Handbook of solid state diffusion volume 2 Diffusion Analysis inMaterial Applications

478 Pages·2017·25.622 MB·English

by  Divinski, Sergiy V., Paul, Aloke

Handbook of
Solid State Diffusion
Diffusion Analysis in Material Applications
Volume 2
Edited by
Aloke Paul and Sergiy Divinski
HANDBOOK OF SOLID
STATE DIFFUSION:
VOLUME 2
This page intentionally left blank
HANDBOOK OF SOLID
STATE DIFFUSION:
VOLUME 2
Diffusion Analysis in Material Applications
Editedby
ALOKEPAUL
SERGIYDIVINSKI
Elsevier
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CONTENTS
Biographies xi
Preface xix
Acknowledgment xxi
1. DiffusionMeasurementsinNanostructures 1
1.1. AnalyticalSolutions 2
1.2. Simulations 5
1.3. AtomProbeTomography 17
1.4. AtomicTransportKineticMeasurements 22
Conclusion 29
References 31
2. Diffusion-ControlledPhaseTransformationsinOpenSystems 37
2.1. GeneralReviewofFlux-DrivenTransformations 37
2.1.1. Flux-DrivenRipeningofCu6Sn5ScallopsDuringReactionCu/LiquidSolder 39
2.1.2. “Anti-Ripening”:Stirring-DrivenDissolution-RecrystallizationWithFormationof
Nanobelts 41
2.1.3. Flux-DrivenAnti-PhaseDomainsCoarseningDuringReaction 42
2.1.4. Flux-DrivenCellularPrecipitationofPorousLamellarStructuresinCu–SnReactions 42
2.1.5. Flux-DrivenCrystallizationofAmorphousNiPDuringReactionWithTin-Based
Solders 43
2.1.6. NucleationinSharpConcentrationGradients 44
2.1.7. Flux-DrivenNucleationatInterfaces(FDN) 48
2.1.8. Flux-DrivenSelf-RegulatedRepeatingNucleationinSiliconNanowiresDuring
Point-ContactReactionWithMetallicNanowiresorNanoparticles 49
2.1.9. Flux-DrivenOrdering 49
2.1.10. Self-OrganizationofTwo-PhaseStructuresUnderElectromigrationand
Thermomigration 50
2.1.11. HollowNanostructuresFormationandCollapseDrivenbyKirkendallEffect 51
2.1.12. DiffusionInducedBifurcationsandInstabilitiesofKirkendallPlanes 53
2.1.13. Flux-DrivenGrainGrowthDuringDeposition 55
2.1.14. SevereDeformationInducedFormationofLow-Viscosity“Phase”inKOBOProcess 56
2.1.15. ElectromigrationInducedGrainRotationUnderElectronWindinAnisotropic
ConductingBeta-Tin 57
2.2. StandardModeloftheSimultaneous,Diffusion-ControlledPhaseLayersGrowthinthe
DiffusionCouple 58
2.2.1. TheStandardModelforanArbitraryNumberofIntermediatePhases 58
2.2.2. TheStandardModelforSingleIntermediatePhase(N=1) 63
2.2.3. TheStandardModelfortheCaseofTwoIntermediatePhases(N=2) 65
2.3. Flux-DrivenRipeningofCu6Sn5ScallopsDuringReactionofCuSubstrateWithLiquid
Tin-BasedSolder 66
v
vi HandbookofSolidStateDiffusion
2.3.1. SimplifiedModelofMonosizedHemispheres 68
2.3.2. TheoreticalPredictionofLiquidChannelWidth 70
2.3.3. AccountofSizeDistribution–BasicEquations 72
2.4. Flux-DrivenLamellarPrecipitationofCu6Sn5intoPorousCu3SnStructure 75
2.4.1. GeneralRemarks 75
2.4.2. ExperimentalObservations 76
2.4.3. ThermodynamicAnalysisofPossibleTransformations 77
2.4.4. KineticModeloftheEutectoid-LikePorousZoneFormationinOpenSystem 79
2.5. Flux-DrivenNucleationDuringReactiveDiffusion 86
2.5.1. GeneralRemarks 86
2.5.2. ExternalFluxDivergenceinOpenSystem–IdeaofFlux-DrivenNucleation(FDN) 88
2.5.3. NucleationandGrowthofSingleIntermediatePhaseatα/βMeta-Equilibrium
Interface 89
2.5.4. NucleationofSingleIMCatanInterfaceinCompetitionWithDiffusionin
NeighboringSolidSolutions 92
2.5.5. Flux-DrivenNucleationoftheSecondIMCattheInterfacetoPureB 95
2.6. Summary 97
References 98
3. Thermodynamic-KineticMethodonMicrostructuralEvolutionsinElectronics 101
3.1. Introduction 101
3.2. ThermodynamicEvaluationofPhaseEquilibria 101
3.2.1. DifferentTypesofEquilibria 103
3.2.2. DifferentThermodynamicDiagramTypes 107
3.3. KineticConsiderations 117
3.4. Thermodynamic-KineticMethod 121
3.5. UtilizationoftheT-KMethodinMicrosystemsTechnology 123
3.5.1. BinaryAu–SnSystem 124
3.5.2. Au–Cu–SnTernarySystem 130
3.5.3. Au–Ni–SnSystem 138
Conclusions 144
References 145
4. MicrostructuralEvolutionbyReaction–Diffusion:Bulk,ThinFilm,and
Nanomaterials 149
4.1. MathematicalFormulationsforEstimationoftheDiffusionCoefficientsUtilizing
PhysicochemicalModel 149
4.2. EstimationoftheDiffusionParametersFollowingPhysicochemicalApproach 156
4.2.1. GrowthofaSingleProductPhaseinanInterdiffusionZoneBetweenTwoOther
Compounds 158
4.2.2. GrowthofaSingleProductPhaseinanInterdiffusionZoneBetweenTwo
End-MembersofaDiffusionCoupleWithPhaseMixture 159
4.2.3. SimultaneousGrowthoftheProductPhasesinanInterdiffusionZoneandtheUse
ofPhysicochemicalApproach 161
Contents vii
4.3. EvolutionofMicrostructureDependingontheLocationofKirkendallMarkerPlane 166
4.4. AFewExamplesofMorphologicalEvolutionsandIndicationsofDiffusionRatesof
Components 168
References 171
5. ElectromigrationinMetallicMaterialsandItsRoleinWhiskering 173
5.1. IntroductiontoElectromigration 173
5.1.1. FundamentalGoverningEquationsforElectromigration 175
5.1.2. PerformingElectromigrationExperimentsinLab 177
5.1.3. StressGenerationduetoElectromigration 180
5.1.4. ElectromigrationinLiquidMetals 182
5.1.5. ElectromigrationinAlloysorMultielementMaterialSystems 183
5.1.6. EffectofElectromigrationonReactionKinetics 184
5.1.7. CouplingBetweenElectromigrationandThermomigration 185
5.2. IntroductiontoWhiskeringinTinCoatings 189
5.2.1. FundamentalsofWhiskeringPhenomenon 190
5.2.1.1.RegenerationofCompressiveStress 190
5.2.1.2.MassTransportFromBulktoWhiskerRoot 191
5.2.1.3.IdentificationofLocationofWhiskerGrain 191
5.2.1.4.EffectofServiceConditionsonWhiskerGrowth 192
5.2.1.5.RoleofStressandStressGradient 193
5.2.2. SuppressionofWhiskeringPhenomenon 193
5.3. RoleofElectromigrationinWhiskering 197
5.3.1. CriticalLengthforElectromigration-InducedWhiskerGrowth 198
5.3.2. MinimizingElectromigration-InducedWhiskeringThroughGrainBoundary
Engineering 198
5.4. Summary 200
Acknowledgements 202
References 202
6. DiffusionCoupleTechnique:AResearchToolinMaterialsScience 207
6.1. Introduction 207
6.2. BasicExperimentalProceduresUsedinDiffusionCoupleMethod 208
6.2.1. PreparationofDiffusionCouples 208
6.2.2. AnalyticalTechniquesandSpecimenPreparation 210
6.3. DerivationofKineticDataFromDiffusionCoupleExperiments 213
6.3.1. GeneralConsiderations:AcquisitionofDiffusionDataforBinarySolidSolution
Systems 213
6.3.2. RelationsBetweenThermodynamicStabilitiesandGrowthKineticsofaBinary
StoichiometricCompound 224
6.3.3. DeficienciesoftheProposedMethod 233
6.4. TheDiffusionCoupleTechniqueinPhaseDiagramDetermination–Revisited 240
6.4.1. GeneralPrinciples 240
6.4.2. VariationsoftheDiffusionCoupleMethod 242
viii HandbookofSolidStateDiffusion
6.4.3. ErrorSourcesEncounteredintheDiffusionCoupleExperiments 251
6.5. ADiffusionCoupleApproachinStudyingComposition–Structure–PropertyRelationships
inSolidSolutionAlloySystems 262
6.5.1. InterdiffusionCoefficientsandHardnessProfilesintheNi–Co–PtSystemat1200°C 262
6.5.2. ScreeningofCompositionDependentShapeMemoryEffectintheTiNi–TiPd
System 268
6.5.3. ConcludingRemarks 271
References 272
7. Diffusion-ControlledInternalPrecipitationReactions 277
7.1. Introduction 277
7.2. BasicExperimentalProceduresUsedinResearchonSolid-StateInternalReactions 279
7.2.1. ThermodynamicActivityofanOxidantSpeciesImposedbyAmbientEnvironment
ontheMetalSurfaceDuringHigh-TemperatureInteraction 280
7.2.2. InvestigationofReactionKinetics 284
7.2.3. ExaminationofReactionProductsandPrecipitationZoneMicrostructure 285
7.3. DiversityofFormsandVariationsofMicrostructuresGeneratedbyInternalPrecipitation
Reactions–SelectedExperimentalResults 287
7.4. Thermodynamic-DiffusionKineticsApproachinEvaluatingInternalSolid-StateReactions 294
7.5. KineticAnalysisoftheInternalPrecipitationReactionsinBinaryAlloys 301
7.5.1. SimplifiedTreatmentofthePrecipitationKinetics 301
7.5.2. Wagner’sTreatmentofInternalOxidation 304
7.5.3. AnalysisoftheEffectofSupersaturationRequirementsonInternalPrecipitation
Kinetics 308
7.5.4. VariationinNumberDensityandSizeofPrecipitatesThroughtheZoneofInternal
Reaction 310
7.5.5. InternalReactionsInvolvingLowStabilityPrecipitatingCompounds 312
7.5.6. TransitionFromInternaltoExternalOxidation 318
7.6. InternalPrecipitationReactionsasa“ResearchTool”forEvaluatingInterstitialTransportin
Metals 320
7.7. DeformationPhenomenaAccompanyingInternalPrecipitationReactionsinMetals 328
7.8. ConcludingRemarks 334
References 335
8. DiffusioninNuclearMaterials 339
8.1. DiffusioninNuclearFuels 340
8.1.1. DifficultiesinDiffusionExperiments 340
8.1.2. DiffusioninMetallicFuels 341
8.1.3. DiffusioninCeramicFuels 344
8.1.3.1.DiffusioninOxideBasedFuels 345
8.1.3.2.DiffusioninCarbideBasedFuels 347
8.1.3.3.DiffusioninNitrideBasedFuels 349
8.1.4. DiffusionofFissionGases 350
8.2. DiffusioninCladMaterials 352
8.2.1. DiffusioninAluminium 353
Contents ix
8.2.2. DiffusioninZirconiumandItsAlloys 356
8.2.2.1.Self-andImpurityDiffusioninZirconium 356
8.2.2.2.DiffusioninZirconiumBasedAlloys 360
8.3. DiffusioninStructuralMaterials 364
8.3.1. Self-DiffusioninIron 364
8.3.2. ImpurityDiffusioninIron 365
8.3.2.1.DiffusionofChromiuminIron 365
8.3.2.2.DiffusionofNickelinIron 366
8.3.2.3.DiffusionofMolybdenumandManganeseinIron 366
8.3.3. DiffusioninIron–NickelSystem 366
8.3.4. DiffusioninFerriticStainlessSteels 367
8.3.5. DiffusioninAusteniticStainlessSteels 367
8.3.6. DiffusioninNickel 368
8.3.6.1.Self-DiffusioninNickel 368
8.3.6.2.ImpurityDiffusioninNickel 369
8.3.6.3.DiffusioninNickelBasedAlloys 369
References 372
9. TheGrowthofSilicidesandGermanides 379
9.1. Introduction 379
9.2. ExperimentalProcedure 381
9.3. GrowthofSilicides:BulkDiffusionCoupleVersusThinFilm 383
9.3.1. GrowthofSilicideinDiffusionCouple 383
9.3.2. LinkBetweenSilicideGrowthinDiffusionCoupleandinThinFilms 384
9.4. MechanismsofFormationofNiSilicidesandGermanides 392
9.4.1. LateralGrowth 393
9.4.2. NormalGrowth 398
9.4.3. SequentialVersusSimultaneousGrowth 404
9.4.4. StressDuringtheFormationofSilicide 413
9.4.5. TransientPhase 418
9.4.6. TextureinSilicidesandGermanides 421
9.5. AlloyElements 421
9.5.1. RoleofPtontheNucleationofNiSi2 423
9.5.2. RoleofPtontheKineticsofFormation 424
9.5.3. RoleofPtontheFormationSequence 427
9.5.4. RoleoftheIntermixedLayerontheFirstPhase 429
9.6. DopantandSilicide 432
9.6.1. DiffusionofAsinδ-Ni2Si 433
9.6.2. PrecipitationofAsinθ-Ni2Si 434
9.7. FormationofSilicideinTransistors 437
9.8. Conclusion 439
Acknowledgements 439
References 439
Index 447