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This book provides a systematic and comprehensive description of high-entropy alloys (HEAs). The authors summarize key properties of HEAs from the perspective of both fundamental understanding and applications, which are supported by in-depth analyses. The book also contains computational modeling in tackling HEAs, which help elucidate the formation mechanisms and properties of HEAs from various length and time scales.



Chapter 1. Overview of High-Entropy Alloys

Alloys have evolved from simple to complex compositions depending on the ability of mankind to develop the materials. The resulting improved functions and performances of alloys enable advancements in civilizations. In the last century, significant evolution and progress have led to the invention of special alloys, such as stainless steels, high-speed steels, and superalloys. Although alloys composed of multiple elements have higher mixing entropy than pure metals, the improved properties are mostly due to mixing enthalpy that allows the addition of suitable alloying elements to increase the strength and improve physical and/or chemical properties. Since the turn of the century, more complex compositions with higher mixing entropies have been introduced. Such complex compositions do not necessarily guarantee a complex structure and microstructure, or the accompanied brittleness. Conversely, significantly higher mixing entropy from complex compositions could simplify the structure and microstructure and impart attractive properties to the alloys. Jien-Wei Yeh and Brian Cantor independently announced the feasibility of high-entropy alloys and equi-atomic multicomponent alloys in reports published in 2004. This breakthrough in alloying concepts has accelerated research on these new materials throughout the world over the last decade.
Jien-Wei Yeh

Chapter 2. Phase Formation Rules

This chapter gives an overview of existing active phase formation rules for high-entropy alloys (HEAs). A parametric approach using physiochemical parameters including enthalpy of mixing, entropy of mixing, melting points, atomic size difference, and valence electron concentration is used to delineate phase formation rules for HEAs, with a reference to other multicomponent alloys like bulk metallic glasses (BMGs). Specifically, rules on forming solid solutions, intermetallic compounds, and the amorphous phase are described in detail; formation rules of solid solutions with the face-centered cubic (fcc) or body-centered cubic (bcc) structure are also discussed. Some remaining issues and future prospects on phase formation rules for HEAs are also addressed at the end.
Yong Zhang, Sheng Guo, C. T. Liu, Xiao Yang

Chapter 3. Physical Metallurgy

Physical metallurgy is a branch of materials science, especially focusing on the relationship between composition, processing, crystal structure and microstructure, and physical and mechanical properties. Because all properties are the manifestation of compositions, structure and microstructure, thermodynamics, kinetics, and plastic deformation, factors as encountered in processing control become very important to control phase transformation and microstructure and thus properties of alloys. All the underlying principles have been well built and physical metallurgy approaches mature. However, traditional physical metallurgy is based on the observations on conventional alloys. As composition is the most basic and original factor to determine the bonding, structure, microstructure, and thus properties to a certain extent, physical metallurgy principles might be different and need to be modified for HEAs which have entirely different compositions from conventional alloys. The most distinguished effects in HEAs are high-entropy, severe lattice distortion, sluggish diffusion, and cocktail effects. This chapter will present and discuss the corresponding subjects of physical metallurgy based on these effects.
Jien-Wei Yeh

Chapter 4. Advanced Characterization Techniques

This chapter first provides a brief introduction to some advanced microstructure characterization tools, such as three-dimensional (3D) atom probe tomography, high-resolution transmission electron microscopy, and neutron scattering. Applications of these techniques to characterize high-entropy alloys (HEAs) are illustrated in model alloys. Utilization of these advanced techniques can provide extremely useful structural and chemical information at the nanoscale. For example, the identification of nano-twins in the fracture-toughness crack region of an HEA may explain the anomalous increases in strength and ductility at cryogenic temperatures. Another striking feature of HEAs is the large local strain among neighboring atoms, which, in general, are arranged in a crystal structure with long-range order. Our understanding of these types of features, and their effect on material properties, will increase as the microstructural characterization techniques described here are further developed and applied to HEA research.
Louis J. Santodonato, Peter K. Liaw

Chapter 5. Fabrication Routes

The high-entropy alloys (HEAs) are essentially solid-solution alloys that contain multiprincipal elements in simple crystal structure such as body-centered cubic (BCC), face-centered cubic (FCC), and hexagonal close-packed (HCP) lattices. The typical manufacturing routes for traditional materials can be applied to producing HEAs. Depending on how the constituent elements are mixed, the processes are divided into liquid melting, solid-state mechanical alloying, and gas-state mixing. This chapter reviews those typical manufacturing routes in producing HEAs, including ingot metallurgy, powder metallurgy, coating, rapid solidification, mechanical alloying, single crystals prepared by using the Bridgman method, laser cladding, and thin film sputtering. Comparisons between these methods and the resulting structures are provided.
Yong Zhang, Carl C. Koch, Sheng Guo Ma, Hui Zhang, Ye Pan

Chapter 6. Mechanical Properties of High-Entropy Alloys

This chapter reviews mechanical properties of high-entropy alloys (HEAs) in the fields of hardness, compression, tension, serration behavior, fatigue, and nanoindentation. It shows that the hardness of HEAs varies widely from 140 to 900 HV, highly depending on the alloy systems and related processing methods. The effects of annealing treatment, alloying, and structure on the hardness are discussed. The hardness at high temperatures is also summarized. For compression tests, several parameters of materials, such as Young’s modulus, compressive yield strength, elastic strain, and plastic strain, are determined and discussed. Various loading conditions, such as temperatures, Al contents, strain rates, sample sizes, and aging/annealing effects, are reported to have influence on the microstructural evolution during compression deformation. Microcompression experiments have been performed on HEAs. Even though the study of tensile properties of HEAs is limited to few alloy systems, the effects of structures, grain sizes, alloying elements, and processing parameters on the yielding stress, ductility, and shape of the stress–strain curve, and fracture behavior are discussed. The characteristic elastic behavior is studied by in situ neutron-diffraction techniques during tension. A mean-field theory (MFT) successfully predicts the slip-avalanche and serration statistics observed in recent simulations of plastic deformation of HEAs. Four-point-bending-fatigue tests are conducted on the Al0.5CoCrCuFeNi HEA at various applied loads and reveal that fatigue properties of HEAs could be generally better, compared with conventional alloys and bulk metallic glasses. Nanoindentation studies on the incipient plasticity and creep behavior are discussed. The future work related to mechanical properties of HEAs is suggested at the end.
Haoyan Diao, Xie Xie, Fei Sun, Karin A. Dahmen, Peter K. Liaw

Chapter 7. Functional Properties

This chapter reviews various functional properties of HEAs: electrical properties (including superconducting), magnetic properties, electrochemical properties, and hydrogen storage properties. Interesting phenomena and potentially promising properties better than those of conventional alloys have been observed. These indicate that HEAs provide attractive functional properties to be explored and developed from both academic and application-oriented viewpoints. In this chapter, compositions, process parameters, and microstructure will be correlated with functional properties to give a better understanding.
Jien-Wei Yeh, Swe-Kai Chen, Han C. Shih, Yong Zhang, Ting Ting Zuo

Chapter 8. Prediction of Structure and Phase Transformations

This chapter introduces calculational methods that can be used for ab initio structure prediction in multicomponent alloy systems, with an emphasis on concepts relevant to high-entropy alloys. Specifically, we will address density functional-based calculation of T = 0 K total energies. Extension to finite temperature will use cluster expansions for the energies to obtain the chemical substitution entropy that characterizes the high-entropy alloy family. Additional contributions such as vibrational and electronic entropies will be included as needed. We describe molecular dynamics and Monte Carlo simulation methods and the types of information that can be obtained from them. Example applications include three high-entropy alloy families, Cr-Mo-Nb-V, Nb-Ti-V-Zr, and Mo-Nb-Ta-W, and their binary and ternary subsystems.
Michael Widom

Chapter 9. Applications of Coherent Potential Approximation to HEAs

This chapter details the coherent potential approximation (CPA) to describe the chemically and magnetically disordered phases for systems of arbitrary number of components. Two widely used CPA implementations, namely, the exact muffin-tin orbitals (EMTO) and the Korringa–Kohn–Rostoker (KKR) methods, are briefly reviewed. Applications to predict lattice stability, electronic and magnetic structure, elasticity properties, and stacking fault energies of single-phase HEAs are presented.
Fuyang Tian, Yang Wang, Douglas L. Irving, Levente Vitos

Chapter 10. Applications of Special Quasi-random Structures to High-Entropy Alloys

Special quasi-random structures (SQSs) are an important tool in modeling disordered alloys with atomic resolution. This chapter first presents the framework and the tools available to generate SQS for high-entropy alloys (HEAs). Examples of SQS in 4- and 5-component equiatomic alloys with face-centered cubic (FCC), hexagonal close-packed (HCP), and body-centered cubic (BCC) crystal structures, which are central to HEAs, are provided with different SQS cell sizes. Using SQS, the phase stability of known single-phase HEAs is examined, and the vibrational, electronic, and mechanical properties are predicted. Finally, the chapter compares the strength and limitations of SQS with hybrid Monte Carlo/molecular dynamics (MC/MD) simulations and coherent potential approximation (CPA) as introduced in prior chapters. First-principles calculations on selected single-phase HEAs show that the vibrational entropy of mixing is small, and the electronic entropy of mixing is truly negligible. Excellent agreement in the electronic density of states of HEAs was observed using SQS versus MC/MD. The accuracy of these SQS models is sensitive to the size of the cell, and larger cells produce more reliable results.
Michael C. Gao, Changning Niu, Chao Jiang, Douglas L. Irving

Chapter 11. Design of High-Entropy Alloys

Identifying single-phase high-entropy alloys is extremely important to understanding HEA formation and their intrinsic properties, but lack of effective guidelines has hindered their discovery. As a result, to date the total number of single-phase HEAs is still very limited. This chapter overviews five major methodologies that may assist in HEA design, including CALPHAD modeling, experimental phase diagrams inspection, empirical parameters criteria, density functional theory calculations, and ab initio molecular dynamics simulations. Strength and weakness of these methodologies are discussed. Experimentally reported equimolar single-phase HEAs are reviewed, and a variety of new compositions with the face-centered cubic (FCC), body-centered cubic (BCC), and hexagonal closed-packed (HCP) structures predicted from modeling and phase diagram inspection are provided.
Michael C. Gao

Chapter 12. CALPHAD Modeling of High-Entropy Alloys

Phase diagrams are the key to understanding of high-entropy alloy formation. This chapter first presents the basics of CALPHAD (acronym of Calculation of Phase Diagrams) methodology and then details the procedures used in developing self-consistent thermodynamic databases tailored for HEA systems. A self-consistent thermodynamic database (PanHEA) has been developed for the Al-Co-Cr-Fe-Ni system that covers the complete compositional ranges for all its constituent binaries and ternaries, and it will be useful for future HEA design and processing optimization. HEA formation from the thermodynamic point of view is then illustrated for three HEA systems using TCNI7 database: FCC-forming Co-Cr-Fe-Mn-Ni, FCC- and BCC-forming Al-Co-Cr-Fe-Ni, and BCC-forming Mo-Nb-Ta-Ti-V-W systems. The FCC system shows large positive excess entropy while the BCC system shows small negative excess entropy, and these results are consistent with their vibrational entropies of mixing predicted from first-principle calculations presented in Chap. 10 “Applications of Special Quasi-random Structures to High-Entropy Alloys.” Addition of Al to CoCrFeNi stabilizes the BCC phase via the dominating enthalpy effect. The present study demonstrates that configurational entropy does not always dominate, and enthalpy and competing phases need to be considered in terms of phase stability. Applications of CALPHAD to high-entropy alloy design and microstructure development are then presented for the case of several alloys and satisfactory agreement between modeling calculations and experimental results is observed. Various isotherms and isopleths of the Al-Co-Cr-Fe-Ni system are predicted. Future perspectives on CALPHAD development including short-range ordering and kinetic database development pertaining to HEAs conclude this chapter.
Chuan Zhang, Michael C. Gao

Chapter 13. High-Entropy Metallic Glasses

This chapter applies the concept of high entropy to metallic glasses (MGs), in particular, to those in a bulk shape: bulk metallic glasses (BMGs). The resultant target materials in this chapter are mainly high-entropy bulk metallic glasses (HE-BMGs), which have recently been developed as alloys with characteristics of both high-entropy alloys (HEAs) and BMGs. The contents in this chapter start by introducing historic background of HE-BMGs and by summarizing the differences between HEAs and BMGs. Then, the fundamental properties of representative HE-BMGs found to date are described mainly in terms of thermodynamic and mechanical behaviors. Besides the experiments, the latest computational approach for clarifying the features of HE-BMGs is described based on the results using ab initio molecular dynamics simulations for the atomic structure, chemical interaction, and diffusivity in this unique class of materials. The current status and future prospects of the HE-BMGs by utilizing their unique features are outlined for their future applications.
Akira Takeuchi, Michael C. Gao, Junwei Qiao, Michael Widom

Chapter 14. High-Entropy Coatings

High-entropy alloys (HEAs) can be deposited on substrates as thick or thin alloy films for protection against wear, corrosion, and heat, and for function enhancement and decorative purposes. In addition, various HEA nitride coatings based on HEAs can be easily deposited using reactive coating technology by allowing the atoms or ions from the targets to react with N2-containing Ar flow during deposition. Similarly, HEA carbides, oxides, and carbonitrides could be deposited under CH4-containing, O2-containing, and CH4 + N2-containing Ar flow, respectively. Such HEA ceramic coatings also show the four core effects observed in HEAs: high-entropy, sluggish diffusion, severe lattice distortion, and cocktail effects. The structure is, in general, much simpler than expected. Amorphous, nanocrystalline, and nanocomposite films are often obtained. The properties of HEA coatings or HEA ceramic coatings can be outstanding, and these coatings have great potential for various applications if proper compositions and deposition parameters are used.
Jien-Wei Yeh, Su-Jien Lin, Ming-Hung Tsai, Shou-Yi Chang

Chapter 15. Potential Applications and Prospects

High-entropy alloys (HEAs) inherently have four core effects that enable improvement in microstructure and properties. During the course of research on HEAs, other special materials, such as high-entropy (HE) superalloys, HE refractory alloys, HE bulk metallic glasses, HE carbides, HE nitrides, and HE oxides, have also been developed. All these materials have promising potential applications, e.g., in fabricating machine components, dies and molds, corrosion-resistant parts, cutting tools, functional coatings, hard-facing, thin-film resistors, diffusion barriers, and high-temperature structural components. Greater understanding of the basic science, accumulated knowledge and experience, and effective simulation and modeling will lead to the successful development of numerous HE materials with better properties in the future. This chapter first addresses several important high-entropy materials with promising potential applications and finally forecasts the trends and prospects in their research and development.
Jien-Wei Yeh, An-Chou Yeh, Shou-Yi Chang


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