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