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Thermodynamic_0

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Thermodynamic_0namic,Ther

    Thermodynamic

    iversi0,ofScienceandTechnologyBeijing,Beijing100083.China ;CollegeofEngineering.PeltingUniversity.Beijing10087l,China ;Received5August2007;receivedinrevisedform27October2007;acceptedt2November2007

    ;Abstract

    ;TheGibbsfreeenergiesofreactionArGrofKNbO3andNaNb0werecalculatedandthenthatofKxNal_

    ;x

    ;NbO3wasestimated.Ontheba-

    ;sisofthethermodyrnamiccalculationresults,thehydrothermaltemperaturesweredesignedat1OO,160,and230.Crespectively.However,

    ;NaNbO1waspreparedwhentheheatingtemperaturewashigherthan16O.C,andKNbO3andKxNal_xNbO3wereobtainedat230.C,sug-

    ;gestingthatonlyatahighertemperaturethekineticrequirementissatisfied.AccordingtotheX-raydiffractionresults,boththesolidsolu-

    ;tions,NaNbO3-basedsolidsolution,Na1_xK~NbO3,andKNb03-basedsolidsolution,KIaxNbO3,werehydrothermallysynthesizedin6

    ;moI/Lalkali(NaOHandKOH)solutionat230.C.

    ;Keywords:KNbO3;NaNbO3;thermodynamiccalculation;hydrothermalsynthesis;Gibbsfreeenergy

    ;1.IntrOductiOn

    ;Leadzirconatetitanate(PZT)ceramicsarewidelyused

    ;aspiezoelectricmaterialsbecauseoftheirexcellentproDer.

    ;ties.especially,thattheircompositionisclosetothemor.

    ;photropicphaseboundary(MPB)[1-3.However,because

    ;ofthehightoxicityoflead.thelead-freepiezoelectricce.

    ;ramieshavebeenusedtoreplacelead.basedceramics.

    ;(K05Nao5)NbO3(KNN),asoneofthemostprominentand

    ;usefulpiezoelectricceramiccompounds.hasattractedmuch

    ;attention.ThepiezoelectricpropertiesofKNNwerefirst

    ;reportedbyEgertonandDillon[4-5usingsolidreaction

    ;process,andrecently,Satioeta1.obtainedahigherpiezo.

    ;electricconstantd3r4l6pC/N)inKNN.basedtexturedce.

    ;ramiescomparedwithunmodifiedPZTceramics61.How.

    ;ever.KNNceramicsaredifnculttobesinteredandinaddi.

    ;tion,K20andNa20areeasilyevaporatedathightempera-

    ;tures51.Researchers,inthepast,havetriedtosolvethe

    ;aboveproblems.Hotpressingorsparkplasmasintering

    ;techniqueswereusedtopreparedenseKNNceramics71.

    ;BaTiO,SrTiO,andLiNb01wereintroducedtoKNN ;compositiontoformhomogeneoussolidsolution,whichex. ;hibitedtheenhancedpiezoelectricandelectromechanical ;properties[8-10].SinteringaidssuchasI<4CuYb8023, ;K5.

    ;4CuL3Tal0029,CuO,andMnO2wereaddedtodecrease ;thesinteringtemperature11.141.WhenactiveKNNisused

    ;c0rresp0ndingauthor:ZHANGMeiE-mail:zhangmei@metatt.ustbeducn ;asarawmaterial,thesinteringtemperatureisgreatlyde- ;creasedanddenseceramiccanbeobtained.Byhydrother- ;malsynthesis,whichisoneoftheceramicsynthesisproc- ;esses,active,fine,anddeagglomeratedpowderscarlbepre- ;paredundermoderateconditionsatalowertemperature(up ;to300.C).However,theKNNpowderssynthesizedby ;hydrothermalmethodhaveseldombeenreported. ;BeforehydrothermalsynthesisofK~Nal_xNbO3,the ;thermodynamiccalculationshouldbecarriedout,whichis ;helpfultodesigntheoptimumsynthesisparameters.Unfor- ;tunately,somethermodynamicdata,suchas?.

    ;KNbo3,

    ;AH298e.

    ;KNbO3,and.

    ;KNbO3areunavailable.Inthisstudy,

    ;?,

    ;KNbo3and,

    ;KNbo3wereestimatedandthe

    ;GibbsfreeenergyofreactionofKxNa)xNbO3preparation,

    ;?rGr,wascalculated.Onthebasisofthethermodynamic ;calculation,theKxNa1xNbO3ceramicpowdersweresue-

    ;cessfullysynthesizedbyhydrothermalmethodundersuit- ;ablepreparingconditions.

    ;2.Estimationofthermodynamicdata

    ;2.1.ThermodynamicreactionofKxNal_xNb03synthesis ;Analyticalgradepotassiumhydroxide(KOH)andso- ;diumhydroxide(NaOH)solutionsandniobiumoxide ;(Nb205)powderswereusedasrawmaterials.

    ;e

    ;C

    ;n

    ;e

    ;??lC

    ;S

    ;(扩

    ;

;

    ;一季

    ;4

    ;

    ;

    ;372

    ;ThedesignedreactionsforKxNal_

    ;x

    ;NbO3preparationare

    ;listedasshowninthefollowingequations: ;Na”(aq)+OH(aq)+?Nb2o5(s)=

    ;1

    ;NaNbO3(s)+?H20(g)(1)

    ;1

    ;(aq)+OH(aq)+~Nb2Os(s)=

    ;1

    ;KNbO3(s)+?H20(g)(2)

    (aq)+Nb2Os(s)= ;(1x)Na+(aq)+K(aIq)+OH

    ;1

    ;KxNal-xNbO3(s)+?H20(g)(3)

    ;IfEq.(3)occurred,theGibbsfleeenergyofreaction ;ArGro)<0.BecauseKxNal-xNbO3hadgeneratedfromthe ;substitutionofNa+forKintheKNbO3latticeorforNa+ ;inNaNbO3crystal,?rGr(3)mustberangedbetween

    ;ArGr(1)andArGrt2),subsequently,ifArGr(1)<0and ;ArGrt2)<0,ArGro)mustbenegative.

    ;ThearG,couldbecalculatedas

    ;?=?G+(4)

    ;whereArGisthestandardGibbsfreeenergyofreaction, ;J/mol;Risthemolegasconstant,8.314kmol;Tisthe ;reactiontemperature,K;Pisthesaturatedvaporpressure, ;MPa;andPlI20isthesteampressureforwater,MPa. ;ArGcanbeobtainedfromthefollowingequation: ;AG=A月一TA(5)

    ;whereAtHisthereactionenthalpyunderstandardcon

    ;dition,kJ/mol;Aristhereactionentropyunderstan

    ;dardcondition.J.mol-1.K-.

    ;?=~.,oiAH2~98+8ACpdT

    ;RAREMETALS,VoL27,No.Aug2008

    ;where.41,A2,

    ;andA3arethecorrelativecoefficients(Table ;21.

    ;Table1.Correlativestandard-statethermodynamicdata ;Note:LThecalculatedvalue(seesections2.2and2_31

    ;Table2.Correlativecoefficientofheatcapacity ;2?2?Estimationofstandardformationenthalpyof ;KNbO38,KNbo3

    ;AccordingtoEq.(9),thestandardenthalpyformationof ;KNbO3M-/2~8isequaltothesumofstandardformation ;enthalpy

    ;,

    ;K+(g),AH29~8

    ;,

    ;Nb0i(g)andlatticeenthalpy

    ;?(Eq.(10)).

    ;(+NbO3-(g)=KNbO3(s)

    ;?

    ;,

    ;KNbo3(s)=M-/29~8

    ;,

    ;K+(g)+?

    ;,

    ;Nboi(g)+

    ;(612.

    ;2.1.calculation

    ;whereDlisthecoefficientoftheequation;AH29~sistheen

    ;thalpyunderstandardconditionat298Kofeachcompound, ;kJ/mol;ACeisthedifferenceofheatcapacitybetween ;productsandreactants.J.mol-?I.

    ;?=?+(7)

    ;whereS29%isentropyat298Kunderstandardcondition, ;J.mol-1.K-1.

    ;Someknownstandardstatethermodynamicparameters ;arelistedinTables1and2[15].Unfortunately,someare ;unavailable,thus,theyneedtobeestimated. ;Heatcapacityiscalculatedbythefollowingequation. ;C=l+A2×l0T+A3×l0T-2(8)

    ;(9)

    ;(10)

    ;ThelatticeenthalpyisobtainedfromEq.(11) ;=.+

    ;

    ;CpdT(11)

    ;whereU0isthelatticeenergy(kJ/mo1),whichcanbecalcu- ;latedfromEq.(12).

    ;u.121400

    ;.

    ;Z+

;

    ;Z-~(1

    ;)(12)

    ;rrrr

    ;whereandZarethenumbersofelectroncharge.here. ;forNaNbO3andKNbO3,=Z-=l:广andrarethe

    ;ionicradii,here,RK+=133xl0_6,RNa+=133xl0,and

    =l33xl0-6;Distheionnumberinonemolecule ;RNb0

    ;,

    ;here,forNaNb03andKNb03,D=2.

    ;0n廿1ebasisofEq.(12),UocouldbecalculatedasV0,sago3= ;

    ;7l0.1kJ/molandU0.

    ;N.Nbo=-789.3kJ/mo1.

    ;

    ;Zh

    ngCetaL.ThermodynamicevaluationandhydrothermalpreparationofKNal_xNbO3

    ;InEq.(11),CpofKNbO3(s)iSunavailableandhastobe ;estimated.Thecalculationwasshownasfollows. ;Fortheionsinioniccrystal,suchasKNbO3andNaNbO3, ;CatomC,1’atom+2(j?K-I.tool-),whereC,.istheconstant ;ofVOlumeheatcapacity.CI,atomofonemolaratomlSequal ;to3R,f.e.,Cvt.=3R=25(j.K-t.mol),thus,,atornof ;onemolaratomisCPi0mCI_-at.m+2:27(J?K-’moF)

    ;[16].

    ;EachofKNbO3,NaNbO3,andKxNal~NbO3,has5molar ;atoms,subsequently,theheatcapacityC=135J.Kq.mol(.

    ;IntroducingU0andintoEq.(11),separately, ;AMO.

    ;NaNbo3and?KNbo3couldbecalculatedas

    ;AMONaNbO

    ;3

    ;|mo1.

    ;

    ;749kJ/moland?KNbo:670

    ;2.2.2.AHKNbO3calculation

    ;AccordingtoEq.(10),

    ;AH2~98

    ;,

    ;KNb=8,K+(g)+8,Nboi(g)+.

    ;Theformationenthalpyofthecationcanbecitedfrom ;Ref.[15]directly.

    ;AH2~98

    ;.

    ;K+(1=515kJ/moland?8,N+(g)611kJ/mo1. ;However,forthepolyatomicionNbO3,H298’oNbo

    ;canbecalculatedfromEqs.(13)(15):

    ;Na+(g)+N(g)=NaNbO3(s)(13)

    ;8,NaNb=AH,

    ;(g)+8,Nboj(g)+(14)

    ;then,

    ;8,Nbo)=8,NaNbO’(s)8,Na*(g)(15)

    ;here,

    ;?-NaNbOl)1316kJ/mol,?-Na)611

    ;kJ/mol,andAHNbo=749kJ/mo1.

    ;TheywereintroducedintoEq.(15),SOthat

    ;AH-Nbom11178kJ/mo1.

    ;ThUS,

    ;8,g)515kJ/mol,8,Nbg)1178kJ/mol,

    ;andAHNbo=670kJ/mo1.

    ;IntroducedintoEq.(10),finally, ;?

    ;,

    ;KNbOII11332kJ/mo1.

    ;2.3.Estimationofstandardentropy,KNb03of

    ;KNbO3(s)

    ;Latimer15]proposedthattheentropyvalueofthe

    ;compoundisthesumofentropyofeveryion.Hence,

    ;s8.

    ;KNbocouldbecalculatedusingEq.(16). ;373

    ;8KNbo,:8,K++s8,Nboi(16)

    ;where$2~

    ;9838J.mol-?K-I[15].

    ;However,8Nboisunavailable;similarly,8,Nboi ;couldbecalculatedfromEq.(17). ;Nboi=,

    ;NNbo,N+(17)

    ;here,8NNbo=117J-molq-K-’and8’Na+31

    ;J.mol-t.K-[15],

    ;thus-$2~

    ;98,NbOi

    ;86J,mOr?K

    ;AccordingtoEq.(16),

    ;8,KNbo:l24J,mol(?K-

    ;2.4.EstimationofGibbsfreeenergyofreaction

    ;2.4.1.EstimationofGibbsfreeenergyofreactionfor

    ;NaNbO3preparation

;ForEq.(1),

    ;?岛?=?G+PH20(18) ;AG(1)=A(1)TA(1)= ;?D8(1)+98ACpdt

    ;ZDiArS2~g8(1】一.(19) ;where

    ;?f?rH8(1):!Ll2-O98, ;Ho+?H8,NNbo

    ;:o,’OH一一16130J/mol,

    ;??,(11:,l{1O+as~8lNaNbo ;18olNaoH=94.75J.mol(?K, ;and

    ;?rG)-_16130-94.75+df_7’. ;AccordingtoEq.(8),AG=1+2×107’+3× ;10.

    ;Then,

    ;?GI11613094.75T+T(AAI×Mi+?2×10j+

    ;AA×10)(20)

    ;where,

    ;=

    ;AI,H20+AI,NaNbO~-- ;

    ;374

    ;11

    ;2

    ;2,Ho+2,o一吉2,Nbo(2,NaoH=105.2,

    ;s=A3,

    ;?0+-43,

    ;?.A3,

    ;?205-A3,

    ;?.n=,2.9.

    ;,andM3aretheintegralitems,describedasfol

    ;lowsI171:

    ;1=ln十一298

    ;1,

    ;298T

    ;2=

    ;(T-298)2

    ;,

    ;aIld

    ;s=

    ;22982T2××

    ;TheywereintroducedintoEq.(2U)asfollows:

    ;A,Gr~(1):15516+6

;

    ;46

    ;.=

    ;0

    ;

    ;00

    ;

    ;125.344T+

    ;TInT+5.26x10T(21)

    ;Finally,

    ;r(1)=ArRT.n=

    ;

    ;15516+646

    ;

    ;000

    ;

    ;125.344T+TinT+ ;5.26x10-2T2+RTlnPH20 ;2P._

    ;2.4.2.EstimationofGibbsfreeenergyofreactionfor

    ;KNbO3preparation ;ThisCanbecarriedoutsimilartotheGibbsfreeenergy

    ;estimationofEq.(22).

    ;r(2)=?G(2)lnPH20AG(22) ;r(2)=?G(2)+{ln(22) ;ARGO2)=ArH~2)TA)=

    ;?(2+8ACPdt

    ;ZOiArS2~998(2)-T~f9(23) ;where??(2)=12-O98IHo+, ;KNb0,

    ;,Nbo,K+,oH一一21770J’tool ;and?f?rS29~8(2)=12-o98,H2o+,

    ;KNbo3

    ;1

    ;2

    ;-

    ;0

    ;98,Nb2o5,

    ;KoH=57.75J’molK(.

    ;Then.

    ;RAREMETALS,Vo1.27,No.Aug2008

    ;ArG)2177057?75T+T(&41 ;2×10+3×105M3)(24) ;where

;AI,

    ;H20+AI, ;一一

    ;I

    ;,

    ;?205-A1,

    ;n=30.2, ;z=

    ;IA

    ;3,H20+A2, ;.A2,

    ;

    ;n82.25, ;and

    ;s=

    ;1A

    ;3,H~O+A3, ;.A3,

    ;?2o~-A3,

    ;n=2

    ;IntroducedintoEq.(24),

    ;ArGrO(2):20758+6 ;

    ;46

    ;=

    ;0

    ;

    ;00

    ;

    ;228.22+ ;30.2TinT4.1125x10(T(25)

    ;Fina11y, ;?rG_?Tz+=

    ;

    ;20758+646 ;

    ;000

    ;

    ;228.22T+ ;30.2TinT4.1125×1O-2+

    ;.

    ;2.4.3.Hydrotherrnaltemperaturedesign

    ;AccordingtostudiesbyWang[17,thePandboof

    ;NaOHorKOHsolution,inapproximately6mol/Lalkali

    ;solutionatvarioustemperatures,alelistedinTables3and4. ;Table3.Relationshipbetweenpressureandtemperaturein6 ;nol/LNaOHsolutiOR

    ;The?rGrofNaNb03andKNb03preparationhavebeen

    ;calculatedandtheresultsareshowninFig.1.

    ;Asobserved,al1theArGratdifferenthydrothermaltem

    ;peraturesarenegative.Hence,accordingtothetherrnody

    ;namiccalculationresults,NaNbO3andKNb03Canbepre. ;paredintherangeof75to250.Cbyhydrothermalmethod. ;

    ;ZhangCetaL,Therm0dynamicevaluationandhydrothermalpreparationofKxNal_xNb

    O3

    ;Table4.Relationshipbetweenpressureandtemperaturein6 ;mol,LKoHsolution

    ;71/?

    ;Fig.1.Gibbsfreeenergies&Gin)andArGo2)asafunctionof ;temperature.

    ;3.Experimental

    ;Accordingtotheabovecalculation,100,160,and230.C ;werechosenasthesynthesizedtemperatures.6mol/Lso- ;diumhydroxidesolutionNaOH(1),potassiumhydroxide ;solutionKOH(5),andmixedsolution(2-4)werepre. ;pared,andthesamplescompositionareshowninTable5. ;Table5.Compositionofthesamples

    ;SampleNfKr

    ;oo

    ;2:l

    ;l:2

    ;l:4

    ;0

    ;1.25gNb2O5wasaddedto25mLof1and25mLof5

    ;alkalisolution.Theresultingmixtureswerestirredfor30 ;min,whiteslurryappearedandtheyweretransferredtoa ;Teflon-linedstainlessautoclavewithafillingcapacityof ;50%andheatedat100,160,and230.Cfor24h.White ;375

    ;powderswereobtainedforsamplel.whereasinsample5 ;Nb,Owasdissolvedandnopowdersweregeneratedafter ;hydrothermaltreatmentatl00andl60.C.Alongwithin- ;creasingtemperature,i.e.,at230.C,whitepowdersappeared ;inbothsampleland5.Subsequently.1.25gNb20swas ;addedtoeachofthe2.4alkalisolutionsandwhitepow. ;derswerefelrmedinallofthem.Thepowderswerewashed ;bydeionizedwateruntiltheywereneutra1.Thewashed

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