材料科学基础下英文chapt3 11b

材料科学基础（II）Chapter3SolidificationandCrystallization-IISomecontentsareadoptedfromPPTby:ProfessorsM.E.GlicksmanandAfinaLupulescu材料科学基础（II）DrivingforcefornucleationofonephasefromasolutionwillbeconsideredinChapter5.Inadditiontothefactorsthatlimitorpromotenucleationinpuremetals,chemicalcompositionfluctuationanddiffusionisanotherfactortoaffectthenucleationrate.§3.GrowthofsinglephasefromliquidalloysDiffusion-ControlledGrowth•Growthlimitedbytherateofdiffusion–Howfastcantheneededatomsbedelivered–Howfastcantheheatbecarriedaway–Howfastcantheatomsbereceivedbycrystalphase材料科学基础（II）solidliquid§3.GrowthofsinglephasefromliquidalloysxSLTieline“jump”solidusliquidusCBTEquilibriumatS/LInterfacesLocalequilibriumassumption:EquilibriumcompositionalwaysmaintainsintheS/Lboundary.Itmaynotbesointhewholesystem,especiallynotinthesolidphase.From:M.E.GlicksmanandAfinaLupulescu2004右侧示意图中合金凝固界面推移的驱动力有多少？材料科学基础（II）Partitioncoefficient:k0=CS/CL

(分配系数)Assumingphasefieldboundarytobeastraightline假想相图，k0=Cs/CL为常数CSoluteLiquidusC0Cmaxk0C0C0/k0C

T

T3T2T1CSCLSolidusTAA§3.Growthofsinglephasefromliquidalloysk0<1不重要很重要：材料科学基础（II）Specialcasesof1Dgrowth（三种特殊条件的一维模型描述）

（假设单位面积的长棒）T2温度下，相应的完全平衡成分，液相增加和固相减少的溶质要守恒，即两个阴影部分面积应该相等。C0T

T3T2T1CSCLC=massperunitvolume(单位体积中质量)assumingequaldensityintwophases1.Equilibriumfreezing固相中的溶质数=Ms=Cs

z1液相中的溶质数=ML=CL

（L–z）1T固相液相热量CLC0CS(a)(b)单位体积中质量zL长度材料科学基础（II）NodiffusioninsolidLocalequilibriumatS/Linterface

CS=K0CLDifferentialmassbalance:(CL–CS)dz=(L-z)dCLBoundarycondition：

z=0,CL=CoCC0k0C0SolidLiquidCC0k0C0SolidLiquidCLzLCSdzdCLstartDistancealongbar,z2.Perfectmixinginliquid

G.Gulliver(1921)andE.Scheil(1942)材料科学基础（II）IntegrationleadstoScheileqn:

p501

non-equilibriumleverrule!!,

wherefs=z/L,fL=1–fsCompleteliquidmixingCL=C0fL(ko–1)zTaveragecompositionofsolidfordifferentTduetonon-equilibriumsolidificationk0<1,fL→0,CL

→∞,

Cs=k0CL

→∞CL

islimitedbyphasediagramC0CmaxC

SolidCC0k0C0finishCs=k0C0(1–fs)(ko–1)从成分可知结晶前沿的T材料科学基础（II）Gulliver–ScheilSegregationEquationPurermaterialFrom:M.E.GlicksmanandAfinaLupulescu2004材料科学基础（II）Gulliver–ScheilSegregationEquationFrom:M.E.GlicksmanandAfinaLupulescu2004材料科学基础（II）3.Steady-state(liquiddiffusioncontrolled)freezing

§3.GrowthofsinglephasefromliquidalloysstartfinishxBoundarylayerTerminaltransient终止瞬态Initialtransient初始瞬态compositionTheboundarylayerstartsto

buildupasfreezebeginssteadystate稳态From:M.E.GlicksmanandAfinaLupulescu2004材料科学基础（II）startfinishsteadystate

稳态bowwave船头波CC0k0C0SolidLiquidXmaxInitialtransientX

CC0k0C0SteadystateDistance0CC0k0C0SolidLiquidFinaltransientD/vD/vC0/k03.Steady-state(liquiddiffusioncontrolled)freezing

材料科学基础（II）AssumptionLocalequilibriumattheS/Linterface.Neglectdiffusioninsolid.Assumesteady–statesolidificationataconstantspeedInacoordinate,x,(x>0)movingwiththeS/Linterface1DModelofDiffusion–LimitedSteady–Statesolidification材料科学基础（II）AtsteadystateBuildanequation

dx=RdtR=migrationspeedChangeofdCatxfordtduetointerfacemigrationis

CL(x,t+dt)–CL(x,t)=CL(x–dx,t)–CL(x,t) =–(

C/

x)dx=–(

C/

x)Rdtduetodiffusionis

CL(x,t+dt)–CL(x,t)=(

C/

t)dt=D(

C2/

x2)dtCL(x,t+dt)=CL(x–dx,t)SecondFick’sLawCC0k0C0SolidLiquid0xC0/k0t+dttdCLR-dxx材料科学基础（II）Solvedfrom(9-32)

D

C2/

x2=–R

C/

x,atboundaryconditions:x=0,CL=C0/k0

andx=∞,CL=C0Onegets

CL(x)=C0[1+((1–k0)/k0)exp(-Rx/D)]p502Eq(9-33)D/R

=characteristicwidthcharacteristicgradientdCL/dxx=0=(C0/k0–C0)/(D/R)SolutionforCL(x)CC0k0C0SolidLiquidD/R0xC0/k0RCL(x)材料科学基础（II）EffectsofConvectionandStirringDuringcrystalgrowthandplane–frontsolidificationstirringoccurs,whichaffectsthesegregationprocess.ThiswasanalyzedbyBurton,PrimandSlichter(BPSTheory).Theysuggestedthreeimportantzones:Solidzone(nodiffusion)A“static”layer,d,(diffusiontransport)Liquidzone(completemixing)From:M.E.GlicksmanandAfinaLupulescu2004材料科学基础（II）4. Freezingwithpartialmixinginliquidp502,Fig.9-28

(convectioneffect,boundarylayerapproach)固体液体k0C0C0无聚集有聚集聚集(CS)i(CL)i(L)Bt1t2t3t4t5(CL)i初始状态(a)液体中溶质的聚集对凝固圆棒的成分影响(b)初始瞬态内溶质聚集的建立接近真实结晶状态的模型，目前研究仍然采用材料科学基础（II）4. FreezingwithpartialmixinginliquidSet: (Cs)i=k0(CL)i,(Cs)i=ke(CL)b, (Cs)i=kL(CLst)x

ke=effectivepartitioncoefficientInanalogytosteady-stateCLst

(x)=C0[1+(1–k0)/k0)exp(-Rx/D)]kL=(Cs)i/(CLst)x=(C0)/(CLst)x=1/[1+((1–k0)/k0)exp(-Rx/D)]kL=k0/[k0+(1–k0)exp(-Rx/D)]ke=(Cs)i/(CL)b=k0/[k0+(1–k0)exp(-R

/D)]K0C0CLCsC0C(Cs)iLocusof(CL)it=0tot(finish)

Instant(CL)atti液体有部分混合时的溶质分布CLs(CL)b材料科学基础（II）InanalogytoScheileqnforcompleteliquidmixing,Letkereplacek0

CL=C0fL(ke–1) Cs=keC0(1–fs)(ke–1)CLinarealsystemisaffectedbyvariousfactorsdvaluedependsonstirring

keCsType0k0k0C0(1–fs)(k0–1)Completeliquidmixing0<

<∞k0<ke<1keC0(1–fs)(ke–1)Partialliquidmixing∞1C0DiffusiononlyFasterstirring§3.Growthofsinglephasefromliquidalloys材料科学基础（II）固体液体C0k0C0(CL)i(CL)B初始瞬态ke=1浓度C0k0C0(CL)i(CL)Bke=k0浓度无聚集无瞬态C0k0C0(CL)i(CL)B初始瞬态K0<ke<1浓度凝固试样中溶质的浓度分布Comparison

有效分配系数ke值不同时，溶质的分布情况,p503C0K0C00浓度已凝固体积的分数abcd=0,ke=ko=∞,ke=1Howtoobtainpurersolids?材料科学基础（II）zonerefinement

区域熔炼示意图MichaelF.AshbyandDavidR.H.Jones1998材料科学基础（II）区域熔炼1次到1000次后的溶质浓度示意图多组加热器可提高区域熔炼效率MichaelF.AshbyandDavidR.H.Jones,1998材料科学基础（II）§4.Constitutionalsupercooling成分(组分)过冷(amilestonecontribution)Assumeliquidusasastraightline: dTL/dCL=-m TL=TA–mCL

T1=TA–mC0 T3=TA–mCo/k0 T1–T3=m(C0/k0–C0) C0kC0C0/k0C

T

T3TLCSCLTAT1材料科学基础（II）ConceptofconstitutionalsupercoolingAssumeequilibriumintheinterface,atsteadystate:ConstitutionallysupercooledstableCL(x)TL(x)T

(x)vvIfTofliquidisbelowitsliquidus

(constitutionallysupercooled)thebumporprotuberanceextendingintotheliquidgrows.IfTofliquidisaboveitsliquidus,anybumpmeltsback.T1T3Co/k0Co溶液的液相线温度实际温度梯度G材料科学基础（II）DistancexT3GCriticalgradientSolidLiquidTConstitutionalsupercoolingconditionD/RvT1TC0CC0/k0CLTheoriginofcomputationalsupercoolingaheadofaplanarsolidificationfront(a)Compositionprofileduringsteady-statesolidification.(b)ThetemperatureoftheliquidaheadofthesolidificationfrontfollowslineTL.Criticalgradient:characteristicwidthdCL/dxx=0=(C0/k0–C0)/(D/R)TLToremembertheconditionneeds:characteristicwidthD/Randdefinitionofk0andm可控参数材料参数产生成分过冷的判据：G<dTL/dxx=0材料科学基础（II）§5.Eutecticsolidification§6.Controlandsolidificationofingot§3.Growthofsinglephasefromliquidalloys1.Equilibriumfreezing2.Perfectmixinginliquid(Scheilmodel)3.Steady-state(liquiddiffusioncontrolled)freezing4.Freezingwithpartialmixinginliquid

温度对以上模式有什么的影响?§4.Constitutionalsupercooling合金凝固时产生枝晶原因必须是液相中有负温度梯度吗？

Whydendritesareoftenpresentinsolidifiedalloys!May12,实际溶液中成分过冷上述模型更容易或困难？材料科学基础（II）

t1t2t3t4t5(cL)i初始状态ConstitutionalsupercoolingconditionformoregeneralcasesT (Cs)i=k0(CL)i,(Cs)i=ke(CL)b,(CL)i=ke(CL)b/k0=(CL)b/[k0+(1–k0)exp(-R

/D)] ke=k0/[k0+(1–k0)exp(-R

/D)]ReplaceC0/k0with(CL)i=f((CL)b)Whend

∞,

twoexpressionsareidenticalD/RvC0CC0/k0CLcharacteristicwidth实际溶液中成分过冷更容易或困难？材料科学基础（II）CellularanddendriticsolidificationduetoconstitutionsupercoolingandrelevantsegregationSolidLiquidTLl(x)xLiquidT

(x)T(x)TLl(x)SolidTs(x)TL(x)>T(x),themeltisthermodynamicallystable,andthesolidadvanceswithplanarinterface.TL(x)<T(x),themeltesconstitutionallysupercooled,andthesolidadvanceswithcellularinterface.From:M.E.GlicksmanandAfinaLupulescu2004材料科学基础（II）CellularmicrostructuresPb-Sn正视侧视四溴化碳Sn-0.1wt%SbAdecantedinterfaceofacellularlysolidifiedPb-SnalloyLongitudinalviewofcellsincarbontetrabromatedFrom:M.E.GlicksmanandAfinaLupulescu2004From:PorterandEasterling1992Hexagonalcells(Sn-Pb)材料科学基础（II）Cells&DendritesAsabumpgrows,itcandevelopasequenceofdisturbancesontheS/Linterface.Thesequicklyeshallowcells,thendeepcells,andeventuallydendrites.From:M.E.GlicksmanandAfinaLupulescu2004材料科学基础（II）SimulatedgrowthofPb-Sndendritesshowing(a)compositionfield;(b)morphologyofPb-1wt%Snalloy(c)compositionfieldand(d)morphologyofPb-5wt%Snalloy.Botharegrowingina10K/mmtemperaturegradientwitha100mm/svelocityRichinsolutesanddefects,harmfultoopticalpropertyofsinglecrystalS.Raghavanetal2003Cellulardendritesincarbontetrabromated四溴化碳（透明有机物）胞状枝晶材料科学基础（II）Timeevolutionofthesolid/liquidinterfacemorphologywhenacceleratingthegrowthratefrom0to3.4m/satatemperaturegradientof6.7K/mm(a)50s(b)55s(c)65s(d)80s(e)135s(f)740sKostorzedited,2001材料科学基础（II）Oftenitisdifficulttoavoidconstitutionalsupercoolinginpracticebecausevelocitytoavoiditisverylow.Directionalsolidificationwithaplanarfrontispossibleonlyatlowgrowthrates(likesinglecrystalSi).Inmostcases,theinterfaceisunstable.G/√RInterfacemorphologydendriticcellularplanarC0影响晶体生长方式的主要因素empiricalcurvep505,Fig.9-33§4.Constitutionalsupercooling材料科学基础（II）0.41Cu-NiWARRENandW.J.BOETTINGER,ActaMater.1995ThemicrostructureofaCu-30%Nialloyshowingacoredstructure材料科学基础（II）Dendritesinanaluminumalloy(x50).DonaldR.Askeland,P.Phule2003Dendritesinasteel(x25).材料科学基础（II）SolidificationmicrostructuresDendrites(Co-Cr)Ascanning-electronmicrographshowingthedevelopmentofdendritesinanickel-basedsuperalloysingle-crystalweld..A.David,S.S.Babu,andJ.M.Vitek,JOM,2003材料科学基础（II）Ahypoeutecticstructurefromthecopper-silverphasediagramcontainingapproximate24%copper.Lightoverregionsareproeutecticdendrites,whilethegra