Elements of Structures and Defects of Crystalline Materials This pageintentionallyleftblank Elements of Structures and Defects of Crystalline Materials Tsang-Tse Fang National Cheng Kung University Elsevier Radarweg29,POBox211,1000AEAmsterdam,Netherlands TheBoulevard,LangfordLane,Kidlington,OxfordOX51GB,UnitedKingdom 50HampshireStreet,5thFloor,Cambridge,MA02139,UnitedStates Copyrightr2018ElsevierInc.Allrightsreserved. Nopartofthispublicationmaybereproducedortransmittedinanyformorbyanymeans,electronicor mechanical,includingphotocopying,recording,oranyinformationstorageandretrievalsystem,without permissioninwritingfromthepublisher.Detailsonhowtoseekpermission,furtherinformationaboutthe Publisher’spermissionspoliciesandourarrangementswithorganizationssuchastheCopyrightClearance CenterandtheCopyrightLicensingAgency,canbefoundatourwebsite:www.elsevier.com/permissions. ThisbookandtheindividualcontributionscontainedinitareprotectedundercopyrightbythePublisher (otherthanasmaybenotedherein). 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BritishLibraryCataloguing-in-PublicationData AcataloguerecordforthisbookisavailablefromtheBritishLibrary LibraryofCongressCataloging-in-PublicationData AcatalogrecordforthisbookisavailablefromtheLibraryofCongress ISBN:978-0-12-814268-4 ForInformationonallElsevierpublications visitourwebsiteathttps://www.elsevier.com/books-and-journals Publisher:MatthewDeans AcquisitionEditor:ChristinaGifford EditorialProjectManager:NaomiRobertson ProductionProjectManager:VijayarajPurushothaman CoverDesigner:VictoriaPearson TypesetbyMPSLimited,Chennai,India Contents Preface ix Acknowledgements xiii Part I Structures of the Crystalline Materials 1. The Electron Configuration of Atoms 1.1 AtomsWithaSingleElectron 3 1.2 AtomsWithMoreThanOneElectron 6 1.2.1 PenetrationandShielding 7 1.2.2 Energeticd-OrbitalCollapseofFreeNeutralAtoms attheBeginningoftheTransitionRows 8 2. Bonding Within Crystal Structures 2.1 BondinginIonicCrystals 13 2.1.1 EnergyforFormingtheIonsFromNeutralAtoms 13 2.1.2 ThermodynamicViewpointofBondEnergy 15 2.2 CovalentBonds 29 2.2.1 FormationEnergyandMechanismofCovalentBonding 30 2.3 MetallicBonds 31 2.3.1 CohesiveEnergyofMetals 31 2.4 EffectofBondingontheMaterialPropertiesbyMeansofthe Potential-WellConcept 32 2.4.1 ElasticModulus 32 2.4.2 MeltingTemperatures 33 2.4.3 ThermalProperty 33 3. The Structures of Crystalline Crystals 3.1 ArrangementsofAtomsandIonsinCrystallineSolids: SpaceLattice 37 3.2 MetallicStructures 39 3.3 IonicStructures 40 3.3.1 Pauling’sRules 41 v vi Contents 3.4 StructuralDistortioninIonicStructures 46 3.4.1 EffectsofCrystalFieldontheStructuresoftheOxides 47 3.4.2 CrystalFieldStabilizationEnergy 51 3.4.3 EffectsofthedElectronConfigurationontheRadiiof TransitionMetalIons 53 3.4.4 Jahn(cid:1)TellerDistortions 55 3.4.5 StructureDistortionsArisingFromAsymmetricElectron DensityorInertPairEffect 59 3.5 StructureofMaterialTechnologicalInterest 59 3.5.1 StructureandtheRelatedFeatureofZnO 61 3.5.2 StructureandtheRelatedFeatureofSiC 62 3.5.3 StructureandtheRelatedFeatureofTiO 63 2 3.5.4 StructureandtheRelatedFeatureofZrO 63 2 3.5.5 StructureandtheRelatedFeatureofSpinel(AB O ) 64 2 4 3.5.6 StructureandtheRelatedFeatureofPerovskiteABO 67 3 Part II Defects of Crystalline Materials 4. Point Defects in Crystalline Materials 4.1 PointDefectsinMetals 83 4.1.1 SolidSolutions 83 4.1.2 FactorsAffectingtheSolubilityofImpurityAtoms inaSubstitutionalSolidSolution 85 4.1.3 FactorsAffectingtheSolubilityoftheImpurityAtoms inanInterstitialSolidSolution 85 4.1.4 EquilibriumConcentrationofPointDefects 86 4.2 PointDefectsinIonicSolids 92 4.2.1 NotationfortheDescriptionofPointDefectsinBinary MetalOxides 92 4.2.2 DefectStructuresinStoichiometricIonicCrystals 94 4.2.3 DefectStructuresinNonstoichiometricIonicCrystals 94 4.2.4 DefectReactions 95 4.2.5 FormulationofDefectEquations 96 4.2.6 DefectEquilibriuminIonicSolids 109 4.2.7 DefectAssociation 126 5. Line Defects in Crystalline Solids 5.1 TheDiscrepancyBetweentheTheoreticalandObserved YieldStressesofCrystals 129 5.2 ObservationsofDislocations 131 5.3 CrystallographicSlip 132 Contents vii 5.4 ElementaryGeometricCharacteristicsofDislocations 132 5.4.1 TheEdgeDislocation 135 5.4.2 TheScrewDislocation 136 5.4.3 TheMixedDislocation 136 5.5 CriticalResolvedShearStress 137 5.6 PlasticFlowAssociatedWiththeSlipoftheDislocation Motion 138 5.7 StressFieldsofDislocations 142 5.7.1 ConstitutiveEquationsWithLameConstants 142 5.7.2 StressFieldofaScrewDislocation 143 5.7.3 StressFieldsofanEdgeDislocation 145 5.8 EnergyofaDislocation 145 5.8.1 StrainEnergyofaScrewDislocation 146 5.8.2 StrainEnergyofanEdgeDislocation 147 5.9 LineTensionofaDislocation 147 5.10 ForcesUponDislocations 148 5.11 TheBowingofaDislocation 149 5.12 ForceBetweenDislocations 150 5.13 Peach(cid:1)KoehlerEquation 151 5.14 ReactionsBetweenDislocations 154 5.14.1 DislocationNodes 154 5.14.2 KinksandJogs 156 5.14.3 IntersectionsofDislocations 157 5.15 ExtendedDislocations 159 5.15.1 PartialDislocations 160 5.15.2 FaultsintheStackinginFCCCrystals 161 5.15.3 EquilibriumSeparationBetweenPartialDislocations 162 6. Two-Dimensional (Interfaces) and Three-Dimensional (Second Phases) Imperfections in Solids 6.1 GrainBoundaries 169 6.1.1 TiltBoundary 171 6.1.2 TwistBoundary 173 6.1.3 CoincidenceSiteLattice 173 6.2 InterphaseBoundariesinSolids 174 6.2.1 CoherentBoundary 174 6.2.2 IncoherentBoundary 175 6.2.3 PartiallyCoherentorSemicoherentBoundary 175 6.3 SurfaceTension,SurfaceStress,andSurfaceFreeEnergy ofInterfaces 176 6.4 FreeSurface 179 6.4.1 CalculatetheSurfaceFreeEnergyofaPureSolid FCCMetal 180 viii Contents 6.5 InterfacesofPhases 181 6.5.1 Wetting 181 6.5.2 EquilibriumShapesofGrains 182 6.5.3 MorphologicalChangesofSecondPhases 184 6.6 EffectofInterfaceCurvatureontheEquilibriumPressure BetweenTwoPhases 188 6.7 EffectoftheInterfaceCurvatureontheEquilibrium SolubilityBetweenTwoPhases 191 6.8 EquilibriumVacancyConcentrationChangesatCurved Surfaces:DrivingForceforSintering 194 AppendixI:SpectroscopicNotation 199 AppendixII:BandStructuresofMott(cid:1)HubbardMaterialsand theTransitionMetalIonicCompounds,andPolaron 201 Bibliography 205 Index 209 Preface As sparked by the discovery of the high T superconductor, growth and char- c acterization of the materials mainly concerned with structures and defects are at the forefront of the research in materials science. The significance is further boosted on account of the subsequent discovery of the materials with so-called colossal properties, including magnetoresistance and dielectric con- stant. These materials are of perovskite or perovskite-like structures with transition metal ions on the B site and show an enormous variety of intrigu- ing electronic or magnetic properties. This variety is not only related to their chemical flexibility concerning the defects, but also to a larger extent related to the complex character concerning the interplay between transition metal ions in certain coordinations and oxygen. Since these new emerging materi- als with multiple functions provide the most interesting and challenging topics in fundamental physics and the cutting edge of new technologies, they have drawn considerable worldwide attention of scientists with highly inter- disciplinary backgrounds. However, research on these subjects is experienc- ing a superfast development and facing more completion. In response to these challenges, the scientists have to gain and grasp the desired knowledge in a short time. For most existing textbooks, they either are inadequate, focusing on one of the structures and defects, or are voluminous, including a wide variety of subjects. By contrast, this book is designed not only to be concise, yet comprehensive to thoroughly cover the fundamental principles of the structures and defects of crystalline materials, but also to provide deep insights into understanding the relationships of properties, defect chemistry, and processing of concerned materials. What is more, the issue concerning the significant effects on the properties of the functional oxides due to the crystal fields is missing from most of the existing related textbooks. This issue has been included in Section 3.4 of this book. In the fast-paced world, it is more important than ever to understand the fundamentals. Thus this book has been focused on the physics and the atomic mechanics of the pro- blems to cover sufficient fundamentals, deep enough to allow the readers to delve into the most recent literature without too much difficulty. In addition, this book appeal to those other than materials science and engineering back- grounds, thus the author has made an effort to write this book so that it does not assume much prior knowledge of the subject from the readers. Furthermore, there are several issues in most existing textbooks that come ix