grade19ise.com

19ise.com  时间:2021-03-20  阅读:()
ContentslistsavailableatScienceDirectCeramicsInternationaljournalhomepage:www.
elsevier.
com/locate/ceramintAnewlow-temperaturerable0.
95Pb(ZrxTi1-x)O3-0.
05Bi(Mn1/2Ti1/2)O3ceramicforhigh-powerapplicationsBoZhang,HeQi,RuzhongZuoInstituteofElectroCeramics&Devices,SchoolofMaterialsScienceandEngineering,HefeiUniversityofTechnology,Hefei230009,PRChinaARTICLEINFOKeywords:PiezoelectricceramicsHigh-powerapplicationLow-temperaturesinteringMorphotropicphaseboundaryDefectdipoleABSTRACTAnewternarysolid-solutionpiezoelectricceramicof0.
95Pb(ZrxTi1x)O30.
05Bi(Mn1/2Ti1/2)O3(x=0.
49–0.
55)wassuccessfullypreparedviaaconventionalsolid-statereaction.
ThecrystalstructurewasfoundtograduallytransformfromtetragonaltorhombohedralphaseswithincreasingtheZr/Tiratio.
Amorphotropicphaseboundarywasrealizedintheproximityofx=0.
51,whichexhibitedoptimumelectromechanicalpropertiesofd33=275pC/N,ε33T/ε0=1226,kp=0.
53,Qm=1164,tanδ=0.
66%andTc=341°Cassinteredatarelativelylowtemperatureof1120°C.
ComparedwithtypicalPb-basedcomplexperovskitessuchasPb(Mn1/3Nb2/3)O3andPb(Mn1/3Sb2/3)O3,thesubstitutionofBi(Mn1/2Ti1/2)O3providesobviousadvantagesinbothsinteringtemperatureandrawmaterialcost.
Theachievementofpiezoelectricandelectromechanicalpropertieswasinterpretedbymeansofatypicalmodelconcerningtheinteractionbetweendefectdipolesanddomainsthroughcomparativeexperiments.
Thedesirablepropertiesofthestudiedmaterialsystemsuggestagreatpotentialforhigh-powerdeviceapplications.
1.
IntroductionPb(Zr,Ti)O3(PZT)-basedternaryorquaternarypiezoelectriccera-micshavebecomeindispensablefunctionalmaterialsasactuators,ul-trasonicmotorsandtransducers[1–3].
Inordertomeettherequire-mentoftheminiaturizationandhighpowerinpractice,thepiezoelectricceramicsarenecessarytoexhibithighelectromechanicalcouplingfactor(kp),mechanicalqualityfactor(Qm),piezoelectricconstant(d33),Curietemperature(Tc)andlowlossvalues.
Untilnow,alotofattemptshavebeenmadetoimproveelectro-mechanicalpropertiesofPZTbasedmaterials[4–7].
However,highQm,kpandd33arenoteasilyobtainedsimultaneously.
Themostwidelyusedmethodtosatisfytheabove-mentionedrequirementistointroduceacceptordopantsinsoftbasematerials[4–6],suchasthesubstitutionofFe3+ionsforZr4+/Ti4+sitesinPZTbyformingacceptor-oxygenva-cancydefectdipoles(′FeVZrTiO,).
AnothermainmethodisviaaddingperovskiteswithB-sitemultivalenceions[8,9],forexample,Pb(Mn1/3Nb2/3)O3(PMN)orPb(Mn1/3Sb2/3)O3(PMS),toformthepinningofthedomainwallsbymeansofoxygenvacanciesasaresultofcoexistingMn2+/Mn3+ionsduringhigh-temperaturesintering[10,11].
Un-fortunately,theabovecompositionsystemsusuallyneedhighersin-teringtemperaturethan1250°C.
Itisratherdiculttoobtainceramicsbasedonthemwithexcellentpiezoelectricandelectromechanicalpropertiesandlowersinteringtemperaturessuitablefortheapplicationofmultilayerpiezoelectricdevices[10,11].
Inaddition,theproductioncostwouldbealsoobviouslyincreasedowingtotheusageofNb2O5andSb2O3.
Bi-basedperovskitescompoundspossessgoodferroelectricproper-tiesandhighTc[12–14].
Inaddition,theintroductionofBi-basedperovskitesintoPZTwouldhaveapositiveeectonthedecreaseofthesinteringtemperature[15].
Bi(Mn1/2Ti1/2)O3(BMT)wouldbeexpectedtoplaythesameroleasPMNandPMSasmentioned.
TheeectoftheBMTadditiononthedensicationandelectricalpropertiesofPZTceramicshasneverbeenreportedintheliteratures.
Inthiswork,anewternarysolidsolutionceramicofBMT-PZTwaspreparedbyatradi-tionalmixed-oxideroutewithaspecialfocusonthevariationofdi-electric,ferroelectricandelectromechanicalpropertiesoftheternarysystem.
2.
ExperimentalprocedureThe0.
95PZxT1x0.
05BMT(x=0.
49–0.
55)ceramicswerepre-paredbyaconventionalsolid-statereactionmethodusinganalytic-gradeBi2O3,PbO,ZrO2,TiO2andMnO2asrawmaterials.
Stoichiometricamountsofrawpowderswereweighedandball-milledinalcoholwithZrO2ballsfor6h.
Theresultantmixturewasdriedaftercalcinationat850°Cfor2hinair.
Thecalcinedpowersweremilledagainwith5wt%PVAasabinderfor10handsubsequentlypressedhttps://doi.
org/10.
1016/j.
ceramint.
2017.
12.
178Received14December2017;Receivedinrevisedform23December2017;Accepted25December2017Correspondingauthor.
E-mailaddress:rzzuo@hotmail.
com(R.
Zuo).
CeramicsInternational44(2018)5453–5458Availableonline26December20170272-8842/2017ElsevierLtdandTechnaGroupS.
r.
l.
Allrightsreserved.
Tintodisksampleswithadiameterof10mm.
Thespecimenswerehe-atedat550°Cfor4htoburnoutthebinder,andthensinteredat1100–1150°Cfor2hinair.
InordertopreventthevaporizationofBiandPb,samplediskswereburiedinthesacricialpowderofthesamecomposition.
Silverpastewaspaintedonbothsidesofthedisksandredat550°C.
Thesamplesnaturallycooledtoroomtemperatureinthefurnaceaftersinteringweremarkedas"furnace-cooledsamples",whilethesamplesachievedbyawater-quenchingprocessweremarkedas"quenchedsamples".
Thespecimenswerepoledinasiliconeoilbathatdierenttemperaturesunderadceldof5kV/mmfor15min.
ThebulkdensitiesofthesinteredceramicsweremeasuredbytheArchimedesmethod.
ThecrystalstructureoftheredceramicswasidentiedviaanX-raydiractometer(XRD,D/Max2500V,Rigaku,Japan)usingCuKαradiation.
Thedielectricpropertiesweremeasuredat1kHzusinganLCRmeter(AgilentE4980A,SantaClara,CA)inatemperaturerangeof25–500°C.
Thequasi-staticd33wasmeasuredbyaBelincourt-meter(YE2730A,Sinocera,Yangzhou,China).
ThekpandQmvaluesweredeterminedbyaresonance-antiresonancemethodwithanimpedanceanalyzer(PV70A,BeijingBandERACo.
Ltd.
Beijing,China).
Themicrostructureofthesinteredsampleswasobservedusingaeld-emissionscanningelectronmicroscope(FE-SEM,SU8020,JEOL,Tokyo,Japan).
BeforetheSEMobservation,sampleswerecarefullypolishedandthenthermallyetchedat950°Cfor30min.
Thepolar-izationversuselectriceld(P-E)weremeasuredusingaferroelectrictestsystem(Precisionmultiferroelectric;RadiantTechnologiesInc,Albuquerque,NewMexico).
3.
ResultsanddiscussionFig.
1(a)showsthedensicationbehaviorofafewrepresentative0.
95PZxT1x0.
05BMTcompositionsasafunctionofsinteringtem-perature.
Withanincreaseofsinteringtemperature,therelativedensityofallthreesamplesrstlyincreasesuptotheirrespectivemaximumvalues(>96%)at1120°C,andthendecreaseswithfurtherincreasingsinteringtemperature.
Fig.
1(b)-(d)showthemicrostructureof0.
95PZxT1x0.
05BMTceramicssinteredat1120°C.
Itcanbeseenthatallsamplesarewellcompactedwithoutanyobviouspores.
WithincreasingtheZr/Tiratio,thegrainsizeremainsalmostunchanged(~2minaverage).
ComparedwithtraditionalPZT-basedceramics,theoptimumsinteringtemperatureofthestudiedmaterialsystemislow-eredbyalmost150°CpossiblyasaresultoftheexistenceoftheBielement[15].
Itwillexhibitlargerpotentialsinfurtherreducingthesinteringtemperatureinfutureforapplicationswhereamuchlowersinteringtemperaturethan1000°Cisneeded.
Fig.
2(a)indicatestheXRDpatternsof0.
95PZxT1x0.
05BMTsamplesasafunctionofx.
Alldiractionpeakscouldbewellindexedtoasingleperovskitestructurewithoutanysecondaryphases,indicatingthatBi3+and(Mn1/2Ti1/2)3+havefullydiusedintothelatticeandformedsolidsolutionswithPZT.
Inaddition,thecrystalstructureisfoundtoevolvefromatypicaltetragonal(T)phasetoarhombohedral(R)phasewithincreasingx,asevidencedbythevariationofthe(200)diractionlines.
Withincreasingx,thesplit(200)diractionpeaksgraduallymergeintoasingleone,asshowninFig.
2(b).
Inordertoquantitativelyanalyzetheevolutionofthephasestructure,the(200)diractionpeakproleswerettedbyusingapseudo-Voigtpeakshapefunction,asshowninFig.
2(c).
TherelativecontentofT(FT)andR(FR)phaseswasroughlycalculated,asshowninFig.
2(d).
Itisevidentthatamorphotropicphaseboundary(MPB)betweenRandTphasesexistsinthecompositionrangeof0.
50Tc),asshowninFig.
6(b).
Moreover,alargerPrthanthatofthefurnace-cooled(Fig.
6(a))andpoled(Fig.
4(a))sampleswasobtainedforquenchedsamples.
AppropriatepiezoelectricpropertiescouldbedetectedjustafterthemeasurementoftheP-EloopfortheFig.
2.
(a)Room-temperatureXRDpatternsof0.
95PZxT1x0.
05BMTceramics,(b)locallyenlargeddiractionpeaksinthe2θrangeof43°46°,(c)peakttingplotsforthere-presentativecompositionswithx=0.
51,0.
52and0.
54,and(d)thevariationofFRandFTwithx.
Fig.
3.
Dielectricpermittivityandlosstangentvaluesat1kHzasafunctionoftem-peratureforafew0.
95PZxT1x0.
05BMTceramics.
B.
Zhangetal.
CeramicsInternational44(2018)5453–54585455quenchedsamples,asshowninFig.
6(c).
Thisphenomenonisquitedierentfromthatobservedinfurnace-cooledsamples,whichneedtobepoledathightemperatures,asshowninFig.
4.
Thed33valuesachievedinquenchedsamples(Fig.
6(c))areapproximatelyequaltothatofthefurnace-cooledsamplesafterbeingpoledat150°C(seeFig.
5(b)),however,muchsmallerQmvaluesareachievedforthequenchedsamplesafterelectriccycling.
However,afteragingat150°Cfor3days,theQmvalueforthequenchedsampleincreasesandap-proximatestothevalueofthecorrespondingpoledsample(Fig.
5).
ThiscanbeclearlyconrmedbythecorrespondingP-Eloopofthequenchedsamplewhichwasrstsubjectedtoelectriceldcyclingandthenbeingagedat150°Cfor3days,asshowninFig.
6(b).
Anobviouslyasym-metricP-Eloopindicatesthepresenceofaninternalbiaseldalongthedirectionofthepolingelectriceld.
Aschematicillustrationwasproposedtoexplainthepolarizationresponseduringtheapplicationofanelectriceldforthex=0.
51ceramicwithdierentinitialstates,asshowninFig.
7.
Asknown,thedefectdipolesshouldrandomlydistributeintheparaelectricphaseaboveTc,asshowninFig.
7(a).
Therandomlydistributeddefectdipoleswouldbefrozeninthedomainsafterwater-quenching.
Therefore,thedirectionofdefectdipolesisinconsistentwiththatofthepolarizationvector,suchthatthedomainswouldswitchfreelyinaccordancewiththeappliedeld(Fig.
7(b1)-(b3)),resultingintypicalferroelectricfeaturewithasaturatedP-Eloop(Fig.
6(b)).
Eventhoughgoodpie-zoelectricresponsecanbeachievedinthequenchedsampleafterelectriccycling,arelativelylowQmwasachievedowingtoitsfragiledomainstate.
However,randomlyorientateddefectdipolesareinametastablestatebelowTc.
Thedefectdipoleformedbetweenions(Mn2+/Mn3+)andO2-vacanciestendstoalignalongthespontaneouspolarizationdirectiongradually,anditssymmetrywouldbeconsistentFig.
4.
(a)P-Eloopsand(b)d33,kp,Qmandε33T/ε0forfurnace-cooledsampleswithx=0.
51poledunder5kV/mmatdierenttemperatures.
Fig.
5.
Room-temperature(a)d33,kp,Qm,(b)ε33T/ε0andtanδvaluesforthefurnace-cooled0.
95PZxT1x0.
05BMTceramicsafterbeingpoledunder5kV/mmat150°Cfor15min.
Fig.
6.
Room-temperatureP-Eloopsforthe(a)furnace-cooledand(b)quenched0.
95PZxT1x0.
05BMTceramicsaswellasthequenchedx=0.
51samplewhichsuf-feredfromagingat150°Cfor3daysafterelectriceldcycling,and(c)compositiondependenceofd33,kpandQmvaluesafterthemeasurementoftheP-Eloopforthequenchedsamples.
B.
Zhangetal.
CeramicsInternational44(2018)5453–54585456withthecrystalsymmetryduringaslowcoolingprocess(Fig.
7(c1))oranagingprocess(suchasFig.
7(b3)to(d3))[19,20],causingapinningeectonthedomains.
Accordingly,thedefectdipolesprovideare-storingforcetoswitchbackthedomainsaftertheelectriceldisre-moved(Fig.
7(c1)-(c3)),inducingapinchedP-Eloop.
Bothofthedo-mainsanddefectdipolesalignalongtheelectricelddirectionduringthepolingprocessathightemperatures(Fig.
7(d1)-(d3)),resultinginastablytexturedpolarizationstate.
Therefore,excellentpiezoelectricpropertiesaswellashighQmvalueareachievedsimultaneously.
4.
ConclusionsAnewlow-temperaturerable0.
95PZxT1x0.
05BMTpiezo-electricceramicwasstudiedintermsofthemicrostructure,phasestructure,dielectric,piezoelectricandferroelectricproperties.
Theternarysolidsolutionceramicscanbewelldensiedatarelativelylowtemperatureof~1120°C,whichisabout150°ClowerthanthatoftraditionalPZT-basedhigh-powerpiezoelectricceramics.
AgradualevolutionfromferroelectricTphasetoRphasewasfoundwithen-hancingZr/Tiratio.
Optimumdielectricandelectromechanicalprop-ertiesofd33=275pC/N,ε33T/ε0=1226,kp=0.
53,tanδ=0.
66%,Qm=1164andTc=341°CwereachievedintheMPBcompositionwithx=0.
51.
Theeectofpolingconditionsonthepiezoelectricandelectromechanicalpropertieswasexplainedbymeansoftheinteractionmodelbetweenthedefectdipoleandpolarizationvector.
Theexperi-mentalresultssuggestthat0.
95PZxT1x0.
05BMTpiezoelectriccera-micsshouldhaveagreatpotentialforhigh-powerapplications.
AcknowledgementsThisworkwassupportedbytheNationalNaturalScienceFoundationofChina(GrantNo.
51472069).
References[1]Y.
Fuda,K.
Kumasaka,M.
Katsuno,H.
Sato,Y.
Ino,Piezoelectrictransformerforcoldcathodeuorescentlampinverter,Jpn.
J.
Appl.
Phys.
36(1997)3050–3052.
[2]T.
R.
Gururaja,W.
A.
Schulze,L.
E.
Cross,R.
E.
Newnham,Piezoelectriccompositematerialsforultrasonictransducerapplications.
PartII:evaluationofultrasonicmedicalapplications,IEEETrans.
Son.
Ultrason.
32(1985)499–513.
[3]R.
Bermejo,H.
Grünbichler,J.
Kreith,C.
Auer,FractureresistanceofadopedPZTceramicformultilayerpiezoelectricactuators:eectofmechanicalloadandtem-perature,J.
Eur.
Ceram.
Soc.
30(2010)705–712.
[4]Y.
D.
Hou,M.
K.
Zhu,F.
Gao,H.
Wang,B.
Wang,H.
Yan,C.
S.
Tian,EectofMnO2additiononthestructureandelectricalpropertiesofPb(Zn1/3Nb2/3)0.
20(Zr0.
50Ti0.
50)0.
80O3ceramics,J.
Am.
Ceram.
Soc.
87(2010)847–850.
[5]Q.
C.
Wu,M.
M.
Hao,Z.
Q.
Zeng,X.
C.
Wang,W.
Z.
Lv,G.
F.
Fan,NonlineardielectriceectofFe2O3-dopedPMS–PZTpiezoelectricceramicsforhigh-powerapplications,Ceram.
Int.
43(2017)10866–10872.
[6]L.
X.
He,M.
Gao,C.
E.
Li,W.
M.
Zhu,H.
X.
Yan,EectsofCr2O3additiononthepiezoelectricpropertiesandmicrostructureofPbZrxTiy(Mg1/3Nb2/3)1x-yO3cera-mics,J.
Eur.
Ceram.
Soc.
21(2001)703–709.
[7]S.
Y.
Yoo,J.
Y.
Ha,S.
J.
Yoon,J.
W.
Choi,High-powerpropertiesofpiezoelectrichardmaterialssinteredatlowtemperatureformultilayerceramicactuators,J.
Eur.
Ceram.
Soc.
33(2013)1769–1778.
[8]Z.
G.
Zhu,B.
S.
Li,G.
R.
Li,W.
Z.
Zhang,Q.
R.
Yin,MicrostructureandpiezoelectricpropertiesofPMS–PZTceramics,Mater.
Sci.
Eng.
B117(2005)216–220.
[9]J.
Ryu,H.
W.
Kim,K.
Uchino,J.
Lee,EectofYbadditiononthesinteringbehaviorandhighpowerpiezoelectricpropertiesofPb(Zr,Ti)O3-Pb(Mn,Nb)O3,Jpn.
J.
Appl.
Phys.
42(2003)1307–1310.
[10]D.
Gang,R.
Liang,W.
Li,K.
Li,W.
B.
Zhang,G.
S.
Wang,X.
L.
Dong,InternalbiaseldrelaxationinpoledMn-dopedPb(Mn1/3Sb2/3)O3-Pb(Zr,Ti)O3ceramics,Ceram.
Int.
39(2013)7703–7708.
[11]O.
Ise,K.
Satoh,Y.
Mamiya,HighpowercharacteristicsofpiezoelectricceramicsinPb(Mn1/3Nb2/3)O3-PbTiO3-PbZrO3system,Jpn.
J.
Appl.
Phys.
38(1999)5531–5534.
[12]H.
F.
Yi,R.
Z.
Zuo,Normal-relaxor-diuseferroelectricphasetransitionandelec-tricalpropertiesofBi(Mg1/2Ti1/2)3-PbZrO3-PbTiO3solidsolutionceramicsnearthemorphotropicphaseboundary,J.
Am.
Ceram.
Soc.
97(2014)1912–1917.
[13]R.
Z.
Zuo,Y.
Liu,X.
C.
Chu,X.
H.
Wang,PhasetransformationbehaviorandelectricalpropertiesofPb(Zr0.
56Ti0.
44)O3-Bi(Zn0.
5Ti0.
5)O3solidsolutionceramics,J.
Am.
Ceram.
Soc.
94(2011)4340–4344.
[14]G.
Catalan,J.
F.
Scott,Physicsandapplicationsofbismuthferrite,Adv.
Mater.
21(2009)2463–2485.
[15]D.
Kim,J.
Yoo,I.
Kim,J.
Song,DielectricandpiezoelectricpropertiesofBi2O3added(Pb,Ca,Sr)(Ti,Mn,Sb)O3ceramicssinteredatlowtemperature,J.
Appl.
Phys.
105(2009)(2225-2150).
Fig.
7.
Aschematicillustrationforthedefectdipoleanddomainresponseduringelectriceldcycling.
B.
Zhangetal.
CeramicsInternational44(2018)5453–54585457[16]Y.
Cheng,Y.
Yang,Y.
P.
Wang,H.
Q.
Meng,StudyonPb(Mg1/3Ta2/3)O3-Pb(Mn1/3Sb2/3)O3-Pb(ZrxTi1x)O3highpowerpiezoelectricceramicsnearthemorphotropicphaseboundary,J.
Alloy.
Compd.
508(2010)364–369.
[17]F.
Gao,L.
H.
Cheng,R.
Z.
Hong,J.
J.
Liu,C.
J.
Wang,C.
S.
Tian,CrystalstructureandpiezoelectricpropertiesofxPb(Mn1/3Nb2/3)O3-(0.
2-x)Pb(Zn1/3Nb2/3)O30.
8Pb(Zr0.
52Ti0.
48)O3ceramics,Ceram.
Int.
35(2009)1719–1723.
[18]Y.
K.
Yan,K.
H.
Cho,S.
Priya,IdenticationandeectofsecondaryphaseinMnO2-doped0.
8Pb(Zr0.
52Ti0.
48)O30.
2Pb(Zn1/3Nb2/3)O3piezoelectricceramics,J.
Am.
Ceram.
Soc.
94(2011)3953–3959.
[19]X.
B.
Ren,Largeelectric-eld-inducedstraininferroelectriccrystalsbypoint-defect-mediatedreversibledomainswitching,Nat.
Mater.
3(2004)91–94.
[20]X.
B.
Ren,K.
Otsuka,Universalsymmetrypropertyofpointdefectsincrystals,Phys.
Rev.
Lett.
85(2000)1016–1019.
B.
Zhangetal.
CeramicsInternational44(2018)5453–54585458

易探云服务器怎么过户/转让?云服务器PUSH实操步骤

易探云服务器怎么过户/转让?易探云支持云服务器PUSH功能,该功能可将云服务器过户给指定用户。可带价PUSH,收到PUSH请求的用户在接收云服务器的同时,系统会扣除接收方的款项,同时扣除相关手续费,然后将款项打到发送方的账户下。易探云“PUSH服务器”的这一功能,可以让用户将闲置云服务器转让给更多需要购买的用户!易探云服务器怎么过户/PUSH?1.PUSH双方必须为认证用户:2.买家未接收前,卖家...

香港E3-1230v2 16GB 30M 326元/月 数脉科技

官方网站:https://www.shuhost.com/公司名:LucidaCloud Limited尊敬的新老客户:艰难的2021年即将结束,年终辞旧迎新之际,我们准备了持续优惠、及首月优惠,为中小企业及个人客户降低IT业务成本。我们将持续努力提供给客户更好的品质与服务,在新的一年期待与您有美好的合作。# 下列价钱首月八折优惠码: 20211280OFF (每客户限用1次) * 自助购买可复制...

DMIT:新推出美国cn2 gia线路高性能 AMD EPYC/不限流量VPS(Premium Unmetered)$179.99/月起

DMIT,最近动作频繁,前几天刚刚上架了日本lite版VPS,正在酝酿上线日本高级网络VPS,又差不多在同一时间推出了美国cn2 gia线路不限流量的美国云服务器,不过价格太过昂贵。丐版只有30M带宽,月付179.99 美元 !!目前美国云服务器已经有个4个套餐,分别是,Premium(cn2 gia线路)、Lite(普通直连)、Premium Secure(带高防的cn2 gia线路),Prem...

19ise.com为你推荐
外挂购买朋友,您好。我想请问一下,我在网络上购买了一个手游辅助器,他需要敬汉卿姓名被抢注为什么最近b站up主都被问是否注册了商标?百度关键词价格查询百度关键字如何设定竟价价格?原代码源代码是什么冯媛甑尸城女主角叫什么名字sss17.comwww.com17com.com是什么啊?www.gegeshe.com有什么好听的流行歌曲www.7788k.comwww.6601txq.com.有没有这个网站lcoc.topoffsettop和scrolltop的区别haole012.com说在:012qq.com这个网站能免费挂QQ,是真的吗?
西部数码vps 187邮箱 securitycenter 冰山互联 樊云 256m内存 腾讯云数据库 koss evssl证书 免费全能空间 好看qq空间 免费个人空间申请 老左来了 域名评估 河南移动m值兑换 atom处理器 江苏徐州移动 网站加速 国内空间 nnt 更多