High-entropy materials for thermoelectric applications: towards performance and reliability

Abstract

High-entropy materials (HEMs), including alloys, ceramics and other entropy-stabilized compounds, have attracted considerable attention in different application fields. This is due to their intrinsically unique concept and properties, such as innovative chemical composition, structural characteristics, and correspondingly improved functional properties. By establishing an environment with different chemical compositions, HEMs as novel materials possessing superior attributes present unparalleled prospects when compared with their conventional counterparts. Notably, great attention has been paid to investigating HEMs such as thermoelectrics (TE), especially for application in energy-related fields. In this review, we started with the basic definitions of TE fundamentals, the existing thermoelectric materials (TEMs), and the strategies adopted for their improvement. Moreover, we introduced HEMs, summarized the core effects of high-entropy (HE), and emphasized how HE will open up new avenues for designing high-entropy thermoelectric materials (HETEMs) with promising performance and high reliability. Through selecting and analyzing recent scientific publications, this review outlines recent scientific breakthroughs and the associated challenges in the field of HEMs for TE applications. Finally, we classified the different types of HETEMs based on their structure and properties and discussed recent advances in the literature.

---

Nouredine Oueldna

Dr Nouredine Oueldna is a postdoctoral researcher in the Applied Chemistry & Engineering Research Centre of Excellence at Mohammed VI Polytechnic University, Morocco. He completed his PhD in condensed matter and nanoscience at Aix-Marseille University in collaboration with the University of Moulay Ismail. He was a lecturer/researcher in the Institute of Materials Microelectronics and Nanoscience of Provence at Aix-Marseille University before starting as a postdoctoral fellow in the Ceramic Materials and Technologies department at the Karlsruhe Institute of Technology in Germany within the YIN fellowship. His research explores new functional materials for energy harvesting and storage, with a focus on thermoelectricity and solid-state electrolytes.

Noha Sabi

Prof. Dr Noha Sabi is currently an assistant professor at the High Throughput Multidisciplinary Research Laboratory at Mohammed VI Polytechnic University. She received her master's degree in functional materials from Cadi Ayyad University and PhD in electrochemistry/materials for batteries from Cadi Ayyad University (UCA) Marrakech, Morocco in collaboration with Mohammed VI Polytechnic University (UM6P) Benguerir, Morrocco. She was awarded with the best oral presentation prize from the Fourth edition of the biannual Conference on materials and renewable energies conference (2017). In 2019, she was a visiting scientist at the Pacific Northwest National Laboratory (PNNL), Washington. She was a post-doctoral fellow researcher within the Materials Synthesis Group at the Karlsruhe Institute of Technology (KIT), Karlsruhe, Germany.

Hasna Aziam

Prof. Dr Hasna Aziam is currently an Assistant Professor at the High Throughput Multidisciplinary Research (HTMR) Laboratory at Mohammed VI Polytechnic University of Ben Guerir in Morocco. She is working on developing materials suitable for application as negative/positive electrodes and/or electrolytes for lithium and post lithium-ion batteries. She joined the HTMR-Lab in the beginning of September 2020 as Post-Doctoral Researcher. Her research work focused on the synthesis and characterization of novel electrode materials for lithium and sodium ion batteries. In December 2019, Hasna received her PhD Degree in Electrochemistry – Battery Materials from Cadi Ayyad University in collaboration with Mohammed VI Polytechnic University.

Vera Trabadelo

Prof. Dr Vera Trabadelo received her PhD in Materials Science (Metallurgy) from the University of Navarra (Spain) in 2006 for the development of high-speed steels for tribological applications. She worked as a postdoctoral researcher at Tekniker (Spain) and Empa (Switzerland). She joined Mohammed VI Polytechnic University in September 2017 as a researcher and in January 2019 she was appointed as an Assistant Professor. She is currently the coordinator of the research line in Metallurgy at HTMR. Her research is focused on the design (by Computational Thermodynamics) and development of novel anti-corrosive and anti-abrasive alloys, together with the study of abrasion-corrosion mechanisms in metals.

Hicham Ben Youcef

Prof. Dr Hicham Ben Youcef is currently an associate professor at Mohammed VI Polytechnic University. He holds a PhD in chemistry and materials science from the Swiss Federal Institute of Technology Zurich, Switzerland. His main research interests focus on the development of smart and nano materials for different applications, such as agriculture, membrane technology, sensors, coatings, energy storage, and conversion toward competitive targets (performance, durability, and cost). He is currently leading the High Throughput Multidisciplinary Research Laboratory and is a co-director of Applied Chemistry & Engineering Research Centre of Excellence.

---

Wider impact

This review reports the definition of high-entropy materials and how this concept has evolved over time. High-entropy materials and their potential thermoelectric applications are in their infancy and no similar review has been reported in the literature. In addition to that, different classes of high-entropy thermoelectric materials have been reported. The entropy-driven effect has also been emphasized and addressed. This review is a breakthrough and will attract researchers’ attention to delve into high-entropy materials for thermoelectric applications.

1. Introduction

With the prime focus on renewable, clean, and safe technologies, much research has been devoted to finding new and alternative energy sources.^1–3 Presently, a large amount of heat is irreversibly lost when running industrial, automotive, and other heavy machinery.^4,5 In addressing these concerns, sustainable power generation technologies, such as TE technology, have been rapidly developing. These technologies allow the production of electrical energy from thermal energy by direct conversion.^6–10 Numerous methods have been suggested to enhance the efficiency of TEMs, such as reducing the effective mass of charge carriers and minimizing scattering phenomena, which can improve electrical conductivity by increasing carrier mobility.^11,12 Furthermore, band convergence and the introduction of resonant levels can augment the effective mass of the density of states (DOS), thereby leading to a higher Seebeck coefficient.^13–17 Additionally, the presence of lattice defects and engineered nanostructures disrupt the pathway for heat-carrying phonons, resulting in reduced thermal conductivity.^18–21

The concept of HE initially found application in the realm of metal alloys, resulting in high-entropy alloys (HEAs) characterized by exceptional properties like remarkable mechanical strength and impressive corrosion resistance, often exceeding those of conventional alloys.^22–28 Since then, the concept of HEAs has been extended to ceramics, polymers, and composites, leading to a new term, high-entropy materials (HEMs), which open the doors to a broad range of applications, such as magneto-caloric systems, superconductors, dielectrics, electro-chemical energy storage devices, supercapacitors, and various catalytic systems.^29–40 Thermoelectricity is one of the fields, where an entropy-driven approach has emerged to enhance the electrical and thermal transport characteristics of TEMs.^41–48 This concept involves increasing the variety of element species within a material system, thereby rapidly elevating the total mixing entropy.^22,49 A fundamental feature of HEMs is the presence of a significant lattice distortion that effectively scatters heat-carrying phonons, leading to reduced lattice thermal conductivity.^44,50–52 In parallel, the stabilization of single-phase structures through increased entropy weakens the electron scattering at phase boundaries in multiphase HEMs. This entropy-driven structural stabilization has a favorable effect on enhancing electrical transport properties.^40,44,45 HEMs are characterized by a higher number of major elements, which allows for the entire periodic table to potentially play a role in future TEM design. Fig. 1 shows the growth in the number of journal articles. More precisely, it can be categorized into two intervals. (i) The first research study related to the TE properties of HEAs was reported in 2015.⁵³ From 2015 to 2019, 32 articles were published, with an average of less than 7 articles per year. (ii) Between 2020 and April 2024, 145 papers have been published, with an average of 26 articles per year, indicating a noteworthy growth trend. Notably, 2020 marks a pivotal year for this field, where researchers have applied the entropy-driven concept on the low-entropy conventional TEMs (Fig. 1). In 2023, 47 papers were published, representing 26.55% of the articles published throughout the past decade. As a result, an influx of forthcoming publications that will explore the TE properties, in greater depth, of various HEMs is expected.^41,43

Fig. 1 Increased number of high-entropy thermoelectric materials publications per year (HETEMs) published from 2015 to April 2024 (obtained from Web of Science).

In this review, an overview of thermoelectricity and TEMs is given first. After that, this review focuses on the parameters underlying the TE properties and the existing strategies to optimize the performance of TEMs. In the following sections, the concept of HE is explained in detail, focusing on the definition, fundamental cores, and classes of different HEMs. This review exclusively elucidates the recent advances in entropy-driven concepts to design high-performance TEMs. In addition to that, the correlation between the fundamental cores of HE and TE properties was emphasized. As this field is still in its infancy stage, this review will shed light on findings, allowing scientists to devote more research work to this type of material.

2. Fundamentals of thermoelectricity

In the following section, the fundamentals of thermoelectricity such as the TE effects, parameters defining the TE performance, strategies for optimizing TE performance to prevent the limitations in traditional TEMs, and the impacts of anharmonic bonding and phonon scattering in reducing thermal conductivity (κ) will be reviewed.

2.1 Thermoelectric effect and its principles

The direct conversion of temperature into electricity is governed by three fundamental effects. These effects, known as the Seebeck effect, Peltier, and Thomson effects, play a key role in steering the development of TEMs^54,55 (Fig. 2A). The first observation in this field was the discovery of the Seebeck effect, attributed to the German physicist Thomas Johann Seebeck. It states that when a temperature gradient is applied between junctions formed by two different conductors, it will induce the migration of charge carriers from the hot end to the cold side.⁵⁶ Consequently, a cumulative charge arises at the cold end, generating an induced potential. When integrated into a circuit, this potential drives a current. This phenomenon serves as the basic principle for thermoelectric generators (TEGs),¹⁰ as depicted in Fig. 2A₁. The Seebeck coefficient (α), approximated under open-circuit electrical conditions, is the ratio of the induced voltage (V) to the temperature gradient (ΔT) at the junction, as expressed in eqn (1).⁵⁷The Peltier effect was discovered for the first time by the French physicist Jean-Charles Athanase Peltier. The passage of an electric current through a thermocouple generates a small amount of heating or cooling, following the direction of the current flow. This behavior can be described using eqn (2):⁵⁷where π is the absolute Peltier factor. Q signifies heat energy, t stands for the time of current passage, and I is the electric current. The underlying principle of the Peltier effect revolves around the transformation of energy conveyed by electrons as an electric current traverses between materials. This phenomenon serves as the fundamental principle underlying TE cooling, as shown in Fig. 2A₂.¹⁰

Fig. 2 (A) Schematic diagram of the (a₁) Seebeck effect, (a₂) Peltier effect, and (a₃) Thomson effect. (B) Relationship between thermoelectric parameters. Reprinted with permission.² © 2020 American Chemical Society. (C) Comparison of figure-of-merit ZTs for various bulk TEMs: (c₁) ZT, (c₂) ZT_max and ZT_ave of high-performance TEMs. Reproduced with permission.⁵⁸ © 2020 Royal Society of Chemistry. (D) Schematic representation of all-scale hierarchical structures in Pb_0.935Na_0.025Cd_0.04Se_0.5S_0.25Te_0.25 HEM, and the red line shows the dependence of the phonon mean free path on the accumulated k_L. Reproduced under terms of the CC-BY 4.0 License.⁴⁵ © 2021 The Authors. Published by Springer Nature.

The Thomson effect was discovered by the Irish mathematical physicist and engineer William Thomson. The coexistence of an electric current and a temperature gradient leads to a reversible cooling or heating effect within a homogeneous conductor, as depicted in Fig. 2A₃.¹⁰ This phenomenon can be explained using eqn (3):⁵⁷

τ represents the Thomson factor and x is the spatial coordinate. The interrelationships among these three effects can be expressed as shown in eqn (4) and (5):⁵⁷

π_ab = S_abT (4)

The Thomson effect makes a notably modest contribution to energy conversion within the context of the TE conversion processes in contrast to the other effects. As a result, its influence could only be considered when large temperature gradients are present in the practical TEGs.

2.2 Thermoelectric parameters

In TEMs, the efficiency of a given material to convert heat into electricity is characterized by its dimensionless figure-of-merit called (ZT) defined as in eqn (6):where α signifies the Seebeck coefficient, σ denotes the electrical conductivity, k_e is the electronic thermal conductivity, k_l is the lattice thermal conductivity, and T is the absolute temperature.^59,60 The product (α²σ) is also called the “power factor” (PF).^59,60 In general, an ideal ZT thermoelectric material should exhibit high α, high σ, and low k.⁵⁷ However, since α, σ, and k depend on the carrier concentration (n), these three parameters are intrinsically intercorrelated, and optimizing one will inevitably sacrifice the others,^10,20,61 as shown in Fig. 2B. Even though k_L is somewhat independent of other parameters, the reduction of k_L through solid solution scattering tends to enhance the scattering of both electrons and holes simultaneously. Consequently, the electronic transport properties are reduced. As a result, achieving a simultaneous enhancement in the PF while reducing k remains a challenging task.

There is a wide range of TEMs operating at different temperature ranges as illustrated in Fig. 2C₁, which include Bi₂Te₃,^17,62,63 SnSe,^64–69 GeTe,^70,71 Cu₂Se,^72–75 Half-Heuslers,^76–79 MgAgSb,^80–83 SnTe,^84,85 PbTe,^86,87 clathrates,^88,89 BiCuSeO,^90,91 and skutterudites.^92,93 Based on the temperature range in which they are most effective, each of these TEMs is generally divided into three groups: (i) low to near room temperature (T < 300 K), the TEMs are often employed in cryogenic applications, such as cooling for superconductors, space exploration (Mars Perseverance rover), and medical devices;⁹⁴ (ii) medium temperature (300 K < T < 500 K), where they can be used in various devices such as mobile electronics and Internet of Things (IoT) devices that require energy harvesting or cooling in daily use;^95,96 and (iii) high temperature (500 K < T < 1200 K), this range covers a wide spectrum of industrial and commercial applications, such as automobile exhaust and industrial waste heat.⁹⁷ Significantly, certain TEMs, such as GeTe, PbTe, SnSe, and Cu₂Se, have exhibited remarkable ZT ≥ 2.4 (as depicted in Fig. 2C₂).² The highest value was measured for polycrystalline SnSe with a ZT of roughly 3.1 at 783 K, which is a record-breaking value among all known TEMs.⁶⁴ However, some of these materials (despite their high ZT values) have the drawbacks of being less reproducible, toxic, and composed of less abundant elements.² Considering this, it is crucial to develop alternative high-performance and low-cost TEMs from non-toxic and earth-abundant elements and/or enhance the performances of the existent materials.

2.3 Strategies to improve the thermoelectric performance

Several strategies have been implemented to improve TE performance (ZT), with a particular emphasis on reducing k_L by decoupling the electron and phonon transport.^98–100 This includes hierarchical architectures,^67–69 band structure engineering,^16,101 nano-structuring,^102–105 energy filtering,^106–108 and exploring materials possessing intrinsically low k.¹¹ A recent addition to the array of promising strategies is the high-entropy approach, which has garnered significant attention in solving the interdependence of TE properties.³⁹ The entropy-driven approach can be adopted to modify the electronic/thermal transport properties of a material and to maintain the crystal symmetry to achieve high α.⁴⁸ Furthermore, HEMs typically crystallize in highly symmetric crystal structures such as body-centered cubic and face-centered cubic. Therefore, the design of new TEMs through doping of multiple elements into the unit cell of the existing low-entropy TEMs is a viable and cost-effective approach, which leads to a unit cell with an increased lattice strain. Such a complex crystal structure is useful for reducing k (as shown in Fig. 2D).¹⁰⁹ Thus, HEMs were proposed as they exhibit reduced k_l due to their complex crystal structure. Additionally, the augmentation of mixing entropy aids in enhancing the stability of the structure while significantly optimizing α.³⁹

3. Introduction to HEMs and their potential use in thermoelectric applications

The HE approach was first applied to the high-entropy alloys (HEAs) in 2004 through two separate studies. Yeh et al.²² were the first to propose and introduce the concept of HEAs. Independently and simultaneously Cantor et al.²³ conducted a comparative study involving five-component single-phase alloys. It is worth noting that Cantor's study did not explicitly employ the term HE, referring to these alloys as multicomponent alloys, instead other terms were used such as multi-principal element alloys and compositionally complex alloys.^110–112 Following these contributions, two primary definitions of HEAs have emerged, based on their composition and configurational entropy.^34,113

3.1 Composition-based definition

HEAs are defined by their composition, which requires at least five principal constituents with equal or near-equal atomic content ranging from 5% to 35%. Moreover, the atomic proportion of each secondary element must remain below the threshold of 5%. This description can be expressed as shown in eqn (7):In these expressions, n_major and n_minor represent the quantities of the major and minor elements, respectively. Moreover, c_i and c_j denote the corresponding atomic percentages.

3.2 Entropy-based definition

From the entropy-based definition, the HEAs are defined by their configurational entropy that should be greater than 1.61R in a random state (R denotes the molar gas constant, 8.31 J mol⁻¹ K⁻¹). Since the total mixing entropy is dominated by configurational entropy (eqn (8)):Hence, alloys can be divided into three categories as shown in Fig. 3A. (i) Low-entropy alloys (LEAs): ΔS_conf < 0.69R, this includes conventional alloys based on two elements; (ii) medium-entropy alloys (MEAs): 0.69R ≤ ΔS_conf ≤ 1.61R, including alloys based on two to four constituent elements, and (iii) high-entropy alloys (HEAs): ΔS_conf exceeds 1.6R, including alloys composed of at least five elements to 13 elements or certain equimolar quaternary alloys.^114,115

Fig. 3 (A) Influence of the element number on the system's mixing entropy. (B) (b₁) Effect of increasing the entropy on the diagram of lattice distortion and (b₂) effect of entropy on ρ and k_L. Reproduced under terms of the CC-BY License.⁴¹ © 2023 The Authors. Published by Lab Academic Press. (C) Summarized thermal conductivity of some typical high-entropy ceramics. Reproduced with permission.²⁹ © 2023 John Wiley and Sons. (D) The crystal structures of (d₁) high-entropy alloys and (d₂) high-entropy ceramics. Reproduced under terms of the CC-BY-NC 3.0 License.³⁴ © 2021 The Authors. Published by The Royal Society of Chemistry. (E) Evolution of compositionally complex materials.

In contrast to conventional alloys, the complexity of HEAs arises from the equimolar concentration of each constituent. In addition, Yeh et al.¹¹⁵ proposed the four fundamental factors that influence the structural–properties of HEAs. These core factors give HEAs versatile properties, making them suitable for various applications such as thermoelectricity. In terms of:

(i) Thermodynamics: HE effects, which enhance the stability of solid solutions with high lattice symmetry and an extended solubility/phase range, result in band convergence, a larger effective band, and expansion of the range for doping to adjust the transport properties.

(ii) Kinetics: sluggish diffusion that leads to the development of a rich hierarchical/multi-scale low-dimensional microstructure, which promotes phonon scattering at all scales. This strategy, aimed at increasing the entropy change (ΔS), exerts a strong influence on reducing lattice k and pushes it towards the limit seen in amorphous materials, resulting in a promising tactic for enhancing energy conversion efficiency.

(iii) Structure: severe lattice distortion that leads to reduced k within the lattice and a degradation in carrier mobility, which is a critical microscopic transport parameter that significantly influences the ZT.

(iv) Properties: cocktail effects that have a synergistic impact on the whole properties from the overall contribution of the constituent elements.

As a result, these core effects have a favorable impact on TE performance, which encompasses the primary requirements for enhancing TE performance and encourages the implementation of the entropy-driven concept to usher in a new paradigm of high-entropy thermoelectric materials (HETEMs).^48,116 For example, each metal in HEAs has an equal chance of occupying a position in the crystal lattice, and because of the size differences, significant lattice distortions could occur in the absence of chemical ordering, as illustrated in Fig. 3B₁. As a result, lattice distortions can impact the electrical, mechanical, optical, thermal, and chemical properties of materials.^117,118 This lattice disorder observed in HEAs leads to strong phonon scattering and anharmonic bonding, and consequently to a significant reduction in lattice k by an order of magnitude, as discussed in Section 2.3.^48,98 Nevertheless, it can also reduce the mean free path of electrons, thereby leading to a substantial reduction in σ (Fig. 3B₂).⁴¹ The reduced carrier mobility of HEMs due to the complex crystal structures and the random distribution of different atoms on the same lattice site is one downside of these core effects, resulting in a limitation of their applicability in TEGs. This reduced carrier mobility can be compensated by several mitigating strategies such as (i) controlled doping of HEMs, which can enhance the carrier concentration.¹¹⁹ (ii) Band structure engineering which may involve adjusting the relative concentrations of the different cationic species to optimize the band alignment and minimize carrier scattering, thus enhancing carrier mobility. (iii) Interface engineering to reduce scattering and improve charge carrier mobility can be an effective strategy by optimizing interfaces between different phases or domains within HEMs. (iv) Crystal structure/defect engineering by introducing specific crystallographic orientations (atomic arrangement) or optimization of structural defects can improve carrier transport properties by reducing the scattering of charge carriers and enhancing their mobility while promoting beneficial defect configurations.¹²⁰ (v) Reducing the dimensionality of HEMs, such as elaborating thin films or nanostructures, can minimize scattering sources and enhance carrier transport along specific directions.¹²¹ Thus, it should be an optimal level of configurational entropy in TEMs that reaches a point where it can trigger one or more of the entropy-driven core effects observed in HEAs, while still maintaining a sufficiently high carrier mobility¹⁰⁰ as shown in Fig. 3B₂. As illustrated in Fig. 3C, in some HEMs a consistent trend of reduced k has been reported.¹²² This unique characteristic of phonon glass-like makes HEMs potential candidates for TE energy harvesting applications.^44,123,124 Furthermore, HEMs exhibit various highly symmetrical crystal structures, such as simple face-centered cubic (FCC), body-centered cubic (BCC), hexagonal close-packed (HCP), and rock-salt arrangements (as shown in Fig. 3D). This symmetry contributes to a remarkable convergence of the valence bands near the Fermi level, which gives rise to a high α.¹⁶ Consequently, HEMs hold considerable attention as promising TEMs for high temperature-applications.^43,125,126 However, the electron-crystal in HEMs still presents a great challenge in fully satisfying the phonon-glass-electron-crystal (PGEC) criteria for ideal TEMs.¹²⁷ The dominant factor determining whether a HEA adopts a BCC, FCC, or HCP crystal structure appears to be its valence electron concentration (VEC) value, as it was suggested by the well-established Hume–Rothery rule. This VEC value is determined by calculating the weighted average of the VEC values of the alloy elements (eqn (9)). Clearly, the FCC structure tends to predominate at a VEC of approximately 8.5, the BCC structure is favored at a VEC of around 5, and the HCP structure emerges around a VEC of 2.8.^35,128

The TE properties could be significantly tuned by changing the VEC of the system with appropriate replacement elements. As the VEC decreases, both electrical and thermal transport properties of the system decrease simultaneously. In general, the high structural complexity and low average VEC can be employed in reducing the total k.¹²⁹

3.3 Classes of high-entropy materials

Motivated by the HEA concept, Rost et al.⁴⁰ were the first to demonstrate the entropy-driven stabilization of five metal oxides in equiatomic fractions to form a single-phase oxide system. Subsequently, the term high-entropy oxides (HEOs) emerged to describe oxides located within the central regions of multi-nary oxide phase diagrams.^40,130–132 Since 2015, the concept of entropy-stabilized solid solutions has been extended beyond metallic, oxide and non-oxide ceramic materials to the development of a new category called high-entropy ceramics (HECs)^24,36,122 such as carbides,¹³³ nitrides,¹³⁴ diborides,¹³⁵ silicides,¹³⁶ sulfides,¹³⁷ bulk metallic glasses^138,139 as well as phosphides¹⁴⁰ and fluorides,¹⁴¹ as depicted in Fig. 3E. In addition, zeolites and metal–organic frameworks (MOFs) that incorporate five near-equimolar active metallic elements designed by an entropy-driven concept belong to the class of organic–inorganic HEMs.^142–145 HE nitrides, introduced in 2004, were the first type of HECs. However, HEOs and HE carbides are the ones that have been investigated the most. Similarly to HEAs, the four fundamental effects applicable to HECs demonstrate enhanced properties in comparison to traditional ceramic solid solutions.²⁴ In contrast to the simple FCC, BCC, and HCP crystal structures of HEAs,³⁴ the structure of HEOs is more complex (Fig. 3D). The heterogeneity of the crystal structure and chemical bonding (metallic, ionic, and covalent) in HEOs could have a significant influence on their properties, offering new avenues for tuning and tailoring their functionalities for various technological applications through band structure engineering and phonon engineering, thus overcoming the bottleneck for materials applications. The presence of multiple cationic species with different sizes and electronegativities in the crystal lattice might result in enhanced structural, thermal, and chemical stability, which arises from the increased configurational entropy, leading to a reduction of phase separation or decomposition, making them suitable for high-temperature application and corrosive environments. Moreover, the heterogeneity of crystal structures could give rise to a simultaneous coexistence of properties. For example, certain compositions of HEOs may exhibit both ferroelectric and magnetic properties,^146,147 enabling applications in multifunctional devices. Also, it can create pathways for ion transport, making them promising materials for applications in solid oxide fuel cells, electrolytes in batteries, and other electrochemical devices. In conclusion, the heterogeneity of the crystal structure of HEOs results in a more abundant combination of compositions, configurations, and properties in HECs than HEAs, offering opportunities to tailor the phase stability for specific applications, such as electrocatalysis, dielectrics, magnetoelectrics, semiconductors, energy storage, and thermoelectrics.¹⁴⁸ However, the structure of HECs is more complex than that of HEAs (Fig. 3D), encompassing all types of Bravais lattices apart from the triclinic system. The atomic bonding in HECs also differs significantly from HEAs, as it includes all bond types: metallic, ionic, and covalent. This results in a more abundant combination of compositions and properties in HECs than HEAs, making them potential candidates for TE applications. In summary, the concept of entropy-driven, specifically focusing on maximizing entropy through the notion of entropy stabilization, offers a novel way to develop advanced materials.^149–151

4. Overview of high-entropy thermoelectric materials

Recently, there has been growing interest in the field of thermoelectricity regarding the entropy-driven concept as a promising and cost-effective strategy, which involves the doping of conventional low-entropy TEMs.^{24,36,39,42,48,152–155} The increase of mixing entropy reinforces the stability of a simple solid solution structure and greatly enhances α.^39,48 This section will highlight the effectiveness of the entropy-driven approach in enhancing TE performance. It will also illuminate the potential role of HEMs in shaping the future of TEMs.

4.1 High-entropy alloys

The first study to investigate the TE properties of HEAs was carried out by Shafeie et al.⁵³ to explore further effective TEMs for high temperature applications. Their findings illustrate that an increased incorporation of aluminum in Al_xCoCrFeNi (x = 0 to x = 3) results in an elevation of S, rising from 1 to 23 mV K⁻¹ Additionally, the low k value (12.5–13 W m⁻¹ K⁻¹ for x = 2.25) further helped in improving TE properties, leading to a ZT exceeding 0.0125 at 778 K for the Al₂CoCrFeNi composition.⁵³ The low k could be attributed to the precipitation of secondary phases (NiAl-B₂ and Cr-rich phases) resulting from the addition of Al, as suggested by Anber et al.¹⁵⁶ where they found that the addition of Al (0.1–0.5 mol fraction) destabilizes the single-phase microstructure and results in the formation of secondary phases and complex coprecipitates. Hasan et al.¹⁵⁷ proved the impact of the Al-content on the TE properties of Al_xCoCrFeNi HEA using first-principles calculations combined with molecular dynamics and semi-classical Boltzmann transport theory. They found that the calculated phonon density of states and TE properties are in reasonable agreement with the experimental results. Even at low Al-concentrations, a significant reduction in phonon conductivity was observed, which they attributed to effective phonon scattering resulting from the significant atomic mass mismatch (m_Al = 26.98 g mole⁻¹ and m_avg,others = 56.37 g mole⁻¹). Furthermore, the shift from the FCC to BCC structure at higher values of x_Al as observed by Shi et al.¹⁵⁸ results in decreased phonon density of states at low energy. This decrease in phonon density of states has the potential to lower heat capacity and may contribute to a further reduction in lattice k.¹⁵⁷ As a result, the ZT values were improved by increasing Al-concentrations. Moreover, optimizing the annealing temperature can lead to additional enhancements in the TE performance. Han et al.¹⁵⁹ investigated the effect of the Nb-content on CoCrFeNiNb_x. As the Nb content increases (0 < x < 0.45), σ decreases. This can be explained by the influence of Nb alloying on the microstructures where CoCrFeNb_xNi (x > 0) HEA exhibits a composition-dependent shift from the FCC solid solution phase to a combination of FCC solid solution and the Laves phase. Specifically, the alloy microstructures transform from an initial single-phase FCC solid solution (x = 0) to a hypoeutectic structure (x = 0.25), and finally to a complete eutectic microstructure (x = 0.45).¹⁶⁰ The increase in the volume fraction of the eutectic structure and phase interfaces impedes the mobility of electrons through scattering at the surface and grain boundaries. As a result, the effective electric charge density decreases, leading to a reduction in σ.¹⁵⁹ CoCrFeNiNb_0.45 with a fully eutectic structure exhibits the lowest k at high temperature (T > 573 K) (Fig. 4A₁), which can be explained by the efficacy of interfaces and boundaries of the in situ formed eutectic structure in scattering phonons. As a result, CoCrFeNiNb_0.45 exhibits the highest ZT at high temperatures (T > 573 K), as shown in Fig. 4A₂. Dong et al.¹⁶¹ investigated the rare-earth metal doped Y_xCoCrFeNi, Gd_xCoCrFeNiCu, and Al_0.3CoCrFeNi HEAs. Controlling phonon scattering through the precipitation of a secondary phase resulted in a reduction of k_L (Fig. 4B₁). However, Fig. 4B₂ illustrates that there was no notable enhancement in the ZT of HEA. Kush et al.¹²⁹ have studied the TE properties of Ni₂CuCrFeAl_x with different Al contents. Their study revealed a dependency of the TE performance on both the Al content and the VEC. The achieved PF was found to be 7.274 μW m⁻¹ K⁻² and ZT reaches a maximum of 0.2731 both at 850 K for Ni₂CuCrFeAl_2.5 with the VEC = 7, as presented in Fig. 4C. Recently, Cheng et al.¹⁶² used first-principles calculations to study the CrFeCoNiCu_x HEA at finite temperatures. Notably, these HEAs show a remarkably low lattice k (9.8 W m⁻¹ K⁻¹ at 100 K). The contribution of long-wavelength phonons to the lattice k exceeds that of short-wavelength phonons by more than ten times, establishing them as the primary contributors to phonon-mediated heat transport in CrFeCoNiCu HEAs. Bag et al.¹⁶³ have investigated the physical properties of NiCoFeMnCr and NiCoFeCrPd HEAs and found that the lattice k reduced due to the Cr/Mn/Pd-alloying by different phonon scattering mechanisms. At 300 K, the k_L values were found to be around ∼7.8 and 5.6 W m⁻¹ K⁻¹ for NiCoFeMnCr and NiCoFeCrPd, respectively.

Fig. 4 (A) (a₁) Thermal conductivity and (a₂) ZT of the CoCrFeNiNb_x (x = 0, 0.25, and 0.45) alloys. Reproduced under terms of the CC-BY License.¹⁵⁹ © 2020 The Authors. Published by MDPI. (B) (b₁) thermal conductivity and (b₂) ZT of the Gd_xCoCrFeNiCu alloys. Reproduced under terms of the CC-BY License.¹⁶¹ © 2018 The Authors. Published by MDPI. (C) Temperature dependence of (c₁) PF and (c₂) ZT of the Ni₂CuCrFeAl alloy. Reproduced under terms of the CC-BY License. 4.0¹²⁹ © 2020 The Authors. Published by IOP Publishing Ltd.

In conclusion, HEAs discussed here still offer considerable potential for further improvement. However, it is crucial to focus efforts on maximizing and optimizing the α (at least 100–200 μV K⁻¹) and σ in HEAs to make them suitable for high-temperature TE applications, which are challenging. Techniques such as nano-structuring and band engineering could result in superior performance, particularly in terms of electrical contact, making them more suitable for the design of TEGs. The TE properties of HEAs are summarized in Table 1.

Table 1 TE properties of HEA-based materials reported in the literature

Compound	T (K)	k (W m^−1 K^−1)	ZT	Ref.	Year
Al2CoCrFeNi	778	12.5	0.0125	Shafeie et al.^53	2015
CoCrFeNiNb0.45	573	58	7.50 × 10^−6	Han et al.^159	2020
Al0.3CoCrFeNi	750	15	0.00175	Dong et al.^161	2018
Gd0.3CoCrFeNi	850	16	0.006
Y0.05CoCrFeNi	800	15	0.095 × 10^−3
Ni2CuCrFeAl2.5	850	7.5	0.2731	Kush et al.^129	2020

---

4.1.1 High-entropy half-Heusler alloys. Half-Heusler (HH) compounds are intermetallic alloys with a chemical composition of XYZ, where X and Y are transition metals and Z indicates a heavy main group metal, typically Sn or Sb, and occasionally Ge, Pb, or Bi. The FCC crystal structure characterizes the structure of these compounds.¹⁶⁴ These alloys exhibit interesting physical properties that have attracted significant attention because they are thermally stable and non-toxic. At a VEC of 18, they exhibit semiconductor characteristics with a narrow band gap (0–1.1 eV), making them a promising candidate for TE applications.¹⁶⁴ Nevertheless, the high k_l of these materials acts as a limitation in achieving a high ZT for TE applications. The entropy-driven approach presents itself as a promising approach to decrease k_l in HH alloys, leading to the formation of a new family of HH-HEAs.

Karati et al. were the first to synthesize a novel single-phase HEA known as Ti₂NiCoSnSb¹⁵⁴ using a two-step process involving vacuum arc melting (VAM) followed by ball-milling (BM). The introduction of the BM proved to be essential to achieve this single-phase. This has been proved through a combination of scanning electron microscopy and 3D atom probe tomography (APT) observations (Fig. 5A₁). In this study, two different HH-type HEAs were elaborated, micro- and nanocrystalline microstructures, using BM for 1 and 5 hours, respectively.

Fig. 5 (A) (a₁) Analyzed 3D APT volume on the nanocrystalline (5h BM) HEA and the concentration profiles showing uniform composition across the cylinder, (a₂) temperature-dependent ZT of Ti₂NiCoSnSb alloy. Reproduced under terms of the CC-BY 4.0 License.¹⁵⁴ © 2022 Springer Nature. (B) (b₁) XRD pattern and (b₂) temperature dependent ZT of MFe_1−xCo_xSb (M = equimolar Ti, Zr, Hf, V, Nb, and Ta) after SPS. Reproduced with permission.¹⁶⁹ © 2021 Elsevier B.V. (C) Temperature dependence of (c₁) PF and (c₂) ZT for Ti(Fe_1/3+xCo_1/3Ni_1/3−x)Sb with (x = 0, ±0.05, ±0.10, ±0.15, and ±0.20) HEMs, compared with TiCoSb and TiFe_0.5Ni_0.5Sb. Reproduced with permission.¹⁷⁰ © 2022 Elsevier Ltd.

An increase in both α and σ in this nanocrystalline HEA (5h BM) contradicts the typical observation for semiconductors (Fig. 2). This phenomenon can be attributed to the increase in the number of interfaces in the sample due to the presence of HH, Ni₃Sn₄, and Ti/O/C rich phases, as shown in Fig. 5A₁. As a result, interfacial scattering may occur. Moreover, the Ni₃Sn₄ phase has been reported as a metallic phase that results in a considerable enhancement of σ in this nanocrystalline HEA. The maximum ZT of 0.047 at 860 K was observed for nanocrystalline HEA, while the microcrystalline HEA (1H BM) exhibited a ZT of 0.144 at 860 K (as illustrated in Fig. 5A₂).¹⁵⁴ This can be attributed to the smaller volume fraction of TiC in the microcrystalline HEA. Motivated by the previous research on the Ti₂NiCoSnSb HEM, which has a VEC of 18, the same group extended this concept by replacing Sn with Sb atoms in Ti₂NiCoSn_1−xSb_1+x (where x = 0.5, 1). This substitution aimed to elevate the VEC from 18 to 18.5.¹⁶⁵ The synthesis of Ti₂NiCoSn_1−xSb_1+x involved a process combining vacuum arc melting, ball milling, and spark plasma sintering (SPS). Notably, Ti₂NiCoSn_0.5Sb_1.5 demonstrated a reduced lattice k of 2.48 W m⁻¹ K⁻¹ and an enhanced ZT of 0.29 at 873 K.¹⁶⁵ Furthermore, they have reported the effect of nano-structuring, along with lattice distortion due to HE engineering and interfacial/boundary scattering for the first time in HH Ti₂NiCoSn_1−xSb_1+x HEAs, and they found that Ti₂NiCoSb₂ exhibits a ZT of 0.26 at 873 K.¹²⁵ Recently, they have reported the synthesis of Ti₂NiCoSnSb using both wet and dry mechanical alloying (MA) combined with SPS and found a ZT of 0.13 at 973 K.¹⁶⁶

These investigations are paving the way for the exploration of HEMs with a VEC above 18 for TE applications.^125,165 Mishra et al. synthesized a HH-HEM, denoted as Ti_2−xNiCoSnSb (x = 0.125, 0.25, 0.375, and 0.5), using the arc melting, ball milling, and SPS techniques.¹⁶⁷ They found that reducing the Ti content led to an increase in the formation of Ni-rich intermetallic compounds (Ni₃Sn₂ and Ni₃Sn₄) and Ni-rich full-Husler (TiNiSn) as secondary phases in the HEM. σ increased, while the lattice k decreased due to the higher concentrations of secondary phases. For instance, TiNiCoSnSb exhibited a reduced lattice k of 3.5 W m⁻¹ K⁻¹ in comparison to 5.4 W m⁻¹ K⁻¹ at 823 K for Ti₂NiCoSnSb, attributed to increased scattering of phonons at HH/Ni₃Sn interfaces. However, despite this reduction in lattice k, the PF decreased as the Ti content decreased. Consequently, the highest ZT value which reached 0.171 at 973 K for Ti_1.875NiCoSnSb was slightly higher compared to that of Ti₂NiCoSnSb. Thus, it was concluded that further adjustments in the composition are important to optimize the PF. Recently, the same group reported the doping of this system with three different elements Al, Ta, and Zr, with an optimum dopant level of 10%, 7.5%, and 25%, respectively.¹⁶⁸ They obtained a low k_l of 1.9 W m⁻¹ K⁻¹ for the Zr-doped HEA and a maximum ZT of 0.29 at 823 K for the three Ti_1.8Al_0.2NiCoSn_0.5Sb_1.5, Ti_1.5Ta_0.5NiCoSn_0.5Sb_1.5, and Ti_1.85Zr_0.15NiCoSn_0.5Sb_1.5 HEAs. Yan et al. elaborated HEA based on Nb_1−xM_xFeSb (M = Hf, Zr, Mo, V, Ti) using the arc melting technique, followed by SPS.¹²⁶ The entropy-driven concept led to a notable reduction in the lattice k of 2.5 W m⁻¹ K⁻¹, alongside a remarkable ZT reaching 0.88 at 873 K for Nb_0.98M_0.02FeSb HEA; an increase by 1367% was observed in comparison to the pristine alloy. Chen et al. successfully synthesized a single phase of HE HH compound MFe_1−xCo_xSb containing six equimolar elements (Ti, Zr, Hf, V, Nb, and Ta) occupying the M site using the MA method, followed by densification via SPS to obtain the single phase.¹⁶⁹ The pure HH phase preserved a VEC between 17.9 and 18.5, as shown in Fig. 5B₁. Notably, this material could behave as both n-type and p-type materials depending on the VEC. The incorporation of multiple elements has resulted in a low lattice k of 0.8–1.5 W m⁻¹ K⁻¹ (300–923 K) for MCoSb, which can likely be attributed to the contrast in mass and the introduction of point defects by these multiple elements. The ZT reached its maximum values of 0.25 for p-type MFe_0.6Co_0.4Sb and 0.3 for n-type MCoSb, both at 923 K (Fig. 5B₂), indicating excellent TE performance.¹⁶⁹ Additionally, the HE-HH samples exhibited thermal stability up to 1073 K. This stability can be assigned to the high degree of configurational entropy present in the samples. Moreover, Luo et al. designed a Ti(Fe/Co/Ni)Sb HH alloy, capable of exhibiting both p-type and n-type conductivity, derived from TiCoSb.¹⁷⁰ They found that the introduction of Fe/Co/Ni elements into the 4c site of the TiCoSb HH lattice induced a significant lattice distortion, resulting in a notable reduction in lattice k in the Ti(Fe_1/3+xCo_1/3Ni_1/3−x)Sb HEM. Also, modulating the sample composition (Fe/Ni ratio) led to a simultaneous alteration of carrier concentration, carrier type, and electronic band structure, thereby, the PF was enhanced for both p- and n-type materials, showing values of 17.3 and 19.8 μW cm⁻¹ K⁻² at 1023 K (Fig. 5C₁), respectively. They achieved a peak ZT of approximately 0.56 for p-type (x = 0.15) and 0.49 for n-type (x = −0.15) materials, both at 1023 K, as illustrated in Fig. 5C₂.¹⁷⁰

Chen et al. introduced an innovative approach to decouple α and σ through the entropy-driven concepts.¹⁷¹ This method relies on band engineering and takes advantage of the energy-filtering effect, by which the entropy-induced quantum confinement effect is harnessed to selectively filter low-energy electrons (Fig. 6A₁). Simultaneously, the increase in entropy facilitates a rapid alteration in the DOS near the Fermi level (Fig. 6A₁). As a result, they achieved an exceptional α of approximately −200 μV K⁻¹ at 923 K for the M_0.85Nb_0.15CoSb (M = Ti, Zr, and Hf) HEA (Fig. 6A₂) and a low k of 0.018 W m⁻¹ K⁻¹at 923 K. Moreover, due to the optimized S and reduction in k, the highest ZT was found to be 0.58 at 923 K for the M_0.85Nb_0.15CoSb HH-HEA, as shown in Fig. 6A₃.¹⁷¹ Rabin et al. synthesized MNiSn (M = Ti, Zr, and Hf), a HE-HH alloy, with Al and Sc added to the M sub-lattice.¹⁷² The obtained ZT of (Ti_0.33Zr_0.33Hf_0.33Al_0.005Sc_0.005)NiSn was found to be around ∼0.77 at 750 K; when compared to (Ti_0.3Zr_0.35Hf_0.35)NiSn without Al and Sc, it shows an improvement of about 40% higher. In another study, Wang et al. conceptualized a novel valence-balanced double HH alloy, denoted as Ti₂Zr₂Hf₂NbVFe₅Ni₃Sb₈, featuring a HE sublattice (Fig. 6B₁).¹⁷³ They recognized an improvement in the electrical properties and a reduction in k. Notably, at 823 K, its k (∼2.2 W m⁻¹ K⁻¹) was reduced by 60% of that reported for Ti₂FeNiSb₂, and the maximum PF exhibited a threefold enhancement to 0.1 W m⁻¹ K⁻² at 823 K (Fig. 6B₂), resulting in a maximum ZT of approximately 0.027 at 823 K (Fig. 6B₃), nearly five times that of Ti₂FeNiSb₂.¹⁷³ Tan et al.¹⁷⁴ have designed multi-element-doped NbFeSb-based alloys by introducing Ti, Zr, and Hf atoms into the Nb sites through a stepwise doping process. This doping resulted in an increase in the n-type hole-carrier concentration and an enhancement in electrical transport properties. In particular, Nb_0.82Ti_0.06Zr_0.06Hf_0.06FeSb exhibited the highest PF value of 40.3 μW cm⁻¹ K⁻² at 973 K and achieved the lowest lattice k of 3.6 W m⁻¹ K⁻¹ at 973 K, which was approximately half that of pristine NbFeSb. Consequently, Nb_0.82Ti_0.06Zr_0.06Hf_0.06FeSb achieved a high ZT value of 0.74 at 973 K and maintained an average ZT of 0.45 ranging from 333 K to 973 K.¹⁷⁴ Zhang et al. have also applied the entropy-driven concept on a Hf-free HH compound and found a k of 3.14 W m⁻¹ K⁻¹ at 870 K and a very low k_l of 0.48 W m⁻¹ K⁻¹ at 870 K of Ti_0.57Zr_0.4Al_0.02Ta_0.01NiSn_0.98Sb_0.02, which represents an 82.3% decrease compared to that of pristine TiNiSn. As a result, ZT has risen from 0.67 for TiNiSn to ∼1.4 for Ti_0.57Zr_0.4Al_0.02Ta_0.01NiSn_0.98Sb_0.02 at 870 K, resulting in an increase of almost 108% that was accomplished through entropy engineering.¹⁷⁵ This constitutes a record for this class of HE-HH TEMs. Rahman et al. have investigated the TE properties of a novel class of Sb-based HEAs.¹⁷⁶ These HEAs exhibit a noteworthy relationship between their electrical properties and the VEC of the system. By changing the VEC from 18.72 to 17 (Fig. 6C₁), the temperature dependent σ changes from metallic to semiconducting behavior. Additionally, this reduction in VEC leads to a decrease in the total k from ∼6 to 4 W m⁻¹ K⁻¹ at 300 K (Fig. 6C₂), which is assigned to a decrease in electronic k. As a result, Zn_25.4Fe₁₄Co_11.5Ni_7.9Mn_7.9Sb_33.33 (VEC = 17) exhibits a ZT of 0.008 at 630 K, compared to 0.002 at 630 K for Zn_16.67Fe_9.17Co_7.5Ni_16.67Mn_16.67Sb_33.33 (VEC = 18.72), as illustrated in Fig. 6C₃.

Fig. 6 (A) (a₁) Schematic illustration of band engineering, energy-filtering effect, and scattering phonons for enhancing the TE properties. Temperature dependence of (a₂) S, (a₃) ZT, and (a₄) ZT_max of medium- and HEHHs. Reproduced with permission.¹⁷¹ © 2023 Elsevier Ltd. (B) (b₁) The schematic illustration of the double half-Heusler structure, Temperature dependence of (b₂) PF and (e₃) ZT of sintered Ti₂Zr₂Hf₂NbVFe₅Ni₃Sb₈ HEM compared with conventional HH Ti₂FeNiSb₂. Reproduced with permission.¹⁷³ © 2023 Elsevier Ltd. (C) (c₁) The calculated configurational entropy of (MnNiSb)_1−x(ZnFe_1−yCo_ySb)_x HEMs with various VEC of the crystallized alloys. Temperature-dependent (c₂) total thermal conductivity and (c₃) ZT for VEC (18.72, 18, and 17). Reproduced under terms of the CC-BY 4.0 license.¹⁷⁶ © 2022 The Authors. Published by Elsevier Ltd.

Zhu et al. used a Sb-pressure controlled annealing process to tune the microstructure and introduce point defects into Nb_0.55Ta_0.40Ti_0.05FeSb.¹⁷⁷ They achieved a maximum PF reaching 78 μW cm⁻¹ K⁻² near RT, the highest ZT of approximately 1.1 at 873 K and an average of 0.86 from RT to 873 K, which underscore the promising potential of this strategy for optimizing high-temperature HH materials for near RT TE applications.¹⁷⁷ However, these compositions do not establish the needed requirements to be classified as an HEM. As a result, applying the entropy concept might further enhance TE performances by reducing k. This also applies to the composition of ZrCoBi_0.65Sb_0.15Sn_0.2 that exhibits a ZT of ∼1.42 at 973 K,¹⁷⁸ for Zr_0.68Hf_0.3Ta_0.02NiSn with a ZT of 0.94 at 923 K,¹⁷⁹ Ti_0.5Zr_0.5NiSn_0.98Sb_0.02 with a ZT ∼ 1.2 at 823 K,¹⁸⁰ Ti_0.50Zr_0.48Nb_0.02NiSn_0.98Sb_0.02 with a ZT of 1.17 at 823 K,¹⁸¹ Ti_0.5Zr_0.5NiSn_0.98Sb_0.02 with a ZT of 1.08 at 800 K,¹⁸² (Hf_0.6Zr_0.4)NiSn_0.99Sb_0.01 with a ZT ∼ 1.4 at 773 K,¹⁸³ Hf_0.75Zr_0.25NiSn_0.99Sb_0.01 with a ZT ∼ 1.0 at 873 K,¹⁸⁴ and (Hf_0.6Zr_0.4)_0.99V_0.01NiSn_0.995Sb_0.005 with a ZT of 1.3 near 850 K.¹⁸⁵

In summary, due to their toxic elements’ free composition and high thermoelectric performance at high temperatures, HH materials are unique (which could be assigned to their alloying behavior). The TE efficiency has been greatly improved by applying the entropy-driven approach. The TE properties of HH-HEAs are summarized in Table 2.

Table 2 TE properties of HH-HEA-based materials reported in the literature

Compound	T (K)	k (W m^−1 K^−1)	ZT	Ref.	Year
Ti2NiCoSnSb	860	6	0.144	Karati et al.^154	2019
Ti2NiCoSn0.5Sb1.5	873	4.646	0.29	Karati et al.^165	2020
Ti2NiCoSb2	873	4.5	0.26	Karati et al.^125	2022
Ti2NiCoSnSb	973	6.25	0.13	Karati et al.^166	2022
Ti1.875NiCoSnSb	973	5.75	0.171	Mishra et al.^167	2023
Ti1.85Zr0.15NiCoSn0.5Sb1.5	823	4.6	0.29	Mishra et al.^168	2023
Ti1.5Ta0.5NiCoSn0.5Sb1.5	823	5.2	0.29
Ti1.8Al0.2NiCoSn0.5Sb1.5	823	5.75	0.29
Nb0.98M0.02FeSb (M = Hf, Zr, Mo, V, Ti)	873	4.54	0.88	Yan et al.^126	2018
MFe0.6Co0.4Sb (M = Ti, Zr, Hf, V, Nb, and Ta)	823	2.5	0.25	Chen et al.^169	2022
MCoSb (M = Ti, Zr, Hf, V, Nb, and Ta)	900	1.5	0.3
Ti(Fe1/3+xCo1/3Ni1/3−x)Sb x = 0.15	1023	3.8	0.56	Luo et al.^170	2022
Ti(Fe1/3+xCo1/3Ni1/3−x)Sb x = −0.15	1023	4.2	0.49
M0.85Nb0.15CoSb (M = Ti, Zr, and Hf)	923	2.55	0.58	Chen et al.^106	2023
(Ti0.33Zr0.33Hf0.33Al0.005Sc0.005)NiSn	750	2.3	0.77	Rabin et al.^172	2021
Ti2Zr2Hf2NbVFe5Ni3Sb8	823	2.2	0.027	Wang et al.^173	2023
Nb0.82Ti0.06Zr0.06Hf0.06FeSb	973	5	0.74	Tan et al.^174	2023
Ti0.57Zr0.4Al0.02Ta0.01NiSn0.98Sb0.02	870	3.14	1.4	Zhang et al.^175	2023
Zn25.4Fe14Co11.5Ni7.9Mn7.9Sb33.33	630	9	0.008	Rahman et al.^176	2022

---

4.2 High-entropy oxides

Oxides have garnered significant attention in recent research, particularly in TE applications, especially for high-temperature TEGs. This is mainly due to the advantages they offer over intermetallics and chalcogenides, including lower processing costs, enhanced temperature stability, and a more environmentally friendly profile, as highlighted by Maiti et al.¹⁸⁶

Among the various oxide TEMs, perovskites based on SrTiO₃ have been a focal point due to their ability to exhibit relatively high ZT values.¹⁸⁷ However, it is worth noting that despite their promise, these oxide TEMs still fall short in comparison to state-of-the-art materials like tellurides and selenides (as shown in Fig. 2C). One of the primary reasons for this discrepancy is the notably high lattice k exhibited by these oxide perovskites. As a result, it is crucial to find solutions to reduce the high lattice k as the conventional approaches like nanostructuring have limited effectiveness in the case of perovskites, which remain challenging because of the high phonon mean-free-path. The application of HE-engineering in oxide TEMs appears to be a promising solution. Banerjee et al.¹⁸⁸ have made a significant breakthrough by investigating the TE properties of high-entropy oxides (HEOs) in 2020. They introduced a novel approach to enhance TE performance by incorporating five transition metals into the B-site and successfully synthesized a highly dense, single-phase solid solution of Sr(Ti_0.2Fe_0.2Mo_0.2Nb_0.2Cr_0.2)O₃ HEO. This material exhibited the lowest k ever reported for oxide TEMs, measuring 0.7 W m⁻¹ K⁻¹ at 1100 K for a single-phase solid solution of rare-earth-free HE perovskites (Fig. 7A₁). Using the Debye Callaway model, the authors demonstrated the higher-order phonon interaction processes for the HE perovskite. The occurring phenomenon is probably due to the increased anharmonicity at the Sr(Ti_0.2Fe_0.2Mo_0.2Nb_0.2Cr_0.2)O₃ HEO, which incorporates five transition metals in the B-site. This stands in contrast to a simple perovskite system like SrTiO₃, depicted schematically in Fig. 7A₂.¹⁸⁸ This innovative approach holds the potential to revolutionize the decoupling of the ‘electron crystal’ and ‘phonon glass’ components in oxide TEMs. However, the highest ZT value obtained for Sr(Ti_0.2Fe_0.2Mo_0.2Nb_0.2Cr_0.2)O₃ HEO is approximately 0.065 at 1043 K (as shown in Fig. 7A₃), indicating the need for significant improvements to make it suitable for commercial use. Another example of perovskite-type HEO was reported by Zheng et al.¹⁸⁹ They synthesized (Ca_0.2Sr_0.2Ba_0.2Pb_0.2La_0.2)TiO₃ HEO by solid-state method and conventional sintering, which incorporates five elements in the A-site and found a remarkably low k, with the minimum value reaching 1.17 W m⁻¹ K⁻¹ at 923 K, an enhanced PF of approximately 295 μW m⁻¹ K⁻² through the introduction of oxygen vacancies, and a ZT of 0.2 at 873 K (Fig. 7B).¹⁸⁹ The same composition was investigated by Gao's group, where they successfully synthesized (Ca_0.2Sr_0.2Ba_0.2Pb_0.2La_0.2)TiO₃ by the solid-state method.¹⁹⁰ This HEO exhibited both short-range chemical disorder and long-range structure, featuring nanoscale grains varying in size from 4–6 nm in its microstructure. The (Ca_0.2Sr_0.2Ba_0.2Pb_0.2La_0.2)TiO₃ HEO annealed at 1300 °C displayed an enhanced α of 272 μV K⁻¹, and a low k of 1.75 W m⁻¹ K⁻¹ both at 1073 K, which led to a maximum ZT of 0.12 at 1073 K (Fig. 7C). Based on this composition, Gao's group¹⁹¹ synthesized two novel lead-free ceramics (Ca_0.25Sr_0.25Ba_0.25Ce_0.25)TiO₃ and (Ca_0.25Sr_0.25Ba_0.25La_0.25)TiO₃ using a conventional solid-state method and this approach results in a low lattice k of 2.5 W m⁻¹ K⁻¹ at 1073 K for (Ca_0.25Sr_0.25Ba_0.25La_0.25)TiO₃. Notably, this value is significantly lower than that observed in SrTiO₃-based perovskite TE ceramics. Furthermore, (Ca_0.25Sr_0.25Ba_0.25La_0.25)TiO₃ displays a PF of 420 μW m⁻¹ K⁻², and the maximum ZT was found to be 0.18 at 1073 K, as illustrated in Fig. 7D. Recently, they added Bi₂O₃ to the pure composition (Ca_0.2Sr_0.2Ba_0.2Pb_0.2La_0.2)TiO₃ and formed (Ca_0.25Sr_0.25Ba_0.25La_0.25)TiO₃/Pb@Bi composite HEO with core–shell grains of an all-scale hierarchical microstructure.¹⁹² This complex microstructure involves core–shell grains, and the presence of precipitated Pb@Bi particles affects the transport properties of electrons and phonons. Thus, a maximum ZT of 0.18 was obtained at 1073 K, surpassing that of the pure (Ca_0.2Sr_0.2Ba_0.2Pb_0.2La_0.2)TiO₃ HEO by 1.5 times.¹⁹⁰ They also successfully synthesized single-phase perovskite-type HEOs, three different compositions, which are (Sr_0.25Ca_0.25Ba_0.25Nd_0.25)TiO₃, (Sr_0.25Ca_0.25Ba_0.25Sm_0.25)TiO₃, and (Sr_0.25Ca_0.25Ba_0.25Eu_0.25)TiO₃, using the solid-state method.¹⁹³ The resulting lattice k exhibited a value of 2.27 W m⁻¹ K⁻¹ for the (Sr_0.25Ca_0.25Ba_0.25Nd_0.25)TiO₃ HEO (Fig. 7E₁), which is reduced by 68.2% when compared to the SrTiO₃-based polycrystal system. The temperature-independent behavior of k aligns with the concept of PGEC, resulting from the synergistic effect of significant lattice distortion, the complex strain field, TiO₆ octahedral distortion, and the presence of dislocations. The highest obtained ZT was 0.15 at 1073 K for the (Sr_0.25Ca_0.25Ba_0.25Nd_0.25)TiO₃ HEO, as illustrated in Fig. 7E₂.¹⁹³ The same group also synthesized Sr_0.9La_0.1(Zr_0.25Sn_0.25Ti_0.25Hf_0.2)O₃ through conventional solid-state method.¹⁹⁴ Their findings revealed that this HEO exhibited interesting properties, such as a high α of 393 μV K⁻¹ and a low k of 1.89 W m⁻¹ K⁻¹, both at 873 K, which are very promising compared to those of other oxide TEMs (see Fig. 7F). Similar to that, Yao et al.¹⁹⁵ successfully synthesized Sr_0.4Ba_0.5La_0.1Ti_0.9Nb_0.1O_3−δ. They found a very low lattice k of 2.93 W m⁻¹ K⁻¹ at 923 K and the highest ZT of 0.15 at 973 K for the Sr_0.7Ba_0.2La_0.1Ti_0.9Nb_0.1O_3−δ HEM. Recently, Li et al.¹⁹⁶ reported another HEO (Sr_0.2La_0.2Nd_0.2Sm_0.2Eu_0.2)TiO₃, synthesized by the solid-state method at high temperature and pressure. The lowest k was 0.82 W m⁻¹ K⁻¹ at 973 K. This value represents the lowest k among all perovskite SrTiO₃-based ceramics.¹⁹⁶

Fig. 7 (A) (a₁) Thermal conductivity of the Sr(Ti_0.2Fe_0.2Mo_0.2Nb_0.2Cr_0.2)O₃ HEO compared with other oxides TEMs, (a₂) schematic illustration of multi-phonon scattering determined by the Debye–Callaway model fitting, and (a₃) temperature-dependent ZT for the HEO. Reproduced with permission.¹⁸⁸ © 2020 American Chemical Society. (B) Temperature dependence of ZT of annealed (Ca_0.2Sr_0.2Ba_0.2Pb_0.2La_0.2)TiO₃. Reproduced under terms of the CC-BY 4.0 license.¹⁸⁹ © 2021 The Author(s). Published by Springer Nature. (C) Temperature dependence of ZT values for (Ca_0.2Sr_0.2Ba_0.2La_0.2Pb_0.2)TiO₃ HEO annealed at different temperatures. Reproduced with permission.¹⁹⁰ © 2022 Elsevier Ltd. (D) Temperature dependence of thermal conductivity and ZT of (Ca_0.25Sr_0.25Ba_0.25La_0.25)TiO₃ (4La) and (Ca_0.25Sr_0.25Ba_0.25Ce_0.25)TiO₃ (4Ce) HEOs. Reproduced with permission.¹⁹¹ © 2022 Elsevier B.V. (E) (e₁) Thermal transport properties and (e₂) ZT values of the (Sr_0.25Ca_0.25Ba_0.25RE_0.25)TiO₃ (RE = Nd, Sm, Eu, Gd, Dy, and Ho) HEOs. Reproduced with permission.¹⁹³ © 2023 Elsevier B.V. (F) Comparison of S and κ between Sr_0.9La_0.1(Zr_0.25Sn_0.25Ti_0.25Hf_0.25)O₃ HEO and other SrTiO₃-based TEMs. Reproduced with permission.¹⁹⁴ © 2022 Elsevier Ltd.

Kumar et al.¹⁹⁷ investigated the thermoelectric properties of the (LaNdPrSmEu)_0.95Sr_0.05CoO₃ HEO nanoparticles. According to the obtained results, an increase in both the Sr concentration and annealing temperature led to a decrease in both the α and electrical resistivity of the material when compared to La_0.95Sr_0.05CoO₃ due to the presence of multiple A-site ions in the HEO. This enhancement was attributed to a reduction in the Co–O–Co bond angle, which increased the PF. Furthermore, the random distribution of cations at rare-earth sites caused a significant reduction in phonon k to 0.67 W m⁻¹ K⁻¹ at RT (as shown in Fig. 8A₁). Consequently, (LaNdPrSmEu)_0.95Sr_0.05CoO₃ demonstrated a maximum ZT of 0.23 at 350 K (Fig. 7A₁), making it one of the best-performing oxide TEMs near RT, as illustrated in Fig. 7A₂.¹⁹⁷ Yang et al.¹⁹⁸ applied for the first time the entropy-driven concept on the Layered Ca₃Co₄O₉ cobaltate, which is a classical PGEC thermoelectric material, and successfully prepared a novel layered (Ca_0.35Sr_0.2Ba_0.15Na_0.2Bi_0.1)₃Co₄O₉ HEO. The obtained PF was increased to 0.27 mW m⁻¹ K⁻² in comparison to that of the pristine Ca₃Co₄O₉ due to the higher carrier mobility resulting from selective orientation along the c-axis. It shows an exceptionally low k of 0.87 W m⁻¹ K⁻¹ because of the effective phonon scattering centers induced by the HE resulting in a higher ZT of 0.3 at 973 K, which is approximately 2.5 times greater than that of Ca₃Co₄O₉, as illustrated in Fig. 8B.¹⁹⁸

Fig. 8 (A) (a₁) Temperature-dependent ZT and phonon thermal conductivity of (LaNdPrSmEu)_0.95Sr_0.05CoO₃ HEO compared to those of simple perovskite La_0.95Sr_0.05CoO₃, and (a₂) comparison of ZT_max of (LaNdPrSmEu)_0.95Sr_0.05CoO₃ HEO with those of conventional polycrystalline oxide TEMs. Reproduced under terms of the CC-BY-NC-ND license.¹⁹⁷ © 2023 The Authors. Published by Elsevier B.V. (B) Temperature dependence of the ZT for Ca₃Co₄O₉ (C-349) and (Ca_0.35Sr_0.2Ba_0.15Na_0.2Bi_0.1)₃Co₄O₉ (HE-349) ceramics. Reproduced with permission.¹⁹⁸ © 2023 Elsevier B.V. (C) (c₁) Schematic illustration of all scale hierarchical microstructure of the phonon scattering mechanism in the HEO Bi_1−x−2yPb_xCa_yYb_yCuSeO (x = y = 0–0.05; x = 0.06–0.08 (x + 2y = 0.12)). (c₂) Comparison of lattice thermal conductivity of Bi_0.88Pb_0.06Ca_0.03Yb_0.03CuSeO with that of other BiCuSeO-based materials, and (c₃) temperature-dependent ZT value of Bi_1−x−2yPb_xCa_yYb_yCuSeO (x = y = 0–0.05; x = 0.06–0.08 (x + 2y = 0.12)). Reproduced with permission.²⁰³ © 2023 Elsevier B.V.

Jana et al.¹⁹⁹ successfully synthesized a single-phase solid solution of a novel (Sr_0.2Ba_0.2Li_0.2K_0.2Na_0.2)Nb₂O₆ HEO. The achieved α of −370 μV K⁻¹ at 1150 K and the impressively low k of 0.8 W W m⁻¹ K⁻¹ at 330 K give rise to ZT of 0.23 at 1150 K. This value is currently the highest observed among TEMs based on rare-earth-free HEOs with a tungsten bronze-type structure. Shi et al.²⁰⁰ applied the entropy-driven concept on the perovskite-type manganite structure RE_0.2Ca_0.2Sr_0.2Ba_0.2Y_0.2MnO₃ (where RE = La, Nd, Ho, and Lu). The achieved total k is very low 0.94 W m⁻¹ K⁻¹ at 1073 K for Lu_0.2Ca_0.2Sr_0.2Ba_0.2Y_0.2MnO₃. The highest ZT was found in the La_0.2Ca_0.2Sr_0.2Ba_0.2Y_0.2MnO₃ HEO with a value of 20.5 × 10⁻³ that was reached at 873 K. In another recent study, Pankratova et al.²⁰¹ successfully synthesized a single-phase HEOs comprised of Co–Cr–Fe–Mn–Ni–O HEO using the spark plasma sintering (SPS) technique within the temperature range of 1200–1300 °C and assessed their TE properties. The highest α reached −112.6 μV K⁻¹ at RT and σ = 0.2148 S cm⁻¹ at 773 K. This new approach resulted in transport properties comparable to those previously reported by Stygar et al.,²⁰² where they synthesized (Co, Cr, Fe, Mn, Ni)₃O₄ HEO employing the solid-state route at 900 °C to 1100 °C and the obtained α is −120 μV K⁻¹ at RT and σ ≈ 0.2009 S cm⁻¹ at 1000 °C.²⁰²

In another work, Zeng et al.²⁰³ successfully synthesized Bi_1−x−2yPb_xCa_yYb_yCuSeO TEMs through the entropy-driven approach. The introduction of Pb, Yb, and Ca leads to a flattening of the energy band and a narrowing of the energy gap, resulting in improved σ and α values (PF ∼ 700 μW m⁻¹ K⁻²). This, in combination with the increase in entropy, leads to a significant lattice distortion, as shown in Fig. 8C₁, giving an extraordinarily low k of 0.244 W m⁻¹ K⁻¹ in the Bi_0.88Pb_0.06Ca_0.03Yb_0.03CuSeO sample (Fig. 8C₂). As a result, Bi_0.88Pb_0.06Ca_0.03Yb_0.03CuSeO exhibited a ZT of 1.2 at 873 K (Fig. 8C₃), exceeding the pristine BiCuSeO by a factor of 2.5.⁹⁰ However, this Bi_0.88Pb_0.06Ca_0.03Yb_0.03CuSeO system is considered as a medium-entropy material. Similar to that, Bi et al.²⁰⁴ synthesized a medium-entropy oxide TEM (Sr_1/3Ba_1/3Ca_1/3)TiO₃via the solid-state reaction and graphite burial sintering and obtained a lattice thermal conductivity of 1.90 W m⁻¹ K⁻¹ and maximum ZT of 0.13 both at 773 K. The same for the two Ca_0.98Lu_0.02Mn_0.96Nb_0.04O₃ and Ca_0.98Yb_0.02Mn_0.99Nb_0.01O₃ compositions reported by Nag et al.²⁰⁵ with a PF of 38 and 29 μW m⁻¹ K⁻² at 950 K, respectively.

Zhao et al.²⁰⁶ investigated the (La_0.2Ce_0.2Nd_0.2Sm_0.2Eu_0.2)₂Zr₂O₇ HEO and found a remarkably low k of 0.76 W m⁻¹ K⁻¹ at RT because of the sluggish diffusion effect within HE solid solutions that leads to a slower grain growth rate as observed in (La_0.2Ce_0.2Nd_0.2Sm_0.2Eu_0.2)₂Zr₂O₇. Zhao et al.²⁰⁷ have also investigated k of oxide nanofibers in the (La_0.2Sm_0.2Eu_0.2Gd_0.2Tm_0.2)₂Zr₂O₇ HEO. This HEO exhibited a lower k of approximately 0.23 W m⁻¹ K⁻¹, which was attributed to a high degree of lattice distortion and the presence of pores within the fibers. Consequently, it is anticipated that (La_0.2Ce_0.2Nd_0.2Sm_0.2Eu_0.2)₂Zr₂O₇ and (La_0.2Sm_0.2Eu_0.2Gd_0.2Tm_0.2)₂Zr₂O₇ HEOs could serve as promising materials for high-temperature TE applications.

The TE properties of HEOs are summarized in Table 3, and the maximum ZT that could be achieved in this class of HEOs is 0.3 at 973 K,¹⁹⁸ and this is enough performance for commercial TEGs because of the interdependence of σ and k on the carrier concentration. Achieving HEOs with high ZT values requires coupling the entropy-driven concept with the other approaches, as discussed in the Section 2.3.

Table 3 TE properties of HEO-based materials reported in the literature

Compound	T (K)	k (W m^−1 K^−1)	ZT	Ref.	Year
Sr(Ti0.2Fe0.2Mo0.2Nb0.2Cr0.2)O3	1043	1.1	0.065	Banerjee et al.^188	2020
(Ca0.2Sr0.2Ba0.2Pb0.2La0.2)TiO3	873	1.09	0.2	Zheng et al.^189	2021
(Ca0.2Sr0.2Ba0.2La0.2Pb0.2)TiO3	1073	1.75	0.12	Zhang et al.^190	2022
(Ca0.25Sr0.25Ba0.25La0.25)TiO3	1073	2.5	0.18	Zhang et al.^191	2022
(Ca0.2Sr0.2Ba0.2Pb0.2La0.2)TiO3/Pb@Bi	1073	1.9	0.18	Zhang et al.^192	2023
(Sr0.25Ca0.25Ba0.25Nd0.25)TiO3	1073	2.6	0.15	Zhang et al.^193	2023
Sr0.7Ba0.2La0.1Ti0.9Nb0.1O3−δ	973	3.7	0.15	Yao et al.^195	2022
(LaNdPrSmEu)0.95Sr0.05CoO3	350	0.75	0.23	Kumar et al.^197	2023
(Ca0.35Sr0.2Ba0.15Na0.2Bi0.1)3Co4O9	973	0.87	0.3	Yang et al.^198	2023
(Sr0.2Ba0.2Li0.2K0.2Na0.2)Nb2O6	1150	1.6	0.23	Jana et al.^199	2023
La0.2Ca0.2Sr0.2Ba0.2Y0.2MnO3	873	1.3	20.5 × 10^−3	Shi et al.^200	2022

---

4.3 High-entropy metal chalcogenides

Metal chalcogenide materials are a class of compounds composed of elements from the chalcogen group, which includes sulfur (S), selenium (Se), and tellurium (Te).⁴⁸ These materials often exhibit interesting electronic, optical, and thermal properties due to the unique characteristics of the chalcogenide atoms. Therefore, they are widely used in various fields such as thermoelectricity and electrocatalysis.^{44,137,208,209} As selenides and tellurides stand out as the most efficient TEMs, there is growing interest in the scientific community to design HEMs using these compounds.²¹⁰ Reducing the lattice k is the main hurdle in improving the ZT of selenides and tellurides. The distinctive feature of chemical disorder inherent in HEAs holds great promise for achieving exceptionally low lattice k by enhancing phonon scattering within the material system. These materials are often used in combination with metals to form high-entropy metal chalcogenides (HEMCs), where the diversity of metal cations and chalcogen anions contributes to unique lattice structures and potential improvements in TE efficiency, as shown in Fig. 9A.

Fig. 9 (A) Illustration of (left) the conventional rock salt structure of a binary metal chalcogenide, with a single cation a (yellow sphere) and an anion (red sphere). In contrast to HEMCs with a rock salt structure (right), where diverse cation metals (multicolored spheres) are randomly dispersed within an orderly single anionic sub-lattice (red spheres). Reproduced under terms of the CC-BY 3.0 license.²¹⁰ © 2022 The Authors. Published by Royal Society of Chemistry. (B) Temperature dependence of (b₁) k and (b₂) ZT for the Cu₃SnS₄–Cu₂MgGeS₄–ZnS composite. Reproduced with permission.¹³⁷ © 2018 American Chemical Society. This publication is licensed under CC-BY.

4.3.1 High-entropy sulfides. Zhang et al.¹³⁷ were the first to investigate the HEMCs, starting with the design and identification of a promising HE sulfide candidate by computational methods, which was subsequently synthesized and tested. The model was created to select suitable compounds based on the bond lengths between cations and sulfur that will reduce the enthalpy of formation. These bond lengths serve as a chemical descriptor for the design of HE sulfide that measures local strain. According to the Hume–Rothery rule, a bit of strain is advantageous for the stabilization of the single phase. The two predicted (Cu₃SnMgInZn)S₇ and (Cu₅SnMgGeZn)S₉ HEMs were synthesized using ball-milling in a glove box and then sintered by SPS under vacuum to get dense ceramics with a uniform distribution of cations. (Cu₃SnMgInZn)S₇ exhibited semiconductor characteristics with very low σ. In contrast, (Cu₅SnMgGeZn)S₉ showed a very good TE performance. The measured σ reached 1000 S cm⁻¹ at 623 K, demonstrating metallic behavior, which is higher than those of the other conventional sulfide TEMs such as the tetrahedrite (Cu,Fe)₁₂Sb₄S₁₃ compound.²¹¹ A new composition (Cu₅Sn_1.2MgGeZn)S₉ was synthesized by adding an amount of Sn (20%) which resulted in reducing the σ and enhancing the α, thus the measured PF of the (Cu₅Sn_1.2MgGeZn)S₉ reached 8 μW cm⁻¹ K⁻² at 773 K, which can be explained by the band convergence near the valence band maximum. Furthermore, it demonstrated a low lattice k of 0.4 W m⁻¹ K⁻¹ at 773 K due to the weak Cu–S bonding and the fine-grain-size produced by SPS and MA (Fig. 9B₁). (Cu₅Sn_1.2MgGeZn)S₉ exhibited a ZT of 0.58 at 773 K by tuning the carrier concentration through Sn excess, as shown in Fig. 9B₂,¹³⁷ which is significantly lower than those of the benchmarked TEMs reported in Fig. 2C. It is true that the conventional Cu–S based TEMs have indeed demonstrated very high ZT values compared to the high-entropy sulfides, such as 1.6 at 800 K and 1.9 at 970 K for Cu_1.9ZnSnS₄-doped and Cu_2−xS, respectively.^212,213 Nevertheless, the HE sulfides remain comparable to other conventional Cu–S based TEMs like the bornite Cu₅FeS₄²¹⁴ and tetrahedrite Cu₁₂Sb₄S₁₃,²¹⁵ which have reported ZT values of 0.55 and 0.56 at 543 K and 673 K, respectively.²¹⁰ Zhou et al.²¹⁶ have applied the entropy-driven concept and Cu vacancy engineering on the Cu_1.8S-based alloys. The obtained peak ZT was 0.79 for the Mn_0.06Cu_1.8S_0.5Se_0.5 system, which is twice as high as that observed for pure Cu_1.8S. However, the latter is classified as a medium-entropy system (1.2R).

4.3.2 High-entropy tellurides. Another family of HEMCs that has also garnered attention to explore their TE properties is the HE tellurides.^210,217 The first investigated system in this class was the GeTe-based TEMs, one noteworthy example is the Ge_0.61Ag_0.11Sb_0.13Pb_0.12Bi_0.01Te HE material based on the (Ge/Ag/Sb/Pb)Te system reported by Jiang et al.⁴² The incorporation of several alloying Ag, Sb, and Pb elements into Ge sites has increased the solubility (by ∼10%) compared to the solubility in the presence of the individual elements. This leads to an improved symmetry in the crystal structure, which is near to the cubic phase in the (Ge/Ag/Sb/Pb)Te system. This simple highly symmetrical phase unexpectedly has enhanced the transport of hole charge in the Ge_0.61Ag_0.11Sb_0.13Pb_0.12Bi_0.01Te HEM, due to the reduction in the coupling effect of electrical field between Ge and Te sites, and the presence of delocalized electrons. Furthermore, the significant symmetry of GeTe allows for the convergence of the split valence band maxima at low temperatures, resulting in improved α without undergoing a phase transition. Also, an ultra-low lattice k ∼ 0.3 W m⁻¹ K⁻¹ was obtained due to the lattice distortion. Hence, an exceptional ZT of 2.7 at 750 K was achieved for the Ge_0.61Ag_0.11Sb_0.13Pb_0.12Bi_0.01Te HE material (Fig. 10A). The energy conversion efficiency achieved a high value of 13.3% at ΔT = 506 K with the fabricated segmented module (GeTe HEMs as the p-type leg and PbTe as the n-type leg).⁴² Zhong et al.²¹⁸ developed (GeTe)_1−x(AgSb_0.5Bi_0.5Te₂)_x with (x = 0.10, 0.15, 0.20, 0.25, 0.30, 0.35, and 0.40) and found that the (GeTe)_0.80(AgSb_0.5Bi_0.5Te₂)_0.20 HEM attains a high ZT of 1.60 at 723 K. Huang et al.²¹⁹ reported a ZT of 1.24 at 723 K for the Ge_0.82Sb_0.08Te_0.90(MnZnCdTe₃)_0.10 HEM. Another example is Ge_0.84In_0.01Pb_0.1Sb_0.05Te_0.997I_0.003 with an ultra-low lattice k of 0.4 W m⁻¹ K⁻¹, a record-high PF of 23 mW cm⁻¹ K⁻², and a ZT of 2.1 at 800 K.²²⁰ Recently, Das et al.²²¹ investigated GeTe doped with Sn, Pb, and Sb in order to increase the system entropy. They reported an ultra-high ZT of 2.3 at 723 K for the Ge_0.84Pb_0.025Sn_0.025Sb_0.11Te HEM and an average ZT of 1.3 in the temperature range (300–723 K). Zhi et al.²²² also reported a state-of-the-art ZT of 2.1 at 873 K for the Ge_0.63Mn_0.15Pb_0.1Sb_0.06Cd_0.06Te material. However, the latter is considered as medium-entropy material. A similar composition of PbGeSnCd_xTe_3+x has been synthesized by alloying CdTe with PbGeSnTe, as reported by Liu et al.²²³ The applied entropy-driven concept reduces the phase-transition temperature and stabilizes PbGeSnCd_xTe_3+x in its cubic structure at RT (Fig. 10B₁). This lattice distortion induced by HE results in a low lattice k of 0.76 W m⁻¹ K⁻¹ due to enhanced phonon scattering (Fig. 10B₂). Notably, the increased crystal symmetry promotes band convergence, leading to a PF of 22.4 μW m⁻¹ K⁻². The obtained maximum ZT value was found to be 1.63 at 875 K, as presented in Fig. 10B₃. Ma et al.²²⁴ reported another p-type AgMnGeSbTe₄ HEM where they incorporated an optimal 1 mol% of Ag₈GeTe₆, which introduced additional scattering for medium-wavelength phonons as schematically presented in Fig. 10C₁. As a result, this incorporation yields the highest PF and ZT values, reaching around 14 mW cm⁻¹ K⁻² and 1.27 at 773 K, respectively, as shown in Fig. 10C₂. The same group has reported another composition AgMnSn_0.25Pb_0.75SbTe₄ that exhibited a very low k of 0.54 W m⁻¹ K⁻¹, leading to a peak ZT of 1.3 at 773 K.²²⁵ Liu et al.⁴⁸ applied the entropy engineering in the CuInTe₂ system by alloying Ag and Ga on the Cu and In sites, respectively, in accordance with the diamond-like structured HEMs. Co-alloying of Ag and Ga resulted in a substantial enhancement of α at high temperatures and an increase in the ZT with a maximum value 1.6 at 900 K for the Cu_0.8Ag_0.2In_0.5Ga_0.5Te₂ HEM. However, it is important to acknowledge that the composition with the highest configurational entropy did not achieve the optimal ZT. This value is higher in comparison to the medium-entropy Cu_0.8Ag_0.2InTe₂ with a peak ZT of 1.07 at 850 K.²²⁶ Similarly, Cai et al.²²⁷ designed a HEM based on CuInTe₂ and found a ZT value of 1.02 at 820 K for Cu_0.8Ag_0.2(ZnGe)_0.1(GaIn)_0.4Te₂. Hu et al.⁴⁶ have studied the (Sn/Te/Ge/Pb/Mn) system and reported a positive correlation between the number of alloying elements and both the absolute value of the α and carrier mobility. At 900 K, it was shown that the Sn_0.555Ge_0.15Pb_0.075Mn_0.275Te HEM exhibited an ultralow lattice k of around 0.32 W m⁻¹ K⁻¹, which falls below the amorphous limit of SnTe. In addition, a state-of-the-art ZT of 1.42 at 900 K was achieved through the fine tuning of Sn, which is accompanied by an increase in α and s. Nevertheless, if the entropy of mixing is very high, the fluctuation increase in strain and local mass may hinder the mobility of carriers, requiring the need for accurate entropy engineering. In another study by Wang et al.²²⁸ they combined PbTe, GeTe, and MnTe with SnTe to create a single-phase solid solution Sn_0.25Pb_0.25Mn_0.25Ge_0.25Te. This blending of various elements at the Sn cationic site resulted in an increase in configurational entropy and significantly boosted phonon scattering, consequently reducing the lattice k to 1.1 W m⁻¹ K⁻¹ at RT and enhancing the α due to modifications in the electronic band structure resulting from this co-alloying process (Fig. 10D₁). Consequently, the obtained ZT was 1.4 at 823 K. Additionally, they found that introducing Ga as a dopant to form Ga_x(Sn_0.25Pb_0.25Mn_0.25Ge_0.25)_1−xTe (x = 0, 0.015, 0.02, 0.025, and 0.03) optimizes the carrier concentration (∼5.7 × 10 cm⁻³), improves the phonon scattering and reduces the lattice k from 1.1 to 0.6 W m⁻¹ K⁻¹ at RT by inducing additional point defects and incorporating different elements at the cationic site that leads to an increase in configurational entropy, with the negligible change of the mobility. This leads to a remarkable maximum ZT of approximately 1.52 at 823 K for the Ga_0.025(Sn_0.25Pb_0.25Mn_0.25Ge_0.25)_0.975Te HEM, as shown in Fig. 10D₂. Acharya et al.²²⁹ suggested a quasi-random distribution of distorted nanostructures (QDDN) on CuGaTe (Fig. 10E₁), which led to a high degree of lattice-strain-induced distortion and thus scattering of the phonons leading to a low k of approximately 0.38 W m⁻¹ K⁻¹ at 850 K. However, the PF remained relatively unchanged due to the high crystallinity of the material. Consequently, an impressive ZT of approximately 1.56 at 850 K was obtained for Cu_0.8Ag_0.2(Ga_0.8In_0.2)_0.99Zn_0.01Te₂, as illustrated in Fig. 10E₂.²²⁹ A close composition was reported by Jiang et al.,²³⁰ where a ZT of 1.02 at 800 K for the Cu_0.8Ag_0.2Zn_0.1Ga_0.4Ge_0.1In_0.4Te₂ HEM was achieved. Another study reported a remarkable ZT of 1.5 at 800 K for the Cd_0.02(Sn_0.59Pb_0.15Ge_0.2Sb_0.06)_0.98Te system.²³¹ However, this composition is classified as a medium-entropy material resulting from the co-alloying of (Pb, Ge, Sb, Cd) and SnTe. Similar to that, Wu et al.²³² reported a ZT of 1.04 at 500 K for (Ag₂Te)_0.42(Sb₂Te₃)_0.58, which could also be considered as a ME material. The same applies for the BiSbTe_1.5Se_1.5 medium-entropy material with a reported ZT of around ∼0.43 at 500 K.²³³

Fig. 10 (A) Temperature dependence of ZT for the HE Ge_0.61Ag_0.11Sb_0.13Pb_0.12Bi_0.01Te alloy. Reproduced with permission.⁴² © 2022 The American Association for the Advancement of Science. (B) (b₁) Schematic of the crystal structures of the PbGeSnCd_xTe_3+x HEM, (b₂) lattice thermal conductivity as a function of temperature and (b₃) ZT of PbGeSnCd_0.08Te_3.08 compared with conventional TEMs. Reproduced with permission.²²³ © 2023 American Chemistry Society. (C) (c₁) Schematic illustration of the phonon scattering schematic diagram at the nanoscale (left) and atomic scale (right) and (c₂) Temperature dependent ZT for AgMnGeSbTe_4−x mol% Ag₈GeTe₆ (x = 0, 1, 2, 3, 4). Reproduced with permission.²²⁴ © 2021 Wiley-VCH GmbH. (D) (d₁) k_L at room temperature as a function of the configurational entropy, (d₂) temperature dependent ZT of Ga_0.025(Sn_0.25Pb_0.25Mn_0.25Ge_0.25)_0.975Te in comparison with SnTe-based materials. Reproduced with permission.²²⁸ © 2021 American Chemistry Society. (E) (e₁) Schematic representation of the phonon transport function in the quasi-random distribution of distorted nanostructures (e₂) and the ZT comparison for the different configurational entropies. Reproduced with permission.²²⁹ © 2023 Elsevier Ltd.

4.3.3 High-entropy selenides. HE selenides have also been investigated for TE applications. Zhao et al.²³⁴ applied the entropy-driven concept to the AgBiSe₂ material. They successfully synthesized a AgBi_0.8Sb_0.2Se_1.98Br_0.02 HEM, which exhibited a very low k of 0.45 W m⁻¹ K⁻¹ at 790 K (Fig. 11A₁) with a PF of 0.45 mW m⁻¹ K⁻² at 790 K leading to a maximum ZT of 0.86 at 790 K, as illustrated in Fig. 11A₂.²³⁴ Roychowdhury et al. applied the entropy-driven concept for a GeSe-based material, and the reported ZT for (GeSe)_0.5(AgBiSe₂)_0.5 was found to be 0.45 at 677 K.²³⁵ The incorporation of AgBiSe into the GeSe portion resulted in a transition of the material's conductivity from the p- to the n-type, leading to a substantial increase in the carrier concentration from 1.2 × 10¹⁷ cm⁻³ recorded for the pure GeSe compound to 3.29 × 10¹⁸ cm⁻³.²³⁵ Ma et al.²³⁶ applied the entropy-driven concept to increase the solubility of Mn in AgSbSe₂, increasing it from 8% to 30% by utilizing the entropy-driven concept by alloying with MnSe. They found a remarkable ZT value of 0.96 and 1.18 at 750 K for (AgSbSe₂)_0.7(MnSe)_0.3 (Fig. 11B₁) and (AgSbSe₂)_0.7(Mn_0.99Se)_0.3 with 1% Mn vacancy, respectively (Fig. 11B₂).

Similarly, Zhang et al.²³⁷ employed the entropy-driven stabilization to enhance the TE properties of AgBiSe₂ by alloying it with PbS. At 773 K, they observed a low k_l of 0.34 W m⁻¹ K⁻¹, and the material exhibited a peak ZT of 0.65 at the same temperature for the (Ag_0.99Nb_0.01BiSe₂)_0.8(PbS)_0.2 sample. In another study focusing on the entropy-driven concept of AgBiSe₂, the alloying with Ag₂Te was investigated. This approach led to a notable ZT of 1.0 at ∼760 K for the (AgBiSe₂)_0.925(Ag₂Te)_0.075 composition.²³⁸ Also, Zhu et al.²³⁹ reported that a peak ZT of 0.8 is reached at 800 K for a cubic n-type (AgBiSe₂)_0.7(PbSe)_0.3-Br 1% sample via the entropy-driven concept. Luo et al.²⁴⁰ synthesized a SnSe-based TE material using the entropy-driven concept to achieve higher ZT values. The incorporation of AgSbSe₂ introduces cation disorder (Fig. 11C₁), which served to limit k and induce distinctive multi-peak electronic valence bands. The obtained k was 0.81 W m⁻¹ K⁻¹ at RT, which results in a ZT of 0.65 at 723 K for the AgSnSbSe₃ sample. Additionally, they introduced Te atoms into Se sites (AgSnSbSe_3−xTe_x), which contributed to both cation and anion presence and facilitated the formation of closely packed dislocation arrays. This investigation revealed that the configurational entropy increases as the Te content increases, reaching its maximum value of 17.3 J mol⁻¹ K⁻¹ at x = 1.5. Thus, for x > 1.5, the configurational entropy drops to lower values. Furthermore, Te alloying leads to a greater convergence of the multiple valence band maximum, promoting a higher PF. This unique combination of factors resulted in a very low k of approximately 0.32 W m⁻¹ K⁻¹ and a high ZT of 1.14 at 723 K for the AgSnSbSe_1.5Te_1.5 HEM. The obtained glass-like lattice k proved the effectiveness of the high-entropy approach. The increase in configurational entropy led to an enhancement in the strength of phonon scattering, which was caused by fluctuations in atomic mass and the strain field. At the same time, a ZT value of approximately 1 was demonstrated to be competitive with those of other SnSe-based materials (see Fig. 11C₂). Furthermore, this approach promoted the convergence of energy bands in the HE sample (AgSnSbSe_1.5Te_1.5), indicating the positive impact of the entropy-driven concept on enhancing the material's electrical behavior.²⁴⁰ Recently, Sun et al.²⁴¹ used first-principles calculations to design HEMs such as Cu_2.1Mn_0.8Fe_0.1SnSe₄, Cu_2.1Mn_0.7Fe_0.1Co_0.1SnSe₄, and Cu_2.1Mn_0.6Fe_0.1Co_0.1Zn_0.1SnSe₄ within the tetragonal structure. They found that increasing configurational entropy contributes to the k reduction. As a result, the lowest K_l of 0.8 W m⁻¹ K⁻¹ was achieved for Cu_2.1Mn_0.7Fe_0.1Co_0.1SnSe₄ and a maximum ZT of 0.4 for Cu_2.1Mn_0.8Fe_0.1Co_0.1SnSe₄, both at 673 K.²⁴¹

Fig. 11 (A) Temperature-dependent (a₁) total k and (a₂) ZT values of AgBi_1−xSb_xSe_2−yBr_y (x = 0.2, 0.3 and 0.4; y = 0, 0.02, 0.04 and 0.06). Reproduced with permission.²³⁴ © 2021 Elsevier Ltd. (B) Temperature dependence of ZT (b₁) (AgSbSe₂)_1−x(MnSe)_x (x = 0, 0.1, 0.2, 0.3, 0.4, 0.5) and (b₂) (AgSbSe₂)_0.7(Mn_1−ySe)_0.3 (y = 0, 0.005, 0.01, 0.015, 0.02). Reproduced with permission.²³⁶ © 2023 The Royal Society of Chemistry. (C) (c₁) Crystal structures for SnSe, AgSnSbSe₃, and AgSnSbSe_1.5Te_1.5 and (c₂) comparison of their PF_ave, ZT_max, and ZT_ave. Reproduced with permission.²⁴⁰ © 2020 American Chemistry Society.

Luo et al.²⁴² found that the order–disorder transition driven by entropy at the cation site, coupled with increased phonon scattering due to CdSe alloying in CuInSe₂, significantly suppresses k, leading to an improved ZT of 0.45 at 780 K for CuCd_1.005InSe₃. Wang et al.²⁴³ successfully synthesized Sn_1−2x(AgBi)_xSe samples using vacuum melting and SPS. Increasing the configurational entropy introduced by the AgBiSe₂ solid solution, a cubic structure is achieved when x > 0.2, which increases the symmetry. This leads to an enhancement in σ and a reduction in k_l attributed to a smaller sound velocity and strong anharmonicity. As a result, a ZT of 0.08 is achieved at 500 K for Sn_0.6(AgBi)_0.2Se. Similarly, Yang et al.²⁴⁴ found a ZT of ∼1.15 for Ag₈Sn_0.5Ga_0.5Se₆, and Zhao et al.²³⁴ found a ZT of 0.86 at 790 K for the cubic AgBi_0.8Sb_0.2Se_1.98Br_0.02. Recently, Wang et al.²⁴⁵ also applied the entropy-driven concept on the GeSe-based materials, and they obtained a ZT of 0.5 at 627 K for Cu₈GeSe_4.2S_1.8. Similar to that, Li et al.²⁴⁶ applied the entropy-driven concept by alloying GeSe with MnCdTe₂, which leads to stabilizing a higher-symmetry rhombohedral structure under ambient conditions for the Ge_1−yBi_ySe(MnCdTe₂)_x compound. Consequently, a remarkable ZT of 1 at 723 K in Ge_0.96Bi_0.04Se(MnCdTe₂)_0.10 was achieved. However, these compositions are classified as medium-entropy materials.

4.3.4 High-entropy multiple chalcogenides. Another route has been explored in TE studies by incorporating multiple chalcogenides, which have a similar effect on the TE performances, as the one discussed earlier in Section 4.3.^45,247 The first study concerns the (Pb, Sb, Sn)(S, Se, Te) system, where pronounced lattice distortions are induced at both positions by different ratios of metal cations and chalcogenide anions.^44,45 The incorporation of Sn into the composition led to enhanced configurational entropy, resulting in the formation of a cubic phase of (Pb/Sn)(Se/Te/S) HEM beyond the solubility limit, which could be beneficial for maximizing the TE performance. The electron mobility remained high with the introduction of Sn, indicating that the atomic lattice remained well-defined despite the increase of the lattice distortion. The controlled manipulation of entropy resulted in achieving a peak PF of 16 mW cm⁻¹ K⁻² at 600 K for Pb_0.89Sb_0.012Sn_0.1Se_0.5Te_0.25S_0.25 HEM. The lattice k of the HEM was significantly reduced to an extremely low value of ∼0.3 W m⁻¹ K⁻¹ (with the total k of 0.5 W m⁻¹ K⁻¹ at 600 K) which is close to the limit observed in amorphous materials. The reason for this is the significant strain caused by the lattice distortion, which leads to intense phonon scattering. This relationship between the composition and lattice k was determined by constructing an alloy model. The Pb_0.89Sb_0.012Sn_0.1Se_0.5Te_0.25S_0.25 HEM exhibited a high ZT value of 1.8 at 900 K, as illustrated in Fig. 12A. This is due to its excellent electrical transport properties (i.e., PF) and greatly reduced lattice k.⁴⁴ The optimized TE performance led to a promising conversion efficiency of 12.3% at a ΔT = 507 K in the fabricated segmented TE module, ranking among the highest reported values for thermoelectric systems. This value was attained by systematic and incremental adjustment of the composition until an optimized configuration was reached. Also, the same group reported a high ZT of 2.0 at 900 K (Fig. 12B), coupled with a high PF of 16 mW cm⁻¹ K⁻¹ within Pb_0.935Na_0.025Cd_0.04Se_0.5S_0.25Te_0.25, highlighting the beneficial effect of disorder induced within the anionic lattice on the TE performance (Fig. 2D).⁴⁵ A high conversion efficiency of 12% at ΔT = 506 K for the fabricated segmented TE modules was achieved with a power output of 2.7 W.⁴⁵ In another study in which Zhang et al.²⁴⁸ have co-alloyed S/Se and Ag in Cu₂Te by a melting and calcination process, the obtained k reached 0.29 W m⁻¹ K⁻¹ at RT, which is even lower than the amorphous limit and, as a result, the peak ZT was found to be 1.4 at 1000 K for the Cu_1.9Ag_0.1Te_0.6S_0.2Se_0.2 HEM (Fig. 12C). In another study for the (Ag, Sb, Ge)(S, Se, Te) system by Yang et al., they found a very low k of ∼0.66 W m⁻¹ K⁻¹ and a high α (>250 μV K⁻¹) both at 700 K, while the reported ZT was found to be 0.3 at 700 K for Ge_0.9−2xAg_2xSb_0.1S_0.5Se_0.1Te_0.4 with (x = 0–0.06) HEM.²⁴⁹ Yang et al.²⁵⁰ have studied the same (Ag, Sb, Sn)(S, Se, Te) system but having different stoichiometries, and the obtained k was remarkably low, measuring only 1.27 W m⁻¹ K⁻¹ at 300 K for the (Ag_0.15Sb_0.15Sn_0.7)(S_0.15Se_0.15Te_0.7) HEM resulting in a maximum ZT of 1.02 at 850 K. For the HEMC (Ag, Pb, Bi)(S, Se, Te) system, Yamashita et al.²⁵¹ applied the entropy-driven concept and the reported properties were an ultra-low lattice k of 0.46 W m⁻¹ K⁻¹ and a maximum PF of 4.4 μW cm⁻¹ K⁻² both at 723 K, which induced a ZT of 0.54 at 723 K for the Ag_0.25Pb_0.50Bi_0.25S_0.40Se_0.50Te_0.10 HEM. Yaprintseva et al.²⁵² synthesized a single-phase (Bi_2/3Sb_1/3)₂(Te_2/5Se_2/5S_1/5)₃ HEM through a multi-step process and the obtained ZT was found to be 0.3 at 570 K. The same group studied the TE properties of the HE Bi–Sb–Te–Se–S system and the obtained maximum ZT was 0.18 at 475 K for the Bi_1.5Sb_0.5Te_1.25Se_1.25S_0.5 HEM.²⁵³ They have also investigated a single-phase PbSbTeSe with a ZT of 0.43 730 K, but the latter is classified as a medium-entropy material.²⁵⁴ Deng et al.²⁴⁷ studied the TE properties of the (Ge, Sn, Pb)(S, Se, Te) HE system. The measured TE properties of a 2% Na-doped Ge_1/3Sn_1/3Pb_1/3S_1/3Se_1/3Te_1/3 HEM are approximately 200 μV K⁻¹ for α and 0.75 W cm⁻¹ K⁻¹ for k both at 600 K. Samanta et al.²⁵⁵ applied the entropy-driven concept on GeTe-based materials where they reported a high ZT of 1.8 at 660 K for the (GeTe)₈₀(AgSbSe₂)₂₀ HEM. Also, Liang et al.²⁵⁶ found a ZT ≈ 1.54 at 773 K for the Ge_0.58Sb_0.22Te_0.8(AgSnSe₂)_0.2 HEM. Zhang et al.²⁵⁷ introduced a novel approach that combines colloidal synthesis and sintering to create nanostructured materials while preserving ligands. The resulting nanostructured sample of Cu_1.87Ag_0.13(In_0.06Sn_0.94)Se₂S in the cubic phase achieves exceptional TE performance, including a high PF of 0.44 mW m⁻¹ K⁻², an incredibly low k of 0.25 W m⁻¹ K⁻¹, and an impressive ZT of 1.52 at 873 K. Similar to that, Raphel et al.²⁵⁸ investigated the TE performances of the nanostructured PbSn_0.875TeSeBi_0.125 HE material using mechanical alloying (MA) and SPS. The entropy-driven approach led to a remarkable result with a peak PF of 12.74 × 10⁻⁴ W m⁻¹ K⁻² and an exceptionally low k of 0.81 W m⁻¹ K⁻¹, leading to a significantly improved ZT of 0.71 at 623 K. With a peak ZT of 0.47, this value is higher in comparison to that of the pure PbSnTeSe.²⁵⁹ The same group has designed a nanocrystalline Pb_0.99SnTeSe-Na_0.01 HEM with a band tuning approach.²⁶⁰ The resulted TE properties are significantly improved, elevating the α from 159.67 μV K⁻¹ to 230 μV K⁻¹, which in turn results in a substantial increase in the PF to 15 × 10⁻⁴ W m⁻¹ K⁻². Consequently, this transformation yields a superior ZT of 0.84 at 573 K.²⁶⁰ Recently, they incorporated Ag with different concentrations (0–0.9 at%) into a nanocrystalline lead tin tellurium selenium (PbSnTeSe).²⁶¹ They combined the entropy-driven concept, band engineering, and nanostructuring techniques, resulting in a significant reduction in k, achieving an exceptionally low value of 0.814 W m⁻¹ K⁻¹. This reduction leads to a substantial enhancement in the PF, reaching 14.16 × 10⁻⁴ W m⁻¹ K⁻² and a remarkable ZT of 0.891 at 573 K for the nanostructured PbSnTeSe-0.9Ag HEM, representing a remarkable 225% improvement compared to the pristine PbSnTeSe HEA.²⁶¹ Xin et al.²⁶² also applied the entropy-driven concept on the (Pb, Sn)(Se, Te) system. They found a ZT value of 0.85 at 773 K for the Sn_0.61Mn_0.09Pb_0.3Te_0.7Se_0.3 HEM, which has increased 113% compared to that of the original SnTe-based TE material, accompanied by an ultralow k_l of 0.48 W cm⁻¹ K⁻¹ at 773 K, which has been obtained via the phonon scattering of the configurational entropy. Similar to that, Fan et al. found that doping 1.5% La into the PbSnTeSe system leads to an increase in the ZT, about 0.8 at 873 K of the PbSnTeSeLa_0.015 HEM.²⁶³ The same group applied the entropy-driven concept by alloying Ag in the (BiSbTe_1.5 Se_1.5) system and found an ultra-low k and a maximum ZT of 0.63 at 450 K for the (BiSbTe_1.5 Se_1.5)_0.1Ag_0.9 HEM, exhibiting approximately threefold improvement compared to 0.2 at 450 K for the pristine material.²⁶⁴ However, increasing the Ag content led to the formation of an Ag-rich secondary phase, which resulted in a reduction of ZT values. This highlights the difficulty and complexity of enhancing the TE performance of HEMs. Li et al.²⁶⁵ have applied the entropy-driven concept on the (SnTe)(AgSe) system. The ZT of (Sn_0.875Ge_0.05Bi_0.075Te)_0.95(Ag₂Se)_0.05 was found to be 0.8 at 750 K compared to 0.22 for pristine SnTe,²⁶⁵ highlighting the effect of the entropy-driven concept in enhancing the TE performances. Recently, Yang et al. combined the entropy-driven concept and electronic structure design of the (Cu₅Sn₂Se₇)_1−x(In₂Te₃)_x system.²⁶⁶ They found a very low k_L of 0.46 W K⁻¹ m⁻¹ and a ZT of 0.7 at 770 K for (Cu₅Sn₂Se₇)_0.9(In₂Te₃)_0.1, which is 4.7 times higher than that of Cu₅Sn₂Se₇. Bo et al. obtained a high ZT of 1.37 at 750 K for Cu_2.91(MnFeNi)_0.09Se_0.99Te_0.01 with a very low k of ∼0.4 W m⁻¹ K⁻¹ at RT²⁶⁷ and a ZT of 0.84 was obtained at 650 K for Cu_2.9Ag_0.1Sb_0.95Te_0.05Se₄.²⁶⁸ Another exploration of the (Co, Fe, Ni)₉(S, Se)₈ material yielded ZT below 0.03 around 325 K, and it decreased with increasing temperature, showcasing the limitations of this combination.²⁶⁹ Similar to that, Wu et al. have applied the entropy-driven concept on AgBi₃(Se_yS_1−y)₅ to boost the TE performance and found a ZT of 0.42 at 723 K for the AgBi₃(Se_0.9S_0.1)_5.08 sample.²⁷⁰ The same system was investigated by Yang et al., and they obtained a maximum ZT of 0.5 at 773 K.²⁷¹ Similar to that, Cherniushok et al.²⁷² found a ZT of 0.75 at 673 K for Cu₇P(S_0.5Se_0.5)₆ with the highest configurational entropy.

Fig. 12 (A) Temperature dependent (a₁) k_l and (a₂) ZT of the Pb_0.99−xSb_0.012Sn_ySe_1−2xTe_xS_x (x = 0 to 0.25 and y = 0 to 0.2) HEM compared to those of some traditional PbSe-based materials. Reproduced with permission.⁴⁴ © 2021 The American Association for the Advancement of Science. (B) Temperature dependent (b₁) k and (b₂) ZT of the Pb_0.975−xCd_xNa_0.025Se_0.5S_0.25Te_0.25 (x = 0, 0.01, 0.02, 0.03, 0.04, and 0.05) HEM compared to that of Pb_0.975Na_0.025Se and Pb_0.935Na_0.025Cd_0.04Se. Reproduced under terms of the CC-BY 4.0 license.⁴⁵ © 2021 The Authors. Published by Springer Nature. (C) Temperature dependence of (c₁) total k and (c₂) ZT for Cu₂Te_1−2xS_xSe_x (x = 0, 0.1, 0.2 and 0.25). The inset shows a comparison of the compressive strength of Cu_2−yAg_yTe_1−2xS_xSe_x ingots at RT. Reproduced with permission.²⁴⁸ © 2022 Elsevier Ltd.

Importantly, some of these compositions are better classified as dual-doped ME materials rather than HE materials since the concentrations of elements are below the 5 mol% threshold established as a requirement for HEMs as discussed in Section 3.1. Hence, this class of HEMCs shows the best thermoelectric performances (Table 4). Firstly, due to the presence of metal chalcogenides, they are appealing as the state-of-the-art TEMs (see Fig. 2C). Secondly, the application of the entropy driven effect leads to the phonon's scattering, resulting in reduced k. Moreover, it should be noted that the combination of metals and chalcogenides is not always favorable in terms of TE performance.²⁶⁹ The HE engineering investigations have revealed that the configurational entropy must be sufficiently high to induce one or more core effects while remaining sufficiently low to maintain a decent carrier mobility. To achieve high-performance TE materials, it is necessary to compensate for the reduced carrier mobility in HEMs through band convergence, effective mass, and carrier concentration.

Table 4 TE properties of HEMC based materials reported in the literature

Compound	T (K)	k (W m^−1 K^−1)	ZT	Ref.	Year
(Cu5Sn1.2MgGeZn)S9	773	1.05	0.58	Zhang et al.^137	2018
Ge0.61Ag0.11Sb0.13Pb0.12Bi0.01Te	750	0.3	2.7	Jiang et al.^42	2022
(GeTe)0.80(AgSb0.5Bi0.5Te2)0.20	723	1.2	1.6	Zhong et al.^218	2022
Ge0.82Sb0.08Te0.90(MnZnCdTe3)0.10	723	0.4	1.24	Huang et al.^219	2022
Ge0.84In0.01Pb0.1Sb0.05Te0.997I0.003	800	0.75	2.1	Qiu et al.^220	2019
Ge0.84Pb0.025Sn0.025Sb0.11Te	723	1.1	2.3	Das et al.^221	2023
PbGeSnCd0.08Te3.08	875	1.2	1.63	Liu et al.^223	2023
AgMnGeSbTe4	773	0.88	1.05	Ma et al.^224	2021
AgMnGeSbTe4-1 mol% Ag8GeTe6	773	0.85	1.27
AgMnSn0.25Pb0.75SbTe4	773	0.65	1.3	Ma et al.^225	2022
Cu0.8Ag0.2In0.5Ga0.5Te2	900	0.55	1.6	Liu et al.^48	2017
Cu0.8Ag0.2(ZnGe)0.1(GaIn)0.4Te2	820	0.5	1.02	Cai et al.^227	2021
Sn0.555Ge0.15Pb0.075Mn0.275Te	900	1.2	1.42	Hu et al.^46	2018
Sn0.25Pb0.25Mn0.25Ge0.25Te	823	1	1.4	Wang et al.^228	2021
Ga0.025(Sn0.25Pb0.25Mn0.25Ge0.25)0.975Te	823	0.75	1.52
Cu0.8Ag0.2(Ga0.8In0.2)0.99Zn0.01Te2	850	0.6	1.56	Acharya et al.^229	2023
Cu0.8Ag0.2Zn0.1Ga0.4Ge0.1In0.4Te2	800	0.6	1.02	Jiang et al.^230	2021
AgBi0.8Sb0.2Se1.98Br0.02	790	0.42	0.86	Zhao et al.^234	2021
(GeSe)0.5(AgBiSe2)0.5	677	0.6	0.45	Roychowdhury et al.^235	2018
(AgSbSe2)0.7(MnSe)0.3	750	0.42	0.69	Ma et al.^236	2023
(AgSbSe2)0.7(Mn0.99Se)0.3	750	0.4	1.18
(Ag0.99Nb0.01BiSe2)0.8(PbS)0.2	773	0.5	0.65	Zhang et al.^237	2023
(AgBiSe2)0.925(Ag2Te)0.075	760	0.3	1.0	Xia et al.^238	2021
(AgBiSe2)0.7(PbSe)0.3-Br 1%	800	0.48	0.8	Zhu et al.^239	2020
AgSnSbSe1.5Te1.5	723	0.7	1.14	Luo et al.^240	2020
Pb0.89Sb0.012Sn0.1Se0.5Te0.25S0.25	900	0.3	1.8	Jiang et al.^44	2021
Pb0.935Na0.025Cd0.04Se0.5S0.25Te0.25	900	0.75	2	Jiang et al.^45	2021
Cu1.9Ag0.1Te0.6S0.2Se0.2	1000	0.7	1.4	Zhang et al.^248	2022
Ge0.82Ag0.08Sb0.1S0.5Se0.1Te0.4-Ag 4%	675	0.66	0.3	Yang et al.^249	2022
(Ag0.15Sb0.15Sn0.7)(S0.15Se0.15Te0.7)	850	1.3	1.02	Yang et al.^250	2021
Ag0.25Pb0.50Bi0.25S0.40Se0.50Te0.10	723	0.62	0.54	Yamashita et al.^251	2021
(Bi2/3Sb1/3)2(Te2/5Se2/5S1/5)3	570	0.97	0.3	Yaprintseva et al.^252	2023
Bi1.5Sb0.5Te1.25Se1.25S0.5	475	0.66	0.18	Vasil’ev et al.^253	2023
(GeTe)80(AgSbSe2)20	660	0.6	1.8	Samanta et al.^255	2017
Ge0.58Sb0.22Te0.8(AgSnSe2)0.2	773	0.9	1.54	Liang et al.^256	2021
Cu1.87Ag0.13(In0.06Sn0.94)Se2S	873	0.25	1.52	Zhang et al.^257	2022
PbSn0.875TeSeBi0.125	623	0.9	0.71	Raphel et al.^258	2021
Pb0.99SnTeSe-Na0.01	573	1.1	0.84	Raphel et al.^260	2022
PbSnTeSe-0.9Ag	573	0.9	0.891	Raphel et al.^261	2023
Sn0.61Mn0.09Pb0.3Te0.7Se0.3	773	1.65	0.86	Xin et al.^262	2022
PbSnTeSeLa0.015	873	1.4	0.8	Fan et al.^263	2016
(BiSbTe1.5Se1.5)0.1Ag0.9	450	0.48	0.63	Fan et al.^264	2016
(Sn0.875Ge0.05Bi0.075Te)0.95(Ag2Se)0.05	750	2.1	0.8	Li et al.^265	2022
(Cu5Sn2Se7)0.9(In2Te3)0.1	770	1.4	0.7	Yang et al.^266	2022

---

5. Conclusions and perspectives

To solve the global energy crisis, TEMs are crucial in renewable energy technologies. TEMs, which allow the direct conversion of heat to electricity, have drawn wide attention over the past few decades. The TE performance of a device is highly dependent on the used type of materials and their properties, such as the Seebeck coefficient and thermal and electrical conductivities. Recently, a brand-new method has been proposed to design alloys with several main elements in equimolar or near-equimolar ratios, called HEAs. This novel class of alloys typically exhibits a severe lattice distortion due to chemical complexity and high configuration entropy as well as high-temperature phase stability, which reduces the lattice k because the phonon scattering is enhanced.

The performance of a HEM is strongly related to its constituent elements, whereas the design of novel sustainable and low-cost materials remains a major challenge especially since the state of the art in TEMs is full of materials with the presence of the toxic and expensive Se and Te. In this review paper, the definition of a HEM, the transition from HEAs to HEMs for TE applications, the TE effect and its characteristic variables were detailed. For TE applications, four main categories of HEMs have been reported in the literature, namely HE-alloys, HE-oxides, HE-metal chalcogenides and HE-HH TEMs. It was commonly concluded that the phase transition was reduced and stabilized, and the phonon scattering led to a low k and high figure of merit. The TE properties of HEMs are summarized in Fig. 13.

Fig. 13 Reported ZT maximum values for HETEMs in the literature.

However, this topic is in its early stages taking into account the unlimited possibility of the HE composition, which allows the exploration of novel high-performance HETEMs. (i) These materials could be engineered to achieve band convergence, leading to high-power factors by the optimization of electrical conductivity and the Seebeck coefficient through tuning the elemental composition and its distribution in band structures. (ii) Designing HETEMs with improved stability at high temperatures and mechanical robustness is essential for ensuring long-term performance and reliability of TE devices, which is crucial for practical applications such as waste heat recovery, energy harvesting, and cooling systems. (iii) The integration of HETEMs with nanostructuring techniques (nanocomposites and interfaces) will further improve TE performance by manipulating charge and phonon transport. (iv) High-throughput synthesis and modeling enable the design of next-generation HETEMs with desirable properties. The development of advanced techniques allows the simultaneous preparation of hundreds of compositions, and automated characterization will create a vast database. Evaluating existing databases using advanced computational modeling is necessary to identify promising candidates with much improved TE performance in comparison to that of conventional materials. (v) It is crucial to consider the environmental implications and the concept of sustainability in the development of HETEMs composed of abundant and non-toxic elements while also examining sustainable synthesis methods to reduce the environmental impact. In conclusion, HEMs exhibit significant potential for the advancement of TE technology. Researchers should direct their research strategies towards these materials, overcoming current obstacles, and fully harnessing their potential in TE applications.

List of abbreviations and acronyms

APT	Atom probe tomography
BCC	Body-centered cubic
DOS	Density of states
FCC	Face-centered cubic
HCP	Hexagonal close-packed
HEAs	High-entropy
HEAs	High-entropy alloys
HECs	High-entropy ceramics
HEMs	High-entropy materials
HEOs	High-entropy oxides
HEMCs	High-entropy metal chalcogenides
HETEMs	High-entropy thermoelectric materials
HH	half-Heusler
MA	Mechanical alloying
MOFs	Metal–organic frameworks
PF	Power factor
PGEC	Phonon glass-electron crystal
SPS	Spark plasma sintering
TE	Thermoelectric
TEGs	Thermoelectric generators
TEMs	thermoelectric materials
ZT	Figure-of-merit
α	Seebeck coefficient

Author contributions

Nouredine Oueldna: conceptualization, investigation, validation, visualization, writing – original draft, and writing – review and editing. Noha Sabi: investigation, validation, and writing – review and editing. Hasna Aziam: validation and writing – review and editing. Vera Trabadelo: validation and writing – review and editing. Hicham Ben Youcef: resources, validation, supervision, and writing – review and editing.

Conflicts of interest

There are no conflicts to declare.

References

1. M. Massetti, F. Jiao, A. J. Ferguson, D. Zhao, K. Wijeratne, A. Wurger, J. L. Blackburn, X. Crispin and S. Fabiano, Chem. Rev., 2021, 121, 12465–12547.
2. X. L. Shi, J. Zou and Z. G. Chen, Chem. Rev., 2020, 120, 7399–7515.
3. C. B. Vining, Nat. Mater., 2009, 8, 83–85.
4. D. B. Gingerich and M. S. Mauter, Environ. Sci. Technol., 2015, 49, 8297–8306.
5. B. Poudel, Q. Hao, Y. Ma, Y. Lan, A. Minnich, B. Yu, X. Yan, D. Wang, A. Muto, D. Vashaee, X. Chen, J. Liu, M. S. Dresselhaus, G. Chen and Z. Ren, Science, 2008, 320, 634–638.
6. Q. Yan and M. G. Kanatzidis, Nat. Mater., 2022, 21, 503–513.
7. L. Yang, Z. G. Chen, M. S. Dargusch and J. Zou, Adv. Energy Mater., 2017, 8, 1701797.
8. J. He and T. M. Tritt, Science, 2017, 357, eaak9997.
9. K. Biswas, J. He, I. D. Blum, C. I. Wu, T. P. Hogan, D. N. Seidman, V. P. Dravid and M. G. Kanatzidis, Nature, 2012, 489, 414–418.
10. L. E. Bell, Science, 2008, 321, 1457–1461.
11. Y. Xiao and L. D. Zhao, Science, 2020, 367, 1196–1197.
12. J. Pei, B. Cai, H. L. Zhuang and J. F. Li, Natl. Sci. Rev., 2020, 7, 1856–1858.
13. A. Nadtochiy, V. Kuryliuk, V. Strelchuk, O. Korotchenkov, P. W. Li and S. W. Lee, Sci. Rep., 2019, 9, 16335.
14. A. Singha and B. Muralidharan, Sci. Rep., 2017, 7, 7879.
15. J. P. Heremans, B. Wiendlocha and A. M. Chamoire, Energy Environ. Sci., 2012, 5, 5510–5530.
16. Y. Pei, X. Shi, A. LaLonde, H. Wang, L. Chen and G. J. Snyder, Nature, 2011, 473, 66–69.
17. J. P. Heremans, V. Jovovic, E. S. Toberer, A. Saramat, K. Kurosaki, A. Charoenphakdee, S. Yamanaka and G. J. Snyder, Science, 2008, 321, 554–557.
18. X. Su, P. Wei, H. Li, W. Liu, Y. Yan, P. Li, C. Su, C. Xie, W. Zhao, P. Zhai, Q. Zhang, X. Tang and C. Uher, Adv. Mater., 2017, 29, 1602013.
19. Z. Chen, B. Ge, W. Li, S. Lin, J. Shen, Y. Chang, R. Hanus, G. J. Snyder and Y. Pei, Nat. Commun., 2017, 8, 13828.
20. G. J. Snyder and E. S. Toberer, Nat. Mater., 2008, 7, 105–114.
21. A. Majumdar, Science, 2004, 303, 777–778.
22. J. W. Yeh, S. K. Chen, S. J. Lin, J. Y. Gan, T. S. Chin, T. T. Shun, C. H. Tsau and S. Y. Chang, Adv. Eng. Mater., 2004, 6, 299–303.
23. B. Cantor, I. T. H. Chang, P. Knight and A. J. B. Vincent, Mater. Sci. Eng., A, 2004, 375–377, 213–218.
24. C. Oses, C. Toher and S. Curtarolo, Nat. Rev. Mater., 2020, 5, 295–309.
25. E. P. George, D. Raabe and R. O. Ritchie, Nat. Rev. Mater., 2019, 4, 515–534.
26. S. Praveen and H. S. Kim, Adv. Eng. Mater., 2017, 20, 1700645.
27. Y. F. Ye, Q. Wang, J. Lu, C. T. Liu and Y. Yang, Mater. Today, 2016, 19, 349–362.
28. O. N. Senkov, J. D. Miller, D. B. Miracle and C. Woodward, Nat. Commun., 2015, 6, 6529.
29. H. Xiang, F.-Z. Dai and Y. Zhou, High-Entropy Materials From Basics to Applications, John Wiley and Sons, 2023.
30. K. Li and W. Chen, Mater. Today Energy, 2021, 20, 100638.
31. Y. Sun and S. Dai, Sci. Adv., 2021, 7, eabg1600.
32. A. Amiri and R. Shahbazian-Yassar, J. Mater. Chem. A, 2021, 9, 782–823.
33. M. Fu, X. Ma, K. Zhao, X. Li and D. Su, iScience, 2021, 24, 102177.
34. Y. Ma, Y. Ma, Q. Wang, S. Schweidler, M. Botros, T. Fu, H. Hahn, T. Brezesinski and B. Breitung, Energy Environ. Sci., 2021, 14, 2883–2905.
35. X. Wang, W. Guo and Y. Fu, J. Mater. Chem. A, 2021, 9, 663–701.
36. H. Xiang, Y. Xing, F.-Z. Dai, H. Wang, L. Su, L. Miao, G. Zhang, Y. Wang, X. Qi, L. Yao, H. Wang, B. Zhao, J. Li and Y. Zhou, J. Adv. Ceram., 2021, 10, 385–441.
37. M. J. R. Haché, C. Cheng and Y. Zou, J. Mater. Res., 2020, 35, 1051–1075.
38. A. Sarkar, Q. Wang, A. Schiele, M. R. Chellali, S. S. Bhattacharya, D. Wang, T. Brezesinski, H. Hahn, L. Velasco and B. Breitung, Adv. Mater., 2019, 31, e1806236.
39. M. C. Gao, D. B. Miracle, D. Maurice, X. Yan, Y. Zhang and J. A. Hawk, J. Mater. Res., 2018, 33, 3138–3155.
40. C. M. Rost, E. Sachet, T. Borman, A. Moballegh, E. C. Dickey, D. Hou, J. L. Jones, S. Curtarolo and J. P. Maria, Nat. Commun., 2015, 6, 8485.
41. J. Dong and Q. Yan, Mater. Lab, 2023, 2, 230001.
42. B. Jiang, W. Wang, S. Liu, Y. Wang, C. Wang, Y. Chen, L. Xie, M. Huang and J. He, Science, 2022, 377, 208–213.
43. M. G. Kanatzidis, Mater. Lab, 2022, 1, 220048.
44. B. Jiang, Y. Yu, J. Cui, X. Liu, L. Xie, J. Liao, Q. Zhang, Y. Huang, S. Ning, B. Jia, B. Zhu, S. Bai, L. Chen, S. J. Pennycook and J. He, Science, 2021, 371, 830–834.
45. B. Jiang, Y. Yu, H. Chen, J. Cui, X. Liu, L. Xie and J. He, Nat. Commun., 2021, 12, 3234.
46. L. Hu, Y. Zhang, H. Wu, J. Li, Y. Li, M. McKenna, J. He, F. Liu, S. J. Pennycook and X. Zeng, Adv. Energy Mater., 2018, 8, 1802116.
47. X. Du and K. Zhang, Nano Energy, 2022, 101, 107600.
48. R. Liu, H. Chen, K. Zhao, Y. Qin, B. Jiang, T. Zhang, G. Sha, X. Shi, C. Uher, W. Zhang and L. Chen, Adv. Mater., 2017, 29, 1702712.
49. N. Dragoe and D. Berardan, Science, 2019, 366, 573–574.
50. C. M. Rost, T. Borman, M. D. Hossain, M. Lim, K. F. Quiambao-Tomko, J. A. Tomko, D. W. Brenner, J.-P. Maria and P. E. Hopkins, Acta Mater., 2020, 196, 231–239.
51. J. L. Braun, C. M. Rost, M. Lim, A. Giri, D. H. Olson, G. N. Kotsonis, G. Stan, D. W. Brenner, J. P. Maria and P. E. Hopkins, Adv. Mater., 2018, 30, e1805004.
52. D. Berardan, A. K. Meena, S. Franger, C. Herrero and N. Dragoe, J. Alloys Compd., 2017, 704, 693–700.
53. S. Shafeie, S. Guo, Q. Hu, H. Fahlquist, P. Erhart and A. Palmqvist, J. Appl. Phys., 2015, 118, 184905.
54. Y. Wang, Y.-J. Hu, B. Bocklund, S.-L. Shang, B.-C. Zhou, Z.-K. Liu and L.-Q. Chen, Phys. Rev. B, 2018, 98, 224101.
55. Y. Pei, A. D. LaLonde, H. Wang and G. J. Snyder, Energy Environ. Sci., 2012, 5, 7963–7969.
56. H. Xie, X. Su, T. P. Bailey, C. Zhang, W. Liu, C. Uher, X. Tang and M. G. Kanatzidis, Chem. Mater., 2020, 32, 2639–2646.
57. X. Zhang and L.-D. Zhao, J. Materiomics, 2015, 1, 92–105.
58. X.-L. Shi, W.-Y. Chen, X. Tao, J. Zou and Z.-G. Chen, Mater. Horiz., 2020, 7, 3065–3096.
59. W. Liu, X. Yan, G. Chen and Z. Ren, Nano Energy, 2012, 1, 42–56.
60. A. J. Minnich, M. S. Dresselhaus, Z. F. Ren and G. Chen, Energy Environ. Sci., 2009, 2, 466–479.
61. G. Tan, L. D. Zhao and M. G. Kanatzidis, Chem. Rev., 2016, 116, 12123–12149.
62. S. I. Kim, K. H. Lee, H. A. Mun, H. S. Kim, S. W. Hwang, J. W. Roh, D. J. Yang, W. H. Shin, X. S. Li, Y. H. Lee, G. J. Snyder and S. W. Kim, Science, 2015, 348, 109–114.
63. D. A. Wright, Nature, 1958, 181, 834.
64. C. Zhou, Y. K. Lee, Y. Yu, S. Byun, Z. Z. Luo, H. Lee, B. Ge, Y. L. Lee, X. Chen, J. Y. Lee, O. Cojocaru-Miredin, H. Chang, J. Im, S. P. Cho, M. Wuttig, V. P. Dravid, M. G. Kanatzidis and I. Chung, Nat. Mater., 2021, 20, 1378–1384.
65. L. Mao, Y. Yin, Q. Zhang, G.-Q. Liu, H. Wang, Z. Guo, H. Hu, Y. Xiao, X. Tan and J. Jiang, Energy Environ. Sci., 2020, 13, 616–621.
66. Y. K. Lee, Z. Luo, S. P. Cho, M. G. Kanatzidis and I. Chung, Joule, 2019, 3, 719–731.
67. C. Chang, M. Wu, D. He, Y. Pei, C. F. Wu, X. Wu, H. Yu, F. Zhu, K. Wang, Y. Chen, L. Huang, J. F. Li, J. He and L. D. Zhao, Science, 2018, 360, 778–783.
68. L. D. Zhao, G. Tan, S. Hao, J. He, Y. Pei, H. Chi, H. Wang, S. Gong, H. Xu, V. P. Dravid, C. Uher, G. J. Snyder, C. Wolverton and M. G. Kanatzidis, Science, 2016, 351, 141–144.
69. L. D. Zhao, S. H. Lo, Y. Zhang, H. Sun, G. Tan, C. Uher, C. Wolverton, V. P. Dravid and M. G. Kanatzidis, Nature, 2014, 508, 373–377.
70. J. Li, X. Zhang, Z. Chen, S. Lin, W. Li, J. Shen, I. T. Witting, A. Faghaninia, Y. Chen, A. Jain, L. Chen, G. J. Snyder and Y. Pei, Joule, 2018, 2, 976–987.
71. S. Perumal, P. Bellare, U. S. Shenoy, U. V. Waghmare and K. Biswas, Chem. Mater., 2017, 29, 10426–10435.
72. D. Byeon, R. Sobota, K. Delime-Codrin, S. Choi, K. Hirata, M. Adachi, M. Kiyama, T. Matsuura, Y. Yamamoto, M. Matsunami and T. Takeuchi, Nat. Commun., 2019, 10, 72.
73. T. Mao, P. Qiu, X. Du, P. Hu, K. Zhao, J. Xiao, X. Shi and L. Chen, Adv. Funct. Mater., 2019, 30, 1908315.
74. A. A. Olvera, N. A. Moroz, P. Sahoo, P. Ren, T. P. Bailey, A. A. Page, C. Uher and P. F. P. Poudeu, Energy Environ. Sci., 2017, 10, 1668–1676.
75. L. L. Zhao, X. L. Wang, J. Y. Wang, Z. X. Cheng, S. X. Dou, J. Wang and L. Q. Liu, Sci. Rep., 2015, 5, 7671.
76. W. Ren, W. Xue, S. Guo, R. He, L. Deng, S. Song, A. Sotnikov, K. Nielsch, J. van den Brink, G. Gao, S. Chen, Y. Han, J. Wu, C. W. Chu, Z. Wang, Y. Wang and Z. Ren, Nat. Commun., 2023, 14, 4722.
77. J. Shen, C. Fu, Y. Liu, X. Zhao and T. Zhu, Energy Storage Mater., 2018, 10, 69–74.
78. C. Fu, T. Zhu, Y. Liu, H. Xie and X. Zhao, Energy Environ. Sci., 2015, 8, 216–220.
79. S. Chen, K. C. Lukas, W. Liu, C. P. Opeil, G. Chen and Z. Ren, Adv. Energy Mater., 2013, 3, 1210–1214.
80. N. Oueldna, A. Portavoce, M. Bertoglio, M. Descoins, A. Kammouni and K. Hoummada, J. Alloys Compd., 2023, 932, 167692.
81. N. Oueldna, A. Portavoce, M. Bertoglio, A. Campos, A. Kammouni and K. Hoummada, J. Alloys Compd., 2022, 900, 163534.
82. X. Li, P. F. Liu, E. Zhao, Z. Zhang, T. Guidi, M. D. Le, M. Avdeev, K. Ikeda, T. Otomo, M. Kofu, K. Nakajima, J. Chen, L. He, Y. Ren, X. L. Wang, B. T. Wang, Z. Ren, H. Zhao and F. Wang, Nat. Commun., 2020, 11, 942.
83. Z. Liu, J. Mao, J. Sui and Z. Ren, Energy Environ. Sci., 2018, 11, 23–44.
84. W. Li, L. Zheng, B. Ge, S. Lin, X. Zhang, Z. Chen, Y. Chang and Y. Pei, Adv. Mater., 2017, 29, 1605887.
85. G. Tan, L. D. Zhao, F. Shi, J. W. Doak, S. H. Lo, H. Sun, C. Wolverton, V. P. Dravid, C. Uher and M. G. Kanatzidis, J. Am. Chem. Soc., 2014, 136, 7006–7017.
86. Y. Pei, A. D. LaLonde, N. A. Heinz and G. J. Snyder, Adv. Energy Mater., 2012, 2, 670–675.
87. Y. Pei, A. LaLonde, S. Iwanaga and G. J. Snyder, Energy Environ. Sci., 2011, 4, 2085–2089.
88. J. Wang, O. I. Lebedev, K. Lee, J. A. Dolyniuk, P. Klavins, S. Bux and K. Kovnir, Chem. Sci., 2017, 8, 8030–8038.
89. X. Shi, J. Yang, S. Bai, J. Yang, H. Wang, M. Chi, J. R. Salvador, W. Zhang, L. Chen and W. Wong-Ng, Adv. Funct. Mater., 2010, 20, 755–763.
90. W. Tang, W. Qian, S. Jia, K. Li, Z. Zhou, J. Lan, Y.-H. Lin and X. Yang, Mater. Today Phys., 2023, 35, 101104.
91. J. Li, J. Sui, Y. Pei, C. Barreteau, D. Berardan, N. Dragoe, W. Cai, J. He and L.-D. Zhao, Energy Environ. Sci., 2012, 5, 8543–8547.
92. Y. Tang, Z. M. Gibbs, L. A. Agapito, G. Li, H. S. Kim, M. B. Nardelli, S. Curtarolo and G. J. Snyder, Nat. Mater., 2015, 14, 1223–1228.
93. X. Shi, J. Yang, J. R. Salvador, M. Chi, J. Y. Cho, H. Wang, S. Bai, J. Yang, W. Zhang and L. Chen, J. Am. Chem. Soc., 2011, 133, 7837–7846.
94. S. M. Pourkiaei, M. H. Ahmadi, M. Sadeghzadeh, S. Moosavi, F. Pourfayaz, L. Chen, M. A. Pour Yazdi and R. Kumar, Energy, 2019, 186, 115849.
95. A. Nozariasbmarz, H. Collins, K. Dsouza, M. H. Polash, M. Hosseini, M. Hyland, J. Liu, A. Malhotra, F. M. Ortiz, F. Mohaddes, V. P. Ramesh, Y. Sargolzaeiaval, N. Snouwaert, M. C. Özturk and D. Vashaee, Appl. Energy, 2020, 258, 114069.
96. C. Li, F. Jiang, C. Liu, P. Liu and J. Xu, Appl. Mater. Today, 2019, 15, 543–557.
97. F. Fitriani, R. Ovik, B. D. Long, M. C. Barma, M. Riaz, M. F. M. Sabri, S. M. Said and R. Saidur, Renewable Sustainable Energy Rev., 2016, 64, 635–659.
98. C.-D. Zhou, B. Liang, W.-J. Huang, J.-G. Noudem, X.-J. Tan and J. Jiang, Rare Met., 2023, 42, 2825–2839.
99. L. Su, D. Wang, S. Wang, B. Qin, Y. Wang, Y. Qin, Y. Jin, C. Chang and L. D. Zhao, Science, 2022, 375, 1385–1389.
100. L. Zhao, Mater. Lab, 2022, 1, 1–3.
101. B. Qin, D. Wang, X. Liu, Y. Qin, J. F. Dong, J. Luo, J. W. Li, W. Liu, G. Tan, X. Tang, J. F. Li, J. He and L. D. Zhao, Science, 2021, 373, 556–561.
102. N. Oueldna, A. Portavoce, M. Bertoglio, M. Descoins, A. Kammouni and K. Hoummada, Mater. Lett., 2020, 266, 127460.
103. C. J. Vineis, A. Shakouri, A. Majumdar and M. G. Kanatzidis, Adv. Mater., 2010, 22, 3970–3980.
104. P. Pichanusakorn and P. Bandaru, Mater. Sci. Eng., R, 2010, 67, 19–63.
105. M. G. Kanatzidis, Chem. Mater., 2009, 22, 648–659.
106. R. Chen, Y. Wang, L. Jiang, R. Min, H. Kang, Z. Chen, E. Guo, X. Yang, X. Jiang and T. Wang, Mater. Today Phys., 2023, 30, 100957.
107. C. Gayner and Y. Amouyal, Adv. Funct. Mater., 2019, 30, 1901789.
108. T. Zou, X. Qin, Y. Zhang, X. Li, Z. Zeng, D. Li, J. Zhang, H. Xin, W. Xie and A. Weidenkaff, Sci. Rep., 2015, 5, 17803.
109. W. Xie, A. Weidenkaff, X. Tang, Q. Zhang, J. Poon and T. M. Tritt, Nanomaterials, 2012, 2, 379–412.
110. N. J. Peter, M. J. Duarte, C. H. Liebscher, V. C. Srivastava, V. Uhlenwinkel, E. A. Jägle and G. Dehm, J. Alloys Compd., 2020, 820, 153149.
111. B. Gwalani, S. Gangireddy, S. Shukla, C. J. Yannetta, S. G. Valentin, R. S. Mishra and R. Banerjee, Mater. Today Commun., 2019, 20, 100602.
112. B. Gludovatz, E. P. George and R. O. Ritchie, JOM, 2015, 67, 2262–2270.
113. W. Zhang, P. K. Liaw and Y. Zhang, Sci. China: Mater., 2018, 61, 2–22.
114. J.-W. Yeh, JOM, 2013, 65, 1759–1771.
115. J.-W. Yeh, Annales de Chimie Science des Matériaux, 2006, 31, 633–648.
116. E. J. Pickering and N. G. Jones, Int. Mater. Rev., 2016, 61, 183–202.
117. Y. Zhang, T. T. Zuo, Z. Tang, M. C. Gao, K. A. Dahmen, P. K. Liaw and Z. P. Lu, Prog. Mater. Sci., 2014, 61, 1–93.
118. Q. He and Y. Yang, Front. Mater., 2018, 5, 2296–8016.
119. J. Dong, D. Zhang, J. Liu, Y. Jiang, X. Y. Tan, N. Jia, J. Cao, A. Suwardi, Q. Zhu, J. Xu, J. F. Li and Q. Yan, Inorg. Chem., 2023, 62, 17905–17912.
120. J. Dong, Y. Jiang, Y. Sun, J. Liu, J. Pei, W. Li, X. Y. Tan, L. Hu, N. Jia, B. Xu, Q. Li, J. F. Li, Q. Yan and M. G. Kanatzidis, J. Am. Chem. Soc., 2023, 145, 1988–1996.
121. J. Dong, A. Suwardi, X. Y. Tan, N. Jia, K. Saglik, R. Ji, X. Wang, Q. Zhu, J. Xu and Q. Yan, Mater. Today, 2023, 66, 137–157.
122. S. Akrami, P. Edalati, M. Fuji and K. Edalati, Mater. Sci. Eng., R, 2021, 146, 100644.
123. S. Lee, K. Esfarjani, T. Luo, J. Zhou, Z. Tian and G. Chen, Nat. Commun., 2014, 5, 3525.
124. H. Wang, A. D. LaLonde, Y. Pei and G. J. Snyder, Adv. Funct. Mater., 2012, 23, 1586–1596.
125. A. Karati, S. Ghosh, M. Nagini, R. C. Mallik, R. Shabadi, B. S. Murty and U. V. Varadaraju, J. Alloys Compd., 2022, 927, 166578.
126. J. Yan, F. Liu, G. Ma, B. Gong, J. Zhu, X. Wang, W. Ao, C. Zhang, Y. Li and J. Li, Scr. Mater., 2018, 157, 129–134.
127. J. L. Cohn, G. S. Nolas, V. Fessatidis, T. H. Metcalf and G. A. Slack, Phys. Rev. Lett., 1999, 82, 779–782.
128. S. Guo, C. Ng, J. Lu and C. T. Liu, J. Appl. Phys., 2011, 109, 103505.
129. L. Kush, S. Srivastava, Y. Jaiswal and Y. Srivastava, Mater. Res. Express, 2020, 7, 035704.
130. M. Anandkumar and E. Trofimov, J. Alloys Compd., 2023, 960, 170690.
131. M. Brahlek, M. Gazda, V. Keppens, A. R. Mazza, S. J. McCormack, A. Mielewczyk-Gryń, B. Musico, K. Page, C. M. Rost, S. B. Sinnott, C. Toher, T. Z. Ward and A. Yamamoto, APL Mater., 2022, 10, 110902.
132. B. L. Musicó, D. Gilbert, T. Z. Ward, K. Page, E. George, J. Yan, D. Mandrus and V. Keppens, APL Mater., 2020, 8.
133. J. Dusza, P. Švec, V. Girman, R. Sedlák, E. G. Castle, T. Csanádi, A. Kovalčíková and M. J. Reece, J. Eur. Ceram. Soc., 2018, 38, 4303–4307.
134. M.-H. Hsieh, M.-H. Tsai, W.-J. Shen and J.-W. Yeh, Surf. Coat. Technol., 2013, 221, 118–123.
135. J. Gild, Y. Zhang, T. Harrington, S. Jiang, T. Hu, M. C. Quinn, W. M. Mellor, N. Zhou, K. Vecchio and J. Luo, Sci. Rep., 2016, 6, 37946.
136. J. Gild, J. Braun, K. Kaufmann, E. Marin, T. Harrington, P. Hopkins, K. Vecchio and J. Luo, J. Materiomics, 2019, 5, 337–343.
137. R. Z. Zhang, F. Gucci, H. Zhu, K. Chen and M. J. Reece, Inorg. Chem., 2018, 57, 13027–13033.
138. H. Y. Ding and K. F. Yao, J. Non-Cryst. Solids, 2013, 364, 9–12.
139. A. Takeuchi, N. Chen, T. Wada, Y. Yokoyama, H. Kato, A. Inoue and J. W. Yeh, Intermetallics, 2011, 19, 1546–1554.
140. X. Zhao, Z. Xue, W. Chen, Y. Wang and T. Mu, ChemSusChem, 2020, 13, 2038–2042.
141. T. Wang, H. Chen, Z. Yang, J. Liang and S. Dai, J. Am. Chem. Soc., 2020, 142, 4550–4554.
142. K. Huang, B. Zhang, J. Wu, T. Zhang, D. Peng, X. Cao, Z. Zhang, Z. Li and Y. Huang, J. Mater. Chem. A, 2020, 8, 11938–11947.
143. W. Xu, H. Chen, K. Jie, Z. Yang, T. Li and S. Dai, Angew. Chem., Int. Ed., 2019, 58, 5018–5022.
144. X. Zhao, Z. Xue, W. Chen, X. Bai, R. Shi and T. Mu, J. Mater. Chem. A, 2019, 7, 26238–26242.
145. S. Yuan, J. S. Qin, J. Li, L. Huang, L. Feng, Y. Fang, C. Lollar, J. Pang, L. Zhang, D. Sun, A. Alsalme, T. Cagin and H. C. Zhou, Nat. Commun., 2018, 9, 808.
146. D. A. Vinnik, V. E. Zhivulin, E. A. Trofimov, S. A. Gudkova, A. Y. Punda, A. N. Valiulina, M. Gavrilyak, O. V. Zaitseva, S. V. Taskaev, M. U. Khandaker, A. Alqahtani, D. A. Bradley, M. I. Sayyed, V. A. Turchenko, A. V. Trukhanov and S. V. Trukhanov, Nanomaterials, 2021, 12, 36.
147. V. E. Zhivulin, E. A. Trofimov, S. A. Gudkova, I. Y. Pashkeev, A. Y. Punda, M. Gavrilyak, O. V. Zaitseva, S. V. Taskaev, F. V. Podgornov, M. A. Darwish, M. A. Almessiere, Y. Slimani, A. Baykal, S. V. Trukhanov, A. V. Trukhanov and D. A. Vinnik, Nanomaterials, 2021, 11, 1014.
148. S. Schweidler, M. Botros, F. Strauss, Q. Wang, Y. Ma, L. Velasco, G. Cadilha Marques, A. Sarkar, C. Kübel, H. Hahn, J. Aghassi-Hagmann, T. Brezesinski and B. Breitung, Nat. Rev. Mater., 2024, 9, 266–281.
149. M. A. Buckingham, J. M. Skelton and D. J. Lewis, Cryst. Growth Des., 2023, 23, 6998–7009.
150. Z. Lei, X. Liu, H. Wang, Y. Wu, S. Jiang and Z. Lu, Scr. Mater., 2019, 165, 164–169.
151. D. B. Miracle and O. N. Senkov, Acta Mater., 2017, 122, 448–511.
152. P. C. Wei, C. N. Liao, H. J. Wu, D. Yang, J. He, G. V. Biesold-McGee, S. Liang, W. T. Yen, X. Tang, J. W. Yeh, Z. Lin and J. H. He, Adv. Mater., 2020, 32, e1906457.
153. A. J. Wright and J. Luo, J. Mater. Sci., 2020, 55, 9812–9827.
154. A. Karati, M. Nagini, S. Ghosh, R. Shabadi, K. G. Pradeep, R. C. Mallik, B. S. Murty and U. V. Varadaraju, Sci. Rep., 2019, 9, 5331.
155. R.-Z. Zhang and M. J. Reece, J. Mater. Chem. A, 2019, 7, 22148–22162.
156. E. A. Anber, N. C. Smith, P. K. Liaw, C. M. Wolverton and M. L. Taheri, APL Mater., 2022, 10, 101108.
157. M. A. A. Hasan, J. Wang, S. Shin, D. A. Gilbert, P. K. Liaw, N. Tang, W. L. N. C. Liyanage, L. Santodonato, L. DeBeer-Schmitt and N. P. Butch, J. Alloys Compd., 2021, 883, 160811.
158. Y. Shi, L. Collins, R. Feng, C. Zhang, N. Balke, P. K. Liaw and B. Yang, Corros. Sci., 2018, 133, 120–131.
159. K. Han, H. Jiang, T. Huang and M. Wei, Crystals, 2020, 10, 762.
160. H. Jiang, L. Jiang, D. Qiao, Y. Lu, T. Wang, Z. Cao and T. Li, J. Mater. Sci. Technol., 2017, 33, 712–717.
161. W. Dong, Z. Zhou, L. Zhang, M. Zhang, P. Liaw, G. Li and R. Liu, Metals, 2018, 8, 781.
162. C. Cheng, S. Ma and S. Wang, J. Alloys Compd., 2023, 935, 168003.
163. P. Bag, Y.-C. Su, Y.-K. Kuo, Y.-C. Lai and S.-K. Wu, Phys. Rev. Mater., 2021, 5, 085003.
164. S. Chen and Z. Ren, Mater. Today, 2013, 16, 387–395.
165. A. Karati, V. S. Hariharan, S. Ghosh, A. Prasad, M. Nagini, K. Guruvidyathri, R. C. Mallik, R. Shabadi, L. Bichler, B. S. Murty and U. V. Varadaraju, Scr. Mater., 2020, 186, 375–380.
166. A. Karati, S. R. Mishra, S. Ghosh, R. C. Mallik, R. Shabadi, R. V. Ramanujan, S. K. Yadav, B. S. Murty and U. V. Varadaraju, J. Alloys Compd., 2022, 924, 166108.
167. S. R. Mishra, A. Karati, S. Ghosh, R. C. Mallik, R. Shabadi, P. S. S. R. Krishnan, S. K. Yadav, R. V. Ramanujan and B. S. Murty, J. Mater. Sci., 2023, 58, 10736–10752.
168. S. R. Mishra, L. P. Tan, V. Trivedi, M. Battabyal, P. S. Sankara Rama Krishnan, D. V. M. Repaka, S. K. Yadav, R. V. Ramanujan and B. S. Murty, ACS Appl. Energy Mater., 2023, 6, 6262–6277.
169. K. Chen, R. Zhang, J.-W. G. Bos and M. J. Reece, J. Alloys Compd., 2022, 892, 162045.
170. P. Luo, Y. Mao, Z. Li, J. Zhang and J. Luo, Mater. Today Phys., 2022, 26, 100745.
171. R. Chen, Y. Wang, L. Jiang, R. Min, H. Kang, Z. Chen, E. Guo, X. Yang, X. Jiang and T. Wang, Mater. Today Phys., 2023, 30, 100957.
172. D. Rabin, A. Meshulam, D. Fuks and Y. Gelbstein, J. Alloys Compd., 2021, 874, 159940.
173. C. Wang, X. Zhou, D. Cong, G. Tang and J. Yang, Mater. Today Phys., 2023, 36, 101172.
174. C. Tan, H. Wang, L. Zhao, Y. Sun, J. Yao, J. Zhai, C. Wang and H. Wang, J. Mater. Chem. A, 2023, 11, 19036–19045.
175. X. Zhang, M. Huang, H. Li, J. Chen, P. Xu, B. Xu, Y. Wang, G. Tang and S. Yang, J. Mater. Chem. A, 2023, 11, 8150–8161.
176. J. U. Rahman, P. A. Carvalho, N. Soltani, M. Schrade, A. E. Gunnaes and T. G. Finstad, Intermetallics, 2022, 143, 107495.
177. H. Zhu, W. Li, A. Nozariasbmarz, N. Liu, Y. Zhang, S. Priya and B. Poudel, Nat. Commun., 2023, 14, 3300.
178. H. Zhu, R. He, J. Mao, Q. Zhu, C. Li, J. Sun, W. Ren, Y. Wang, Z. Liu, Z. Tang, A. Sotnikov, Z. Wang, D. Broido, D. J. Singh, G. Chen, K. Nielsch and Z. Ren, Nat. Commun., 2018, 9, 2497.
179. X. Yang, Y. Wang, R. Min, Z. Chen, E. Guo, H. Kang, L. Li, X. Jiang and T. Wang, Acta Mater., 2022, 233.
180. M. Gürth, G. Rogl, V. V. Romaka, A. Grytsiv, E. Bauer and P. Rogl, Acta Mater., 2016, 104, 210–222.
181. G. Rogl, P. Sauerschnig, Z. Rykavets, V. V. Romaka, P. Heinrich, B. Hinterleitner, A. Grytsiv, E. Bauer and P. Rogl, Acta Mater., 2017, 131, 336–348.
182. G. Rogl, K. Yubuta, V. V. Romaka, H. Michor, E. Schafler, A. Grytsiv, E. Bauer and P. Rogl, Acta Mater., 2019, 166, 466–483.
183. H. B. Kang, B. Poudel, W. Li, H. Lee, U. Saparamadu, A. Nozariasbmarz, M. G. Kang, A. Gupta, J. J. Heremans and S. Priya, Mater. Today, 2020, 36, 63–72.
184. G. Joshi, X. Yan, H. Wang, W. Liu, G. Chen and Z. Ren, Adv. Energy Mater., 2011, 1, 643–647.
185. L. Chen, Y. Liu, J. He, T. M. Tritt and S. J. Poon, AIP Adv., 2017, 7, 065208.
186. T. Maiti, M. Saxena and P. Roy, J. Mater. Res., 2018, 34, 107–125.
187. X.-L. Shi, H. Wu, Q. Liu, W. Zhou, S. Lu, Z. Shao, M. Dargusch and Z.-G. Chen, Nano Energy, 2020, 78, 105195.
188. R. Banerjee, S. Chatterjee, M. Ranjan, T. Bhattacharya, S. Mukherjee, S. S. Jana, A. Dwivedi and T. Maiti, ACS Sustainable Chem. Eng., 2020, 8, 17022–17032.
189. Y. Zheng, M. Zou, W. Zhang, D. Yi, J. Lan, C.-W. Nan and Y.-H. Lin, J. Adv. Ceram., 2021, 10, 377–384.
190. P. Zhang, Z. Lou, M. Qin, J. Xu, J. Zhu, Z. Shi, Q. Chen, M. J. Reece, H. Yan and F. Gao, J. Mater. Sci. Technol., 2022, 97, 182–189.
191. P. Zhang, L. Gong, Z. Lou, J. Xu, S. Cao, J. Zhu, H. Yan and F. Gao, J. Alloys Compd., 2022, 898, 162858.
192. P. Zhang, Z. Lou, G. Hu, Z. Wu, J. Xu, L. Gong and F. Gao, J. Materiomics, 2023, 9, 661–672.
193. P. Zhang, Z. Lou, L. Gong, J. Xu, Q. Chen, M. J. Reece, H. Yan, Z. Dashevsky and F. Gao, J. Alloys Compd., 2023, 937, 168366.
194. Z. Lou, P. Zhang, J. Zhu, L. Gong, J. Xu, Q. Chen, M. J. Reece, H. Yan and F. Gao, J. Eur. Ceram. Soc., 2022, 42, 3480–3488.
195. J. Yao, T. Chen, H. Wang, M. Khan, C. Tan, Y. Sun, W. Su, H. Wang and C. Wang, J. Mater. Chem. A, 2022, 10, 24561–24572.
196. X. Li, H. Yu, S. Gao, X. Fan, D. Zhou, W. Ji, Y. Chen, Y. Zhang, H. Ma and X. Jia, Mater. Charact., 2023, 199, 112792.
197. A. Kumar, D. Dragoe, D. Berardan and N. Dragoe, J. Materiomics, 2023, 9, 191–196.
198. C. Yang, H. Wu, H. Song, X. Wang, S. Chen, X. Xu, L. Chen, Z. Zhao, L. Yu and B. Liu, J. Alloys Compd., 2023, 940, 168802.
199. S. S. Jana and T. Maiti, Mater. Horiz., 2023, 10, 1848–1855.
200. Z. Shi, J. Zhang, J. Wei, X. Hou, S. Cao, S. Tong, S. Liu, X. Li and Y. Zhang, J. Mater. Chem. C, 2022, 10, 15582–15592.
201. D. Pankratova, S. M. Giacomelli, K. Yusupov, F. Akhtar and A. Vomiero, ACS Omega, 2023, 8, 14484–14489.
202. M. Stygar, J. Dąbrowa, M. Moździerz, M. Zajusz, W. Skubida, K. Mroczka, K. Berent, K. Świerczek and M. Danielewski, J. Eur. Ceram. Soc., 2020, 40, 1644–1650.
203. X. Zeng, Z. Ma, W. Li, B. Yang, Y. Qian, Y. Luo, J. Yang, Y. Liu and Q. Jiang, Chem. Eng. J., 2023, 474, 145663.
204. J. Bi, Y. Liang, Y. Bai, B. Cui, Z. Lu and B. Li, J. Eur. Ceram. Soc., 2023, 44, 2189–2197.
205. A. Nag and R. S. C. Bose, Mater. Res. Bull., 2016, 74, 41–49.
206. Z. Zhao, H. Xiang, F.-Z. Dai, Z. Peng and Y. Zhou, J. Mater. Sci. Technol., 2019, 35, 2647–2651.
207. W. Zhao, F. Yang, Z. Liu, H. Chen, Z. Shao, X. Zhang, K. Wang and L. Xue, Ceram. Int., 2021, 47, 29379–29385.
208. T. X. Nguyen, Y. H. Su, C. C. Lin and J. M. Ting, Adv. Funct. Mater., 2021, 31, 2106229.
209. M. Cui, C. Yang, B. Li, Q. Dong, M. Wu, S. Hwang, H. Xie, X. Wang, G. Wang and L. Hu, Adv. Energy Mater., 2020, 11, 2002887.
210. M. A. Buckingham, B. Ward-O'Brien, W. Xiao, Y. Li, J. Qu and D. J. Lewis, Chem. Commun., 2022, 58, 8025–8037.
211. X. Lu, D. T. Morelli, Y. Xia, F. Zhou, V. Ozolins, H. Chi, X. Zhou and C. Uher, Adv. Energy Mater., 2012, 3, 342–348.
212. G. Rey, F. Babbe, T. P. Weiss, H. Elanzeery, M. Melchiorre, N. Valle, B. E. Adib and S. Siebentritt, Thin Solid Films, 2017, 633, 162–165.
213. L. Zhao, X. Wang, F. Y. Fei, J. Wang, Z. Cheng, S. Dou, J. Wang and G. J. Snyder, J. Mater. Chem. A, 2015, 3, 9432–9437.
214. H. Wang, S. Zheng, H. Wu, X. Xiong, Q. Xiong, H. Wang, Y. Wang, B. Zhang, X. Lu, G. Han, G. Wang and X. Zhou, Small, 2022, 18, e2104592.
215. P. Vaqueiro, G. Guélou, A. Kaltzoglou, R. I. Smith, T. Barbier, E. Guilmeau and A. V. Powell, Chem. Mater., 2017, 29, 4080–4090.
216. W. Zhou, H. Li, Z. Shan, R. Zhang, S. Lu, J. Pei, Z. Ge, M. Zhou, Y. Wang and B. Zhang, Sci. China: Mater., 2023, 66, 2051–2060.
217. W. Li and M. Liu, ACS Appl. Electron. Mater., 2023, 5, 4523–4533.
218. J. Zhong, G. Liang, J. Cheng, W. Ao, C. Zhang, J. Li, F. Liu, S. Zhang and L. Hu, Sci. China: Mater., 2022, 66, 696–706.
219. Y. Huang, S. Zhi, S. Zhang, W. Yao, W. Ao, C. Zhang, F. Liu, J. Li and L. Hu, Materials, 2022, 15, 6798.
220. Y. Qiu, Y. Jin, D. Wang, M. Guan, W. He, S. Peng, R. Liu, X. Gao and L.-D. Zhao, J. Mater. Chem. A, 2019, 7, 26393–26401.
221. A. Das, P. Acharyya, S. Das and K. Biswas, J. Mater. Chem. A, 2023, 11, 12793–12801.
222. S. Zhi, J. Li, L. Hu, J. Li, N. Li, H. Wu, F. Liu, C. Zhang, W. Ao, H. Xie, X. Zhao, S. J. Pennycook and T. Zhu, Adv. Sci., 2021, 8, 2100220.
223. Y. Liu, H. Xie, Z. Li, Y. Zhang, C. D. Malliakas, M. Al Malki, S. Ribet, S. Hao, T. Pham, Y. Wang, X. Hu, R. Dos Reis, G. J. Snyder, C. Uher, C. Wolverton, M. G. Kanatzidis and V. P. Dravid, J. Am. Chem. Soc., 2023, 145, 8677–8688.
224. Z. Ma, T. Xu, W. Li, Y. Cheng, J. Li, D. Zhang, Q. Jiang, Y. Luo and J. Yang, Adv. Funct. Mater., 2021, 31.
225. Z. Ma, Y. Luo, W. Li, T. Xu, Y. Wei, C. Li, A. Y. Haruna, Q. Jiang, D. Zhang and J. Yang, Chem. Mater., 2022, 34, 8959–8967.
226. H. Xie, S. Hao, S. Cai, T. P. Bailey, C. Uher, C. Wolverton, V. P. Dravid and M. G. Kanatzidis, Energy Environ. Sci., 2020, 13, 3693–3705.
227. J. Cai, J. Yang, G. Liu, H. Wang, F. Shi, X. Tan, Z. Ge and J. Jiang, Mater. Today Phys., 2021, 18, 100394.
228. X. Wang, H. Yao, Z. Zhang, X. Li, C. Chen, L. Yin, K. Hu, Y. Yan, Z. Li, B. Yu, F. Cao, X. Liu, X. Lin and Q. Zhang, ACS Appl. Mater. Interfaces, 2021, 13, 18638–18647.
229. S. Acharya, J. Hwang, K. Kim, J. Kim, W. Hwang, A. Soon and W. Kim, Nano Energy, 2023, 112, 108493.
230. J. Jiang, G. Liu, H. Wang and J. Cai, J. Inorg. Mater., 2021, 36, 399–404.
231. Q. Zhang, Z. Guo, R. Wang, X. Tan, K. Song, P. Sun, H. Hu, C. Cui, G. Q. Liu and J. Jiang, Adv. Funct. Mater., 2022, 32, 2205458.
232. Y. Wu, Q. Liang, X. Zhao, H. Wu, P. Zi, Q. Tao, L. Yu, X. Su, J. Wu, Z. Chen, Q. Zhang and X. Tang, ACS Appl. Mater. Interfaces, 2022, 14, 3057–3065.
233. O. Ivanov, M. Yaprintsev, A. Vasil’ev and E. Yaprintseva, J. Alloys Compd., 2021, 872, 159743.
234. T. Zhao, H. Zhu, B. Zhang, S. Zheng, N. Li, G. Wang, G. Wang, X. Lu and X. Zhou, Acta Mater., 2021, 220, 117291.
235. S. Roychowdhury, T. Ghosh, R. Arora, U. V. Waghmare and K. Biswas, Angew. Chem., Int. Ed., 2018, 57, 15167–15171.
236. Z. Ma, Y. Luo, W. Li, Y. Wei, C. Li, A. Y. Haruna, Z. Zhang, X. Li, Q. Jiang and J. Yang, J. Mater. Chem. A, 2023, 11, 13720–13728.
237. L. Zhang, W. Shen, Z. Zhang, C. Fang, Q. Wang, B. Wan, L. Chen, Y. Zhang and X. Jia, J. Materiomics, 2024, 10, 70–77.
238. Q. Xia, P. Ying, Y. Xia, X. Li and J. Cui, Appl. Phys. Lett., 2021, 119, 161901.
239. H. Zhu, T. Zhao, B. Zhang, Z. An, S. Mao, G. Wang, X. Han, X. Lu, J. Zhang and X. Zhou, Adv. Energy Mater., 2020, 11, 2003304.
240. Y. Luo, S. Hao, S. Cai, T. J. Slade, Z. Z. Luo, V. P. Dravid, C. Wolverton, Q. Yan and M. G. Kanatzidis, J. Am. Chem. Soc., 2020, 142, 15187–15198.
241. Y. Sun, H. Wang, J. Yao, F. Mehmood, C. Tan, L. Wang, J. Zhai, H. Wang and C. Wang, Chem. Eng. J., 2023, 462, 142185.
242. T. Luo, Y. Hu, S. Liu, F. Xia, J. Qiu, H. Peng, K. Liu, Q. Guo, X. Li, D. Yang, X. Su, J. Wu and X. Tang, Mater. Today Phys., 2023, 37, 101211.
243. H. Wang, C. Tan, A. Romanenko, Y. Sun, J. Feng, M. Khan, G. Chebanova, L. Wang, J. Yao, H. Wang and C. Wang, J. Eur. Ceram. Soc., 2023, 43, 3383–3389.
244. C. Yang, Y. Luo, Y. Xia, L. Xu, Z. Du, Z. Han, X. Li and J. Cui, ACS Appl. Mater. Interfaces, 2021, 13, 56329–56336.
245. W. Wang, Z. Zhou, S. Zheng, Q. Xiong, X. Hu, B. Zhang, G. Wang, G. Wang, X. Lu and X. Zhou, ACS Appl. Energy Mater., 2022, 6, 580–587.
246. X. Li, Z. Liang, J. Li, F. Cheng, J. He, C. Zhang, J. Li, F. Liu, T. Lyu, B. Ge and L. Hu, Nano Energy, 2022, 100, 107434.
247. Z. Deng, A. Olvera, J. Casamento, J. S. Lopez, L. Williams, R. Lu, G. Shi, P. F. P. Poudeu and E. Kioupakis, Chem. Mater., 2020, 32, 6070–6077.
248. Z. Zhang, K. Zhao, H. Chen, Q. Ren, Z. Yue, T.-R. Wei, P. Qiu, L. Chen and X. Shi, Acta Mater., 2022, 224, 117512.
249. M.-J. Yang, M. Yusuf Fakhri, C.-N. Liao and K.-H. Chen, Mater. Lett., 2022, 311, 131617.
250. J. Yang, J. Cai, R. Wang, Z. Guo, X. Tan, G. Liu, Z. Ge and J. Jiang, ACS Appl. Energy Mater., 2021, 4, 12738–12744.
251. A. Yamashita, Y. Goto, A. Miura, C. Moriyoshi, Y. Kuroiwa and Y. Mizuguchi, Mater. Res. Lett., 2021, 9, 366–372.
252. E. Yaprintseva, A. Vasil’ev, M. Yaprintsev and O. Ivanov, Mater. Lett., 2023, 346, 134568.
253. A. E. Vasil’ev, O. N. Ivanov, M. N. Yapryntsev, E. N. Yapryntseva and A. V. Efremenko, Glass Ceram., 2023, 80, 52–57.
254. E. Yaprintseva, A. Vasil’ev, M. Yaprintsev and O. Ivanov, Mater. Lett., 2022, 309, 131416.
255. M. Samanta, S. Roychowdhury, J. Ghatak, S. Perumal and K. Biswas, Chemistry, 2017, 23, 7438–7443.
256. G. Liang, T. Lyu, L. Hu, W. Qu, S. Zhi, J. Li, Y. Zhang, J. He, J. Li, F. Liu, C. Zhang, W. Ao, H. Xie and H. Wu, ACS Appl. Mater. Interfaces, 2021, 13, 47081–47089.
257. W. Zhang, Y. Lou, H. Dong, F. Wu, J. Tiwari, Z. Shi, T. Feng, S. T. Pantelides and B. Xu, Chem. Sci., 2022, 13, 10461–10471.
258. A. Raphel, P. Vivekanandhan, A. K. Singh and S. Kumaran, J. Solid State Chem., 2021, 303, 122531.
259. A. Raphel, A. K. Singh, P. Vivekanandhan and S. Kumaran, Phys. B, 2021, 622, 413319.
260. A. Raphel, P. Vivekanandhan, A. K. Rajasekaran and S. Kumaran, Mater. Sci. Semicond. Process., 2022, 138, 106270.
261. A. Raphel, P. Vivekanandhan, A. K. Rajasekaran and S. Kumaran, Mater. Today Commun., 2023, 35, 105880.
262. X.-Y. Xin, J. Ma, Y.-F. Wang and H.-Q. Liu, Appl. Phys. A, 2022, 128, 791.
263. Z. Fan, H. Wang, Y. Wu, X. Liu and Z. Lu, Mater. Res. Lett., 2016, 5, 187–194.
264. Z. Fan, H. Wang, Y. Wu, X. J. Liu and Z. P. Lu, RSC Adv., 2016, 6, 52164–52170.
265. M.-R. Li, P.-Z. Ying, X. Li and J.-L. Cui, Acta Phys. Sin., 2022, 71, 237302.
266. C. Yang, L. Qu, Y. Luo, Y. Xia, C. Li, X. Li and J. Cui, ACS Appl. Energy Mater., 2023, 6, 5388–5395.
267. L. Bo, R. Zhang, H. Zhao, Y. Hou, X. Wang, J. Zhu, L. Zhao, M. Zuo and D. Zhao, ACS Appl. Energy Mater., 2022, 5, 6453–6461.
268. L. Bo, F. Li, Y. Hou, L. Wang, X. Wang, R. Zhang, M. Zuo, Y. Ma and D. Zhao, J. Mater. Sci., 2022, 57, 4643–4651.
269. A. Mikula, J. Dabrowa, A. Kusior, K. Mars, R. Lach and M. Kubowicz, Dalton Trans., 2021, 50, 9560–9573.
270. Y. Wu, X. Su, D. Yang, Q. Zhang and X. Tang, ACS Appl. Mater. Interfaces, 2021, 13, 4185–4191.
271. X. Tang, J. Wu, X. Su, T. Luo and D. Yang, J. Inorg. Mater., 2021, 36, 991–998.
272. O. Cherniushok, T. Parashchuk, J. Tobola, S. D. N. Luu, A. Pogodin, O. Kokhan, I. Studenyak, I. Barchiy, M. Piasecki and K. T. Wojciechowski, ACS Appl. Mater. Interfaces, 2021, 13, 39606–39620.

---