研一-材料結(jié)構(gòu)imperfections.一般指固體中晶體缺陷也就

Chapter5Imperfectionsinorderedmedia

NanjingBriefThestructureoforderedmaterialsalwaysincludessome Theimperfectionsresultinbreakingofsymmetryonawithanidealreference(3)Classofimperfectionswithanidealreference(3)Classofimperfectionsaccordingtotheeachofthesecategoriesofimperfectionsinvolvessomesymmetriesoftheorderedreferenceimperfection,surface4Thischaterwillbeintroduced ointimimperfection,surface

Nanjing缺陷對物理性能的1晶體的主要特征是其原子（分子）的周期性規(guī)則排。

Nanjing缺陷對物理性能的物理性能可大致分2結(jié)構(gòu)敏感性—如屈服強度與斷裂強度等，對于同2結(jié)構(gòu)敏感性—如屈服強度與斷裂強度等，對于同種材料的不同樣品進量的結(jié)果，往往差異很大，

Nanjing實際情況相對

Nanjing因為理想完整的沒有任何晶體缺陷的固體材料是不存在的多或少地都受到晶體缺陷的影響。，絕對非結(jié)構(gòu)敏感的固體性能也是不存在的 一種性能多或少地都受到晶體缺陷的影響。金屬的晶體結(jié)構(gòu)與電子結(jié)構(gòu)，在金屬電子論的基礎(chǔ)上進行理論計算，再將計算結(jié)果直接和實驗數(shù)據(jù)相比較，即可以判定理論(6)但是在研究結(jié)構(gòu)敏感的性能時，由于晶體中的缺陷的類型、分布和運動起關(guān)鍵作用，因此，必須首先研究晶體缺陷的具

Nanjing具體事體密度的變化。金屬晶體中出現(xiàn)空位 體密度的變化。金屬晶體中出現(xiàn)空位其體積膨脹、密度下

Nanjing例如，在NaCl晶體中摻入適量Ca2+離子以替位的方式占保持晶體的電中性，必將出現(xiàn)一些正保持晶體的電中性，必將出現(xiàn)一些正

Nanjing金屬材料中點缺陷引起的電阻升高可達金屬材料中點缺陷引起的電阻升高可達

Nanjing賴于溫度和晶體的純度。因為溫度升高和發(fā)向空帶提供電子或接受滿帶電子，使離發(fā)向空帶提供電子或接受滿帶電子，使離現(xiàn)出類似于半導(dǎo)體的導(dǎo)電特

Nanjing淀出相應(yīng)的離子的原子，這說明載流子是正負實淀出相應(yīng)的離子的原子，這說明載流子是正負這些實驗事實都證實了離子晶體的導(dǎo)電性與缺NaC這些實驗事實都證實了離子晶體的導(dǎo)電性與缺

Nanjing擴散及相關(guān)的相點缺陷是不斷運動著的，面以位為說明運動。位周圍原子的熱 給空的運創(chuàng)造空位是通過與周圍原子不斷地換位實現(xiàn)運動。空運動時必然會引起晶格點陣發(fā)生而要服能空位運動過程中如遇到間隙原，位便 ，種現(xiàn)稱為復(fù)。空位運動到錯晶界及表面晶體陷處將 這樣點缺陷在能量起伏的支，斷產(chǎn)、運和消亡點缺陷的運動實際上是原子移的這種缺陷的動所造成的原子遷移正是擴現(xiàn)象基。

Nanjing由于離子晶體的由于離子晶體的價帶與導(dǎo)帶間有很寬的禁可以束縛電子或者空穴在其周圍形成束縛態(tài)，這樣可以束縛電子或者空穴在其周圍形成束縛態(tài)，這樣

Nanjing色心，Color的基獲一個自由電子或自由空穴時才是一個吸收的基

Nanjing色心，Color

Nanjing色心，Color捕獲電子的色心兩個相鄰的F心構(gòu)成F2心三個相鄰的F心構(gòu)成F3心4兩個相鄰的負離子空位俘獲一個電子構(gòu)成心

NanjingColorNanjingA+X-中的俘獲電子形成的各種色心，Color把堿鹵晶體在鹵素蒸汽中加熱后淬火，可出1V心：一個正離子空位俘獲一個空穴，是F心的反型。兩個相鄰的V心構(gòu)成V2心，是F2心的反型兩個相鄰的正離子空位俘獲一個空穴構(gòu)成V3心R心的反型

Nanjing色心，Color空NanjingA+X-中的俘獲空穴形成的各種利用點缺陷可以引起晶體光學(xué)性能變化的原理，可以為透 色玻璃、彩色水泥、彩釉、色料等。例如，藍寶石是Al2O3單晶呈無色，而紅寶石是在這種單晶氧化物中加入少量的Cr2O3。這

Nanjing色心 作用例如在激光晶體中，由于色心的存在（比量熱能，使得其性能降低，甚至炸由于晶體量熱能，使得其性能降低，甚至炸

Nanjing比熱容“反?！?/p>

Nanjing力學(xué)缺陷是非平衡點缺陷，是不穩(wěn)定的缺陷是非平衡點缺陷，是不穩(wěn)定的，最后又趨于平衡在加熱過程中，最后又趨于平衡

Nanjing缺陷分

NanjingPoint

Linede

Surace/Inter

VoidsVoids/

Nanjing

Nanjing5.1PointIngeneral,singlecomponentmaterials:vacanciesAcrystalisinastateofthermodynamicequilibriumitsfreeenergyG=H-TSisWhenacrystaliscomple yfreeofimperfections,theenthalpyHisminimizedandthebindingenergybetweentheconstituentsis ized.ThusatT=0K,thisistheequilibriumconfiguration.TheentropySincreaseswhenimperfectionsareadded,thus,atnonzerotemperaturestheequilibriumstatemaycontainimperfections.

NanjingG(perfectGG(perfectG(GibbsfeeCertainCertainequilibriumnumberofvacanciesarepreferredatT>

NanjingPoint

NanjingSchottkySchottky(PointFrenkelImperfectImperfectpoint-likeregionsinthecrystalaboutthesizeof1-atomic

NanjingAvacancyexistswhenasitethatisnormallyoccupiedintheperfectcrystalisunoccupied.Forexample,avacancycanbecreatedbyforcinganatomontoaninterstitialsite,toadislocationcore,toa rainboundar,ortothefreesurface.Thefollowingfigureshowstheprocessofmovinganfromthebulktothesurfacein2DByremovingtheatomtoasiteatasurfacestep,theesfromfour-coordinatedtotwo-coordinated.Thechangeincoordinationisresponsibleforapositiveenthalpyofformationhf foreachvacancy.

Nanjing

NanjingAtomsaroundthevacancy

NanjingvacancieswithNatomsandN+nsites.ThevacancieswithNatomsandN+nsites.ThestateisaperfectcrystalofNatomsandasetofnvacantsurfaceHfWherehfistheenthalpyofformationofasinglesurroundingthevacantsite.Boltzmann’sisgivensurroundingthevacantsite.Boltzmann’sisgivenmSc

k Nanjing cklnmkln(NWheremisthenumberofdistinguishablewaysofarrangingNatomsandnvacanciesonN+nConsideringGHn(hfTSv)kT[(Nn)ln(Nn)NlnNnlnTheSterling’sapproximationoflnX!XlnXisused

NanjinggiventemperatureisthatwhichminimizesTheequilibriumnumbergiventemperatureisthatwhichminimizesG

fTsvkT

NTheequilibriumfractionofvacancyis2GxxvnN kT

NanjingcannowbeobservedIncannowbeobservedInhistory,vacancyisproventoexistbySimmonsandBalluffiin1960s.Acubiccrystaluniformlyheated,LoistheaxiallengthattemperatureandListhedifferencebetweenlengthandlengthandLo.So,we Byconsideringthechangesinnumbersofunitcell,ratherthanchangesinlength,asimplerelationcanbederivedforthefractionofvacancysiteasfollows.

NanjinglengthofthespecimenintermsofthereferenceL0lengthofthespecimenintermsofthereferenceL0and 0Theactualnumberofcellsalongthespecimenchangesduringheatingduetovacancycreation NNccL0a0Whichtofirstorderisequal

NanjingL0 L aNcNc

L

a0 0 0 aNc1 0ThefractionofvacantsitesisthereforegivenN axv c a0

NanjingSimmonsandBalluffimeasuredtheodependenceofL/ anda/ inseveralmetals,oforaluminumareplottedinthefollowingfigure.ItdemonstratedthatvacanciesarethepredominantpointdefectinAl.

NanjingForbetterunderstandingthetemperaturedependenceoftheequilibriumfractionofvacancies,itisinstructivetomakesomecalculationsbyassumingThefollowingtablerapidincreaseofequilibriumThefollowingtablerapidincreaseofequilibriumfractionwithincreasingtemperature.rapiddecreaseofequilibriumfractionincreasingenthalpyof

Nanjing

NanjingExperimentsshowthatvaluesofhfformetalsrangefrom0.4to4eVandexp(sv/k)~1,asshowninthefollowingtable

Nanjing(1)Interstitialscomprisethesecondmajorcategoryofpoint ogoustovacancy,bytakinganatomfromasurfacesiteandinsertingitintoaninteriorsitethatisnot occuied.Asshowninthefollowin fiure.

Nanjing

Nanjing(2)(2)Forsinglecomponentcrystal(self-interstitial),equilibriumfractionofinterstitialsisgivenxinN kT

NanjingNonequilibriumpointSofar,weonlyconsideredequilibriumpointdefectsvacancyandMuchhighernon-equilibriumconcentrationsofpointdefectsincrstalcanbecreatedb thefollowin (i)Annealing:ifthecoolingrateissufficientlyrapid,thepointdefectscannotmigratetofreesurfaceorothersinks,sousuallyhighconcentrationofpointdefectscanbeIrradiationbyenergeticIonthediffusionalprocessescannotoccuratsignificantColdworking:thisinvolvesirreversiblemechanicaldeformationthediffusionalprocessescannotoccuratsignificant

NanjingMobilityofpointPointdefects emobileathighTherateofmigrationRate~

hm kTwherehmistheenthalpyofmigrationofthepointdefect,thus,migrationofpointdefectdependsstronglyonPointdefectmigrationisimportant:deformationof(chargeddefects)ionicconduction,

NanjingGenerally,interstitialdiffuserapidthan

NanjingSolid(1)Aalloyisformedwhenmorethanonespeciesismixed.Indilutealloys,theminoritycomponentatomcanbeconsideredaspointdefect.

NanjingSolid(2)Ifthesiteoccupiedbyminorityspeciesisnormallyunoccupied,thecrystaliscalledinterstitialsolidsolution,otherwise,substitutionalsolidsolution.3The fiNiOinMgO:NisubstitutedforCaOinZrO2,bothinterstitialandpointdefectsareNinFe(fcc):interstitialpointdefectsoctahedral

Nanjing

Nanjingorder-disorderoccurs:above683K,theCuandAuatomsformfccstructurewithrandomsites,asshownintheorder-disorderoccurs:above683K,theCuandAuatomsformfccstructurewithrandomsites,asshowninthefollowingfigure(a)and(b).Below683K,itformstetragonalstructurewithCu(0,0,0)andAu(?,?,highertemperaturedisorderedsolidsolutiontolowertemperatureorderedsolidsolution;somesymmetriesarebroken:e.g.,a/2[0,1/2,1/2]transition,3-foldaxisalonghightemperaturecubicphase[111]axis,4-foldaxis,etc.

Nanjing

Nanjing

NanjingInoneInoneword,substitutional/interstitialimpuritypointForeignForeignatomsittinginthevoidofaE.g.CsittingintheoctahedralvoidinHTFCC-ForeignatomreplacingtheparentatomintheE.g.CusittinginthelatticesiteofFCC-INTERSTITIAL

NanjingSubstitutionalpoint

NanjingInterstitialInterstitialCsittingintheoctahedralvoidinHTFCC-rOctahedralvoid/rFCCatom=rFe-FCC=1.29 rC=0.71

rOctahedralvoid=0.414x1.29=0.53CompressivestrainsaroundtheCSolubilitylimitedto2wt%(9.3

NanjingPointdefectsinionicusuallyhaveanassociatedThenetchargeinaunitcelliszero,thefollowingfigureifacationvacancyiscreated,thevacancyhasaneativechareassumin thattheelectronoriinall bythecationremainslocalizednearthevacantsite),asshowninfigure(b).anioninterstitialinfigure(c)hasnetnegative

Nanjing

NanjingPointdefectsinionicKr?nger-VinkYpointdefectsarerepresentedbyXYX:whatisonthesite,eitherVforvacanc or,ifoccuiedbanelement,theelementsymbol.Y:whattypeofthesiteisoccupiedbyX,eitheriforaninterstitialor,ifnormallyoccupiedbyanelement,thesymbolforthatelement.Z:ThechargerelativetothenormalionchargeonthesiteY,usingdotstorepresentpositiverelativecharge,primestoindicatenegativerelativecharge,andxtoindicatezerorelativecharge.

Nanjing PointdefectsinionicKr?nger-VinkExampleinKCl,thecationandanionvacancyisrepresentedbyVKandV ,Example-2:theanioninterstitialinUO:(3)Example-3:(3)Example-3:AcationonacationsiteinpureUO2U

Nanjing5.1.6PointdefectsinionicSchottkyandFrenkelInordertomaintainchargeneutrality,pointdefectshavingchargesofoppositesignmustcoexist.Twoidealizedforms pensatingpointdefectsareSchottkyandFrenkeldefect.ASchottkydefectconsistsofanionandcationvacanciesinKCl:V. andV'inTiO2:inTiO2:VO

Nanjing5.1.6PointdefectsinionicSchottkyandFrenkelAFrenkeldefectisformedwhenaionmovesfromnormalsiteinthecrystalintoanearbyintersititialCationFrenkelpairinLi

V

Li. AnionAnionFrenkelpairin V..and Oi

Nanjing5.1.6PointdefectsinionicSchottkyandFrenkel

Nanjing5.1.6PointdefectsinionicSchottkyandFrenkelTounderstandavarietyofprocessesandphenomenarelatingtopointdefectsinioniccrystal,thepointdefectsareexpressedasachemicalequation.Forexample,theformationreactionforcationFrenkelpairformationinAgBr is

Agx Ag.VTheformationreactionforaSchottkdefectinAl2O3Null2V'''3V The“Null”denotestherelocationofoneAl2O3“formulaunit”ofionstothesurface,soastocreatefivevacantsitesintheinteriorofthecrystal.

Nanjing5.1.6PointdefectsinionicSchottkyandFrenkelSuchequationsmustchargebalance:thesumofchargeonbothsidesmassbalance:thetotalnumberofionsoratomsissameonbothsitebalance:sitesmustbecreatedinproportionsforthestoichiometryofthe

Nanjing5.1.6PointdefectsinionicSchottkyandFrenkelTheequilibriumconcentrationsofchargedSchottkyandFrenkeldefectscanbederivedsimilarlytothoseforunchargedpointdefects,asdiscussedabove.Butitisnecessarytoaccountfortheformationofpairsofdefects.ifhfistheformationenthalpyforapairofions(i.e.,onecationcationandoneanion),thentheequilibriumfractionofx2k2kT2kT

NanjingPointdefectsinionicSchottkyandFrenkel

NanjingPointdefectsinionicSchottkyandFrenkel

Nanjing5.1.6PointdefectsinionicDefectsassociatedwithoff-ZnOheatedinZnvapour→ (yTheexcesscationsoccupyinterstitialTheelectrons(2e)releasedstayassociatedtotheinterstitial

Nanjing5.1.6PointdefectsinionicDefectsassociatedwithoff-FeOheatedinoxygenatmosphere→ (xVacantcationsitesareChargeiscompensatedbyconversionofferroustoferricFe2+→Fe3++DepartmentanjingForeveryvacancy(ofFecation)Departmentanjing5.1.6PointdefectsinionicDefectsassociatedwithIntrinsicdefect:pointdefectsinvolvingtheconstituentExtrinsicdefect:defectsassociatedwithimurit,whichisgenerallydominantatlowtemperaturebecauseatlowtemperature,thethermodynamicequilibriumdefectshaveverylowcontent.

Nanjing5.1.6PointdefectsinionicDefectsassociatedwithTherelationshipbetweenintrinsicandextrinsicpoint

Nanjing5.1.6PointdefectsinionicDefectsassociatedwithImpuritiesareelementspresentinthematerialthatarefromthoseinthecompoundDopantsareintentionallyaddedimpurities(tomakealloysoraffectchangesinproperties).Alloyformationmostlikelywhendopantanionsandcationsarecloseinsizetooriginalmaterial.

Nanjing5.1.6PointdefectsinionicDefectsassociatedwithIsovalentdopants:substitutionspecieshavethesameNaCl:AgCl→Na1-

(alloyoncationsite)(alloyonanionsite)Aleovalentdopant:substitutionspecieshasdifferentNaCl:CaCl2couldbeeitherNa1-orNa1-xCaxClCli’,orotherformations,asshown

Nanjing5.1.6PointdefectsinionicDefectsassociatedwith(1)Generally,wedonotdistinguishimpuritiesand Hereweconsidertheimuritieshavin differentvalencefromhostlattice.AsimpleexampleistheincorporationofsmallamountCaCl2intoKCl,asdiscussedinthelast CaCl V' 2KClindicatestheremovaloftwopairsofthehostcrystal’sanionandcationstothecrystalsurface.CaClCa..2VCaClCa..2V'2Clx2iK

Nanjing5.1.6PointdefectsinionicDefectsassociatedwithExperimentaldatafordensitychangeversusimpuritycontentcanhelpindistinguishingbetweenvariousimpurityincororationreaction.Asanexamle,weconsidertheincorporationofZrO2intoY2O3.

V

Nanjing5.1.6PointdefectsinionicDefectsassociatedwith3ZrO6Ox2OYVY3ZrO6Ox2OYVYNanjing2YOi2ZrO

2Zr

5.1.6PointdefectsinionicDefectsassociatedwithGenerally,therearemanypossibleschemesforimpurityionincorporationintoahostlattice.Predicationofimpuritysitescanbe uidedb considerationofthelocalcharearoundasiteandgeometricconstraintsimposedbytreatingtheionsashardspheres.

NanjingLine thatlocalizedalongaspacecurvethroughanorderedmediumarecalledTwomaincategoriesoflinedislocation:involvestranslationofonepartwithrespecttoanotherpart,nearlypresentinallcrystallinematerialsandinliquidcrystalsdisclination:involvesrotationofonepartrelativetoanotherpart,commonlypresentinliquidcrystals.Linedefectsarenonequilibrium

Nanjing5.2LineVolterra,amathematician,studiedtheelasticpropertiesoflinedefectsbeforetheexistenceofsuchdefectsinmaterialswasknown.ContinuouselasticmediumwaschosenasTheprocessforcreatingthevarioustypesofimperfectionsareshowninthefollowingthedetailsthedetailsofatomicandmolecularstructureinthisregionareofspecial

Nanjing

Nanjing5.2LineFigure(b)thecylindricalbodyiscutfromitsoutsidetoitscentralaxis,e.g.,cutinthex-zFigure(c)aforceisappliedtointroduceatranslationofcutsurfacerelativetotheFigure(d)Thecutsurfacesarerejoinedinsuchawaythattheoriginalsymmetryrelationsofthematerialarepacrosstherejoinedcutsurface,thismayrequirethatmaterialisaddedorremovedfromthecutsurfacespriorto

Nanjing5.2LineVarioustypesoflinedefectscanbeformedbyconsideringthepossibleorientationswithrespecttothecylinderaxisforrelativetranslationsorrotationaxes.Translationscanbeparalleltothreeaxesofx,y,andshowninthefollowingFigure(c)formsscrewdislocation,paralleltothethisleadstotwocasesforthestructureofdislocation:Figure(a)and(b)areequivalent,formingedgedislocation,whichisresultedFigure(c)formsscrewdislocation,paralleltotheDislocationsincrystalbreakthetranslationalsymmetrylocallyalongthedislocationline,crystalsymmetryis intheimmediatevicinityofthedislocationline.

Nanjing

Nanjing5.2LineInasimilarmanner,typesofdisclinationscanbeclassifiedbconsiderintherotationsaroundx,,andzaxes,showninthefollowingfigure.Figure(a):wedgedisclination:rotatedaroundtheaxistothedisclinationFigure(b)and(c):twistdisclination:rotatedaroundthenormaltothedisclinationDisclinationsinvolvebreakingtherotationallocally,alongthedisclinationenergiesincrystalsothatessentiallyallenergiesincrystalsothatessentiallyallcrystalsdisclination-free.OrientationalchangesarelesscostlymuchlowerelasticconstantliquidcrystalsanddefectsarequiteNanjing

NanjingLine1Inhistor,SirLawrenceBra ,etal.simulatedthe2Ddislocationbyusingsoapbubbles.Surfacetensionforcescausethebubblestohavealong-rangeattractiveinteractionandashort-rangerepulsiveinteraction,similartotheatomsincrystal.Soclosepacked120rhombuslatticeisThereare0-Dand1-DThedefectnearthesingleanddoublelines:itistheendofan“extrarow”ofbubbles,edgedislocationImportantfeaturesofdislocation:first,itislocalized,second,thesymmetryoperationsoftheperfectcrystalare awayfromthecoreoftheimperfection.

Nanjing

NanjingLine2Thestructureofdislocationsattheatomiclevelinasimplecrystalcanbeconsideredwiththeaidofa“ball-and-stick”modelofamonatomicprimitivecubicstructure.ThefollowingFig-(a)isaedgeThelargestdisplacementsfromtheidealsitesconcentratedalongaline,whichiscalledadislocationcore.(iii)Thecenterofthedislocationcoreregiondefinesthepositionofthedislocationintheofthecrystal,alongtheline(v)Alongwiththisofthecrystal,alongtheline(v)Alongwiththisedgedislocationisanextra“halfplane”atomsABCDthatextendsupwardfromthedislocation

Nanjing

NanjingLine2Theball-and-stickmodeofascrewdislocationisalsoshownintheabovefigure.TheatomicdisplacementareconcentratedalongaThe lineextendsfromthefrontsurfacetobacksurface,alonglineThesurfacestepsarestructureaboutthedislocationTheterm“screwdislocation”arisesbecausethesedisplacementscausetheatomplanesnormaltothedislocation nnectedstructureaboutthedislocation

NanjingLineEvidenceforBeforetheadventofmicroscopictechniques,themainexperimentalevidencefordislocationconsistedoftheobservationof“slipbands”onthesurfaceofasinglecrystal,whichishighlypolished,afteruniaxialdeformation.Afterdeformation,numerousmicroscopicstepsarepresentonthesurface,schematicallyshowninthefollowingfigure.(4)Stressis(4)Stressisdefinedastheratiooftheappliedforcetotheofthematerialonwhichitisacting,ashearstresspresentwhentheforceactingonaplanehasanin-

Nanjing

NanjingLineEvidencefor Carefulcharacterizationofslipbandsshowthattheplasticdeformationofcrystalsoccurspreferentiallyoncertainplaneshavingahighnumberofatomsperunitarea,whichalsoareplaneswithrelativelylargeinterplannarspacing. Generally,thereareseveralsymmetry-relatedplanesmeetingsuchcriteria. Theslipplanesthatwillbeactivatedarethoseonwhichtheresolvedshearstressisthehighest.

NanjingLineEvidencefor Thefollowingsimple ysisofthetheoreticalstrengthofaperfectcrystalwillshowthatperfectcrystalwouldbemuchstrongerthanactualcrystal,anditdirectlyimpliesthatdislocationsplayaprincipleroleintheplasticdeformationofcrystals. Asimple1Dinteratomicforcemodelcanbeusedtoestimatedthetheoreticalshearstrengthofaperfect3Dcrystal.Theatomicmotionsinvolvedinthesimultaneousshearofoneplaneofatomsoverthe“saddlepoint”configurationintheadjacentplaneareillustratedinaclosepackedcrystalinthefollowingfigure

NanjingLineEvidenceforTheatomdiameterisd.Theinteratomicpotentialfunctionforthesheardisplacementmustbeaperiodicfunctionofx,withperiodd.thepotentialUperatomintheshearplane(xyplane)canbeapproximated:U(x) Ucos(2x WhereU0andU1areconstantandxistheNanjingNanjing

NanjingLineEvidencefor(11)Theshear necessarytocausetheoffigure(b)isgiven(x) dU2NAU1sin(2xA WhereNAisthenumberofatomsperunitareaintheshear12Theshearstressiszeroatx=0stableeuilibrium andalsoatx=d/2(unstableequilibrium).The umshearstressoccursatx=d/4:

NanjingLineEvidencefordThedTheconstantU1canbeestimatedbyusingHooke’slaw,relatedtheshear totheshear bythe

2Ninterplanarspacing istheshearmodulus istheratioofinterplanarspacing

NanjingTheinterplanarspacingTheinterplanarspacingforsuchplanesisd1112dAnd 6x/6Inaddition,NA22d33/2dU1NanjingEvidencefordislocations tativeestimateofthetheoreticalstrengthcanbeobtainedbyusinggeometricvaluesappropiateforshearofaperfectmonatomicFCCcrystalonthe(111)planinthe[110]LineEvidencefordislocationsAndthusthetheoreticalshearstrength 6 Amore ysisindicatesatheoreticalshear

foraperfectmonatomicFCC

NanjingLineEvidencefordislocationsNowwecomparethetheoreticalstrengthofacrystalwiththeobservedstrengthofanactualcrystal.

4.5104

,givingatheoreticalstrength3103MPaTheactualshearstrengthhowever,is0.3MPa,lowerbyafactorofsome104.ThatisattributedtotheThisfindingledtothenearlysimultaneousbutseparateproposalsin1934byTaylor,PolanyiandOrowanthatdislocationshouldberesponsibleforplasticdeformationofcrystal.TEMfrom1950sconfirmedtheirproposals.

NanjingLineDislocationsinsideaverythin(typicallylessthan0.5micrometer)crystalcanbeimagedintheTEMbecauseofthelocalizedatomicdisplacementandresultingelasticstrainfield,whicharever lareonl neardislocationcore.ThedarklinesinthefollowingfigurecorrespondtodislocationinNiAlsinglecrystal.Thetypicalwidthofthedislocationisabout10nm,farinexcessofthelatticeconstantof0.36nm.

Nanjing

NanjingLineDislocationsarealsopresentinsmecticliquidtypicallyshowninthefollowing

Nanjing

NanjingLineCharacterizationofdislocation:tanentvectorandBurersThegeometryofadislocationisdefinedbytwovectors:unittangentvector andtheburgersvectorbThetangentvectorisaunitvectorthatistangentialtodislocationlineat Becauseofthedislocationlinemaybecurved,thevectorwillgenerallyvaryalongagivendislocationThesenseoftangentvectorisarbitrary,i.e.,whetheritpointforwardorbackwardalongtheline,butonceitisset,itwilldeterminethesenseofBurgersvector.

NanjingLineCharacterizationofdislocation:tanentvectorandBurers TheburgersvectorbisdefinedinreferencetotheBurgerscircuit.HereweusetheSF/RH(start-finish,right-hand)ruletodefinethebasfollows.Arbitrarilychoosethepositivesenseoftheunit(ii)Bytraversingrows(ii)Bytraversingrowsoflatticepointsinthecrystal,makeright-handcircuitcontainingthedislocation,thewouldbeaclosedcircuitinaperfectcrystal.(iii)Generallyitisconvenienttochooseaquadrilateralwith(iv)Thevectorfromstartingpointtofinishing(iv)ThevectorfromstartingpointtofinishingpointisBurgersvectorofthe

NanjingLineCharacterizationofdislocation:tanentvectorandBurers

NanjingLineCharacterizationofdislocation:tanentvectorandBurerszyzyx

NanjingLineCharacterizationofdislocation:tangentvectorandBurgersInthefollowingfigure,ifwe

t

bytakinga?handcircuitsurroundingthedislocationcore,for?fromStoFwe

b

whereaisthewefind

a??

pointstowardtheextraplanethatisassociatedwiththisedgeiftaking?

,

b

t?ba

pointstowardtheextra

Nanjing

NanjingLineCharacterizationofdislocation:tangentvectorandBurgersThesameprocedureisappliedtocharacterizetheofascrew ? b ? is

Nanjing

NanjingLineCharacterizationofdislocation:tangentvectorandBurgersSomepropertiesofdislocationarelistedTheBurgersvectorisconserved;agivendislocationhasoneconstantBurersvectorevenasthetanentvectorAdislocationcannotendinsideacrystal,itmustendonagrainboundary,freesurface,oranotherdislocationorrejoinitselftoformadislocationloopApureedgehas?perpendiculartobeverywherethedislocationcurve.Thevector? pointstowardextrahalfplaneofApurescrewdislocationhas?eitherparallelorantiparalleltobeverywherealongthedislocationcurve.Arighthandscrewdislocationhas?andbparallelandaleftonehas?and

NanjingLineCharacterizationofdislocation:tangentvectorandBurgersAdislocationthatisneitherpureedgenorpurescrewistobeamixeddislocation.Thevectorcomponentofarallelto?iscalledthescrewcomonentofdislocation,bs,andisgivenbybs(b?)?.

thatcomponentbe thatisperpendicularto?iscalledtheedgecomponentofthedislocation.Itisgivenbybebbs.Reservingthesense

?alsoreservesthesenseof

NanjingLineCharacterizationofdislocation:tangentvectorandBurgers Thedislocationdensity isanimportantdescriptorforacrystalthatcontainsdislocation.Thedislocationdensityisdefinedasthetotallenthofdislocationlines erunitvolumeofmaterial,sothe hastheunitof(length)-2.Ifdislocationlinesarerandomlyorientedinacrystal,thenthedislocationdensityisequaltotheaveragenumberofdislocationlinesthatpenetratearepresentativeunitareaofthemicrostructure.Theaveragedislocationspacingis yequalto

Nanjing小1、b是描述位錯點陣畸變的重要物理即：沿著x方向前進n1步，y方向前進n2步z方向n3步，步長為晶格常數(shù)abc。如果沒有位則而如果有位錯，則3、只要回路包含的位錯沒有變化，不論回路的大小得到的Burgers矢量不變

Nanjing矢量來描述這種疊加。6、如果幾條位錯線交于一點（結(jié)點），這這些位錯線Burgers矢量之和為

Nanjing

NanjingLineDislocationmotionbyslipand

Nanjing

NanjingLineDislocationmotionbyslipanddislocationmotioniscalled(2)Ingeneral,dislocationcandislocationmotioniscalled(2)Ingeneral,dislocationcanmovebyslipinanycontainsandb.Inparticular,dislocationtendshavehighestmobilityonplaneswithahighdensityof(3)Thefollowingfigure(a)showsthatacrystalissubjectbyshearstress.ThedislocationmovestotherightsideendsatthepositionCD,leavingastepontheleft(4)ThedislocationlineDCseparatestheslippedandunslippedregionsofthecrystal.

Nanjing??z,b

NanjingLineDislocationmotionbyslipand(5)Thefigure(b)showsthesamesortofdislocationbutwithreferencelattice,clearlyshowingtheextrahalfplaneuniversallytoindicatethecoreofanedge(6)Usinguniversallytoindicatethecoreofanedge(6)UsingtheSF/RHconvention,wecandefine

whichis??,b

Nanjing

Nanjing

Nanjing

Nanjing

Nanjing

Nanjingyyy5.2LineDislocationmotionbyslipandAscrewdislocationcanalsobegeneratedasillustratedthefollowingInthiscase,thedirectionofthestressisparalleltothedislocationline.ThedislocationmovesfromEFintothecrystalandend(4)(4)Thedislocationseparatestheslippedandportionsofthe(5)Thestepontherightandleftfacesareintroduced(6).It(6).Itisapureright-hand

Nanjing

Nanjing

Nanjing5.2LineDislocationmotionbyslipandSo,byconsideringtheabovetwocases,weAnedgedislocationmovesparallelandascrewdislocationmovesperpendiculartothedirectionoftheshearstress.Inbothcases,thestresscausesadisplacementalongshearstressbecauseitinvolvessmallatomicdisplacementsanddisplacementsbecauseitinvolvessmallatomicdisplacementsanddisplacementsofagivenatomarecloselywiththoseofits

Nanjing5.2LineThemotionofanedgedislocationThemotionofanedgedislocationfromitsslipplanetoadjacentparallelslipplaneiscalled

Nanjing5.2Line(4)Climbofdislocationinvolvesdiffusive(4)Climbofdislocationinvolvesdiffusivemotionofdefectstowardorawayfromthedislocationcore.Aspointdefectsareemittedorabsorbedbythedislocationcore,thecorestructurecan erearrangedandthecorecanmove.(5)ThefollowingFigure(a)showsthereisaedgedislocationinamonatomiccrystalwithsquarelattice,(b)lshowtheedgeoftheextrahalf-planecanemitavacancy:anatomoccupyingasiteadjacenttothecoreofthedislocationcanjumptoasiteattheedgeofthehalf-plane,andthusextendtheextrahalf-panedownwardbyoneatomicdistance,(c)inthisprocedure,avacancyiscreatedandisfreetomigrateaway