Physical Metallurgy Principles, Fifth Edition
Reza Abbaschian, Lara Abbaschian
Contents
Preface xix
About the Authors xxi
Digital Resources xxii
Chapter 1 The Structure of Metals 1
1.1 The Structure of Metals 2
1.2 Unit Cells 2
1.3 The Body-Centered Cubic Structure (BCC) 4
1.4 Coordination Number of the Body-Centered
Cubic Lattice 4
1.5 The Face-Centered Cubic Lattice (FCC) 5
1.6 The Unit Cell of the Hexagonal Closed-Packed (HCP) Lattice 6
1.7 Comparison of the Face-Centered Cubic and Close-Packed Hexagonal Structures 7
1.8 Coordination Number of the Systems of Closest Packing 8
1.9 Anisotropy 8
1.10 Textures or Preferred Orientations 9
1.11 Miller Indices 10
Direction Indices in the Cubic Lattice 11
Cubic Indices for Planes 12
Miller Indices for Hexagonal Crystals 14
1.12 Crystal Structures of the Metallic Elements 15
1.13 The Stereographic Projection 16
1.14 Directions that Lie in a Plane 18
1.15 Planes of a Zone 18
1.16 The Wulff Net 20
Rotation About an Axis in the Line of Sight 21
Rotation About the North–South Axis of the Wulff Net 21
1.17 Standard Projections 23
1.18 The Standard Stereographic Triangle for Cubic Crystals 24
Problems 27
References 30
Chapter 2 Characterization Techniques 31
2.1 The Bragg Law 32
2.2 Laue Techniques 36
2.3 The Rotating-Crystal Method 38
2.4 The Debye-Scherrer or Powder Method 38
2.5 The X-Ray Diffractometer 42
2.6 The Transmission Electron Microscope 43
2.7 Interactions between the Electrons in an Electron Beam and
a Metallic Specimen 49
2.8 Elastic Scattering 49
2.9 Inelastic Scattering 49
2.10 Electron Spectrum 51
2.11 The Scanning Electron Microscope 51
2.12 Topographic Contrast 53
2.13 The Picture Element Size 56
2.14 The Depth of Focus 57
2.15 Microanalysis of Specimens 58
2.16 Electron Probe X-Ray Microanalysis 58
2.17 The Characteristic X-Rays 59
2.18 Auger Electron Spectroscopy (AES) 61
2.19 The Scanning Transmission Electron Microscope (STEM) 63
Problems 64
References 65
Chapter 3 Crystal Binding 66
3.1 The Internal Energy of a Crystal 66
3.2 Ionic Crystals 67
3.3 The Born Theory of Ionic Crystals 68
3.4 Van Der Waals Crystals 72
3.5 Dipoles 72
3.6 Inert Cases 74
3.7 Induced Dipoles 74
3.8 The Lattice Energy of an Inert-Gas Solid 76
3.9 The Debye Frequency 76
3.10 The Zero-Point Energy 78
3.11 Dipole-Quadrupole and Quadrupole-Quadrupole Terms 79
3.12 Molecular Crystals 80
3.13 Refinements to the Born Theory of Ionic Crystals 80
3.14 Covalent and Metallic Bonding 81
Problems 84
References 85
Chapter 4 Introduction to Dislocations 86
4.1 The Discrepancy Between the Theoretical and Observed Yield Stresses
of Crystals 86
4.2 Dislocations 89
4.3 The Burgers Vector 97
4.4 Vector Notation for Dislocations 100
4.5 Dislocations in the Face-Centered Cubic Lattice 101
4.6 Intrinsic and Extrinsic Stacking Faults in Face-Centered Cubic Metals 105
4.7 Extended Dislocations in Hexagonal Metals 106
4.8 Climb of Edge Dislocations 107
4.9 Dislocation Intersections 108
4.10 The Stress Field of a Screw Dislocation 111
4.11 The Stress Field of an Edge Dislocation 112
4.12 The Force on a Dislocation 115
4.13 The Strain Energy of a Screw Dislocation 118
4.14 The Strain Energy of an Edge Dislocation 119
Problems 119
References 122
Chapter 5 Dislocations and Plastic Deformation 123
5.1 The Frank-Read Source 124
5.2 Nucleation of Dislocations 125
5.3 Bend Gliding 128
5.4 Rotational Slip 130
5.5 Slip Planes and Slip Directions 133
5.6 Slip Systems 134
5.7 Critical Resolved Shear Stress 134
5.8 Slip on Equivalent Slip Systems 138
5.9 The Dislocation Density 138
5.10 Slip Systems in Different Crystal Forms 138
Face-Centered Cubic Metals 138
Hexagonal Metals 140
Easy Glide in Hexagonal Metals 142
Body-Centered Cubic Crystals 142
5.11 Cross-Slip 143
5.12 Slip Bands 145
5.13 Double Cross-Slip 145
5.14 Extended Dislocations and Cross-Slip 147
5.15 Crystal Structure Rotation during Tensile and Compressive Deformation 149
5.16 The Notation for the Slip Systems in the Deformation of fcc Crystals 151
5.17 Work Hardening 153
5.18 Considere’s Criterion 155
5.19 The Relation Between Dislocation Density and the Stress 156
5.20 Taylor’s Relation 157
5.21 The Orowan Equation 158
Problems 159
References 161
Chapter 6 Elements of Grain Boundaries 163
6.1 Grain Boundaries 163
6.2 Dislocation Model of a Small-Angle Grain Boundary 164
6.3 The Five Degrees of Freedom of a Grain Boundary 167
6.4 The Stress Field of a Grain Boundary 168
6.5 Grain-Boundary Energy 169
6.6 Low-Energy Dislocation Structures, LEDS 172
6.7 Dynamic Recovery 177
6.8 Surface Tension of the Grain Boundary 179
6.9 Boundaries between Crystals of Different Phases 180
6.10 The Grain Size 183
6.11 The Effect of Grain Boundaries on Mechanical
Properties: Hall-Petch Relation 185
6.12 Grain Size Effects in Nanocrystalline Materials 187
6.13 Coincidence Site Boundaries 190
6.14 The Density of Coincidence Sites 191
6.15 The Ranganathan Relations 191
6.16 Examples Involving Twist Boundaries 192
6.17 Tilt Boundaries 194
Problems 197
References 198
Chapter 7 Vacancies and Thermodynamics 200
7.1 Thermal Behavior of Metals 200
7.2 Internal Energy 202
7.3 Entropy 202
7.4 Spontaneous Reactions 203
7.5 Gibbs Free Energy 203
7.6 Statistical Mechanical Definition of Entropy 205
7.7 Vacancies 209
7.8 Vacancy Motion 215
7.9 Interstitial Atoms and Divacancies 217
Problems 220
References 222
Chapter 8 Annealing 223
8.1 Stored Energy of Cold Work 223
8.2 The Relationship of Free Energy to Strain Energy 225
8.3 The Release of Stored Energy 225
8.4 Recovery 227
8.5 Recovery in Single Crystals 228
8.6 Polygonization 231
8.7 Dislocation Movements in Polygonization 232
8.8 Recovery Processes at High and Low Temperatures 236
8.9 Recrystallization 236
8.10 The Effect of Time and Temperature on Recrystallization 237
8.11 Recrystallization Temperature 239
8.12 The Effect of Strain on Recrystallization 239
8.13 The Rate of Nucleation and the Rate of Nucleus Growth 240
8.14 Formation of Nuclei 241
8.15 Driving Force for Recrystallization 243
8.16 The Recrystallized Grain Size 243
8.17 Other Variables in Recrystallization 245
8.18 Purity of the Metal 245
8.19 Initial Grain Size 247
8.20 Grain Growth 247
8.21 Geometrical Coalescence 249
8.22 Three-Dimensional Changes in Grain Geometry 251
8.23 The Grain Growth Law 252
8.24 Impurity Atoms in Solid Solution 256
8.25 Impurities in the Form of Inclusions 256
8.26 The Free-Surface Effects 259
8.27 The Limiting Grain Size 260
8.28 Preferred Orientation 261
8.29 Secondary Recrystallization 262
8.30 Strain-Induced Boundary Migration 263
Problems 264
References 265
Chapter 9 Solid Solutions 267
9.1 Solid Solutions 267
9.2 Intermediate Phases 268
9.3 Interstitial Solid Solutions 269
9.4 Solubility of Carbon in Body-Centered Cubic Iron 269
9.5 Substitutional Solid Solutions and the Hume-Rothery Rules 273
9.6 Interaction of Dislocations and Solute Atoms 274
9.7 Dislocation Atmospheres 274
9.8 The Formation of a Dislocation Atmosphere 275
9.9 The Evaluation of A 277
9.10 The Drag of Atmospheres on Moving Dislocations 277
9.11 The Sharp Yield Point and Luders Bands 279
9.12 The Theory of the Sharp Yield Point 281
9.13 Strain Aging 282
9.14 The Cottrell-Bilby Theory of Strain Aging 283
9.15 Dynamic Strain Aging 287
Problems 291
References 292
Chapter 10 Phases 293
10.1 Basic Definitions 293
10.2 The Physical Nature of Phase Mixtures 295
10.3 Thermodynamics of Solutions 295
10.4 Equilibrium between Two Phases 298
10.5 The Number of Phases in an Alloy System 299
One-Component Systems 299
Two-Component Systems 304
Ideal Solutions 304
Nonideal Solutions 305
10.6 Two-Component Systems Containing Two Phases 308
10.7 Graphical Determinations of Partial-Molar Free Energies 310
10.8 Two-Component Systems with Three Phases in Equilibrium 312
10.9 The Gibbs Phase Rule 313
10.10 Ternary Systems 315
Problems 316
References 317
Chapter 11 Binary Phase Diagrams 318
11.1 Phase Diagrams 318
11.2 Isomorphous Alloy Systems 319
11.3 The Lever Rule 320
11.4 Equilibrium Heating or Cooling of an Isomorphous Alloy 323
11.5 The Isomorphous Alloy System from the Point of View of Free Energy 325
11.6 Maxima and Minima 327
11.7 Superlattices 329
11.8 Miscibility Gaps 333
11.9 Eutectic Systems 334
11.10 The Microstructures of Eutectic Systems 335
11.11 The Peritectic Transformation 340
11.12 Monotectics 343
11.13 Other Three-Phase Reactions 347
11.14 Intermediate Phases 348
11.15 The Copper-Zinc Phase Diagram 350
11.16 Ternary Phase Diagrams 353
Problems 356
References 357
Chapter 12 Diffusion in Substitutional Solid Solutions 358
12.1 Diffusion in an Ideal Solution 359
12.2 The Kirkendall Effect 362
12.3 Pore Formation 366
12.4 Darken’s Equations 367
12.5 Fick’s Second Law 371
12.6 The Matano Method 373
12.7 Determination of the Intrinsic Diffusivities 377
12.8 Self-Diffusion in Pure Metals 378
12.9 Temperature Dependence of the Diffusion Coefficient 380
12.10 Chemical Diffusion at Low-Solute Concentration 383
12.11 The Study of Chemical Diffusion Using Radioactive Tracers 384
12.12 Diffusion along Grain Boundaries and Free Surfaces 388
12.13 Fick’s First Law in Terms of a Mobility and an Effective Force 391
12.14 Diffusion in Non-Isomorphic Alloy Systems 392
Problems 397
References 399
Chapter 13 Interstitial Diffusion 400
13.1 Measurement of Interstitial Diffusivities 401
13.2 The Snoek Effect 402
13.3 Experimental Determination of the Relaxation Time 409
13.4 Experimental Data 415
13.5 Anelastic Measurements at Constant Strain 416
Problems 417
References 418
Chapter 14 Solidification of Metals 419
14.1 The Liquid Phase 420
14.2 Nucleation 423
14.3 Metallic Glasses 425
14.4 Atomic Movement at S/L Interface 431
14.5 The Heats of Fusion and Vaporization 432
14.6 The Nature of the Liquid-Solid Interface 434
14.7 Continuous Growth 436
14.8 Lateral Growth 438
14.9 Stable Interface Freezing 439
14.10 Dendritic Growth in Pure Metals 441
14.11 Freezing in Alloys with Planar Interface 444
14.12 The Scheil Equation 446
14.13 Dendritic Freezing in Alloys 449
14.14 Freezing of Ingots 451
14.15 The Grain Size of Castings 454
14.16 Segregation 455
14.17 Homogenization 457
14.18 Inverse Segregation 461
14.19 Porosity 462
14.20 Eutectic Freezing 466
Problems 471
References 473
Chapter 15 Nucleation and Growth Kinetics 475
15.1 Nucleation of a Liquid from the Vapor 476
15.2 The Becker-Doring Theory 483
15.3 Freezing 485
15.4 Solid-State Reactions 487
15.5 Heterogeneous Nucleation 490
15.6 Growth Kinetics 493
15.7 Diffusion Controlled Growth 496
15.8 Interference of Growing Precipitate Particles 500
15.9 Interface Controlled Growth 501
15.10 Transformations That Occur on Heating 504
15.11 Dissolution of a Precipitate 505
Problems 508
References 509
Chapter 16 Precipitation Hardening 511
16.1 The Significance of the Solvus Curve 512
16.2 The Solution Treatment 513
16.3 The Aging Treatment 514
16.4 Development of Precipitates 517
16.5 Aging of Al-Cu Alloys at Temperatures above 100°C (373 K) 519
16.6 Precipitation Sequences in Other Aluminum Alloys 522
16.7 Homogeneous Versus Heterogeneous Nucleation of Precipitates 523
16.8 Interphase Precipitation 525
16.9 Theories of Hardening 527
16.10 Additional Factors in Precipitation Hardening 529
Problems 531
References 532
Chapter 17 Deformation Twinning and Martensite Reactions 533
17.1 Deformation Twinning 534
17.2 Formal Crystallographic Theory of Twinning 536
17.3 Twin Boundaries 542
17.4 Twin Nucleation and Growth 543
17.5 Accommodation of the Twinning Shear 546
17.6 The Significance of Twinning in Plastic Deformation 547
17.7 The Effect of Twinning on Face-Centered Cubic Stress-Strain Curves 548
17.8 Martensite 550
17.9 The Bain Distortion 551
17.10 The Martensite Transformation in an Indium-Thallium Alloy 553
17.11 Reversibility of the Martensite Transformation 554
17.12 Athermal Transformation 554
17.13 Phenomenological Crystallographic Theory of Martensite Formation 555
17.14 Irrational Nature of the Habit Plane 561
17.15 The Iron-Nickel Martensitic Transformation 562
17.16 Isothermal Formation of Martensite 564
17.17 Stabilization 564
17.18 Nucleation of Martensite Plates 565
17.19 Growth of Martensite Plates 566
17.20 The Effect of Stress 566
17.21 The Effect of Plastic Deformation 567
17.22 Thermoelastic Martensite Transformations 567
17.23 Elastic Deformation of Thermoelastic Alloys 569
17.24 Stress-Induced Martensite (SIM) 569
17.25 The Shape-Memory Effect 571
Problems 572
References 574