Table of contents for Phase transformations in metals and alloys.


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Chapter 1     Thermodynamics and Phase Diagrams .............................. 1
1.1   Equilibrium   ............................. .....  ....... ............... ...............   1
1.2   Single-Component Systems ........................................................  4
1.2.1   Gibbs Free Energy as a Function of Temperature...................... 4
1.2.2  Pressure   Effects................................ ........................................   7
1.2.3   Driving Force for Solidification......................    ..............  9
1.3   Binary Solutions ...................     ......... ........    ................... 11
1.3.1   Gibbs Free Energy of Binary Solutions...................................... 11
1.3.2   Id eal  Solu tion s  ........................................ ................. ................  13
1.3.3   Chem  ical Potential .................. ........... .............. .........  ..... 15
1.3.4   Regular  Solutions  ............................................. .........................  17
1.3 .5  A ctiv ity  ................................. ....... ................................. . . ...  21
1.3.6   Real  Solutions  ...................................................... ...............  23
1.3.7   O rdered  Phases..................................... ........... ... .......... ... 24
1.3.8   Interm ediate  Phases............................................. ............. ... 26
1.4   Equilibrium   in Heterogeneous Systems................................... 28
1.5   Binary Phase Diagrams .......................................... .. ..................... 31
1.5.1   Sim ple  Phase  D iagram  ............................................. .................. . 31
1.5.2   Systems with a Miscibility Gap ................................. ............. 32
1.5.3   O rdered  A lloys  ........................ ................. .......... ................ 33
1.5.4   Simple Eutectic Systems............................................................... 34
1.5.5   Phase Diagrams Containing Intermediate Phases .................. 34
1.5.6   Gibbs  Phase  Rule.........................................................  34
1.5.7   Effect of Temperature on Solid Solubility ............................... 39
1.5.8   Equilibrium   Vacancy Concentration........................................... 40
1.6  Influence of Interfaces on Equilibrium............................... ............ 42
1.7   Ternary  Equilibrium   ......................................... ....... .. ....... ................ 45
1.8   Additional Thermodynamic Relationships for Binary Solutions......... 50
1.9   Computation of Phase Diagrams.................          ..   ................ 52
1.9.1   Pure Stoichiometric Substances.................................. ................ 52
1.9.2   Solution  Phases............................ .......  ................. . 56
1.9.2.1  Substitutional Solutions...................... ....... .............. 56
1.10   Kinetics of Phase Transformations ................................ ................... 57
Exercises............................................... 58
R eferences  ....................... ........................................... .............. ............... ........ 60
Further Reading................................................................ 61
Chapter   2   D iffusion   ......................................................................... 63
2.1   Atomic Mechanisms of Diffusion .................... ............................. 65
2.2   Interstitial D iffusion..................................................... ................... 67
2.2.1  Interstitial Diffusion as a Random Jump Process...................... 67
2.2.2   Effect of Temperature-Thermal Activation.............................. 69
2.2.3  Steady-State   D iffusion  .................................... ....................... 72
2.2.4   Nonsteady-State Diffusion........................     ................... 72
2.2.5  Solutions to the Diffusion Equation ....................................... 74
2.2.5.1   H om ogenization   ........................................ ..............  74
2.2.5.2   Carburization of Steel ............................... ..........   76
2.3   Substitutional  D iffusion  ............................................... ....................... 78
2.3.1   Self-D iffusion  ........................................ ................... ............  78
2.3.2   Vacancy   D iffusion  ............................................. .................. 83
2.3.3   Diffusion in Substitutional Alloys .........................   .......... . 84
2.3.4   Diffusion in Dilute Substitutional Alloys ................................ 92
2.4   Atom  ic  M obility  ............................................................  93
2.5   Tracer Diffusion in Binary Alloys........................................................... 95
2.6   Diffusion  in  Ternary  A lloys........................................ ........................ 98
2.7   H igh-D iffusivity  Paths.......................................... ........................... 100
2.7.1   Diffusion along Grain Boundaries and Free Surfaces ........... 100
2.7.2   Diffusion along Dislocations ................................ ................. 103
2.8   Diffusion in Multiphase Binary Systems........................................ 104
Exercises................... .......... ........................................  . 106
R eferences........................... ..................................................................... . . . .  109
Fu rther  R ead ing ................................ ....................................... .............. .......  110
Chapter 3     Crystal Interfaces and Microstructure............................ 111
3.1   Interfacial Free Energy .................................... 112
3.2   Solid/Vapor   Interfaces...................................................... ..................  113
3.3   Boundaries in Single-Phase Solids................................... ........... 117
3.3.1   Low-Angle and High-Angle Boundaries................................... 118
3.3.2   Special High-Angle Grain Boundaries.................................... 121
3.3.3   Equilibrium   in Polycrystalline Materials................................... 124
3.3.4  Thermally Activated Migration of Grain Boundaries.............. 129
3.3.5   Kinetics  of Grain  Grow  th.........  ................... ........... ....... . 137
3.4  Interphase Interfaces in Solids ............................. ................... 140
3.4.1   Interface  Coherence.......................................................... 141
3.4.1.1   Fully Coherent Interfaces.......................................... 141
3.4.1.2   Semicoherent Interfaces.............................................. 143
3.4.1.3   Incoherent Interfaces...............      ................. 144
3.4.1.4   Complex Semicoherent Interfaces................................ 145
3.4.2   Second-Phase Shape: Interfacial Energy Effects ..................... 147
3.4.2.1  Fully Coherent Precipitates........................................   147
3.4.2.2  Partially Coherent Precipitates................................ ... 148
3.4.2.3  Incoherent Precipitates ............................................ 150
3.4.2.4  Precipitates on Grain Boundaries .............................. 151
3.4.3   Second-Phase Shape: Misfit Strain Effects............................... 152
3.4.3.1  Fully Coherent Precipitates........................ ........... 152
3.4.3.2  Incoherent Inclusions ................................ ............... 155
3.4.3.3  Platelike  Precipitates.................. ........ .................... 156
3.4.4   Coherency   Loss.............................................. 157
3.4.5   Glissile Interfaces   ............................................ 160
3.4.6  Solid/Liquid   Interfaces.........  ... ................................... 165
3.5   In terface  M igration ............................................................. .................  167
3.5.1   Diffusion-Controlled and Interface-Controlled Growth.......... 170
E xercises...................................................... .... ..... ..... ............ ....  176
R eferen ces  ..................................... ............ . . ........... ..................  178
Fu rth er  R ead in g ...... ................................................................... .............  179
Chapter 4     Solidification ............................................................ 181
4.1   Nucleation in Pure Metals .................. ....................................... 181
4.1.1   Homogeneous Nucleation ..................... ................. ......... 182
4.1.2   Homogeneous Nucleation Rate ............................................ 186
4.1.3   Heterogeneous Nucleation........................................... 188
4.1.4  Nucleation   of M elting.......... ..    ................................... 192
4.2   G row th  of  a  Pure  Solid... .................. ......................... ..... ........  193
4.2.1  Continuous Growth .................................. ....... ........  193
4.2.2   Lateral Grow  th  .................................. ............... ........ 194
4.2.3   Heat Flow and Interface Stability....................................... 197
4.3   Alloy  Solidification.................. .......... ... .  ....... ................. 200
4.3.1   Solidification of Single-Phase Alloys.................................... 200
4.3.2   Eutectic  Solidification  ................................................................  212
4.3.3   O ff-Eutectic  A lloys  .............. ................. ....... ........ ...................... 218
4.3.4   Peritectic  Solidification  ................................ ....................... 220
4.4   Solidification of Ingots and Castings ............................................... 221
4.4.1   Ingot  Structure  ......................... ............................ . 222
4.4.2   Segregation in Ingots and Castings................................ . 225
4.4.3   C ontinuous  C asting  ......................................... ...................... 226
4.5   Solidification  of Fusion  W elds  ........................................ .................. 230
4.6   Solidification during Quenching from the Melt.................................. 235
4.7   M etallic  G lasses  ....... ....... .................................................................  236
4.7.1   Therm  odynam   ics  and  Kinetics................................................. 237
4.8   Case Studies of Some Practical Castings and Welds......................... 239
4.8.1  Casting of Carbon and Low-Alloy Steels.................................. 239
4.8.2  Casting of High-Speed Steels ..................... ......................... 241
Exercises.................  ......      .........      .........................   247
R eferen ces ................................................................................ .....................  24 9
Further Reading.......    ........   . .......    .........     ................   249
Chapter 5     Diffusional Transformations in Solids ........................ 251
5.1    Homogeneous Nucleation in Solids............................................. 253
5.2    H eterogeneous  N ucleation..................................................... 259
5.2.1   Rate of Heterogeneous Nucleation...................................... 263
5.3    Precipitate  G row th  ...................................................... ................... 265
5.3.1   Growth behind Planar Incoherent Interfaces...................... 266
5.3.2   Diffusion-Controlled Lengthening of Plates or Needles..... 269
5.3.3   Thickening of Platelike Precipitates....................................... 271
5.4    Overall Transformation Kinetics: TTT Diagrams......................... .... 273
5.5    Precipitation in Age-Hardening Alloys ............................................ 276
5.5.1   Precipitation in Aluminum-Copper Alloys........................ 277
5.5.2    Precipitation in Aluminum-Silver Alloys ............................. 285
5.5.3   Quenched-In Vacancies............................ ...................... 286
5.5.4    Age Hardening ..................................... 288
5.5.5    Spinodal Decom   position  ................................ ....................  290
5.5.6    Particle  C oarsening  ...................................... ........ ....................... 295
5.6    Precipitation of Ferrite from Austenite ........................................ 299
5.6.1   Case Study: Ferrite Nucleation and Growth....................... 304
5.7    C ellular  Precipitation .............................. ... ................................ 310
5.8    Eutectoid Transformations.......................................... 314
5.8.1   Pearlite Reaction in Fe-C Alloys...................... ................. 314
5.8.2    Bainite  Transform ation  ................ ................. .................. 319
5.8.3    Effect of Alloying Elements on Hardenability.................... 327
5.8.4   Continuous Cooling Diagrams........................................... 332
5.8.5    Fibrous and Interphase Precipitation in Alloy Steels .......... 334
5.8.6   Rule  of Scheil ............................... ............. .. .............. 336
5.9    Massive Transformations........................................................ 337
5.10   Ordering  Transform  ations ........................................... .............. 342
5.11   C ase  Stud ies  ........................................... ............... .......................   349
5.11.1  Titanium   Forging  Alloys.....................................................  349
5.11.2  Weldability of Low-Carbon and Microalloyed
Rolled  Steels ........................................................................... 353
5.11.3   Very Low-Carbon Bainitic Steel with High Strength
and  Toughness............................................ 356
5.11.4   V ery  Fine  Bainite  ........................................ ....................... 357
Exercises ..................................                            .... ... 360
R eferences.............................. .........               ............... 362
Further  Reading..........................                     .................... 364
Chapter 6     Diffusionless Transformations ...................................... 367
6.1    Characteristics of Diffusionless Transformations............................... 368
6.1.1   Solid Solution of Carbon in Iron...................... ........... 371
6.2    Martensite Crystallography ............   ....................... 373
6.2.1  Bain Model of the fcc -+ bct Transformation............................ 375
6.2.2  Comparison of Crystallographic Theory
w ith  Experim ental Results............................ .................. . 379
6.3   Theories of M  artensite  Nucleation  .......................... ................... ... 380
6.3.1  Formation of Coherent Nuclei of Martensite............................ 381
6.3.2  Role of Dislocations in Martensite Nucleation ....................... 384
6.3.3  Dislocation Strain Energy Assisted Transformation.............. 387
6.4   M artensite  Grow th.............................. ....... .. .............. .... 391
6.4.1  Growth of Lath Martensite....................  ...................... ... 392
6.4.2  Plate  M artensite................................ ........... ...................  394
6.4.3  Stabilization ....................................          ........... 397
6.4.4  Effect of External Stresses ...................................................... 397
6.4.5  Role  of  G rain  Size.......................................... ....................  397
6.5   Premartensite Phenomena .............................................................. 398
6.6   Tem pering  of Ferrous M  artensites ................................... ................... 399
6.7   C ase  Studies  ....................................... .... ........................................  408
6.7.1  Carbon and Low-Alloy Quenched and Tempered Steels....... 408
6.7.2  Controlled Transformation Steels ...................... 409
6.7.3  TRIP-Assisted Steels................................................ 411
6.7.4   "Shape-Memory" Metal: Nitinol......................................... 415
Exercises................................    ............. ........................  417
R eferen ces  ................................................................................................ . . ....  4 18
Further  R ead in g ....................................................................................... .... 420



Library of Congress subject headings for this publication: Physical metallurgy, Phase rule and equilibrium