Preface ........................................................ xv
Authors ...................................................... xvii
Chapter 1 Applied Thermodynamics ............................... 1
1.1 Free Energy-Composition Relationships for Binary
Substitutional Solid Solutions ............................. 1
1.1.1 Basic Free Energy-Composition Relationship .......... 1
1.1.2 Gibbs Free Energy of the Standard States of Pure
Elements ............................................ 1
1.1.3 Mixing Free Energy, ΔGM ............................. 4
1.1.3.1 Fundamentals ............................... 4
1.1.3.2 Ideal Solution Approximation ............... 7
1.1.3.3 Regular Solution Approximation ............. 7
1.1.3.4 Subregular and Other-Type Solutions ....... 12
1.1.3.5 Relationships for Partial Molar Free
Energies, Phase Equilibria, and Critical
Temperature ............................... 12
1.1.3.6 Comparison between Regular Solutions
and Nonregular Solutions .................. 16
1.2 Free Energy-Composition Diagram and Applications to
Driving Force Calculations ................................ 17
1.2.1 Some Considerations on the Free Energy vs.
Composition Curve .................................. 17
1.2.2 Total Free Energy Change Attending Precipitation ... 21
1.2.3 Free Energy Change Attending the Precipitation
of a Small Amount of α ............................. 24
1.2.4 Division of the Total Free Energy Change between
Capillarity and Diffusion .......................... 25
1.2.5 Influence of Capillarity upon Solubility ........... 27
1.2.6 Division of ΔG between Diffusion and Uniform
Interfacial Reaction ............................... 29
1.2.7 Permissible Range of Nonequilibrium Precipitate
Compositions ....................................... 30
1.3 Thermodynamics of Interstitial Solid Solutions through
Application to the Proeutectoid Ferrite Reaction in Fe-C
Alloys .................................................... 31
1.3.1 Introduction ....................................... 31
1.3.2 Free Energy and Positional Entropy of Ideal
Interstitial Solid Solutions ....................... 32
1.3.3 Free Energy and Positional Entropy of Nonideal
Interstitial Solid Solution ........................ 33
1.3.4 Evaluation of Constants in a Partial Molar Free
Energy Equation .................................... 35
1.3.5 Application of Partial Molar Free Energy
Equations .......................................... 36
1.3.5.1 Calculation of the γ/(α + γ) or Ae3
Phase Boundary ............................ 36
1.3.5.2 Driving Force for the Massive
Transformation in Fe-C Alloys ............. 37
1.3.5.3 Driving Force for the Precipitation of
Proeutectoid Ferrite ...................... 37
1.3.5.4 Graphical Presentations of the Results
of Sections 1.3.5.1 through 1.3.5.3 ....... 38
1.3.6 Interpretation of z in Terms of Carbon-Carbon
Interaction Energy ................................. 39
1.3.7 More Sophisticated Treatments of Interstitial
Statistical Thermodynamics ......................... 41
References ................................................ 46
Chapter 2 Diffusional Nucleation in Solid-Solid
Transformations ................................................ 49
2.1 Introduction through Qualitative General Statements ....... 49
2.2 Brief Comparative Survey of Nucleation in the Four Basic
Types of Phase Transformation ............................. 52
2.2.1 Vapor-to-Liquid Transformation ..................... 52
2.2.2 Vapor-to-Solid Transformation ...................... 52
2.2.3 Liquid-to-Solid Transformation (Solidification) .... 52
2.2.4 Solid-to-Solid Transformation ...................... 53
2.2.5 General Remarks .................................... 53
2.3 Outline of Approach for Development of Nucleation Theory .. 53
2.4 Proof That the Equilibrium Concentration of Critical
Nuclei Is Proportional to exp(—ΔG*/kT) .................... 53
2.5 Fictitious Equilibrium Nucleation Rate .................... 55
2.6 Derivation of Steady-State Nucleation Rate ................ 55
2.7 Estimation of β* .......................................... 59
2.8 Time-Dependent Nucleation Rate ............................ 59
2.9 Feder et al.'s Treatment of τ ............................. 63
2.9.1 Relationships for δ and for τδ ..................... 64
2.9.2 Relationship for t' ................................ 65
2.9.3 Total Value of τ ................................... 66
2.10 Time-Dependent Nucleation Rate for Homogeneous
Nucleation with Isotropic γ ............................... 66
2.10.1 Introduction ....................................... 66
2.10.2 Activation Energy of Nucleation ΔG* ................ 67
2.10.2.1 Introduction to the Critical Nucleus
Shape Problem ............................. 67
2.10.2.2 G-x Diagram Approach ...................... 67
2.10.2.3 Introduction to the Volume Strain Energy
Incorporation Problem ..................... 68
2.10.2.4 Conventional Gibbsian Approach ............ 69
2.10.2.5 Wulff Volume Approach for ΔG* ............. 69
2.10.2.6 Nucleus Volume Approach for ΔG* ........... 71
2.10.3 Frequency Factor β* ................................ 72
2.10.4 Zeldovich Factor, Incubation Time and the
Re-Derivation of Frequency Factor .................. 72
2.10.5 Nucleation Site Density, N ......................... 75
2.10.6 Time-Dependent Nucleation Rate ..................... 75
2.11 Ancillary Parameters ...................................... 75
2.11.1 Volume Diffusivity ................................. 75
2.11.2 Volume Free Energy Change .......................... 76
2.11.3 Volume Strain Energy ............................... 79
2.11.3.1 Elementary Calculation of Dilatational
Strain Energy for a Plate-Shaped Nucleus .. 80
2.11.3.2 Volume Strain Energy of Fully Coherent
Precipitates .............................. 82
2.11.3.3 Volume Strain Energy of Incoherent
Precipitates .............................. 89
2.11.3.4 Volume Shear Strain Energy ................ 90
2.11.3.5 Unsolved Major Problems in Volume Strain
Energy .................................... 91
2.11.4 Interfacial Energy ................................. 91
2.11.4.1 Scope ..................................... 91
2.11.4.2 Energy of Coherent Interphase Boundaries .. 92
2.11.4.3 Energy of Partially Coherent Interphase
Boundaries ............................... 125
2.11.4.4 Energy of Disordered Interphase
Boundaries ............................... 126
2.12 Preliminary Consideration of the Approximation for ϕ =
ΔGV + W .................................................. 132
2.13 Nonclassical Nucleation Theory ........................... 134
2.13.1 Continuum Theory .................................. 134
2.13.1.1 General Introduction ..................... 134
2.13.1.2 Calculation of the Nonclassical ΔG* ...... 135
2.13.1.3 General Properties of the Critical
Nucleus .................................. 140
2.13.1.4 Nucleation in a Regular Solution ......... 149
2.13.1.5 Applicability Region of Classical
Theory ................................... 155
2.13.2 Discrete Lattice Point Theory ..................... 156
2.14 Modifications of Homogeneous Nucleation Kinetics by
Anisotropic Interfacial Energy ........................... 159
2.14.1 Equilibrium Shape Problem ......................... 159
2.14.1.1 Rudimentary Solution of the Equilibrium
Shape Problem ............................ 160
2.14.1.2 γ-Plot and Some Properties ............... 161
2.14.1.3 Wulff Construction ....................... 163
2.14.1.4 Simple Approach to Calculation of
γ-Plots .................................. 164
2.14.1.5 Wulff Construction of Equilibrium Shape
vs. Temperature in a Regular Solution,
fee Miscibility Gap ...................... 165
2.14.2 Sphere Faceted at One Boundary Orientation ........ 169
2.14.2.1 7-Plot and Force Balance ................. 170
2.14.2.2 Calculation of r* and ΔG* ................ 171
2.14.2.3 Calculation of β* ........................ 173
2.14.2.4 Calculation of Zeldovich Factor, Z, and
Incubation Time, τ ....................... 174
2.14.3 Nonspherical Critical Nucleus Shapes with
a Finite Number of Interfacial Energies and
Analytically Describable Interfaces ............... 179
2.15 Nucleation Kinetics at the Faces of Disordered Grain
Boundaries ............................................... 180
2.15.1 Introductory Comments on Grain Boundary Geometry
and Structure ..................................... 180
2.15.2 Equilibrium Shape Problem at Grain Boundaries ..... 180
2.15.3 Shape-Dependent Nucleation Kinetics Factors for
the Two Spherical Cap Nucleus with Isotropic γαβ .. 182
2.15.3.1 ΔG* and R* ............................... 182
2.15.3.2 β*, Z, τ, and Transport by Interfacial
Diffusion ................................ 183
2.15.4 Nucleation Kinetics of the Double Spherical Cap
Faceted at One Boundary Orientation ............... 184
2.15.4.1 When ϕ ≤ ϕС1 and γcαβ > γββ/2 ............ 184
2.15.4.2 Two-Dimensional Nuclei ................... 185
2.15.4.3 Three-Dimensional Nuclei When ϕ > ϕС1 .... 191
2.16 Comparative Nucleation Kinetics at Grain Faces, Edges,
and Corners Relative to Homogeneous Nucleation: Trade-
Offs between N and ΔG* When γαβ Is Isotropic ............. 196
2.17 Nucleation at Dislocations ............................... 201
2.17.1 Incoherent Nucleation ............................. 202
2.17.1.1 The Cahn Treatment ....................... 202
2.17.1.2 The Gomez-Ramirez and Pound Treatment .... 205
2.17.2 Coherent Nucleation ............................... 210
2.18 Comparisons of Theory and Experiment ..................... 211
2.18.1 Homogeneous Nucleation ............................ 211
2.18.1.1 Homogeneous Nucleation of Co-Rich
Precipitates in Cu-Rich Cu-Co Alloys ..... 212
2.18.1.2 Homogeneous Nucleation of Ni3Al
Precipitates in Ni-Rich Ni-Al Alloys ..... 226
2.18.1.3 Homogeneous Nucleation in Liquids ........ 228
2.18.2 Nucleation at Grain Boundaries .................... 230
2.18.2.1 Nucleation of Proeutectoid Ferrite at
Austenite Grain Boundaries in Fe-C
Alloys ................................... 230
2.18.3 Nucleation at Grain Faces vs. Grain Edges ......... 238
2.18.4 Nucleation at Dislocations ........................ 239
2.18.5 Secondary Sideplate Selectivity ................... 244
References ............................................... 245
Chapter 3 Diffusional Growth ................................. 249
3.1 Basic Differences between Diffusional Nucleation
and Diffusional Growth ................................... 249
3.2 A General Theory of Precipitate Morphology ............... 249
3.3 Disordered Interphase Boundaries ......................... 252
3.3.1 Introduction ...................................... 252
3.3.2 Volume Diffusion-Controlled Growth Kinetics ....... 253
3.3.2.1 Mathematics for Diffusion and Flux
Equations ................................ 253
3.3.2.2 Comparisons with Experiment .............. 303
3.3.3 Growth Faster than Volume Diffusion Control
Allows ............................................ 332
3.3.3.1 Grain Boundary Allotriomorphs ............ 332
3.3.3.2 Dissolution of Grain Boundary
Allotriomorphs ........................... 340
3.3.3.3 Plate Lengthening ........................ 342
3.3.4 Growth Slower than Volume Diffusion Control
Allows ............................................ 343
3.4 Partially and Fully Coherent Interphase Boundaries ....... 347
3.4.1 Introduction ...................................... 347
3.4.2 Misfit Dislocations at Partially Coherent
Interphase Boundaries ............................. 347
3.4.2.1 Theory ................................... 347
3.4.2.2 Comparisons of Theory and Experiment ..... 354
3.4.3 Acquisition of the Misfit Dislocation Structure
of Partially Coherent Interphase Boundaries ....... 368
3.4.3.1 Theory ................................... 368
3.4.3.2 Comparisons of Theory with Experiment .... 378
3.4.4 Growth Ledges at Partially and Fully Coherent
Interphase Boundaries ............................. 386
3.4.4.1 Prevalence and Role in Interface
Crystallography .......................... 386
3.4.4.2 Visibility Conditions for Ledges ......... 387
3.4.4.3 Sources of Ledges ........................ 389
3.4.4.4 Ledge Heights ............................ 394
3.4.4.5 Inter-Ledge Spacings ..................... 395
3.4.5 Structural Ledges at Partially Coherent
Interphase Boundaries ............................. 397
3.4.6 Migration of Partially and Fully Coherent
Interphase Boundaries by Growth Ledges ............ 409
3.4.6.1 Theory ................................... 409
3.4.6.2 Comparison of Theory and Experiment for
Growth of Ledged Interphase Boundaries ... 419
3.5 Relative Growth Kinetics of Disordered and Partially
Coherent Interphase Boundaries ........................... 425
References ............................................... 427
Chapter 4 Precipitation ...................................... 433
4.1 Introduction ............................................. 433
4.2 Metastable Equilibrium Phase Boundaries .................. 433
4.2.1 Types of Metastable Equilibrium Phases ............ 433
4.2.2 Calculation of Metastable Equilibrium Phase
Boundaries ........................................ 435
4.3 GP Zones ................................................. 438
4.3.1 Definition ........................................ 438
4.3.2 Early History and Methods of Experimental
Detection ......................................... 438
4.3.3 GP Zone Solvus Curves ............................. 442
4.3.4 Description of GP Zones: Morphology, Size,
Number Density, and Composition ................... 444
4.3.5 Kinetics of GP Zone Formation ..................... 448
4.3.6 Origins of GP Zone Formation ...................... 451
4.4 Transition Phases ........................................ 458
4.4.1 Definition and Basic Characteristic ............... 458
4.4.2 Occurrence and Thermodynamics ..................... 459
4.4.3 Crystallography ................................... 459
4.4.4 Nucleation Sequence of Transition Phases .......... 462
4.4.4.1 From the Viewpoint of ΔGV ................ 463
4.4.4.2 From the Viewpoint of Interfacial
Energy ................................... 463
4.4.4.3 Nucleation Sites of Successive
Transition Phases ........................ 464
4.5 Nucleation Sites ......................................... 465
4.5.1 Homogeneous Nucleation ............................ 465
4.5.2 Nucleation at Large-Angle Grain Boundaries ........ 466
4.5.3 Nucleation Kinetics at Small-Angle Boundaries ..... 467
4.5.4 Nucleation at Dislocations ........................ 469
4.5.4.1 General Remarks .......................... 469
4.5.4.2 Stacking Fault Nucleation and Edgewise
Growth ................................... 469
4.5.4.3 Nucleation on Displaced and Freshly
Generated Dislocations ................... 470
4.5.5 Nucleation at Point Defect Clusters ............... 472
4.5.6 Nucleation on Precipitates ........................ 475
4.5.6.1 Nucleation on Precipitates of a
Different Phase .......................... 475
4.5.6.2 Sympathetic Nucleation ................... 478
4.6 Successive Reactions Involving Different Phases .......... 478
4.7 Precipitate Free Zones ................................... 479
4.8 Coarsening (Ostwald Ripening) ............................ 482
4.9 Overall Evolution of the Microstructure .................. 488
4.9.1 Effects of the Ratio of Growth Rates of
Disordered-to-Partially Coherent Boundaries ....... 488
4.9.2 Effects of Diffusion Distance-to-Matrix Grain
Radius Ratio ...................................... 488
4.9.3 Effects of the Lever Rule and of Nucleation-to-
Growth Rate Ratio ................................. 490
References ............................................... 491
Chapter 5 Massive Transformation ............................. 495
5.1 Definition and History ................................... 495
5.2 Phase Diagrams ........................................... 495
5.3 Thermodynamics ........................................... 497
5.3.1 Free Energy Composition Diagram ................... 497
5.3.2 Experimental Evaluation of Enthalpy Change
Associated with Massive Reaction .................. 497
5.4 Overall Reaction Kinetics and the Existence Range ........ 499
5.5 Nucleation of Massive Transformation ..................... 508
5.5.1 Nucleation during Continuous Cooling .............. 508
5.5.2 Nucleation during Isothermal Transformation ....... 514
5.5.3 Nucleation Sites and Massive Crystal Morphology ... 516
5.6 Growth Kinetics .......................................... 523
5.6.1 Theory ............................................ 523
5.6.1.1 Disordered Interphase Boundaries ......... 523
5.6.1.2 Partially Coherent Interphase
Boundaries ............................... 524
5.6.2 Comparison with Experiment ........................ 525
5.7 Interfacial Structure, Habit Planes, Orientation
Relationships, and Growth Mechanisms ..................... 532
5.8 Note on the Driving Force for Trans-Interphase Boundary
Diffusion during Massive Transformation in a Two-Phase
Field .................................................... 540
References ............................................... 541
Chapter 6 Cellular Reaction .................................. 543
6.1 Definition and Introduction .............................. 543
6.2 Systematics of Cellular Reactions ........................ 545
6.3 Nucleation of Cellular Reactions ......................... 552
6.3.1 Crystallography-Based Mechanisms .................. 552
6.3.1.1 Tu-Turnbull Replacive Mechanism .......... 552
6.3.1.2 Proposals of Aaronson and Aaron .......... 554
6.3.2 Noncrystallographic Mechanism of Fournelle and
Clark ............................................. 555
6.3.3 Other Mechanisms for Inducing Grain Boundary
Motion before and during Cellular Reaction,
Including DIGM .................................... 556
6.4 Growth Kinetics of Cells ................................. 561
6.4.1 Introductory Comments ............................. 561
6.4.2 Turnbull Theory of Cell Growth Kinetics ........... 562
6.4.3 Cahn Theory of Cell Growth Kinetics ............... 564
6.4.4 Comparisons with the Experiment of the Turnbull
and Cahn Theories ................................. 567
6.4.5 Hillert Theory of Growth Kinetics ................. 570
6.4.6 Volume versus Boundary Diffusion Control and
Interactions with Continuous Precipitation ........ 572
References ............................................... 573
Chapter 7 Pearlite Reaction .................................. 575
7.1 Systematics .............................................. 575
7.1.1 Definition ........................................ 575
7.1.2 Pearlite in the Context of Eutectoid
Decomposition Products ............................ 575
7.1.3 Occurrence of Pearlite ............................ 575
7.1.3.1 In Steel ................................. 575
7.1.3.2 In Other Alloy Systems ................... 575
7.1.4 Preliminary Discussion of Pearlite Nucleation ..... 576
7.1.5 Morphology of Pearlite ............................ 576
7.2 Crystallography, Nucleation, and Growth Mechanisms ....... 582
7.2.1 Hull and Mehl Concept ............................. 582
7.2.2 Hillert Concept ................................... 584
7.2.3 Reprise ........................................... 586
7.3 Edgewise Growth Kinetics of Pearlite ..................... 588
7.3.1 Comparative Thermodynamics with Cellular
Reaction .......................................... 588
7.3.2 Role of Growth in Pearlite Reaction ............... 589
7.3.3 Approximate Treatments of Edgewise Growth ......... 590
7.3.3.1 Volume Diffusion-Controlled Growth ....... 590
7.3.3.2 Growth Controlled by Diffusion along
Colony Boundary .......................... 592
7.3.4 Improved Treatments ............................... 593
7.3.4.1 Volume Diffusion-Controlled Growth ....... 593
7.3.4.2 Boundary Diffusion-Controlled Growth ..... 594
7.3.5 Experimental Measurements for Growth Kinetics
Studies ........................................... 595
7.3.5.1 Interlamellar Spacing .................... 595
7.3.5.2 Rate of Growth ........................... 595
7.3.6 Comparisons of Theory and Experiment and the
Problem of S ...................................... 596
References ............................................... 599
Chapter 8 Martensitic Transformations ........................ 601
8.1 Definition ............................................... 601
8.2 Salient Characteristics (Described Briefly) .............. 601
8.2.1 Crystallography ................................... 601
8.2.2 Morphology ........................................ 601
8.2.3 Surface Relief Effects ............................ 602
8.2.4 Time-Dependence of Martensite Formation ........... 602
8.2.5 Temperature Dependence of Martensite Formation .... 604
8.2.6 Reversibility ..................................... 606
8.2.7 Influence of Applied Stress ....................... 606
8.2.8 Thermal Stabilization ............................. 608
8.3 Thermodynamics of Martensite Transformation .............. 608
8.3.1 T0 Temperature .................................... 608
8.3.2 Difference between T0 and Ms ...................... 612
8.4 Overall Kinetics of Martensite Transformation ............ 615
8.4.1 Qualitative Kinetics .............................. 615
8.4.2 Quantitative Kinetics ............................. 615
8.4.2.1 Anisothermal Martensite Formation ........ 615
8.4.2.2 Isothermal Martensite Formation .......... 617
8.5 Nucleation of Martensite ................................. 620
8.6 Crystallography and Growth (or Propagation) of
Martensite ............................................... 622
8.6.1 Physics of Phenomenological Theory of Martensite
Crystallography ................................... 622
8.6.2 Comparisons with Experiment ....................... 625
References ............................................... 632
Chapter 9 Bainite Reaction and Role of Shear in Diffusional
Phase Transformations ......................................... 635
9.1 Introduction ............................................. 635
9.2 Three Definitions of Bainite ............................. 635
9.2.1 Generalized Microstructural Definition ............ 635
9.2.2 Kinetic Definition of Bainite ..................... 643
9.2.3 Surface Relief Definition of Bainite .............. 649
9.3 Upper Bainite versus Lower Bainite, and Inverse Bainite .. 651
9.4 Sources of Carbide Precipitation ......................... 651
References ............................................... 654
Further Readings ......................................... 655
Index ......................................................... 657
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