High-Entropy Materials: Theory, Experiments, and Applications

Preface
Contents
Chapter 1: A Personal Perspective on the Discovery and Significance of Multicomponent High-Entropy Alloys
	1.1 Introduction
	1.2 Discovery of Multicomponent High-Entropy Alloys
		1.2.1 Cantor Alloys
		1.2.2 Equiatomic Substitution
		1.2.3 High-Entropy Alloys
		1.2.4 Multicomponent Alloys
	1.3 Multicomponent Phase Space
		1.3.1 The Number of Different Materials
		1.3.2 Multicomponent Phases
		1.3.3 Multicomponent Hume-Rothery Rules
	1.4 Thermodynamics of Multicomponent High-entropy Alloys
		1.4.1 The Free Energy of Multicomponent Alloys
		1.4.2 The Entropy of Multicomponent Alloys
		1.4.3 The Stability of Multicomponent Alloys
		1.4.4 Local Atomic Distributions in Multicomponent Alloys
		1.4.5 Lattice Distortions in Multicomponent Alloys
	1.5 Some Properties of Multicomponent High-Entropy Alloys
		1.5.1 Diffusion in Multicomponent Alloys
		1.5.2 Dislocation Slip in Multicomponent Alloys
		1.5.3 Mechanical Properties of Multicomponent Alloys
	1.6 Autobiographical Note
	1.7 Philosophical Reflections
	References
Chapter 2: My Trip from Physics to High-Entropy Materials
	2.1 Brief Biography
	2.2 My Trip in Research and Development
		2.2.1 Old Nanotechnology
		2.2.2 My Trip in Nano-glass
		2.2.3 My Trip in Nano-metals
	2.3 My Important Milestones in the Growth of the HEMs Field
	2.4 Share my Experience with Younger People: Why and How to Apply What You´ve Learned to Good Use
	2.5 Social Impacts from HEMs
		2.5.1 Academic Activities
		2.5.2 Social Effects and Impacts
	References
Chapter 3: Harnessing the Complex Compositional Space of High-Entropy Alloys
	3.1 Background
	3.2 Current Methods for Predicting High-Entropy Phase Formation
		3.2.1 Approaches Using Empirical Parameters
			3.2.1.1 Free Energy Parameters
			3.2.1.2 Parameters from Hume-Rothery Theory
			3.2.1.3 Other Parameters
			3.2.1.4 Correlation Between the Parameters and Phase Formation
		3.2.2 Thermodynamic and First-Principles Calculations
			3.2.2.1 CALPHAD
			3.2.2.2 Ab-initio Simulations and Density Functional Theory
		3.2.3 Statistical and Machine Learning Studies
	3.3 Phenomenological Approach
		3.3.1 Rationale
		3.3.2 Description of the Approach
			3.3.2.1 Phase-Diagram-Based Parameters
			3.3.2.2 Visualization of the Phase Fields in Parameter Space
			3.3.2.3 Machine Learning Optimization
			3.3.2.4 Experimental Validation and Future Development
	3.4 Material Properties
	3.5 Critical Challenges and Future Endeavors
	3.6 Conclusions
	References
Chapter 4: Machine Learning and Data Analytics for Design and Manufacturing of High-Entropy Materials Exhibiting Mechanical or...
	4.1 Introduction
		4.1.1 High-Entropy Materials: Materials with Large Composition Space
		4.1.2 Additive Manufacturing of HEA Metallic Components
			4.1.2.1 Introduction
			4.1.2.2 Primary Categories of Metal AM Technologies
				Powder-Bed Fusion
				Direct Energy Deposition
			4.1.2.3 Key Differentiating Characteristics Between Metal AM and Conventional Manufacturing
			4.1.2.4 Main Limitations of Metal AM Processes
			4.1.2.5 Review of Sources Impacting Properties and Performance of AM Metallic Components
			4.1.2.6 Interrelationships between Sources Impacting Properties of AM Components and the Underlying Physics
			4.1.2.7 More on Relationship of AM Processes with Material and Geometry Properties and Component Level Properties
		4.1.3 Phase Diagrams and Integrated Computational Materials Engineering
		4.1.4 High-Temperature Applications
			4.1.4.1 Motivation
			4.1.4.2 Role of AI and ML for Development of Alloys Suitable for High-Temperature Applications
			4.1.4.3 Role of AM for High-Temperature Applications
			4.1.4.4 Environmental (Corrosion) Resistance
		4.1.5 Applications of AI or ML to Material Design or Manufacturing
			4.1.5.1 For Rapid Screening of Material Data Sets - For Accelerated Identification of HEMs with Desired Properties
			4.1.5.2 To Account for All Sources of Variations in AM Processes - Or for Real-Time In-Situ AM Quality Control
			4.1.5.3 Practical Approach to Material Design
			4.1.5.4 Practical Approach to Additive Manufacturing
		4.1.6 Review of Selected Background Work
	4.2 Standard Machine Learning in Context with a Generic System Model
		4.2.1 Key Take-Aways
		4.2.2 Fundamental Principles
			4.2.2.1 Data Filtering (Curation)
				Key Principles
				General Guidelines for Devising the Data Filtering
				Simplistic Illustration of Application-Specific Nature of Data Filtering
			4.2.2.2 Main Categories
			4.2.2.3 Brief Summary of Bayesian Inference
				Bayes´ Theorem
				The Prior Probability Distribution
				The Likelihood Function
				The Posterior Probability Distribution
				Salient Aspects of Bayesian Networks and Inference
			4.2.2.4 Occam´s Razor: Preference to Simple Models (Case of Overfitting)
			4.2.2.5 Estimation of How Much Input Data Is Needed for a Given ML Algorithm (Model) to Be Suitable
		4.2.3 The Generic System Model Assumed
		4.2.4 Statistical Regression
			4.2.4.1 Model Structure
			4.2.4.2 Least-Squares Solution
			4.2.4.3 Residuals
			4.2.4.4 Sum of Squares
			4.2.4.5 Coefficient of Multiple Determination
			4.2.4.6 Properties of Estimators and Residuals - Before Gaussian Assumption
			4.2.4.7 Properties of Estimators and Residuals - After Gaussian Assumption
			4.2.4.8 Confidence Intervals
			4.2.4.9 Predictors Limited to a Continuous Range
			4.2.4.10 Categorical Predictors
			4.2.4.11 Priorities Assigned to Predictors (Features) in the Feature Set
			4.2.4.12 Variance Analysis
			4.2.4.13 Sensitivity Analysis
			4.2.4.14 Application of Regression Analysis for Optimization of a Feature Set (Input Predictors)
			4.2.4.15 Inferences Utilizing the Regression Model Derived
			4.2.4.16 Alternative Regression Models
			4.2.4.17 Quadratic Regression
		4.2.5 AI Predictor (Neural Network)
			4.2.5.1 Single-Layer Feed-Forward Neural Network
			4.2.5.2 Two-Layer Feed-Forward Neural Network
			4.2.5.3 Training of Two-Layer Feed-Forward Neural Network
			4.2.5.4 Approximation Capability of Two-Layer Feed-Forward Neural Network
		4.2.6 ML in Context with Bayesian Inference Revisited
			4.2.6.1 Neural Network Learning (Training) in Context with Bayesian Inference
			4.2.6.2 Approach to Estimating the Number of Samples Needed to Enable ML Models to Approximate Underlying Distributions with G...
	4.3 ``Inverse´´ Design Representations Accomplished Through ``Forward´´ and ``Backward´´ Prediction
		4.3.1 Key Take-Aways
		4.3.2 ``Inverse´´ Design Representations
		4.3.3 Overall Approach to ``Forward´´ and ``Backward´´ Prediction
		4.3.4 Preprocessing
		4.3.5 Feature Selection
		4.3.6 ``Forward´´ Prediction
			4.3.6.1 Approach to Building a Generic System Model Through ``Forward´´ Prediction
			4.3.6.2 Review of Modeling Techniques for ``Forward´´ Prediction
				Statistical Regression
				K-Nearest Neighbor Averaging
				Feed-Forward Neural Network
				Other Modeling Techniques
			4.3.6.3 Example: ``Forward´´ Prediction of Fatigue Endurance Limit
		4.3.7 ``Backward´´ Prediction
			4.3.7.1 General Approach to Inferring the Feature Set (e.g., Composition) through ``Backward´´ Prediction
			4.3.7.2 Specific Approaches for ``Backward´´ Prediction
				Starting Point: Microstructure of the Nearest Neighbor
				Baseline Approach: Generalization of
				Combining Metrics: Method to Address Non-Uniqueness
			4.3.7.3 Toward Simplification - Suitability of ML vs. Polynomial Fit in Absence of Discrete Jumps in Data
			4.3.7.4 More on a Custom, Hybrid Solution for ``Backward´´ Prediction: Polynomial Fit Employed for Complexity Reduction
			4.3.7.5 Prediction of Distributions (Mean and Variance) - Stochastic Prediction
	4.4 Physics-Based Models
		4.4.1 Key Take-Aways
		4.4.2 Generic Approach to Incorporating Physics-Based Models
		4.4.3 Overview Over the Primary Physics-Based Models Considered
			4.4.3.1 Thermodynamics: Interaction of ML with Phase Stability Models from CALPHAD
			4.4.3.2 First-Principle Effects
			4.4.3.3 Empirical Rules
			4.4.3.4 Mesoscale Models
			4.4.3.5 Models Involving Dislocation Dynamics, Solid Solution Strengthening or Slip Band Information
			4.4.3.6 Environmental Resistance (Oxidation, Corrosion, or Radiation)
		4.4.4 General Approach to Construction of a Physics-Based Model - Application to Prediction of Ultimate Tensile Strength
			4.4.4.1 Approach
			4.4.4.2 Further Theoretical Considerations (Justifications)
		4.4.5 Necessary Steps toward Accurate Prediction: Characterization of Expected Sources of Variations - Application to Predicti...
			4.4.5.1 Expected Dependence of Tensile Strength on Alloy Type
			4.4.5.2 Expected Dependence of Tensile Strength on Temperature
			4.4.5.3 Expected Dependence of Tensile Strength on Manufacturing Technique
			4.4.5.4 Expected Impact of Grain Size on Yield or Tensile Strength
			4.4.5.5 Expected Dependence of Endurance Limit on UTS, for Fixed Defect Level and Heat Treatment Process
			4.4.5.6 Expected Dependence of Endurance Limit on Defect Levels, for Fixed UTS and Heat Treatment Process
		4.4.6 Necessary Steps Toward Accurate Prediction: Characterization of Sources of Observed Variations - Application to Predicti...
			4.4.6.1 Comparison across Compositions, Process Parameters, Defect Levels, and Grain Sizes for a Given UTS - Further Explanati...
				UTS  1100 MPa
				UTS  1340 MPa
			4.4.6.2 Comparison Across Process Parameters, Defect Levels, Grain Sizes, and UTS for a Given Composition
				Comparison for AlCoCrFeNi2.1
				Further Comparison for CoCrFeNiMn
			4.4.6.3 Comparison for 4340 Steel
		4.4.7 Example 1: Identification of Compositions Yielding High Tensile Strength
			4.4.7.1 Review of the Original Data Set - Rational for Restricting Analysis to Room-Temperature Data
			4.4.7.2 Analysis of Variations in UTS for the Pure Elements - Selection of a Suitable Prediction Model
			4.4.7.3 Selection of a Suitable Optimization Technique
			4.4.7.4 Setting up the Optimization Problem
				Multi-Variate Linear Regression
				Quadratic Regression with Diagonal Matrix (for Comparison)
			4.4.7.5 Prediction of Composition Yielding Higher UTS, and Presumably More Attractive Fatigue Resistance, Than Previously Obse...
			4.4.7.6 Toward Understanding What Is Causing Limitations of the Model - Analysis of Variance (Outliers)
			4.4.7.7 Assessing the Need for a More Sophisticated Prediction Model - Further Analysis of Data Set C
				Criterion for Assessment of Suitability of the Linear Regression, Upon Addition of New Data
				Prediction of Compositions with Higher UTS Than Previously Observed, Based on Data Set C
				Suitability of Linear Regression for Data Set C
				Suitability of Quadratic Regression for Data Set C
			4.4.7.8 Verifying Feasibility of the Predicted Compositions - Empirical Rules
				Expected Properties of Al0.5Mo0.5Nb1.5Ta0.5Zr1.5, Based on the Empirical Rules
				Expected Properties of Mo1.25Nb1.25Ti0.5V0.75Zr, Mo1.25Nb1.25Ti0.5V0.5Zr1.25, and MoNbZr, Based on the Empirical Rules
			4.4.7.9 Initial Efforts Toward Experimental Verification
		4.4.8 Example 2: Prediction of Fatigue Resistance (Endurance Limit)
			4.4.8.1 Formulation of the Input Combinations
			4.4.8.2 Estimating the Tensile Strength, Given an Input Combination
			4.4.8.3 Arriving at the Fatigue Resistance, Given the Tensile Strength and the Remaining Inputs
		4.4.9 Example 3: Toward Coatings and Base Alloys Resistant to Hot Corrosion
			4.4.9.1 Overall Goal
			4.4.9.2 Brief Background on Thermal Barrier Coatings
			4.4.9.3 Brief Background on Deposition Models for Hot Corrosion
			4.4.9.4 Essence of CMAS and Calcium Sulfate Corrosion Attacks
			4.4.9.5 Specifics of Interaction of CMAS with the Thermal Barrier Coating
			4.4.9.6 Specifics of Interaction of Calcium Sulfate with the Thermal Barrier Coating and Base Alloy
			4.4.9.7 Overview of the Reaction Space
			4.4.9.8 List of Features Jointly Characterizing CMAS and Calcium Sulfate Corrosion Attacks
			4.4.9.9 Canonical Component Analysis for Deriving Distinguishing Characteristics between CMAS and Calcium Sulfate Hot Corrosio...
			4.4.9.10 Joint Optimization
		4.4.10 Example 4: Optimization of Tensile Strength for CMCs or PMCs
			4.4.10.1 Motivation
			4.4.10.2 Approach
			4.4.10.3 Physics-Based Models Available
			4.4.10.4 Data Available
		4.4.11 Example 5: Joint Optimization of Material Strength, Ductility, and Oxidation Resistance
			4.4.11.1 Motivation
			4.4.11.2 High-Level Approach
			4.4.11.3 Design Objectives Presented to Alloy Designers
			4.4.11.4 Pareto Optimality: Concept of Key Importance for Multi-Objective Optimization
			4.4.11.5 Primary Approaches to Multi-Objective Optimization
			4.4.11.6 Sample Frameworks for Joint Optimization of Strength and Ductility for Low-Carbon Steels
			4.4.11.7 Sample Joint Optimization Framework for Single-Crystal Nickel-Based Superalloys
			4.4.11.8 Extensions to HEMs: Improvements Through Incorporation of Physics-Based Models
	4.5 Statistical Models
		4.5.1 Key Take-Aways
		4.5.2 Key Advantages of ML for Prediction of Fatigue Life of AM HEA Components
		4.5.3 Statistical Modeling Compared and Contrasted to Physics-Based Modeling
		4.5.4 Statistical Fatigue Life Model for Analytical Representation of Stress/Life (S/N) Curves
		4.5.5 Augmentation of the Statistical Fatigue Life Model
		4.5.6 Example 6: Prediction of Fatigue Life (Stress Life or Strain Life) and Crack Growth
			4.5.6.1 Prediction of Fatigue Life Remaining (S/N Curve), in Absence of Cracks
				Objective
				Preferred Method
				Alternative Method
				Expected Results
			4.5.6.2 Prediction of Fatigue Life Remaining, Given a Crack
	4.6 Other Applications of ML, AI, and Data Analytics to Material Science or Manufacturing
		4.6.1 ML or AI for Real-Time Quality Control in Powder Bed AM - Multi-Beam Approach
			4.6.1.1 Motivation Revisited
			4.6.1.2 General Approach to AM Parameter Optimization
			4.6.1.3 Challenges with Powder Bed AM
			4.6.1.4 Addressing the Challenges with a Real-Time AI Controller and a Multi-Beam Approach - Intelligent AM
		4.6.2 ML or AI for Real-Time Quality Control in a Generic AM System - Reinforcement Learning
			4.6.2.1 Reinforcement Learning in Context with Robotics and Aerostructure Manufacturing
			4.6.2.2 More on the Challenge Addressed
			4.6.2.3 Application of Reinforcement Learning to in-Situ Quality Control of a Generic AM System
		4.6.3 ML in Low-Data Environments
			4.6.3.1 Estimates of Sample-Complexity
			4.6.3.2 Surrogate Modeling
		4.6.4 ML for Prediction of Solid Solution Phases
		4.6.5 Other Applications of Machine Learning to Optimization of Mechanical Properties
			4.6.5.1 Sequential Learning Through Random Forrest Modeling with Well-Calibrated Uncertainty Estimates
			4.6.5.2 Canonical Component Analysis and Genetic Algorithms for Prediction of Hardness
			4.6.5.3 Artificial Neural Networks for Prediction of Material Hardness
			4.6.5.4 Gradient Boosting Tree Algorithm for Estimating Elastic Moduli
		4.6.6 Other Applications of Machine Learning to Optimization of AM Processes
	4.7 Future Work
	4.8 Conclusions
	References
Chapter 5: Additive Manufacturing of High-Entropy Alloys: Microstructural Metastability and Mechanical Properties
	5.1 Introduction
	5.2 Metal Additive Manufacturing
		5.2.1 Working Principles
		5.2.2 Defect Formation
			5.2.2.1 Estimation of Melt Pool Geometry
			5.2.2.2 Gas Pores and Lack-of-Fusion Defects
			5.2.2.3 Balling
			5.2.2.4 Cracking
			5.2.2.5 Printability Map
		5.2.3 Grain Structure Formation
	5.3 Microstructures, Mechanical Properties, and Potential Applications of AM-ed HEAs
		5.3.1 FCC-Based HEAs
		5.3.2 BCC-Based HEAs
		5.3.3 Metastable HEAs
		5.3.4 Compositionally Graded HEAs
		5.3.5 Laminated HEAs
	5.4 Conclusions and Future Outlook
	References
Chapter 6: Electronic Effects on the Mechanical Properties of High-Entropy Alloys
	6.1 Introduction
	6.2 Atomic-Level Stresses
		6.2.1 Definition of Atomic-Level Stresses
		6.2.2 DFT Calculation of Atomic-Level Stresses
	6.3 Electronic States in High-Entropy Alloys
		6.3.1 Electronic Heterogeneity in High-Entropy Alloys
		6.3.2 Atomic-Level Pressure in HEAs
		6.3.3 Atomic-Level Shear Stresses and Intra-atomic Charge Transfer
	6.4 Properties of High-Entropy Alloys
		6.4.1 Mechanical Strength of High-Entropy Alloys
		6.4.2 Effective Atomic Size
		6.4.3 Solid-Solution Strengthening in 3d Transition Metal-Based f.c.c. HEAs
		6.4.4 b.c.c. HEAs
		6.4.5 Electronic Effect on Irradiation Resistance
	6.5 Concluding Remarks
	References
Chapter 7: Efficient First-Principles Methodologies for Calculating Stacking Fault Energy in FCC and BCC High-Entropy Alloys
	7.1 Introduction
		7.1.1 Stacking Faults
			7.1.1.1 Stacking Faults in FCC Lattices
			7.1.1.2 Stacking Faults in BCC Lattices
		7.1.2 Challenges When Using DFT for Stacking Fault Energy Calculations
		7.1.3 Literature Review: Current DFT Methodologies for Handling HEAs
	7.2 Computational Methods
		7.2.1 Calculation of Stacking Fault Energy
		7.2.2 Efficient Methodology #1: Lower-Order Averaging
		7.2.3 Efficient Methodology #2: Inferential Statistics
		7.2.4 Computational Details
	7.3 Stacking Fault Energy in FCC: Simple Lower-Order Averaging
		7.3.1 Calculation Benchmarks
		7.3.2 Stacking Fault Energy Using Simple Lower-Order Averaging in FCC HEAs
			7.3.2.1 CoCrFeNiMn
			7.3.2.2 CoCrFeNiPd
	7.4 Stacking Fault Energy in an AlNbTaTiV BCC HEA: Advanced Lower-Order Averaging
		7.4.1 Calculation Benchmarks
		7.4.2 Stacking Fault Energy of Constituent Ternary Systems
	7.5 Stacking Fault Energy in an AlNbTaTiV BCC HEA: Inferential Statistics
		7.5.1 Inferential Statistics on an NTS Faulted Structure
		7.5.2 Stacking Fault Energy Calculations
		7.5.3 Application of the Inferential Statistics Method to Materials Properties Database Generation
	7.6 Lingering Challenges
		7.6.1 Suggestions for Future Work
	7.7 Conclusions
	References
Chapter 8: High-Entropy Ceramics
	8.1 Introduction
	8.2 High-Entropy Ceramic General Theory
		8.2.1 Entropy-Stabilized Effect of HEC
		8.2.2 Single Phase of HEC
		8.2.3 Element Distribution
		8.2.4 Local Environment of Each Species
		8.2.5 Crystal Distortion
		8.2.6 Element Selection and Descriptors
	8.3 Syntheses of HECs
	8.4 Properties and Applications of Various HECs
		8.4.1 Oxides
			8.4.1.1 Factors for Phase Transition
			8.4.1.2 Charge Compensation Effect
			8.4.1.3 Thermal Properties
			8.4.1.4 Magnetic Properties
			8.4.1.5 Optical Properties
			8.4.1.6 Electrical Properties
			8.4.1.7 Mechanical Properties
			8.4.1.8 Electrochemical Properties
			8.4.1.9 Chemical Properties
		8.4.2 Nitrides
		8.4.3 Carbides
		8.4.4 Silicides
		8.4.5 Diborides
	8.5 Computational Materials Modeling
		8.5.1 Modeling Methods
		8.5.2 Lattice Distortion Analysis
		8.5.3 Thermodynamic Analysis
		8.5.4 Chemical Reaction Analysis
	8.6 Conclusion and Prospects
	References
Chapter 9: Experimental Characterization of High-Entropy Oxides with In Situ High-Temperature X-Ray Diffraction Techniques
	9.1 Introduction
	9.2 Experiment and Theory
		9.2.1 Experimental Details
	9.3 Kinetic Theory
	9.4 Results
		9.4.1 Determining Kinetic Behavior from Time- and Temperature-Dependent Data
		9.4.2 Comparison of Synthesis Methods
		9.4.3 Complementary Thermal Analysis Techniques
	9.5 Discussion
	9.6 Conclusions
	References
Chapter 10: Mechanical Behavior of High-Entropy Alloys: A Review
	10.1 Introduction
	10.2 Major Characteristics of HEAs
		10.2.1 Single Phase
		10.2.2 Super Solid Solutions
	10.3 Elastic Properties of HEAs
	10.4 Hardness and Compression Behavior of HEAs
	10.5 Tensile Behavior of HEAs
	10.6 Strengthening of HEAs
		10.6.1 Strain Hardening
		10.6.2 Grain-Boundary Strengthening
		10.6.3 Solid-Solution Strengthening
		10.6.4 Particle Strengthening
			10.6.4.1 Coarse Two-Phase HEAs
			10.6.4.2 Strengthening by Fine Particles
		10.6.5 Other Strengthening Mechanisms
	10.7 Mechanical Behaviors of HEAs at Low and High Temperatures
	10.8 Fatigue, Creep, and Fracture Properties of HEAs
	10.9 Future Prospects
		10.9.1 Lightweight HEAs
		10.9.2 HEA Films and Coatings
		10.9.3 Additive Manufacturing
		10.9.4 HT Method
		10.9.5 ML Method
	10.10 Summary
	References
Chapter 11: Serrated Flow in Alloy Systems
	11.1 The Portevin-Le Chatelier Effect and Beyond
		11.1.1 Introduction
		11.1.2 Portevin-Le Chatelier Effect
		11.1.3 Macroscopic Scale
			11.1.3.1 Statistics of Stress Serrations
			11.1.3.2 Multifractal Analysis
			11.1.3.3 Phase Space Reconstruction and Other Approaches
			11.1.3.4 A Possible Dynamical Mechanism
		11.1.4 Mesoscopic Scale: Acoustic Emission (AE)
			11.1.4.1 AE Recording and Application of Statistical Analysis
			11.1.4.2 AE Amplitude Statistics
			11.1.4.3 Further Steps to Analyze the Dynamical Mechanism
			11.1.4.4 What Can Be Learnt from Multifractal Analysis of AE?
		11.1.5 Conclusions and Perspectives: Wave-Intermittence Duality
			11.1.5.1 Intermittence of Plastic Flow on Multiple Scales
			11.1.5.2 Wave-Intermittence Duality on Small Scales
	11.2 The Serrated-Flow Behavior in High-Entropy Alloys
		11.2.1 Introduction
		11.2.2 Modeling and Analytical Techniques
			11.2.2.1 Mean-Field Theory and the Mean-Field Interaction Model
			11.2.2.2 Chaos Analysis
			11.2.2.3 Complexity Analysis
			11.2.2.4 Multifractal Modeling and Analysis
		11.2.3 Serration Studies in HEAs
			11.2.3.1 Tension Testing
				Al0.5CoCrFeNi HEA
				Al5Cr12Fe35Mn28Ni20 HEA
				AlxCrMnFeCoNi (x = 0, 0.4, 0.5, and 0.6) HEA
				CoCrFeNi HEA
				CoCrFeMnNi HEA (Cantor Alloy)
				HfNbTaTiZr HEA
			11.2.3.2 Compression Testing
				Ag0.5CoCrCuFeNi HEA
				Al0.1CoCrFeNi HEA
				Al0.3CoCrFeNi HEA
				Al0.5CoCrCuFeNi HEA
				AlxMoNbTiV HEA
				AlxMoNbTaTiV (x = 0, 0.2, 0.4, 0.6, and 1) HEA
				CoCrFeMnNi HEA (Cantor Alloy)
				CoCrFeMnNiVx (x = 0, 0.07, 0.3, 0.7, and 1.1) HEA
				CoCuFeNiTi HEA
				MoNbTaW HEA
			11.2.3.3 Nanoindentation Testing
				Al0.3CrCoFeNi HEA
				Al0.7CrCoFeNi HEA
				Al0.5CoCrCuFeNi HEA
		11.2.4 Summary
		11.2.5 Future Directions
		11.2.6 Conclusions
	References
Chapter 12: Radiation Damage in Concentrated Solid-Solution and High-Entropy Alloys
	12.1 Introduction
	12.2 Defect Properties at the Early Stage of Irradiation
		12.2.1 Chemical Complexity on Energy Dissipation
		12.2.2 Chemical Complexity on Defect Energetics
		12.2.3 Chemical Complexity on Defect Dynamics
	12.3 Defect and Microstructure Evolution upon Radiation
		12.3.1 Damage Accumulation and Defect Evolution Under Low Radiation Doses
		12.3.2 Radiation-Induced Segregation and Precipitation
		12.3.3 Evolution of Cavities and Dislocations at Elevated Temperatures
	12.4 Summary and Outlook
	References
Chapter 13: High-Entropy Coatings
	13.1 Introduction
	13.2 Fabrication Processes
		13.2.1 Magnetron Sputtering Deposition
		13.2.2 Thermal Spray
		13.2.3 Laser Cladding
	13.3 Properties and Applications of HECs
		13.3.1 Mechanical Properties
		13.3.2 Corrosion Properties
		13.3.3 Diffusion Barrier
		13.3.4 Thermal Stability and Oxidation Resistance
		13.3.5 Electrical and Magnetic Properties
	13.4 Conclusions
	References
Chapter 14: Future Research Directions and Applications for High-Entropy Materials
	14.1 Future Research Directions
		14.1.1 Design of New High-Entropy Materials
			14.1.1.1 Traditional High-Entropy Alloy Design Criteria
			14.1.1.2 New Approach to the Design of High-Entropy Materials
		14.1.2 Lightweight High-Entropy Materials
			14.1.2.1 Use Lightweight Elements to Design and Prepare High-Entropy Alloys
			14.1.2.2 Addition of Lightweight Elements to Conventional High-Entropy Alloys
		14.1.3 High-Throughput Preparation of High-Entropy Materials
		14.1.4 Nanostructured High-Entropy Materials
		14.1.5 Three-Dimensional (3D) Printing High-Entropy Materials
		14.1.6 High-Entropy Ceramics
		14.1.7 Further Expansion of High-Entropy Materials
	14.2 Future Applications
		14.2.1 High Strength and Toughness High-Entropy Materials
		14.2.2 High-Entropy Materials for Low-Temperature Applications
		14.2.3 High-Entropy Materials for Elevated-Temperature Applications
		14.2.4 High-Entropy Materials for Nuclear Applications
		14.2.5 High-Entropy Alloys for Mechanical Tool Applications
		14.2.6 High-Entropy Materials for Biomedical Applications
	14.3 Conclusions
	References
Index