Solidification and Crystallization Processing in Metals and Alloys PDF
Preview Solidification and Crystallization Processing in Metals and Alloys
Solidification and Crystallization Processing in Metals and Alloys Solidification and Crystallization Processing in Metals and Alloys Hasse Fredriksson KTH, Royal Institute of Technology, Stockholm, Sweden and (cid:2) Ulla Akerlind University of Stockholm, Stockholm, Sweden Thiseditionfirstpublished2012 (cid:2)2012JohnWiley&Sons,Ltd. Registeredoffice JohnWiley&SonsLtd,TheAtrium,SouthernGate,Chichester,WestSussex,PO198SQ,UnitedKingdom Fordetailsofourglobaleditorialoffices,forcustomerservicesandforinformationabouthowtoapplyforpermissionto reusethecopyrightmaterialinthisbookpleaseseeourwebsiteatwww.wiley.com. TherightoftheauthortobeidentifiedastheauthorofthisworkhasbeenassertedinaccordancewiththeCopyright,Designs andPatentsAct1988. Allrightsreserved.Nopartofthispublicationmaybereproduced,storedinaretrievalsystem,ortransmitted,inanyformorby anymeans,electronic,mechanical,photocopying,recordingorotherwise,exceptaspermittedbytheUKCopyright,Designs andPatentsAct1988,withoutthepriorpermissionofthepublisher. Wileyalsopublishesitsbooksinavarietyofelectronicformats. Somecontentthatappearsinprintmaynotbeavailablein electronicbooks. Designationsusedbycompaniestodistinguishtheirproductsareoftenclaimedastrademarks.Allbrandnamesandproduct namesusedinthisbookaretradenames,servicemarks,trademarksorregisteredtrademarksoftheirrespectiveowners.Thepublisher isnotassociatedwithanyproductorvendormentionedinthisbook.Thispublicationisdesignedtoprovideaccurateand authoritativeinformationinregardtothesubjectmattercovered.Itissoldontheunderstandingthatthepublisherisnotengaged inrenderingprofessionalservices.Ifprofessionaladviceorotherexpertassistanceisrequired,theservicesofacompetent professionalshouldbesought. Thepublisherandtheauthormakenorepresentationsorwarrantieswithrespecttotheaccuracyorcompletenessofthecontents ofthisworkandspecificallydisclaimallwarranties,includingwithoutlimitationanyimpliedwarrantiesoffitnessforaparticular purpose. Thisworkissoldwiththeunderstandingthatthepublisherisnotengagedinrenderingprofessionalservices. Theadvice andstrategiescontainedhereinmaynotbesuitableforeverysituation. Inviewofongoingresearch,equipmentmodifications, changesingovernmentalregulations,andtheconstantflowofinformationrelatingtotheuseofexperimentalreagents,equipment, anddevices,thereaderisurgedtoreviewandevaluatetheinformationprovidedinthepackageinsertorinstructionsforeachchemical, pieceofequipment,reagent,ordevicefor,amongotherthings,anychangesintheinstructionsorindicationofusageandfor addedwarningsandprecautions.ThefactthatanorganizationorWebsiteisreferredtointhisworkasacitationand/orapotential sourceoffurtherinformationdoesnotmeanthattheauthororthepublisherendorsestheinformationtheorganizationorWebsite mayprovideorrecommendationsitmaymake. Further,readersshouldbeawarethatInternetWebsiteslistedinthisworkmay havechangedordisappearedbetweenwhenthisworkwaswrittenandwhenitisread. Nowarrantymaybecreatedorextendedby anypromotionalstatementsforthiswork. Neitherthepublishernortheauthorshallbeliableforanydamagesarisingherefrom. LibraryofCongressCataloging-in-PublicationData Fredriksson,Hasse. Solidificationandcrystallizationprocessinginmetalsandalloys/Hasse FredrikssonandUllaA˚kerlind. p.cm. Includesbibliographicalreferencesandindex. ISBN978-1-119-99305-6(cloth) 1.Metalcrystals–Growth. I.A˚kerlind,Ulla. II.Title. TN690.F732012 6690.94–dc23 2011014030 AcataloguerecordforthisbookisavailablefromtheBritishLibrary. ISBN:978-1-119-99305-6 Setin10/12pt,TimesbyThomsonDigital,Noida Contents Preface ix 1 ThermodynamicConcepts and Relationships 1 1.1 Introduction 2 1.2 ThermodynamicConcepts and Relationships 2 1.3 ThermodynamicsofSingle-Component Systems 10 1.4 ThermodynamicsofMultiple-Component Systems 16 1.5 ThermodynamicsofAlloys 21 1.6 ThermodynamicsofIdealBinarySolutions 25 1.7 ThermodynamicsofNon-Ideal Binary Solutions 26 1.8 Experimental DeterminationofThermodynamicQuantities of Binary Alloys 34 Summary 36 Further Reading 41 2 ThermodynamicAnalysis ofSolidification Processes inMetals and Alloys 42 2.1 Introduction 42 2.2 ThermodynamicsofPureMetals 43 2.3 ThermodynamicsofBinary Alloys 44 2.4 Equilibrium Between Phases inBinarySolutions. Phase Diagrams of BinaryAlloys 50 2.5 Driving Force of Solidificationin Binary Alloys 76 2.6 ThermodynamicsofTernary Alloys 78 2.7 ThermodynamicsofVacanciesinPureMetalsand Alloys 83 Summary 90 Exercises 94 References 98 Further Reading 98 3 Properties ofInterfaces 99 3.1 Introduction 99 3.2 Classical Theory ofInterface EnergyandSurface Tension 100 3.3 ThermodynamicsofInterphases 114 3.4 Structures of Interfaces 123 3.5 Equilibrium Shapes of Crystals 145 Summary 155 Exercises 161 References 165 4 Nucleation 166 4.1 Introduction 166 4.2 Homogeneous Nucleation 167 4.3 HeterogeneousNucleation. Inoculation 179 4.4 Nucleation ofBubbles 190 4.5 Crystal Multiplication 193 Summary 194 Exercises 197 References 200 vi Contents 5 CrystalGrowth in Vapours 201 5.1 Introduction 202 5.2 Crystal Morphologies 202 5.3 Chemical Vapour Deposition 203 5.4 Crystal Growth 206 5.5 NormalCrystal Growth of Rough Surfaces inVapours 210 5.6 Layer Crystal Growth ofSmooth Surfaces inVapours 214 5.7 Influence ofImpurities on Crystal Growth inVapours 238 5.8 Epitaxial Growth 244 5.9 Whisker Growth 249 5.10 Mechanical Restrictions on ThinFilms 251 Summary 256 Exercises 263 References 266 6 CrystalGrowth in Liquids and Melts 267 6.1 Introduction 268 6.2 Structures of Crystalsand Melts 268 6.3 Growth Methods 275 6.4 Crystal Growth 278 6.5 Volume Changes and RelaxationProcesses during Anelastic Crystal Growth in Metal Melts 279 6.6 NormalCrystal Growth inPureMetal Melts 289 6.7 Layer Crystal Growth ofSmooth Surfaces inLiquids 297 6.8 NormalCrystal Growth inBinary Alloys 310 6.9 Diffusion-Controlled Growth ofPlanarCrystals inBinaryAlloys 318 6.10 Diffusion-Controlled Growth of SphericalCrystalsin Alloys 324 6.11 Impingement 338 6.12 Precipitation of Pores 340 Summary 343 Exercises 355 References 360 7 HeatTransport during Solidification Processes. ThermalAnalysis 361 7.1 Introduction 362 7.2 BasicConcepts andLawsofHeatTransport 362 7.3 Convection 366 7.4 Theory ofHeatTransport at Unidirectional Solidification 378 7.5 Production ofSingleCrystals by Unidirectional Solidification 385 7.6 Thermal Analysis 395 7.7 Variable Heat of Fusion ofMetals andAlloys 408 7.8 Variable Heat Capacitivity ofMetalsand Alloys 416 Summary 422 Exercises 429 References 432 8 CrystalGrowth Controlled by Heatand Mass Transport 433 8.1 Introduction 433 8.2 Heat and Mass Transports in Alloys during Unidirectional Solidification 434 8.3 ZoneRefining 443 8.4 SingleCrystal Productionby Czochralski Technique 450 8.5 CellularGrowth. Constitutional Undercooling. Interface Stability 454 Summary 465 Exercises 469 References 474 Contents vii 9 Faceted and Dendritic Solidification Structures 475 9.1 Introduction 476 9.2 Formation ofFaceted Crystals 476 9.3 Growth ofFacetedCrystals inPure Metal Melts 476 9.4 Growth ofFacetedCrystals inAlloy Melts 485 9.5 Growth ofDendrite Crystals 503 9.6 Development of Dendrites 529 9.7 Transitions between StructureTypesinAlloys 565 Summary 573 Exercises 580 References 585 10 Eutectic Solidification Structures 587 10.1 Introduction 588 10.2 Classification of Eutectic Structures 588 10.3 NormalEutecticGrowth 589 10.4 Degenerate and Coupled Eutectic Growth 620 10.5 Structures of Ternary Alloys 635 10.6 SolidificationofFe-C Eutectics 646 10.7 SolidificationofAl-Si Eutectics 658 10.8 Transition between NormalLamellar and Rod Eutectic Growth 665 Summary 669 Exercises 675 References 680 11 Peritectic Solidification Structures 681 11.1 Introduction 681 11.2 Peritectic Reactions and Transformations 682 11.3 Peritectic Reactions and Transformationsin Iron-Base Alloys 693 11.4 Metastable Reactionsin Iron-Base Alloys 702 11.5 Metatectic Reactions and Transformations 704 11.6 Microsegregation inIron-Base Alloys 708 11.7 Transitions between Peritectic and Eutectic Reactions inIron-Base Alloys 716 Summary 719 Exercises 724 References 727 12 Metallic Glasses and Amorphous Alloy Melts 729 12.1 Introduction 730 12.2 Basic Concepts andDefinitions 731 12.3 Production ofMetallic Glasses 735 12.4 Experimental Methods for StructureDeterminationof Metallic Glassesand AmorphousAlloyMelts 741 12.5 Structures of Metallic Glasses 744 12.6 Comparison ofthe Structures ofMetallicGlassesand Amorphous Alloy Melts. Rough Models ofMetallicGlasses andAmorphous Alloy Melts 753 12.7 Casting of Metallic Glasses.CrystallizationProcesses in Amorphous Alloy Melts 759 12.8 Classification of Metallic Glasses 763 12.9 Properties and Applications ofMetallic Glasses 764 Summary 771 Exercises 775 References 779 Answersto Exercises 781 Index 803 Preface The present bookisthe thirdand last book ina series of three: 1. MaterialsProcessing during Casting, Wiley2006 2. Physicsof FunctionalMaterials,Wiley2008 3. Solidification and CrystallizationProcessing inMetalsand Alloys, Wiley2012 SolidificationandCrystallizationProcessinginMetalsandAlloysrepresentsadeeperinterpretation ofthesolidificationandcrystallizationprocessesthanthattreatedinthebookMaterialsProcessing duringCasting,writtenfortheundergraduatelevel.Theaimofthepresentbookistoanalyzethe solidification and crystallization processes from a general point of view and in accordance with generallyacceptedresultsandexperimentalevidenceofmodernresearchinthefield.Hence,thebook does nottreat applicationson casting otherthan asoccasionalexamples. ThebookmaybeusefulandsuitableasatextbookoncoursesattheMasterandPhDlevel.The mathematicallevelisnotdiscouraginglyhigh.OrdinarybasiccoursesinMathematicsatuniversity levelareenough.Ontheotherhand,genuineknowledgeofPhysicsisoftenrequired.Thesecond book,PhysicsofFunctionalMaterials,oranyotherPhysicsbookwithanyotherequivalentcontent, willcoverthiswantforthosewhoneedit.Numerouscitationstothesecondbookaregiveninthe present book. SolidificationandCrystallizationProcessinginMetalsandAlloysstartswithachapterofbasic thermodynamics.Chapter1isareviewofthethermodynamicsthatlaterwillbeappliedonmetalsand alloys.Itmaybeatoughandabstractintroduction.Alternatively,itcanbestudiedinconnectionwith laterapplications.Energyconditionsplayanimportantroleforunderstandingthedrivingforcesof solidificationprocessesinmetalsandalloys.ThesetopicsaretreatedinChapter2.Thestructureand properties ofinterfaces between two phases and the nucleation of embryos and forming of stable nucleiarecloselyrelatedtocrystallizationprocesses.Thebasicoutlinesofthesefieldsaregivenin Chapters3 and4, respectively. Afterthesefourbasicandgeneralchapters,Chapters5and6follow,wherethemechanismsofthe solidification and crystallization processes invapours and liquids are extensively discussed. Heat transportduringsolidificationprocessesistreatedinChapter7,whichalsoincludesanorientation aboutmodernmethodsofthermalanalysis.Chapter8dealswithcrystalgrowthcontrolledbyheat and mass transport. Therestofthebookisdevotedtothestructuresofthesolidphasesthatformduringdifferenttypes of solidification processes, i.e. faceted and dendritic structures (Chapter 9), eutectic structures (Chapter10),peritectic structures (Chapter 11)and structure ofMetallicGlasses(Chapter 12). SolidificationandCrystallizationProcessinginMetalsandAlloyscontainsmanysolvedexamples inthetextandexercisesforstudentsattheendofeachchapter.Answerstoalltheexercisesaregiven attheendofthebook.Ina‘GuidetoExercises’fullsolutionstoalltheexercisesaregivenonthe Internetat http://www.wiley.com/go/fredriksson3 Acknowledgements ThisbookisbasedonlecturesandexercisespresentedtoPhDandMasterstudentsovertheyears. Wewanttoexpressoursincerethankstothemfortheirengagementandforthefruitfuldiscussionswe x Preface havehadwiththemaboutdifferentscientifictopicsinthefield.Thecommunicationwiththemhelped ustoidentifytheitemsthatweredifficultforthemtounderstand.Inthisway,wecouldtrytoexplain better and improve the book. We are most grateful toMSc Per OlovNilsson for manyfruitful mathematical discussions and (cid:2) general support through theyears.We alsowish toexpressoursincere thanks toDr Jonas Aberg, Thomas Bergstr€om (Casting of Metals, KTH, Stockholm), Dr Gunnar Edvinsson (University of Stockholm),DrBengtO¨rjanJonsson(KTH),DrHaniNasserandDrSatheesRanganathan(Casting ofMetals,KTH)fortheirvaluablesupportconcerningpracticalmatterssuchasannoyingcomputer (cid:2) problems and application of some special computer programs. We also thank Dr Lars Akerlind warmlyfor patient assistancewith checking parts of the manuscript. WeareverygratefulforfinancialsupportfromtheIronMastersAssociationinSwedenandthe FoundationofSvenandAstridToresson,whichmadeitpossibleforustofulfillthelastpartofthis project. (cid:2) In particular, wewant to express our sinceregratitude to Karin Fredriksson and Lars Akerlind. Withouttheirconstantsupportandgreatpatiencethroughtheyearsthisbookwouldneverhavebeen written. Finally,wewanttothankeachotherforamorethan10yearslongandpleasantcooperation.Ithas been the perfect symbiosis. Neither of us could have written this trilogy without the other. We complementedeachotherwell.Oneofus(guesswho)contributedmanyyearsofresearchinthefield and an ever-lasting enthusiasm to his devoted subject. The other one contributed with some Mathematics and Physics together with many years experience of book production and teaching Physicsat universitylevelandalsoplentyoftimefor the extensiveproject. HasseFredriksson (cid:2) UllaAkerlind Stockholm,May 2010 1 Thermodynamic Concepts and Relationships 1.1 Introduction 2 1.2 Thermodynamic Concepts and Relationships 2 1.2.1 First LawofThermodynamics. Principle ofConservationof Energy 2 1.2.2 Enthalpy 2 1.2.3 Second LawofThermodynamics. Entropy 3 1.2.4 Gibbs’ Free Energy 8 1.2.5 Intensiveand ExtensiveThermodynamic Quantities 9 1.3 Thermodynamics ofSingle-Component Systems 10 1.3.1 Clausius–Clapeyron’s Law 10 1.3.2 EquilibriumbetweenLiquid andSolid Phases. Influence ofPressure 11 andCrystal Curvature on Melting Point 1.3.3 EquilibriumbetweenLiquid andGaseous Phases.Influence ofPressure on 13 Boiling Point.Bubble Formationin Melts 1.3.4 Molar Gibbs’ Free Energyofa Pure Metal 15 1.4 Thermodynamics ofMultiple-Component Systems 16 1.4.1 Partial Molar ThermodynamicQuantities 16 1.4.2 RelativeThermodynamicQuantities and Reference States. RelativePartial 18 Molar ThermodynamicQuantities or PartialMolar Quantities ofMixing 1.4.3 RelativeIntegral MolarThermodynamicQuantities or IntegralMolar 19 Quantities ofMixing 1.4.4 Other Thermodynamic Functions andRelationships 21 1.5 Thermodynamics ofAlloys 21 1.5.1 Heat of Mixing 22 1.5.2 Ideal and Non-Ideal Solutions 23 1.6 Thermodynamics ofIdeal Binary Solutions 25 1.6.1 Molar Gibbs’ Free EnergyofIdealBinary Solutions 25 1.7 Thermodynamics ofNon-Ideal Binary Solutions 26 1.7.1 Activitiesof Non-Ideal SolutionsRaoult’s and Henry’s Laws 26 1.7.2 Excess Quantities ofNon-Ideal Solutions 30 1.7.3 Molar Gibbs’ Free EnergiesofNon-Ideal Binary Solutions 32 1.8 Experimental Determination of Thermodynamic Quantities ofBinary Alloys 34 1.8.1 DeterminationofMolarHeat ofMixing ofBinaryAlloys 34 1.8.2 DeterminationofPartialMolarGibbs’FreeEnergyofMixingofBinaryAlloys 35 Summary 36 Further Reading 41 SolidificationandCrystallizationProcessinginMetalsandAlloys,FirstEdition.HasseFredrikssonandUllaA(cid:2)kerlind. (cid:2)2012JohnWiley&Sons,Ltd.Published2012byJohnWiley&Sons,Ltd. 2 Solidification andCrystallizationProcessing inMetalsand Alloys 1.1 Introduction Solidification or crystallization is a process where the atoms are transferred from the disordered liquidstatetothemoreorderedsolidstate.Therateofthecrystallizationprocessisdescribedand controlledbykineticlaws.Theselawsgiveinformationofthemovementsoftheatomsduringthe rearrangement.Inmostcasesadrivingforceisinvolvedthatmakesitpossibletoderivetherateofthe solidification process. The aim of this book is to study the solidification processes in metals and alloys. The laws of thermodynamics and other fundamental physical laws, which control the solidification, rule these processes. In this preparatory chapter the basic concepts and laws of thermodynamics are introduced. They will be the tools in following chapters. In particular, this is true for the second chapter, where the driving forces of solidification for pure metals and binary alloys are derived and therelationshipbetweenenergycurvesofsolidmetalsandmetalmeltsandtheirphasediagrams is emphasized. 1.2 Thermodynamic Concepts and Relationships 1.2.1 First Law of Thermodynamics. Principle of Conservation of Energy Oneofthemostfundamentallawsofphysicsisthelawofconservationofenergy.Sofar,itisknown to be valid without any exceptions. When applied in thermodynamics it is called the first law of thermodynamicsand iswritten Q¼UþW ð1:1Þ where Q ¼ heat energyadded toa closed system U ¼ the internal energyof the system or the sum ofthe kinetic andpotential energiesof the atoms W ¼ work done bythe system. Differentiating Equation(1.1) givesthe relationship dQ¼dUþdW ¼dUþpdV ð1:2Þ The added heat dQ is used for the increase dU of the internal energy of the system and for the externalworkpdVagainstthesurroundingpressurepwhenthevolumeofthesystemincreasesby the amount dV. 1.2.2 Enthalpy The enthalpy ofa closed system isdefinedas H ¼UþpV ð1:3Þ The enthalpy H can be described as the ‘heat content’ of the system. In the absence of phase transformations we have ðT H ¼ nC dT ð1:4Þ p 0
Description:The list of books you might like
