http://www.paper.edu.cn-1-Size-inducedacoustichardeningandopticsofteningofphononsinCdS,InP,CeO2,SnO2,andSinanostructuresChangQSunSchlEEE,NTU,Singaporeecqsun@ntu.edu.sg;www.ntu.edu.sg/home/ecqsun/IthasbeenpuzzlingthattheRamanopticalmodesshifttolowerfrequency(ortermedasopticalmodesoftening)associatedwithcreationofRamanacousticmodesthatshifttohigherenergy(orcalledasacoustichardening)uponnanosolidformationandsizereduction.Understandingsofthemechanismbehindthesize-inducedacoustichardeningandopticsofteninghavebeenquitecontroversial.Onthebasisoftherecentbondorder-length-strength(BOLS)correlation[Phys.Rev.B69045105(2004)],weshowthattheopticalsofteningarisesfromatomiccohesiveenergyweakeningofsurfaceatomsandtheacousticmodehardeningispredominatedbyintergraininteraction.AgreementbetweenpredictionsandobservationshasbeenreachedforSi,CdS,InP,TiO2,CeO2,andSnO2nanostructureswithelucidationofvibrationfrequencyofthecorrespondingisolateddimers.Findingsfurtherevidencetheimpactofbondorderlosstolow-dimensionalsystemsandtheessentialityoftheBOLScorrelationindescribingthebehaviorofnanostructures.PACS:61.46.+w;78.30.-j;78.67.-n;63.22.+mKeywords:nanostructures;Ramanshift;BOLScorrelation;surfacebondcontraction;interparticleinteractionhttp://www.paper.edu.cn-2-IIntroductionAtomicvibrationisofhighinterestbecausethebehaviorofphononsinfluencedirectlyontheelectricalandopticalpropertiesinsolidmaterialsanddevicessuchaselectron-phononcouplinginphotoabsorptionandphotoemission,andphononscatteringindevicetransportdynamics.1Ithasbeenlongsurprisingthatwithstructuralminiaturizationdowntonanometerscalethetransverseandthelongitudinaloptical(TO/LO)Ramanmodesshifttowardslowerfrequency(orcalledasopticalmodesoftening)2accompaniedwithgenerationoflow-frequencyRaman(LFR)acousticmodesatwavenumbersofafeworafewtenscm-1.TheLFRpeakshiftsup(orcalledasacousticmodehardening)towardshigherfrequencyuponthesolidsizebeingreduced.3,4Generally,thesizedependentRamanshiftsfollowascalingrelation:2,4κωωjfjKAK+∞=)()(whereAfandκareadjustableparametersfordatafitting.Kj,thedimensionlessformofsize,isthenumberofatomswithdiameterdlinedalongtheradius(Rj)ofasphericaldot.Foropticalredshift,Af<0.ForSiexample,ω(∞)=520cm-1correspondstowavelengthof2×104nmandtheindexκvariesfrom1.08to=1.44oreven2.0,varyingfromsourcetosource.5FortheLFRblueshift,Af>0,κ=1,andω(∞)=0.Therefore,theLFRdisappearsforlargeparticles.TheunderlyingmechanismbehindtheRamanshiftisunderdebatewithnumeroustheories.Theoreticalstudiesofphononfrequencyshiftareoftenbasedoncontinuumdielectricmechanism.6,7Sophisticatedcalculationshavebeencarriedoutusingmodelsofcorrelationlength,8bulkphonondispersion,9lattice-dynamicmatrix,10associatedwithmicroscopicvalenceforcefield,4phononconfinement,11andbondpolarization.2ThemechanismofquadrupolarvibrationtakingtheindividualnanoparticleasawholewasassumedtoberesponsiblefortheLFRacousticmodes.Thephononenergiesaresizedependentandvarywithmaterialsofthehostmatrix.TheLFRscatteringfromsilvernanoclustersembeddedinporousalumina12andSiO213wassuggestedtoarisefromthequadrupolarvibrationmodesthatareenhancedbytheexcitationofthesurfaceplasmasoftheencapsulatedAgparticles.TheselectionofmodesbyLFRscatteringissuggestedtoarisefromthestrongerplasmon-phononcouplingforthesemodes.ForanAgparticlesmallerthanfournanometers,thesizedependenceofthepeakfrequencycanbeexplainedusin...
