压电理论.docx
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压电理论.docx
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压电理论
Piezoelectricity
In1880,JacquesandPierreCuriediscoveredanunusualcharacteristicofcertaincrystallineminerals:
whensubjectedtoamechanicalforce,thecrystalsbecameelectricallypolarized.Tensionandcompressiongeneratedvoltagesofoppositepolarity,andinproportiontotheappliedforce.Subsequently,theconverseofthisrelationshipwasconfirmed:
ifoneofthesevoltage-generatingcrystalswasexposedtoanelectricfielditlengthenedorshortenedaccordingtothepolarityofthefield,andinproportiontothestrengthofthefield.Thesebehaviorswerelabeledthepiezoelectriceffectandtheinversepiezoelectriceffect,respectively,fromtheGreekwordpiezein,meaningtopressorsqueeze.
Althoughthemagnitudesofpiezoelectricvoltages,movements,orforcesaresmall,andoftenrequireamplification(atypicaldiscofpiezoelectricceramicwillincreaseordecreaseinthicknessbyonlyasmallfractionofamillimeter,forexample)piezoelectricmaterialshavebeenadaptedtoanimpressiverangeofapplications.Thepiezoelectriceffectisusedinsensingapplications,suchasinforceordisplacementsensors.Theinversepiezoelectriceffectisusedinactuationapplications,suchasinmotorsanddevicesthatpreciselycontrolpositioning,andingeneratingsonicandultrasonicsignals.
Inthe20thcenturymetaloxide-basedpiezoelectricceramicsandotherman-madematerialsenableddesignerstoemploythepiezoelectriceffectandtheinversepiezoelectriceffectinmanynewapplications.Thesematerialsgenerallyarephysicallystrongandchemicallyinert,andtheyarerelativelyinexpensivetomanufacture.Thecomposition,shape,anddimensionsofapiezoelectricceramicelementcanbetailoredtomeettherequirementsofaspecificpurpose.Ceramicsmanufacturedfromformulationsofleadzirconate/leadtitanateexhibitgreatersensitivityandhigheroperatingtemperatures,relativetoceramicsofothercompositions,and"PZT"materialscurrentlyarethemostwidelyusedpiezoelectricceramics.
Howarepiezoelectricceramicsmade?
Atraditionalpiezoelectricceramicisamassofperovskitecrystals,eachconsistingofasmall,tetravalentmetalion,usuallytitaniumorzirconium,inalatticeoflarger,divalentmetalions,usuallyleadorbarium,andO2-ions(Figure1.1).Underconditionsthatconfertetragonalorrhombohedralsymmetryonthecrystals,eachcrystalhasadipolemoment(Figure1.1b).
Toprepareapiezoelectricceramic,finepowdersofthecomponentmetaloxidesaremixedinspecificproportions,thenheatedtoformauniformpowder.Thepowderismixedwithanorganicbinderandisformedintostructuralelementshavingthedesiredshape(discs,rods,plates,etc.).Theelementsarefiredaccordingtoaspecifictimeandtemperatureprogram,duringwhichthepowderparticlessinterandthematerialattainsadensecrystallinestructure.Theelementsarecooled,thenshapedortrimmedtospecifications,andelectrodesareappliedtotheappropriatesurfaces.
Aboveacriticaltemperature,theCuriepoint,eachperovskitecrystalinthefiredceramicelementexhibitsasimplecubicsymmetrywithnodipolemoment(Figure1.1a).AttemperaturesbelowtheCuriepoint,however,eachcrystalhastetragonalorrhombohedralsymmetryandadipolemoment(Figure1.1b).Adjoiningdipolesformregionsoflocalalignmentcalleddomains.Thealignmentgivesanetdipolemomenttothedomain,andthusanetpolarization.Thedirectionofpolarizationamongneighboringdomainsisrandom,however,sotheceramicelementhasnooverallpolarization(Figure1.2a).
Thedomainsinaceramicelementarealignedbyexposingtheelementtoastrong,directcurrentelectricfield,usuallyatatemperatureslightlybelowtheCuriepoint(Figure1.2b).Throughthispolarizing(poling)treatment,domainsmostnearlyalignedwiththeelectricfieldexpandattheexpenseofdomainsthatarenotalignedwiththefield,andtheelementlengthensinthedirectionofthefield.Whentheelectricfieldisremovedmostofthedipolesarelockedintoaconfigurationofnearalignment(Figure1.2c).Theelementnowhasapermanentpolarization,theremanentpolarization,andispermanentlyelongated.
Analogoustocorrespondingcharacteristicsofferromagneticmaterials,apoledferroelectricmaterialexhibitshysteresis.Figure1.3showsatypicalhysteresiscurvecreatedbyapplyinganelectricfieldtoapiezoelectricceramicelementuntilmaximumpolarization,Ps,isattained,reducingthefieldtozerotodeterminetheremanentpolarization,Pr,reversingthefieldtoattainanegativemaximumpolarizationandnegativeremanentpolarization,andre-reversingthefieldtorestorethepositiveremanentpolarization.Thetracingbelowthehysteresiscurveplotstherelativechangeinthedimensionoftheceramicelementalongthedirectionofpolarization,correspondingtothechangeintheelectricfield.Therelativeincrease/decreaseinthedimensionparalleltothedirectionoftheelectricfieldisaccompaniedbyacorresponding,butapproximately50%smaller,relativedecrease/increaseinthedimensionperpendiculartotheelectricfield.
Figure1.3.EffectsofElectricField(E)onPolarization(P)andCorrespondingElongation/ContractionofaCeramicElement
Whatcanpiezoelectricceramicsdo?
Mechanicalcompressionortensiononapoledpiezoelectricceramicelementchangesthedipolemoment,creatingavoltage.Compressionalongthedirectionofpolarization,ortensionperpendiculartothedirectionofpolarization,generatesvoltageofthesamepolarityasthepolingvoltage(Figure1.4b).Tensionalongthedirectionofpolarization,orcompressionperpendiculartothedirectionofpolarization,generatesavoltagewithpolarityoppositethatofthepolingvoltage(Figure1.4c).Theseactionsaregeneratoractions--theceramicelementconvertsthemechanicalenergyofcompressionortensionintoelectricalenergy.Thisbehaviorisusedinfuel-ignitingdevices,solidstatebatteries,force-sensingdevices,andotherproducts.Valuesforcompressivestressandthevoltage(orfieldstrength)generatedbyapplyingstresstoapiezoelectricceramicelementarelinearlyproportionaluptoamaterial-specificstress.Thesameistrueforappliedvoltageandgeneratedstrain.
Ifavoltageofthesamepolarityasthepolingvoltageisappliedtoaceramicelement,inthedirectionofthepolingvoltage,theelementwilllengthenanditsdiameterwillbecomesmaller(Figure1.4d).Ifavoltageofpolarityoppositethatofthepolingvoltageisapplied,theelementwillbecomeshorterandbroader(Figure1.4e).Ifanalternatingvoltageisapplied,theelementwilllengthenandshortencyclically,atthefrequencyoftheappliedvoltage.Thisismotoraction--electricalenergyisconvertedintomechanicalenergy.Theprincipleisadaptedtopiezoelectricmotors,soundorultrasoundgeneratingdevices,andmanyotherproducts.
Figure1.4.GeneratorandMotorActionsofaPiezoelectricElement
Generatoractionisusedinfuel-ignitingdevices,solidstatebatteries,andotherproducts;motoractionisadaptedtopiezoelectricmotors,soundorultrasoundgeneratingdevices,andmanyotherproducts.
PiezoelectricConstants
Becauseapiezoelectricceramicisanisotropic,physicalconstantsrelatetoboththedirectionoftheappliedmechanicalorelectricforceandthedirectionsperpendiculartotheappliedforce.Consequently,eachconstantgenerallyhastwosubscriptsthatindicatethedirectionsofthetworelatedquantities,suchasstress(forceontheceramicelement/surfaceareaoftheelement)andstrain(changeinlengthofelement/originallengthofelement)forelasticity.ThedirectionofpositivepolarizationusuallyismadetocoincidewiththeZ-axisofarectangularsystemofX,Y,andZaxes(Figure1.6).DirectionX,Y,orZisrepresentedbythesubscript1,2,or3,respectively,andshearaboutoneoftheseaxesisrepresentedbythesubscript4,5,or6,respectively.Definitionsofthemostfrequentlyusedconstants,andequationsfordeterminingandinterrelatingtheseconstants,aresummarizedhere.Thepiezoelectricchargeconstant,d,thepiezoelectricvoltageconstant,g,andthepermittivity,e,aretemperaturedependentfactors.
Figure1.6-ThedirectionofpositivepolarizationusuallyismadetocoincidewiththeZ-axis.
PiezoelectricChargeConstant
Thepiezoelectricchargeconstant,d,isthepolarizationgeneratedperunitofmechanicalstress(T)appliedtoapiezoelectricmaterialor,alternatively,isthemechanicalstrain(S)experiencedbyapiezoelectricmaterialperunitofelectricfieldapplied.Thefirstsubscripttodindicatesthedirectionofpolarizationgeneratedinthematerialwhentheelectricfield,E,iszeroor,alternatively,isthedirectionoftheappliedfieldstrength.Thesecondsubscriptisthedirectionoftheappliedstressortheinducedstrain,respectively.Becausethestraininducedinapiezoelectricmaterialbyanappliedelectricfieldistheproductofthevaluefortheelectricfieldandthevalueford,disanimportantindicatorofamaterial'ssuitabilityforstrain-dependent(actuator)applications.
d33
inducedpolarizationindirection3(paralleltodirectioninwhichceramicelementispolarized)perunitstressappliedindirection3
or
inducedstrainindirection3perunitelectricfieldappliedindirection3
d31
inducedpolarizationindirection3(paralleltodirectioninwhichceramicelementispolarized)perunitstressappliedindirection1(perpendiculartodirectioninwhichceramicelementispolarized)
or
inducedstrainindirection1perunitelectricfieldappliedindirection3
d15
inducedpolarizationindirection1(perpendic
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