective about what to include in a book. This problem is compounded, in the present instance, because of the interdisciplinary nature of study of polar materials. Hopefully the future will reveal that our use of the hatchet for selection has been more perceptive than arbitrary. Wherever feasible, principles have been emphasised so as to make the book most valuable to students and newcomers to the field. The examples of single crystal and ceramic materials used to illustrate the principles involved have been selected, as much as possible, from recent publications. Thus the book should be useful for experienced scientists working with or familiar with polar materials. The examples of devices have been selected on the basis of their currentness, as well as the scientific and economic significance-criteria which are most meaningful to engineers utilising or wishing to utilise polar materials. We begin Part I, 'Basic Properties', with chapter 2 giving outlines of the methods by which the materials of interest may be prepared, either for specific applications or for study and understanding of the physical properties of the materials, with a view to their attempted exploitation. Often the material preparation will consist of crystal growing or ceramic manufacture; ceramic materials are polycrystalline structures. For study of the properties, crystals will usually be preferred as being likely to give results more easily interpretable in terms of reasonably simple models. If the crystals contain imperfections or impurities this may be unavoidable or it may have resulted from deliberate attempts to modify the properties in some way—as for example in bringing the transition temperature, or Curie point, Tc, into some more convenient temperature range. For applications, the more complicated structures of ceramic materials may well be the price we pay for their ease of fabrication and relative cheapness. It is also a test of our ability to understand these materials if we can satisfactorily extend our models to include ceramic structures. Very interesting and prominent examples are the PZT ceramics, which have replaced crystal materials in many piezoelectric devices; more recently it became possible to grow PZT compositions as crystals. In this chapter we discuss also the technique of annealing, and the processes of poling, cutting, electroding, and several methods of making thin films.

INTRODUCTION

5

Chapters 3 - 6 give introductions to various aspects of the physical properties—electrical, optical, mechanical and thermal. In each case a prominent effect is the anomaly (or peak) which occurs in nearly every physical property in the neighbourhood of Tc. In chapter 3 we describe the dielectric anomaly and the non-linearities, reversal of the spontaneous polarisation P s by means of electric fields (switching), and the techniques for observing it, the relationship of switching behaviour to the parameters of the driving impulses, and various ways in which these effects are observed to decay or 'age'. In principle the perfect ferroelectric is an insulator, but some rather interesting possibilities arise when doping has added semiconduction to its properties. Brief reference is also made to some photoconductive properties. In chapter 4 we consider the optical properties, and their variation with frequency (mostly within the visible region), with temperature, with applied mechanical and electrical stress, and with incident light. Many of these properties form the basis of applications which are to be discussed. The variation of refractive index, or of birefringence, with electric field (electrooptics) is of particular interest in these materials, where the field involved may well not be an exterior applied field, but may follow the development of internal fields when the material undergoes the transition into its polar state. Non-linear optical effects are also important. An important application of this effect is second harmonic generation. Some absorption-edge, photoluminescent, electroluminescent and luminescent effects are described. Chapter 5 includes not only the elastic anomalies, but also the piezoelectric coefficients, since these link the mechanical and electrical parameters. Mechanical loss effects are considered, just as were the electrical loss effects in the chapter 4. Above Tc, in a ferroelectric-to-non-ferroelectric transition, P s is zero, and there may or may not be 'ordinary' piezoelectricity, unrelated to P s of course. Nevertheless interest does attach to the differences between those materials which do or do not possess that 'ordinary' piezoelectricity. The quadratic effect, conventionally called electrostriction, is also discussed. The effect of applied stress on various properties is considered in section 5.5, and improper and ferroelastic materials are covered in section 5.6. Surface acoustic waves are also briefly mentioned. In discussing the thermal properties in chapter 6 the well-known and very useful Devonshire form of thermodynamic function is introduced. Its purpose is to summarise and interrelate a vast range of experimental information. The thermal-electrical and the thermal-mechanical properties are listed in table 6.1, which includes also the interesting anomalies. The properties discussed here include the pyroelectric and electrocaloric effects, as well as the anomalous behaviours in specific heat and in thermal conductivity. Chapter 7 links the classical description of the co-operative transition, and the anomalies which occur there, to a more recent viewpoint available from studies of lattice vibrations; the soft-mode concept is in the first place only a change of terminology, though later it will be seen to be capable of many new

6

INTRODUCTION

extensions. The antiferroelectric transition is considered in section 7.4. In section 7.5 is given a brief indication of some recent attempts to clarify the classification of the increasingly complicated phenomena under study. Anharmonic effects require more elaborate mathematical treatment than we are able to give in this book, but an introduction to some of those studies is included. The materials in this book are distinguished experimentally by their extreme non-linearities and by the anomalies. Conceptually, the application of the principles of symmetry to them is very significant, and this is dealt with in chapter 8, not in detail, but in a manner which we hope will enable interested readers to follow up in more detailed studies elsewhere. In Chapter 9 we give, for reference, a brief summary of aspects of the transition in some of the materials which have been used for illustration elsewhere in the book. There are hundreds of materials in our sphere of interest, and reference is made to places where more complete listings are available. Chapters 10 and 11 carry some of the previous ideas into the region of spectroscopy, and show how the dispersion phenomena may be used to elucidate the underlying microscopic mechanisms involved in these polar transitions. Attention is paid to the importance of fluctuation phenomena when the transition is approached, and to the central peak which has in recent years become distinguishable from the soft mode. Section 11.5 deals with KDP-type materials and the 'pseudospin' descriptions. An appendix to chapter 10 provides a convenient summary of the related optical and dielectric parameters. Almost all the properties of polar materials are modified considerably by the presence and mobility of domains. The methods of studying them, and the models which seem to be successful, are described in chapter 12. Part II of this book, chapter 13-18, 'Applications', is concerned with devices and systems that have been or can be built with polar and ferroelectric materials. The applications covered range from those that already have a well established commercial market to those that are still at a developmental stage. Such a detailed treatment of the applications of polar materials is well overdue, since earlier books on polar and ferroelectric materials have only given a cursory treatment of this economically very significant subject. Chapter 13 details some fundamental aspects of memories and displays, two of the major components in computers and communication systems. The basic parameters of memories and displays, including addressing techniques, are analysed. This analysis is then applied to the properties of polar materials. As is described in the succeeding chapters, polar materials are being used or actively considered for use in a variety of memory and display applications. The next three chapters, 14-16, contain a description of a wide range of devices that utilise the reversible spontaneous polarisation property, i.e. the switching, of ferroelectric, polar materials. For convenience, this material is divided between three chapters. Chapter 14 deals with devices that involve only

INTRODUCTION

7

the reversal of the spontaneous polarisation of the polar material. Chapter 15 is concerned with polar material devices in which use is made of changes in the piezoelectric, optical and thermal properties that are associated with the reversal of the spontaneous polarisation. In chapter 16 the devices have a complex structure in that the reversible polar material is combined with another electrically active material, such as an electroluminescent material, a photoconductor or a semiconductor material. Chapter 17 describes a large number of polar material devices in which the common factor is that no large signal switching, or reversal, of spontaneous polarisation is involved. Instead, the devices utilise the anomalously high values of dielectric permittivity, linear and non-linear optic and electro-optic coefficients or photo-refractive, pyroelectric, piezoelectric and elasto-optic constants of polar materials. Some of the devices in this chapter, such as capacitors and piezoelectric transducers, are of great commercial importance. Others, such as optical holographic storage media and colour projection TV systems, are still at a developmental stage but may prove to be economically very significant in the future. This book concludes with a short treatment in chapter 18 of the basic physics and the electro-optic and thermo-optic applications of an important group of liquid materials having polar molecules. These materials are generally referred to as liquid crystals, since they simultaneously exhibit the physical properties of liquids and the electrical and optical characteristics of an ordered, polar crystalline structure. References 1. S. B. Lang, Source Book of Pyroelectricity, Vol. 2 in book series Ferroelectricity and Related Phenomena (ed. I. Lefkowitz and G. W. Taylor), Gordon and Breach, London (1974) 2. L. A. Shuvalov, J. phys. Soc. Japan, 28, Supplement, 38 (1970) 3. J. Valasek, Phys. Rev., 17, 475 (1921) 4. F. U. T. Aepinus, Histoire de iAcademie Royale des Sciences et Belles Lettres, Berlin, 12, 105 (1756) 5. First International Meeting on Ferroelectricity, Prague, Czechoslovakia, June-July, 1966. Proceedings published by Institute of Physics of the Czechoslovakian Academy of Sciences (1966) Second International Meeting on Ferroelectricity, Kyoto, Japan, Sept., 1969. Published as Supplement to J. phys. Soc. Japan, 28 (1970) Third International Meeting on Ferroelectricity, Edinburgh, Scotland, Sept., 1973. Published in Ferroelectrics, 7 and 8, Nos. 1 and 2 (1974) 6. First European Meeting on Ferroelectricity, Saarbrucken, 1969. Stuttgart, Wissenschaftliche, Verlagsgesseilschaft m b H (1970) Second European Meeting on Ferroelectricity, Dijon, 1971. Published in J. Physique, 33, Supplement C2 (1972)

8

INTRODUCTION

Third European Meeting on Ferroelectricity, Zurich, Sept., 1975. Pub lished in Ferroelectrics, 12, 13 and 14, Nos. 1 and 2 (1976) 7. 1969 IEEE Symposium on the Applications of Ferroelectrics, Washington DC, June, 1968. Published in IEEE Trans. Electron Devices, ED16, No. 6 (1969) 1971 IEEE Symposium on the Applications of Ferroelectrics, Yorktown Heights, New York, June, 1971. Published in Ferroelectrics, 3, Nos. 2 - 4 (1972) 1975 IEEE Symposium on the Applications of Ferroelectrics, Albuquerque, New Mexico, June, 1975. Published in Ferroelectrics, 10 and 11 Nos. 1 and 2 (1976) 8. Transactions of the First All Union Conference on Ferroelectricity, Leningrad. Izv. Akad. Nauk SSSR, Ser. Fiz., 21, Nos. 2 and 3 (1957) Transactions of the Second All Union Conference on Ferroelectricity, Rostov on Don. Izv Akad. Nauk SSSR, Ser. Fiz., 22, No. 12 (1958) Transactions of the Third All Union Conference on Ferroelectricity, Moscow. Izv. Akad. Nauk SSSR, Ser. Fiz., 24, Nos. 10 and 11 (1960) Transactions of the Fourth All Union Conference on Ferroelectricity, Rostov on Don. Izv. Akad. Nauk SSSR, Ser. Fiz., 29, Nos. 6 and 11 (1965) Transactions of the Fifth All Union Conference on Ferroelectricity and Physics of Inorganic Dielectrics, Dnepropetrovsk. Izv. Akad. Nauk SSSR. Ser. Fiz., 31, Nos. 7 and 11 (1967) Transactions of the Sixth All Union Conference on Ferroelectricity, Riga Izv. Akad. Nauk SSSR, Ser. Fiz., 33, Nos. 2 and 7 (1969) Transactions of the Seventh All Union Conference on Ferroelectricity. Voronezh. Izv. Akad. Nauk SSSR, Ser. Fiz., 34, No. 12 (1970) and 35, Nos 9 and 12 (1971) Transactions of the Eighth All Union Conference on Ferroelectricity. Uzhgovod. Izv. Akad. Nauk SSSR, Ser. Fiz., 39, Nos. 4, 5 and 6 (1975) Symposium on Semiconductors and Ferroelectrics, Rostov on Don. Ferroelectrics, 6, Nos. 1 and 2 (1973) 9. Ferroelectricity—Proceedings of Symposium held at Warren, Michigan. 1966. Elsevier, Amsterdam (1967). Symposium Proceedings on Practical Applications of Ferroelectrics, Tokyo, Sept. (1969). Oyo Buturi, 39 (1970) 10. Ferroelectrics (eds. I. Lefkowitz and G. W. Taylor) published by Gordon and Breach, New York, Vol. 1 (1970), to present 11. Landolt-Börnstein New Series, Group III, Volume 3. Ferroelectric and Antiferroelectric Substances. Springer-Verlag, Berlin (1969). Landolt-Bornstein New Series, Group III, Volume 9. Ferroelectric and Antiferroelectric Substances. Supplement and extension to III/3, Springer-Verlag, Berlin (1975) 12. S. B. Lang. Literature Guide to Pyroelctricity, published annually in Ferroelectrics beginning with Ferroelectrics, 5, 125 (1973)

INTRODUCTION

9

13. Koichi Toyoda. Bibliography of Ferroelectrics, published in most issues of Ferroelectrics beginning with Ferroelectrics, 1, 43 (1970) 14. Digest of Literature on Dielectrics, published by U.S. National Research Council of National Academy of Sciences, Washington D.C., beginning in 1954 15. Oak Ridge National Laboratory Literature Guides, Vol. 1. Ferroelectric Materials and Ferroelectricity. Authors T. F. Connolly and E. Turner, IFI/Plenum, New York (1970) Ibid., Vol. 6. Ferroelectric Materials and Ferroelectricity. Authors T. F. Connolly and D. T. Hawkins, IFI/Plenum, New York (1974)

2 Preparation of Polar Materials

This chapter summarises the techniques used for fabricating polar materials in single crystal, ceramic, thin film and glass forms. It then goes on to discuss the various post-fabrication procedures such as annealing, poling, cutting, thinning, polishing and electroding which are usually needed before the polar materials can be used for either experiments or applications. For basic studies, where the polar material should be as near perfect as possible, it is desirable to use single crystals. For applications, where dimensions, reproducibility and cost are crucial factors then the polar material is usually fabricated in ceramic, thin film or glass form. This division is not precise. For example, some materials have not yet been grown as single crystals and hence basic studies must be made in the ceramic form. In other cases, the larger dielectric, piezoelectric, pyroelectric, electro-optic, etc., coefficients obtainable with particular single crystal materials can make this fabrication form mandatory for certain applications. And yet again thin films offer an important advantage for studying surface layer physics. The two major problems in fabricating large samples of high quality polar materials are the maintenance of the correct stoichiometry and the avoidance of strains. Chemical, thermal and optical methods, as well as sophisticated

14

BASIC PROPERTIES

techniques such as X-ray, electron, neutron and proton diffraction scattering are used to determine the quality of the fabricated material. By comparison, the fabrication techniques themselves are still much of an art, as evidenced by the variety of 'recipes' reported for particular materials. This however may be changing. For example, it is now customary to make a careful determination of the phase diagram of the material so as to choose the optimum fabrication conditions. These diagrams can be quite complex, as can be seen from figures 2.1 and 2.2, the phase diagrams for BaTi0 3 and Pb(ZrSnTiNb)0 3 . Note that in figure 2.2 because of the ternary nature of the material, (a) the material is best considered a Nb doped P b Z r 0 3 - P b S n 0 3 - P b T i 0 3 solid solution, (b) a different phase diagram is needed for each temperature. Another example of the scientific approach is the use of fluid dynamic principles to try to understand circulation currents in the melt during growth 3 .

Ti0 2 (mo)«%)

Figura 2.1 Barium titanate. Phase diagram (Rase and Roy 1 )

Many measurements can be made to determine the degree to which a ceramic, thin film or glass material approaches the properties of its single crystal counterpart. The hysteresis loop is a simple yet powerful criterion for making this determination. The squarer the loop and the larger its polarisation, then the better the orientation of the crystallites and the smaller the

15

PREPARATION OF POLAR MATERIALS

AT-Frilt BOUNDAF AFTER POLING

55

60

65

70

75

80

85

90

95

Figure 2.2 Part of the phase diagram of Pb 0 99(ZrSnTi) 0 9 8 Nb002O 3 at 2 5 ° C (poled at 2 5 ° ) F = Ferroelectric, A - antiferroelectric, T = tetragonal, R = rhombohedral, LT = low temperature phase, HT = high temperature phase (Raider and Cook 2 )

percentage of non-polar material and voids present. In general, doctor-bladed ceramics and epitaxial thin films are the fabrication techniques producing materials closest to the single crystal form, whilst the glasses and conventionally sintered ceramics are the furthest away.

2.1 Growth of Single Crystals The two major methods that have been used to date for fabricating single crystals have been the solution (or flux) growth technique and the melt growth technique. 2.1a Solution Grown Crystals This method has been successfully used for both water soluble materials and those that are soluble in other liquids or fluxes. The first stage in growing a water soluble crystal is to prepare an aqueous saturated solution of the polar material. Crystals can be grown by either keeping the solution at a constant temperature and allowing a gradual evaporation of the solvent or by slowly lowering the temperature while keeping the solution saturated. Slow growth, taking a thousand hours or more, usually produces the best and largest crystals. Other factors which affect the crystal

16

BASIC PROPERTIES

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p>

o" m £.0 o z 1/5 > OC CJ-

x ^ t 2 I O O o " J oc M 2-

CJ z

. a * Z ra

6" « 2

BO 5

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m « I - h , ™ . 5 « £ £ w w i= ra ra ra v 2 ( - i t H ( f l t tncûoooDCJ—^^-i-it/îiiw

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j Z O 2 XI-O 3 ( J —1 -J O < W

z

"

O

o

ra ® 3 O £ h-

ll-l -I o O OC a B . For B a T i 0 3 , d0 has been calculated to be about 50 fim. Further details on surface layer effects are given in section 12.12. U p to this stage we have implicitly assumed, and in figure 3.8 have shown, that the E pulse has a width i w which exceeds the switching time t f If, however, for a particular E, t w is less than i s at that value of E, then partial switching will occur. There are two types of partial switching. Stable partial switching can be achieved in all ferroelectrics. Unstable partial switching only occurs in certain ferroelectric materials for which the transition from stable to unstable partial switching is determined by the width of the applied E pulse. Figure 3.10 shows the form that the stable partial switching takes in most materials when the switching is done with N successive narrow pulses of the

46

BASIC PROPERTIES E

Figure 3.10 (Top) Applied voltage pulse pattern and (bottom) resultant stable current partial switching transients in a ferroelectric same polarity. As shown, the pulses do not have to be of the same width, nor equally separated. The partial switching transients if sequentially combined together form a 'patchwork' transient approximately equivalent to the complete switching transient obtained with a single wide pulse (figure 3.8 (bottom)). Mathematically this can be expressed by

lV=2/Ve

r =1

(310a)

and r= N

I

r =1

iwr=ifs

(3.10b)

where f wr is the width of a narrow pulse of amplitude E that causes a charge Q r to be liberated in the rth partial switching transient and f fs is the full switching time for a field of E. The type of partial switching shown in figure 3.10, corresponds to reversing the polarisation by traversing a succession of minor hysteresis loops (see figure 3.7). The partial switching is cumulative and stable and is not affected by the interval between the partial switching pulses. In certain ferroelectric materials, an unstable or elastic type of partial switching is observed 19 . Specifically, if the width of the applied pulse is less than some critical value t *, then the current transients have the form shown in figure 3.11. When the narrow pulse is applied, a certain amount of polarisation reversal occurs; however, as soon as the pulse is completed, the material relaxes back to very nearly its initial polarisation state. The t* effect is sharp but not

ELECTRICAL AND RELATED PROPERTIES

47

E

Figure 3.11 (top) Applied voltage pluse pattern and (bottom) resultant unstable current partial switching transients in a ferroelectric

absolute, in that A j, the area of the current transient when the pulse is on, is always slightly larger than A 2 , the area of the relaxation transient. Thus superimposed on the unstable partial switching is a small amount of stable partial switching which only becomes evident after a very large number of applied pulses. T h e t* unstable partial switching effect is only observed in certain ferroelectrics, the most notable being T G S , B i 4 T i 3 0 1 2 , Y M n 0 3 , K N 0 3 , and some P Z T ceramics. T h e value of t* decreases as the field and temperature increase. It is also a function of dislocations in, and surface conditions of, the material. Depending on the material, the temperature and E, t* can vary from 0.001 f s to l.Ofj. The t* effect has important application potential (see section 14.4). It also reveals information on the mechanism of polarisation reversal. F o r example in T G S , t* appears t o represent the transition between the forward growth and the subsquent sideways growth of domains. In some ferroelectric materials, it is found that t s a n d i m a r e influenced by the time the material has been left standing, with n o £ applied, since the previous reversal. The longer the delay time (t J between reversals, the smaller will be the i m a n d the longer the r s of the subsequent reversal. This behaviour, termed the delay time (r d ) effect 2 0 is closely related to the t* efTect, since it occurs in the same materials, namely TGS, B i 4 T i 3 0 , 2 and K N 0 3 . It should be emphasised that the t d effect is not an ageing phenomenon, for irrespective of the delay time between reversals, the switched charge per reversal remains constant. Measurements that have been m a d e 2 0 indicate that the r d effects are intimately associated with domain wall movement. The longer the delay time, the more the walls relax or lock into favourable energy configurations, such as dislocations, making subsequent switching more difficult and hence slower.

48

BASIC PROPERTIES

A more detailed treatment of the switching process in ferroelectrics, which takes into account the effects of domains, is given in chapter 12. 3.2c Ageing Large signal electrical switching can cause several types of permanent ageing or fatigue effects in polar materials. The usual manifestation of the ageing is a gradual decrease in the amount of polarisation switched per reversal, i.e. a decrease in the area under the switching current transient. This lack of stability represents an important limitation in the use of polar materials for certain applications—see Chapters 13-16. The experimental results reported on ageing are complicated and somewhat contradictory. However, some basic conclusions can be drawn concerning the decay. (a) The ageing can vary greatly between materials. For example, some materials such as TGS show no ageing, while others like B a T i 0 3 exhibit a large amount. (b) The electrode material used can be crucial in that ageing can occur with metal electrodes and not with liquid electrodes. (c) The ageing per reversal can increase dramatically as the applied field is decreased. This is shown in figure 3.12 for metal electroded, single crystal BaTiOj. (d) In many single crystal materials ageing will only occur when the switching waveform has off times between the alternate polarity pulses. The greater (he asymmetry in the pulse wave duty cycle then the greater the ageing rate. Contrariwise no ageing occurs in some materials if the polarisation reversals are done with a square or sine wave.

Figure 3.12 Ageing characteristics of metal electroded BaTi0 3 (a) at high field (b) at low field (Taylor 21 ). Number of polarisation reversals, n; time of application of field, t

ELECTRICAL AND RELATED PROPERTIES

49

It is possible to distinguish three different types of ageing. The first type is an electrode artifact. If conductive silver paste electrodes are used on certain materials, particularly ceramics, then it is found that the silver ions migrate into the material causing chemical changes to occur with a resultant decrease in the switchable volume5. The migration of the silver occurs even with the material in an unactivated state; it is, however, accelerated by an applied field. The second type of ageing is microcracking3. It is caused by the large strains that are introduced into the polar material during the polarisation reversal. This type of ageing will occur irrespective of whether or not off-times exist in the applied field waveform. The microcracking breaks the continuity of the applied field either in the bulk and/or at the electrode interface. As a result, as the microcracking proceeds, progressively less of the material is switched by the applied field. Microcracking has been observed more in ceramics than in single crystal materials. The third type of ageing is the more general and basic phenomenon. The most plausible explanation for it is that the divergence of the polarisation at the internal domain walls involved in the polarisation reversal causes mobile space charge to flow inside the polar dielectric. This charge 'locks-in' some of the partially switched domains or potential sites from which domains can nucleate and grow. The net result is a reduction in the amount of switchable polarisation. This theory explains most of the experimental evidence. For example, the ofT time between the applied pulses is necessary to provide time for the space charge to move. The lack of ageing with liquid electrodes is due to the liquid being an ionic conductor which inhibits the injection of charge into the material. The variable nature of space charge distribution within materials, resulting from the random nature of dislocations and surface conditions, explains the variation in the ageing characteristics for different materials and even for different samples of the same material. There exists other experimental evidence in support of the space charge theory for the basic ageing behaviour. Campbell22 found that after ageing, single crystal BaTiO 3 contains domains that do not extend through the bulk of the crystal. Such domains suggest the presence of space charge in the material. In some materials which have been aged by a waveform containing off-times, it is found that recovery (increase) of the switchable polarisation is obtained by applying a switching waveform that has no off-time. Apparently such switching sweeps the space charge in and out causing some of the locked-in domains to be freed. Karan 23 has developed the following theoretical expression for space charge ageing: P = P j [ 1 - e -'w*i(l - e -'o/')]'1

(3.11)

where Pi is the initial (unaged) value of polarisation; P is the value of polarisation after rj polarisation reversals; i w is the on-time of the applied field pulse E; t 0 is the off-time between pulses of opposite polarity and for an

50

B A S I C PROPERTIES

asymmetric waveform is the average of the two ofT-times; r is the mobile space charge time constant; R , is a constant related to rate of nucleation of new domains. R t is usually considered11 to have an £ dependence of the form R, =

E

(3.12)

where P is a constant having a value similar to the a of equation (3.7). Substituting equation (3.11) into equation (3.12) gives P = P i [ l - e -«.*e-""(i_e-«^T)]»

(3.13)

If fi is chosen as 760 kV as 107 and r anywhere in the range 1 0 " 3 - Is then equation (3.13) is a reasonable approximation to both the high-£ and low-£ ageing curves of figure 3.12. There appears to be a close connection between the t* and the f d effects described earlier in section 3.2b and the third type of ageing effect. In order to occur, all three effects require 'ofT-times between the application of the £ pulses. In addition all three effects are intimately related to domains and their motion and to imperfections in the material. It could well be that each is a manifestation of the same basic effect. For example, what has in some measurements been previously identified as ageing may be in reality partial switching resulting from the i

1000-1400 1500 — 4000 50-380 2800 2800 37-250 500

61

OPTICAL AND RELATED PROPERTIES

Another related parameter commonly used in evaluating the Pockels effect is the half wave voltage, Vx/2. This is the voltage required to cause a n radian change in the optical retardation of the material. For the modulators, deflectors and displays of sections 15.2 and 17.4 this represents the maximum usable change in retardation and hence is a very practical parameter. Some values for are listed in table 4.2. The values are calculated for a 1 cm cube of the material and hence are dimensionally applicable to both transverse and longitudinal operation. In the Kerr effect An varies in a quadratic fashion with the polarisation P according to the expression An = -$gn3P2

(4.8)

where g, a fourth rank tensor proportional to the qijkl of equation (4.5), is the quadratic electro-optic coefficient. Unlike the linear coefficient r, g is always positive in sign. The Kerr effect is best utilised by operating the ferroelectric material, well above in its paraelectric phase. In this non-ferroelectric phase, the material is optically isotropic when E = 0. The application of E induces a polarisation and as a result induces a An. In some applications a permanent D.C. bias £ is applied creating in equation (4.8) the equivalent of the K of equation (4.7). For most materials the largest quadratic electro-optic effect can be obtained by utilising the difference between g u and gl2- Values of ( g n - g 1 2 ) for the most promising quadratic electro-optic materials operated in a transverse mode and measured at 6328 A are listed in table 4.3. As can be seen from table 4.3, with the exception of the PLZT ceramics, the values of ( # n — g 1 2 ) are remarkably similar for all the single crystal materials. Table 4.3 Quadratic e l a c t r o - o p t i c coefficient (j/i-! - *)E2eiUu>'-k'*>]

(4.11)

A special and most important case is when £ , and E2 have the same frequency, i.e. co, = a>2 = u>. Then from equation (4.11) it can be seen that the polarisation has components at 2a> and 0. This condition is referred to as second harmonic generation (S.H.G.). What essentially happens in S.H.G. is that the propagating, high energy light beam induces non-linearities in the optical material. The non-linearities cause the emergent light to contain both fundamental and second harmonic frequencies, as well as a D.C. component. To maximise the second order polarisation components of equation (4.11), phase matching' 5 should occur, that is A/c should be 0. In the case of S.H.G., phase matching requires that n 2a> = n co' f o r some materials this condition cannot be achieved because dispersion effects cause the refractive index to decrease with increasing frequency. The equality can however be achieved in many negative birefringent materials by suitable orientation of the crystal and arranging for the fundamental (input) frequency to correspond to the ordinary ray and the second harmonic (output) to the extraordinary ray. For positive birefringent materials these conditions are reversed. In some birefringent materials it is also necessary to heat the crystal to a particular temperature to obtain a precise equality between the refractive indices of the fundamental and harmonic frequencies. The application of a D.C. electric field or mechanical stress are two other techniques that have been used to achieve exact phase matching. As indicated above, phase matching is a difficult process and has not been achieved in all materials. The first demonstration of S.H.G. was by Franken et al.i6 in 1961. Using suitably oriented quartz they were able, with the simple arrangement of figure 4.S, to generate the second harmonic of a ruby laser. Since then S.H.G. has been observed in many materials. Table 4.4 lists some of these materials and their measured susceptibilities rj ffj! for S.H.G. It is interesting to note that many of the most promising non-linear optic materials are ferroelectrics. This is because the ferroelectric materials can be readily phase matched by virtue of their birefringence and the sharp dependence of their refractive indices on temperature. Miller 17 has developed an alternative theory for S.H.G., in which the energy is expressed in terms of polarisations rather than fields. The basic coefficient in his theory is 8 fy which is related to rj „ti>by the expression 2to „2d> iA | Ma> m 2 o 5 = n,i ijjikktiijk (4.i2)

64

B A S I C PROPERTIES T a b l e 4.4 N o n - l i n e a r o p t i c a l s u s c e p t i b i l i t i e s f o r v a r i o u s m a t e r i a l s Material

Ba2NaNb5015 BaTi0 3 CdS GaP KDP ADP LiNb03 LiTa0 3 Quartz PbTiO a

nfr

Axes (//*) 3, 3. 3, 1, 1, 3. 2. 2. 1. 3,

1, 1, 3, 2, 2, 2, 2, 2, 1. 1,

1 1 3 3 3 1 2 2 1 1

42 x 10 ~ 9 esu 57 x 1 0 " 9 190x10-® 600 x 10 ~ 9 1.5 x 1 0 - 9 1.8 x 1 0 - 9 9.5 x 1 0 " 9 6.5 x 1 0 - 9 2.4 x 1 0 " 9 12.8 x 1 0 - 9

RED TRANSMITTING

1.06 x 10" 6 esu 3.08x10-® 1.25 x 1 0 " 6 3.25x10-® 2.95 x I O ' 6

1.90 x I O ' 6

UV TRANSMITTING

NON-LINEAR CRYSTAL

Figure 4.5 Experimental arrangement for second harmonic generation (Kielich36)

where t] jyand rj are the linear optical susceptibilities measured at frequency a> and r¡ Jf j is the linear optical susceptibility measured at frequency 2to. Values of 5 }fj¡ calculated from the measured susceptibilities are listed for some of the materials in table 4.4. It is most significant that the numerical values of the 6 coefficients show much less variation between the materials than d o the f¡ ff¡¡ coefficients. This suggests that polarisation is the basic motivating parameter. A similar result can be deduced from the data on g and r (the electro-optic coefficients) in section 4.5. It can be seen that r, the field derived coefficient, is much more material-dependent than is g, the polarisation derived coefficient. The applications of non-linear optical effects to second and third harmonic generation, and to frequency mixing is described in section 17.S. 4.7 Photo-Refractive Effect Several polar materials undergo localised changes in refractive index when exposed to intense optical radiation 1 8 . Changes of n in the range 0.00001-0.001

65

OPTICAL AND RELATED PROPERTIES

have been measured in single crystals of BaTi0 3 , B a 2 N a N b 5 0 1 5 , B i 4 T i 3 0 1 2 , L i N b 0 3 , Sr x Ba,-jjNbjOg, K.TN and PLZT ceramics. The refractive index changes, originally, referred to as optical damage, have more recently been termed the photo-refractive effect. The optically induced changes in n are relatively permanent after the light is removed if thermal 1 9 or electrical 20 fixation techniques are used. However the material can be restored to its original optical state by heating, typically to between 200 and 300°C, by intense optical radiation, by y-radiation and in some materials by the application of large electric fields. The photo-refractive effect is basically electro-optic in nature. Despite much experimental data, some detailed below and some in section 17.6, the exact mechanism has not been resolved. Amodei 21 has postulated that the intense light creates free carriers in the polar material. These carriers drift or diffuse from their original deep traps to new traps, creating a charge displacement and hence an internal electric field which changes the refractive index n of the material. Johnson 2 2 has proposed that the light directly induces microscopic polarisation changes, and that these changes create the internal electric fields which cause the variation in n. The optical energy needed to create a significant photo-refractive effect is large, typically of the order of 1-100 J c m - 2 . Such energies are conveniently obtained from lasers. There are large quantitative differences in the photorefractive effect between different materials. Within the one material the effect is strongly dependent on such parameters as crystal quality, type and percentage of doping, X or y-ray radiation pretreatment, temperature and the wavelength of the incident light. This is partially illustrated in figure 4.6 which

460

470

480

490

500

510

520

£11

530

X(nm)

Figure 4.6 Photo-refractive sensitivity versus wavelength (Kurz 2 3 ). A L i N b 0 3 : Fe annealed in argon for 1 h at 650° C; o L i N b 0 3 : Fe annealed in oxygen f o r 5 hat 800° C;« L i N b 0 3 : Feasgrown. All samples doped with 0.5% Fe

66

BASIC PROPERTIES

shows how the photo-refractive sensitivity of iron doped single crystal L i N b 0 3 varies as a function of the annealing treatment and the wavelength of the incident light. In figure 4.6 the photo-refractive sensitivity is defined as the slope of the index change versus applied optical energy curve. For this data, the refractive index is measured at a wavelength of 633 nm. The photo-refractive efTect can be used as the basis of both a reversible and a non-reversible optical storage medium. These applications are described in section 17.6. However it should be noted that the photo-refractive effect can also be a limiting factor for certain applications. For example the intensity of the laser beam used in electro-optic (see section 17.4) and non-linear optic devices (see section 17.5) may have to be reduced because of the possibility of optical damage to the polar material from which the device is built. 4.8 Light Scattering Effects Light scattering in polar materials has been used as (a) a diagnostic tool for studying fundamental properties such as the dynamics of phase transitions and (b) in the case of some coarse grained P Z T a n d PLZT ceramics (section 15.2) as the basic mechanism for a display device. The use of Raman scattering to investigate the behaviour of lattice modes of vibration, and of Brillouin scattering to investigate acoustic modes in particular, are described in section 11.1.

As described in section 15.2, two electrically controlled light scattering effects have been found in P Z T ceramics that have grain size diameters in excess of 2 /jm. The first of these scattering effects 2 5 utilises 90° electrical switching of the polar axis direction in a P Z T ceramic doped with small amounts (typically 2 % ) of either Bi or La. The second efTect 36 uses electrical switching between zero and remanent polarisation states in a P Z T ceramic modified with relatively large amounts (typically 7%) of La. The La modified PZT ceramic is often referred to as PLZT. Various theories have been proposed to explain these light scattering effects. Initially Nettleton 2 4 devised a theory based on Rayleigh scattering at 180° domain walls in the ceramic. Land 2 5 subsequently suggested that the effects are caused by multiple reflection and refraction at the strain-relieving 71° and 109° domain walls. Such walls are more common in the coarse-grained rhombohedral ceramics than in the fine-grained specimens. Recently Dalisa and Seymour 2 6 have developed an elegant convolution scattering model to explain multiple light scattering in a ferroelectric ceramic medium containing randomly oriented domains whose refractive index can vary from 4- n to - n. 4.9 Absorption Most dielectric materials are transparent in the visible and begin to absorb at U.V. and I.R. wavelengths. In some polar materials it has been found that the absorption edge can be moved to shorter wavelengths by the application of an

67

O P T I C A L AND RELATED PROPERTIES

electric field. This shift, opposite in direction and much larger in magnitude than the Franz-Kelydish effect 27 seen in classical semiconductors, has been measured at the U.V. absorption edge of BaTi0 3 (Ref. 28) and the I.R. absorption edge of SbSI (Ref. 29). Typical of the results is figure 4.7 which shows the change in absorption wavelength resulting from the application of an electric field parallel and perpendicular to the c-axis of SbSI at room temperature. Experimentally it is found that the shift in wavelength increases with increasing applied field and temperature. In SbSI the maximum shift observed is about 80 A. F = 3.2

0.60

£ J.c

» 103 V/cm

0.62

0.64

0.66

0.68

0.70

Figure 4.7 Shift in I.R. absroption edge of SbSI with field applied perpendicular and parallel to c-axis of crystal (Kern 2 9 ). • No field applied; o field of 3.2 kV/cm applied

4.10 Photoluminescence. Electroluminescence and Luminescence Photoluminescence has been observed in several polar materials, including BaTi0 3 , TGS, SrTi0 3 , SbSI and BiSI. Specifically, it has been found that the application of broad spectrum light causes these materials to emit light (that is, to luminesce), at certain wavelengths. In some instances 30 the photoluminescence is directly attributable to impurity ions intentionally placed in the polar material, e.g. Sm + + + in BaTi0 3 . The luminescence from these ions has been used as a means for studying the ferroelectric phenomenon. In other cases, the photoluminescent behaviour appears to be an intrinsic property of certain polar materials. For example, Krolevets et al.31 have measured the photoluminescent spectra in SbSI, BiSI and their isomorphs, resulting from activation with incandescent light, at wavelengths in the range

68

BASIC PROPERTIES

0.8-2.5 fim. In SbSI the peaks in the luminescence spectra occurred at wavelengths of 0.975, 1.65 a n d 2.00/¿m. In most cases t h e intensity of the luminescence increased with decreasing temperature. T h e y have concluded that in these materials, the luminescence is due to tunnel recombination processes involving d o n o r - a c c e p t o r pairs. Interestingly, the luminescence, unlike the measured photocurrent, is not affected by traversing the phase transition boundaries. Several types of electroluminescent p h e n o m e n a have been reported in polar materials. Bhide a n d Shringi 3 2 have measured light generated d u r i n g polarisa t i o n reversal in B a T i 0 3 . Similar measurements have been also recently m a d e by G o d e f r o y et a/. 3 3 in T G S . Schmidt et a/. 3 4 have also observed the generation of light pulses in T G S during electrical switching, and also by heating and cooling the crystal. T h e light pulses they measured had energies in the range 10" 1 0 - 1 0 ~ 1 6 J. They concluded that these pulses were essentially the electrical b r e a k d o w n (glow discharge) of the s u r r o u n d i n g air caused by the high surface charge densities within the T G S . Recently Yockey and Aseltine 3 7 have reported a luminescent effect in K D P . They irradiated with neutrons a crystal well below its T c which resulted in a t r a p p i n g of free charge at the d o m a i n boundaries. As the crystal was w a r m e d up, light pulses were observed, which the authors have hypothesised as resulting f r o m a laser action. It is clear that more work is needed to determine whether the p h o t o luminescent, electroluminescent and luminescent effects in polar materials are intrinsic effects or artifacts. Also it should be noted that n o n e of these optical effects is presently sufficiently s t r o n g or controllable to m a k e t h e m useful for devices.

References 1. J. Kobayashi, I. Mizutani, H. Hara, N. Yamada, O. N a k a d a , A. K u m a d a and H. Schmid, J. phys. Soc. Japan, 28, Supplement 67 (1970) 2. F. Pockels, Lehrbuch der Krystalloptik, Teubner, Leipzig (1906) 3. A. R. J o h n s t o n , J. appl. Phys., 42, 3501 (1971) 4. N. R. Ivanov and L. A. Shuvalov, J. phys. Soc. Japan, 28, Supplement 72 (1970) 5. M. Born and E. Wolf, Principles oj Optics, 2nd rev. edn., Macmillan, New York, p. 96 (1964) 6. J. F. Nye, Physical Properties of Crystals, Clarendon Press, O x f o r d (1960) 7. C. F. Q u a t e , C. D. W. Wilkinson and D. K. Winslow, Proc. IEEE. 5 3 , 1 6 0 4 (1965) 8. R. W. Dixon, J. appl. Phys. 38, 5149 (1967) 9. A. Korpel, R. Adler, P. Desmares and W. Watson, Proc. IEEE, 54, 1429 (1966) 10. E. G . Spencer, P. V. Lenzo a n d A. A. Ballman, Proc. IEEE, 5 5 , 2 0 7 4 (1967)

OPTICAL AND RELATED PROPERTIES

69

11. J. Kerr, Phil. Mag., 4, 50, 337 (1875) 12. H. Futama and R. Pepinsky, J. phys. Soc. Japan, 17, 725 (1962) 13. H. Twasaki, K. Sugii, N. Niizeki and H. Toyoda, Ferroelectrics, 3, 157 (1972) 14. N. Bloembergen, Nonlinear Optics, W. A. Benjamin Inc., New York (1965) 15. J. A. Giordmaine, Phys. Rev., A138, 1599 (1965) 16. P. A. Franken, A. E. Hill, C. W. Peters and G. Weinreich, Phys. Rev. Letters, 7, 118 (1961) 17. R. C. Miller, Appi Phys. Utters, 5, 17 (1964) 18. A. Ashkin, G. D. Boyd, J. M. Dziedzic, R. G. Smith, A. A. Ballman, H. J. Levinstein and K. Nassau, Appi Phys. Letters, 9, 72 (1966) 19. D. L. Staebler and J. J. Amodei, Ferroelectrics, 3, 107 (1972) 20. F. Micheron and G. Bismuth, Appi Phys. Letters, 20, 79 (1972) and 23,71 (1973) 21. J. J. Amodei, Appi. Phys. Letters, 18, 22 (1971) 22. W. D. Johnson Jr., J. appi Phys., 41, 3279 (1970) 23. H. Kurz, Ferroelectrics, 8, 437 (1974) 24. R. E. Nettleton, J. appi Phys., 39, 3646 (1968) 25. C. E. Land and P. D. Thacher, Proc. IEEE, 57, 751 (1969) C. E. Land, P. D. Thacher and G. H. Haertling, Electro-optic Ceramics. In Applied Solid State Science, 4, 137 (ed. R. Wolfe), Academic Press, New York (1974) 26. A. L. Dalisa and R. J. Seymour, Proc. IEEE, 61, 981 (1973) 27. W. Franz, Z. Naturf., 13a, 484 (1958) 28. C. Gaehwiller, Helv. Phys. Acta, 38, 361 (1965) 29. R. Kern, J. phys. Chem. Solids, 23, 249 (1962) 30. S. Makishima, K. Hasegawa and S. Shionoya, J. Phys. Chem. Solids, 23, 749 (1962) 31. N. M. Krolevets, M. K. Sheinkman and E. A. Savchenko, Ferroelectrics, 6, 133 (1973) 32. V. G. Bhide and S. N. Shringi, J. appi Phys., 37, 810 (1966) 33. L. Godefroy, P. Jullien, B. Morion and G. Godefroy, Ferroelectrics, 8,421 (1974) 34. G. Schmidt, J. Petersson and H. E. Müser, J. phys. Soc. Japan, 28, Supplement 147 (1970) 35. S. Kielich, Ferroelectrics, 4, 257 (1972) 36. W. D. Smith and C. E. U n d , Appi Phys. Letters, 20, 169 (1972) 37. H. P. Yockey and C. L. Aseltine, Phys. Rev., Bll, 4373 (1975)

5 Mechanical Properties

5.1 Introduction We saw in chapter 3 how the electric and dielectric coefficients may have unusually large values in a small temperature region near the transition temperature Tc. Such 'anomalies' occur also in other properties, including the mechanical properties such as elasticity. Piezoelectric coefficients describe properties which form a link between electric and mechanical properties, in materials in which piezoelectricity exists. All ferroelectrics are piezoelectric below Tc, and many are also piezoelectric above Tc; examples of the former group are the perovskites, such as barium titanate, B a T i 0 3 , and strontium titanate, S r T i 0 3 ; examples of the latter group are the members of the potassium dihydrogen phosphate (KDP) group. Thermodynamics provides a theoretical description of the principles underlying the way properties vary with temperature. In particular, a number of thermodynamic functions has been developed (often empirically, in the first place) which serve to summarise in a simple way the relationships between many different properties in a single material. Thermodynamics does not describe the microscopic mechanisms underlying the behaviours of materials. Those mechanisms can often be investigated by studying the variations of properties with frequency, and by paying

71

MECHANICAL PROPERTIES

particular attention to those special frequencies at which the property values may change rather rapidly; these are called the dispersions. At the dispersion frequencies there may be significant losses; that is, the response to an applied 'A.C\ stimulus (electrical or mechanical) may not remain in phase with the stimulus, so that a dissipative mechanism occurs in that frequency region. In short then, as discussed in section 5.2, although elasticity is the most significant mechanical property, the piezoelectric parameters will be of equal interest because they link elasticity to the dielectric parameters, and because they are easy to measure, and because the elastic anomalies and the piezoelectric anomalies are related. However, it is as well to point out that, although this link is guaranteed by familiar thermodynamic relationships, the explicit thermodynamic functions, referred to above, do not guarantee it. The piezoelectric information is usually given in terms of parameters, such as the proportionality constant between variations of mechanical strain and electric field. The term electrostriction is conventionally reserved for seconddegree effects, in which strain is proportional to the square of the field or of the polarisation.

(In w) Figure 5.1 Symbolic representation of permittivity measured on discs, including piezoelectric resonances. (T: isothermal; S: adiabatic) The low-frequency values of the elastic and piezoelectric parameters will not remain valid at frequencies much higher than about 10 s Hz; the dispersions at characteristic frequencies above that require us to recognise the use of complex elastic and piezoelectric magnitudes, which provide the mathematical description of the phase lags mentioned above; the imaginary component of a complex elasticity is closely related to a mechanical loss. These losses will be

72

BASIC PROPERTIES

discussed from the point of view of the coupling between lattice vibrations, in section 5.4. Because of the way in which the piezoelectric parameters are defined, the mechanical properties—the elasticities—can if desirable be derived rather than measured. They can be derived from measured values of permittivities and of the piezoelectric parameters. A. C. methods are usually chosen. Care must be taken to eliminate the effects of non-linearities and dispersions. As an example, figure 5.1 shows measurements of permittivity £ made up to 107 Hz on a disc in which the spontaneous polarisation is parallel to the thickness. The isothermal permittivity eT is found by extrapolation through the resonant frequency at about 106 Hz, as indicated by the full line; theory shows that the adiabatic permittivity £ s should be found by extrapolation of the linear plot at higher frequencies, as indicated by the dotted line; in both cases the dispersion has been eliminated by the extrapolation. Section 5.5 is concerned with the effects of mechanical stresses on the various values. The so-called 'improper' ferroelectrics are described in section 5.6. Finally brief introductions are given to the topics of surface waves (section 5.7) and lead zirconate titanate (PZT) ceramics (section 5.8). 5.2 Elasticities and piezoelectric coefficients Elasticities and piezoelectric coefficients are presented by matrices like the following examples. However, for the most part we shall introduce the conceptions in their simpler one-dimensional or scalar form. For example, an elastic compliance s is strain/stress. The elastic compliance is a fourth-rank tensor siJU (sA in the reduced 'matrix notation 1 ) with 81 components. In principle, though, the high crystal symmetries we are often concerned with reduce this number. In K D P , as an example, at room temperature, the components which are non-zero are only six in number: S

5

S

11 12 s 13 0 0

12 11 S 13 0 0

13 13 S 33 0 0

0

0

0

s

S

S

0 0 0 S44

0 0 0 0

0 0

S44

0 0 0 0 0

0

S(

In Rochelle salt between the two transition temperatures, where it is orthorhombic, they number nine: Sll «12 *13

«12 *22 *23

Sl3 *23 *33

0 0 0

0 0 0

0 0 0

73

MECHANICAL PROPERTIES 0

0

0

S44

0

0

0

0

0

0

0

0

0 S55 0

0 0 *66

F o r typical values of elastic coefficients see table 5.1, which gives data known for barium titanate.

Tabla S.1 Barium titanata: Elaatic and electrostrictive parameters •

x= -sX+QPjPj X'-^Pj 0.725 x 1 0 - 1 1 -0.315 x 10-11 -0.326 x10"11 1.08 x 10" 1 1

,2 , 3 ~~ S23 S33 S S

N"1m2 N "1m2 N-'m2 N"1m2

3.1 x10-2OC"2m4 - 1 . 2 3 x 10~ 2 0 C _ 2 m 4 3.2 x I O - 9 N m 2 C - 2 0.28 x TO" 9 N m 2 C - 2

0,1

0,2