Activation and Deactivation Kinetics of Oxygen Reduction over a La0.8Sr0.2Sc0.1Mn0.9O3 Cathode

18690J.Phys.Chem.C2008,112,18690–18700

ActivationandDeactivationKineticsofOxygenReductionoveraLa0.8Sr0.2Sc0.1Mn0.9O3Cathode

YaoZheng,RanRan,andZongpingShao*

StateKeyLaboratoryofMaterials,OrientedChemicalEngineering,CollegeofChemistryandChemical

Engineering,NanjingUniVersityofTechnology,No.5XinMofanRoad,Nanjing,210009,People’sRepublicofChinaReceiVed:August4,2008;ReVisedManuscriptReceiVed:September2,2008

Electrochemicalimpedancespectroscopy,stepcurrentpolarization,andcyclicvoltammetrywereappliedtoinvestigatetheactivationanddeactivationkineticsofoxygenreductionoveranovelLa0.8Sr0.2Sc0.1Mn0.9O3(LSSM)cathodematerial.Oxygenvacancieswerecreatedaftercathodicpolarizationforacertainperiodoftime.Thegeneratingratewascloselyrelatedwithoxygenpartialpressureofsurroundingatmosphere(PO2),polarizationtime,temperature,andvoltage.TheinsitucreatedoxygenvacanciescouldpropagatebothoverthesurfaceandintothebulkoftheLSSMelectrodeafterahighcathodicpolarization.Bothchemicaloxidationbyambientairandelectrochemicaloxidationbyanodicpolarizationwereexploitedtodemonstratethedeactivationmechanismoftheseinsitucreatedoxygenvacancies.Therate-determiningstepofoxygenreductionreactionoverLSSMelectrodebeforeandaftertheactivationwasalsoinvestigated.Itwasbyoxygenionsurfacediffusionat800°Cinair,whileasteadychangetoanelectron-transferprocesswasobservedwithdecreasingtemperatureandPO2.

1.Introduction

Asolid-oxidefuelcell(SOFC)isanallsolidstateelectro-chemicaldeviceapplyinghydrogenorhydrocarbonasfuelswithlowemissionsandhighenergyconversionef?ciency.Becausetheoxygenelectrocatalyticreductionovercathodetypicallyhasslowerkineticsandhigheractivationenergythanhydrogenelectrocatalyticoxidationoveranode,maincellpolarizationlossisfrequentlycontributedfromthecathodeatloweroperatingtemperatures.Therefore,developingcathodematerialswithhighelectrocatalyticactivityforoxygenreductionandbetterunder-standingthemechanismofoxygenreductionreaction(ORR)areofgreattechnologicalorscienti?cimportancetowardthecommercializationofSOFC.1,2

Inthepast30years,manyperovskiteoxideshavebeenexploitedascathodesofSOFCs.3-7Amongthesematerials,lanthanumstrontiummanganese(LSM)hasbeenthemostwidelyinvestigatedsincemid1980s.Theseinvestigationsmainlyfocusedonitschemicalcomposition,8-10defectchem-istry,nonstoichiometry,11-15chemicalandthermalmatchingwithaclassicalelectrolyteofyttria-stabilizedzirconia(YSZ),16-18electronicstructure,electronicconductivity,Seebeckcoef?-cient,19-21mechanicalandsinteringcapabilities,22,23andsoon.ThemechanismofoxygenelectrochemicalreductionoverLSMcathodehasalsobeenintensivelyexploitedbyisotopetracing,24,25secondaryionmassspectrometer,26,27electrochemicalimpedancespectroscopy(EIS)andstepcurrentpolarizationbasedonporouselectrode,densepatternedthin-?lm,28,29or?negeometricalmicrocon?gurationelectrode,30-32orbytheoreticalsimulation.33-37EISandstepcurrentpolarizationincombinationwithpropermathematicmodesarethetwomostpowerfultoolstoinvestigateORRovercathode.38-48

TheORRoveranoxideelectrodeinvolvesmanysubpro-cesses,whicharecloselyrelatedwithsurfaceandbulkoxygenvacancyconcentrationoftheoxide.LSMtypicallyexhibits

*Towhomcorrespondenceshouldbeaddressed.Phone:862583587722.Fax:862583365813.E-mail:shaozp@http://wendang.chazidian.com.

apparentoxygenexcessnonstoichiometry(δ<0)inairandaweaklyreducingatmosphere,whichissigni?cantlydifferentfromionic-electronicmixedconductorperovskiteasstrontiumcobaltbasedoxides.8,9Becauseofitsnegligiblebulkoxygenionicconductivity,theactivesiteforORRoverLSMelectrodeismainlyalongtheelectrolyte-electrode-airtriple-phaseboundary(TPB)regionunderopencircuitvoltage(OCV).Alargecathodicpolarizationresistance(Rp)isusuallyexperiencedatlowoperatingtemperature.ManystrategieshavebeentriedtoimprovethecathodeperformanceofLSMatreducedtemperature,suchasintroducinganionicconductingphaseYSZintoLSMtoformacompositeelectrode.49-53SuchimprovementisduetotheextensionofactivesitesfromthetraditionalTPBintothewholebulkofcompositeelectrode.ThemostdirectandsimplestmethodtoactivateLSMelectrodeisstillviathecathodicpolarization,whichcancreateoxygenvacancyinthebulkand/oroverthesurfaceofelectrode.AgreatextensionofoxygenreductionsitesandreductioninRpisthenexpected.Thegenerationofoxygenvacancybycathodicpolarizationisfairlycomplicated.Therearemanyliteraturesdescribingthisprocesswithfocusonthegeneratingsiteanddiffusionpath.42-44,54-56Uptonow,theinvestigationshavebeenprimarilyconductedbystaticmeasurementwhiletheelectrodekineticsanalysiswaslessinvolved.Previously,wehavesuccessfullydemonstratedanewLSM-basedcathodeLa0.8Sr0.2ScyMn1-yO3whichshowedabettercathodeperformancethanLSM.57-59Inthepresentwork,EIS,cyclicvoltammetry,andTafelslopehavebeenconductedtoevaluatetheformationkineticsofoxygenvacancyinthisnewLa0.8Sr0.2Sc0.1Mn0.9O3(LSSM)electrodeandalsothepropagatingpathofthesegeneratedoxygenvacancies.Thedeactivationkineticsoftheseinsitucreatedoxygenvacancieswerealsoexploitedviaelectrochemicaloxidationbyanodicpolarizationandchemicaloxidationbyambientair.

10.1021/jp806941dCCC:$40.75?2008AmericanChemicalSociety

PublishedonWeb11/05/2008

OxygenReductionoveraLa0.8Sr0.2Sc0.1Mn0.9O3Cathode2.ExperimentalSection

LSSMoxidepowderwassynthesizedbyacombinedEDTA-citratecomplexingsol-gelprocess.60La(NO3)3·xH2O,Sr(NO3)3,Sc2O3,andMn(Ac)2·4H2O,(allA.R.grade)http://wendang.chazidian.com(NO3)3·xH2Owas?rstpreparedintoanaqueoussolutionaround1Mwithitspreciseconcentra-tiondeterminedbystandardEDTAtitrationtechnique.Sc2O3waspreparedin1MaqueousSc(NO3)3solutionbydissolvingin6Mnitricacidunderheatingandthendilutedwithaproperamountofdeionizedwater.RequiredamountsofLa(NO3)3,Sr(NO3)2,Sc(NO3)3,andMn(Ac)2·4H2Owerethenpreparedintoamixedaqueoussolution.EDTA-NH3·H2OsolutionandcitricacidsolidatamoleratiooftotalmetalionstoEDTAtocitricacidof1:1:2wereaddedinsequenceunderstirringandheating.Thewaterwasevaporatedfromthesolutionbyheatingat90°cuntilatransparentgelwasobtained,whichwaspre?redat250°candfurthercalcinatedat950°cinairfor5htogetthe?nalproductswiththedesiredlatticestructure.

ElectrochemicalcharacterizationofLSSMwasconductedbasedonathree-electrodecon?gurationwithhomemade(Sc2O3)0.1(ZrO2)0.9(ScSZ)aselectrolyte.Tofabricateasinglethree-electrodecell,ScSZpowderswerepressedintodisk-shapepelletsandthensinteredinairat1500°Cfor5htoachievedenseelectrolytesubstratewithadiameterof?13mmandathicknessof?0.3mm.Theas-preparedLSSMpowdersweredispersedinapremixedsolutionofglycerol,ethyleneglycol,andisopropylalcoholtoformacolloidalsuspensionbyahigh-energyballmiller(Fritsch,Pulverisettle6)atarotationalspeedof400rpmfor1h.Thesuspensionslurrywassprayedontoonesideofelectrolytesubstrateandthencalcinatedat1100°Cinairfor2htoperformasworkingelectrode(WE);ethanol-basedsilverslurrywasusedascurrentcollector.Ptpaste(PE-Pt-7840,Guizhou,China)wasappliedtotheothersideofelectrolyteassymmetricallyaspossiblewithWEandcalcinatedat950°Cinairfor1htoactascounterelectrode(CE).Agpaste(DAD-87,Shanghai,China)wasusedasreferenceelectrode,whichwaspaintedasaringsurroundingtheCE.ThegapbetweenCEandREwas?4mm;theareaoftheWE,CE,andREwas0.26,0.26,and0.3cm2,respectively.

ThecathodicpolarizationresistancewasinvestigatedbyEISusingaSolartron1260FrequencyResponseAnalyzerincombinationwithaSolartron1287Potentiostat.ThefrequencyofEISwasrangedfrom0.1Hzto1000kHz,andsignalamplitudewas10mV.SamplesweretestedunderOCVconditionsandconstantcathodicoranodicpolarizationvoltagesof(0.5V.DatawerecollectedusingZ-View2.9csoftware.Theoverallimpedancedatawere?ttedbyacomplexnonlinearleast-squares(CNLS)?ttingprogramviaZ-Plot2.9csoftware.Thecathodeoverpotentialwasobtainedbystepcurrentpolar-izationmeasurementcontrolledbyCorrware2.9csoftware;polarizationcurrentdensityrangedfrom0the1000mAcm-2at10mAS-1perstep.CyclicvoltammogramofLSSMelectrodewerealsoobtainedthroughCorrware2.9csoftware.Theelectrodewas?rstscannedfrom0to+0.25Vtoconsumethepossibleoxygenvacanciesinthebulkoroverthesurfaceoftheoxide,apositivescanfrom+0.25to-1.00Vandthenreversescanfrom-1.0to0Vweresuccessivelyconducted.Each?ttingdatafromtheEIS,CV,andstepcurrentpolarizationistheaveragevalueofthreesuccessivemeasure-ments.ApostfactumcorrectionoftheIRdropinthealloverpotentialandCVmeasurementswasconducted,whereRcanbeobtainedfromEIS.ThevariousPO2werebalancedbyO2(99.999%),N2(99.999%)and1vol.%O2/Ar.

J.Phys.Chem.C,Vol.112,No.47,200818691

Figure1.Polarizationcurrentsrespondingtopolarizationtimeundersequentialcathodic,anodic,cathodicpolarizationof(0.5Vat800°Cinvariousoxygenpartialpressures.

3.ResultsandDiscussion

Underdischargestate,oxygeniselectrocatalyticallyreducedtooxygenionoverthecathodesurfaceoralongtheTPBregioninaSOFC.ByuseofKroger-Vinknotation,theoverallORRcanbewrittenas

1??2

O2+VO

+2efO×

O(1)

whereV??O

notesdoublechargedoxygenvacancyinelectrolytelatticeorbulkand/orsurfaceofcathode;OO×isoxygenioninanormaloxygensite.Accordingtoeq1,theORRiscloselyrelatedwiththeoxygenvacancyconcentration.WepreviouslydemonstratedthatintrodcutionofasmallamountofSc3+intotheBsiteofLSMdidnotcreateintrinsicoxygenvacancyintothebulkofLSSM,i.e.,theORRstilloccurredattheTPBregioninLSSMelectrodeunderzerodirectcurrentpassage.However,Sc3+dopingfacilitatedthecreationofoxygenvacancyinLSSMunderpolarizationcondition.57Figure1showsthedependenceofpolarizationcurrentonpolarizationtimeundersequentialcathodic,anodic,cathodicpolarizationof-0.5,+0.5,-0.5Vat800°CundervariousatmosphereswithdifferentPOcathodicpolarization,thepolarizationcurrentexperienced2.UnderaasharpincreaseintheinitialstageandreachedasteadyvalueafteracertaintimeunderatmosphereswithrelativehighPO(0.21and1atm).Thisimpliestheresistanceforoxygen2activationdecreasedobviouslyafterthepolarization.ItisgenerallybelievedthatMn4+inaperovskitelatticecanbepartiallyreducedafteracathodiccurrentpassageinconcomi-tancewiththeformationofoxygenvacancy,whichcaneffectivelyfacilitatetheORR.ItalsoshouldbenotedthatthesurfaceSrOsegregationhasturnedouttobeanormalphenomenonforLSMelectrode.Itseffectoncathodicpolariza-tionwasdetailedstudiedbyJiangetal.61,62TheyreportedthatsuchsurfaceenrichedSrOwouldbeincorporatedintotheLSMlatticeduringthecathodicpolarization.61,62AstoLSSM,viathetechniqueofwaterboilingoftheoxideandthenmonitoringchangeofthepHvalueofthewater,57wehavedemonstratedpreviouslythattheSrOsurfacesegregationwasgreatlysup-pressedbecauseoftheSc3+doping.Therefore,theSrOsegregationwasnotconsideredintheactivationanddeactivationkineticsofoxygenreductionoverLSSMcathodeinthisstudy.AscanbeseenfromFigure2,thecathodicresistanceofLSSMdiddecreaseobviouslyafterthepolarization.Itreducedfromaninitialvalueof1.45?cm2to0.20?cm2at800°Cinairafteracathodicpolarizationfor40min.UnderlowPO2,

for

18692J.Phys.Chem.C,Vol.112,No.47,2008Figure2.CathodicpolarizationresistanceofLSSMtestedinvarious

conditions.

example,0.01atm,thechangeofpolarizationcurrentwith

respecttopolarizationtimewasnotsoobvious.

Afterthecathodicpolarization,thesamplewasimmediatelyswitchedtoananodicpolarizationof0.5Vforasameperiodoftime.Differentfromthecathodicpolarization,theanodiccurrentdecreasedquicklyintheinitialperiodandreachedanequilibriumvaluefor10-30min.AtlowerPOrequiredalongerperiod2,suchachangewasmoresigni?cantandtoreachitssteadystate.Thedecreaseinpolarizationcurrentunderanodicpolarizationindicatesthattheoxygenactivationwasblockedduetothedecreaseinoxygenvacancyconcentration.Whenasecondcathodicpolarizationwasappliedaftertheanodicpolarization,thecurrentcurvematchedwellwiththepreviousone.Thisimpliesthegenerationofoxygenvacancybycathodicpolarizationhasahighlyreversiblekinetics.

3.1.OxygenVacancyFormationKineticsviaDCPolar-ization.Byapplicationofcathodicpolarizationvoltageof-0.5V(PO2)2.2×10-10atm)toLSSM,Mn4+inLSSMlatticewaspartialreducedtoMn3+.Tosustainthemacroscopicelectricalneutrality,theconcomitantgenerationofoxygenvacancyattheelectrode/electrolyteinterfaceregionwashap-pened.Suchelectrochemicalreactioncanbewrittenas

O×???k1

O,LSSM+2MnMn+VO,ScSZ+2e′982Mn×Mn+

V??O,LSSM

+O×

O,ScSZ(2)whereMn?MnandMnMn×denoteMn4+andMn3+,O×O,LSSMand

O×O,ScSZareoxygenionsinLSSMandScSZlatticesites,V??O,LSSM

andV??O,ScSZareoxygenvacanciesinLSSMandScSZ,respec-tively.Ontheotherhand,theseformedoxygenvacancieswerealsoconsumedfromchemicaloxidationbyambientoxygenviathereaction

V??

1O,LSSM+

×k2

2

O+2Mn98O×

?2MnO,LSSM+2MnMn

(3)

Thegeneratingrateofoxygenvacancyundercathodicpolarizationisthedifferencebetweentheoxygenvacancycreatingrateandeliminatingrate,whichcanbedescribedas54

Zhengetal.

d[V??O,LSSM]dt)k[O×2??O,LSSM][Mn?Mn][VO,ScSZ]

RcnFE1

[O××2exp-O,ScSZ

][MnMn

]

[RT]

k[V??p0.5

O,LSSM]O×22[MnMn]2

[O×2(4)

O,LSSM][Mn?Mn]

Equation4canbesimpli?edto

d[V??

O,LSSM]dt)k??[Rc1expnFERT

]

-k????p0.5

2[VO,LSSM]O2

(5)

where

[O×?k??]2[V??O,LSSM][MnMnO,ScSZ]

[V??×2

1)k1

kO,LSSM][MnMn][O×][Mn×2

k??2)2

O,ScSZMn]

[O×?2O,LSSM][MnMn]

Interationofeq5thenmakes

k??Rexp

cnFE

1

[V??

RT0.5O,LSSM])

k??p0.5

(1-e-k??2pO2t)(6)

2O2

Onthebasisofeq6,thedependencesofoxygenvacancy

concentrationontemperature,polarizationtime,andPOsurroundingare

2ofthelog([V??

O,LSSM])∝log(t)(7)log([V??

O,LSSM])∝log(PO2)(8)log([V??

O,LSSM])∝

1

T

(9)

Underthesteadystate,variouscationsandlatticeoxygenwillgettheirequilibriumconcentrations.Themaximumoxygenvacancyconcentrationis

k??RcnFE

1exp

[V??RTO,max])

k??0.5(10)

2pO2

Itwasreachedatthelimitingtimeof

t)

1-0.5k??pO(11)

2

2whichdependsonlyonsurroundingPOunder2.Onthebasisofeqs7-11,thosephenomenaobservedcathodicpolarizationwithvarioustestingconditionsasshowninFigure1canbewellexplained.

Partsa-cofFigure3showthetypicalCVofLSSMelectrodeundervarioustestingconditions.EveryCVexhibitsatypicalhysteresisloop(counterclockwiseresponse).Theareaofloopcanberegardedastheconcentrationofinsitucreatedoxygenvacancyfromthecathodicpolarization.54,55InFigure3,thehighertemperatureorPOamountofoxygenvacancies2orthelongerpolarizationtime,themoreweregenerated.Furthermore,alinearresponseofhysteresisloopareatoPOrateandanidempotentrelationshipwithtemperature2andscanningwereobserved.Suchphenomenaareinwellagreementwitheqs7-9.3.2.PropagationoftheinSituCreatedOxygenVacancies.Ineq2,theinsitucreatedoxygenvacanciesareallcongregatedattheelectrode/electrolyteinterface.Becauseoftheirlowmigrationenergy(?0.7eV),63thesehighlymobileoxygenvacanciesmaypropagatetobothsurfaceandbulkoftheelectrode.Therearegenerallytwomechanismstodescribe

the

OxygenReductionoveraLa0.8Sr0.2Sc0.1Mn0.9O3CathodeJ.Phys.Chem.C,Vol.112,No.47,200818693

Figure3.TypicalCVofLSSMundervarioustestingconditions.(a)Scanrate)20mVS1-,T)800°C,undervariousPO2.(b)PO2)0.21atm,T)800°C,withvariousscanrates.(c)PO2)0.21atm,scanrate)20mVS1-,undervarioustemperatures.Insetislogarithmicloopareadependingonvarioustesting

parameters.

propagatingpathofoxygenvacanciesinvolvedduringthecathodicpolarization.HammoucheandSiebertetal.proposedthatanewpathwayfortheORRwascreatedbased

2-onthebulkdiffusioninelectrode.56,66O-ad,Oad,orOadformed

overtheelectrodesurfacecaneasilytransferinthesepathwaysinsidetheelectrodebulktotheelectrode/electrolyteinterfaceandthenincorporateintotheelectrolyteviaanion-chargetransferprocess.Accordingtoanothermechanism,theformedoxygenvacanciesspreadovertheelectrodesurfacemostlybysurfaceorgrain-boundarydiffusionwiththeconcomitantenlargementofTPBlength.54,55VanHeuvelnandBouwmeesterfurtherdemonstratedthatthebulkdiffusionpathwaywaspredominantunderhighcathodicoverpotentialwhilethesurfacediffusionpathwaywassigni?cantonlyatlowcathodicover-potential.42Figure4isthedependenceofRponcathodicpolarizationvoltage.Inthelowvoltagezonerangingfrom0to50mV(equivalentPO2from0.21to0.024atm),denotedaszoneA,Rpkeptalmostunchangedandapproximatedtotheoriginalvalue?1.45?cm2beforepolarization.ThisimpliesMn4+inLSSMwasnotreducedtoMn3+undersuchalowvoltage.Inotherwords,notanyoxygenvacancywasgeneratedattheelectrode/electrolyteinterface,andtheactivesiteforORRwasstillrestrictedtotheTPBregion.Withincreasingcathodicpolarizationvoltage,thereductionofMn4+inLSSMtoMn3+wasinitializedinconcomitancewiththeformationofhighlymobileoxygenvacancies.ItthenledtoasharpdecreaseofRpasshowninzoneB.TomaintainelectricalneutralitytheoxygenvacancyinLSSMshouldbecompensatedbythedecreaseofoxidationstateofMn4+intheBsiteofLSSM.TheaveragevalenceofMninLSSMis3.187at800°Cdeterminedbyquenchthepowderandthensubjectedtoaniodometrictitrationtechniqueintheroomtemperature.

Figure4.Thedependenceofpolarizationresistanceoncathodicpolarizationvoltageat800°C.

Asthecathodicpolarizationvoltagehighthan500mV,Rpgotaconstantvalueabout0.25?cm2.Thiscanbeexplainedbythefollowingaspect.UnderhighcathodicvoltagewithlowPO2,Mn4+(eventhoughnotthewhole)wasreducedtoMn3+orMn2+inconcomitancewiththesteadilyincreasingconcentra-tionofoxygenvacancy,resultinginadecreasingRp.However,thehighertheoxygenvacancyconcentration,themorelikelyoxygenvacancieswillbeorderedviatheformationofdefectassociation.Thisreactioncanbedescribedas

×??????

2Mn×Mn+OOf(MnMn-VO-MnMn)+0.5O2

(12)

′whereMnMndenotesMn2+.Suchcluster-defecthasanegativeeffectonthemobilityofoxygenvacancyandthenmakesR

p

18694J.Phys.Chem.C,Vol.112,No.47,2008Zhengetal.

bothlowandhighfrequencyarcswasreduced,implyingtheoxygenvacancywassuccessfullypenetratedintothebulkofelectrodetoformmoreactivesitesforORR,correspondingtozoneBinFigure4.AboveresultsalsosupportedthemodelproposedbyVanHeuvelnandBouwmeesterfortheORRandpropagationpathoftheoxygenvacancy.42

3.3.DeactivationKineticsofinSituCreatedOxygenVacancies.Asdemonstratedpreviously,bothsurfaceandbulkoxygenvacanciescouldbegeneratedafterthepolarizationatapropervoltageforalimitedperiodoftime.However,theoxygenvacancycouldbeslowlyeliminatedoncethepolarizationwasstoppedduetothereoxidationbysurroundingatmosphereviareactionasexpressedineq3.IndeedithasbeendemonstratedthattheRpreliedstronglyontheactivationanddeactivationprocesses,asshowninFigure2.Toexploittheeliminationmechanismoftheseoxygenvacancies,twodifferentoxidizationtechniqueswereapplied,i.e.,chemicaloxidationbygasphaseoxygenandelectrochemicaloxidationviathehelpofanodiccurrent.

AftertheLSSMelectrodewasactivatedbycathodicpolariza-tionforaperiodoftime,itwassubjectedforrelaxationunderzerocathodicoranodiccurrentpassage.Theinsitucreatedoxygenvacancieswouldslowlyreactwithoxygenfromatmosphereovertheelectrodesurfaceas

Figure5.EISofLSSMtestingunderthreetypicalcathodicvoltagesat800°

C.

decreasemuchmoreslowly.Therefore,whenthepolarizationvoltagereceivedacertainvalue,inthiscasearound500mV,thepolarizationresistancewasleveledofforevenincreasedwiththefurtherincreaseinpolarizationvoltage,asshowninzoneC.

Figure5showsthetypicalEIScurvesofLSSMcathodetestedundervariouscathodicvoltagesat800°C.Under-10and-100mVcathodicpolarizationvoltages,thelow-frequencyarcsofEISdecreasedrapidly,whilehighfrequencyarcskeptalmostunchanged.ItmeanstheinsitucreatedoxygenvacanciesspreadmostlyoverthesurfaceofelectrodeoralongtheTPBregionunderthesecathodicvoltages,correspondingtozoneAinFigure4.Underacathodicpolarizationvoltageof-0.5V,thesizeof

1??×

VO,LSSM+O2+e-fOO,LSSM

2

(13)

wheree-wassuppliedbyMn3+fMn4+.Theoxidizingrateofoxygenvacancycanbewritten

as

Figure6.ThevalueofrelaxingRpdependingontimeinvariousstates(a)0.01atm;(b)0.21atm;(c)1atm.InsetsarethelinearrelationshipbetweenRpandt1/2.ThevaluesofRpinoriginalandafteranodepolarizationarealsoshownas?xedvalues.