Table Of ContentThermodynamics, Kinetics and
Microstructure Modelling
Thermodynamics, Kinetics and
Microstructure Modelling
Simon P A Gill
School of Engineering, University of Leicester, University Road, Leicester,
LE1 7RH, United Kingdom
IOP Publishing, Bristol, UK
ªIOPPublishingLtd2022
Allrightsreserved.Nopartofthispublicationmaybereproduced,storedinaretrievalsystem
ortransmittedinanyformorbyanymeans,electronic,mechanical,photocopying,recording
orotherwise,withoutthepriorpermissionofthepublisher,orasexpresslypermittedbylawor
undertermsagreedwiththeappropriaterightsorganization.Multiplecopyingispermittedin
accordancewiththetermsoflicencesissuedbytheCopyrightLicensingAgency,theCopyright
ClearanceCentreandotherreproductionrightsorganizations.
PermissiontomakeuseofIOPPublishingcontentotherthanassetoutabovemaybesought
[email protected].
SimonPAGillhasassertedhisrighttobeidentifiedastheauthorofthisworkinaccordancewith
sections77and78oftheCopyright,DesignsandPatentsAct1988.
ISBN 978-0-7503-3147-0(ebook)
ISBN 978-0-7503-3145-6(print)
ISBN 978-0-7503-3148-7(myPrint)
ISBN 978-0-7503-3146-3(mobi)
DOI 10.1088/978-0-7503-3147-0
Version:20220301
IOPebooks
BritishLibraryCataloguing-in-PublicationData:Acataloguerecordforthisbookisavailable
fromtheBritishLibrary.
PublishedbyIOPPublishing,whollyownedbyTheInstituteofPhysics,London
IOPPublishing,TempleCircus,TempleWay,Bristol,BS16HG,UK
USOffice:IOPPublishing,Inc.,190NorthIndependenceMallWest,Suite601,Philadelphia,
PA19106,USA
Coverimage:Surfacehardeningofsteels.Imagecredit:Leica-microsystems.
To my mother.
Contents
Preface x
About the author xi
1 Introduction 1-1
1.1 Motivation 1-1
1.2 Microstructural features 1-3
1.2.1 Crystals and grains 1-3
1.2.2 Phases and precipitates 1-4
1.2.3 Defects in crystals 1-5
1.3 Microstructure–property relationships 1-6
1.3.1 Yield stress 1-6
1.3.2 Creep strength 1-9
1.4 A framework for microstructure evolution 1-11
1.4.1 PANDAT software and TDB databases 1-11
1.4.2 A mathematical framework 1-13
References 1-13
Part I Thermodynamics and phase diagrams
2 Thermodynamic quantities 2-1
2.1 Enthalpy 2-1
2.2 Entropy 2-4
2.3 Gibb’s free energy 2-5
2.4 Phase diagrams for pure substances 2-7
References 2-8
3 Binary systems 3-1
3.1 A single phase system with two components 3-2
3.1.1 Entropy of mixing 3-2
3.1.2 Energy of mixing 3-3
3.1.3 Total Gibbs free energy 3-4
3.1.4 A simple TDB file 3-5
3.1.5 A simple binary phase diagram 3-6
3.1.6 Chemical potential 3-8
vii
Thermodynamics,KineticsandMicrostructureModelling
3.2 A two phase system with two components 3-10
3.2.1 Phase diagram for case with zero excess energy 3-11
3.2.2 Equilibrium conditions in two phase regions 3-15
3.2.3 The lever rule 3-16
3.2.4 Effect of excess (mixing) energies on phase diagrams (exercise) 3-19
3.2.5 Solute partitioning and the partition coefficient 3-24
3.3 Sub-lattice models and stoichiometric phases 3-27
3.3.1 The sub-lattice model 3-27
3.3.2 Phase diagrams with stoichiometric phases 3-30
3.4 Real binary systems 3-33
References 3-37
4 Ternary systems and beyond 4-1
4.1 How to read a ternary phase diagram 4-1
4.2 A simple ternary system 4-2
4.3 Examples with four or more components 4-9
References 4-11
5 Driving force for nucleation and growth 5-1
5.1 Phase energy change for nucleation and growth 5-1
5.2 Calculating the phase energy change 5-4
5.3 The total driving force for nucleation 5-7
5.3.1 Homogeneous nucleation 5-8
5.3.2 Heterogeneous nucleation 5-9
Reference 5-13
Part II Kinetics and microstructure evolution
6 Kinetic processes 6-1
6.1 An atomic model of diffusion 6-2
6.2 Defining diffusion parameters in TDB files 6-6
6.2.1 Diffusion parameters in a unary system 6-6
6.2.2 Diffusion parameters in a binary system 6-8
6.3 Diffusion in a regular solution 6-10
6.4 Mass conservation 6-11
6.5 Determining the concentration field 6-12
viii
Thermodynamics,KineticsandMicrostructureModelling
6.5.1 An example non-linear diffusion problem: carburisation 6-15
of a ferritic steel
References 6-20
7 Nucleation, growth and coarsening in solids 7-1
7.1 Nucleation 7-1
7.2 Growth of a solid phase in a solid matrix 7-4
7.2.1 Interface-controlled growth 7-4
7.2.2 Diffusion-controlled growth 7-5
7.3 Coarsening 7-8
7.3.1 A globally averaged model for coarsening 7-9
7.3.2 A local mechanism for coarsening 7-11
References 7-12
8 Modelling solid–solid phase transitions 8-1
8.1 A two particle model 8-1
8.2 Population balance (or KWN) models 8-5
8.3 Massive transformations 8-12
8.4 A simplified model for phase transformations 8-14
References 8-16
9 Modelling liquid–solid phase transitions 9-1
9.1 Simple solidification models for a binary system 9-1
9.1.1 Global equilibrium 9-2
9.1.2 Scheil equation 9-3
9.1.3 Steady state growth 9-5
9.2 A phase field model for solidification 9-7
9.3 Stability of the liquid–solid interface 9-10
References 9-14
10 Exercises 10-1
References 10-4
11 Solutions 11-1
Reference 11-6
ix
