材料热力学与动力学-4

Chapter4:Solidification4-1Chapter4.SolidificationProf.Dr.X.B.ZhaoDepartmentofMaterialsScienceandEngineeringZhejiangUniversityChapter4:Solidification4-24.1NucleationinPureMetalsNucleationTypeHomogeneousHeterogeneousFreeEnergyChangeNucleationRateKeyProblemsChapter4:Solidification4-34.1.1HomogeneousNucleationLiquidLiquidSolidr,ADG?VGLV=VL+VSGL,GS,gDG=-VSDGv+AgDGv=GL-GSexcessfreeenergypervolumeg2V3434rGrD-(forasphereofradiusr)Chapter4:Solidification4-44.1.1HomogeneousNucleationrDG0-volumefreeenergyr3interfacialenergyr2DGr*DG*v2*GrDgChapter4:Solidification4-54.1.1HomogeneousNucleationHowformsolidnucleiinliquidatmeltingpoint?liquidvolume:2~4%largerthantheclosepackedsolidphaseinstantaneous2DpictureofliquidstructureStructureFluctuationsomesmalltemporarilyclosepackedclustersarepossible,duetothelargemovementfreedomofatoms.clusternumberinasystemwithn0atoms:kTGnnrrD-exp0Chapter4:Solidification4-64.1.1HomogeneousNucleationkTGnnrrD-exp0mostclustersaretoosmalltobestableintheliquidcriticalnucleussizer*kineticconsiderationTrmaxsinceatommovementrTTmrmaxthermodynamicconsiderationDT0DG0,r*r*T=Tm-DTundercoolingDT0needed!rr*Chapter4:Solidification4-74.1.2HomogeneousNucleationRatekTGCfN*hom00homexpD-22V2m3*hom1316TLTGDDgLV:latentheatoffusionperunitvolume200homexpTACfND-NhomDT0DTNnucleationexplosion@DT=DTNformostmetalsDTN~0.2TmChapter4:Solidification4-84.1.3HeterogeneousNucleation22V2m3*hom1316TLTGDDggDTonmouldwall,impurity,etc.solidliquidmouldrgMLgSMgSLqDGhet=-VSDGVASLgSLASM(gSM-gML)*hom22V2m3SLV3SL*het131616GSTLTSGGDDDDqgqg4cos1cos22qqq-SVSL*2GrDgsameashomogeneousnucleation,butsmallervolume&lessatoms!Chapter4:Solidification4-94.1.3HeterogeneousNucleation09018030601201500.21.00.80.60.4wettingangle,degreeshapefactorS(q)Chapter4:Solidification4-104.1.3HeterogeneousNucleationrDG0r**homGDhomGDhetGD*hetGDv2*GrDgChapter4:Solidification4-114.1.3HeterogeneousNucleation*GDnucleationrate,NDTDT*homGDNhomdetectablenucleation(N~1cm-3s-1)criticalvaluefordetectablenucleation(p.191)(DG*~78kT)*hetGDNhetTmuchlowerundercoolingnecessaryforheterogeneousnucleationChapter4:Solidification4-124.2GrowthofaPureSolidroughinterfaceformostmetalsflatinterfaceformostcompoundsChapter4:Solidification4-134.2.1Continuousgrowthliquidsolidatomsinliquidphasemigratetothesolidphaseeasilyevenatasmallundercoolingduringsolidificationdisorderedinterfaceatoms“packing”atrandomsolidpositionwithoutdisruptiontheinterfaceequilibriuminterfacialundercooling:afractionofadegreesolidificationrate:controlledbydiffusionheatdiffusionforpuremetalssolutediffusionforalloysChapter4:Solidification4-144.2.2LateralgrowthDG=DU+DPV)-TDSliquid/solidequilibrium:DG=0DUTDS~0highmeltingentropy(largeDSandDU)highbondenergy(solid)liquidsolidarrivingatom4newbrokenbondsunstable,jumpbackintoliquidatomsrarelyattachonthesolidsurfacesolidliquidledge2newbrokenbondsjog0newbrokenbonds,butabletojointheledges&jogshowledges&jogscanbesupplied???Chapter4:Solidification4-154.2.2Lateralgrowth:surfacenucleationledgecreationbysurfacenucleationlargenumberofatomsforma2-DdisccriticalradiusofthediscdependsonundercoolingChapter4:Solidification4-164.2.2Lateralgrowth:spiralgrowthdislocationscreateledgesledgesneverrunoutoftheinterfaceChapter4:Solidification4-174.2.2Lateralgrowth:twinintersectionstwininterfaceChapter4:Solidification4-184.2.3HeatflowandinterfacestabilityTxsolidliquidvTmyxsolidliquidyxsolidliquidunstableTxsolidsupercooledliquidvTmyxsolidliquidyxsolidliquidautomaticallyChapter4:Solidification4-194.3AlloySolidificationliquid&solid:differentcompositionphasediagramnecessarysolidificationoccursofteninatemperaturerangeheatandmasstransferinvolved(normally)solutediffusioncontrolledChapter4:Solidification4-20(1)SolidificationofsinglephasealloysTxsoluteliquidaxExmaxTEassume:straightsolidus&liquidusx0T1kx0xSxLequilibriumsolidificationT2x0/kpartitioncoefficientk=xS/xLChapter4:Solidification4-21(2)EquilibriumsolidificationliquidaTxsoluteTET1T2x0kx0x0/kdistance,yliquidsolidxLxST1TT2Chapter4:Solidification4-22(3)Nodiffusioninsolid,perfectmixinginliquidliquidaTxsolutexExmaxTEx0T1kx0T2x0/kdistance,ySxxintChapter4:Solidification4-23(4)Nodiffusioninsolid,diffusionalmixinginliquidliquidaTxsolutexExmaxTEx0T1kx0T2x0/kdistance,yinterfaceequilibriumexsolutionofFick’s2ndlawship-head-wavesteadystateChapter4:Solidification4-24(5)constitutionalsupercoolingliquidaTxsolutexExmaxTEx0T1kx0T2x0/kdistance,yTT2T1TeqTrealconstitutionalsupercoolingChapter4:Solidification4-25(6)Cellular&dendriticsolidificationTyTeqTrealsolidliquidzsolidliquidequilibriumliquiduspointChapter4:Solidification4-26(7)T&xdistributionincellularsolidificationcellliquideutecticdistancealongAA,yxLTAAxEx0TEBBdistanceonBBxSxExmaxChapter4:Solidification4-27(8)Cellular&dendriticmicrostructuresCellularlysolidifiedPb-Snalloy(Fig.4.26a,page218)Columnardendritesinatransparentorganicalloy(Fig.4.28,page220)Chapter4:Solidification4-28EndofChapter4