Title Details

Preface XIX

Foreword XXI
by Robert W. Cahn

Motto XXIII

List of Contributors XXV

1 Introduction 1
Wolfgang Pfeiler

1.1 The Importance of Alloys at the Beginning of the Third Millennium 1

1.2 Historical Development 5

1.2.1 Historical Perspective 5

1.2.2 The Development of Modern Alloy Science 9

1.3 Atom Kinetics 12

1.4 The Structure of this Book 13

References 18

2 Crystal Structure and Chemical Bonding 19
Yuri Grin, Ulrich Schwarz, and Walter Steurer

2.1 Introduction 19

2.2 Factors Governing Formation, Composition and Crystal Structure of Intermetallic Phases 20

2.2.1 Mappings of Crystal Structure Types 21

2.3 Models of Chemical Bonding in Intermetallic Phases 25

2.3.1 Models Based on the Valence (or Total) Electron Numbers 25

2.3.2 Quantum Mechanical Models for Metallic Structures 29

2.3.3 Electronic Closed-Shell Configurations and Two-Center Two-Electron Bonds in Intermetallic Compounds 31

2.4 Structure Types of Intermetallic Compounds 36

2.4.1 Classification of the Crystal Structures of Intermetallic Compounds 37

2.4.2 Crystal Structures Derived from the Closest Packings of Equal Spheres 37

2.4.3 Crystal Structures Derived from the Close Packings of Equal Spheres 40

2.4.4 Crystal Structures Derived from the Packings of the Spheres of Different Sizes 43

2.4.5 Selected Crystal Structures with Complex Structural Patterns 44

2.5 Quasicrystals 48

2.5.1 Introduction 48

2.5.2 Quasiperiodic Structures in Direct and Reciprocal Space 50

2.5.3 Formation and Stability 52

2.5.4 Structures of Decagonal Quasicrystals (DQCs) 53

2.5.5 Structures of Icosahedral Quasicrystals 55

2.6 Outlook 59

References 60

3 Solidification and Grown-in Defects 63
Thierry Duffar

3.1 Introduction: the Solid–Liquid Interface 63

3.1.1 Structure of the Solid–Liquid Interface 63

3.1.2 Kinetics of the Solid–Liquid Interface 65

3.1.3 Chemistry of the Solid–Liquid Interface: the Segregation Problem 67

3.1.4 Temperature of the Solid–Liquid Interface 69

3.2 Solidification Structures 70

3.2.1 The Interface Stability and Cell Periodicity 71

3.2.2 Dendrites 74

3.2.3 Rapid Solidification 86

3.2.4 Eutectic Structures 90

3.3 Defects in Single and Polycrystals 93

3.3.1 Defects in Single Crystals 94

3.3.2 Grain Structure of an Alloy 101

3.3.3 Macro- and Mesosegregation 110

3.4 Outlook 114

References 117

4 Lattice Statics and Lattice Dynamics 119
Véronique Pierron-Bohnes and Tarik Mehaddene

4.1 Introduction: The Binding and Atomic Interaction Energies 119

4.2 Elasticity of Crystalline Lattices 124

4.2.1 Linear Elasticity 125

4.2.2 Elastic Constants 125

4.2.3 Cases of Cubic and Tetragonal Lattices 127

4.2.4 Usual Elastic Moduli 128

4.2.5 Link with Sound Propagation 130

4.3 Lattice Dynamics and Thermal Properties of Alloys 132

4.3.1 Normal Modes of Vibration in the Harmonic Approximation 133

4.4 Beyond the Harmonic Approximation 149

4.4.1 Thermal Expansion 150

4.4.2 Thermal Conductivity 151

4.4.3 Soft Phonon Modes and Structural Phase Transition 153

4.5 Experimental Investigation of the Normal Modes of Vibration 156

4.5.1 Raman Spectroscopy 156

4.5.2 Inelastic Neutron Scattering 157

4.6 Phonon Spectra and Migration Energy 160

4.7 Outlook 165

References 168

5 Point Defects, Atom Jumps, and Diffusion 173
Wolfgang Püschl, Hiroshi Numakura, and Wolfgang Pfeiler

5.1 Point Defects 173

5.1.1 A Brief Overview 173

5.1.2 Point Defects in Pure Metals and Dilute Alloys 187

5.1.3 Point Defects in Ordered Alloys 197

5.2 Defect Migration: Microscopic Diffusion 217

5.2.1 The Single Atom Jump 217

5.2.2 Solid Solutions 222

5.2.3 Atom Migration in Ordered Alloys 238

5.3 Statistical Methods: from Single Jump to Configuration Changes 252

5.3.1 Master Equation Method 253

5.3.2 Continuum Approaches to Microscopic Diffusion and their Interrelationship with Atom Jump Statistics 253

5.3.3 Path Probability Method 255

5.3.4 Monte Carlo Simulation Method 255

5.4 Macroscopic Diffusion 256

5.4.1 Formal Description 256

5.4.2 Phase Transformations as Diffusion Phenomena 263

5.4.3 Enhanced Diffusion Paths 265

5.5 Outlook 272

References 274

6 Dislocations and Mechanical Properties 281
Daniel Caillard

6.1 Introduction 281

6.2 Thermally Activated Mechanisms 283

6.2.1 Introduction to Thermal Activation 283

6.2.2 Interactions with Solute Atoms 285

6.2.3 Forest Mechanism 292

6.2.4 Peierls-Type Friction Forces 293

6.2.5 Cross-Slip in fcc Metals and Alloys 305

6.2.6 Dislocation Climb 309

6.2.7 Conclusions on Thermally Activated Mechanisms 316

6.3 Hardening and Recovery 316

6.3.1 Dislocation Multiplication versus Exhaustion 317

6.3.2 Dislocation–Dislocation Interaction and Internal Stress: the Taylor Law 321

6.3.3 Hardening Stages in fcc Metals and Alloys 323

6.4 Complex Behavior 330

6.4.1 Yield Stress Anomalies 330

6.4.2 Fatigue 333

6.4.3 Strength of Nanocrystalline Alloys and Thin Layers 336

6.4.4 Fracture 338

6.4.5 Quasicrystals 339

6.5 Outlook 342

References 342

7 Phase Equilibria and Phase Transformations 347
Brent Fultz and Jeffrey J. Hoyt

7.1 Alloy Phase Diagrams 347

7.1.1 Solid Solutions 347

7.1.2 Free Energy and the Lever Rule 351

7.1.3 Common Tangent Construction 353

7.1.4 Unmixing and Continuous Solid Solubility Phase Diagrams 354

7.1.5 Eutectic and Peritectic Phase Diagrams 356

7.1.6 More Complex Phase Diagrams 357

7.1.7 Atomic Ordering 359

7.1.8 Beyond Simple Models 362

7.1.9 Entropy of Configurations 363

7.1.10 Principles of Phonon Entropy 365

7.1.11 Trends of Phonon Entropy 367

7.1.12 Phonon Entropy at Elevated Temperatures 369

7.2 Kinetics and the Approach to Equilibrium 371

7.2.1 Suppressed Diffusion in the Solid (Nonequilibrium Compositions) 371

7.2.2 Nucleation Kinetics 373

7.2.3 Suppressed Diffusion in the Liquid (Glasses) 374

7.2.4 Suppressed Diffusion in a Solid Phase (Solid-State Amorphization) 375

7.2.5 Combined Reactions 376

7.2.6 Statistical Kinetics of Phase Transformations 377

7.2.7 Kinetic Pair Approximation 378

7.2.8 Equilibrium State of Order 380

7.2.9 Kinetic Paths 380

7.3 Nucleation and Growth Transformations 382

7.3.1 Definitions 382

7.3.2 Fluctuations and the Critical Nucleus 384

7.3.3 The Nucleation Rate 387

7.3.4 Time-Dependent Nucleation 391

7.3.5 Effect of Elastic Strain 393

7.3.6 Heterogeneous Nucleation 395

7.3.7 The Kolmogorov–Johnson–Mehl–Avrami Growth Equation 397

7.4 Spinodal Decomposition 399

7.4.1 Concentration Fluctuations and the Free Energy of Solution 400

7.4.2 The Diffusion Equation 402

7.4.3 Effects of Elastic Strain Energy 404

7.5 Martensitic Transformations 406

7.5.1 Characteristics of Martensite 406

7.5.2 Massive and Displacive Transformations 411

7.5.3 Bain Strain Mid-Lattice Invariant Shear 412

7.5.4 Martensite Crystallography 413

7.5.5 Nucleation and Dislocation Models of Martensite 415

7.5.6 Soft Mode Transitions, the Clapp Lattice Instability Model 417

7.6 Outlook 418

References 420

8 Kinetics in Nonequilibrium Alloys 423
Pascal Bellon and Georges Martin

8.1 Relaxation of Nonequilibrium Alloys 424

8.1.1 Coherent Precipitation: Nothing but Solid-State Diffusion 425

8.1.2 Cluster Dynamics, Nucleation Theory, Diffusion Equations: Three Tools for Describing Kinetic Pathways 426

8.1.3 Cluster Dynamics 427

8.1.4 Classical Nucleation Theory 432

8.1.5 Kinetics of Concentration Fields 436

8.1.6 Conclusion 438

8.2 Driven Alloys 438

8.2.1 Examples of Driven Alloys 439

8.2.2 Identification of the Relevant Control Parameters: Toward a Dynamical Equilibrium Phase Diagram 450

8.2.3 Theoretical Approaches and Simulation Techniques 454

8.2.4 Self-Organization in Driven Alloys: Role of Length Scales of the External Forcing 468

8.2.5 Practical Applications and Extensions 481

8.3 Outlook 484

References 484

9 Change of Alloy Properties under Dimensional Restrictions 491
Hirotaro Mori and Jung-Goo Lee

9.1 Introduction 491

9.2 Instrumentation for in-situ Observation of Phase Transformation of Nanometer-Sized Alloy Particles 492

9.3 Depression of the Eutectic Temperature and its Relevant Phenomena 494

9.3.1 Atomic Diffusivity in Nanometer-Sized Particles 494

9.3.2 Eutectic Temperature in Nanometer-Sized Alloy Particles 496

9.3.3 Structural Instability 500

9.3.4 Thermodynamic Discussion 503

9.4 Solid/Liquid Two-Phase Microstructure 508

9.4.1 Solid–Liquid Phase Transition 508

9.4.2 Two-Phase Microstructure 514

9.5 Solid Solubility in Nanometer-Sized Alloy Particles 518

9.6 Summary and Future Perspectives 521

References 522

10 Statistical Thermodynamics and Model Calculations 525
Tetsuo Mohri

10.1 Introduction 525

10.2 Statistical Thermodynamics on a Discrete Lattice 527

10.2.1 Description of Atomic Configuration 527

10.2.2 Internal Energy 534

10.2.3 Entropy and Cluster Variation Method 536

10.2.4 Free Energy 542

10.2.5 Relative Stability and Intrinsic Stability 544

10.2.6 Atomistic Kinetics by the Path Probability Method 549

10.3 Statistical Thermodynamics on Continuous Media 552

10.3.1 Ginzburg–Landau Free Energy 552

10.3.2 Diffusion Equation and Time-Dependent Ginzburg–Landau Equation 554

10.3.3 Width of an Interface 557

10.3.4 Interface Velocity 559

10.4 Model Calculations 560

10.4.1 Calculation of a Phase Diagram 561

10.4.2 Microstructural Evolution Calculated by the Phase Field Method 572

10.5 Future Scope and Outlook 580

Appendix: CALPHAD Free Energy 582

References 585

11 Ab-Initio Methods and Applications 589
Stefan Mu¨ller, Walter Wolf, and Raimund Podloucky

11.1 Introduction 589

11.2 Theoretical Background 590

11.2.1 Density Functional Theory 590

11.2.2 Computational Methods 594

11.2.3 Elastic Properties 598

11.2.4 Vibrational Properties 601

11.3 Applications 606

11.3.1 Structural and Phase Stability 606

11.3.2 Point Defects 612

11.3.3 Diffusion Processes 616

11.3.4 Impurity Effects on Grain Boundary Cohesion 622

11.3.5 Toward Multiscale Modeling: Cluster Expansion 625

11.3.6 Search for Ground-State Structures 639

11.3.7 Ordering and Decomposition Phenomena in Binary Alloys 641

11.4 Outlook 648

References 649

12 Simulation Techniques 653
Ferdinand Haider, Rafal Kozubski, and T.A. Abinandanan

12.1 Introduction 653

12.2 Molecular Dynamics Simulations 654

12.2.1 Basic Ideas 654

12.2.2 Atomic Interaction, Potential Models 656

12.2.3 Practical Considerations 659

12.2.4 Different Thermodynamic Ensembles: Thermostats, Barostats 659

12.2.5 Implementation of MD Algorithms 661

12.2.6 Practical Aspects: Time Steps 662

12.2.7 Evaluation of Data: Use of Correlation Functions 662

12.2.8 Applications to Alloys, Alloy Dynamics, and Alloy Kinetics 664

12.3 Monte Carlo Simulations 667

12.3.1 Foundations of Stochastic Processes – Markov Chains and the Master Equation 667

12.3.2 The Idea of Sampling 668

12.3.3 Markov Chains as a Tool for Importance Sampling 670

12.3.4 General Applicability 671

12.3.5 Limitations: Finite-Size Effects and Boundary Conditions 674

12.3.6 Numerical Implementation of MC 675

12.3.7 Applications to Alloys 678

12.3.8 Practical Aspects 681

12.3.9 Review of Current Applications in Studies of Alloys 682

12.3.10 Going beyond the Ising Model and Rigid-Lattice Simulations 685

12.3.11 Monte Carlo Simulations in View of other Techniques of Alloy Modeling 686

12.4 Phase Field Models 686

12.4.1 Introduction 686

12.4.2 Cahn–Hilliard Model 687

12.4.3 Numerical Implementation 691

12.4.4 Application: Spinodal Decomposition 693

12.4.5 Cahn–Allen Model 694

12.4.6 Generalized Phase Field Models 696

12.4.7 Other Topics 700

12.5 Outlook 702

Appendix 702

References 703

13 High-Resolution Experimental Methods 707

13.1 High-Resolution Scattering Methods and Time-Resolved Diffraction 707
Bogdan Sepiol and Karl F. Ludwig

13.1.1 Introduction: Theoretical Concepts, X-Ray, and Neutron Scattering Methods 707

13.1.2 Magnetic Scattering 710

13.1.3 Spectroscopy 721

13.1.4 Time-Resolved Scattering 749

13.1.5 Diffuse Scattering from Disordered Alloys 756

13.1.6 Surface Scattering – Atomic Segregation and Ordering near Surfaces 762

13.1.7 Scattering from Quasicrystals 763

13.1.8 Outlook 764

References 765

13.2 High-Resolution Microscopy 774
Guido Schmitz and James M. Howe

13.2.1 Surface Analysis by Scanning Probe Microscopy 775

13.2.2 High-Resolution Transmission Electron Microscopy and Related Techniques 791

13.2.3 Local Analysis by Atom Probe Tomography 817

13.2.4 Future Development and Outlook 853

References 857

14 Materials and Process Design 861

14.1 Soft and Hard Magnets 861
Roland Grössinger

14.1.1 What do ‘‘Soft’’ and ‘‘Hard’’ Magnetic Mean? 861

14.1.2 Soft Magnetic Materials 865

14.1.3 Hard Magnetic Materials 873

14.1.4 Outlook 883

References 883

14.2 Invar Alloys 885
Peter Mohn

14.2.1 Introduction and General Remarks 885

14.2.2 Spontaneous Volume Magnetostriction 888

14.2.3 The Modeling of Invar Properties 889

14.2.4 A Microscopic Model 893

14.2.5 Outlook 894

References 895

14.3 Magnetic Media 895
Laurent Ranno

14.3.1 Data Storage 895

14.3.2 Magnetic Recording Media 905

14.3.3 Outlook 909

Further Reading 910

14.4 Spin Electronics (Spintronics) 911
Laurent Ranno

14.4.1 Electrical Transport in Conductors 911

14.4.2 Magnetoresistance 915

14.4.3 Outlook 921

Further Reading 921

14.5 Phase-Change Media 921
Takeo Ohta

14.5.1 Electrically and Optically Induced Writing and Erasing Processes 921

14.5.2 Phase-Change Dynamic Model 925

14.5.3 Alternative Functions 933

14.5.4 Outlook 938

References 938

14.6 Superconductors 939
Harald W. Weber

14.6.1 Fundamentals 939

14.6.2 Superconducting Materials 944

14.6.3 Technical Superconductors 946

14.6.4 Applications 952

Further Reading 953

Index 955