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1、ScriptaMaterialia,Vol.37,No.7,pp.955-962,1997PergamonElse&rScienceLtdCopyright01997ActaMetallurgicaInc.FrintedintheUSA.Allrightsreserved1359~6462l9lS17.00+.OOPI1S1359-6462(97)00191-7THEGIBBS-THOMSONEFFECTDURINGCELLULARANDDENDRITICSOLIDIFICATIONv.LaxmarlanMetallurgyDepartment,GeneralMotorsResea
2、rch&DevelopmentCenter,MailCode480-106-212,Warren,MI48090-9055(ReceivedOctober15,1996)(AcceptedApril20,1997)IntroductionThefundamentalimportanceoftheGibbs-Thomson(G-T),orthesurfaceenergy,effectinanalyzingthekineticsofvariousphasetransformationshaslongbeenrecognized,startingwiththeworkofZener(1,
3、2),Fisher(3,4),Temkin(5),HorvayandCahn(6),andSekerkaetal.(7).Theimportanceofin-cludingtheG-Teffectinasystematicmannerintheanalysisofsolidificationproblemsis,perhaps,mosteloquentlyillustratedbytheclassicalMullinsandSekerkaanalysis(8,9)forstabilityofaplanarsolid-liquidinterface.Themainpurposeher
4、eistoreconsidertheroleplayedbytheG-TeffectwithinthecontextofthemodificationstothetheoryofcellularanddendriticgrowthproposedbyLaxmanan.Thismodifiedtheoryhasbeendiscussedinsomedetailinarecentarticle(IO).TheMeltingPointofaCurvedSolid-LiquidInterfaceThemeltingpointofacurvedsolid-liquidinterfaceisd
5、epressedbelowtheequilibriummeltingpointofaplanarinterfacebyanamountAT,=~TMK;seethetextbyChalmers(11)foraderivationofthisbasicresult.Herer=y&isthecapillarylengthscale,yisthesurfaceenergyofthesolid-liquidinter-face(J/m),L,,theheatoffusionperunitvolume(J/m3),Tutheequilibriummeltingpointoftheflati
6、nterface,andKisthecurvatureoftheinterface.Thecurvedinterfacecouldbeasphericalparticleofradiusr(K=2/r),oradendrite/celltip(K=2/r,),growinginthemelt.Thedepressionintheequilib-riummeltingtemperature,ortheundercooling,duetotheG-Teffectwouldthusbequitesmallifthedendriteorcelltipradiusrt>>r.Thisistr
7、ueformostcellularanddendriticstructures.risontheorderoflo-mwhereastipradiiofdendritesorcellsareontheorderof10m5m,ormore(12-15).Thus,theabsolutevalueofAT,inCorK,isquitesmall.Nevertheless,indeterminingtherelativeimpor-tanceoftheG-Teffect,
