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1、J.Mater.Res.13,2363(1998).Docarbonnanotubesspinwhenbundled?Young-KyunKwonandDavidTomanekDepartmentofPhysicsandAstronomy,MichiganStateUniversity,EastLansing,Michigan48824-1116YoungHeeLeeDepartmentofPhysicsandAstronomy,MichiganStateUniversity,EastLansing,M
2、ichigan48824-1116DepartmentofPhysicsandSemiconductorPhysicsResearchCenter,JeonbukNationalUniversity,Jeonju561-756,KoreaKeeHagLeeDepartmentofPhysicsandAstronomy,MichiganStateUniversity,EastLansing,Michigan48824-1116DepartmentofChemistry,WonKwangUniversity,
3、Iksan,Chonbuk570-749,KoreaSusumuSaitoDepartmentofPhysics,TokyoInstituteofTechnology,1-12-1Oh-okayama,Meguro-ku,Tokyo152,Japan(Received5February1998accepted15May1998)Usingabinitioandparametrizedtechniques,wedeterminetheequilibriumstructureofanorderedbund
4、le"of(10,10)carbonnanotubes.Duetothesmallinter-tubeinteractionandlatticefrustration,;1wepredictaverysoftlibrationmodetooccurat12cm.Thismodeispredictedtodisappearabovetheorientationalmeltingtemperaturewhichmarkstheonsetoffreetuberotationsabouttheiraxis.W
5、ediscussthee ectoftheweakinter-tubecouplingandorientationaldisorderontheelectronicstructureneartheFermilevel.PACSnumbers:61.48.+c,61.50.Ah,73.61.WpI.INTRODUCTIONElectronicstatesinvolvedinthesuperconductingbe-haviorofthealkali-dopedCsolidderivefromthisAmon
6、gcarbonbasedmaterials,fullerenes(suchasthe60molecule'sdegeneratelowestunoccupiedtmolecularCbuckyball"[1])andnanotubes[2]havereceived1u60orbital[10]thatextendstoan0:5eVwidebandduemuchattentionrecentlyduetotheirhighstructuralsta-totheinter-Cinteractions,w
7、hichinturndependonbilityandinterestingelectronicproperties.Structurally60themolecularorientation[10,11].Similarly,interactionsrigid[3]andhighlyconducting[4]ropes"ofcarbonnan-betweencarbonnanotubesinropes",whichdependonotubesarethemolecularcounterpartsof
8、carbon bersthemutualorientationofadjacenttubes,areexpectedto[5].a ectstatesattheFermileveltoanimportantdegree.PerfectlysphericalCmoleculesareknowntospin60Thispointisespeciallyintriguing,sincerecentcalcula-freelyatro
