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Study_6

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    Study

1伽地oFRAREEARTHS

    ;Vo1.21,No.1,Feb.2003,P.13

    ;StudyonSpectralOverlapModelforEnergyTransferbetweenJ-?Multip-?

    ;letsinRareEarthDopedCrystals

    ;WangDianyuan(王殿元)‟,XiaShangda(夏上达),YinMin(尹民)‟

    ;(J.StructureResearchLaboratory,UniversityofScienceandTechnologyofChina,AcademiaSinica,Hefei230026,

    ;China;2.DepartmentofPhysics,UniversityofScienceandTechnologyofChina,Hefei230026,China) ;Abstract:BasedontheexperimentaldataofKY3F1o:TmrepoaedbyDiaf,Kushidasspectraloverlapmodel(SOM)of

    ;energytransferbetween.,.multipletswasstudied.Firstly,withthehelpoftheInokutiHirayamaandYo

    kotaTanimoto

    ;models,theluminescencedecaycurveofH4ofTm?ionwasfitted,andthefittedValuesofcorrespondinginteractionpa-

    ;rametersGDAofenergytransferandCDDofenergymigrationwereobtained.Secondly,bycomparedwithKushidasSOM

    ;inwhichtherelevantJudd.Ofeltapproximativetransitionratesareknown,theaverageoverlapintegralsofSDDandSDA

    ;wereobtained.ForSDD,howtotreatthecontributionoftheelectronicdipole(ED)crystalfieldtransiti

    onforbiddenby

    ;C4sitesymmetryinthecalculationofSDDwasdiscussed.ForSDAwesuggestedthat,byincludingthecontributionofthe

    ;phononsidebandsintheanalysisofoseillatorstrengthoftransition,KushidasSOMofEDEDresonant

    energytransferrate

    ;canbeextendedtonon.resonantphonon.assistedD.Aenergytransfer.Thestrengthsandwidthsofphononsidebandsin

    ;thisexamplewerediscussed,andtheresultswerereasonablygood.

    ;Keywords:luminescence;energytransfer;energymigration;spectralovedapmodel;rareearths ;CLCnumber:0482.3Documentcode:AArticleID:10020721(2003)01001306

    ;In1953,Dexterextendedtheresonancetheoryof

    ;Forstertoaccountforthotransferofexcitationenergy

    ;ininsulatorsfromasensitizertoanacceptor…,and

    ;presentedaconvenientspectralovedapmodel(SOM)

    ;forcalculatingtherateofresonantenergytransferbe.

    ;tweencertainenergylevelsbymeansoftheemission

    ;spectraofdonorionsandtheabsorptionspectraofac

    ;ceptoriOHS.In1973,basedonDextersSOM,Kushi.

    ;dapresentedasimilarSOMthatisforcalculatingthe

    ;energytransferratebetweenJmultipletsinrareearth

    ;(RE)dopedcrystals.ComparingwithDexters ;S0M,Kushidashasaremarkableadvantage:both ;theemissionspectraofdonorandtheabsorptionspec. ;traofacceptorusedintheanalysisaretheoveral ;transitionspectrabetweenJmuhipletsofREions,

    ;thereforetheiroscillatorstrengthsareeasytobeob. ;tained.Besides.inordertotakeintoaccountthepop. ;ulationdistributionamongtheStarkcomponents, ;KushidaintroducedareasonableBoltzmannfactorz= ;exp()insteadof”avemgepopulati.n”,where?

    ;istheenergyseparationbetweenthei-thlevelandthe ;lowestlevelwithinthemanifoldinquestion.However, ;uptonowquantitativeanalysisonenergytransterrate ;usingKushidasSOMwasralelyreported.Herewe ;madeananalysisoftheenergytransferrateinRE ;dopedcrystalsusingKushidasSOM.

    ;Inthisstudy.alltheanalysiswasbasedonthe ;experimentaldataofKY3F10:Tm?reportedbyDiafet ;al‟.Firstly.withthehelpoftheInokuti—Hirayama

    ;model(IHmode1)tS]andtheYokotaTanimotomodel

    ;(Y-Tmode1)j,wefittedtheluminescencedecay ;curveofH4of,Ih?,andobtainedthefittedvaluesof ;interactionparameterCDAofthedonoraceeptor(DA)

    ;energytransfer(H4+H6)(F4+F4)andCDDof

    ;thedonordonor(DD)energymigration(H4+H6)

    ;(H6+H4).Then,withtherelevantspectra

    ;strengthdataandtheaboveCDDandCOA,Kushidas ;SOMgavethefittedvaluesofaverageoverlapintegrals ;ofSDDand5DA.Basedonthecaleulation,Kushidas ;SOMwasdiscussedindetails.ForSDD,therelevant ;

    ;sumandaverage”andthecontributionoftheED

    ;crystalfieldtransitionforbiddenbyC4sitesymmetry ;werediscussed.ForSDA,byincludingtheeontribu

    ;tionofthephononsidebandsintheanalysisofoscil

    ;Receiveddate:200ll220:reviseddate:2002O420

    ;Foundationitem:PmjectsupposedbytheNationalNaturalScienceFoundationofChina(10074061)and

    bytheFosterPmjectFoundationof

    ;MinistryofEducationforStridingCenturyElitist ;Biography:WangDianyuan(1975),Male,Doctoralcandidate ;*Correspondingauthor(Emall:xiasd@ustc.edu.ca)

    ;

    ;14

    ;latorstrengthoftransition,KushidasSOMforelec.

    ;tronicdipoleelectronicdipoleresonantenergytransfer ;couldbeextendedtonon..resonantphonon..assistedD.. ;Aenergytransfer.Thestrengthsandwidthsofphonon ;sidebandsofthissampleinthecalculationofSDAwere ;alsodiscussed.

    ;1Theory

    ;1.1Luminescencedynamicsmodel

    ;Whentheacceptorconcentrationisverylow,the ;.

    ;interactionbetweendonorsandacceptorsmaybeBe. ;glectedandthedonorluminescencedecaycurveex

    ;hibitsasingleexponentialbehavior.Astheacceptor ;concentrationincreases.theDAenergytransferbe

    ;comesimportantandthedonorluminescencedecay ;curveshowsnon.exponentialbehavior.Sobyanalyz. ;ingthedonorluminescencedecaycurves,wecan ;studythemechanismoftheD.-Aenergytransferpro.- ;cessandderivetheenergytransferrate.Hereweonly ;introducetheI.HmodelandtheY.Tmode1.which ;willbeusedinsection2.

    ;1.1.1I.HmodelIn1965,Inokutiand

    ;Hirayamainvestigatedtheresonantenergytransfer ;duetotheelectrostaticmuhipoleinteractionsindetail ;andpresentedthefollowingequation

    ;,(t)=,(o)exp[tI1(1一寻)(?)寻】

    ;(1)

    ;and

    ;CDA=.=PDA~(2)

    ;whereI(0)istheinitialexcitation,risthedonorin

    ;trinsiclifetime.NAistheacceptorconcentrationin ;ions/cm.s=6,8,and10forelectronicdipoleelec.

    ;tronicdipole,electronicdipoleelectronicquadrupole

    ;(EDEQ),andelectronicquadrupoleelectronicqua

    ;drupoleinteractions,respectively.R0isthecritical ;distance,whichisrelatedtotheenergytransferinter

    ;actionparameterCDAandtheenergytransferratePDA ;inEq.(2).ThismodelworkswellonlywhentheD.D ;energymigrationcanbeneglectedandwhenorienta

    ;tionaveragingisassumed.

    ;1.1.2YTmodelWhenthedonorconcentration

    ;isincreased,theDDinteractionbecomesimportant

    ;andtheenergymigrationamongdonorsshouldbecon

    ;sidered.In1967,YokotaandTanimotopresenteda ;generalsolutionforthedonorluminescencedecay

;function,includingtheDDenergymigrationandthe

    ;DAenergytransferviadipoledipolecoupling,and

    ;treatingtheD?-Denergymigrationasadiffusionpro.- ;cessasfollows

    ;JOURNALOFAREEARTHS,Vo1.21,No.1,Feb.2003 ;,(t)=l(0)exp

    ;[?(1+10.87z+15.50z1+8.

    ;743z)寻】

    ;(3)

    ;z=((4)

    ;D:()c

    ;(4)

    ;whereDisthediffusioncoecient,NDisthedonor

    ;concentrationinions/cm,CDDistheDDenergymi-

    ;grationinteractionparameter,whichisrelatedtothe ;energymigrationratePDDbythefollowingEq. ;CDD=PDD?RD(4)”

    ;1.2Kushidasspectraloverlapmodel

    ;Forsimplification,theithcomponentstateof

    ;theI4f,rj>manifoldwasdenotedasI‟,ai

    ;>.Hereadoublydegeneratestatewasregardedas ;twostateswiththesanleenergy(andsoon),andthe ;indexrangesfrom1to2‟,+1.Further,forthecon—

    ;ciseness,theabbreviationsuchasIa;>andIai,> ;wasusedrespectivelyfortheinitialandfinalstatesof ;theionA,andthemanifoldI4f,rj>willbesim

    ;plYdenotedasIJ>.SimilarnotationsforionBwere ;used.Fortheresonantenergytransferbetweentwo ;ionsAandB.assumingthattheseionsareinthe ;statesaandbbeforeandinthestatesaandbafter ;thetransfer,wemayexpressthetransferrateas ;PAB=()I<abIHABIa‟b>Ig(E)g(E)

    ;dE(5)

    ;whereHABisthedonor?-acceptorinteractionHamihoni?- ;an,g(E)isthenormalizedlineshapefunctionfor ;theindividualtransitions.?—‟?or6}bforexaln

    ;pie.Bytakingintoaccountthepopulationdistribution ;amongtheStarkcomponentswiththeBoltzmanndistil

    ;butionfactoexp(),theI‟,a>.I‟,b>I‟,a

    ;>?IJb,>transferratecanbeexpressedas ;PAB----()l<.

    ;?iI,>l,

    ;(E)g(E)dE(6)

    ;Z.=r_gZ(7)

    ;Asanapproximation,thesquareofthematrixelement ;I<aibjIHAIa‟i,b‟j,>IinEq.(6)isreplacedbyits

    ;averageinI<?IHABIa‟vb,>Iinthefollowing

    ;Eq.

    ;<?6IHABI?6,>II<?6IHABI?,b‟=JG,(E)G(E)dE(10)

    ;with

    ;Gw(

    ;“.(E)

    ;(E)

    ;(10)

    ;(10)

    ;FortheREsitewithoutinversionsymmetry,there ;existsnon..zerostaticodd..paritycrystalfieldcompo.. ;nents,whichmakesantipailtyconfiguration(suchas ;4fN5d)mixedintothe4fNconfiguration.Sincethera

    ;tiobetweenEDEDenergytransferrateP(EDED)

    ;andtheEDEQenergytransferrateP(EDEQ)

    ;

    ;P(ED-ED)()=()>>1foP(ED-EQ)r1.0%——,_,>>l?u

    ;1‟m”:KY3Fl0whereRDAistheaveragedistancebe.

    ;tweendonorionsandacceptorionsandistheradiusof ;TIlljion….Therefore.theED—EDinteractionwould

    ;bethemostimportantenergytransfermechanism, ;whichistakenastheonlyenergytransfermechanism ;consideredinthispaper,aswasdonefortheothertwo ;Tm??dopedsystems[„.Withthehelpoftwoapprox—

    ;imation(theJudd.OfeItclosureapproximation,and ;theDextersaverageoftheI<ai6,II,6,,>I

    ;overallpossibleorientationsofRAB),theaverage ;transferrateofthedipoledipoleprocesswasobtained

    ;asfoHows:

    ;-

    ;(E

    ;e

    ;D-ED)=(227r,e4)×

    ;?I_了八八

    ;[<JoIIu”IIJo,>][m<JbIIU”IIJb,

    ;>]S(11)

    ;where.==2,4,6and0isthephenomenolocal

    ;JuddOfeltintensityparameters,whichdependson ;boththehostlatticeandthespeciesoftherareearth ;ion.<JllU(l1.,>isthereducedmatrixof.=or.

    ;dersunittensoroperatorU?.

    ;Soif[?,>]=3(2+1)

;64n

    ;A

    ;(12)

    ;Thenthetransferratecanbewrittenas ;

    ;ED-ED)

    ;=

    ;()()()AeAdDeBdRvAB

    ;S(13)

    ;wherenisrefractiveindexofthehostcrystal,Aand ;I,JBarethecenterfrequencyofthe

    ;0fAionsandabsorptiontransition

    ;tively.

    ;2Simulati0nOf

    ;DecayCurves

    ;emissiontransition

    ;ofBions,respec?

    ;In1999,M.Diafetal‟preparedtheKY3Flo:

    ;Tm”crystalsample.andmeasuredtheluminescence

    ;decaycurvesofHdofTm”atroomtemperaturefor

    ;differentconcentration(0.1%and1.0%Tm). ;Theyfoundthattherewasstrongconcen~ation ;quench,whichisduetotheCroSSrelaxationenergy ;transfer(H4+H6)(F4+F4)assistedbyenergy ;migration(H4+H6)(H6+H4)(Fig.1).

    ;ThedecaycurveforluminescenceH4H60f

    ;sampleKY3Flo:0.1%1‟m?exhibitsasingleexpo—

    ;nentialbehavior.Sincethe1fn1fninteraction

    ;maybeneglectedinsuchalowconcentrationsystem, ;thedecaytimer=1.96msofthissamplewasconsid

    ;eredtobetheintrinsicdecaytimeofHdatroomtem. ;perature.ForsampleKY3F1o:0.1%Tm?,theNAis ;1.5576×1ion/cm.andtheluminescencedecay ;curveshowsanetdeparturefromasingleexponential ;decayattheinitialshorttimes.Wefitteditbymeans ;oftheIHmodelandtheYTmode1.Asmentioned

    ;above,weconsideronlytheEDEDDAinteraction,

    ;sothevalueofsinEq.(1).wastakenas6.Fig.2 ;givesthefitteddecaycllrv~,indicatingthatthefour ;solidlines(a),(b),(c),(d)fittedbytheIHmod

    ;elareallquitepoor,whilethedotlinefittedbytheY

    ;Tmodelisverygood,andtheparametersRoandD ;werederivedtobe0.84nmand6.54×10cm?

    ;s,respectively.TheseresultsindicatethatDDen

;ergymigrationcannotbeneglectedattheconcen~a

    ;(a)

    ;ADD

    ;Fig.1DAenergytransfer(a)andDDenergymigration(b)

    ;forTm”inKY3Flo

    ;..??

    ;T,

    ;T

    ;T

    ;

    ;16

    ;f/l4S

    ;Fig.2DecaycurvesoftheH4H6luminescenceofTmin ;KY3F10atroomtemperature.Thedotsshowtheexpert

    ;mentalresults.Thedotlineisthebestfittinggivenby ;theYTmodel(R0=0.84am,D=6.54(10cm?

    ;s).Thesolidlinesarefourbestfittingsgivenbythe ;IHmodel

    ;(a)R0=0.84nm;(b)R0=0.88nm;(c)R0=0.92 ;nm;(d)R0=0.96illnforthedipoledipoleinteraction

    ;tionof1.0%Tm?.

    ;AccordingtoEqs.(2)and(4),

    ;theD-AenergytransferinteractionparameterCDAand ;DDenergymigrationinteractionparameterCDOare ;1.792×10?cm6?sand2.33×10cm6?s.re.

    ;spectively.

    ;Table1listsdifferenthostvaluesoftheparame

    ;tersCDAandCDD,whichareallobtainedbyfittingthe ;luminescencedecaycurvesofH4ofTmindifferent ;hostcrystals.ItiseasytofindthatthevalueofCDA ;obtainedinKY3Flo:Tm”istwotimeslargerthanthat

    ;inLiYF4:Tm”.whichisconsistentwiththereport

    ;thatenergytransferismoreefficientinKY3Flothanin ;LiYF4.Furthermore,thevaluesofCDDinthreehost ;crystalsareinthesanleorder.Alltheseindicatethat ;thevaluesofCDAandCDDobtainedbyourfittingare ;reasonable.

    ;3FittingValuesofAverageOverlap

    ;IntegralsSDDandSDA

    ;ForKY3Flo:Tm?,rgis1.47.Theaverage

    ;frequencyofthetransitionH4H6is12897cm.

    ;TheemissionrateAofH4H6is760.62s-3J.

    ;Table1EnergytrlHlb-ferinteractionparameterCOAand ;energymigrationinteractionCoointhreeTms-

;dopedcrystals

    ;JOURNALOFRAREEARTHS,Vo1.21,No.1,F.2003

    ;Withthesevalues,thevalueofSDDiscalculatedtobe ;1.02×10cmbyEq.(13).Similarly,withiJA=

    ;7092cm(H4F4),B=5555cm(H6F4)

    ;andA=66.78s(H4+F4),A=106.3s(F4

    ;4H6)[,thevaluesSDDandSDAarecalculatedtobe ;1.02×10and0.8×10cmrespectively.

    ;4DirectCalculationofSDD

    ;TheparameterSDDcanalsobedirectlycalculated ;bythedefinitionEq.(1O),(1O)and(10)”ofthe

    ;averageoverlapintegra1.Forsimplicityandasanav- ;erageestimation,inthecalculationofSDD,thenor- ;inalizedlineshapefunctionsg(E)forallthetransi- ;tionsa—‟aandb—‟bweretakenastheLorentz

    ;functionwithanaverageline-widthAV:

    ;AiJ/2iJiJ()+(0)

    ;(14)

    ;wherev0isthecenterfrequencyofacrystalfieldtran. ;sition,whichisforeRef.[3J.HeretheD-Denergy ;migrationwastreatedasaresonantenergytransferpro‟

    ;cessandtheenergymismatchcausedbytheStokes ;shiftwasignored.InthecalculationofSDD,thefactor ;iisgiveninTable2,andthevaluesofJ,andJb,are ;6and4respectivelyfortheenergymigrationH4 ;HH6.Inaddition,itisapparentthatthematrixele- ;mentoftheforbiddencrystalfieldtransitioniszero.so ;thelineshapefunctiong(E)oftheforbiddentransi. ;tionshouldbetakenoutaccordingtoKushidasSOM. ;Inourcase,sincesitesymmetrygroupisC4,theED ;operatorsand(x,Y)arebasisesofIRAlandEre- ;spectively,sosomeEDtransitionsaleforbiddenby ;theC4sitesymmetry(forexample,Al—‟A2,Bl,B2,

    ;forH4H6ofTm?.FromaUl17crystalfieldtran. ;sitions.totallythereare26EDforbiddentransitions ;underC4.,sitesymmetryinourcase.ThiskindofED ;forbiddentransitionswi11bemuchmoreunder0hsite ;symmetry,soitisaproblemtotreatpropeflywhenwe ;useKushidasformulawhichisanapproximativeone ;averagedwithinmuhiplets.).Thecolumn1inTable ;3showsthesecalculatedvaluesofSDDbyEq.(1O), ;(1O)and(1O)”.Fromthesedata.itseemsthatthe

    ;calculatedvalueofSDDisclosertothefittedvalueof ;SDDwhentheaverageline.widthistakenas10cm.

;However,the10cmaverageline.widthdisagrees

    ;withthetypicalaverageline-width(40cm)ofa ;crystalfieldtransitionatroomtemperature,whichis ;basedontheexperimentaldatainLaF:pr3l.Jandin ;KYsF1o:1.0%Tm”system.T0solvethedisagree.

    ;

    ;WangDYeta1.SpectralOverlapModelI”orEnergyTransferbetweenJ-MultipletsinRE-DopedCrystals

    ;ment,itisnoticedthatinthe”average‟‟approximation

    ;oftheEq.(8),thezeromatrixelementoftheforbid

    ;dentransitionisreplacedbythenonzeroaverage

    ;<aibjIIa‟i,b,Therefore,ifthelineshape

    ;functiong(E)oftheEDforbiddentransitionsisnot ;includedinEqs.(10)and(10),thecontributionof ;theEDforbiddentransitionstothePASinEq.

    ;(9)

    ;wouldstillhavenotbeenconsidered,whichisnot ;consistentwiththemeaningofthe‟‟sumandaverage‟‟

    ;oftheEq.(8).Andthenwesuggestedthattheline ;shapefunctiong(E)oftheforbiddentransitionsalso ;shouldbeconsideredinthecalculationofSDD.e

    ;columnIIinTable3showsthecalculatedvaluesof ;SDDwiththeaboremodification.Itiseasytofindthat ;thecalculatedvalueofSDDisclosertothefittedvalue ;0fSDDwhentheaveragelinewidthistakenas50

    ;cm.whichisconsistentwiththeexperimentaldata. ;Fig.3showsthecalculatedH4H6emissionspectra ;andH6H4absorptionspectrawiththeaverageline

    ;width50cm,whichagreewiththeex?

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