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An up-to-date guide to understanding, designing, and using high entropy materials
In Functional High Entropy Alloys and Compounds, a team of distinguished researchers delivers a comprehensive exploration of high entropy materials for functional applications. It’s an interdisciplinary discussion highlighting the role of high entropy materials in various industries and examines the real-world applications of high entropy alloys and compounds. The authors illustrate the potential of these materials to transform different industries and cover both bulk HEA materials and HEA nanoparticles.
Functional High Entropy Alloys and Compounds offers a structured and in-depth exploration of high entropy materials. It examines critical fundamentals, including their characteristics, structures, phase transformations, and microstructures, as well as corrosion, anti-oxidation, and additive manufacturing and phase control.
Readers will also find:
- A thorough introduction to the functional properties of high entropy materials
- Comprehensive explorations of the real-world applications of high entropy materials, including 3D printing, thermoelectrics, optoelectronics, thermal catalysts, electro-catalysts, and energy storage
- Practical discussions of nanoscale high entropy materials and high entropy materials for thermal-catalytic applications
- Complete treatments of clean energy and electrocatalysis and high entropy materials for energy storage
Perfect for materials scientists, metallurgists, electrochemists, and catalytic chemists, Functional High Entropy Alloys and Compounds will also benefit aerospace engineers and physicians and thermodynamics physicists.
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Veröffentlichungsjahr: 2025
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Table of Contents
Cover
Table of Contents
Title Page
Copyright
Contributors
Foreword
Preface
Chapter 1: High-Entropy Alloys and Compounds: Fundamentals
1.1 Introduction (Historical Background and Development)
1.2 Definition of HEAs and Compounds
1.3 Characteristics, Structures, Phase Transformations, and Microstructures
1.4 Diverse Applications of Functional HEAs and Compounds
References
Chapter 2: Extreme Conditions and Novel Structure Design
2.1 Introduction to Extreme Conditions and Harsh Requirements
2.2 HEMs for Extreme Temperatures
2.3 HEMs Sustain Under Strong Irradiations
2.4 Fiber and Single-Crystal HEMs
References
Chapter 3: Corrosion and Antioxidation
3.1 Introduction to Corrosion and Antioxidation Scenario
3.2 Anticorrosion Design in High-Entropy Materials
3.3 High-Temperature Oxidation Resistance
References
Chapter 4: Additive Manufacturing and Phase Control
4.1 Introduction to Additive Manufacturing Technologies
4.2 3D Printing of High-Entropy Materials
4.3 Shape Design and Phase Control in High-Entropy Materials by 3D Printing
4.4 Applications of 3D Printed High-Entropy Materials
References
Chapter 5: Functional Properties: Thermal, Electric, Magnetic, and Optics
5.1 Introduction to Functional Properties and Applications
5.2 Thermal and Electronic Properties in HEMs
5.3 Magnetic and Optical Properties in HEMs
5.4 Materials Design for Functional Applications
References
Chapter 6: Nanoscale High-Entropy Materials
6.1 Introduction to Evolution from Bulk to Nanoscale HEMs
6.2 Synthesis and Advanced Characterization
6.3 Diverse Applications of Nanoscale HEMs
6.4 Emerging Nano-HEAs
References
Chapter 7: High-Entropy Materials for Thermal-Catalytic Applications
7.1 Introduction to Thermal Catalysis and Important Concepts
7.2 Catalysts Evolution to HEMs
7.3 Typical Reactions and Their High-Entropy Catalysts
7.4 Understanding of High-Entropy Catalysts
References
Chapter 8: Clean Energy and Electrocatalysis
8.1 Introduction to Electrocatalysis and Its Importance
8.2 Application of High-Entropy Alloys in Key Reactions of Electrocatalysis
8.3 Advanced
Ex/In Situ
Characterization Techniques
8.4 High-Throughput and Data-Driven Techniques in High-Entropy Catalyst Development
References
Chapter 9: High-Entropy Materials for Energy Storage Applications
9.1 Introduction to High-Entropy Materials for Battery Applications
9.2 High-Entropy Anode Materials
9.3 High-Entropy Cathode Materials
9.4 High-Entropy Solid-State Electrolytes
9.5 High-Entropy Liquid Electrolytes
9.6 Perspectives on High-Entropy Battery Materials
References
Chapter 10: Future Trends and Concluding Regards
10.1 Key Challenges Presented in Functional High-Entropy Alloy and Compounds
10.2 Future Development of Functional HEA and Compounds
10.3 Concluding Regards: Materials Evolution from Simple to a Complex Yet Fruitful Future
References
Index
End User License Agreement
Guide
Cover
Table of Contents
Title Page
Copyright
Contributors
Foreword
Preface
Begin Reading
Index
End User License Agreement
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Functional High Entropy Alloys and Compounds
Edited by
Yong Zhang
Fuyao University of Science and Technology & UST Beijing
Yonggang Yao
Huazhong University of Science and Technology
Haojie Liu
Huazhong University of Science and Technology
Editors
Professor Yong Zhang
Uni of Science and Technology Beijing
No.30 Xueyuan Rd
Haidian District
Beijing
CH, 100083
Professor Yonggang Yao
Huazhong Uni of Science and Technology
1037 Luo Yu Road
Wuhan
CH, 430074
Haojie Liu
Huazhong Uni of Science and Technology
1037 Luo Yu Road
Wuhan
CH, 430074
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Contributors
Yong Zhang, Rongzhi Li, Hang Xiang, Yuxin Wen
School of Materials Science and Engineering, Fuyao University of Science and Technology & UST Beijing
Yonggang Yao, Haojie Liu
School of Materials Science and Engineering, Huazhong University of Science and Technology
Di Ouyang
Department of Metallic Engineering, Wuhan University of Technology
Cheng Zhang
School of Materials Science and Engineering, Huazhong University of Science and Technology
Bo Song, Yan Liu
School of Materials Science and Engineering, Huazhong University of Science and Technology
Yuhua Wang, Yifan Wan, Yitong Wang
College of Science, Wuhan University of Science and Technology
Pengfei Xie, Huibin Wang
College of Chemical and Biological Engineering, Zhejiang University
Dongshuang Wu, Bing Zhu
School of Materials Science and Engineering, Nanyang Technological University
Wei Luo, Yuwei Chen
School of Materials Science and Engineering, Tongji University
Foreword
The emergence of high-entropy materials (HEMs) has revolutionized the field of materials science and engineering, offering a bold departure from traditional alloy design paradigms. Unlike conventional materials, which typically revolve around one or two principal elements, HEMs combine multiple principal components in near-equimolar proportions. This unique approach yields materials with exceptional configurational entropy, stabilizing simple solid solutions and delivering extraordinary mechanical, thermal, and chemical properties.
Since their introduction in the early 2000s, HEAs and their derivatives, including high-entropy ceramics and oxides, have captured the attention of researchers worldwide. These materials have demonstrated outstanding performance in extreme environments, such as aerospace, nuclear, and energy applications, where traditional materials often fall short. Their resistance to high temperatures, corrosion, and radiation, coupled with their mechanical robustness, positions HEMs as pivotal for next-generation technologies.
This book represents a comprehensive exploration of HEMs, covering their fundamental principles, advanced characterization methods, and diverse applications. It provides an invaluable resource for both seasoned researchers and newcomers to the field, fostering a deeper understanding of the underlying mechanisms and inspiring innovative applications.
The editors have meticulously compiled insights from leading experts, offering a balanced perspective that bridges theoretical foundations and practical implementation. As you navigate through these chapters, you will discover the transformative potential of HEMs, which not only redefine material performance but also pave the way for sustainable, high-efficiency technologies.
We are witnessing the dawn of a new era in materials science, and this book serves as a beacon, guiding us toward the exciting possibilities that lie ahead. It is my privilege to introduce this seminal work, which I believe will significantly influence the scientific community and industry alike.
Yong Zhang, Yonggang Yao, and Haojie Liu
Preface
The concept of high-entropy materials emerged in the early 2000s as a transformative idea in materials science. Driven by the vision to overcome the limitations of traditional alloys, researchers pioneered the design of materials comprising multiple principal elements in near-equimolar ratios. This approach harnesses configurational entropy to stabilize simple solid solutions, unlocking properties that were previously unattainable in conventional materials.
This book is the culmination of years of research and innovation in the field of high-entropy materials. It aims to provide a comprehensive understanding of these materials, bridging fundamental principles with cutting-edge advancements and practical applications. The structure of the book reflects this holistic approach:
The initial chapters delve into the theoretical underpinnings of HEMs, detailing the core effects of high entropy, severe lattice distortion, sluggish diffusion, and the cocktail effect.
Subsequent sections focus on the synthesis, characterization, and tailored design of HEMs for specific applications, highlighting their performance in extreme environments, nanoscale synthesis, energy storage systems, and catalytic processes.
The book concludes with a forward-looking perspective, addressing the challenges of scalability, cost, and environmental sustainability while envisioning the future of HEMs in emerging technologies.
This work would not have been possible without the contributions of our colleagues, collaborators, and students, whose dedication and expertise have enriched every chapter.
As the field of high-entropy materials continues to evolve, we hope this book serves as both a foundation and a catalyst for further exploration. Whether you are a researcher, engineer, or student, we invite you to join us in uncovering the vast potential of these extraordinary materials.
Yong Zhang
Fuyao University of Science and Technology & UST Beijing
Yonggang Yao & Haojie Liu
Huazhong University of Science and Technology
11 January 2025
Chapter 1High-Entropy Alloys and Compounds: Fundamentals
Haojie Liu, Yonggang Yao*
School of Materials Science and Engineering, State Key Laboratory of Materials Processing and Die & Mould Technology, Huazhong University of Science and Technology, Wuhan, P.R. China
*Corresponding author: [email protected]
1.1 Introduction (Historical Background and Development)
High-entropy alloys (HEAs) were first conceptualized and introduced in the early 2000s (Figure 1.1), pioneered by J.W. Yeh and his colleagues in 2004 [1]. Traditional alloy design typically revolves around a single principal element, supplemented with smaller amounts of secondary elements as dopants to achieve desired property enhancements. However, HEAs challenge this paradigm by combining five or more elements in nearly equal proportions, creating a fundamentally distinct multicomponent system characterized by high configurational entropy and complex microstructures or atomic coordination. The elevated entropy arising from the random distribution of multiple principal elements can stabilize simple solid-solution phases, such as face-centered cubic (FCC) or body-centered cubic (BCC) structures rather than the formation of more complex intermetallic compounds. This stabilization is a direct consequence of entropy-driven thermodynamics, where the high configurational entropy counteracts enthalpic contributions that typically drive phase separation.
Figure 1.1 Rising trend of alloy chemical complexity versus time (IMs: intermetallics, HEA: high-entropy alloy) [2].
Source: [2] / with permission of Springer Nature.
The initial HEAs, often consisting of transition metals like Fe, Ni, Co, Cr, and Mn, exhibited outstanding properties [3–5], including high hardness, excellent wear resistance, and remarkable thermal stability. These properties stem from the synergistic combination of elements, which collectively enhance the material’s performance under extreme conditions. The high configurational entropy in these alloys plays a key role in suppressing the formation of brittle intermetallic phases but instead promoting ductile and tough solid solutions [6].
Building on the foundational work of Yeh and others, the field of HEAs rapidly expanded in scope and application. Researchers began exploring diverse compositional systems, incorporating elements from various groups of the periodic table, including refractory metals (e.g., Mo, W, Ta), lightweight elements (e.g., Al, Mg, Li), and even nonmetallic elements (e.g., Si, B, C) [7]. This diversity allowed for the tailoring of HEA properties to meet the specific demands of various applications. For instance, refractory HEAs demonstrated exceptional high-temperature strength and oxidation resistance, while lightweight HEAs became promising candidates for aerospace applications requiring materials with low density and high strength. HEAs have also shown remarkable potential in harsh environments, such as those encountered in aerospace, nuclear reactors, energy generation, and deep-sea exploration. These environments demand materials that can withstand extreme temperatures, radiation, corrosion, and oxidation. For example, corrosion-resistant HEAs have been developed for marine and chemical processing industries, while high-strength refractory HEAs are being evaluated for use in hypersonic vehicles and fusion reactors [8, 9].
The continued exploration of HEAs is fueled by advancements in computational modeling, materials processing techniques, and experimental characterization. Computational tools such as high-throughput simulations and machine learning algorithms are enabling the design and optimization of novel HEA compositions with tailored properties [10, 11]. These tools allow researchers to predict phase stability, mechanical performance, and environmental resistance with unprecedented accuracy, significantly reducing the time and cost associated with traditional trial-and-error approaches. In parallel, innovations in materials processing techniques, including additive manufacturing (AM), powder metallurgy, and advanced casting methods, are facilitating the scalable production of HEAs with complex geometries and microstructures [12–14]. Moreover, state-of-the-art characterization tools, such as atom probe tomography (APT), transmission electron microscopy (TEM), and synchrotron-based techniques, provide deep insights into the atomic-scale structure and properties of HEAs, driving a better understanding of the underlying mechanisms that govern their exceptional performance [15, 16].
HEAs hold great promise for addressing critical challenges in materials science and engineering. Their unique combination of properties—including high strength, excellent thermal stability, superior corrosion resistance, and exceptional wear resistance—makes them highly attractive for applications in next-generation technologies. Furthermore, HEAs are poised to play a pivotal role in sustainable development by enabling materials with enhanced durability, reduced resource consumption, and improved energy efficiency. As research continues to advance, the integration of interdisciplinary approaches, combining theoretical modeling, experimental validation, and industrial-scale implementation, will be essential to unlocking the full potential of HEAs. The development of HEAs tailored to specific applications will not only expand the boundaries of materials science but also contribute to the creation of environmentally resilient and economically viable technologies. These advancements position HEAs as key enablers of innovation and sustainability across a broad range of industries (Figure 1.2).
Figure 1.2 Schematic diagram of the development of high-entropy nanoparticles with multielemental composition and enhanced functionality [17].
Source: [17] / with permission of American Association for the Advancement of Science.
1.2 Definition of HEAs and Compounds
The concept of high-entropy materials (HEMs), which are composed of at least five elements or components, represents a shift in how materials are designed and understood, leveraging entropy as a key factor in their creation. Typical examples are HEAs and high-entropy compounds (HECs), offering a wide array of unique properties derived from their multicomponent systems. While the effects of entropy have long been recognized in traditional materials and could be explained through thermodynamic principles, the impact of entropy in systems with multiple principal elements was historically overlooked or considered insignificant. This changed with the development of HEAs, which prompted a new focus on multicomponent systems and introduced a paradigm shift in materials science.
Composition Definition. Alloys containing five or more elements with an atomic percentage of each element greater than 5% and less than 35% are defined as HEAs. The idea behind HEAs is to take advantage of multielement mixing and the large configurational entropy (discussed later) that results from the mixing of these elements into a single-phase alloy. HEMs are a broader category of materials that, like HEAs, are composed of multiple elements in near-equal or equimolar proportions to replace the used one/few components position. The term “HEMs” extends beyond just metallic alloys, which also include nonmetallic systems, such as ceramics and polymers, that exhibit the same principle of high entropy. For example, high-entropy ceramics are ceramic materials wherein multiple metal or nonmetal elements are mixed to create a stable phase with desirable properties such as high hardness, thermal stability, and oxidation resistance, as in complex oxide ceramics of (Ti, Zr, Hf, Nb, Ta)O₂. In the later text, we will use HEA as the most important example in HEMs to illustrate those basic concepts.
Entropy Definition. The key defining characteristic of HEAs is their “high-entropy” composition, where the term “entropy” refers to the number of ways atoms can be arranged in a system. By mixing several elements in nearly equal amounts, the number of possible atomic arrangements increases, leading to a higher-entropy state, which can stabilize the solid-solution phase at room temperature, resulting in improved properties. This definition specifies the kinds and ratios of components and introduces the concept of high entropy, which aims to overcome the formation of intermetallic phases through high mixing entropy, thereby obtaining a single-phase solid-solution structure. According to Boltzmann formula, the entropy of a system is related to a given state as the following relationship:
where is the Boltzmann constant and is the probability that a given state exists. The entropy of the system includes four parts: configurational entropy , vibrational entropy , magnetic entropy , and electronic randomness entropy . The total mixing entropy of HEAs is depicted by the equation:
But compared with vibrational entropy, magnetic entropy, and electronic entropy, configurational entropy plays a dominant role, in general. Therefore, to avoid the difficulties caused by the calculation of vibrational entropy, magnetic entropy, and electron entropy, the configuration entropy of the system is generally regarded as the mixing entropy of the ideal solid solution, which can be expressed as:
where is the molar gas constant , is the mole fraction of each constituent element. The mixing entropy of the alloy can be maximized by designing the alloy with equimolar ratios of multiple elements, that is:
Based on , Figure 1.3 clearly shows the relationship between the number of equimolar elements and the mixing entropy of the system. When the number of HEA elements is greater than or equal to 5, the system’s mixing entropy is greater than or equal to . Therefore, entropy can be used as a criterion for distinguishing HEAs/medium-entropy alloys.
Figure 1.3 Basic definition of HEAs, in which , , , and are the Gibbs free energy of mixing, the enthalpy of mixing, the entropy of mixing, and the temperature, respectively. The increase in total entropy as the separate systems of different compositions are mixed without chemical reactions. is the configurational entropy, a portion of a system’s entropy related to discrete representative positions of its constituent particles.
Extended Definition. HEAs, initially defined as alloys with a single-phase solid-solution structure and containing more than five principal elements in near-equiatomic ratios, have been a focus of research for decades. Over time, this strict definition has evolved, breaking traditional constraints and paving the way for the development of more versatile materials. This progression has allowed researchers to shift from rigidly adhering to classic definitions to prioritizing tailored compositions that address specific functional needs. The so-called second generation of HEAs, often characterized by non-equimolar compositions and multiphase structures, exemplifies this shift (Figure 1.4): at least mixing of four elements would be good, and even multiple phases are allowed in the extended definition of HEAs. By carefully adjusting the proportions of components and introducing minor elements, these materials can be optimized to stabilize specific phases or enhance performance through mechanisms such as precipitation or composite strengthening. For example, alloys like Fe50Mn30Cr10Co10 demonstrate transformation-induced plasticity effects, while (FeCoNiCr)94Ti2Al4 leverages precipitation hardening, and eutectic HEAs such as AlCoCrFeNi2.1 combine exceptional phase stability with high mechanical strength.
Figure 1.4 (a) The evolution of traditional alloys and HEAs [18]. (b) Characteristics for the traditional alloys and two generations of HEAs [18].
Source: [18] /with permission of Springer Nature.
This evolution reflects a broader trend in material design, where compositional or phase complexity is used as a tool to unlock novel properties, transcending the boundaries of traditional single-phase alloys. By embracing this expanded perspective, researchers are exploring not only alloys but also other high-entropy systems, creating opportunities for materials tailored to specific high-performance applications, from extreme environments to advanced structural and functional technologies. This holistic approach is driving the next wave of innovations, emphasizing adaptability and multifunctionality over rigid adherence to initial definitions.
1.3 Characteristics, Structures, Phase Transformations, and Microstructures
Expanding beyond alloys, the high-entropy concept has been applied to ceramics, carbides, nitrides, oxides, and intermetallic compounds, creating materials with superior mechanical, thermal, and particularly functional properties. The shared underlying principle of configurational entropy plays a critical role in stabilizing crystalline phases in both metallic alloys and compounds. This section explores the characteristics, crystal structures, phase transformations, and microstructures of these HEMs in detail.
1.3.1 Characteristics of HEAs and Compounds
The four core effects for HEAs are high entropy, severe lattice distortion, sluggish diffusion, and the cocktail effect—each corresponding to four key aspects of material behavior: thermodynamics, structure, kinetics, and performance. The high-entropy effect promotes the formation of stable multielement solid solutions, especially at high temperatures. Severe lattice distortion arises from varying atomic sizes, affecting structural properties and altering thermodynamics and kinetics. Sluggish diffusion slows down atomic movement, delaying phase transformations and enhancing stability. The cocktail effect refers to the synergistic improvement in properties like strength, toughness, and conductivity, surpassing predictions from traditional alloy theory. Together, these effects define the unique behavior and superior performance of HEAs compared to conventional alloys.
High-Entropy Effect. The concept of the high-entropy effect, initially introduced by Yeh, posits that an increase in entropy results in a reduction in the Gibbs free energy of solid-solution phases. High-entropy systems are driven by the concept of maximizing configurational entropy, which arises from the random distribution of multiple principal elements, as discussed in Section 1.2. In contrast to conventional materials where one or two elements dominate, the presence of multiple elements in nearly equal concentrations promotes the formation of simpler phases (e.g., solid solutions in alloys or basic crystal structures in compounds) rather than complex, brittle intermetallic or ordered phases [19, 20]. Rost et al. found an endothermic reaction upon cyclic heat treatment of rock salt (CoCuMgNiZnO high-entropy oxide [HEO]) [21]. They attributed this to the enthalpic penalties of Zn and Cu for the crystallization of a rock salt structure. To lower the barrier of formation of a single solid solution, these two elements were excluded from HEO. However, this was not the case; the exclusion of Zn and/or Cu led to the formation of multiphases. This was a strong indication that the role of mixing entropy was prominent since it decreased when one cation was removed. Besides, the overall degrees of order in HEAs are expected to decrease with the increase in temperature. Therefore, even as-cast alloys containing ordered phases can also be transformed into disordered solid-solution phases at elevated temperatures. However, it is noted that a single solid solution in HEAs is less likely to form as the number of constituent elements increases, which contradicts the high-entropy effect. As they have articulated, the configurational entropy rises slowly with the number of the increasing elements, whereas the probability of the formation of IMs increases more rapidly [22].
While the high-entropy effect is crucial for the formation of HEMs, it is not the sole determinant of phase formation in multicomponent alloys and ceramics. However, it remains a fundamental influence on HEM formation, minimizing the number of phases, as indicated by Gibbs phase rule, which allows for an increase in the number of equilibrium phases with the addition of components [23, 24] (Figure 1.5).
Figure 1.5 High-entropy effect in reducing the number of inorganic crystal structures. Points denote the numbers of inorganic crystal structures with different elements. has a maximum of 19,000 [24].
Source: [24] / with permission of Springer Nature.
Severe Lattice Distortion. Severe lattice distortion in HEAs is primarily caused by the presence of multiple principal elements with differing atomic sizes, bonding characteristics, and random distribution throughout the crystal lattice [25, 26] (Figure 1.6). The significant atomic size mismatch among these elements results in irregular stretching and compression of the lattice, as atoms of different sizes struggle to fit into the same crystallographic positions. This size disparity disrupts the regular arrangement of atoms, causing considerable strain on the lattice structure. Additionally, the bonding differences between the various elements, which have distinct electron configurations and bonding strengths, further contribute to this disruption. These nonuniform bonding forces lead to uneven interactions between atoms, creating additional strain and preventing the formation of a smooth, ordered lattice (Figure 1.6).
Figure 1.6 (a) Schematic representation of atomic size difference-induced distortion: introducing multiple different elements into the same crystal structures leads to severe lattice distortions. (b) Schematic representation of bonding energy difference-induced distortion. The bonding interaction between A and B is stronger than between A and A and between A and C, so the distance between A and B will be smaller than between A and C, which creates the lattice distortion.
Moreover, the random atomic distribution of elements in HEAs, where each element is distributed randomly across lattice sites, increases the disorder [27]. Unlike traditional alloys, where a single principal element typically dominates, HEAs have near-equal concentrations of multiple elements, leading to greater structural complexity. This random placement of atoms of different sizes and bonding energies increases lattice distortion, as the structure cannot easily accommodate the varying atomic characteristics.
This lattice distortion has important effects on the properties of HEAs. The distorted lattice hinders the movement of dislocations, which are defects in the crystal structure that allow materials to deform. By impeding dislocation movement, the distorted lattice increases the strength and hardness of HEAs [28]. Additionally, the severe distortion enhances the alloy’s resistance to deformation, improving its toughness and wear resistance. Overall, the severe lattice distortion in HEAs, caused by atomic size mismatch, bonding differences, and random distribution, is a key factor contributing to their superior mechanical properties [29].
Sluggish Diffusion. The random arrangement of atoms with varying sizes and bonding preferences in HEAs and HECs disrupts atomic mobility, leading to lower diffusion rates, particularly at high temperatures. This phenomenon of sluggish diffusion arises from two key factors [30].
First, each lattice site in HEAs and HECs is occupied by atoms with different neighboring atoms, creating unique local environments. When an atom moves into a vacant site, the surrounding atoms and bonding energies differ from its original location. Due to these varying local configurations and bonding energies, an atom that moves into a site with lower energy becomes “trapped,” making it difficult to transition to a higher-energy site (Figure 1.7). Conversely, if an atom is in a higher-energy site, it has a higher likelihood of returning to its original position. These energy differences slow the rate of diffusion. This sluggish behavior, combined with the high activation energy of diffusion in HEAs, is attributed to the significant variation in lattice potential energy (LPE) across different sites within the crystal lattice. Low LPE sites act as obstacles that impede atomic movement, contributing to what is known as the diffusion retardation effect (Figure 1.7b).
Figure 1.7 (a) Schematic representation of the neighbors an atom interacts with before and after jumping into a vacancy in different matrices. (b) Regular (top) and irregular (bottom) fluctuations of lattice potential energies along the diffusion path for an atom in pure element and HEA lattice. The potential energy of each lattice site in pure elements is nearly identical. By contrast, HEAs are present sites in which the configuration of bonding is preferable for the diffusing species to others; these sites act as traps, and their presence lowers the diffusion rate.
Second, the various components in HEAs diffuse at different rates. Some elements move less actively than others, making it more difficult for those components to fill vacancies compared to faster-moving elements. However, processes such as phase changes require the simultaneous diffusion of all components to achieve the desired composition. For example, forming a new phase or facilitating grain growth demands the collective diffusion of all elements to allow effective migration of grain boundaries. In such cases, the slow diffusion of certain components becomes a limiting factor, slowing down the overall transformation process.
Despite this, the sluggish diffusion phenomenon offers several advantages [31], which include the formation of supersaturated states, increased recrystallization temperature, delayed grain growth, reduced grain coarsening, and the formation of fine precipitates. These benefits enhance microstructure and property control, leading to improved material performance.
The Cocktail Effect. The “cocktail effect” refers to the synergistic interaction between different elements in an alloy, resulting in superior material performance. While this effect is also seen in conventional alloys, it is more significant in HEAs due to the complexity of their compositions. The cocktail effect describes the deviation from the simple rule of mixtures and encompasses all factors and mechanisms that contribute to this deviation. In HEMs, the cocktail effect can lead to unexpected and highly beneficial properties, such as increased strength, wear resistance, and stability at high temperatures.
For instance, a heat-treated HEA coating demonstrates superior hardness and wear resistance compared to various steels and non-heat-treated HEA coatings [32] (Figure 1.8a). This improvement is due to silicon, which promotes the formation of wear-resistant Cr3Si precipitates, hardening the coating. Another example involves increasing the aluminum (Al) content in an HEA, leading to solution hardening because of Al’s larger atomic radius and stronger bonding with other elements [33]. This results in a structural shift from an FCC to a mixed FCC and BCC and ultimately to a purely BCC structure as the Al content rises, enhancing the alloy’s hardness. Additionally, multielement synergy in materials arises from the complex interplay of multiple elements rather than from the individual contributions of each element in isolation. This synergy allows the material to harness the diverse properties of the constituent elements, leading to enhanced overall performance. In the context of material design, electrochemically inert elements—such as Zn and Ti—are often chosen to stabilize the host structure, improving its structural integrity. These elements act as stabilizers, preventing phase degradation under operational stresses. On the other hand, electrochemically active elements like Co, Mn, Ni, Fe, and others serve as redox-active centers, facilitating charge transfer and improving the material’s electrochemical capacity [34–36]. An example of this synergistic approach can be found in the work of Wang et al. [37], who designed a novel O3-type cathode material, NaNi₀.₂Fe₀.₂Mn₀.₃₅Cu₀.₀₅Zn₀.₁Sn₀.₁O₂. In this material, Mn, Zn, and Sn are critical in mitigating interlayer slipping during the charge–discharge process, effectively reducing the structural degradation that can occur due to irreversible phase transitions. Meanwhile, Ni, Fe, and Cu contribute as redox-active elements, providing additional charge compensation during electrochemical reactions. As a result, this high-entropy cathode material exhibits significant improvements, including enhanced cycling stability (87% capacity retention after 500 cycles at 3C) and a superior discharge capacity of 128 mAh g−1 at 0.1C [38].
Figure 1.8 (a) The wear resistance of an as-prepared HEA, tool steel SKD61, bearing steel SUJ2, and a thermal-sprayed HEA coating is compared [32].
Source: [32] /with permission of IOP.
(b) The cocktail effect increases the synergy effects of a vast number of different multielement active sites and expands the capabilities of tuning catalytic properties in HEMs [38].
Source: [38] /with permission of John Wiley & Sons.
Importantly, the synergy effect in these materials is not just the simple summation of the individual properties of the elements involved. Instead, it results from a complex interaction where changes in element concentrations and types can dramatically influence the material’s overall behavior. This highlights the considerable flexibility offered in customizing material performance, as adjusting the composition and proportions of the constituent elements can fine-tune the material’s properties for specific applications, offering new pathways for innovation in electrochemical devices and other technologies (Figure 1.8b).
While some researchers argue that the cocktail effect is redundant, this is a misconception. The overall properties of an alloy are the result of the combined contributions of all related factors. Therefore, understanding the interactions at play when elements are mixed and processed is key to improving or developing new alloy designs. The cocktail effect influences many aspects, including composition, atomic interactions, crystal structure, and microstructure. For materials scientists, it is essential to comprehend the factors that affect a material’s properties to select optimal compositions and processing techniques for creating new materials with enhanced characteristics. By minimizing negative factors and amplifying positive ones, better materials can be engineered.
1.3.2 Crystal Structures of HEAs and Compounds
HEMs exhibit a variety of crystal structures, depending on the type of material and the elements involved. Both HEAs and HECs tend to form simple crystal structures, although HEAs, particularly ceramics, can display more complex behaviors. From the concept of HEMs, although having multiple elements, they should possess the same (at least similar) phase with the parent structure but in a high-entropy configuration. Severe phase separation or a very complex mixture of multiple phases will fail the definition to be HEMs.
HEAs primarily crystallize into simple solid-solution phases (Figure 1.9). FCC structures based on 3d transition metals (Co, Cr, Cu, Fe, Mn, Ni), with possible additions of Al and other elements, are common, which offer good ductility and toughness, especially at low temperatures, and are suitable for applications requiring high toughness and moderate strength [40]. The arrangement of atoms in the FCC structure is highly symmetrical, with atoms positioned at each corner and the center of each face of the unit cell. This configuration allows for numerous slip systems, which enhances the material’s ability to deform plastically, contributing to its toughness. Moreover, the high-entropy effect in FCC HEAs suppresses the formation of brittle intermetallic phases, stabilizing the alloy in a homogeneous solid-solution form, which leads to improved toughness and resistance to cracking.
Figure 1.9 Graphic illustration displaying different lattice structures of HEAs.
In contrast, some HEAs, particularly those incorporating refractory metals such as Nb, Mo, Ta, and W, crystallize into the BCC structure. The BCC structure is typically harder and stronger than FCC but exhibits lower ductility, which makes BCC HEAs suitable for high-temperature applications that require high strength and stability [41]. BCC structures are characterized by a single atom at the center of the unit cell and additional atoms at the cube’s corners. These structures tend to have fewer slip systems compared to FCC, leading to lower ductility but increased strength due to stronger atomic bonds and a more compact atomic arrangement. BCC HEAs can also exhibit enhanced thermal stability, which is vital for their use in environments that involve extreme temperatures, such as aerospace, power plants, and nuclear reactors. Hexagonal close-packed (HCP) structures can form in alloys containing elements such as Ti or Zr. HCP structures are often more brittle, but they can offer advantages in specific mechanical or corrosion-resistant applications [42]. The HCP structure consists of layers of atoms arranged in a repeating ABAB pattern, where each layer is tightly packed. The fewer slip systems in HCP structures make these materials more prone to brittle fracture under stress; however, the ordered atomic arrangement can confer specific properties that are advantageous for applications that demand high wear resistance, such as cutting tools or coatings.
Besides, high-entropy intermetallic compounds are a main part of metallic materials, formed from combinations of elements that favor ordered atomic arrangements, that often crystallize in structures such as B2 (CsCl-type), L12 (Cu3Au-type), or sigma phases. The B2 phase exhibits a simple cubic structure with alternating metal atoms occupying the corners and center of the unit cell. This structure tends to provide good mechanical strength and resistance to thermal degradation, though it is typically more brittle compared to FCC or BCC structures. The B2 structure is often favored in HEAs that involve elements with a large size difference, which helps stabilize the ordered arrangement of atoms. The L12 structure is characterized by an FCC lattice with a more complex atomic arrangement than the simple FCC structure. This phase is often found in HEAs that involve elements such as Ni, Al, or Ti, and it imparts superior strength and creep resistance at elevated temperatures. The L12 phase can enhance the high-temperature stability of alloys, making them suitable for applications in aerospace and high-performance engineering. The sigma phase is an ordered, high-temperature phase that typically forms in HEAs with certain combinations of transition metals. This phase exhibits complex crystal structures that not only often lead to increased brittleness but also provide exceptional resistance to oxidation and thermal damage [43, 44].
HEOs exhibit various crystal structures [45, 46], including rock salt, fluorite, perovskite, spinel, bixbyite, pyrochlore, and layered O3-type (Figure 1.10). Rock salt HEOs [47, 48], identified first, are the most extensively studied due to their facile formation. This structure features a single Wyckoff site for cations, facilitating a homogenous arrangement with superior chemical stability, thus enhancing their electrochemical application potential. Perovskite [49] and spinel-type HEOs are also of significant interest in energy conversion, possessing multiple cation sites that allow for complex atomic arrangements and greater compositional tunability. Other structures such as fluorite, bixbyite, pyrochlore, and O3-layered [50] have been less explored in electrochemistry but exhibit excellent thermal stability. The phase-formation mechanisms for these HEOs vary significantly due to differences in crystal structures, elemental combinations, and compositions. Nevertheless, all demonstrate enhanced high-temperature stability, attributed to the random distribution of metals within the cation sublattice, leading to uniformly dispersed metal oxide solid solutions.
Figure 1.10 Graphic illustration displaying different lattice structures and compositions of HECs [58].
Source: [58] /with permission of The Royal Society of Chemistry.
Bulk high-entropy borides [51], carbides [52], nitrides [53], carbonitrides [54], borocarbides [55], and silicides frequently exhibit enhanced hardness that exceeds predictions based on the rule of mixtures. This phenomenon can be attributed to solid-solution hardening or alterations in the availability of lattice slip systems. Similar to (MgCoNiCuZn)O, both carbides and nitrides generally crystallize in a rock salt structure. In contrast, borides predominantly adopt the AlB2 hexagonal structure, characterized by alternating two-dimensional boride and high-entropy cation layers. Silicides, on the other hand, typically display relatively low-symmetry structures, with (MoNbTaTiW)Si2 [56] adopting the C40 crystal structure and (MoNbTaWZr)Si2 [57] exhibiting a hexagonal configuration.
1.3.3 Phase Transformations in HEAs and Compounds
As mentioned in Section 1.3.2, there are numerous HEA types and crystal structures, and, similarly, these structures are capable of transforming into each other under certain circumstances and external stimuli. Phase transformations in HEMs are complex and highly dependent on composition, temperature, and external conditions. These phase transformations influence the mechanical properties, microstructure, and stability of the material. Particularly, the phase structure transformation of HEA can be modified using two main approaches. The first approach is chemical tuning, which involves five key physical parameters: mixing entropy, mixing enthalpy, electronegativity difference, valence electron concentration (VEC), and atomic size difference. These parameters significantly influence the atomic arrangement and lattice parameters of HEAs [59]. High mixing entropy in HEAs facilitates the formation of a solid-solution phase [60]. The VEC affects the stacking character of the HEAs’ phase structure, determining whether they exhibit FCC or BCC characteristics. The electronegativity difference is associated with phase segregation while mixing enthalpy and atomic size difference are crucial for predicting whether the HEAs will form a solid-solution phase, intermetallic compound phase, or amorphous phase [61, 62]. The second approach is physical field tuning, which also has considerable potential for inducing phase transitions in HEAs. For instance, temperature can cause atomic rearrangement, alter stacking fault energy, and help prevent phase separation. Strain can reduce the magnetic moment, modify dislocation glide, and trigger transitions to metastable phases [63]. Additionally, applying a magnetic field provides energy for atomic movement and alignment while decreasing the Gibbs free energy difference between phases, such as FCC and HCP [64]. In summary, effective property modification of HEAs can be achieved by tailoring their phase structures. This modification not only enhances performance but also offers significant opportunities to attain desired phases with predictable characteristics.
From Solid-Solution to Solid-Solution Phase. The transitions from one solid-solution phase to another demonstrate the complex interplay of many factors in determining the structural phases of HEAs. This ability to switch between various phases under different conditions reveals that solid-solution HEAs can exhibit a much broader range of structural behaviors than might be expected from the simple combination of their constituent elements. Wang et al. studied the Al0.6CoCrFeNi HEA and observed several interesting phase transitions [65] (Figure 1.11). They found that the BCC phase transforms to an orthorhombic phase under pressure, starting at about 10.6 GPa and completing around 21.4 GPa. Upon pressure release, a body-centered tetragonal phase emerges alongside the orthorhombic phase, suggesting that the orthorhombic phase may be metastable at ambient conditions due to a significant energy barrier. Additionally, annealing at 1000 °C for 2 hours converts the initial BCC phase into a stable FCC phase. Under compression, the FCC phase can transform into an HCP phase, similar to Cantor’s alloy. The study highlights that lattice distortion, influenced by pressure or temperature, plays a crucial role in the formation and transition of different phases in the HEA.
Figure 1.11 A schematic illustration of the atomic structure for five polymorphs observed in the Al0.6CoCrFeNi HEA and the transition paths between them [66].
Source: [66] / with permission of Elsevier.
Form Solid-Solution Phase to Intermetallics. The transition from solid-solution alloys to intermetallic phases marks a significant change in atomic structure, profoundly affecting the material’s mechanical and thermal properties. In solid solutions, the atoms of different elements are randomly distributed across the crystal lattice, which provides a good balance of ductility and strength. In contrast, intermetallics are ordered phases where atoms of different elements occupy specific lattice positions, forming compounds with defined stoichiometric ratios and more complex crystal structures, such as B2 (CsCl-type), L12 (Cu3Au-type), or sigma phases. These ordered structures are generally more chemically stable due to their strong atomic bonds but tend to be more brittle than solid solutions. The transformation to intermetallics is often triggered by thermal treatments, such as annealing or long-term aging, where atoms diffuse and segregate into ordered patterns (Figure 1.12a). This transition reduces configurational entropy but increases the overall chemical stability of the material.
Figure 1.12 (a) Illustration of atomic distribution in a conventional B2-type binary intermetallic, a quinary high-entropy B2-type intermetallic and a quinary HEA in solid solution. It is assumed that A and B occupy one sublattice while C, D, and E occupy the other [71].
Source: [71] /with permission of Springer Nature.
(b) Schematic presentation of the alloy design strategy. A, B, C, D … and E, F, G, H … are constituent elements of the crystal and the glass phases, having small mixing enthalpy
