High-Entropy Alloys (eBook)

Dr. Michael C. Gao is a Principal Materials Scientist of AECOM at US Department of Energy National Energy Technology Laboratory and a courtesy faculty at Oregon State University. Professor Jien-Wei Yeh is a member of the Department of Materials Science and Engineering at National Tsing Hua University. Peter K. Liaw is a Professor and Ivan Racheff Chair of Excellence in the Department of Materials Science and Engineering at The University of Tennessee. Yong Zhang is a Professor of State Key Laboratory for Advanced Metals and Materials at the University of Science & Technology Beijing.

Preface 6
Contents 10
Contributors 12
Chapter 1: Overview of High-Entropy Alloys 15
1.1 Historical Development of Alloys 15
1.2 The Concept of Multicomponent Alloys 16
1.3 Ignition of the Research on High-Entropy Alloys 17
1.3.1 Brian Cantor´s Pioneering Work 18
1.3.2 Jien-Wei Yeh´s Pioneering Work 19
1.3.3 Srinivasa Ranganathan´s Alloyed Pleasure in 2003 21
1.4 Definition of High-Entropy Alloys 22
1.5 Clarification on Some Misunderstandings 26
1.6 Recent Activities for HEAs and HE-Related Materials 27
1.7 Research Fields in HEAs and HE-Related Materials 28
1.8 The Scope of This Book 30
References 31
Chapter 2: Phase Formation Rules 34
2.1 Introduction 35
2.2 Thermodynamics and Geometry Effect 36
2.3 Electron Concentration 48
2.3.1 VEC and e/a 50
2.3.2 VEC or e/a? 52
2.3.3 The Effect of VEC on the Phase Stability of HEAs 53
2.4 Remaining Issues and Future Prospects 56
2.4.1 Phase Formation Rules for HEAs Containing Mainly Non-TM Elements 56
2.4.2 Justification of the VEC Rule 56
2.4.3 Beyond fcc and bcc Solid Solutions 57
2.4.4 On e/a 58
2.5 Summary 58
References 59
Chapter 3: Physical Metallurgy 63
3.1 Introduction 63
3.2 Four Core Effects of HEAs 65
3.2.1 High-Entropy Effect 65
3.2.2 Severe Lattice Distortion Effect 68
3.2.3 Sluggish Diffusion Effect 71
3.2.4 Cocktail Effect 74
3.3 Crystal Structures and Phase Transformation in HEAs 76
3.3.1 The Number of Crystal Structures in Alloy World 76
3.3.2 Factors Affecting Solubility Between Metal Elements 78
3.3.3 Phase Transformation in Different Processing for HEAs 80
3.4 Defects and Defect Energies in HEAs 84
3.4.1 Defects in Distorted Lattice and Origin of Defect Energy 84
3.4.2 Lattice Distortion and Distortion Energy 86
3.4.3 Vacancies 88
3.4.4 Solutes 89
3.4.5 Dislocations 92
3.4.6 Stacking Faults 94
3.4.7 Grain Boundaries 101
3.5 Basic Mechanism of Sluggish Diffusion 104
3.6 Plastic Deformation in HEAs 106
3.6.1 Yielding and Serration Phenomenon 106
3.6.2 Effect of Low Stacking Fault Energy on Ductility and Toughness 107
3.6.3 Deformation Mechanisms in BCC or HCP HEAs 109
3.6.4 Strengthening Mechanisms in HEAs 109
3.7 Creep and Creep Mechanisms in HEAs 113
3.7.1 Creep Behavior and Extrapolation Method to Predict Creep 113
3.7.2 Creep Mechanisms 114
3.7.3 Potential of HEAs to Have Improved Creep Resistance 116
3.8 Conclusions and Perspective 121
References 121
Chapter 4: Advanced Characterization Techniques 126
4.1 Overview of Advanced Characterization Techniques 127
4.2 Microstructural Features of the AlxCoCrCuFeNi System: Integrated SEM, TEM (Bright and Dark Field), SAED, EDX, and XRD 129
4.3 Understanding the Fracture-Resistant Behavior of the CoCrFeMnNi Alloy: BSE Imaging, EBSD, EDX, and Stereomicroscopy 135
4.4 Phase Decomposition in AlCoCrCuFeNi: High-Resolution TEM and APT 138
4.5 Nature of the Phase Interfaces in Al1.5CoCrCuFeNi: HAADF Imaging 142
4.6 Chemical Disorder Verified Using Anomalous X-Ray Diffraction and Neutron Scattering 145
4.7 Local Atomic Structure in the Ternary HfNbZr Alloy 147
4.8 Deviations from High-Entropy Atomic Configurations Characterized Using Complementary Neutron and X-Ray Diffraction Techniq... 151
4.9 In Situ Neutron Diffraction Study of the Deformation Behavior of the CoCrFeNi HEA 154
4.10 Future Work 158
4.11 Conclusion 159
References 159
Chapter 5: Fabrication Routes 162
5.1 Introduction 163
5.2 Liquid-State Route 163
5.2.1 Arc Melting 163
5.2.2 Bridgman Solidification Casting 165
5.2.3 Synthesis of Single-Crystal HEA by BST 168
5.2.4 Laser Melting and Laser Cladding 171
5.3 Solid-State Route 175
5.3.1 Introduction: Description of Mechanical Alloying and Milling 175
5.3.2 Examples of ``Equilibrium´´ Phases Produced by Mechanical Alloying 177
5.3.3 Examples of Metastable Phases Produced by Mechanical Alloying 177
5.3.4 Examples of Solid-Solution HEAs Produced by Mechanical Alloying 179
5.4 Vapor-State Route 182
5.4.1 Physical Vapor Deposition 182
5.5 Discussion 185
5.5.1 Mechanical Properties and Application Prospects 185
5.5.2 Thermodynamic Analysis of the Phase Formation 185
5.6 Summary 187
References 187
Chapter 6: Mechanical Properties of High-Entropy Alloys 191
6.1 Introduction 192
6.2 Hardness 192
6.2.1 Annealing Treatment 193
6.2.2 Alloying Effects 195
6.2.3 Structure Effects 198
6.2.4 Hot Hardness 198
6.3 Compressive Properties 199
6.3.1 Compressive Stress-Strain Curves 199
6.3.2 Fracture Morphology 205
6.3.3 Temperature Effects 206
6.3.4 Strain-Rate Effects 210
6.3.5 Sample-Size Effects 211
6.3.6 Microcompression 211
6.4 Tensile Properties 212
6.4.1 Stress-Strain Curves 212
6.4.2 Yield Strength and Ductility 214
6.4.3 Deformation Mechanisms 217
6.4.4 Fracture 218
6.4.5 Comparison Among Hardness, Compression, and Tension Properties 220
6.5 Modeling of Serration Behavior 221
6.6 Fatigue Properties 227
6.6.1 Stress-Life (S-N) Curve 227
6.6.2 Fractography 229
6.6.3 Weibull Mixture Predictive Model for Fatigue Life 230
6.6.4 Comparison with Conventional Alloys 231
6.7 Nanoindentation 231
6.7.1 Nanoindentation and Modeling 231
6.7.2 Elevated-Temperature Nanoindentation 233
6.7.3 Indentation and Nanoindentation Creep 234
6.8 Conclusions 236
6.9 Future Work 237
References 238
Chapter 7: Functional Properties 247
7.1 Introduction 247
7.2 Electrical Properties of HEAs 248
7.2.1 Normal Conducting Behaviors 248
7.2.2 Superconducting Behaviors 251
7.3 Magnetic Properties of HEAs 253
7.4 Electrochemical Properties of HEAs 258
7.4.1 Electrochemical Kinetics 258
7.4.2 Alloying for Corrosion Resistance 261
7.4.3 Corrosion Protection 267
7.5 Hydrogen Storage Properties of HEAs 270
7.6 Conclusions and Perspectives 272
References 273
Chapter 8: Prediction of Structure and Phase Transformations 276
8.1 Introduction 276
8.2 Total Energy Calculation, T=0K 277
8.2.1 Density Functional Theory 278
8.2.2 Ground-State Prediction 279
8.2.3 Cluster Expansion 283
8.3 Extension to Finite Temperature 284
8.3.1 Example: Configurational Free Energy 286
8.3.2 Example: Vibrational Free Energy 288
8.3.3 Electronic Free Energy 292
8.4 Monte Carlo and Molecular Dynamics Simulation 292
8.4.1 Pair Correlation Functions 294
8.4.2 Route to the Entropy 294
8.5 Structure and Thermodynamic Modeling of High-Entropy Alloys 296
8.5.1 Cr-Mo-Nb-V 296
8.5.2 Nb-Ti-V-Zr 299
8.5.3 Mo-Nb-Ta-W 301
8.6 Conclusion 304
References 305
Chapter 9: Applications of Coherent Potential Approximation to HEAs 308
9.1 The Coherent Potential Approximation 309
9.2 The EMTO-CPA Method 311
9.3 Assessing the EMTO-CPA Method for HEAs 312
9.4 EMTO-CPA Applications to 3d HEAs 314
9.4.1 Equilibrium Volumes 314
9.4.2 Magnetic Properties 314
9.4.3 Elastic Properties of 3d HEAs 316
9.4.4 The fcc-bcc Phase Transformation in Al-Doped 3d HEAs 320
9.4.5 Elastic Properties of Al-Doped 3d HEAs 322
9.5 Refractory HEAs 325
9.5.1 Structural Properties 325
9.5.2 Electronic Structure 326
9.5.3 Elastic Properties 328
9.6 Stacking Fault Energy of HEAs 332
9.7 The KKR-CPA Method 334
9.8 Application of the KKR-CPA Approach 336
9.9 Conclusions 338
References 338
Chapter 10: Applications of Special Quasi-random Structures to High-Entropy Alloys 342
10.1 Introduction 343
10.2 Generation of SQS for High-Entropy Alloys 343
10.3 Quaternary and Quinary HEA SQS 345
10.4 Applications of SQS 357
10.4.1 Phase Stability at T=0 K 358
10.4.2 Vibrational and Electronic Entropies 360
10.4.3 Mechanical Properties 366
10.5 Comparison with Other Methods and Future Work 370
10.5.1 Electronic Structure 372
10.5.2 Atomic Structure 372
10.5.3 Sensitivity to Atomic Positions 373
10.5.4 Other Issues 374
10.6 Conclusions 375
References 376
Chapter 11: Design of High-Entropy Alloys 378
11.1 Introduction 378
11.2 CALPHAD Modeling 381
11.3 Phase Diagram Inspection 389
11.3.1 Exclusively Isomorphous Solid Solution in All Edge Binaries 390
11.3.2 Combination of Isomorphous Solid Solution and Large Terminal Solubility 391
11.3.3 Intermediate Phases with Wide Compositional Homogeneity Range 391
11.4 Empirical Parameters 392
11.5 DFT Calculations 396
11.6 AIMD Simulations 399
11.7 Summary and Outlook 403
References 404
Chapter 12: CALPHAD Modeling of High-Entropy Alloys 408
12.1 Introduction 409
12.2 CALPHAD Methodologies 410
12.2.1 Elements 412
12.2.2 Substitutional Solution Model 412
12.2.3 Stoichiometric Compound Model 414
12.2.4 Compound Energy Formalism (CEF) 415
12.2.5 Optimization 416
12.3 Thermodynamic Analysis of HEA Formation 418
12.3.1 FCC Co-Cr-Fe-Mn-Ni HEA System 419
12.3.2 HEA Formation of AlxCoCrFeNi in Comparison to CoCrFeMnxNi 423
12.3.3 BCC Mo-Nb-Ta-Ti-V-W HEA System 425
12.4 Computational Thermodynamics-Aided HEA Design 430
12.4.1 Phase Diagrams of the Al-Co-Cr-Fe-Ni System 430
12.4.1.1 Isopleth of AlxCoCrFeNi 430
12.4.1.2 Phase Evolution in Al0.3CoCrFeNi and Al0.875CoCrFeNi 432
12.4.1.3 Phase Evolution in Al0.7CoCrFeNi 433
12.4.1.4 Phase Diagram Predictions 436
12.4.1.5 Modeling Solidification 437
12.4.2 Phase Diagrams of Al-Cr-Cu-Fe-Ni System 440
12.4.3 Phase Diagrams of Mo-Nb-Ta-Ti-V-W System 441
12.5 Outlook 442
12.5.1 Impact of Chemical Ordering on Entropy 444
12.5.2 Kinetics Modeling of HEAs 447
12.6 Conclusions 448
References 449
Chapter 13: High-Entropy Metallic Glasses 454
13.1 Introduction 455
13.1.1 Differences Between BMGs and HEAs 455
13.1.2 Historical Background of HE-BMGs and Derivation of HE-BMGs from BMGs 456
13.1.3 Similarities Between BMGs and HEAs in Their Alloy Designs 458
13.2 HE-BMGs, Relevant Alloys and Their Characteristics 459
13.2.1 Cu20Ni20P20Pd20Pt20 HE-BMG and Relevant Alloys 461
13.2.2 Be20Cu20Ni20Ti20Zr20 HE-BMG and Its Mechanical Properties 465
13.2.3 Ca20Mg20Sr20Yb20Zn20-Based HE-BMGs and Their Unique Mechanical Properties 467
13.2.4 Factors Affecting the Mechanical Properties of HE-BMGs 468
13.2.5 AIMD Simulations 469
13.3 Expected Applications of HE-BMGs 472
13.4 Conclusions 473
References 474
Chapter 14: High-Entropy Coatings 478
14.1 Introduction 478
14.2 HEA Coatings 480
14.2.1 Thermal-Sprayed Coatings 480
14.2.2 Claddings 482
14.2.3 Diffusion Barriers 483
14.3 HEAN Coatings 486
14.3.1 Hard Coatings 486
14.3.2 Diffusion Barriers 492
14.4 Other HEA-Based Coatings 493
14.4.1 Low-Friction Hard Coatings 493
14.4.2 Biomedical Coatings 496
14.5 Conclusions and Perspective 496
References 497
Chapter 15: Potential Applications and Prospects 501
15.1 Introduction 501
15.2 Potential Applications 502
15.2.1 High-Entropy Superalloys 502
15.2.2 Refractory High-Entropy Alloys 506
15.2.3 Carbides and Cermets with HEA Binders 508
15.2.4 HEA Hard Coatings 509
15.2.5 HEA Diffusion Barriers 511
15.2.6 Irradiation-Resistant HEAs 512
15.3 Future Trends and Prospects 513
References 516
Index 521