現(xiàn)代材料研究方法TEM1

現(xiàn)代材料研究方法TEM1現(xiàn)代材料研究方法引言:1.現(xiàn)代材料科學(xué)2.材料科學(xué)發(fā)展趨勢3.電子顯微鏡及微區(qū)分析在材料科學(xué)研究中的作用性能成份組織加工性能成份組織成本（性能、價格比）成份組織加工性能成本成份組織環(huán)境性能加工材料科學(xué)概念材料科學(xué)發(fā)展趨勢

傳統(tǒng)材料(Traditionalmaterials):提高性能/價格比

先進(jìn)材料(Advancedmaterials):用于各種極端條件

功能材料（Functionalmaterials)

低維材料（

Lowdimensionmaterials）

納米技術(shù)和納米材料（Nanotechnologyandnanomaterials）

生物醫(yī)學(xué)材料（Biomaterials）

環(huán)境材料（Environmentalmaterials）…………….

本課程的內(nèi)容:PartI透射電子顯微學(xué)及其在材料科學(xué)研究中的應(yīng)用PartII高分辯電子顯微學(xué)及其在材料科學(xué)研究中的應(yīng)用PartIII分析電子顯微學(xué)及其在材料科學(xué)研究中的應(yīng)用PartI透射電鏡及其在材料科學(xué)研究中應(yīng)用1.引言2.電子衍射（Electrondiffraction）3.衍襯理論（Theoryofdiffractioncontrast）4.完整晶體的特征圖像（Characteristicimagesfromperfectcrystals）5.位錯和層錯的襯度（Contrastfromdislocationsandstackingfaults）6.第二相粒子的襯度（Contrastfromsecondphaseparticles）參考資料（References）:

1.ElectronMicroscopyofThinCrystals,M.A.Hirshetal.,19772.TransmissionElectronMicroscopyofMaterials,G.Thomas,19793.PracticalElectronMicroscopyinMaterialsScience,J.W.Edington,1974-774.DefectAnalysisinTransmissionElectronMicroscopy,R.E.Smallman,19805.電子衍射圖在晶體學(xué)中的應(yīng)用,郭可信等6.金屬電子顯微分析,上海交大1.引言（Introduction）1.1.阿貝成象理論（Abby’stheoryofimageformation）1.2.電子顯微鏡（Electronmicroscope）1.3.襯度的起源（Originofimagecontrast）1.4.電鏡圖像舉例（Examplesofelectronmicroscopyphotographs）阿貝成象理論（Abby’sTheoryofImageFormation）OpticalMicroscopeElectronMicroscopeAB非晶樣品（AmorphousSpecimen）晶態(tài)樣品（CrystallineSpecimen）2.電子衍射（ElectronDiffraction）2.1.電子衍射（Electrondiffraction）2.2.選區(qū)電子衍射（Selectedareaelectrondiffraction(SAD)）2.3.相機(jī)常數(shù)（Cameraconstant）2.4.簡單電子衍射花樣的標(biāo)定（IndexingofsimpleSADpatterns）2.5.衍射花樣的形狀效應(yīng)（Shapeeffectofdiffractionpatterns）2.6.取向關(guān)系（Orientationrelationship)2.7.入射束方向的精確確定（Accuratedeterminationofbeamdirection）2.8.復(fù)雜衍射花樣（ComplicatedSADpatterns）2.9偏移參數(shù)（Deviationparametersg）2.1.電子衍射（Electrondiffraction）2.2.選區(qū)電子衍射（Selectedareaelectrondiffraction(SAD)）2.3.相機(jī)常數(shù)（Cameraconstant）Ll叫作相機(jī)常數(shù),且dhkl=Ll/R’2.4簡單SAD花樣的標(biāo)定（IndexingofsimpleSADpatterns）2.4.1嘗試校核法（Trieranderror:）2.4.2已知相機(jī)常數(shù)法（Knowncameraconstant）2.4.3標(biāo)準(zhǔn)衍射譜法（Standarddiffractionpatterns）2.4.4計算機(jī)標(biāo)定法（Computersimulation）000h1k1l1h2k2l2h3k3l3aR1R2R3fcc:N=3,4,8,11,12,16,19,…….bcc:N=2,4,6,8,10,…….B=R1xR2(1)PhotographAisfromonegrainofathinfoilof-iron.Chooseonespotastheoriginandmeasurethedistanceofanumberofadjacentspotsfromit.Itisalwayshelpfultomakeareasonablesketchofthepatternandtolabelthespots.Fromtheratioofthedistancesbetweentheoriginandthemeasuredspots,andtheknownpossibilitiesforvaluesof,assignaconsistentsetofindicestoallthespotsandhencedeterminetheindicesofthedirectionoftheelectronbeam.Giventhattheunitcelldimensionof-ironis2.86?,whatisthe"cameraconstant"forthephotograph?(2)IndexthepatternBgiventhatitisfromaluminum,a=4.04?andthatthecameraconstantisapproximately4.4cm.?(3)ThediffractionpatternCisfrom-ironcontainingprecipitatesofCrN(fcc,a=4.15?

whichhaveadefiniteorientationrelationshipwiththematrix.Theprecipitatesoccurasthinplatesonthethreesetsof(100)planessotherearethreeprecipitatepatternspresentonthephotograph.ThesketchDshowsonlyoneprecipitatepattern,plusthematrixpattern.Notethesymmetryofthematrixpatternandindexitbyinspection.Indextheprecipitatepatternanddeterminetheorientationrelationshipbetweenprecipitateandmatrix.Accountfortheobservedmorphologyoftheprecipitateparticles.EM1ElectronDiffractionPatterns2.5.衍射花樣的形狀效應(yīng)Shapeeffectofdiffractionpatterns2.6.取向關(guān)系（Orientationrelationship）2.7.入射束方向的精確確定Accuratedeterminationofbeamdirection2.8.IndexingofsimpleSADpatternsfromhexcrystals2.8.1Weiss’szonelaw2.8.2ApplicationofWeiss’szonelawtohexsystem2.8.3Threeaxisandfouraxissystemforhexcrystals2.8.4Theindicesofaplaneanditsnormalinhexcrystals

Weiss’sZoneLaw1.Basiclaw: hu+kv+lw=0.2.AdditionruleIf(h1k1l1)and(h2k2l2)belongto[uvw],then(h3k3l3)alsobelongsto[uvw]when:

h3=±nh1±m(xù)h2 k3=±nk1±m(xù)k2 l3=±nl1±m(xù)l23.ZoneaxisIf(h1k1l1)and(h2k2l2)belongto[uvw],then: [uvw]=(h1k1l1)x(h2k2l2)oru=k1l2–k2l1v=l1h2–l2h1w=h1k2–h2k14.Ifaplane(hkl)containsthezoneaxis[u1v1w1]and[u2v2w2],then: (hkl)=(u1v1w1)x(u2v2w2)orh=v1w2–v2w1k=w1u2–w2u1l=u1v2–u2v1Planes:

(hkil)=(HKL)h+k+i+l=0h=Hk=Kl=LDirections:

[uvtw]=[UVW]

w=WU=u–tV=v–tW=wAngles:

Threeaxistofouraxissystemhkl→uvw:uvw→hkl:Ref.:InterpretationofElectronDiffractionPattern,K.W.Andrews,D.Jyson,S.R.KeownTheindicesofaplaneanditsnormalinhexcrystalsPhotographsDandEshowaneedle-shapedprecipitateanditscorrespondingelectrondiffractionpatternwhichhasbeensuperimposedwithacalibrationringpatternfrompolycrystallinegold.MeasureandindexthefccgoldpatternbycompilingalistofringdiametermeasurementandcomparingthosewithalistofN-valueforgold.Determinethevalueofthecameraconstant,(L),foreachreflectionandhencethemeanvalue.Measurethesinglecrystalspotspacinganddeterminethedhklvaluesforeachreflection.AluminumnitridehasahexagonalstructureandgiventhevalueofdhklinTable1,indexthepatternanddeterminethevaluesof"a"and"c"foritsunitcell.Checkforaconsistentsetofindicesbycomparingthemeasuredanglesbetweenthereciprocallatticevectorsandthecalculatedvalues.Whatistheplaneoftheprecipitate?TheimagerotationcalibrationforthemicroscopeisgiveninTable2fortheconditionsusedtoobtainthemicrographs.IfthemagnificationofphotographDisx18,500,determinetherotationofthebrightfieldimagewithrespecttothediffractionpatternandhencedeterminetheplaneofthegrowthaxisoftheprecipitate.Theprecipitateislyingflatonthereplicas.

Table1

Table2

hkld(A)

Magnificationclockwiserotationof 100 2.700 imagew.r.t.diffraction pattern 002 2.490

110 1.557 3,500 7o

103 1.414 16,000 10o

202 1.186 22,000 15o

210 1.019 58,000 30oEM2ElectronDiffractionPatternsExperimentaldeterminationofimagerotation

2.8復(fù)雜衍射花樣（ComplicatedSADpatterns）2.9.偏移參數(shù)（Deviationparametersg）3.衍襯理論（TheoryofDiffractionContrast）3.1衍射襯度（Diffractioncontrast）3.2晶柱假設(shè)（Columnapproximation）3.3運(yùn)動學(xué)衍襯理論（Kinematicaltheoryofdiffractioncontrast）3.3.1基本假設(shè)（Basicassumptions）3.3.2計算公式（Formulation）3.3.3理論預(yù)測與實(shí)驗(yàn)觀察對照Comparisonoftheoreticalpredictionstotheexperimentalobservations3.3.4運(yùn)動學(xué)理論的應(yīng)用及其局限性Applicationandlimitationofthekinematicaltheory3.4動力學(xué)衍襯理論（Dynamicaltheoryofdiffractioncontrast）3.4.1基本假設(shè)（Basicassumptions）3.4.2計算公式（Formulation）3.4.3理論預(yù)測與實(shí)驗(yàn)觀察對照Comparisonoftheoreticalpredictionstotheexperimentalobservations3.4.4在顯微鏡下辨認(rèn)動力學(xué)衍襯條件Recognitionofdynamicconditioninthemicroscope3.1衍射襯度（Diffractioncontrast）3.2晶柱假設(shè)（Columnapproximation）3.3運(yùn)動學(xué)衍襯理論（Kinematicaltheoryofdiffractioncontrast）3.3.1基本假設(shè)（Basicassumptions）3.3.2公式（Formulation）3.3.3理論預(yù)測與實(shí)驗(yàn)觀察的對照Comparisonoftheoreticalpredictionstotheexperimentalobservations3.3.4運(yùn)動學(xué)理論的應(yīng)用及其局限性Applicationandlimitationofthekinematicaltheory運(yùn)動學(xué)理論的基本假設(shè)運(yùn)動學(xué)理論（Kinematictheory）:厚度消光條紋Thicknessfringes彎曲消光條紋（Bendextinctioncontours）如果sg=0,那么|Fg|2=(pt/g)2假定t>g/p則有|Fg|2>1違反能量守恒定律!!所以,理論不適用!!所以必須,|sg|>>0,或t<g/p動力學(xué)理論（DynamicTheory）:樣品對電子的吸收:—均勻吸收系數(shù)（Uniformabsorptioncoefficient）—反常吸收系數(shù)（Abnormalabsorptioncoefficient）4.完整晶體特征圖像（CharacteristicImagesfromperfectcrystals）4.1完整晶體的動力學(xué)衍襯公式4.2運(yùn)動學(xué)理論是動力學(xué)理論的一個特例4.3在完整晶體中可以看到的特征圖像4.3.1厚度消光條紋Thicknessextinctioncontours(Thicknessfringes)4.3.2彎曲消光條紋（Bendextinctioncontours）4.3.3彎曲條紋（Bendcontours）4.3.4彎曲中心（Bendcenter）4.4確定薄膜樣品厚度（Determinationofthefoilthickness）4.4.1厚度消光條紋4.4.2彎曲條紋4.1完整晶體的動力學(xué)公式：Ifsg>>1/g,then運(yùn)動學(xué)理論是動力學(xué)理論的一個特例!4.3.1厚度消光條紋條紋間距（Fringespacing）:

Ifsg=0,then

PhotographGshowsadarkfieldimagefromanfccmaterialwhichexhibitsthicknessfringes.Theoperatingreflectionis{111}.Calculatesin/fortheoperatingreflectionandusingthedataofTable1obtainedbyinterpolationavalueoffx-rayforthatreflection.Thethicknessofafoilunderkinematicalconditionscanbeapproximatelyexpressedasnwherenisthenumberoffringesforanextinctiondistance=V/F,andVisthevolumeoftheunitcell.Calculatefor100kvelectronsandevaluatethestructurefactorFforafcccellfrom:F=ifelec.cos2(hui+kvi+lwi)wherefelec=(z-fx-ray)(/sin)2KDeterminethevalueofthefoilthicknessandexpresstheanswerobtainedtothenearest5nm.Table1

sin/

0 0.1 0.2 0.3 0.4 0.5 0.6 fx-ray

13 11 8.95 7.75 6.0 5.5 4.5 z=13 atomicweight=26.97 K=0.0024nm a0=4.049EM3ExtinctionContoursEM4ExtinctionContoursAssumingthatdarkfieldexperimentshaveshownthattheinsetdiffractionpatterninphotographIisassociatedwiththeextinctioncontoursinthemicrographasshownbythenumbering.IndexthepatternbycomparingthespacingofthereflectionswithalistofN-valuesforanf.c.cunitcell.Whatisthefoilorientation?Determinethenatureofthebucklingofthefoil,i.e.,isitbentasacylinder,asaucer,adomeorasaddle?Thevalueoftthefoilthicknesscanbecalculatedfromthesubsidiaryfringeformula:wherenisthenuumberofthesubsidiaryfringe1,2,3etc.s=g2.l/2isthedeviationparameter,andxg

theextinctiondistancefortheoperatingreflection.Determinesforthemaincontourinset1andhencedeterminethefoilthicknessbyevaluatingsforthefirstsubsidiaryfringe.hu+kv+lw=0l=0.037?a0=4.04?hkl(?)

111 556 200 673 220 1057 311 1300 222 1377 400 1672運(yùn)動學(xué)衍襯和動力學(xué)條件的識別

SADP BFimages Dynamicalkinematical Dynamicalkinematical brightKikuchilinesbrightkikuchiliness+vewelldefines;fewthicknessveryclosetostrongsomedistancefromdiffractionspotstrongdiffractionthicknessfringesfringesBF,exceptw=-1～+1.0spotw>>±1.0followingthe1-2verynearthe contoursoftheedgeofspecimenedgeofthespecimenahighcontrastalowcontrastimageisobtainedimageisobtained

aslightoveralltheoverallnaturegraininessoftheoftheimageisbackgroundisdiffusevisibleinmanymaterials5.1有缺陷晶體的衍射襯度理論Theoryofdiffractioncontrastfromcrystalscontainingdefects5.2完全位錯的襯度（Contrastfromperfectdislocations）5.3層錯的襯度（Contrastfromstackingfaults）5.4不全位錯的襯度（Contrastfrompartialdislocations）5.5弱束暗場技術(shù)（Weakbeamtechnique）5.6其它面缺陷的襯度分析（Contrastfromotherplanardefects）5.7第二相粒子的襯度分析（Contrastfromsecondphaseparticles）5.位錯和層錯的襯度（Contrastfromdislocationsandstackingfaults)5.1.1帶應(yīng)變場的晶體缺陷5.1.有缺陷晶體的衍射襯度理論5.1.3衍射襯度理論與晶體缺陷分析晶體缺陷分類(1)帶局部應(yīng)變場的缺陷(2)分割兩半完整晶體的面缺陷（Planardefect）(3)薄膜試樣中空洞和氣泡（Voidsandbubbles）(4)產(chǎn)生局部消光距離變化的缺陷晶體缺陷分析需要的參數(shù)(1)操作矢量（operationvectorg）(2)偏移參數(shù)（Deviationparametersg）(3)消光距離（Extinctiondistance

xg）(4).反常吸收系數(shù)（ANO=xg/xg’）

局部應(yīng)變場使晶柱發(fā)生變形（位移）5.1.2運(yùn)動學(xué)公式和動力學(xué)公式運(yùn)動學(xué)公式:動力學(xué)公式:5.2完全位錯（perfectdislocations）的襯度

完全位錯的圖像是在位錯核心一側(cè)的一條黑線不可見準(zhǔn)則（Invisibilitycriteria）位錯柏氏矢量的確定（DeterminationoftheBurgersvector）位錯圖像的一般特征：(1)位于位錯核心一側(cè)的一條黑線(2)傾斜位錯（Inclineddislocations）(3)圖像寬度（Imagewidth）:當(dāng)sg0,g/3時為最大(4)當(dāng)sg0時可見性最佳(5)當(dāng)sg0及時呈現(xiàn)雙線(6)位錯偶極子（Dislocationdipoles）(7)垂直表面的位錯（Endondislocations）不可見準(zhǔn)則（InvisibilityCriteria）螺位錯（screwdislocations）:可見（Visible）不可見（Invisible）刃位錯（edgedislocations）:and混合位錯（mixeddislocations）:不可見（Invisible）不可見（Invisible）DislocationConfigurationinthefoilScrew,//foilsurfaceInclinetofoilsurfaceEdge,and//foilsurfaceand//foilnormalEdge,//foilsurface,thatisMixed,and//foilsurfaceInvisibilityCriteria運(yùn)動學(xué)理論:動力學(xué)理論:位錯圖像寬度S=0S0ggDislocationDipoleDislocationPair5.3層錯的襯度（Contrastfromstackingfaults）

5.3.1面心立方晶體中的層錯（Stackingfaultsinfcccrystals）5.3.2動力學(xué)公式（Dynamicformulation）5.3.3層錯的圖像特征（Imagecharacteristicsofstackingfaults）(1)條紋花樣,BF:對稱;DF:不對稱(2)與試樣上表面的交線:明暗場最外面的條紋襯度相同

與試樣下表面的交線:明暗場最外面的條紋襯度相反(3)上表面最外一根條紋:當(dāng)是亮的當(dāng)是暗的(4)當(dāng)時不可見(5)試樣厚度增加時增加的新條紋5.3.4抽出型（intrinsic）或插入型（extrinsic）層錯的識別Dynamicformulation層錯性質(zhì)的識別將操作矢量g置于層錯暗場象的中心，如果g指向最外一根亮條紋，那么對于所有A類型反射({200},{222},{440}等）,層錯是抽出型的。如果g背離最外的亮條紋，那么層錯是插入型的.對于所有B類反射({400},{111},{220}etc),則正好相反。EM5DislocationsandStackingFaults

TheStackingfaultenergyofamaterialcanbeestimatedfromtheseparationofpartialdislocationsbytheequation:whereGistheshearmodulusandandaretheBurgersvectorsofthepartialdislocations.Measuretheseparation,,ofthepartialdislocationsinphotographLandcalculateforthedislocationreaction:

Analternationmethodofmeasuringstackingfaultenergycanbeappliedwithamaterialcontainingastablearrayofdislocationnodes.Whensuchnodeisimagedindarkfield,thenthosedislocationsforwhichwillbeoutofcontrast.InthedarkfieldimageofgraphiteinphotographMtheoperatingvectorsareshownonthediffractionpattern.Identifythedislocationsinquestion.MeasuretheradiusofcurvatureR,ofeachpartialandbyindexingthediffractionpatternfindtheBurgersvectors.Findthestackingfaultenergy,g,from:

Commentonthevaluesofobtained.G=2.5x109J.m-3graphitehasahexagonalunitcellMagnifications:L=x31,200M=x54,000a=2.462?

c=6.701?hkld(?)

002 3.35100 2.13101 2.04102 1.801004 1.675103 1.541110 1.230b1b2b3Forspot1:Converttofouraxissystem:Forspot2:Converttofouraxissystem:Forspot3:Converttofouraxissystem:5.4弱束暗場技術(shù)（WeakBeamTechnique）5.4.1弱束暗場象原理（Principlesofweakbeamimaging）5.4.2弱束暗場象特征（Imagecharacteristics）(1)位錯的弱束暗場象是在漆黑背底上的一條亮線(2)位錯圖像的位置與位錯核心距離小于<20?(3)位錯圖像寬度非常小,~15?(4)位錯圖像的位置與位錯在薄膜試樣中所處的深度無關(guān)ForKinematictheory:ForDynamictheory:FortheEdwaldspherecuttingthelowofsystematicreflectionsgatng

(nnotnecessaryinteger),thevalueofsisgivenbys=(n-1)g2/2KwhereK=1/Experimentalconditions5.4.4弱束暗場技術(shù)在材料研究中的應(yīng)用5.4.5弱束暗場技術(shù)的優(yōu)缺點(diǎn)(1)優(yōu)點(diǎn)*可以采用普通含有高密度缺陷的薄膜試樣,t=2~4xg

*圖像分辯力可根據(jù)實(shí)際問題通過實(shí)驗(yàn)條件加以控制*象散的問題不重要*圖像襯度非常好*可以使用不可見準(zhǔn)則，如(2)缺點(diǎn)*曝光時間非常長*圖像的分辯力并不太高5.5不全位錯（partialdislocations）的襯度5.5.1面心立方晶體中的位錯5.5.2對不全位錯襯度效應(yīng)的一般性考慮5.5.3定性分析（Qualitativeanalysis）5.5.4計算機(jī)模擬（Computersimulation），略面心立方晶體中的不全位錯肖克萊位錯（Shockleypartial）弗蘭克位錯（Frankpartial）樓梯棒位錯（Stair-rodpartial）FaultedloopinSi(a),B-near[112],faultvisible,dislocationvisibleor2/3p,(b),B=[111],faultinvisible,dislocationinvisibleforand(c),B=[111],faultinvisible,dislocationinvisibleforbutnotforXmustbeandmustbepureedgedislocationXmustbesessile.ParametersneededforcomputersimulationStiffnesscoefficientsC11,C12,AbnormalabsorptioncoefficientANOBurgersvectorbDirectionvectoruOperationvectorgBeamdirectionBThenormalofthefoilFNDeviationparametersorw=sggFoilthicknesstPossibledislocationsin-Brass1/2<111><111><100><110>5.6其它類型面缺陷（Otherplanardefects）

5.6.1反相疇界（Antiphaseboundaries）5.6.2薄片狀沉淀（Planarprecipitates）5.6.3晶界（Grainboundaries）(1)小角度晶界（smallanglegrainboundaries）(2)大角度晶界（Largeanglegrainboundaries）6.第二相粒子的襯度Contrastfromparticlesofasecondphase

6.1雙相材料的衍射和襯度6.1.1一般性考慮(1)共格粒子（coherentparticles）(2)半共格粒子（partiallycoherentparticles）(3)非共格粒子（incoherentparticles）6.1.2.第二相粒子的襯度基體襯度（Matrixcontrast）沉淀相襯度（Precipitatecontrast）6.2基體襯度（Matrixcontrast）

6.2.1帶球?qū)ΨQ應(yīng)變場的第二相粒子：在粒子外面在粒子內(nèi)部6.2.2帶球?qū)ΨQ應(yīng)變場的第二相粒子的襯度分析Ref.:AshbyM.F.andBrownL.M.,Phil.Mag.8,(1963)10836.2.3非球狀粒子（Non-sphericalsecondphaseparticles）如果粒子很小，那么