材料物理性能3

7.8Piezoelectricity,Ferroelectricity,andPyroelectricity7.8.1PiezoelectricityCertaincrystals,forexample,quartz(crystallineSiO2)andBaTiO3,becomepolarizedwhentheyaremechanicallystressed.1Thepiezoelectriceffect.(a)Apiezoelectriccrystalwithnoappliedstressorfield.(b)Thecrystalisstrainedbyanappliedforcethatinducespolarizationinthecrystalandgeneratessurfacecharges.(c)Anappliedfieldcausesthecrystaltobecomestrained.Inthiscasethefieldcompressesthecrystal.(d)Thestrainchangesdirectionwiththeappliedfieldandnowthecrystalisextended.Onlycertaincrystalscanexhibitpiezoleectricitybecausethephenomenrequiresaspecialcrystalstructure2ANaCl-typecubicunitcellhasacenterofsymmetry.Intheabsenceofanappliedforce,thecentersofmassforpositiveandnegativeionscoincide.(b)Thissituationdoesnotchangewhenthecrystalisstrainedbyanappliedforce.IfwegrawavectorfromOtoanychargeanddrawthereversevector,wewillfindthesametypeofcharge.3(a)Intheabsenceofanappliedforcethecentersofmassforpositiveandnegativeionscoincide.(b)UnderanappliedforcealongythecentersofmassforpositiveandnegativeionsareshiftedwhichresultsinanetdipolemomentPalongy.(c)Whentheforceisalongadifferentdirection,alongx,theremaynotbearesultingnetdipolemomentinthatdirectionthoughtheremaybeanetPalongadifferentdirection(y).Ahexagonalunitcellhasnocenterofsymmetry.IfwegrawavectorfromOtoanychargeanddrawthereversevector,wewillfindanoppostecharge.4PiezoelectricEffectPi=inducedpolarizationalongtheidirection,dij=piezoelectriccoefficients,Tj=mechanicalstressalongthejdirectionPi=dijTjConversePiezoelectricEffectSj=inducedstainalongthejdirection,dij=piezoelectriccoefficients,Ei=electricfieldalongtheidirectionSj=dijEi56Electro-MechanicalCouplingFactork=electromechanicalcouplingfactorElectro-MechanicalCouplingFactork=electromechanicalcouplingfactor78Thepiezoelectricsparkgenerator.9PiezoelectricVoltageCoefficientE=electricfield,

g

=piezoelectricvoltagecoefficient

T=appliedstressE=gTMechanicalstandingwavesareformedinthepiezoelectriccrystaln=aninteger,=wavelengthofcrystalvibrations,

l

=crystal(sample)lengthalongwhichthewavesaretraveling107.8.2Piezoelectricity:QuartzOscillatorsandFiltersWhenasuitablycutquartzcrystalwithelectrodesisexcitedbyanacvoltageas(a),itbehavesasifithastheequivalentCircuitin(b).(c)and(d)ThemagnitudeoftheimpedancesZandreactance(bothbetweenAandB)versusfrequency,neglectinglosses.11MechanicalResonantFrequencyfs=mechanicalresonantfrequency,L=massofthetransducer,C=stiffnessAntiresonantFrequencyfa=antiresonantfrequency,L=massofthetransducer,CisCoandCinparallel,whereCoisthenormalparallelplatecapacitancebetweenelectrodes12Piezoelectrictransducers|SOURCE:PhotobySOK1314(a)Intheabsenceofanappliedforcethecentersofmassforpositiveandnegativeionscoincide.(b)UnderanappliedforcealongythecentersofmassforpositiveandnegativeionsareshiftedwhichresultsinanetdipolemomentPalongy.(c)Whentheforceisalongadifferentdirection,alongx,theremaynotbearesultingnetdipolemomentinthatdirectionthoughtheremaybeanetPalongadifferentdirection(y).Ahexagonalunitcellhasnocenterofsymmetry.IfwegrawavectorfromOtoanychargeanddrawthereversevector,wewillfindanoppostecharge.157.8.3FerroelectricandPyroelectricCrystalsFerroelectricCrystalsCertaincrystalsarepermanentlypolarizedevenintheabsenceofanappliedfield.Thecrystalalreadypossessesafinitepolarizationvectorduetotheseparationpfpositiveandnegativechargesinthecrystal.Thesecrystalsarecalledferroelectric.ExampleBaTiO316BaTiO3hasdifferentcrystalstructuresaboveandbelow130Cthatleadtodifferentdielectricproperties.Aboveapproximately130℃,thecrystalstructureofBaTiO3hasacubicunitcell,.Thecentersofmassofthenegativecharges（O2-）andthepositivecharges,Ba2+andTi4+coincideattheTi4+ion.ThereisthereforenonetpolarizationandP=0.below130℃,thestructureofbariumtitanateistetragonal,inwhichtheTi4+atomisnotlocatedatthecenterofmassofthenegativecharges.Thecrystalisthereforepolarizedbytheseparationofthecentersofmassofthenegativeandpositivecharges.ThecrystalpossessesafinitepolarizationvectorPandisferroelectric.

17Animportantandtechnologicalusefulcharacteristicofaferroelectriccrystalisitsabilitytobepoled.Above130℃,thereisnopermanentpolarizationinthecrystal.IfweapplytemporaryfieldEandletthecrystalcooltobelow130℃,wecaninducethespontaneouspolarizationPtodevelopalongthefielddirection.Inotherwords,weshoulddefinethecaxisbyimposingatemporaryexternalfield.Thisprocessiscalledpoling.ThecaxisisthepolaraxisalongwhichPdevelops.Italsocalledtheferroelectricaxis.18Allferroelectriccrystalsarealsopiezoelectric,butthereverseisnottrue:notallpiezoelectriccrystalsareferroelectric.WhenastressalongyisappliedtotheBaTiO3crystalinFigure7.45a,thecrystalisstretchedalongy,asaresultofwhichtheTi4+atombecomesdisplaced,asshowninFigure7.45b.Thereis,noshiftinthecenterofmassofthenegativecharges,whichmeansthatthereisachange△Pinthepolarizationvectoralongy.Thus,theappliedstressinducesachangeinthepolarization,whichisapiezoelectriceffect.Ifthestressisalongx,asillustratedinFigure7.45c,thenthechangeinthepolarizationisalongy.Inbothcases,△Pisproportionaltothestress,whichisacharacteristicofthepiezoelectriceffect.19Thebariumtitanatecrystalisalsosaidtobepyroelectricbecausewhenthetemperatureincreases,thecrystalexpandsandtherelativedistancesofionschange.TheTi4+ionbecomesshifted,whichresultsinachangeinthepolarization.Thus,atemperaturechangeδTinducesachangeδPinthepolarizationofthecrystal.Thisiscalledpyroelectricity,whichisillustratedinFigure7.46.20Themagnitudeofthiseffectisquantizedbythepyroelectriccoefficientp,whichisdefinedbyAfewtypicalpyroelectriccrystalsandtheirpyroelectriccoefficientsarelistedinTable7.9.Verysmalltemperaturechanges,eveninthousandthsofdegrees,inthematerialcandevelopvoltagesthatcanbereadilymeasured.21Forexample,foraPZT-typepyroelectricceramicinTable7.9,takingδT=10-3Kandp≈380*10-6，wefindδP=3.8*10-7Cm-2.FromδP=εo(εr-1)δEwithεr=290,wefindδE=148Vm-1Ifthedistancebetweenthefacesoftheceramicwherethechargesaredevelopedis0.1mm,thenδV=0.0148or15mV221Piezoelectricity:Certaincrystals,becomepolarizedwhentheyaremechanicallystressed.2.Certaincrystals