1.DiffractionandtheX-RayPowderDiffractometer ........ 1
1.1Diffraction.............................................1
1.1.1IntroductiontoDiffraction........................1
1.1.2Bragg’sLaw.....................................3
1.1.3StrainEffects....................................6
1.1.4SizeEffects......................................7
1.1.5ASymmetryConsideration.......................9
1.1.6MomentumandEnergy...........................10
1.1.7ExperimentalMethods............................10
1.2TheCreationofX-Rays.................................13
1.2.1Bremsstrahlung..................................14
1.2.2CharacteristicRadiation..........................16
1.2.3SynchrotronRadiation............................20
1.3TheX-RayPowderDiffractometer........................23
1.3.1PracticeofX-RayGeneration......................23
1.3.2GoniometerforPowderDiffraction.................25
1.3.3Monochromators,Filters,Mirrors...................28
1.4X-RayDetectorsforXRDandTEM......................30
1.4.1DetectorPrinciples...............................30
1.4.2Position-SensitiveDetectors.......................34
1.4.3ChargeSensitivePreamplifier......................36
1.4.4OtherElectronics.................................37
1.5ExperimentalX-RayPowderDiffractionData..............38
1.5.1*IntensitiesofPowderDiffractionPeaks............38
1.5.2PhaseFractionMeasurement......................45
1.5.3LatticeParameterMeasurement....................49
1.5.4*RefinementMethodsforPowderDiffractionData...52
FurtherReading............................................54
Problems..................................................55
2.TheTEManditsOptics .................................. 61
2.1IntroductiontotheTranissionElectronMicroscope.......61
2.2WorkingwithLensesandRayDiagrams...................66
2.2.1SingleLenses....................................66XIIContents
2.2.2Multi-LensSystems...............................69
2.3ModesofOperationofaTEM...........................71
2.3.1Dark-FieldandBright-FieldImaging...............71
2.3.2SelectedAreaDiffraction..........................76
2.3.3Convergent-BeamElectronDiffraction..............79
2.3.4High-ResolutionImaging..........................81
2.4PracticalTEMOptics...................................85
2.4.1ElectronGuns...................................85
2.4.2IlluminationLensSystems.........................87
2.4.3ImagingLensSystems............................88
2.5GlassLenses...........................................91
2.5.1Interfaces.......................................91
2.5.2LensesandRays.................................92
2.5.3LensesandPhaseShifts...........................95
2.6MagneticLenses........................................97
2.6.1Focusing........................................97
2.6.2ImageRotation..................................99
2.6.3PolePieceGap...................................100
2.7LensAberrationsandOtherDefects......................102
2.7.1SphericalAberration..............................102
2.7.2ChromaticAberration............................103
2.7.3Diffraction.......................................104
2.7.4Astigmati.....................................104
2.7.5GunBrightness..................................108
2.8Resolution.............................................110
FurtherReading............................................112
Problems..................................................113
3.Scattering ................................................ 119
3.1WavesandScattering...................................119
3.1.1Wavefunctions...................................119
3.1.2CoherentandIncoherentScattering.................122
3.1.3ElasticandInelasticScattering.....................123
3.1.4WaveAmplitudesandCross-Sections...............124
3.2X-RayScattering......................................128
3.2.1ElectrodynamicsofX-RayScattering...............128
3.2.2*InelasticComptonScattering.....................132
3.2.3X-RayMassAttenuationCoefficients...............134
3.3CoherentElasticScattering..............................136
3.3.1 ‡ BornApproximationforElectrons................136
3.3.2AtomicFormFactors–PhysicalPicture.............141
3.3.3 ‡ ScatteringofElectronyModelPotentials........144
3.3.4 ‡ *AtomicFormFactors–GeneralFormulation......148
3.4*NuclearScattering....................................153
3.4.1PropertiesofNeutrons............................153ContentsXIII
3.4.2Time-VaryingPotentialsandInelasticNeutronScat-
tering...........................................155
3.4.3*CoherentM¨ osauerScattering...................158
FurtherReading............................................160
Problems..................................................160
4.InelasticElectronScatteringandSpectroscopy ........... 163
4.1InelasticElectronScattering.............................163
4.2ElectronEnergy-LossSpectrometry(EELS)................165
4.2.1Instrumentation..................................165
4.2.2GeneralFeaturesofEELSSpectra..................167
4.2.3*FineStructure.................................169
4.3PlaonExcitations....................................173
4.3.1PlaonPrinciples...............................173
4.3.2*PlaonsandSpecimenThickness................175
4.4CoreExcitations.......................................177
4.4.1ScatteringAnglesandEnergies–Qualitative........177
4.4.2 ‡ InelasticFormFactor............................180
4.4.3 ‡ *Double-DifferentialCross-Section,d2σin/dφ dE ...184
4.4.4*ScatteringAnglesandEnergies–Quantitative......186
4.4.5 ‡ *DifferentialCross-Section,dσin/dE ..............187
4.4.6 ‡ PartialandTotalCross-Sections, σin ..............189
4.4.7QuantificationofEELSCoreEdges.................191
4.5Energy-FilteredTEMImaging(EFTEM)..................193
4.5.1SpectrumImaging................................193
4.5.2EnergyFilters...................................193
4.5.3ChemicalMappingwithEnergy-FilteredImages......196
4.5.4ChemicalysiswithHighSpatialResolution......197
4.6EnergyDispersiveX-RaySpectrometry(EDS).............200
4.6.1ElectronTrajectoriesThroughMaterials............200
4.6.2FluorescenceYield................................203
4.6.3EDSInstrumentationConsiderations................205
4.6.4Thin-FilmApproximation.........................208
4.6.5*ZAFCorrection................................211
4.6.6ArtifactsinEDeasurements....................213
4.6.7LimitsofMicroysis...........................215
FurtherReading............................................217
Problems..................................................217
5.DiffractionfromCrystals ................................. 223
5.1SumsofWaveletsfromAtoms............................223
5.1.1ElectronDiffractionfromaMaterial................224
5.1.2WaveDiffractionfromaMaterial...................226
5.2TheReciprocalLatticeandtheLaueCondition............230
5.2.1DiffractionfromaSimpleLattice...................230XIVContents
5.2.2ReciprocalLattice................................231
5.2.3LaueCondition..................................233
5.2.4EquivalenceoftheLaueConditionandBragg’sLaw..233
5.2.5ReciprocalLatticesofCubicCrystals...............234
5.3DiffractionfromaLatticewithaBasis....................235
5.3.1StructureFactorandShapeFactor.................235
5.3.2StructureFactorRules............................237
5.3.3SymmetryOperationsandForbiddenDiffractions....242
5.3.4SuperlatticeDiffractions...........................243
5.4CrystalShapeFactor...................................247
5.4.1ShapeFactorofRectangularPri.................247
5.4.2OtherShapeFactors..............................252
5.4.3allParticlesinaLargeMatrix...................252
5.5DeviationVector(DeviationParameter)...................256
5.6EwaldSphere..........................................257
5.6.1EwaldSphereConstruction........................257
5.6.2EwaldSphereandBragg’sLaw.....................259
5.6.3TiltingSpecimensandTiltingElectronBeams.......259
5.7LaueZones............................................262
5.8*EffectsofCurvatureoftheEwaldSphere................262
FurtherReading............................................266
Problems..................................................266
6.ElectronDiffractionandCrystallography ................. 273
6.1IndexingDiffractionPatterns............................273
6.1.1IssuesinIndexing................................274
6.1.2Method1–StartwithZoneAxis...................276
6.1.3Method2–StartwithDiffractionSpots.............279
6.2StereographicProjectionsandTheirManipulation..........282
6.2.1ConstructionofaStereographicProjection..........282
6.2.2RelationshipBetweenStereographicProjections
andElectronDiffractionPatterns...................284
6.2.3ManipulationsofStereographicProjections..........284
6.3KikuchiLinesandSpecimenOrientation..................290
6.3.1OriginofKikuchiLines...........................290
6.3.2IndexingKikuchiLines............................294
6.3.3SpecimenOrientationandDeviationParameter......296
6.3.4TheSignof s ....................................299
6.3.5KikuchiMaps....................................299
6.4DoubleDiffraction......................................302
6.4.1OccurrenceofForbiddenDiffractions................302
6.4.2InteractionetweenCrystallites...................303
6.5*Convergent-BeamElectronDiffraction...................304
6.5.1ConvergenceAngleofIncidentElectronBeam.......306
6.5.2DeterminationofSampleThickness.................307ContentsXV
6.5.3MeasurementsofUnitCellParameters..............309
6.5.4 ‡ DeterminationofPointGroups...................314
6.5.5 ‡ DeterminationofSpaceGroups...................325
6.6FurtherReading........................................330
Problems..................................................330
7.DiffractionContrastinTEMImages ...................... 337
7.1ContrastinTEMImages................................337
7.2DiffractionfromCrystalswithDefects....................339
7.2.1ReviewoftheDeviationParameter, s ...............339
7.2.2AtomDisplacements, δr ..........................340
7.2.3ShapeFactorand t ...............................341
7.2.4DiffractionContrastand {s, δr, t} .................342
7.3ExtinctionDistance.....................................342
7.4ThePhase-AmplitudeDiagram...........................345
7.5FringesfromSampleThicknessVariations.................347
7.5.1ThicknessandPhase-AmplitudeDiagrams...........347
7.5.2ThicknessFringesinTEMImages..................348
7.6BendContoursinTEMImages..........................353
7.7DiffractionContrastfromStrainFields....................357
7.8DislocationsandBurgersVectorDetermination............359
7.8.1DiffractionContrastfromDislocationStrainFields...359
7.8.2The g·b RuleforNullContrast....................362
7.8.3ImagePositionandDislocationPairsorLoops.......368
7.9Semi-QuantitativeDiffractionContrastfromDislocations....369
7.10Weak-BeamDark-Field(WBDF)ImagingofDislocations....378
7.10.1ProceduretoMakeaWBDFImage.................378
7.10.2DiffractionConditionforaWBDFImage............379
7.10.3ysisofWBDFImages.........................380
7.11FringesatInterfaces....................................384
7.11.1PhaseShiftsofElectronWaveletsAcrossInterfaces...384
7.11.2Moir´ eFringes....................................387
7.12DiffractionContrastfromStackingFaults.................391
7.12.1KinematicalTreatment............................391
7.12.2ResultsfromDynamicalTheory....................397
7.12.3DeterminationoftheIntrinsicorExtrinsicNature
ofStackingFaults................................399
7.12.4PartialDislocationoundingtheFault.............399
7.12.5AnExampleofaStackingFaultysis............400
7.12.6SetsofStackingFaultsinTEMImages..............402
7.12.7RelatedFringeContrast...........................403
7.13Antiphase(π)Boundariesand δ Boundaries...............404
7.13.1AntiphaseBoundaries.............................404
7.13.2 δ Boundaries....................................405
7.14ContrastfromPrecipitatesandOtherDefects..............407XVIContents
7.14.1Vacancies.......................................407
7.14.2CoherentPrecipitates.............................408
7.14.3SemicoherentandIncoherentParticles..............413
FurtherReading............................................413
Problems..................................................414
8.DiffractionLineshapes .................................... 423
8.1DiffractionLineBroadeningandConvolution..............423
8.1.1CrystalliteSizeBroadening........................424
8.1.2StrainBroadening................................426
8.1.3InstrumentalBroadening–Convolution.............430
8.2FourierTransformDeconvolutions........................433
8.2.1MathematicalFeatures............................433
8.2.2*EffectsofNoiseonFourierTransformDeconvolutions436
8.3SimultaneousStrainandSizeBroadening..................440
8.4DiffractionLineshapesfromColumnsofCrystals...........446
8.4.1WaveletsfromPairsofUnitCellsinOneColumn....446
8.4.2AColumnLengthDistribution.....................448
8.4.3 ‡ IntensityfromColumnLengthDistribution........450
8.5CommentsonDiffractionLineshapes......................451
FurtherReading............................................454
Problems..................................................455
9.PattersonFunctionsandDiffuseScattering ............... 457
9.1ThePattersonFunction.................................457
9.1.1Overview........................................457
9.1.2AtomCentersatPointsinSpace...................458
9.1.3DefinitionofthePattersonFunction................459
9.1.4PropertiesofPattersonFunctions..................461
9.1.5 ‡ PerfectCrystals................................463
9.1.6DeviationsfromPeriodicityandDiffuseScattering....467
9.2DiffuseScatteringfromAtomicDisplacements..............469
9.2.1UncorrelatedDisplacements–HomogeneousDisorder.469
9.2.2 ‡ Temperature...................................472
9.2.3*CorrelatedDisplacements–AtomicSizeEffects.....477
9.3DiffuseScatteringfromChemicalDisorder.................481
9.3.1UncorrelatedChemicalDisorder–RandomAlloys....481
9.3.2 ‡ *SROParameters..............................485
9.3.3 ‡ *PattersonFunctionforChemicalSRO...........487
9.3.4Short-RangeOrderDiffuseIntensity................488
9.3.5 ‡ *IsotropicMaterials............................488
9.3.6*PolycrystallineAverageandSingleCrystalSRO....490
9.4*Amorphouaterials.................................491
9.4.1 ‡ One-DimensionalModel.........................491
9.4.2 ‡ RadialDistributionFunction.....................495ContentsXVII
9.4.3 ‡ PartialPairCorrelationFunctions................500
9.5allAngleScattering..................................502
9.5.1ConceptofallAngleScattering..................502
9.5.2*GuinierApproximation(all Δk)................504
9.5.3*PorodLaw(large Δk)...........................508
9.5.4 ‡ *Density-DensityCorrelations(all Δk)............510
FurtherReading............................................512
Problems..................................................513
10.High-ResolutionTEMImaging ........................... 517
10.1HuygensPrinciple......................................518
10.1.1WaveletsfromPointsinaContinuum...............518
10.1.2HuygensPrincipleforaSphericalWavefront–
FresnelZones....................................523
10.1.3 ‡ FresnelDiffractionNearanEdge..................527
10.2PhysicalOpticsofHigh-ResolutionImaging................532
10.2.1 ‡ WavefrontsandFresnelPropagator...............532
10.2.2 ‡ Lenses.........................................534
10.2.3 ‡ Materials......................................536
10.3ExperimentalHigh-ResolutionImaging....................538
10.3.1DefocusandSphericalAberration..................538
10.3.2 ‡ LensesandSpecimens...........................543
10.3.3LensCharacteristics..............................546
10.4*SimulationsofHigh-ResolutionTEMImages.............555
10.4.1PrinciplesofSimulations..........................555
10.4.2PracticeofSimulations............................561
10.5IssuesandExamplesinHigh-ResolutionTEMImaging......562
10.5.1ImagesofNanostructures..........................562
10.5.2ExamplesofInterfaces............................565
10.5.3*SpecimenandMicroscopeParameters.............568
10.5.4*SomePracticalIssuesforHRTEM................576
FurtherReading............................................580
Problems..................................................581
11.High-ResolutionSTEMImaging .......................... 583
11.1CharacteristicsofHigh-AngleAnnularDark-FieldImaging...583
11.2ElectronChannelingAlongAtomicColumns..............586
11.2.1OpticalFiberogy............................586
11.2.2 ‡ CriticalAngle..................................588
11.2.3*TunnelingBetweenColumns.....................589
11.3ScatteringofChanneledElectrons........................591
11.3.1ElasticScatteringofChanneledElectrons...........591
11.3.2*InelasticScatteringofChanneledElectrons........593
11.4*ComparisonofHAADFandHRTEMImaging............594
11.5HAADFImagingwithAtomicResolution.................595XVIIIContents
11.5.1*EffectofDefocus...............................595
11.5.2ExperimentalExamples...........................597
11.6*LensAberrationsandTheirCorrections.................599
11.6.1 Cs CorrectionwithMagneticHexapoles.............599
11.6.2 ‡ Higher-OrderAberrationsandInstabilities.........602
11.7Examplesof Cs-CorrectedImages........................604
11.7.1Three-DimensionalImaging........................605
11.7.2HighResolutionEELS............................606
FurtherReading............................................607
Problems..................................................608
12.DynamicalTheory ........................................ 611
12.1ChapterOverview......................................611
12.2 ‡ *MathematicalFeaturesofHigh-EnergyElectrons
inaPeriodicPotential..................................613
12.2.1 ‡ *TheSchr¨ odingerEquation......................613
12.2.2 ‡ KinematicalandDynamicalTheory...............619
12.2.3*TheCrystaPhaseGrating..................621
12.3FirstApproachtoDynamicalTheory–BeamPropagation...623
12.4 ‡ SecondApproachtoDynamicalTheory–BlochWaves
andDispersionSurfaces.................................627
12.4.1DiffractedBeams, {Φg},areBeats
ofBlochWaves, {Ψ(j)
} ............................627
12.4.2CrystalPeriodicityandDispersionSurfaces..........633
12.4.3EnergiesofBlochWavesinaPeriodicPotential......637
12.4.4GeneralTwo-BeamDynamicalTheory..............640
12.5EssentialDifferenceBetweenKinematical
andDynamicalTheories.................................646
12.6 ‡ DiffractionError, sg,inTwo-BeamDynamicalTheory....651
12.6.1BlochWaveAmplitudesandDiffractionError........651
12.6.2DispersionSurfaceConstruction....................653
12.7DynamicalDiffractionContrastfromCrystalDefects.......655
12.7.1DynamicalDiffractionContrastWithoutAbsorption..655
12.7.2 ‡ *Two-BeamDynamicalTheory
ofStackingFaultContrast.........................660
12.7.3DynamicalDiffractionContrastwithAbsorption.....664
12.8 ‡ *Multi-BeamDynamicalTheoriesofElectronDiffraction..669
FurtherReading............................................672
Problems..................................................672
Bibliography .................................................. 677
FurtherReading............................................677
ReferencesandFigures......................................682ContentsXX
A.Appendix ................................................. 691
A.1IndexedPowderDiffractionPatterns......................691
A.2MassAttenuationCoefficientsforCharacteristic Kα X-Rays.692
A.3AtomicFormFactorsforX-Rays.........................693
A.4X-RayDispersionCorrectionsforAnomalousScattering.....697
A.5AtomicFormFactorsfor200keVElectrons
andProcedureforConversiontoOtherVoltages............698
A.6IndexedSingleCrystalDiffractionPatterns:fcc,bcc,dc,hcp.703
A.7StereographicProjections................................713
A.8ExamplesofFourierTransforms..........................717
A.9Debye–WallerFactorfromWaveAmplitude...............720
A.10ReviewofDislocations.................................721
A.11TEMLaboratoryExercises..............................728
A.11.1Preliminary–JEOL2000FXDailyOperation........728
A.11.2Laboratory1–MicroscopeProcedures
andCalibrationwithAuandMoO3 ................732
A.11.3Laboratory2–Diffractionysisof θ
Precipitates.735
A.11.4Laboratory3–Chemicalysisof θ
Precipitates..739
A.11.5Laboratory4–ContrastysisofDefects.........740
A.12FundamentalandDerivedConstants.....................742
Index ......................................................... 745
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