西安交大英文chapter4 part

94.4ForceondislocationForcefromexternalstressPeach-KoehlerequationForcebetweendislocationsForcebetweendislocationandsoluteatomLinetensionofdislocationLatticeresistanceofdislocationmovementImageforceZYXGEHFObBCDAEx.1Inacubiccrystal,asquaredislocationloopABCD,itsslipplaneEFGH∥bothbases.AB∥EF,Burgersvectorb⊥AB.Shearstressτ∥bonbothbases.JudgetheDis.typeanddirectionofmovementofeachsectionofdislocation.DA:gliding，directionＸCD:gliding，directionＹBC:gliding，direction－ＸAB:gliding，direction－ＹAnswer：Imagineaforceexist!Itsdirection=dis.motiondirec.Whydoesthedis.move?Directionofdis.motionVSτ?Deformationwork=

virtualworkbythevirtualforceondislocationThenweget(1)、Forcefromexternalstress1.CalculationbyvirtualworkprincipleAttention:thefistheforceperunitlength

Discussion(1)Foredged.,thestressrefersto(a)shearstressonaplane//slipplaneandadirection//b;

(b)normalstressonaplane//halfatomicplaneandadirection//b(a)glide(b)climb(3)Thevirtualforce┴dislocationline,sameasmovementofdislocationline(2)Forscrewd.,thestressreferstoshearstressonaplane//slipplaneandadirection//b

Calculatetheforceonadislocationofaunitlengthactedbyastressfield.(2)、Peach-Koehlerequation1.ApplicationofPeach-Koehlerequation2.Peach-Koehlerequation

isstressfieldisBurgersvectorisunitdirectionvectorofdislocationline

3.Peach-Koehlerequation

3.Peach-KoehlerequationEx.2,squared.loopABCDinacubiccrystal,glideplaneEFGH//baseplane,AB∥EF,

b⊥AB,τ

∥b,τisactedonthebases.Forceonaunitlengthd.line?ZYXGEHFOBCDAbDA:gliding，direction-ＸCD:gliding，direction-ＹBC:gliding，directionＸAB:gliding，directionＹf=τbEx.3,squared.loopABCDinacubiccrystal,glideplaneEFGH//baseplane,AB∥EF,

b⊥AB,τ∥b,τisactedonthefrontandbacksides.Forceonaunitlengthd.line?ZYXGEHFOBCDAb???bEx.4

Apositiveedged.withbinacubiccrystal,slipplane//baseplane.ifτ∥b,τisactedonthebases.forceonaunitlengthd.line?

=τbj

Assumethat：ThenWeget

2.CalculationbyPeach-KoehlerequationZYXEx.5

Apositiveedged.withbinacubiccrystal,slipplane//baseplane.ifτ∥b,τisactedonthefrontandbacksides.forceonaunitlengthd.line?2.CalculationbyPeach-KoehlerequationAB:noBC:τb，//ＺCD:noDA:τb，//－ＺEx.6Arightscrewd.inacubiccrystal,b//baseplane.Ifτisactedonbaseplanes,forming45°withb,forceonaunitlengthd.line?AssumeThenWeget

ZYXHowtounderstandthedirectionaldisagreementbetweenexternalstressanddislocationmotion/force?Foredgedislocation,theyareconsistent.Forscrewdislocation,theyarevertical!Wecanimaginethatthisedgedislocationisthedirectresultofthestress,andthescrewdislocationistheresultoftheedgedislocationsweeping.Anedgedislocationisformedbeforetheformationofascrewdislocation.E.D.VSS.D.EndEnd10

—Stressfieldresultingfromd.1(locatedongridorigin)

—Burgersvectorofd.2

—Unitdirectionvectorofd.2(3)、ForcebetweendislocationsUsingPeach-Koehlerequation(右手直角坐標系)db1b2d.1d.2Discussthedb1b2d.1d.21.Forcebetweentwo//screwd.Rightscrewdis.DACBb(2)Rectangularcoordinatesystemdb1b2d.1d.21.Forcebetweentwo//screwd.Repulsionforlikescrewd.,forunlikescrewd.?ZYoutsideXHowtounderstandtheinteractionbetweentwoscrewdislocations?Dislocation1producesacertaindistortion,leadingtoastressfield/strainenergy.Dis.2tendstofurtherchangethedistortion,leadingtochangethestressfield/strainenergy.Discussion:Howaboutthedifficultytoproducetheseconddislocationnearthefirstone?LikeVSUnlike?Engineeringapplication!Whydenselydistributeddislocationstorestricttheplasticdeformation?d2.Forcefortwo//edged.onsameglideplaneb1b2d.2d.1bisnotcontained.d2.Forcefortwo//edged.onsameglideplaneb1b2d.2d.1YisoutsidescreenTheny=0plane.ZYoutsideXy=0x=-dd2.Forcefortwo//edged.onsameglideplaneb1b2d.2d.1Repulsionforlikee.d.,attractionforunlikee.d.YisoutsidescreenTheny=0plane.ZYoutsideXdb1b2d.1d.23.Noforcebetweenedged.//screwd.YisoutsidescreenTheny=0plane.ZYoutsideX(θ)ⅠⅡb2b1θXrOY4.Ffortwo//edged.ontwo//glideplanePositivezaxis:outsidescreen(x,y)a)Liked.YXb)Unliked.XYGenerally,fy>fx,likedis.tendtodepartandformdis.wallresultinginlowgrainboundary(thengrainrefinement).Ex.6d.1//d.2locatedatadistanceofd,theincludedangleforb1/b2isπ/4,forceonaunitlengthd.2line?Positivezaxis:outsidescreenEx.6d.1//d.2locatedatadistanceofd,theincludedangleforb1/b2isπ/4,forceonaunitlengthd.2line?Positivezaxis:outsidescreenEx.7d.(AB)andd.(CD):locatedfromd,┴butnotcoplanar.|b1|=|b2|=b.Calculate:(1)forceonaunitlengthd.(CD),(2)totalforceond.(CD),(3)totaltorqueond.(CD),(4)resultantmovement.

fordifferentd.combinations.

(a)twoscrewd.(b)twoedged.

(c)edgeandscrew(1)twoscrew

f=(σ·b2)×l02

f=(σ·b2)×l02(2)twoedge

f=(σ·b2)×l02(3)edgeandscrewDiscussion(1)Thereareattractionandrepulsionbetweendislocations.Foreachsectionofadislocation,therearethedifferentinteractions/forces(orzeroatsomepoint)(2)Theinteractiontendstomovedislocations,wesupposethatthemovementresultsfromthevirtualforces.(3)Theinteractiontendstodecreasethesystemenergy.11XYMakeapore(radiusr0)inanelasticsolid,thenputarigidsphere(radiusr1)intothepore.AworkWisactedbythenormalstressofthedislocationbyresistingorpromotingtheprocess.1)Cottrellatmosphereisdegreeofmisfit(4)Forcebetweendislocationandimpurityatom1.Elasticinteraction:d.VSsoluteisaveragenormalstressattherigidsphereForsolidsolutionalloy,oneimpurityatomisarigidsphere.Assumethattheinteractionenergybetweenimpurityatomandd.isE.Then為何取負：對外做功則能量降低Isoenergeticline(dashed)andforceline(solid)fortheinteractionbetweenedged.andimpurity(interstitialatomsorlargesubstitutionalatoms)XYForinterstitialatomsandlargesubstitutionalatoms,β>0.Tominimizeenergy,theytendtosegregatejustbelowdislocationXYIsoenergeticline(dashed)andforceline(solid)fortheinteractionbetweenedged.andimpurity(smallsubstitutionalatoms)Forsmallsubstitutionalatoms,β<0Tominimizeenergy,theytendtosegregatejustabovedislocation.Cottrellatmosphere:theimpurityatomssegregatedaroundtheedgedislocation.

TheypresentBoltzmannconcentrationdistribution

—averageconcentrationofimpurity

—temperature

—BoltzmannconstantNote:Cottrellatmospherecanimpededislocationmovementbypinningdislocation.EngineeringapplicationSharpyieldpointinstress-straincurveStrainaging:timeandtemperaturedependentBCC;C/N/O2)Snoekatmosphere

Soluteatomsregularlylocatedaroundscrewd.duetothenonsphericalsymmetrydistortionofcrystallattice.Itcanimpededislocationmovement.Inmetal,electrostaticdipolecanbeformedduetothemovementoffreeelectronsfromcompressivestressregiontotensilestressregionaroundd..Itchangestheconcentrationdistributionofsoluteatomwithdifferentelectronvalencefromsolventatomsintheregionnearslipplaneofanedged..ChargedjogSlipplane2.Electrostaticinteraction:d.VSsoluteInionicsolid,theconcentrationdistributionofsoluteionsischangedby:theelectrostaticinteractionbetweenthechargedjog

ofedged.andthechargedsolute.Thereischemicalinteractionbetweensoluteatomsandthestackingfaultsofextendedd.Itresultsinthedifferentconcentrationfromthatinbulkaroundthestackingfaultsareaofextendeddislocation.Suzukiatmosphere:theconcentratedsoluteatomsinthestackingfaultsofextendeddislocation.Itimpedesthedislocationmovement.

3.Chemicalinteraction:d.VSsoluteSoluteconcentrationinstackingfaultsC1MeansoluteconcentrationC0>

5.Linetensionofd.LinetensionLineenergydensity:J·m-1=(N·m)·m-1=

N:Linetension(force)Equaltostrainenergyperunitlengthd.Forcetoresistextendingorbendingofd.Surfacetension:Surfaceenergydensity:J·m-2=(N·m)·m-2=

N·m-1:Surfacetension(forceperunitlength)Surfacetension外力外力TendtoshrinkandstretchLinetensionofdislocation:Forcetoresistextendingorbendingofd.,Tendtobeshrinkableand

straightIfadislocationiscurving,theremustbesomeblockingandexternalstress(outofthedis.).Forceond.dsactedbyshearstressτ:ResistingforceondsbylinetensionT:

,assumeThenＲisinverselyproportionaltoτ.RdsABEx.ShearstressτVSradiusofcurvatureforad.withtwopointsfixedb)ABEdged.movesfromlatticepointA(a）toanotheroneB(b)

6.Ｐ-Ｎforce（Peirls-Nabarrostress）a)a)ABＰ-Ｎforce:resistanceofd.movementfromonelatticepointtoanotherifnotconsideranyotherforce(comefromtheattractionofatomsaboveandbelowslipplane).Theshearstresscausesthatthed.starttomovea—thedistancebetweenglideplanesb—interatomicdistanceonglidedirectionν

—Poisson’sratiow—widthofd.d.MobilityVSd.widthDiscussion：（?。ヾ.glideprefers：planewithlargestplanedistance(大a)andsmallestinteratomicdistance(小b).（ⅱ）w↑→↓→mobility↑（ⅲ）wdependsoncrystalstructureandbondtype

covalentandionic<metallicformetallic:bcc<fccorcpha—thedistancebetweenglideplanesb—interatomicdistanceonglidedirectionν

—Poisson’sratiow—widthofd.Forceond.nearinsidesurfacebysurfaceForceond.bytheimaged.outsidesurfaceElasticstrainenergyofadislocationdependsontheactiveradiusofdislocationstressfield.

Ifdislocation/surfacedistanceλ<R，

λ↓→E↓－meansthattheforcedirects

toenergydecreasing,Therefore,imageforcedirectstosurface7.Imageforce:actedbycrystalsurfaceAttractionbysurface廣義能量變化、廣義力Sincenostressonsurface,thecompositeforcefromd.andimaged.mustbezeroatsurface.FlatsurfaceReals.d.Images.d.XcrystalvacuumλYOb–bλEx.Screwd.ImageF2.Imaged.anditsattraction(近似)Samed.directionandoppositebEngineeringapplicationItisextremelyimportantforthinfilm.Wearmechanism:Sub-surfacelayerspallingoffforhard/softconterpart12PerfectdislocationStackingfaultsImperfectdislocationDislocationreaction5.ThedislocationinrealcrystalsEndClassificationofdislocationsSimplecubicb=latticeparameter

Realcrystalsb>L.P.b=L.P.b<L.P.Integer:Perfectdis.

b=L.P.Unitdis.Notinteger:Imperfectdis.

b<L.P.Partialdis.End(111)(111)B′CBbBurgersvectorofthedislocation(isequaltotheintegralmultipleof)/(isequalto)theatomicspacingalongtheslipdirection=(Perfectd.)/(Unitd.)(1)Perfect(orUnit)d.1.Concept:bccfcccph2.bforunitdislocationinmetalsEndFCCBurgersVectorsinMetalsFCCMetalWhatisthelengthofb[110]

?Letthelatticeparameterbeao

ao[110]=ao*(12+12+02)1/2=21/2

ao

TheBurgersvectorishalfthatlength:

|b

[110]|=(ao/2)[110]=(ao/2)21/2

TheBurgersvectorisusuallydenotedusingthisterminology,i.e.,

b

[110]=(ao/2)[110]a0[110]EndBurgersVectorsandSlipSysteminFCCStructures

4slipplane×3slipdirection=12slipsystemEnd(111)(111)CB′Bbbccfcccph2.bforunitdislocationinmetalsTrytowritebyyourself!EndNormalsequenceAABBCC△△△△△Trytowritebyyourself!ABCBCA△△▽△△ExtractAlayerABABCB△▽△△▽InsertB

layerGlide(a<112>/6)3.SeveralexamplesofSFinFCC(111)BCEnd

planardefectsbystackingsequenceerror(2)Stackingfaults1.Concept:Theenergyincrementresultingfromstackingfaults.Irregularstackingalthoughlatticedistortionisnegligible.SpecificSFE:SFEonaunitareaofSF.

2.StackingfaultsenergySSFE(J/m2

)

MetalsAuCo

Ni

Al

CuAg0.02

0.20

0.04

0.06

0.25

0.02

EndBurgersvectorofthedislocation(isnotequaltotheintegralmultipleof)/(islessthan)theatomicspacingalongtheslipdirection=(Imperfectd.)/(Partiald.)OnlyglideShockley

p.d.Frank

p.d.Edge,screw,mixedbd.typeMovementEdgeOnlyclimb(111)3.Imperfect(orPartial)dislocation1.Concept:2.Commonp.d.inFCCEndShockleyp.d.line3.RelationshipbetweenP.d.andS.F.P.d.isalwayslinkedtoS.F.(111)P.d.S.F.However,S.F.maybeornotbelinkedtoP.d.End

isbofd.beforereaction

isbofd.afterreactionEx.Mayitoccurspontaneously？

(1)fcc:

(2)fcc:①Geometry:②Energy:

(1)G:Ybut，no

(2)G:Yand，yes4.d.reaction1.SpontaneousconditionsEnd1)Extendedd.inFCCExam：2.Exam.ford.reactionUnitd.on｛111｝planeinFCCcanbeposedintotwopartialdislocationsandstackingfaultsbetweenthem.EndUnitedged.posesintoextendedd.Unitmixedd.posesintoextendedd.1)Extendedd.inFCCExam：2.Exam.ford.reactionUnitd.on｛111｝planeinFCCcanbeposedintotwopartialdislocationsandstackingfaultsbetweenthem.Force!End2)Equilibriumwidthofextendedd.,,,areedgeandscrewcomponentsofthetwoBurgersvectorsoftwopartialdislocations.G—shearmodulus

γ—SSFE(similarwiththesurfaceenergydensityorsurfacetension)=Equilibriumdistancebetweentwop.d.ofextendedd.Repulsionforcebetweentwopartiald.separatesthem.AttractionforcefromS.F.impedestheseparation.Theequilibriumoftherepulsionandattractionleadstotheequilibriumdistance(d0)betweenthetwopartiald.Nof:s//eEndEx.8Forfcc,shearmodulus,latticeparameter

,stackingfaultsenergy.Calculatetheequilibriumwidthofextendedd.on(111)plane.

SubstituteＧ,a,γ,ν=1/3Wegetd0≈3.6nm

G=4.8×1010Paa=0.36nmEnd3)EffectofS.S.F.E.onequilibriumwidthofextendedd.

S.S.F.E.↓→attraction↓→E.W.↑S.S.F.E.(J/m2

)E.W.ofE.D.(nm)MetalsAuCoNi

Al

Cu

Ag

0.02

0.20.04

0.06

35.0

2.0

12.0

0.25

1.5

0.02

5.7

10.0

S.F.E.andequilibriumwidthofextendedd.formetalsEndThompsontetrahedrona)FCCunitcellb)foldedc)unfoldedEndcccThompsontetrahedrona)FCCunitcellb)foldedc)unfoldedEndPerfectd.Shockleyp.d.Frankp.d.L-Cd.Discussion1.WhatisthedifferencebetweenthethreetypesofstackingfaultsinFCC?2.Howtoproduceedge,screwormixedShockley

partialdislocationbyslip?3.HowcanyouwriteThompsontetrahedronbyyourself?Discussion5.Howtounderstandthedefinitionofdislocation?(1)imperfectioninvolvingarowofatoms,(2)theboundarylinebetweenthepartslippedandtobeslipped.6.Couldyouproduceadislocation?Ifyes,trytodescribeit.(1)insertahalfextraplaneofatoms,(2)inserta20*20nmsquareatomplane,(3)insertahalfcylindricalplaneofatoms.(4)insertalineofatoms,(5)extractalineofatoms13Discussion144.6

PlanedefectsGrainboundary晶界

Subgrainboundary亞晶界

Twinboundary孿晶界

Phaseboundary相界

Stackingfaults堆垛層錯

Surface表面

4.6

PlanedefectsGrainboundarystructureandGBenergySurfaceandsurfaceenergyAdsorptionatsurfaceorgrainboundaryWettingMicrostructureevolutiondependenceoninterfaceenergyGrainBoundariesAgrainboundaryistheinterfacebetweentwocrystals(orgrains)ofthesamematerial,whichhavedifferentorientations(meaningthattheirlatticesdonotmatchup).GrainboundarystructureisathinlayerofatomicdisorderbetweenthetwolatticesBecauseofthelocaldisorder,atomsonthegrainboundaryhaveahigherenergythanthosewithinthegrain(justlikesurfaces)Grainboundariesalsohavea(specific)grain

boundaryenergy:gG(J/m2)GrainboundarystructureandGBenergy

Subgrainboundary:orientationdifference<10oLow-angletiltboundaryTypicalstructure:Alineofdislocationwiththesameb,informofdislocationwall.DislocationdistanceＤ：1.Low-angleGBstructureTwotypesoflow-angleGBLow-angletiltboundaryLow-angletwistboundaryLow-angleGBcomposedofdislocationpit

(1500×)2.NormalGBOrientationdifference>10o;GrainboundarystructureisthecomplicatedstructurewithvariousmodelsEnergyincrementresultingfromaunitareaGBGBenergyforlow-angleGB()

isaconstant,whereGisshearmodulusbisBurgersvector,visPoisonratioBisaconstantassociatedwiththeradiusofdislocationcentralareaθisorientationdifference3.晶界能3.GBenergy2)GBenergyforhigh-angleGB()

Low-angleGBenergy;Inspiteof△orientation;Nearlyaconstant;WellrelatedtoelasticmodulusE.CuGBenergyVS△orientationE（GPa）HAGBenergy（J/m2）SnNiFeCuAu40193196115770.160.690.780.600.36MetalsOtherplanedefectsTwinBoundaries(~0.02J/m2)TwinningdeformationandslidingdeformationOtherplanardefectsTwinBoundariesOtherplanedefectsPhaseBoundariesbetweenthealpha(gray)andbeta(white)phasesinTi6Al4ValloyPlanardefectsbystackingsequenceerrorSSFE(J/m2

)

MetalsAuCo

Ni

Al

CuAg0.02

0.20

0.04

0.06

0.25

0.02

EndStackingfaultNormalsequenceAABBCC△△△△△ABCBCA△△▽△△ExtractAlayerABABCB△▽△△▽InsertB

layerOtherplanedefectsStackingfaultenergy15Surfaceandsurfaceenergy

WhySurfacesAreImportantinMater.Sci.Eng.Surfacesinsolidaretheinterfacebetweenasolidanditsenvironment

Chemicalandphysicalinteractionsoccuratsurfacescorrosionphenomenaoxidationelectrochemicalreactionschemicalreactionsadsorption/desorption

Surfacescanhavecatalyticactivity

Processessuchaswelding,soldering,thinfilmdepositiondependonsurfacecleanlinessorstructure.ⅰ)Unsaturatedbondsⅱ)vanderWaalsforceCrosssectionofNaClsurface1.Atomicstructureofsurface(VSbulk)Surfaces(FreeSurfaces)Surfaceenergy(surfacetension)SupposeacrystalisfracturedcleanlytoexposetwofreshlatticeplanesWork,W,isexpendedtocleavethecrystalinhalf(strikingwithahammer,etc).ThequantityW/AistheworkrequiredtoformunitareaoffreshsurfaceThisiscalledthesurfaceenergyγs---Usuallygiventhesymbolσs

(surfacetension)

Dependsonthetypeoflatticeplaneexposed(anisotropy)/isotropyClose-packedplanestendtohavelowvaluesCrystalstendtoadoptshapesthatexposethelowγssurfacesasmuchaspossible(Anisotropycausesmanycrystalstohavefacetedpolyhedralshapes).Energyincrementresultingfromaunitareasurface

—GBenergy

E—Elasticmodulus

b—Distancebetweensurfaceatoms

2.Surfaceenergyⅰ)Mutationofnano-powderⅱ)DrivingforceofpowdersinteringTerrace-likemorphology3.SurfacemorphologyofcrystalGenerally,Close-packedplaneSecondaryCPplane4.EffectofSEonmaterialpropertySurfaces(FreeSurfaces)AtomicstructureofcrystalsurfacesdescribedbytheTerrace-Ledge-Kink(TLK)model(臺地-棱階-彎結(jié)模型)Growthordissolutionofcrystalsoftenoccursbyatomsattaching/detachingatledgeandkinksitesonthesurface.Asatomscontinuallyattach/detach,theledgeeitheradvancesorrecedesThiscausesoneterracetogroworshrinkKossel-Stranski-VolmermodelSurfaces(FreeSurfaces)107108Surfaces(FreeSurfaces)AtomicstructureofcrystalsurfacesdescribedbytheTerrace-Ledge-Kink(TLK)Model:Growthordissolutionofcrystalsoftenoccursbyatomsattaching/detachingatledgeandkinksitesonthesurface.Asatomscontinuallyattach/detach,theledgeeitheradvancesorrecedesThiscausesoneterracetogrowandanothertoshrinkFrankmodelScrewdislocationatsurfaceofSiCsinglecrystal.DarklinesaretheatomicstepsatthesurfaceScrewdislocationatsurfaceofSiCsinglecrystal.DarklinesaretheatomicstepsatthesurfaceFrankmodelJacksonmodel

Enrichmentofforeignatomsormoleculesatsurfaceorgrainboundaryⅰ)Decreasethefreeenergy,spontaneouslyⅱ)ExothermicreactionT↑desorptio