FERROELECTRICS - CHARACTERIZATIONAND MODELING Edited by Mickal Lallart Ferroelectrics - Characterization and Modeling Edited by Mickal Lallart Published by InTech Janeza Trdine 9, 51000 Rijeka, Croatia Copyright 2011 InTech All chapters are Open Access articles distributed under the Creative CommonsNon Commercial Share Alike Attribution 3.0 license, which permits to copy,distribute, transmit, and adapt the work in any medium, so long as the originalwork is properly cited. After this work has been published by InTech, authorshave the right to republish it, in whole or part, in any publication of which theyare the author, and to make other personal use of the work. Any republication, referencing or personal use of the work must explicitly identify the original source. Statements and opinions expressed in the chapters are these of the individual contributors and not necessarily those of the editors or publisher. No responsibility is acceptedfor the accuracy of information contained in the published articles. The publisherassumes no responsibility for any damage or injury to persons or property arising outof the use of any materials, instructions, methods or ideas contained in the book.

Publishing Process Manager Silvia Vlase Technical Editor Teodora Smiljanic Cover Designer Jan Hyrat Image Copyright Noel Powell, Schaumburg, 2010. Used under license from Shutterstock.com First published July, 2011 Printed in Croatia A free online edition of this book is available at www.intechopen.com Additional hard copies can be obtained from orders@intechweb.org Ferroelectrics - Characterization and Modeling, Edited by Mickal Lallart p.cm.ISBN 978-953-307-455-9 free online editions of InTech Books and Journals can be found atwww.intechopen.com Contents PrefaceIX Part 1Characterization: Structural Aspects1 Chapter 1Structural Studies inPerovskite Ferroelectric Crystals Based on Synchrotron Radiation Analysis Techniques3 Jingzhong Xiao Chapter 2Near-Field Scanning Optical MicroscopyApplied to the Study of Ferroelectric Materials23 Josep Canet-Ferrer and Juan P. Martnez-Pastor Chapter 3Internal Dynamics of theFerroelectric (C3N2H5)5Bi2Cl11

Studied by 1H NMR and IINS Methods41 Krystyna Hoderna-Natkaniec,Ryszard Jakubas and Ireneusz Natkaniec Chapter 4Structure Property Relationships of Near-EutecticBaTiO3 CoFe2O4Magnetoelectric Composites61 Rashed Adnan Islam, Mirza Bichurin and Shashank Priya Chapter 5Impact of Defect Structure onBulk and Nano-Scale Ferroelectrics79 Emre Erdem and Rdiger-A. Eichel Chapter 6Microstructural Defects inFerroelectrics and Their Scientific Implications97 Duo Liu Part 2Characterization: Electrical Response115 Chapter 7All-Ceramic PercolativeComposites with a Colossal Dielectric Response117 Vid Bobnar, Marko Hrovat, Janez Holc and Marija Kosec VIContents Chapter 8Electrical Processes in Polycrystalline BiFeO3 Film135 Yawei Li, Zhigao Hu and Junhao Chu Chapter 9Phase Transitions inLayered Semiconductor - Ferroelectrics153 Andrius Dziaugys, Juras Banys, Vytautas Samulionis,Jan Macutkevic, Yulian Vysochanskii,Vladimir Shvartsman and Wolfgang Kleemann Chapter 10Non-Linear Dielectric Response ofFerroelectrics, Relaxors and Dipolar Glasses181 Seweryn Miga, Jan Dec and Wolfgang Kleemann Chapter 11Ferroelectrics Study at Microwaves203 Yuriy Poplavko, Yuriy Prokopenko, Vitaliy Molchanov and Victor Kazmirenko Part 3Characterization: Multiphysic Analysis227 Chapter 12Changes of Crystal Structure and Electrical Propertieswith Film Thickness and Zr/(Zr+Ti) Ratio for Epitaxial Pb(Zr,Ti)O3 Films Grown on (100)cSrRuO3//(100)SrTiO3

Substrates by Metalorganic Chemical Vapor Deposition229 Mohamed-Tahar Chentir, Hitoshi Morioka,Yoshitaka Ehara, Keisuke Saito, Shintaro Yokoyama, Takahiro Oikawa and Hiroshi Funakubo Chapter 13Double Hysteresis Loop inBaTiO3-Based Ferroelectric Ceramics245 Sining Yun Chapter 14The Ferroelectric DependentMagnetoelectricity in Composites265 L. R. Naik and B. K. Bammannavar Chapter 15Characterization of FerroelectricMaterials by Photopyroelectric Method281 Dadarlat Dorin, Longuemart Stphane and Hadj Sahraoui Abdelhak Chapter 16Valence Band Offsets of ZnO/SrTiO3, ZnO/BaTiO3,InN/SrTiO3, and InN/BaTiO3 HeterojunctionsMeasured by X-Ray Photoelectron Spectroscopy305 Caihong Jia, Yonghai Chen, Xianglin Liu,Shaoyan Yang and Zhanguo Wang Part 4Modeling: Phenomenological Analysis325 Chapter 17Self-Consistent AnharmonicTheory and Its Application to BaTiO3 Crystal327 Yutaka Aikawa ContentsVII Chapter 18Switching Properties of Finite-Sized Ferroelectrics349 L.-H. Ong and K.-H. Chew Chapter 19Intrinsic Interface Coupling inFerroelectric Heterostructures and Superlattices373 K.-H. Chew, L.-H. Ong and M. Iwata Chapter 20First-Principles Study of ABO3:Role of the BO Coulomb Repulsionsfor Ferroelectricity and Piezoelectricity395 Kaoru Miura Chapter 21Ab Initio Studies ofH-Bonded Systems: The Cases ofFerroelectric KH2PO4 and Antiferroelectric NH4H2PO4411 S. Koval, J. Lasave, R. L. Migoni, J. Kohanoff and N. S. Dalal Chapter 22Temperature Dependenceof the Dielectric Constant CalculatedUsing a Mean Field Model Close to theSmectic A - Isotropic Liquid Transition437 H. Yurtseven and E. Kilit Chapter 23Mesoscopic Modeling ofFerroelectric and Multiferroic Systems449 Thomas Bose and Steffen Trimper Chapter 24A General Conductivity Expressionfor Space-Charge-Limited Conduction inFerroelectrics and Other Solid Dielectrics467 Ho-Kei Chan Part 5Modeling: Nonlinearities491 Chapter 25Nonlinearity and ScalingBehavior in a Ferroelectric Materials493 Abdelowahed Hajjaji, Mohamed Rguiti, Daniel Guyomar,Yahia Boughaleb and Christan Courtois Chapter 26Harmonic Generation in Nanoscale Ferroelectric Films513 Jeffrey F. Webb Chapter 27Nonlinear HystereticResponse of Piezoelectric Ceramics537 Amir Sohrabi and Anastasia Muliana Chapter 28Modeling and NumericalSimulation of Ferroelectric MaterialBehavior Using Hysteresis Operators561 Manfred Kaltenbacher and Barbara Kaltenbacher Preface Ferroelectricityhasbeenoneofthemost usedandstudiedphenomenainbothscien-tific and industrial communities. Properties of ferroelectrics materials make them par-ticularly suitable for a wide range of applications, ranging from sensors and actuators toopticalormemorydevices.SincethediscoveryofferroelectricityinRochelleSalt (which used to be used since 1665) in 1921 by J. Valasek, numerous applications using such an effect have been developed. First employed in large majority insonars in the middle of the 20th century, ferroelectric materials have been able to be adapted to more and more systems in our daily life (ultrasound or thermal imaging, accelerometers, gy-roscopes, filters), and promising breakthrough applications are still under develop-ment(non-volatilememory,opticaldevices),makingferroelectricsoneoftomor-rows most important materials. The purpose of this collection is to present an up-to-date view of ferroelectricity and its applications, and is divided into four books: MaterialAspects,describingwaystoselectandprocessmaterialstomake them ferroelectric. Physical Effects, aiming at explaining the underlying mechanisms in ferroelec-tric materials and effects that arise from their particular properties. CharacterizationandModeling,givinganoverviewofhowtoquantifythe mechanismsofferroelectricmaterials(bothinmicroscopicandmacroscopic approaches) and to predict their performance. Applications, showing breakthrough use of ferroelectrics. Authors of each chapter have been selected according to their scientific work and their contributions to the community, ensuring high-quality contents. Thepresentvolumeaimsatexposingcharacterizationmethodsandtheirapplication toassesstheperformanceofferroelectricmaterials,aswellaspresentinginnovative approaches for modeling the behavior of such devices. Thebookisdecomposedintofivesections,includingstructuralandmicrostructural characterization (chapters 1 to 6), electrical characterization (chapters 7 to 11), multiphysic characterization(chapters12to16),phenomenologicalapproachesformodelingthe XPreface behavior of ferroelectric materials (chapters 17 to 24), and nonlinear modeling (chapters 25 to 28). I sincerely hope you will find this book as enjoyable to read as it was to edit, and that it will help your research and/or give new ideas in the wide field of ferroelectric mate-rials. Finally, I would like to take the opportunity of writing this preface to thank all the au-thorsfortheirhighqualitycontributions,aswellastheInTechpublishingteam(and especiallythepublishingprocessmanager,Ms.SilviaVlase)fortheiroutstanding support. June 2011 Dr. Mickal Lallart INSA Lyon, Villeurbanne France Part 1 Characterization: Structural Aspects 1 Structural Studies inPerovskite Ferroelectric Crystals Based on Synchrotron Radiation Analysis Techniques Jingzhong Xiao1,2 1CEMDRX, Department of Physics, University of Coimbra, Coimbra, 2International Centre for Materials Physics,Chinese Academy of Sciences, Shenyang, 1Portugal 2China 1. Introduction Perovskiteoxidematerials,havingthegeneralformulaABO3,formthebackboneofthe ferroelectrics industry.Thesematerialshavecomeintowidespreaduseinapplications that rangeinsophisticationfrommedicalultrasoundandunderwatersonarsystems,relatively mundane devices to novel applications in active and passive damping systems for sporting goods and automobiles [1-3]. Recent developments in regard to relaxor-based single crystal piezoelectrics,suchasPb(Zn1/3Nb2/3)O3PbTiO3(PZNT),Pb(Fe1/2Nb/1/2)O3PbTiO3

(PFNT)andPb(Mg1/3Nb2/3)O3PbTiO3(PMNT)haveshownsuperiorperformance compared to the conventional Pb(Zr,Ti)O3 (PZT) ceramics[4, 5]. Particularly, their ultrahigh piezoelectricandelectromechanicalcouplingfactorsinthedirectioncanreachto d33>2000pC/N and k3394%, which have attracted tremendous interests and still make these materials very hot. However,theoriginandstructuralnatureoftheirultrahighperformancesremainsone inquisitivebutobscuresubjectofrecentscientificinterest.Tobetterunderstandthe structuralnatureoftheoutstandingproperties,itisveryimportantforinvestigatingthe ferroelectric domain structure in these materials. In ferroelectrics, according to the electrical and mechanical compatibility conditions, domain structures of 180o and non-180o will form withrespecttocrystalsymmetry.Thereisacloselyrelationshipbetweenthedomain structureandthecrystalsymmetry.Throughtheobservationonferroelectricdomain configurations,thecrystalstructurescanbeconfirmed.Ferroelectricdomainsare homogenousregionswithinferroelectricmaterialsinwhichpolarizationsliealongone direction,thatinfluencethepiezoelectricandferroelectricpropertiesofthematerialsfor utilization in memory devices, micro-electromechanical systems, etc. Understanding the role of domain structure on properties relies on microscopy methods that can inspect the domain configuration and reveal the evolution or the dynamic behaviour of domain structure.It is also well known that the key to solve this issue of exploring the origin of the excellent properties is to reveal the peculiar complex perovskite crystal structures in these materials. Through study in structure behavior under high-pressure and local structure at atomic level will be helpful for better understanding this problem. Ferroelectrics - Characterization and Modeling 4 2. Synchrotron radiation X-ray structure investigation on ferroelectric crystalsPb(Zn1/3Nb2/3)O3-PbTiO3 (PZNT)andPb(Fe1/2Nb/1/2)O3PbTiO3(PFNT)crystalaremodel ABO3-typerelaxorferroelectricmaterials(orferroelectrics),whichdemonstratesexcellent performance in the filed of dielectrics, piezoelectrics, and electrostriction, etc. To explore the common issues of structural nature and the relationship between structure and performance ofultrahigh-performanceinthesematerials,inthischapter,thenovelX-rayanalysis techniquesbasedonsynchrotronradiationlight,suchassynchrotronradiationX-Ray topography,high-pressureinsitusynchrotronradiationenergydispersivediffraction,andXAFSmethod,areutilizedtoinvestigatethedomainconfiguration,structureandtheir evolution behavior induced by temperature changes and external field.2.1 Application of white beam synchrotron radiation X-ray topography for in-situ study of ferroelectric domain structuresFerroelectricdomainscanbeobservedbyvariousimagingtechniquessuchasoptical microscopy, scanning electron microscopy (SEM), transmission electron microscopy (TEM), X-rayimaging,andetc.Imagingisnormallyassociatedwithlenses.Unlikevisiblelightor electrons, however, efficient lenses are not available for hard X-rays, essentially because they interact weakly with matter. Comparatively as an X-ray imaging method, X-ray topography plays a vital role in providing a better understanding of ferroelectric domain structure.[6] X-raysaremorepenetratingthanphotonsandelectrons,andtheadventofsynchrotron radiation with good collimation, a continuous spectrum (white beam) and high intensity has givenX-raytopographyadditionalpowers.ThediffractionimagecontrastinX-ray topographscanbeaccessedfromvariationsinatomicinterplanarspacingsorinterference effectsbetweenX-rayanddomainboundariessothatdomainstructurecanbedirectly observed (with a micrometer resolution). Especially, via a white beam synchrotron radiation X-raydiffractiontopographytechnique(WBSRT),onecanstudythedynamicbehaviourof domainstructureandphaseevolutioninferroelectriccrystalsrespectivelyinducedbythe changes of sample temperature, applied electric field, and other parameter changes. In this chapter, a brief introduction to principles for studying ferroelectric domain structure by X-raydiffractionimagingtechniquesisprovided.Themethodsanddevicesforin-situ studying domain evolution by WBSR are delineated. Several experimental results on dynamic behavior of domain structure and induced phase transition in ferroelectric crystals accessed at beam line 4W1A of the Beijing Synchrotron Radiation Laboratory (BSRL) are introduced. 2.1.1 Principle of synchrotron radiation X-ray topography a. X-ray topography approach X-ray diffraction topography is an imaging technique based on Bragg diffraction. In the last decades,X-raydiffractiontopographytocharacterizecrystalsforthemicroelectronics industryweredevelopedandcompletelyrenewedbythemodernsynchrotronradiation sources. [6] Itsimages(topographs)recordtheintensityprofileofabeamofX-raysdiffractedbya crystal.Atopographthusrepresentsatwo-dimensionalspatialintensitymappingof reflected X-rays, i.e. the spatial fine structure of a Bragg spot. This intensity mapping reflects thedistributionofscatteringpowerinsidethecrystal;topographsthereforerevealthe Structural Studies in Perovskite FerroelectricCrystals Based on Synchrotron Radiation Analysis Techniques 5 irregularitiesinanon-idealcrystallattice.Thebasicworkingprincipleofdiffraction topography is as follows: An incident, spatially extended X-ray beam impinges on a sample, asshowninFig.1.Thebeammaybeeithermonochromatic,orpolychromatic(i.e.be composed of a mixture of wavelengths (white beam topography)). Furthermore, the incident beammaybeeitherparallel,consistingonlyofrayspropagatingallalongnearlythesame direction, or divergent/convergent, containing several more strongly different directions of propagation. Fig. 1. The scheme of basic principle of diffraction topography. A homogeneous sample (with a regular crystal lattice) would yield a homogeneous intensity distributioninthetopograph(a"flat"image).Intensitymodulations(topographiccontrast) arise from irregularities in the crystal lattice, originating from various kinds of defects such ascracks,surfacescratches,dislocations,grainboundaries,domainwalls,etc.Theoretical descriptionsofcontrastformationinX-raytopographyarelargelybasedonthedynamical theoryofdiffraction.Thisframeworkishelpfulinthedescriptionofmanyaspectsof topographic image formation: entrance of an X-ray wave-field into a crystal, propagation of thewave-fieldinsidethecrystal,interactionofwave-fieldwithcrystaldefects,alteringof wave-fieldpropagationbylocallatticestrains,diffraction,multiplescattering,absorption. Theoretical calculations, and in particular numerical simulations by computer based on this theory,arethusavaluabletoolfortheinterpretationoftopographicimages.Contrast formation in white beam topography is based on the differences in the X-ray beam intensity diffracted from a distorted region around the defect compared with the intensity diffracted fromtheperfectcrystalregion.Theimageofthisdistortedregioncorrespondstoan increased intensity (direct image) in the low absorption case. Toconductatopographicexperiment,threegroupsofinstrumentsarerequired:anx-ray source,potentiallyincludingappropriatex-rayoptics;asamplestagewithsample manipulator (diffractometer); and a two-dimensionally resolving detector (most often X-ray filmorcamera).Thex-raybeamusedfortopographyisgeneratedbyanx-raysource, typically either a laboratory x-ray tube (fixed or rotating) or a synchrotron source. The latter offersadvantagesduetoitshigherbeamintensity,lowerdivergence,anditscontinuous wavelength spectrum. The topography technique combinning with a synchrotron source, is well adapted to in-situ experiments, where the material, in an adequate sample environment device,isimagedwhileanexternalparameter(temperature,electricalfield,andetc)is changed. Ferroelectrics - Characterization and Modeling 6 Fig. 2. Experimental arrangement for synchrotron radiation white beam Laue topography. b. White beam X-ray topography A simple way to understand the creation of X-ray topographic images is to consider a Laue photograph(Fig.2).Apolychromatic(white)X-raybeam,containingX-rayenergiesfrom about 6 keV to 50 keV (X-ray wavelengths from approximately 2 to 0.25 ), impinges on a crystal. [6] The beam is diffracted in manydirections, creating Laue spots. The positions of the diffraction spots appear according to the Bragg equation: 2 sinBhcEd = , or2 sinBd = (1) whereEistheincidentX-rayenergy(andistheincidentwavelength)selectedbycrystal planes with spacing d, h is Plancks constant, c is the speed of light, and B is the Bragg angle. Each spot contains uniform intensity if the crystal is perfect.If, however, the crystal is strained, streaks appear instead of spots due to variations in lattice spacing.Infact,eachLauespotcontainsaspatialdistributionofdiffractedintensity attributable to the presence of defects in the crystal. This distributed intensity is difficult to seebecauseLauespotsaretypicallythesamesizeastheX-raybeampinhole,andthe incident X-ray beam is divergent, but each tiny Laue spot is actually an X-ray topograph. At synchrotronradiationfacilities,acollimatedwhiteX-raybeamcanbeusedtoilluminatea sample crystal, and spots with the much larger cross section of the synchrotron X-ray beam are recorded. The resulting data are an array of Laue spots, as shown in Fig. 2, each of which is an X-ray topograph arising from a different set of atomic planes. c. Ferroelectric domain characterizations Theexistenceofantiparallel180domainsisoneofthefundamentalpropertiesof ferroelectrics and direct observation of these domains is invaluable to the understanding of thepolarizationreversalmechanismofferroelectricstructures.Amongthetechniquesof visualizingantiparalleldomains,conventionalx-raytopographyisanimportantand efficientmethodalthoughitsapplicationislimitedbytheonlyavailablecharacteristic radiations.However,thislimitationiseasilyovercomebythewhite-beamsynchrotron radiationtopography(WBSRT).AuniqueaspectofWBSRTistheopportunityitaffordsto selectoutofthecontinuousspectrumanyintendedwavelengthstoactivatestrong anomalousscattering.And,withtheWBSRT,itispossibleforseveraldiffractionimages Structural Studies in Perovskite FerroelectricCrystals Based on Synchrotron Radiation Analysis Techniques 7 with anomalous dispersion effect to be activated simultaneously so that the contrast reversal of 180 domains can be directly observed.[7-9] The natural collimation and high intensity of the radiation also make the real-time observation of domain dynamics feasible. As shown in Fig.3,whenworkingwithacoherentx-raybeam,andifthephasesofthestructurefactors are different, the 180 ferroelectric domains can be revealed.Consideringthemechanicalandelectricalcompatibilityconditions,alloweddomainsin ferroelectrics are the 180o or non-180o ones with the different planes as the domain walls.[8, 9] The extinction condition for a domain wall is: 0 P g = (2) wheregisthereciprocalvectorofthediffractingplane, 1 2P P P = isthedifferenceofthe polarization vectors across the domain wall. Non-180o domain structure is illustrated in Fig.4. Fig. 3. (Colour on the web only) Scheme of 180o domain. Fig. 4. Scheme of non-180o domain. 2.1.2 In-situ topography measurements Whitebeamsynchrotronradiationtopographynotonlyovercomesthedrawbackoflong exposuretimefortheconventionalx-raytopography,butalsoextendsthescopeof topography study. The excellent collimation and high intensity of the synchrotron radiation makesthepossibilityofenlargingthedistancebetweenthelightsourceandsample,to improve the image resolution and enlarge the distance between the sample and the detector. Theseallowonesabletoinstallthesamplesinsidelargeenvironmentalchamberswith changesoftemperature,electricfield,orotherparameters,tocarryoutthein-situ topography studies. [10] Ferroelectrics - Characterization and Modeling 8 a. High temperature condition A high-temperature chamber was used for in situ topography study. The cylindrical furnace inusewasmadeofpuregraphite.Twoberylliumwindowswereusedforincidentand outgoingx-rays.Twothermocouplesattachedclosetothespecimenwereusedtomonitor andcontrolthetemperature.Adigitalcontrolpowersupplycanramptheelectriccurrent smoothly when starting to heat. The temperature control system is based on the Eurotherm controller (model 818) and solid state relay (SSR). By using PID control and time proportion method,thetemperaturestabilityisabout0.05Cwhenholdingand0.1Cwhenramping. Theon-linePCcansetandmonitorthetemperatureviaRS-232interface.Asketchofthis chamber is shown in Fig. 5. Fig. 5. Sketch of the high temperature sample chamber: 1-entrance Be window; 2-water cooling environment chamber; 3-furnace; 4-specimen; 5-exit Be window; 6-film. Fig. 6. The experimental arrangement for applying electric field. b. DC electric fieldThechangeoftheferroelectricdomainstructureduetotheappliedDCfieldcanalsobe observedbywhitebeamsynchrotronradiationtopography.Fig.6istheexperimental arrangementofapplyingtheDCfield.Thedistancebetweenthetwoelectrodeswas4mm andtheappliedDCvoltagerangedfrom0to4400V.Thesamplescanbeinstalledonthe surface of plastic plates. The DC electrical field can be applied on two Al electrodes covering on the surface of two X-ray transparent organic materials. 2.1.3 In-situ topography study in ferroelectric crystals The in-situ experiments are performed at Beijing Synchrotron Radiation Facility (BSRF). The x-ray topography station and attached 4W1A beamline are part of the BSRF. The 4W1A is a 45mlongwhite/monochromaticwigglerbeamline.WhentheBEPCisoperatedatthe Structural Studies in Perovskite FerroelectricCrystals Based on Synchrotron Radiation Analysis Techniques 9 energyof2.2GeVandthemagneticfieldofthewigglerat1.8T.Thetopographystation situatedattheendofthebeamline4W1Aismainlyusedforthestudyoftheperfectionof singlecrystals,highresolutionmulti-crystaldiffractionandx-raystandingwaveresearch. Themainequipmentofthestationconsistsofawhiteradiationtopographycamera,three environmentalsamplechambers,anx-rayvideoimagingsystemandafourcrystal monochromatic camera. The white radiation topography camera and three environmental sample chambers are used forthedynamictopographicexperimentswithchangeoftemperature,stress,electricfield or other parameters. The white radiation camera has five axes to rotate the specimen to any orientationwiththeincidentbeamandtorotatethedetectortocollecttheanydiffracted beam. a.Domainandtemperature-inducedphasetransformationin0.92Pb(Zn1/3Nb2/3)O30.08PbTiO3 crystals Theaimofthispresentworkistoinvestigatetemperature-dependencephaseevolutionin 0.92Pb(Zn1/3Nb2/3)O30.08PbTiO3(PZN8%PT)crystals,byemployingarealtimewhite-beamsynchrotronX-rayradiationtopographymethod(WBSRT).Bycombiningthis techniquewithothercomplementarystructuralexperiments,anovelpictureoflow symmetry phase transformation and phase coexistence is suggested.PZN8% PT single crystals used in this experiment were grown by the PbO flux method. A plateperpendicularto[001]axisiscutandwellpolishedtoapproximately200min thickness.Realtimeobservationisperformedatthetopographystationatthe4W1Abeam lineofBeijingSynchrotronRadiationLaboratory(BSRL).Thestorageringis2.2GeVwith beamcurrentvariedfrom50mAto90mA.Acylindricalfurnacewithcoiledheating elementsarrangedaxiallyaroundthesamplespaceisusedforinsitutopography investigation. After carefully mounted the samples on the hot-stage, we heat them at a slow rateof0.5 oC/min,observeandrecordthedynamictopographyimagesbyphotofilms. Throughthetopographyimagesobtainedbythismethod,wecanclearlyobservethe ferroelectricdomainconfigurationsandtheirevolutionasafunctionoftemperaturein PZN8% PT crystals.[11] Fig. 7 shows a series of synchrotron radiation topography images with (112) reflection of the (001)crystalplatetakenatdifferenttemperatures.FromFig.7(a)to(i),wefindthatthe domainstructuresareverycomplex.Theycanbecategorizedintothreekindsofdomains and addressed as A, B, and C, as shown in Fig. 7 (j). TheAdomainwalls,whichareatapproximately45otothe[100]axis,canbeobviously observedatroomtemperature.Thesedomainwallsareconsideredtobethe71o(or109o) onesinrhombohedralPZNPTcrystals,andcanbeclearlyobservedbeforeheatingthe sample to 132 oC. With increasing temperature from 75 oC to 131 oC, as shown in Fig. 7 (b)(c), the B domain laminates become progressively obvious and coexist with the A domains. On the other hand, these domain laminates are along the [010] axis, which can be classified into90otetragonaldomainwalls.Atthepointof131 oC,thetetragonaldomainsbecome most clear. With heating the sample to above 132 oC, as shown in Fig. 7 (d), we find that the rhombohedral71o(or109o)domainwalls(Alaminates)becomevague,andtheimage backgroundbecomesbrighterthanbefore.However,thetetragonaldomainwallsarestill clear.Thisphenomenonshowsthatthephasetransitionfromrhombohedraltotetragonal phase (RT transition) starts at 75 oC, and the tetragonal domains grow gradually. Ferroelectrics - Characterization and Modeling 10 Fig. 7. (Colour on the web only) Images of the in situ synchrotron radiation topography in PZN8% PT crystals, the x-rays incident direction to the crystal is [001], the diffraction vector is g = (112): (a) room temperature (20 oC); (b) heating to 75 oC; (c) heating to 131 oC; (d) heating to 132 oC; (e) heating to 190 oC; (f) heating to 262 oC; (g) cooling to 190 oC; (h) cooling to 75 oC; (i) cooling to room temperature; (j) Schematic picture for presenting the ferroelectric domain configurations in the topography images of PZN8% PT crystals; (k) enlarged images of C domain walls from 75 oC to 190 oC. Most particularly, a set of unique domain walls (C domain walls) appear at this temperature, whichisquitedifferentfromtheAandBdomains.Thiskindofdomainwallsisshownin Fig.7 (k), through the enlarged images taken from 75 oC to 190 oC. As the figures show, the C domain laminates deviate from the (010) direction at 15 o20 o. According to the knowledge of domainsorientationincrystalswithdifferentsymmetryandX-raydiffractionextinction relations, as formula (2) shows, these laminates can be considered to be neither rhombohedral nor tetragonal domain structures, but a new monoclinic phase domain structure.Withfurtherheatingofthesystemtoabout132 oC,wefindthisdomainstructureisvery stableandcoexistswithBtetragonaldomains.UponfurtherheatingtoaboveTc(170 oC), themonoclinicCdomainstructurealsoremains.Thiscaseshowsthatamonoclinicphase notonlyappearsintheprocessofferroelectricferroelectricphasetransformation,butalso coexistswiththecubicphasewellaboveTC.Withthetemperatureelevatingtoabout262 oC, we find nearly all the ferroelectric domains disappear, as shown in Fig. 7 (f). Whilstcoolingthesamplefrom262 oCto75 oC,themonoclinicdomains(Claminates),as wellasthetetragonaldomains(Blaminates),arefoundtoreappear,whereasthe rhombohedral domains (A laminates) cannot be recovered by cooling to room temperature. Duringthecrystalgrowth,arapidcoolingprocesswasemployedforquickcrystallization andtoavoidthegenerationofapyrochlorephase,whichresultsinastrainfieldinthe crystal. The rhombohedral A domains are expected to be induced by this kind of strain field and preserved at room temperature. Thus A domains do not reappear after the crystals are re-cooledfrom260 oCtoroomtemperaturewithaslowcoolingrate,sincethiscooling processpossiblyreleasesthecrystalstrainfield.However,themonoclinicphasewasnot generatedbythestrainfieldinducedduringthecrystalgrowth,sincetheparticularC domains as well as B domains can be recovered at 75 oC by slow cooling. Structural Studies in Perovskite FerroelectricCrystals Based on Synchrotron Radiation Analysis Techniques 11 Generally,withthesampletemperaturereachestotheCurietemperature,thereoccursa ferroelectric-paraelectric phase transition in conventional ferroelectrics, which results in the disappearance of the domain structure. However in relaxor ferroelectrics, as shown in Fig. 8 thedomainstructurecanbeobservedclearlyon(111)faceofPZN-8%PTcrystalwhenthe sampletemperatureismuchhigherthantheCurietemperature.Thisphenomenoncanbe induced by the micro-polarization-region in relaxor crystals.Through in situ synchrotron radiation topography under various temperatures, the complex configurationanddynamicevolutionofferroelectricdomainsinferroelectriccrystalsare obtained.Itisexpectedthatthepresentresultswillencouragemoreresearchinterestin exploringtheoriginoftheultra-highpiezoelectricandelectrostrictionpropertiesin ferroelectrics and other advanced materials. Fig. 8. (Colour on the web only) The temperature induced evolution of the domain structure on (111) face of PZN-8%PT crystal, observed by in situ synchrotron radiation topography. b. Electrical field induced domain structure The Gd2(MoO4)3 (GMO) crystals were grown by the induction-heated CZ technique. The (0 0 1)crystalpiecesof1015mmdiameterwerecutandpolishedinto2.0or0.5mmin thickness. The transparent pieces were using to study the DC electric field induced domain structurebytransmissionX-raytopographyatbeamline4W1AoftheBeijingSynchrotron RadiationLaboratory(BSRL)ThechangeofthedomainstructureduetotheappliedDC fieldwasalsoobserved.Fig.6istheexperimentalarrangementofapplyingtheDCfield. The distance between the two electrodes was 4mm and the applied DC field ranged from 0 to 4400 V. Fig. 9. The domain structure of GMO varies with the applied DC field. Ferroelectrics - Characterization and Modeling 12Fig. 9 is a set of series topographs when an applied DC field was added on the GMO crystal piece. Fig. 9 (a) and (b) are the results obtained when the applied voltage was 600 and 700 V, respectively,andthedomainstructurediddisappear.Fig.9(c)wastheresultwhenthe voltage was lowered to zero. From these photographs, we concluded that the multidomain couldbetransformedtosingledomainbyapplyingaDCfieldandthatthesingledomain could be kept even if the applied DC field was taken away. This experimental result shows usthatitispossibletomakeaperiodicallypoledGMOcrystal,despitethepresenceof ferroelectricandferroelasticdomainsintheunpoledGMOcrystal.Fromtheseresults,we concludedthattheferroelectricandferroelasticmultidomainscouldbetransformedtoa singledomainbytheappliedDCfield,andthesingledomaincouldbekeptevenifthe applied DC field was taken away.[12] 2.2 High-pressure structural behavior in PZN-PT relaxor ferroelectricsThe ideal structure of ABO3-type perovskite can be described as a network of corner-linked octahedra, as shown in Fig.10. With B cations at the centre of the octahedra and A cations in the space (coordination 12) between the AO12 and BO6 polyhedra. As its B cation comprised byZn2+,Nb5+, andTi4+ ions, aswellasthe AcationcomprisedbyPb2+ion,PZNTdeviates from the ideal perovskite by cation displacements or a rotation (or tilting) of BO6 octahedra. The possible off-centering of the B cations makes the crystal structure more complex than that of the ideal ABO3-type perovskites and reasonably influence the properties. Previously, approachestowardstheunderstandingoftherelaxorferroelectricswerefocusedonthe structuralevolutioninducedbythechangesofchemicalcomposition,electricalfieldor temperatureenvironment.[13-14]Virtually,theseabovevariablesinducephasetransitions bymainlyplayingaroleofcausingdisplacementofthecationandanionandrotationof BO6 octahedra in perovskite. Nevertheless,directlycompressingthematerialscanalsoinducesimilarresultsthatwill provide a new ken and approach to investigate the complex structure in the ferroelectrics andotherfunctionalmaterials.Itispointedoutthattheeffectofpressureisacleaner variable, since it acts only on interatomic interactions.[15] Compared to other parameters, asanextremevariable,high-pressureisoftheuniqueimportanceinelucidating ferroelectrics,fortheuniquestructuralchangeissusceptibletopressure.Studyingthe structuralchangesandcompressivebehaviorsunderhigh-pressureconditionisableto facilitatetheunderstandingforstructuralnatureofthehigh-performancesinrelaxor ferroelectricsorothernovelfunctionalmaterialsundernormalstate.Thus,recently,the high-pressurestructuralinvestigationsinrelaxorferroelectricshadbecomevery popular.[16,17]Forinstance,Kreisel,etalperformedahigh-pressureinvestigationby RammanspectroscopyofPb(Mg1/3Nb2/3)O3(PMN),andhadobtainedtheunusual pressure-dependentRammanrelaxor-specificspectraandphasechange.Bycombining theexternalparameterhighpressurewithx-raydiffusescatteringmethod,apressure-inducedsuppressionofthediffusescatteringinPMNwasindicated.Theirobserved pressure-inducedsuppressionofdiffusesedscatteringabove5GPaisalsoageneral featureinrelaxorsathighpressure.[18]Inthispresentwork,weperformedahigh-pressuresynchrotronradiationenergy-dispersivex-raydiffraction(EDXD)investigation on0.92PZN-0.08PTferroelectrics,tostudythecompressivebehaviorofthematerials under high-pressure condition. Structural Studies in Perovskite FerroelectricCrystals Based on Synchrotron Radiation Analysis Techniques 13 Fig. 10. Illustration of ideal ABO3-type perovskite structure, which can be described as a network of corner-linked octahedral. 2.2.1 High-pressure synchrotron radiation energy-dispersive x-ray diffraction (EDXD) Thehigh-pressureX-raydiffractionpatternsemployedanenergy-dispersivemethodand wererecordedonthewigglerbeamline(4W2)oftheBeijingSynchrotronRadiation Laboratory(BSRL).[19]AWA66B-typediamondanvilcell(DAC)wasdrivenbyan accuratelyadjustablegear-worm-levelsystem.The0.92PZN-0.08PTpowdersandpressure calibratingmaterials(Platinumpowder)wereloadedintothesamplechamberofaT301 stainless steel gasket. A mixture of methanol/ ethanol 4:1 was used as the pressure medium. Pressure was determined from (111), and (220) peaks of Pt along with its respective equation ofstate.Thed-valuesofthespecimenscanbeobtainedaccordingtotheenergydispersion equation: 0.619927( )sinE d keV nm = (3) ThepolychromaticX-raybeamwascollimatedtoa4030msizedspotwiththestorage ring operating at 2.2 G eV. The diffracted beam was collected between 5 and 35 k eV and the diffraction 2 angle between the direct beam and the detector was set at about 15.9552 o. The experimentsetupisshowninFig.11.Thepressure-inducedcrystallographicbehaviorwas studiedupto40.73GPaatroomtemperaturein22stepsduringthepressure-increasing process, and the evolution of high-pressure EDXD patterns is obtained. Fig. 11. The setup of high-pressure X-ray energy-dispersive diffraction experiment. Ferroelectrics - Characterization and Modeling 142.2.2 High-pressure compressive behavior in PZNT-PT crystals Fig.12showstheselectedEDXDpatternsof0.92PZN-0.08PTsampleunderdifferent pressures,fromwhichthepeaksof(110),(111),(200),(210),and(211)indexedintermsof rhombohedralstructurecanbeobserved.Thestrongpeaksof(111)and(200)ofPt,whose photonic energy is 19.72keV and 22.77keV respectively, will also be clearly observed. Apart fromthesediffractionlines,severalfluorescencepeaksofPbandNbareemergedinthe low-energy side of the curve. Withincreasingpressuresfromtheambientpressure(0GPa),the(110)and(200)peak becomebroader,theintensityof(210)and(211)peaksstarttodecreasefrom5.17GPa.On furtherincreasingpressure,theintensityof(210)and(211)peaksbecomeweakerfrom 21.34GPa, and the (210) peak vanishes at the pressure of 28.38 G Pa. at about 40.73GPa, these two peaks seem to be vanished. The abrupt changes of the EDXD patterns indicates that the phasetransitionscanpossiblybeinducedbyapplyingpressures,andtheestimated transition pressure point is at about 5.17GPa and 28.38GPa, respectively. Fig. 12. (Colour on the web only)The EDXD curves of PZNT sample under different pressures, the maximum pressure applied here is 40.73 G Pa. Pb (F) and Nb (F) indicate the fluorescence peaks of Pb and Nb emerged in the low-energy side. Inordertobetterunderstandthepressure-inducedphasetransitionandcompressive behaviorof0.92PZN-0.08PT,wecalculatedthestructureparameterssuchasinterplanar spacingvalue(d-value)evolvingundervariouspressuresaccordingtoexperimentresults and equation (1), as shown in Fig.13. It is noticed that, as a function of pressure, the d-value decreasingissuesofdifferentpeaksof(110),(200),and(211)aregreatlydifferent,reveals thatthecompressibilityofstructuralparametersisanisotropic.Toinvestigatethe compression behavior of the sample in different pressures, we divided the d (110) vs. pressure curve into several zones. It shows the decreasing rate of d (110) spacing in different pressure zonesisdifferent,i.e.,thedecreasingrateofthezonesofA,C,E,andGarenotidentical, which should demonstrate that the change of compressibility is also nonlinear. Structural Studies in Perovskite FerroelectricCrystals Based on Synchrotron Radiation Analysis Techniques 15 Fig. 13. The curves of d-spacing parameters of different diffraction peaks under various pressures. Top part: d (110) vs. pressure; Middle part: d (200) vs. pressure; and Bottom part: d (211) vs. pressure. The abrupt changes appeared in B, D, and F zones of the curve, which are corresponding to thethreepressurerangesofabout5.17-7.5GPa,15.2GPa-21.4GPa,and30.3-34.5GPa, respectively,showingseveralkinkyranges.[20]Wenamethisphenomenonasmulti-kinkypressurebehavior.Thisbehaviorisconsiderednottobeinducedbythe measurementerrors according to the error analysis. Generally, the energy resolution of the detectorinEDXDexperimentisakeyparametertodeterminediffractionpeakposition.In the present experiment, Si (Li) detector is adopted and its energy resolution is estimated to beabout170eV,fromwhichthemeasuringerrorofdiffractionpeakpositionmaybe calculatedtobelessthan3eV,correspondingtoarelativemeasuringerrorofstructural parameter of (d/d) 10-4. But for instance, in Fig.13a, the calculated (d/d) of the (110) face in kinky ranges is estimated to be at the order of 10-2. Therefore, the abnormal change ofd-spacingunderhigh-pressureshouldbeintimatelyrelatedtothestructural characteristicsofABO3compounds.Particularly,inBandDzones,thed (110)valuefirstly increasesandthendecreaseswiththeappliedpressures,whichseemstoshowaabnormal compressivebehavior.WhileinFzone,thed (110)valuedecreaseswiththeincreased pressure. This behavior can be ascribed to the abruptly changed strain induced by structural transformation from phase E to the phase G. The B, D, and F zones can also be considered as theareasforphase-coexistence,ortransformationregions.[21]Thed-spacingvs.pressure curves of (200) and (211) peaks also exhibit multi-kinky changes and nonlinear compressive behavior.Therefore,itisestimatedthatthismulti-kinkybehaviorisindicativeofpressure-inducedmulti-phasetransitionandphasecoexistenceoccursin0.92PZN-0.08PTcrystals. Theaccuratepressure-inducedlatticechangesextractedfromthehigh-pressureEDXD experiments will be published elsewhere. Ferroelectrics - Characterization and Modeling 16 Fig. 14. The curves of the relative volume V/V0 vs. pressure curve of 0.92PZN-0.08PT sample. Fig.14showstherelativevolumeV/V0vs.pressurecurveof0.92PZN-0.08PT,fromwhich can be seen that the volume of the unit cell changes with the increasing pressure. Similar to thecurveofd (110)vs.pressure,thiscurvecanalsodemonstrateinterestingmulti-kinky compressivebehavior.WeroughlyfittheexperimentaldatatoBirch-Murnaghan(BM) equation and get the equation of state (EOS) of 0.92PZN-0.08PT as following: ( )7 5 23 3 310 00 0 03 31 4 12 4V V VP B BV V V ((| | | | | | ((= ||| ` ((\ . \ . \ . (( )(4) thebulkmodulusB0anditsfirst-orderderivativeB01for0.92PZN-0.08PTsystemare obtained as B0 = 26715GPa, B01 = 4.AsshowninFig.13andFig.14,thestructureparameters(dandV)displayseveralabrupt changesaroundseveralcrossoverpressures(orduringseveralpressureranges),whichare the suggestive of the anomalous phase transitions and multi-kinky compressive behavior of 0.92PZN-0.08PTcrystalsunderhigh-pressurecondition.Itisspeculatedthatthiskinky behaviorofthestructuralparametersof0.92PZN-0.08PTcouldalsobeamoregeneral feature in ABO3-type perovskite oxides. For instance, some similar anomalous behaviors had alsobeenpresentedinBaTiO3andPbTiO3.[20]Throughthecalculationsusingafirst-principlesapproachbasedondensity-functionaltheory,anenormoustetragonalstraincan beinducedinthesetwosimpleperovskitesbyapplicationofanegativehydrostatic pressure.Theirstructuralparameterssuchascellvolumeandatomicdisplacementswere foundtodisplayakinkybehaviorsuggestiveofproximitytoaphasetransition. Comparatively, in the present work, a multi-kinky compressive behavior in 0.92PZN-0.08PT whichismorecomplexthansinglekinkybehaviorappearedinBaTiO3andPbTiO3was obtained.Inaway,thedifferentcompressivebehaviorbetween0.92PZN-0.08PTandthe Structural Studies in Perovskite FerroelectricCrystals Based on Synchrotron Radiation Analysis Techniques 17 simple peroveskites may be ascribed to the chemical composition variation. The B cation of BaTiO3 and PbTiO3 is only comprised by Ti4+ ion, while that of 0.92PZN-0.08PT is comprised byZn2+,Nb5+,andTi4+ions,whichmakesthestructureof0.92PZN-0.08PTmorecomplex than that of BaTiO3 and PbTiO3.Theuniquenonlinearbehaviorin0.92PZN-0.08PTcanalsobeexplainedintermsofthe relativecompressibilitiesoftheoctahedral(BO6polyhedral)anddodecahedral(AO12 polyhedral)cationsitesintheperovskitesstructure,orofthecompressibilitiesoftheA-O and B-O bonds, as shown in Fig.10. It is clearly that the relative compressibilities of the AO12 and BO6 sites must play an important role in determining whether the perovskite structure becomes more or less distorted with increasing pressure.[22] From the curves of cell volume ord-spacingVspressure,wefoundthatthebulkcompressibilitiesin0.92PZN-0.08PT varying with applying pressures. Since 0.92PZN-0.08PT is of perovskite structure comprised byAO12andBO6polyhedra,wethinktheevolutionofthebulkcompressibilitiesinitcan also be ascribed to the relative compressibilities of the AO12 and BO6. Theso-calledpolyhedralapproachisbasedontheobservationthattheidentificationof cationoxygenpolyhedra,MxOy,notonlysimplifiesthedescriptionofcomplexcrystal structures,butalsoallowsabetterunderstandingofphysicalpropertiesformaterials containingsimilarpolyhedra.[23,24]Consideringtheinfluenceofthebondlengthandthe anion/cation charge of a given polyhedron on the compressibility, the empirical expression for the compressibility of a given polyhedron were derived: 312043polyadK GPaS Z Z=(5) Za is the anion charge, Z0 the cation charge, d the bond length in and S 2 an ionicity scaling factor equal to 1/2 for oxygen-based polyhedra. The extension of this approach is to assume that the compressibility of complex crystals with linked polyhedra can be derived when poly foreachpolyhedronisknown.Basedontheconsiderationoftheinfluenceofcationanion distancesandanglesbetweenpolyhedra(polyhedratilting),J.Kresieletalproposeda simplemodeltodeducethebulkcompressibility,bulk,fromthecompressibilityofeach constituent polyhedron: 0poly ibulk i iiVK x kV= (6) wheretheindexireferstoagiventypeofcationanionpolyhedronandxiisthe concentrationonacrystallographicsite.Vi andV0arethevolumesofagivenpolyhedron and the unit cell, as described by 01iiiVxV| |= |\ .(7) Since in PZN-PT crystal, the AO12 polyhedron is PbO12 dodecahedra and the BO6 polyhedra is comprised by Zn-O group, Nb-O group, and Ti- O group. The equation (6) was modified to estimate the compressive behavior of 0.92PZN-0.08PT as following: 12 6 6 6 PbO ZnO NbO TiOPZNTPZNT PZNT PZNT PZNTV V V VK x y zV V V V= + + +(8) Ferroelectrics - Characterization and Modeling 18where x, y, z implies the concentration of Pb2+, Zn2+, Nb5+, and Ti4+ ions, respectively. Due to these cations being chemically very different, it is believed that the compessibilities of these MO6polyhedrawillbedifferentonapplyingvariouspressures,whichinfluencethetotal compressibilitiesin0.92PZN-0.08PTcrystals.Therefore,althoughthishigh-pressure diffractiontechniqueonlyallowthedeterminationofthemeanbonddistance,d,averaged overtheentirecrystalforeachdistinctpolyhedron,themodifiedmodelcanbeconsidered asanapproachtoexplainthecompressivebehaviorandthechangeofcompressibilitiesof 0.92PZN-0.08PT crystal under high-pressure conditions. Therefore, through the method of high pressure synchrotron radiation energy-dispersive x-ray diffraction, the abnormal compressive behavior in 0.92PZN-0.08PT under high-pressure havebeenobserved,whichisconsideredtobeintimatelyrelatedtothestructural characteristics of0.92PZN-0.08PTcrystals.The high-pressurecompressivebehaviorreflects and uncovers abundant structural information under extreme conditions, which is helpful to intriguesignificantinterestsinexploringthestructuralnatureandchemical(orphysical) originofultrahighperformanceinrelaxorferroelecricmaterialsandotherfunctional materials.2.3 XAFS study in relaxor ferroelectrics Relaxorferroelectricsareaclassofferroelectricsthathaveadiffuse,frequency-dependent permittivity maximum, with a relaxation spectrum much broader than the Debye type. But these features do not provide a direct link to the key structural element that is essential for relaxor ferroelectrics. A common, crucial element in all Pb containing relaxors, Pb(B, B)O3, isasizemismatchbetweentheferroelectricallyactiveBcationsandtheferroelectrically inactive B cations.The data of extended X-ray absorption fine structure (EXAFS) based on synchrotronradiationcanprovidelocalstructuralevidenceinindicatingthestructural origin of the anomanous properties in relaxors. 2.3.1 Synchrotron radiation XAFS approach X-ray absorption fine structure (XAFS) refers to the details of how x-rays are absorbed by an atomatenergiesnearandabovethecore-levelbindingenergiesofthatatom,asshownin Fig.15. Specifically, XAFS is the modulation of an atoms x-ray absorption probability due to thechemicalandphysicalstateoftheatom.XAFSspectraareespeciallysensitivetothe formal oxidation state, coordination chemistry, and the distances, coordination number and speciesoftheatomsimmediatelysurroundingtheselectedelement.Becauseofthis dependence, XAFS provides a practical and simple way to determine the chemical state and local atomic structure for a selected atomic species. XAFS can be used in a variety of systems and bulk physical environment.X-ray absorption measurements are relatively straightforward, provided one has an intense andenergy-tunablesourceofx-rays,suchasasynchrotronradiationsource.Many experimentaltechniquesandsampleconditionsareavailableforXAFS,includingsuch possibilities as very fast measurements of high spatial resolution. Since the characteristics of synchrotronsourcesandexperimentalstationdictatewhatenergyranges,beamsizes,and intensitiesareavailable,thisoftenputspracticalexperimentallimitsontheXAFS measurementsthatcanbedoneeveniftherearefewinherentlimitsonXAFS.Thex-ray absorptionspectrumistypicallydividedintotworegimes:x-rayabsorptionnear-edge spectroscopy (XANES) and extended x-ray absorption fine-structure spectroscopy (EXAFS). Structural Studies in Perovskite FerroelectricCrystals Based on Synchrotron Radiation Analysis Techniques 19 Thoughthetwohavethesamephysicalorigin,thisdistinctionisconvenientforthe interpretation.XANESisstronglysensitivetoformaloxidationstateandcoordination chemistry(e.g.,octahedral,tetrahedralcoordination)oftheabsorbingatom,whilethe EXAFSisusedtodeterminethedistances,coordinationnumber,andspeciesofthe neighbors of the absorbing atom. Fig. 15. (Colour on the web only) Illumination of XAFS measurements. 2.3.2 XAFS study in Pb(Fe1/2Nb1/2)1-xTixO3 (PFNT) relaxor crystals Lead iron niobate Pb(Fe1/2Nb1/2)O3 (PFN) has been studied of great interest recently because ofitsmultiferroicandrelaxorferroelectricproperties.Pb(Fe1/2Nb1/2)1-xTixO3(PFNT)isa modified material which has been also studied extensively in recent years. PFNT undergoes a rhombohedral-tetragonal phase transition with the increase of Ti concentration.[25] Recent study reveals that the morphotropic phase boundary (MPB) is in the range 0.06 0atall temperatures,inparticularalsoabovePT(Ikedaetal.,1987).Fortunatelyfroman Ferroelectrics - Characterization and Modeling 184 experimentalpointofview3isgivenbythissameequation(8)withinparaelectricphase independentoftheferroelectricPTorder.Thesignof3isasensitiveprobefor discrimination between continuous and discontinuous ferroelectric PTs. Inallknownferroelectricstheparaelectricphaseislocatedabovethestabilityrangeofthe ferroelectricone.However,sodiumpotassiumtartratetetrahydrate(Rochellesalt,RS) (Valasek,1920,1921)apartfromaclassichightemperatureparaelectricphasehasan additional,unusualonelocatedbelowtheferroelectricphase.BothPTs,betweenthe paraelectricphasesandtheferroelectriconehavecontinuouscharacter.Inordertopredict thesignof3 withinthelow-temperatureparaelectricphaseonecanrefertothetheoryof Mitsui (Mitsui, 1958). Within this theory the electric equation of state for RS is similar to Eq. (4)withapositivecoefficientofthecubicterm,P3.Thereforeanegativesignof3is expected within low-temperature paraelectric phase (Miga et al., 2010a). Anotherclassofdielectricsarerelaxorferroelectrics.Theyareusuallyconsideredas structurallydisorderedpolarmaterials,whicharecharacterizedbytheoccurrenceofpolar nanoregions(PNRs)ofvariantsizebelowtheso-calledBurnstemperature,Td(Burns& Dacol,1983)farabovetheferroelectricCurietemperature,Tc.Incontrasttoconventional ferroelectrics,relaxorsdonotexhibitanyspontaneousmacroscopicsymmetrybreaking.In additiontheyarecharacterizedbyalarge,broadandfrequency-dependentpeakinthe temperaturedependenceofdielectricsusceptibility.Accordingtothesphericalrandom-bond-random-field(SRBRF)model(Pirc&Blinc,1999)thedipolemomentsofindividual nanopolar clusters interact via a spin-glass-type random exchange coupling, and are subject toquenchedrandomlocalelectricfields.ThemodelHamiltonianofsuchasystemis formally written as 12ij i j i i iij i iH J S S h S gE S = ,(10) where Jij are glass-like random intercluster couplings or bonds, ih andE random local and uniformexternalelectricfields,respectively.Inthedynamicapproximationitisassumed that PNRs reorient by means of stochastic flips described by a relaxation time . This model yieldsnegative3withtwoextremesobservedatthefreezingtemperature,Tf,andatthe peak temperature of 1, Tm.The measured values of 1 and 3 can be used for calculating the so-called scaled non-linear susceptibility, a3, which is given by (Pirc & Blinc, 1999) 333 40 11a = .(11) Withintheparaelectricphaseofclassicferroelectricsa3isequaltothenonlinearity coefficientB,cf.Eqs.(8)and(11).ForferroelecticsdisplayingacontinuousPT,a3 =-8B withinferroelectricphase.TheSRBRFmodelyieldsnegative3andpositivea3withtwo extremesobservedat thefreezingtemperature, Tf,and atthepeak temperatureof 1,Tm. Itshouldbenoticedthatsystemslikedipolarglassesa3arealsoexpectedtoexhibita critical singularity at Tf , where 3 (T Tf )- with the mean field exponent = 1 (Pirc et al., 1994). A schematic comparison of predictions of the above theories is presented in Fig. 1. Non-Linear Dielectric Response of Ferroelectrics, Relaxors and Dipolar Glasses 185 (a) 10 30Tc a3(b) Tc Temperature(c) TmTf Fig. 1. Schematic presentation of linear and nonlinear responses of classic ferroelectrics with (a) continuous PTs, (b) discontinuous PTs, and (c) relaxor ferroelectrics (see text). 3. Methods of measurement of nonlinear dielectric response Nonlineardielectricresponsecanbemeasuredusingtwodifferentkindsofexperimental methods.Thefirstoneisbasedontheinvestigationofthe aclineardielectricsusceptibility as a function of a dc bias field. A schematic presentation of this method is shown in Fig. 2a. Oneappliestothesampleaweakprobingacelectricfieldwithfixedamplitude(that warrantsalinearresponse)andasuperimposedvariabledcbiasfield,EB.Thebiasfield amplitudemayreachvaluesupto5.5107 Vm-1(Leontevetal.,2003).Inbariumtitanatea strongdcfieldinducesthePTbetweenparaelectricandferroelectricphases(Wangetal., 2006). By changing the value of the dc electric field the local slope of the polarization curve is probedinmanypoints.Forsuchakindofexperimentonecanusecommerciallyavailable LRC meters or impedance analyzers, e.g. Agilent E4980A or Solartron 1260. The electric field dependence of the linear susceptibility of ferroelectrics displaying continuous PT fulfils the following relations (Mierzwa et al., 1998): 3 203 2 31 3 427( ) ( ) (0) (0)BEE E + =(12) for the paraelectric phase and 3 203 2 31 3 127( ) 2 ( ) (0) 2 (0)BEE E + =(13) Ferroelectrics - Characterization and Modeling 186 for the ferroelectric one. (E) and (0) are the susceptibilities for bias, E, and zero electric field, respectively.ByuseofEqs.(12)and(13)onecancalculatethenonlinearitycoefficientB.Its knowledge allows us to calculate the third-order nonlinear susceptibility 3. Unfortunately, the above described method has at least one restriction when investigating the nonlinear dielectric response. Namely, during so-called field heating/cooling runs, unwanted poling and remnant polarization of the investigated sample can evolve under a high bias field. EB2EB1(a)PE(b)PE Fig. 2. Presentation of methods of measurement of nonlinear dielectric response using (a) a weak probing ac electric field with fixed amplitude and a superimposed variable dc bias field, and (b) an enhanced ac field. The effects are exaggerated for visualisation. Thesecondkindofmethodisfreefromthisrestriction.Aschematicpresentationofthis method is shown in Fig. 2b. During the experiment the sample is exposed to an ac probing field with sufficiently large amplitude. Consequently, under this condition the temperature dependencesofthelinearandnonlinear susceptibilitiesaredetermined underzero dcfield in heating and cooling runs.That is why the nonlinear susceptibility detected this way can bereferredtoasadynamicnonlinearsusceptibilityrelatedtoacdielectricnonlinearity. Usuallytheamplitudeofthisfieldismuchsmallerthanthebiasfieldstrengthusedinthe abovedescribedexperiment.AsaresultofthenonlinearP(E)dependence,theoutputno longerremainsharmonic.ThedistortedsignalmaybesubjectedtoFourieranalysis revealing all harmonic components in the polarization response. This is the main idea of our nonlinearacsusceptometer(Migaetal.,2007).Usingharmonicsofdisplacementcurrent density ji one can calculate the linear and nonlinear dielectric susceptibilities i as follows: ( )( )11 0 1 3 5 7022 0 2 4 6033 0 3 5 7044 0 4 6055 0 5 7011,12 3 ,1 44 8 ,31( 2 8 ),1 16165E j j j jE j j jE j j jE j jE j j= + + + = + = = + = + (14) Non-Linear Dielectric Response of Ferroelectrics, Relaxors and Dipolar Glasses 187 whereandE0aretheangularfrequencyandtheamplitudeoftheappliedelectricfield respectively. In Eq. 14 the terms up to seventh order are involved, hence, susceptibilities up tothefifthordercanberegardedasreliableevenforstronglynonlinearmaterials. Neglectingharmonicshigherthantheorderofaconsideredsusceptibilitymayleadto artificialeffects.Thenextimportantpointisthesimultaneousmeasurementofall displacementcurrentcomponents,whichconsiderablyimprovestheaccuracyofthe measuredsusceptibilities(Bobnaretal.,2000).Incasethatthephaseshiftsofthe displacementcurrentharmonicsareknownitispossibletocalculatethereal,i,and imaginary, i, parts of all susceptibilities. This is impossible, when measurements are done withadcbias electricfield. Itshouldbenotedthatupto nowcommercialinstruments for the dynamic measurement of complex nonlinear dielectric susceptibilities are unavailable.4. Experimental results 4.1 Ferroelectrics displaying continuous PTsTriglycinesulphate,(NH2CH2COOH)3H2SO4(TGS)isamodelferroelectricdisplayinga continuous PT. Sodium potassium tartrate tetrahydrate (Rochelle salt, RS), NaKC4H4O64H2O, andleadgermanate,Pb5Ge3O11(LGO)exhibitcontinuousPTs,aswell.Despitethequite different structures of the crystals and different mechanisms of their PTs, a negative sign of the real part of the third-order nonlinear susceptibility is expected in their paraelectric phases. Fig. 3 shows the temperature dependences of the real parts of the linear, the third order nonlinear dielectricsusceptibilities,andthescaledsusceptibility,a3.ThelinearsusceptibilityofaTGS crystal (Fig. 3a) obeys a Curie-Weiss law within the paraelectric phase very well with a critical exponent=1.0000.006.Accordingtopredictionsofthephenomenologicaltheoryof ferroelectric PT, 3 changes its sign at the PT point (Fig. 3b). 24(a) 1 [103]-4-2024(b) 3 [10-6m2/V2]320 322 324 326-4-2024(c)a3 = -8Ba3 = B a3 [1013m5VC-3]Temperature [K] Fig. 3. Temperature dependences of the real parts of the linear (a) and third order non-linear (b) susceptibilities and a3 coefficient (c) of TGS. The amplitude of the probing ac electric field was 5kVm-1. Ferroelectrics - Characterization and Modeling 188 WhilebelowTcthethird-ordersusceptibilityhaspositivevalues,itisnegativeaboveTc. Aswasmentionedearliersuchchangein thesignof 3isoneoftheprimaryfeaturesof thecontinuousferroelectricPT.Thescalednon-linearsusceptibilityhasbeenevaluated usingEq. (11).Themeasuredvaluesof1and3wereusedforcalculations.The temperaturedependenceofa3ofTGScrystalisshowninFig.3c.Withintheparaelectric phasea3isequalto Bandhasapositivevalue.ThisisanattributeofthecontinuousPT. Moreover,a3ispracticallytemperatureindependentwithinthetemperaturerangeof Tc + 0.2 K < T < Tc + 2 K above the PT point. This behaviour is consistent with predictions ofthescalingtheoryandconfirmsthatTGSbelongstotheLandauuniversalityclass. Weak temperature dependence of a3 and 1/|T-Tc| dependence of 1 leads to a 1/|T-Tc|4 anomaly of3(see Eq. 11).Thereforethe temperature dependence of 3 ismuch sharper thanthatof1.Consequently,3rapidlyvanishesinthesurroundingofthePT.An increaseofa3asobservedwithintheparaelectricphaseclosetoTcisprobablydueto crystaldefects.Asimilareffectwasreportedfora-raydamagedTGScrystal(Cach, 1988). Then within the ferroelectric phase a3 changes slowly due to the contribution of the domainwallstotheresultantdielectricresponse.Intheferroelectricstatethemeasured valuesofthelinearandnon-linearsusceptibilities,whichwereusedforcalculation, involvedtheresponsesnotonlyfromthepureferroelectricsystembutalsofromthe domain walls, which were forced to move under the probing electric field. Fig. 4. Temperature dependences of the real parts of the linear (a), the second (b) and the third (c) order nonlinear susceptibilities of Rochelle salt. The amplitude of the probing ac electric field was 500 Vm-1. Fig.4showsthetemperaturedependencesofthelinear,thesecond,andthethird-order nonlinearsusceptibilitiesofRochellesalt.Thetemperaturedependencesof1and3are, close to the high temperature ferroelectric-paraelectric PT ( 297.4 K), qualitatively similar to 0123(a)1 [103]0.00.51.0(b) 2 [10-2 mV-1]250 260 270 280 290 300024(c) Temperature [K] 3 [10-5 m2V-2]295 3000.00.30.6 254 2560.000.05 Non-Linear Dielectric Response of Ferroelectrics, Relaxors and Dipolar Glasses 189 thoseoftheTGScrystal.Aswasmentionedearlier,RSdisplaysanadditionallow temperaturePT.Thistransitionbetweentheferroelectricandthelowtemperature paraelectricphaseappearsatabout254.5 K.AtthisPT3changesitssignascomparedto the high temperature PT (Fig. 4c). As a result of the inverse order of phases, 3 is negative belowandpositiveabovethelowtemperaturePT.Inthiswaythethird-ordernonlinear susceptibilityisnegativeinbothparaelectricphasesclosetoPTpoints.Fig.4bshowsthe temperaturedependenceofthesecond-ordernonlinearsusceptibility.Thesignofthis susceptibilitydependsonthenetpolarizationorientation.Thereforeitcanbechangedby polarization of the sample in the opposite direction. The simplest way to change the sign of 2 is a change of the wires connecting the sample to the measuring setup. So, in contrast to sign of the 3, the sign of the second order nonlinear susceptibility is not very important. In thecaseof2mostimportantisitsnonzerovalueandtheobservedchangeofsignofthis susceptibilityat273 K.Thishintsatamodificationofthedomainstructurewithinthe ferroelectricphase.ThenextchangeofsignatthelowtemperaturePTpointisoriginating from different sources of the net polarization above and below this point. Above 254.5 K this polarization comes from the uncompensated ferroelectric domain structure, whereas within thelow-temperatureparaelectricphaseitoriginatesmerelyfromchargesscreeningthe spontaneous polarization within the ferroelectric phase.Lead germanate (LGO) displays all peculiarities of a continuous ferroelectric PT (see Fig. 5 a, c, e) (Miga et al., 2006). However, a small amount of barium dopant changes this scenario (Miga et al., 2008). Ba2+ ions replacing the host Pb2+ influence the dielectric properties. 2% of barium dopantcausesadecreaseofthelinearsusceptibility,broadeningofthetemperature dependenceof1,andadecreaseofthePTtemperature.Despiteallthesechangesthe temperature dependencesof 1 for pureandbarium dopedLGOare qualitatively similar.A completelydifferentsituationoccurs,whenoneinspectsthenonlineardielectricresponse. Small amounts of barium dopants radically change the temperature dependence of the third-order nonlinear susceptibility(Fig.5 b). Similarly to linear one the anomaly of the third-order nonlinear susceptibility shifts towards lower temperatureand decreases. The most important difference is the lacking change of sign of 3. In contrast to pure LGO for barium doped LGO thethird-ordernonlinearsusceptibilityispositiveinthewholetemperaturerange.Therefore one of the main signatures of classic continuous ferroelectric PTs is absent. Due to the positive value of 3 the scaled nonlinear susceptibility is negative in the whole temperature range (Fig. 5d).Nochangeofa3isobserved.Thisexampleshowsthehighsensitivityofthenonlinear dielectric response to the character of the PT. In the discussed case a change of character of the PTisduetothepresenceofbariuminducedpolarnanoregions(PNRs).Theoccurrenceof PNRs results in weak relaxor properties of barium doped LGO.4.2 Ferroelectrics displaying discontinuous PT Bariumtitanate,BaTiO3(BT),isamodelferroelectricdisplayingthreediscontinuous ferroelectric PTs (von Hippel, 1950). Two of them appear at rising temperatures - between rhombohedral,orthorhombicandtetragonalferroelectricphasesatabout200 Kand280 K respectively.ThefinaldiscontinuousPTappearsbetweentheferroelectrictetragonaland the cubic paraelectric phase at about 400 K. Fig. 6 shows the temperature dependences of the real parts of the linear (a) and third-order nonlinear (b) susceptibilities, and the a3 coefficient(c)ofaBTcrystalinthevicinityoftheferroelectric-paraelectricPT.Theamplitudeofa probing ac electric field was equal to 7.5 kVm-1. Ferroelectrics - Characterization and Modeling 190 02468LGOLGO:Ba 31 Hz 100 316 1000(a)1 [103]-10-50510x5(b) 3 [10-8m2/V2](c) 400 420 440-1013-1012-1011-1010(d) a3 [m5VC-3]Temperature [K]460(e) 480-505 a3 [1012 m5VC-3] Fig. 5. Temperature dependences of the real part of the linear dielectric susceptibility (a) for LGO:Ba 2% and LGO, real part of third-order nonlinear dielectric susceptibility for (b) LGO: Ba 2% and (c) LGO, and scaled nonlinear susceptibility a3 for (d) LGO:Ba 2%, and (e) LGO crystals. The amplitude of the probing ac electric field was 15 kVm-1. 0.00.40.81.2 (a)1 [104]012(b) 3 [10-6 m2V-2]380 390 400 410 420-1014-1012-1010(c) Temperature [K] a3 [m5VC-3] Fig. 6. Temperature dependences of the real parts of the linear (a) and third order non-linear (b) susceptibilities and of the a3 coefficient (c) of a BaTiO3 crystal. The amplitude of the probing ac electric field was 7.5kVm-1. TemperaturehysteresisisoneofthetypicalfeaturesofdiscontinuousPT.Thereforefor viewingthisphenomenonFig.6presentsresultsforcoolingandheatingruns.Thethird- Non-Linear Dielectric Response of Ferroelectrics, Relaxors and Dipolar Glasses 191 ordernonlinearsusceptibilityispositive,bothwithintheferroelectricandtheparaelectric phases (Fig. 6b). Just below Tc a rapid decrease of the third-order dielectric susceptibility is observed. For that reason, the value of 3 is much smaller within the paraelectric phase than intheferroelectricone,yetitisstillpositive.Thepositivesignof3asdetectedinBTis consistentwithpredictionsofthephenomenologicaltheoryofdiscontinuousferroelectric PTs. Unlike the scaled nonlinear susceptibilities of crystals displaying a continuous PT, a3 of BaTiO3 is negative in the whole investigated temperature range (Fig. 6c). However, similarly toTGS(Fig.3)orRS(Fig.4)ajump-likechangeofa3occursatthePT.Withinthe paraelectricphasea3isequaltoB(seesection4.1)anddisplaysweaktemperature dependence.Wangetal.(Wangetal.,2007)proposedincorporationofhigherorderterms (uptotheeighthpower)intheLandaupotentialforthetemperatureindependenceofthe experimentallyobtainedBcoefficient.Thispropositionwasgivenforanalyzingthedata collected with a bias field up to 1500 kV/m. Fig. 6 showsdata collected for a two hundred timessmallerelectricfield,forwhichtermsatsuchhighorderarenotimportant.They cannotexplainthetemperaturedependenceofthenonlinearitycoefficientB.Hence, although the nonlinear properties of BaTiO3 have been investigated already for six decades, the question of the temperature dependence of the nonlinearity parameter B is still open.4.3 Relaxor ferroelectrics The classic relaxor ferroelectric lead magno-niobate (PbMg1/3Nb2/3O3, PMN) (Smolenskii et al.,1960)displaysanaveragecubicstructureinthewholetemperaturerange(Bonneauet al.,1991).Nospontaneousmacroscopicsymmetrybreakingisobservedinthisrelaxor.On theotherhandandincontrasttoPMN,therelaxorstrontium-bariumniobate Sr0.61Ba0.39Nb2O6 (SBN61)spontaneouslyundergoesastructuralphasetransition.On cooling the vanishing of a mirror plane leads to a lowering of the tetragonal symmetry from 4/mmm to 4mm at a temperature of about 348 K (Oliver et al., 1988). 01231 Hz(b)(a)1 kHz 31 Hz 90 319 1000 1 [104]-2-101 2 [10-4m/V]0510f(c) 3 [10-7m2/V2]200 250 300 350-1010-1011f(d) Temperature [K] a3 [m5VC-3]200 250 300 350-1010-1011 Fig. 7. Temperature dependences of 1 (a), 2 (b), 3 (c) and a3 (d) of a PMN crystal measured at f = 31, 100, 319, and 1000 Hz. A probing ac electric field with an amplitude of 12 kV/m was applied along the [100] direction. Ferroelectrics - Characterization and Modeling 192 02468(a)10 Hz 31 100 318 10001 kHz10 Hz 1 [104]-9-6-30(b)f 2 [10-2 mV-1]0102030(c)f 3 [10-6 m2V-2]300 320 340 360 380 400-1010-1011-1012(d) f Temperature [K] a3 [m5VC-3] Fig. 8. Temperature dependences of 1 (a), 2 (b), 3 (c) and a3 (d) of a SBN61 crystal measured at f = 10, 31, 100, 318, and 1000 Hz. A probing ac electric field with anamplitude of 7.5 kV/m was applied along the [001] direction. Fig. 7 presents the temperature dependences of the real parts of the linear, 1 (a), second-order, 2 (b), and third-order, 3 (c), dielectric susceptibilities and of the scaled nonlinear susceptibilitya3(d)ofthePMNsinglecrystalrecordedalong[100]direction(Decetal., 2008).Thelinearsusceptibilitydisplaysfeaturesofarelaxori.e.alarge,broadand frequency-dependentpeakinthetemperaturedependence.Nonzero2aspresentedin Fig.7bisanindicatorofnetpolarizationofthecrystal.Thepresenceofthispolarization was independently confirmed by measurements of thermo-stimulated pyroelectric current ofanunpoledsample.Integrationofthiscurrentindicatesanapproximatevalueofthe averagepolarizationaslowas310-5 C/m2.Thispolarizationismuchsmallerthanthe spontaneouspolarizationofferroelectrics,butiswelldetectable.Theobserved pyroelectric response and nonzero 2 hints at an incomplete averaging to zero of the total polarizationofthePNRsubsystem.Fig.7cshowsthetemperaturedependenceofthe third-order nonlinear susceptibility. In contrast to the predictions of the SRBRF model, 3 is positive in the whole temperature range. The positive sign of 3 may result from a term 180BP21exceedingunityinEq.7.Positivesignof3resultsinanegativesignofa3. Consequentlythesignofa3differsfromthatpredictedbytheSRBRFmodel.Havingin mindthatcorrectionsduetothefifthharmoniccontributionproducelargenoiseat temperaturesbelow210Kandabove310K(Fig.7d,mainpanel),lessnoisya3data calculatedonlyfromfirstand thirdharmonics arepresented in theinset toFig.7d. Since both 1 and 3 do not display any anomalies in the vicinity of the freezing temperature Tf 220 K, also a3 does not exhibit any maximum in contrast to SRBRF model predictions. It continues to increase monotonically by almost two orders of magnitude when decreasing the temperature from 260 to 180 K. This result is independent of the number of harmonics usedforexperimentaldataanalysis.Itisworthstressingthatdespitetheremarkable Non-Linear Dielectric Response of Ferroelectrics, Relaxors and Dipolar Glasses 193 dispersionof1and3,thescaledsusceptibilitya3doesnotdisplayanysizable frequency dependence,evenaroundthetemperaturesofthesusceptibilitypeaks.Itmay, hence, be considered as a static quantity (Glazounov & Tagantsev, 2000). According to our resultthedispersionofa3isevenweakerthanreportedpreviously(Glazounov& Tagantsev, 2000). Fig.8showsresultsofmeasurementsofthelinearandnonlineardielectricresponseof SBN61crystal(Miga&Dec,2008).Theprobingelectricacfieldwasappliedalong[001], whichisthedirectionofthepolaraxisbelowTc.Thepeaktemperaturesofthelinear susceptibility(Fig.8a)areafewdegreesabovethetemperatureofthestructuralphase transition.Fig.8bpresentsthetemperaturedependenceofthesecond-ordersusceptibility. SimilarlytoresultsobtainedonPMNthissusceptibilityisnon-vanishing.However,the valuesof2ofSBN61arealmosttwoordersofmagnitudelargerthanthosemeasuredon PMN.Therefore2isdetectableevenfortydegreesaboveTc.Analysisofthethermo-stimulated current indicates a net polarization of a nominally unpoled SBN61 crystal equal to510-2 C/m2.Thehighervalueofthispolarization(incomparisonwithPMN)resultsin higher values of 2. Fig. 8c shows the temperature dependence of 3. This susceptibility is positivewithinboththeferroelectricandtheparaelectricphase.Again,thesignof3 disagrees with predictions of the SRBRF model. As was discussed above, the positive sign of 3 presumably originates from the presence of net polarization (detected by 2, see Fig. 8b). Thedisagreeingsignof3leadstoadisagreementofthesignofa3aswell(Fig.8d).The scaled nonlinear susceptibility shows an anomaly related to the phase transition, but it does not exhibit any additional peak as predicted by the SRBRF model. The results obtained for bothrelaxor ferroelectrics are qualitatively similar. Therefore, they are independent of the presence or absence of a structural phase transition and macroscopic symmetry breaking. As discussed in Section 2 the dielectric properties of relaxors are mainly determined by PNRs, which were detected in both of the above relaxors. Unfortunately, the earlyversionoftheSRBRFmodel(Pircetal.,1994)predictsanegativesignofthethird-ordernonlineardielectricsusceptibility,whichisnotconfirmedinexperiments. Consequentlythesignofthescalednonlinearsusceptibilitya3isincorrectaswell.Very probablythisunexpectedresultisduetothefactthatthePNRsprimarydonotflipunder theacelectricfield,butmerelychangetheirshapeandshifttheircentersofgravityinthe sense of a breathing mode (Kleemann et al., 2011). 4.4 Dipolar glasses 4.4.1 Orientational glasses The formation of dipolar glasses in incipient ferroelectrics with perovskite structure, ABO3, suchasSrTiO3andKTaO3,byA-sitesubstitutionwithsmallcationsatlowconcentrations has been a fruitful topic since more than 20 years (Vugmeister & Glinchuk, 1990). For a long timeprobablythebest-knownexamplehasbeentheimpuritysystemK1-xLixTaO3(KLT for short) with x2,agivenanomalyinthethermaldiffusivity,producesan enhanced signal anomaly; -Foragivensample,theexponentinEq.(2.7)canbeadjustedbychangingthe modulationfrequencyand/orsamplesthickness,inordertoachieveanoptimum trade-off between sensitivity and signal-to-noise ratio. Basedonthesetheoreticalpredictions,onecanstartinvestigatingtheferroelectric-paraelectricphasetransitionofTGScrystal,byperformingaroomtemperaturefrequency scanofthephaseofthePPEsignal,inordertoobtaintheroomtemperaturevalueofthe thermal diffusivity. A typical result is presented in Fig. 4.7. Fig. 4.7 Room temperature frequency scan for the phase of the PPE signal Characterization of Ferroelectric Materials by Photopyroelectric Method 297 TypicaltemperaturescansoftheamplitudeandphaseofthePPEsignal,inatemperature range including the Curie point of TGS are displayed in Fig.4.8 10 20 30 40 50 60116117118119120121122 Lm=370mf=0.3HzTemperature (C)PPE phase (deg.)10 20 30 40 50 60616263646566676869PPE amplitude (pA)Temperature (C) Lm=370mf=0.3Hz Fig. 4.8 Temperature scan for the phase and the amplitude of the PPE signal UsingEqs.(2.7)-(2.8),thevalueofthethermaldiffusivityobtainedfromtheslopeofthe curveinFig.4.7,andthevalueofthethermalconductivityfromdelCerroetal.,1987,one gets the critical behaviour of all four thermal parameters (Fig.4.9) 10 20 30 40 50 600.81.01.21.41.61.82.02.22.42.6 volume specific heat x106 (JK-1m-3)temperature (C) Lm=370mf=0.3Hz10 20 30 40 50 600.920.940.960.981.001.021.041.061.081.101.12 thermal diffusivity x10-7(m2s-1)Temperature (C) Lm=370mf=0.3Hz 10 20 30 40 50 600.080.100.120.140.160.180.200.220.24 thermal conductivity (Wm-1K)Temperature (C) Lm=370mf=0.3Hz10 20 30 40 50 60300400500600700800 thermal effusivity (Ws1/2m-2K-1)Temperature (C) Lm=370mf=0.3Hz Fig. 4.9 Temperature behaviour of the volume specific heat, thermal diffusivity, conductivity andeffusivity of TGS around the Curie point Ferroelectrics - Characterization and Modeling 298 Sometechnicaldetailsconcerningtheexperimentare:TGSsinglecrystal,370mthick, pyroelectricsensorLiTaO3,300mthick,choppingfrequencyforthetemperaturescanf = 0.3 Hz. Asmentionedabove,oneofthemostimportantfeaturesconcerningEq.(2.7)isthe possibility of enhancing the critical anomaly of the thermal diffusivity, by a proper handling of the chopping frequency and samples thickness. Suchanexample,foraTGScrystalwithtwodifferentthicknesses(230mand500m), investigatedatdifferentfrequencies(6Hzand25Hz)isdisplayedinFig.4.10.Inthis experiment, the pyroelectric sensor was a 1mm thick PZT ceramic. Fig. 4.10 Normalized PPE amplitude as a function of temperature for two TGS single crystals and for two different chopping frequencies (different thermal diffusion length) Fig. 4.10. indicates that the critical anomaly of the PPE amplitude, V/V, increases from 0.14 upto1.22withincreasingexponentinEq.(2.7),forthesamecriticalanomaly(about0.2 jumpinthespecificheat(delCerroetal.,1987)).Thisfactsupportsthesuitabilityofthe methodforinvestigationsofphasetransitionswithsmallcriticalanomaliesofthethermal parameters. 4.2.2 TGS as a pyroelectric sensor ThisconfigurationisbasedontheinformationcontainedinthephaseoftheFPPEsignal andcollectedfromaferroelectricmaterial,usedaspyroelectricsensorinthePPE detection cell. Characterization of Ferroelectric Materials by Photopyroelectric Method 299 Aspresentedinthetheoreticalsection,thenormalizedphaseoftheFPPEsignal,fora detectioncellcomposedbythreelayers-air,pyroelectricsensorandsubstrate-isgiven by: (1 )exp( )sin( )arctan1 (1 )exp( )cos( )sp p p p psp p p p pR a L a LR a L a L+ = + (4.10) Eq.(4.10)isvalidforopaquepyroelectricsensorandforthermallythicksubstrate.The normalization signal was obtained with empty, directly irradiated sensor. When performing measurements at two different chopping frequencies we obtain: )]2tan( )2sin( )2)[cos(2exp()]1tan( )1sin( )1)[cos(1exp()2tan()1tan( + + =paPLpaPLpapLpaPLpaPLpapL(4.11) with ap1,2 = ( f1,2/p)1/2. Eq. (4.11) indicates that one can obtain the thermal diffusivity of the pyroelectric material, used as sensor in the detection cell, by performing two measurements attwodifferentchoppingfrequencies,providingthegeometricalthicknessofthesensoris known. Typicalresults,obtainedforthephaseofthePPEsignalfora500mthickTGSsingle crystal,withsiliconoilassubstrate(togetherwiththenormalizationsignal-directly irradiatedemptysensor)aredisplayedinFig.(4.11).Anexternalelectricfieldof6kV/m was additionally applied. 42 44 46 48 50 52-3.2-3.0-2.8-2.6-2.4-2.2-2.0-1.8-1.6-1.4-1.2-1.0 with substratewith substrate : full symbolnormalization signal : empty symbolnormalization signalf=12Hzf=3HzPPE phase (rad)Temperature (0C) Fig. 4.11 Temperature scans of the phase of the PPE signal, for a 500m thick TGS single crystal, around the ferroelectric Curie temperature, for 3Hz and 12Hz chopping frequencies, and an external electric field of 6kV/m. Ferroelectrics - Characterization and Modeling 300 42 44 46 48 50 52-0.10-0.050.000.050.100.150.200.250.30 f=12Hzf=3HzNormalized PPE phase (rad)Temperature (C) Fig.4.12 Same as Fig.4.11, but for the normalized phase. Fig.4.12presentsthenormalizedphasesofthePPEsignalforthetwofrequencies.The criticalbehaviourofthethermaldiffusivityforthreevaluesofthe externalelectricfield,as obtained from Eq.(4.11), is displayed in Fig. 4.13. 46 47 48 49 50 517.58.08.59.09.510.010.511.0 0 kV/m 1 kV/m 10 kV/m Temperature (C)thermal diffusivity x108(m2/s) Fig. 4.13 Critical behaviour of the thermal diffusivity of TGS for 0 kV/m (squares); 1 kV/m (circles) and 10 kV/m (triangles). Fig.4.13displaysatypicalbehavior(criticalslowingdown)ofthermaldiffusivityfora secondorderphasetransition.Theexternalelectricfieldhasthewellknowninfluenceon the phase transition: it increases the Curie temperature and enlarges the critical region. The Characterization of Ferroelectric Materials by Photopyroelectric Method 301 valuesoftheCuriepointsareingoodagreementwiththoseobtainedfromthedirect measurement of the PPE amplitude (Fig. 4.14). 42 44 46 48 50 520.0000.0020.0040.0060.0080.0100.0120.0140.016 0 kV/m 1kV/m 10kV/m0 2 4 6 8 1048.048.248.448.648.849.049.249.449.649.850.0PPE amplitudeth . d if fusivityCurie temperature (0C)electr ic f ield (k V/m)TGS sing lecr ystalPPE amplitude (V)Temperature (C) Fig. 4.14 Typical behaviour of the amplitude of the PPE signal for empty TGS sensor and for three values of the external electric field. Insertion: The Curie temperature vs. electric field, as obtained from thermal diffusivity and PPE amplitude (inflection point). In conclusion to this sub-section, the PPE calorimetry, in the front detection configuration, was used to measure the critical behaviour of the thermal diffusivity of TGS single crystal. InastandardPPEexperiment(section4.3.1)theinformationonthesamplespropertiesis collectedandprocessed.Inthisapproach,wecollecttheinformationonthethermal properties of the pyroelectric sensor itself. WeselectedthephaseofthePPEsignal(andnottheamplitude)assourceofinformation duetothewellknownadvantages:thephaseisindependentonthefluctuationsofthe incidentradiationandthesignaltonoiseratioishigherthaninthecaseofusingthe amplitudeofthesignal.Measurementsattwodifferentchoppingfrequenciesand calibrationprocedureswere necessaryin ordertoeliminatetheinstrumentalfactorsandto obtainamathematicalequationdependingonsolelyonethermalparameter,whichisthe thermal diffusivity. Theappliedexternalelectricfieldhasatypicalinfluenceonthecriticalregionofthepara-ferroelectricphasetransitionofTGS:boththeCurietemperatureandthethicknessofthe critical region slightly increase with increasing value of the electric field.The results obtained for the value of the thermal diffusivity of TGS and for the value of the Curie temperatures are in good agreement with data reported in the literature and obtained by other techniques (del Cerro et al., 1987). Finally, we must emphasize that this configuration speculates the fact that the investigated ferroelectric material is pyroelectric as well. The method was used on a classical TGS crystal, butitappearstobeasuitablealternativeinstudyingthethermalpropertiesofthe ferroelectricliquidcrystals,whentheferroelectricstateisimposedbyagivenlayered geometry. Ferroelectrics - Characterization and Modeling 302 5. Discussions and conclusions 5.1 Comparison with other techniques ItisnotpossibletoperformanexhaustiveanalysisandcomparisonofthePPE calorimetrywithothertypesofcalorimetry,butsomeparticularadvantagesofthis technique can be mentioned. First of all, due to the fact that the pyroelectric sensor feels thetemperaturevariation(andnotthetemperature),nospecialthermostaticprecautions arerequested.Thisisanadvantagecomparedwithadiabatictypesofcalorimetry,for example.IfwecomparePPEwithdifferentialscanningcalorimetry(DSC),PPEismore accurateindetectingthecriticaltemperature(Curiepointforferroelectrics),duetothe possibilityofscanningveryslow(fewmK/minseeforexampleMarinellietal.,1992) thetemperatureofthedetectioncell.InthecaseofDSC,itisknownthatthesensitivity increaseswithincreasingtemperaturevariationrate(decreasingtheaccuracyin measuring the critical temperature). WecannotovertaketwogeneralfeaturesthatmakethePPEcalorimetryunique:(i)itis the only calorimetric technique able to give in one measurement the value of two (in fact all four) thermal parameters; (ii) it is the only technique which, in the critical region of a phase transition,foragivenanomalyinthethermalparameters,producesanenhancedsignal anomaly. Finally,somecomparisonwithotherPTtechniquesiswelcome.Marinellietal.,1992tried tocomparetheperformancesofthePPEtechniqueindetectingphasetransitions,with anotherphotothermaltechniquelargelyusedforphasetransitionsinvestigations:the photoacoustic (PA) method. Ifwefollowonlythephasechannels,theyaregiveninthestandardconfiguration,with optically opaque and thermally thick sample by the equations (Zammit et al., 1988; Marinelli et al., 1992): ( ) pPA/ 2 1 tan1 = ; ( )1/22 /s sp =(5.1) for PA phase, and ( ) qe PPE/ 1 tan1 = ; ( )( )2 / 1/ 2 / 1 s sL q =(5.2) for PPE phase. The sensitivity of the two techniques to changes in p and q, respectively, are: ( )122PAdp pdp | |= + + |\ . (5.3.a) 2 =||.|

\|qdqdPPE (5.3.b) An analysis of Eqs. (5.3.a,b)leads to the conclusion that the maximum sensitivity of the PA technique is reached when p=0 and has the value . In the mean time the sensitivity of the PPE technique can go (at least theoretically) to infinity, denoting once again the suitability of this technique for phase transitions detection. Characterization of Ferroelectric Materials by Photopyroelectric Method 303 5.2 General features of the PPE calorimetry PPEtechniqueisasensitiveandaccuratecalorimetryforthermalinspectionofsolidstate matter.Concerningferroelectricmaterials,themainfeatureofthemethodisthattwo detection configurations can be separately or together used for thermal characterization; the ferroelectric material under investigation can be sample or sensor in the PPE detection cell. All four static (specific heat) and dynamic (thermal conductivity, diffusivity and effusivity) thermalparameterscanbemeasuredbythistechnique,andphenomenaassociatedwith changes in time, composition or temperature (phase transitions-for example) can be studied. Thesensitivityofthemethodandtheaccuracyoftheresults,wheninvestigating ferroelectricmaterials,dependonvariousexperimentalparameters.Thepossibilityof selectingandadjustingtheseexperimentalparameterscanleadtoanoptimizationofthe performances of the method. Theperformancesofthemethoddependpracticallyon:thesensor'sdetectivity,the precisioninmonitoringthemainexperimentalparameters(choppingfrequency,sample's thicknesscontrol,temperature,etc),thequalityofthesensor-samplethermalcontact,the wayofperformingtheacquisitionandprocessingofexperimentaldata.Sometypical experimentaldataare:thedetectivityofthepyroelectricLiTaO3sensorsishigherthan108 cmHz1/2W-1;minimumdetectabletemperaturevariation:1K;minimumcontrollable temperature variation rate: 10 mK; frequency stability: 10-4 Hz. The main limitations of the technique concerning ferroelectric materials are imposed by the Curie temperature of the pyroelectric sensor, by the properties of the coupling fluid (always necessary when inserting the ferroelectric material as a sample) and by the geometry of the investigated sample (it must be a disk of tens-hundreds of micrometers thick, with polished surfaces).6. References Bentefour E.H., Glorieux C., Chirtoc M. &Thoen J. (2003). Characterization of pyroelectric detectors between 170 and 300 K using the photopyroelectric technique, Review of Scientific Instruments, Vol. 74, No. 1,(January 2003), pp. 811-813, ISSN 0034-6748 BhallaA. S. , LiuS. T. (1993). 4.2.3 Pyroelectriccoefficients offerroelectricpyroelectrics, In: ElectricalProperties-LowFrequencyPropertiesofDielectricCrystals-Piezoelectric, Pyroelectric, and Related Constants , The Landolt-Brnstein Database , D.F. Nelson (Ed.), Vol. 29b, Springer Verlag, ISBN 978-3-540-55065-5. Chirtoc,M.,Glorieux,C.&Thoen,J.(2009).ThermophysicalPropertiesandCritical PhenomenaStudiedbyPhotopyroelectric(PPE)Method,In:ThermalWavePhysics andRelatedPhotothermalTechniques:BasicPrinciplesandRecentDevelopments,E.M. Moraes,(Ed),125-159,TransworldResearchNetwork,ISBN978-81-7895-401-1, Kerala, India Chirtoc, M. & Mihailescu, G.(1989). Theory of Photopyroelectric Method for Investigation of OpticalandThermalMaterialsProperties.PhysicalReview,Vol.B40,No.14, (November 1989), pp. 9606-9617, ISSN 1098-0121 ClarkN.andLagerwallS.T.(1980).SubmicrosecondBistableElectro-OpticSwitchingin Liquid Crystals. Applied Physic. Letters. 36 (1980) pp899-901, ISSN 0003-6951 Coufal,H.(1984).PhotothermalSpectroscopyUsingaPyroelectricThin-FilmDetector. Applied Physics. Letters, Vol. 44, No. 1, (January 1984), pp.59- 61, ISSN 0003-6951 Ferroelectrics - Characterization and Modeling 304 delCerro,J.,Ramos,S.&Sanchez-Laulhe,J.M.(1987).FluxCalorimeterforMeasuring Thermo-physicalPropertiesofSolids:StudyofTGS.JournalofPhysicsE:Scientific Instruments, Vol. 20, No. 6, (June 1987), pp. 612-615, ISSN 0957-0233 Delenclos,S.,Chirtoc,M.,HadjSahraoui,A.,Kolinsky,C.&Buisine,J.M.(2002). AssessementofCalibrationProceduresforAccurateDeterminationofThermal ParametersofLiquidsandtheirTemperatureDependenceUsingthe Photopyroelectric Method. Review of Scientific Instruments, Vol. 73, No.7, (July 2002), pp.2773-2780, ISSN 0034- 6748 Fullem,T.Z.,andY.Danon,Electrostaticsofpyroelectricaccelerators. JournalofApplied Physics Vol. 106, No 7, (October 2009), ISSN0021-8979 Jalink,H.,Frandas,A.,vanderSchoor,R.&Bicanic,D.(1996).NewPhotothermalCell EquipedwithPeltierElementsforPhaseTransitionStudies.ReviewofScientific Instruments, Vol. 67, No. 11, (November 1996), pp.3990-3993, ISSN 0034- 6748 LagerwallS.T.,FerroelectricandAntiferroelectricLiquidCrystals.(1999).Wiley-VCH,ISBN 978-3527298310, New York Mandelis,A.(1984).FrequencyDomainPhotopyroelectricSpectroscopyofCondensed Phases:ANew,SimpleandPowerfulSpectroscopicTechnique.ChemicalPhysics Letters, Vol. 108, No. 4, (July 1984), pp. 388-392, ISSN 0009-2614 Mandelis, A. & Zver, M. M. (1985) J. Theory of Photopyroelectric Effect in Solids. Journal of Applied Physics, Vol. 57, No. 9, (May 1985), pp. 4421-4430, ISSN 0021-8979 Mandelis, A., Care, F., Chan, K. K. & Miranda, L. C. M. (1985). Photopyroelectric Detection of Phase Transitions in Solids. Applied Physics A, Vol. 38, No. 2, (October 1985), pp. 117-122, ISSN 0947-8396 Marinelli,M.,Zammit,U.,Mercuri,F.&Pizzoferrato,R.(1992).HighResolution SimultaneousPhotothermalMeasurementsofThermalParametersataPhase Transition with the Photopyroelectric Technique. Journal of Applied Physics, Vol. 72, No. 3, (August 1992), pp.1096-1100, ISSN 0021-8979 Nakamura M., Takekawa S & Kitamura K, Anisotropy of thermal conductivities in non- and Mg-dopednear-stoichiometricLiTaO3crystals,OpticalMaterials,Vol.32,No11, (September 2010), pp. 1410-1412, ISSN 0925-3467 Tam,A.C.(1986).ApplicationsofPhotoacousticSensingTechniques.ReviewofModern Physics, Vol. 58, No. 2, (February 1986), pp. 381-431, ISSN 0034-6861 Zammit,U.,Marinelli,M.,Mercuri,F.,Pizzoferrato,R.,Scudieri,F.&Martelucci,S. PhotoacousticsasaTechniqueforSimultaneousmeasurementofThermal ConductivityandHeatCapacity.JournalofPhysicsE-ScientificInstruments,Vol.21, No. 10, (October 1988), pp.935-941, ISSN 0957-0233WhatmoreR.W.,PyroelectricDevicesandMaterials,ReportsonProgressinPhysics,Vol.49 (December 1986), pp1335-1386, ISSN 0034-4885 For many years, heterojunctions have beenone of the fundamental researchareas ofsolidstate science. The interest inthis topic is stimulatedby the wide applicationsof heterojunctioninmicroelectronics. Devicessuchasheterojunctionbipolartransistors,quantumwell lasers and heterojunction eld effect transistors (FET), already have a signicanttechnological impact. The semiconductor-ferroelectric heterostructures have attracted muchattentionduetotheirlargepotential forelectronicandoptoelectronicdeviceapplications(Lorentz et al., 2007; Losego et al., 2009; Mbenkum et al., 2005; Voora et al., 2009; 2010). Theferroelectric constituent possesses switchable dielectric polarization, which can be exploitedformodicatingtheelectronicandoptical