Phase Transitions in Materials

587 Pages·2014·43.465 MB·English

by  Brent Fultz

PhaseTransitionsinMaterials
Offering a fresh viewpoint on phase changes and the thermodynamics of materials, this
textbookcoversthethermodynamicsandkineticsofthemostimportantphasetransitions
in materials science, spanning classical metallurgy through to nanoscience and quantum
phasetransitions.
Clear,concise,andcompleteexplanationsrigorouslyaddresstransitionsfromtheatomic
scale up, providing the quantitative concepts, analytical tools, and methods needed to
understand modern research in materials science. Topics are grouped according to com-
plexity, ensuring that students have a solid grounding in core topics before they begin
to tackle more advanced material, and are accompanied by numerous end-of-chapter
problems.
Withexplanationsfirmlyrootedinthecontextofmodernadvancesinelectronicstructure
and statistical mechanics, and developed from classroom teaching, this book is the ideal
companion for graduate students and researchers in materials science, condensed matter
physics,solidstatescience,andphysicalchemistry.
BrentFultz is the Barbara and Stanley R. Rawn, Jr., Professor of Materials Science and
Applied Physics at the California Institute of Technology. He has been awarded a Presi-
dentialYoungInvestigatorAward,theEMPMDDistinguishedScientistAward(2010),and
hasledlargeprojectssuchasthestate-of-the-artneutronscatteringinstrument,ARCS,and
dataanalysisforneutronscatteringexperiments,DANSE.
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Phase Transitions in Materials
BRENT FULTZ
CaliforniaInstituteofTechnology
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UniversityPrintingHouse,CambridgeCB28BS,UnitedKingdom
CambridgeUniversityPressispartoftheUniversityofCambridge.
ItfurtherstheUniversity’smissionbydisseminatingknowledgeinthepursuitof
education,learningandresearchatthehighestinternationallevelsofexcellence.
www.cambridge.org
Informationonthistitle:www.cambridge.org/9781107067240
©B.Fultz2014
Thispublicationisincopyright.Subjecttostatutoryexception
andtotheprovisionsofrelevantcollectivelicensingagreements,
noreproductionofanypartmaytakeplacewithoutthewritten
permissionofCambridgeUniversityPress.
Firstpublished2014
PrintedintheUnitedKingdombyTJInternationalLtd,Padstow,Cornwall
AcatalogrecordforthispublicationisavailablefromtheBritishLibrary
LibraryofCongressCataloginginPublicationdata
Fultz,B.(Brent),author.
Phasetransitionsinmaterials/BrentFultz,CaliforniaInstituteofTechnology.
pages cm
Includesbibliographicalreferencesandindex.
ISBN978-1-107-06724-0
1. Phasetransformations(Statisticalphysics)–Textbooks. 2. Thermodynamics–Textbooks.
3. Materials–Thermalproperties–Textbooks. 4. Statisticalmechanics–Textbooks. I. Title.
QC175.16.P5F86 2014
530.4(cid:2)74–dc23
2013046223
ISBN978-1-107-06724-0Hardback
Additionalresourcesforthispublicationatwww.cambridge.org/fultz
CambridgeUniversityPresshasnoresponsibilityforthepersistenceoraccuracyof
URLsforexternalorthird-partyinternetwebsitesreferredtointhispublication,
anddoesnotguaranteethatanycontentonsuchwebsitesis,orwillremain,
accurateorappropriate.
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ThisbookisdedicatedtoEmily,Eric,andElissa
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Contents
Preface pagexiii
Acknowledgments xvii
Notation xix
PartI Basicthermodynamicsandkineticsofphasetransformations 1
1 Introduction 3
1.1 Whatisaphasetransition? 3
1.2 Atomsandmaterials 4
1.3 Pureelements 6
1.4 Alloys:unmixingandordering 9
1.5 Transitionsandtransformations 11
1.6 Briefreviewofthermodynamicsandkinetics 14
Problems 18
2 EssentialsofT–cphasediagrams 20
2.1 Overviewoftheapproach 20
2.2 Intuitionandexpectationsaboutalloythermodynamics 22
2.3 Freeenergycurves,soluteconservation,andtheleverrule 26
2.4 Commontangentconstruction 28
2.5 Continuoussolidsolubilityphasediagram 30
2.6 Solidsolutions 31
2.7 Unmixingphasediagrams 37
2.8 Eutecticandperitecticphasediagrams 39
2.9 Ternaryphasediagrams 42
2.10 Long-rangeorderinthepointapproximation 44
2.11 Alloyphasediagrams 48
Problems 49
3 Diffusion 52
3.1 Thediffusionequation 52
3.2 Gaussiananderrorfunctionsolutionstothe1Ddiffusion
equation 56
3.3 Fourierseriessolutionstothediffusionequation 61
3.4 Bessel functions and other special function solutions to the
diffusionequation 66
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viii Contents
3.5 Kineticmasterequationandequilibrium 69
3.6 Linearkineticresponse 71
Problems 72
4 Nucleation 74
4.1 Terminologyandissues 75
4.2 Criticalnucleus 76
4.3 Heterogeneousnucleation 79
4.4 Freeenergycurvesandelasticenergy 81
4.5 Thenucleationrate 85
4.6 Time-dependentnucleation 92
Problems 94
5 Effectsofdiffusionandnucleationonphasetransformations 96
5.1 Nonequilibriumprocessingofmaterials 96
5.2 Alloysolidificationwithsolutepartitioning 99
5.3 Alloysolidification:suppresseddiffusioninthesolidphase 100
5.4 Alloysolidification:suppresseddiffusioninthesolidandliquid 105
5.5 Practicalissuesforalloysolidificationandevaporation 106
5.6 Heatflowandkinetics 109
5.7 Nucleationkinetics 111
5.8 Glassformation 112
5.9 Solid-stateamorphizationandsuppresseddiffusioninasolidphase 114
5.10 Reactionsatsurfaces 115
5.11 Theglasstransition 120
Problems 121
PartII Theatomicoriginsofthermodynamicsandkinetics 125
6 Energy 127
6.1 Molecularorbitaltheoryofdiatomicmolecules 127
6.2 Electronicenergybandsinsolids 134
6.3 Elasticconstantsandtheinteratomicpotential 145
6.4 Linearelasticity 149
6.5 Misfittingparticle 153
6.6 Surfaceenergy 158
Problems 161
7 Entropy 163
7.1 Staticanddynamicsourcesofentropy 163
7.2 Short-rangeorderandthepairapproximation 165
7.3 Localatomicstructuresdescribedbyclusters 168
7.4 Thermodynamicswithclusterapproximations 170
7.5 Conceptofvibrationalentropy 172
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ix Contents
7.6 Phononstatistics 175
7.7 Latticedynamicsandvibrationalentropy 176
7.8 Bondproportionmodel 179
7.9 Bond-stiffness-versus-bond-lengthmodel 187
Problems 190
8 Pressure 194
8.1 Materialsunderpressureatlowtemperatures 194
8.2 Thermalpressure,astepbeyondtheharmonicmodel 199
8.3 Freeenergiesandphaseboundariesunderpressure 200
8.4 Chemicalbondingandantibondingunderpressure 202
8.5 Two-levelsystemunderpressure 205
8.6 Activationvolume 208
Problems 209
9 Atommovementswiththevacancymechanism 211
9.1 Randomwalkandcorrelations 211
9.2 Phenomenainalloydiffusion 220
9.3 Diffusioninapotentialgradient 227
9.4 Nonthermodynamicequilibriumindrivensystems 232
9.5 Vineyard’stheoryofdiffusion 235
Problems 240
PartIII Typesofphasetransformations 245
10 Melting 247
10.1 Freeenergyandlatentheat 247
10.2 Chemicaltrendsofmelting 248
10.3 Freeenergyofasolid 250
10.4 Entropyofaliquid 257
10.5 ThermodynamicconditionforT 259
m
10.6 Glasstransition 261
10.7 Twodimensions 264
Problems 266
11 Transformationsinvolvingprecipitatesandinterfaces 268
11.1 Guinier–Prestonzones 268
11.2 Surfacestructureandthermodynamics 270
11.3 Surfacestructureandkinetics 276
11.4 Chemicalenergyofaprecipitateinterface 278
11.5 Elasticenergyandshapeofgrowingprecipitates 280
11.6 Precipitationatgrainboundariesanddefects 282
11.7 Theeutectoidreactionandferrousmetallurgy 285
11.8 TheKolmogorov–Johnson–Mehl–Avramigrowthequation 291
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x Contents
11.9 Coarsening 293
Problems 296
12 Spinodaldecomposition 298
12.1 Concentrationfluctuationsandthefreeenergyofsolution 298
12.2 AddingasquaregradienttermtothefreeenergyF(c) 300
12.3 Constrainedminimizationofthefreeenergy 304
12.4 Thediffusionequation 309
12.5 Effectsofelasticenergy 311
Problems 313
13 Phasefieldtheory 315
13.1 Spatialdistributionofphasesandinterfaces 315
13.2 Solidification 318
13.3 Ginzburg–Landauequationandorderparameter 319
13.4 Interfacesbetweendomains 322
Problems 330
14 Methodofconcentrationwavesandchemicalordering 332
14.1 Structureinrealspaceandreciprocalspace 332
14.2 Symmetryandthestar 338
14.3 Thefreeenergyink-spacewithconcentrationwaves 341
14.4 SymmetryinvarianceoffreeenergyandLandau–Lifshitzrulefor
second-orderphasetransitions 344
14.5 Thermodynamicsoforderinginthemeanfieldapproximationwith
long-rangeinteractions 349
Problems 353
15 Diffusionlesstransformations 355
15.1 Dislocationsandmechanisms 356
15.2 Twinning 360
15.3 Martensite 362
15.4 Thecrystallographictheoryofmartensite 368
15.5 Landautheoryofdisplacivephasetransitions 370
15.6 First-orderLandautheory 374
15.7 Crystalinstabilitiesandphonons 377
Problems 381
16 Thermodynamicsofnanomaterials 383
16.1 Grainboundarystructure 384
16.2 Grainboundaryenergy 386
16.3 Gibbs–Thomsoneffect 387
16.4 Energiesoffreeelectronsconfinedtonanostructures 390
16.5 Configurationalentropyofnanomaterials 392
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