材料科學(xué)基礎(chǔ)英文Chapter Imperfections in Solids

材料科學(xué)基礎(chǔ)英文ChapterImperfectionsinSolids第1頁/共53頁WHYSTUDYImperfectionsinSolids?Thepropertiesofsomematerialsareprofoundlyinfluencedbythepresenceofimperfections.Consequently,itisimportanttohaveaknowledgeaboutthetypesofimperfectionsthatexistandtherolestheyplayinaffectingthebehaviorofmaterials.Forexample：brass(70%copper/30%zinc)ismuchharderandstrongerthanpurecopper.第2頁/共53頁LearningObjectives

Afterstudyingthischapter,youshouldbeabletodothefollowing:1.Describebothvacancyandself-interstitialcrystallinedefects.2.Calculatetheequilibriumnumberofvacanciesinamaterialatsomespecifiedtemperature,giventherelevantconstants.3.Namethetwotypesofsolidsolutionsandprovideabriefwrittendefinitionand/orschematicsketchofeach.4.Giventhemassesandatomicweightsoftwoormoreelementsinametalalloy,calculatetheweightpercentandatompercentforeachelement.第3頁/共53頁5.Foreachofedge,screw,andmixeddislocations:(a)describeandmakeadrawingofthedislocation,(b)notethelocationofthedislocationline,and(c)indicatethedirectionalongwhichthedislocationlineextends.6.Describetheatomicstructurewithinthevicinityof(a)agrainboundaryand(b)atwinboundary.第4頁/共53頁3.1INTRODUCTIONThusfarithasbeentacitlyassumedthatperfectorderexiststhroughoutcrystallinematerialsonanatomicscale.However,suchanidealizedsoliddoesnotexist;allcontainlargenumbersofvariousdefectsorimperfections.Asamatteroffact,manyofthepropertiesofmaterialsareprofoundlysensitivetodeviationsfromcrystallineperfection;theinfluenceisnotalwaysadverse,andoftenspecificcharacteristicsaredeliberatelyfashionedbytheintroductionofcontrolledamountsornumbersofparticulardefects.第5頁/共53頁Acrystallinedefectreferstoalatticeirregularityhavingoneormoreofitsdimensionsontheorderofanatomicdiameter.Classificationofcrystallineimperfectionsisfrequentlymadeaccordingtothegeometryordimensionalityofthedefect.Severaldifferentimperfectionsarediscussedinthischapter,includingpointdefects(thoseassociatedwithoneortwoatomicpositions);linear(orone-dimensional)defects;andinterfacialdefects,orboundaries,whicharetwo-dimensional.Impuritiesinsolidsarealsodiscussed,becauseimpurityatomsmayexistaspointdefects.Finally,techniquesforthemicroscopicexaminationofdefectsandthestructureofmaterialsarebrieflydescribed.第6頁/共53頁3.2PointDefects（1）VACANCIESANDSELF-INTERSTITIALSThesimplestofthepointdefectsisavacancy,orvacantlatticesite,onenormallyoccupiedbutfromwhichanatomismissing.Scanningprobemicrographthatshowsavacancyona(111)-typesurfaceplaneforsilicon.Two-dimensionalrepresentationsofavacancyandaself-interstitial.第7頁/共53頁inessence,thepresenceofvacanciesincreasestheentropy(i.e.,therandomness)ofthecrystal.TheequilibriumnumberofvacanciesNvforagivenquantityofmaterial(usuallypermetercubed)dependsonandincreaseswithtemperatureaccordingtoNisthetotalnumberofatomicsites(mostcommonlypercubicmeter),Qvistheenergyrequiredfortheformationofavacancy(J/moloreV/atom),Tistheabsolutetemperatureinkelvins,andkisthegasorBoltzmann’sconstant.Thevalueofkis1.38×10-23J/atom·K,or8.62×10-5eV/atom·K,dependingontheunitsofQv.第8頁/共53頁Thus,thenumberofvacanciesincreasesexponentiallywithtemperature—thatis,asTincreases,soalsodoesthetermexp(-Qv/kT).Formostmetals,thefractionofvacanciesNv/Njustbelowthemeltingtemperatureisontheorderof10-4—thatis,onelatticesiteoutof10,000willbeempty.第9頁/共53頁Aself-interstitialisanatomfromthecrystalthatiscrowdedintoaninterstitialsite—asmallvoidspacethatunderordinarycircumstancesisnotoccupied.Two-dimensionalrepresentationsofavacancyandaself-interstitial.第10頁/共53頁Inmetals,aself-interstitialintroducesrelativelylargedistortionsinthesurroundinglatticebecausetheatomissubstantiallylargerthantheinterstitialpositioninwhichitissituated.Consequently,theformationofthisdefectisnothighlyprobable,anditexistsinverysmallconcentrationsthataresignificantlylowerthanforvacancies.第11頁/共53頁AFrenkeldefectisatypeofdefectincrystallinesolidswhereinanatomisdisplacedfromitslatticepositiontoaninterstitialsite,creatingavacancyattheoriginalsiteandaninterstitialdefectatthenewlocationwithinthesameelementwithoutanychangesinchemicalpropertiesFrenkelpairFrenkelvacancyvacancy+interstitial第12頁/共53頁movinganatomtothesurfaceproducesavacancySchottkydefectIfinanioniccrystaloftypeA+B?

anequalnumberofcationsandanionsaremissingfromtheirlatticesites(sothatelectricalneutralityaswellas

stoichiometry

ismaintained),thenthisdefectiscalledaSchottkydefect.第13頁/共53頁第14頁/共53頁EXAMPLEPROBLEM1Calculatetheequilibriumnumberofvacanciespercubicmeterforcopperat1000℃.Theenergyforvacancyformationis0.9eV/atom;theatomicweightanddensity(at1000℃)forcopperare63.5g/moland8.4g/cm3,respectively.Solutionitisfirstnecessary,however,todeterminethevalueofN—thenumberofatomicsitespercubicmeterforcopper,fromitsatomicweightACu,itsdensityr,andAvogadro’snumberNA,accordingto第15頁/共53頁第16頁/共53頁(2)metallicsolidsolutionsApuremetalcomposedofonlyonetypeofatomisimpossibleinreality.Itisdifficulttorefinemetalstoapurityof99.99999%Thereisalwayssomelevelofimpurityorforeignatomsinametal,leadingtotheformationofanalloyAlloys–whichimpurityatomshavebeenaddedintentionallytoimpartspecificcharacteristicstothematerial;amixtureoftwoormoremetalsorametalandanonmetal.Concept:solvent–thematrixorhost;solute–minorcomponent,e.g.Al-2.5%Cualloy

Zn-30%Cualloy

Pt900,950第17頁/共53頁Solidsolutions:thesimplesttypeofalloyAsolidsolutionisasolidthatconsistsoftwoormoreelementsatomicallydispersedomasingle-phasestructure.SeveraltermsSolventistheelementorcompoundthatispresentinthegreatestamount,alsocalledhostatoms.Soluteisusedtodenoteanelementorcompoundpresentinaminorconcentration.Asolidsolutionformswhen,asthesoluteatomsareaddedtothehostmaterial,thecrystalstructureismaintainedandnonewstructuresareformed.第18頁/共53頁Classificationofsolidsolutions(a)Substitutionalsolidsolution–soluteorimpurityatomsreplaceorsubstituteforthehostatoms(b)Interstitialsolidsolution–soluteatomsfitintothespaces/voidsbetweenthesolventorparentatoms第19頁/共53頁Severalfeaturesofthesoluteandsolventatomsdeterminethedegreetowhichtheformerdissolvesinthelatter.TheseareexpressedasfourHume–Rotheryrules,asfollows:(a)Substitutionalsolidsolution1.Atomicsizefactor.Appreciablequantitiesofasolutemaybeaccommodatedinthistypeofsolidsolutiononlywhenthedifferenceinatomicradiibetweenthetwoatomtypesislessthanabout15%.Otherwise,thesoluteatomscreatesubstantiallatticedistortionsandanewphaseforms.2.Crystalstructure.Forappreciablesolidsolubility,thecrystalstructuresformetalsofbothatomtypesmustbethesame.第20頁/共53頁3.Electronegativityfactor.Themoreelectropositiveoneelementandthemoreelectronegativetheother,thegreaterthelikelihoodthattheywillformanintermetalliccompoundinsteadofasubstitutionalsolidsolution.4.Valences.Otherfactorsbeingequal,ametalhasmoreofatendencytodissolveanothermetalofhighervalencethantodissolveoneofalowervalence.第21頁/共53頁Anexample:asubstitutionalsolidsolutionofcopperandnickel.Thesetwoelementsarecompletelysolubleinoneanotheratallproportions.Withregardtotheaforementionedrulesthatgoverndegreeofsolubility,theatomicradiiforcopperandnickelare0.128and0.125nm,respectively;bothhavetheFCCcrystalstructure;andtheirelectronegativitiesare1.9and1.8(Chapter1).Finally,themostcommonvalencesare1forcopper(althoughitsometimescanbe2)and2fornickel.第22頁/共53頁formwhentheatomicdiameterofaninterstitialimpuritysubstantiallysmallerthanthatofthehostatoms.atoms:hydrogen,carbon,nitrogenandoxygen.(b)Interstitialsolidsolution第23頁/共53頁Carbonformsaninterstitialsolidsolutionwhenaddedtoiron;themaximumconcentrationofcarbonisabout2%.Theatomicradiusofthecarbonatomismuchlessthanthatofiron:0.071nmversus0.124nm.Normally,themaximumallowableconcentrationofinterstitialimpurityatomsislow(lessthan10%).Evenverysmallimpurityatomsareordinarilylargerthantheinterstitialsites,andasaconsequence,theyintroducesomelatticestrainsontheadjacenthostatoms.第24頁/共53頁Summary:pointdefects第25頁/共53頁3.3LinearDefects-DISLOCATIONSAdislocation

isalinearorone-dimensionaldefectaroundwhichsomeoftheatomsaremisaligned.anextraportionofaplaneofatoms,orhalf-plane,theedgeofwhichterminateswithinthecrystal.Thisistermedanedgedislocation;第26頁/共53頁itisalineardefectthatcentersonthelinethatisdefinedalongtheendoftheextrahalf-planeofatoms.Thisissometimestermedthedislocationline,whichfortheedgedislocation,isperpendiculartotheplaneofthepage.第27頁/共53頁Withintheregionaroundthedislocationlinethereissomelocalizedlatticedistortion.TheatomsabovethedislocationlineinFigurearesqueezedtogether,andthosebelowarepulledapart;thisisreflectedintheslightcurvaturefortheverticalplanesofatomsastheybendaroundthisextrahalf-plane.位錯(cuò)線注意這個(gè)面第28頁/共53頁Themagnitudeofthisdistortiondecreaseswithdistanceawayfromthedislocationline;atpositionsfarremoved,thecrystallatticeisvirtuallyperfect.negativeedgedislocationpositiveedgedislocationtheedgedislocationisrepresentedbythesymbol⊥,indicatesthepositionofthedislocationlineAnedgedislocationmayalsobeformedbyanextrahalf-planeofatomsthatisincludedinthebottomportionofthecrystal;itsdesignationisa⊥第29頁/共53頁刃型位錯(cuò)刃型位錯(cuò)運(yùn)動(dòng)示意圖第30頁/共53頁Anothertypeofdislocation,calledascrewdislocationmaybethoughtofasbeingformedbyashearstressthatisappliedtoproducethedistortion滑移方向第31頁/共53頁theupperfrontregionofthecrystalisshiftedoneatomicdistancetotherightrelativetothebottomportion.Theatomicdistortionassociatedwithascrewdislocationisalsolinearandalongadislocationline,lineABττ螺型位錯(cuò)線ABCD第32頁/共53頁滑移面上下原子的錯(cuò)排情況

未滑移錯(cuò)排重合第33頁/共53頁螺型位錯(cuò)的運(yùn)動(dòng)第34頁/共53頁Mostdislocationsfoundincrystallinematerialsareprobablyneitherpureedgenorpurescrewbutexhibitcomponentsofbothtypes;thesearetermedmixeddislocations.AllthreedislocationtypesarerepresentedschematicallyinFigure4.6;thelatticedistortionthatisproducedawayfromthetwofacesismixed,havingvaryingdegreesofscrewandedgecharacter.第35頁/共53頁圖混合位錯(cuò)的原子組態(tài)第36頁/共53頁BurgersvectorThemagnitudeanddirectionofthelatticedistortionassociatedwithadislocationareexpressedintermsofaBurgersvector,denotedbyb.thenatureofadislocation(i.e.,edge,screw,ormixed)isdefinedbytherelativeorientationsofdislocationlineandBurgersvector.Foranedge,theyareperpendicular，whereasforascrew,theyareparallel，theyareneitherperpendicularnorparallelforamixeddislocation.第37頁/共53頁eventhoughadislocationchangesdirectionandnaturewithinacrystal,theBurgersvectoristhesameatallpointsalongitsline.第38頁/共53頁3.4INTERFACIALDEFECTSInterfacialdefectsareboundariesthathavetwodimensionsandnormallyseparateregionsofthematerialsthathavedifferentcrystalstructuresand/orcrystallographicorientations.Theseimperfectionsincludeexternalsurfaces,grainboundaries,phaseboundaries,twinboundaries,andstackingfaults.第39頁/共53頁(a)ExternalSurfacesOneofthemostobviousboundariesistheexternalsurface,alongwhichthecrystalstructureterminates.Surfaceatomsarenotbondedtothemaximumnumberofnearestneighborsandarethereforeinahigherenergystatethantheatomsatinteriorpositions.Thebondsofthesesurfaceatomsthatarenotsatisfiedgiverisetoasurfaceenergy,expressedinunitsofenergyperunitarea(J/m2orerg/cm2).第40頁/共53頁Thehigherenergyoftheatomsonthesurfacemakesthesurfacesusceptibletoerosionandreactwithelementsintheenvironment.Toreducethisenergy,materialstendtominimize,ifatallpossible,thetotalsurfacearea.Forexample,liquidsassumeashapehavingaminimumarea—thedropletsbecomespherical.Ofcourse,thisisnotpossiblewithsolids,whicharemechanicallyrigid.第41頁/共53頁(b)GrainBoundariesboundaryseparatingtwosmallgrainsorcrystalshavingdifferentcrystallographicorientationsinpolycrystallinematerials.Withintheboundaryregion,whichisprobablyjustseveralatomdistanceswide,thereissomeatomicmismatchinatransitionfromthecrystallineorientationofonegraintothatofanadjacentone.第42頁/共53頁Theatomicpackingingrainboundariesislowerthanwithinthegrainsbecauseoftheatomicmismatch.Grainboundariesalsohavesomeatomsinstrainedpositionthatraisetheenergyofthegrain-boundaryregion.thehighenergyofthegrainboundariesandtheirmoreopenstructuremakethemamorefavorableregionforthenucleationandgrowthofprecipitates.allowformorerapiddiffusionofatomsinthegrainboundaryboundariesrestrictplasticflowbymakingitmoredifficultforthemovementofdislocationsinthegrainboundaryregion.第43頁/共53頁Whenthisorientationmismatchisslight,ontheorderofafewdegrees,thenthetermsmall-(orlow-)anglegrainboundary

isused.Theseboundariescanbedescribedintermsofdislocationarrays.Onesimplesmall-anglegrainboundaryisformedwhenedgedislocationsarealignedinthemannerofFiguretiltboundaryangleofmisorientation,?第44頁/共53頁Theatomsarebondedlessregularlyalongagrainboundary,an