Table Of ContentElements 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).
Notices
Knowledgeandbestpracticeinthisfieldareconstantlychanging.Asnewresearchandexperiencebroaden
ourunderstanding,changesinresearchmethods,professionalpractices,ormedicaltreatmentmaybecome
necessary.
Practitionersandresearchersmustalwaysrelyontheirownexperienceandknowledgeinevaluatingand
usinganyinformation,methods,compounds,orexperimentsdescribedherein.Inusingsuchinformationor
methodstheyshouldbemindfuloftheirownsafetyandthesafetyofothers,includingpartiesforwhomthey
haveaprofessionalresponsibility.
Tothefullestextentofthelaw,neitherthePublishernortheauthors,contributors,oreditors,assumeany
liabilityforanyinjuryand/ordamagetopersonsorpropertyasamatterofproductsliability,negligenceor
otherwise,orfromanyuseoroperationofanymethods,products,instructions,orideascontainedinthe
materialherein.
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
