材料热力学与动力学5

Chapter5:DiffusionalTransformationsinSolids5-1LabABT0T1xa/bxb/awhathappenswhenalloyiscooledfromT0toT1?aissupersaturatedB-atomsdiffusetogethertoformasmallvolumewithbcomposition(xb/a)B-atomsrearrangeintobcrystalstructurea/binterfacewillbecreated,leadstoanactivationenergybarrier5.1HomogeneousNucleationinSolidChapter5:DiffusionalTransformationsinSolids5-2energychangesinvolvinginb-nucleationavolumefreeenergyreductionofVDGVainterfacefreeenergyincreaseofAgamisfitstrainenergyincreaseofVDGStotalfreeenergychange:DG=-VDGV+Ag+VDGSforasphericalnucleuswiththeradiusofr:gDDD23434rGGrGSV--Chapter5:DiffusionalTransformationsinSolids5-3DG=-V(DGV-DGS)+AggDD23434rGGrSV--rG0--VDGV-V(DGV-DGS)r3Agr2DG0rGcriticalradiusSVGGrDDg-2*energybarrier23*316SVGGGDDgD-r*DG*rr*:rDGrr*:rDGChapter5:DiffusionalTransformationsinSolids5-4DGVforprecipitationtonucleate?TT1T2x0xBABababTeDTDxaxexbxB01G@T2GaGbx0xexbbAbBaAaBDG0parallelDGnGbsteeprisenearxb2tangentpointsonGboverlapatxboverlappingof2tangentpointsbbbbababDBABAnxxxxG---11DGVperunitvolumeofb:bDDmnVVGGfordilutesolutions:DGVDxDTChapter5:DiffusionalTransformationsinSolids5-5dependenceofnucleationrateontemperatureTeT'e0x0aab(a)(a)thephasediagram0DGVDGSDGV-DGSDG*DG(b)(b)theeffectivedrivingforceandtheresultantenergybarrierDTC0kTGe-DkTGmeD-(c)(c)exponentialtermsinNhom0NNhom(d)(d)homogeneousnucleationrate--kTGkTGANmDDexpexphomChapter5:DiffusionalTransformationsinSolids5-6dependenceofnucleationrateontemperatureT0N--kTGkTGANmDDexpexphomkTGmeD-kineticfactor(diffusion)kTGe-Dthermodynamicfactor(energybarrier)verysmallundercooling:Nhom~0sinceDGVistoosmallverylargeundercooling:Nhom~0sincediffusionistooslowChapter5:DiffusionalTransformationsinSolids5-7DG=-V(DGV-DGS)+AgSVGGrDDg-2*criticalradius(sphericalnucleus)23*316SVGGGDDgD-energybarrier(sphericalnucleus)rG0--VDGVVDGSAgDGr*DG*--kTGkTGANmDDexpexphomnucleationrate[summary]Chapter5:DiffusionalTransformationsinSolids5-8(a)volumefreeenergy(-)xB01GGaGbx0xe@T2xbbAbBx0xBABxexbT1T2ababTeDTDxaaAaBDG0perunitvolumeofb:bDDmnVVGGbbbbababDBABAnxxxxG---11perunitmoleofb:DGnfordilutesolutions:DGVDxDTChapter5:DiffusionalTransformationsinSolids5-9(b)interfacefreeenergy()102360120180misorientation,qdeg.rotationaxis||11070.5twinrelativeboundaryenergyg-plotforaprecipitateOggcohgincequilibriumshapeChapter5:DiffusionalTransformationsinSolids5-10(c)misfitstrainenergy()volumemisfitD=DV/VcoherencystrainsincoherencystrainsacfVGS232DDspherediscneedlec/ac/a10.5012f(c/a)minsiiGADgChapter5:DiffusionalTransformationsinSolids5-11aprecipitateatthetripleboundarybetweengrainA,BandC(Fig.3.46)ABCaincoherencysemicoherency5.2HeterogeneousNucleationinSolidChapter5:DiffusionalTransformationsinSolids5-12nucleationinsolidsisalmostalwaysheterogeneoussuitablenucleationsites:excessvacanciesdislocationsgrainboundariesstackingfaultsinclusionsfreesurfaces•non-equilibriumdefects•freeenergy:DGd•ifremovedbynucleation,DGdwillbereleasedDGhet=-V(DGV-DGS)Ag-DGdChapter5:DiffusionalTransformationsinSolids5-13b-precipitateshapeina-matrixisdeterminedby:thermodynamicconsiderationminimizationofthetotalinterfacialenergy(coherent—semicoherent—incoherent)kineticconsiderationmaximizationoftheboundarymigrationrate(incoherent—semicoherent—coherent)5.3PrecipitateGrowthChapter5:DiffusionalTransformationsinSolids5-14Widmanstättenmorphology(thindiscorplate)semicoherentsmallerinterfacialenergylowerboundarymigrationrateslowerincoherentlagerghighermfasterChapter5:DiffusionalTransformationsinSolids5-15aslabofb-precipitateformedonagrainboundaryandgrownfroml=0,whenalloyx0iscooledfromT1toT2TT1T2x0xBABababTeDTDxaxexbxByxbx0xelbavinterface5.3.1growthbehindplanarincoherentinterfacesChapter5:DiffusionalTransformationsinSolids5-16bxbaxeneartheinterfaceforunitareaofinterfacetoadvancedl,equationmolesBmustbesuppliedbydiffusionthroughthea.bbmeVdlxx-thefluxofBthroughunitareaintimedtisgivenby,therefore:amVdtdydxDabbmmeVVdydxxxDdtdlv-if,oneobtains:bammVVdydxxxDdtdle-bneededinordertocalculatethegrowthrateofthebplateChapter5:DiffusionalTransformationsinSolids5-17dydxxxDdtdle-bxByxbx0xelbavinterfacedx/dydx/dydecreaseswithtime.Zener:itcouldbereplacedby(x0-xe)/L,whereListhewidthofthediffusionzone.L(x0-xe)/Ltwoshadedareasshouldbeequalsoluteconservation:(xb-x0)·l=(x0-xe)·L/2itgives:lDxxxxxxdtdlvee2))((020---bbChapter5:DiffusionalTransformationsinSolids5-18lDxxxxxxdtdlvee2))((020---bbintegrationgives:DtxxxDtxxxxxlee---bbbDD))((0tDxxxve-)(2bDlt-1/2:precipitatethickeningobeysaparabolicgrowthlawvDx:growthrateisproportionaltothesupersaturationChapter5:DiffusionalTransformationsinSolids5-19bravsemicoherentinterfacecross-sectionprofileofabprecipitateplatewithconstantthicknessandcurvedincoherentedgeofradiusrababTT1xexbx0xBGaGbG@T1xexbxBbrGxrxrg/rforplate2g/rforneedle5.3.2lengtheningofplatesorneedlesChapter5:DiffusionalTransformationsinSolids5-20ababTT1xexbx0