High-entropy materials for catalysis: A new frontier

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Science Advances  12 May 2021:
Vol. 7, no. 20, eabg1600
DOI: 10.1126/sciadv.abg1600


Entropy plays a pivotal role in catalysis, and extensive research efforts have been directed to understanding the enthalpy-entropy relationship that defines the reaction pathways of molecular species. On the other side, surface of the catalysts, entropic effects have been rarely investigated because of the difficulty in deciphering the increased complexities in multicomponent systems. Recent advances in high-entropy materials (HEMs) have triggered broad interests in exploring entropy-stabilized systems for catalysis, where the enhanced configurational entropy affords a virtually unlimited scope for tailoring the structures and properties of HEMs. In this review, we summarize recent progress in the discovery and design of HEMs for catalysis. The correlation between compositional and structural engineering and optimization of the catalytic behaviors is highlighted for high-entropy alloys, oxides, and beyond. Tuning composition and configuration of HEMs introduces untapped opportunities for accessing better catalysts and resolving issues that are considered challenging in conventional, simple systems.


Entropy-driven behaviors of molecular species, including adsorption of reactants, as well as translation, rotation, and vibration of intermediates bound to active sites, fundamentally determine the reaction pathway of catalytic reactions and have thus been extensively studied (1). For instance, entropic contributions are important driving forces that accelerate enzyme catalysis by lowering the activation energy (2). For acid catalysis in zeolites, enthalpy-entropy compensation is mediated by the molecular confinement in micropores (3). Beyond catalysis, separation of structural isomers can be realized through preferential adsorption of the targeted molecules in carefully designed zeolite cages, which is dependent on the rotational entropy correlated with the internal space of the pores (4). Exquisite tuning of the enthalpic and entropic parameters gives rise to efficient optimization of stabilization and transformation of molecules under various conditions.

Entropy-centered discussions on the catalyst side, especially the configurational entropy dictated by the mixing of different components, have not remained in balance. Most studies have focused on topics that can be rationalized using enthalpic parameters, such as metal-support interactions depending on the relative strengths of the metal-metal and metal/oxide bonds (5), and charge transfer–induced stabilization of transition metal oxide nanoparticles on layered perovskite oxides (6). Meanwhile, entropic factors have been underexplored because of the limited configurational tunability in multicomponent systems, and increased structural and compositional complexities that are difficult to decouple. Entropy-directed strategies have been used to fabricate well-tailored nanocrystal assemblies (7), whereas their applications in catalysis are hindered by the compromised stabilities under reaction conditions.

Recent progress in high-entropy materials (HEMs) has afforded a versatile platform to investigate the influence of entropy on the catalyst side. A broad scope of entropy-stabilized multicomponent systems with tailored compositions, structures, and architectures can be readily accessed using unconventional synthetic methods. Confining multiple atomic species into the same lattice, which is enabled by the enhanced entropic contributions, drastically expands the tuning range of the catalytic active sites. In addition, pronounced lattice distortion in HEMs lowers the overall system energy and thus facilitates activation and transport of active species. For example, favorable formation of oxygen defects in entropy-stabilized oxides has shown to improve the catalytic performances for various oxidation reactions (8, 9). Modifying the entropic effects also constitutes a transformative paradigm, making it possible to mitigate and fundamentally resolve some of the challenging issues in traditional, enthalpy-dominated systems.

Several recent papers have reviewed the catalytic applications mainly based on high-entropy alloys (HEAs), while entropy-stabilized systems beyond HEAs have been rarely covered (1016). Elucidation of the structure-property relationships of HEMs, particularly across different subcategories, is crucial to leverage the enhanced entropic effects for catalysis. Rapid development of HEMs also necessitates thorough comparisons to unveil the enthalpy-entropy correlation on the catalyst side. Here, we summarize recent advances in HEMs for catalysis. We first introduce the evolvement from conventional multicomponent systems to entropy-stabilized solid solutions from a fundamental perspective. Advanced synthetic and characterization techniques coupled with powerful computational tools provide atomistic insights into the surface, interface, lattice, and defects of HEMs, which are important to understand the associated catalytic behaviors. Case studies of HEAs, high-entropy oxides (HEOs), and novel high-entropy systems for catalysis are then performed, highlighting the link between modulation of the geometric and electronic properties and optimization of the catalytic properties. In the end, we discuss the upcoming opportunities and challenges for this emerging and highly promising field. We hope the insights provided here can help probe the origin for the traits of HEMs, which present a game-changing forefront for the discovery and design of high-performance, cost-effective catalytic materials.


Alloying is one of the most common and effective approaches to constructing multicomponent systems with tunable properties, where different atoms are randomly distributed or packed in an ordered manner for intermetallics. Unique yet advantageous catalytic properties emerge in alloys due to the pronounced multielemental interactions. This has been evidenced in numerous cases, such as lattice oxygen activation in the CeO2-ZrO2 solid solutions (17) and improved electrochemical activation of CO2 through altering the atomic ordering of the AuCu nanoparticles (18). For cases where individual species are not miscible to each other, phase segregation unavoidably constrains the tunability in composition and structure. Delicate control is also needed to construct active interfacial domains, as impurity formation could block the active sites from surface exposure. Therefore, maintaining the single-phase state is vital to realize atomic mixing of different species and obtain synergistic properties that are inaccessible with each individual constituent.

From a fundamental perspective, formation of a uniform single-phase or a multiphase state is dependent on parameters including electronegativity difference, valence electron concentration, atomic size difference, and mixing entropy and mixing enthalpy (19). The first three factors are intrinsic properties and thus difficult to alter, whereas enthalpic and entropic contributions during the mix of different components can be manipulated with external approaches. In general, the phase stability in a multicomponent system can be estimated using the Gibbs free energy equationΔGmix=ΔHmixTΔSmixwhere ΔGmix, ΔHmix, and ΔSmix are the changes of the Gibbs free energy, mixing enthalpy, and mixing entropy, respectively, and T is the thermodynamic temperature (20). In this way, the ΔGmix value is directly determined by the relative values of ΔHmix and −TΔSmix. A negative value for ΔGmix indicates that the system is favorable toward a single-phase state with random distributions, while a positive one suggests a thermodynamic-driven phase separation. The mixing entropy in an ideal case can be expressed as belowΔSmix=RΣxilnxiwhere R is the gas constant and xi is the mole fraction of the ith component (20). It can be deduced that equal molar fractions of each component would maximize the value for ΔSmix, which are calculated to be 1.10R, 1.39R, 1.61R, 1.79R, and 2.20R for equiatomic ternary, quaternary, quinary, senary, and nonary alloys, respectively (20, 21). The value of ΔHmix, on the other hand, varies in phase-segregated mixtures and ordered intermetallics, leading to different critical temperatures at which the entropic contributions (TΔSmix) exceed the enthalpic ones (ΔHmix) (22). For single-phase solid solutions, the ΔHmix value is generally considered negligible, which is the same for the nonconfigurational entropy (23). Therefore, the above two equations qualitatively depict the enthalpy-entropy correlations at different temperatures, and two key conclusions can be drawn: Configurational entropy will become the determining factor for the phase stability of the multicomponent system at sufficiently high temperatures, and incorporating more species with near-equal mole fractions markedly increases the entropic contributions, which subsequently lowers the overall free energy. These two inferences, which correlate the adjustment in composition and configuration with phase stability in multicomponent systems, lay basic foundations for understanding the formation and properties of HEMs.

In 2004, two groups independently reported a new type of alloys (21, 24), where multiple (≥5) principal elements are unexpectedly stabilized in a homogeneous single-phase state. These two discoveries are considered the prototype of HEAs, and the concept of entropy-induced stabilization has therefore been gradually established. The ability to confine multiple principal elements in a single lattice is intriguing for the design of advanced catalysts with desirable activity, selectivity, and stability. First, properties of traditional alloys are mainly determined by one or two principal elements. Incorporating dopants in low concentrations would only fine-tune the predefined features. Discovery of HEMs makes it possible to embrace unprecedented compositional diversities and structural complexities. In parallel, the multielemental incompatibility that originated from the large enthalpic differences can be compensated by the enlarged configurational entropy. The concentrations of the principal elements can be elevated in this way, which may even surpass the miscibility barriers in the bulk phase (25). Accordingly, a broader range of geometric and electronic properties become accessible. Second, severe lattice distortion caused by the atomic size difference induces a thermodynamically nonequilibrium state (10). This could hypothetically reduce the energy barrier for adsorption, activation, and conversion of molecules. Distortion-derived local strain, which is inevitable for a diverse and complex system like HEM, also has substantial impacts on modifying the energy levels of bound intermediates (26). Third, the higher diffusion activation energies of HEMs result in sluggish diffusion kinetics, which has been recognized as the main impetus for the enhanced chemical, thermal, and mechanical stabilities (27). Counterintuitively, the entropy-stabilized single-phase state would be more thermodynamically favorable at even higher temperatures according to the Gibbs free energy equation, while how to maintain the exposed active sites on an antisintering surface becomes challenging. These unconventional yet advantageous traits render HEMs as attractive candidates for better catalysts, as well as versatile platforms to probe the enthalpy-entropy correlations on the catalyst side.


At sufficiently high temperatures, the entropic contributions surpass the enthalpic ones, leading to a homogeneous yet random distribution of different elemental species in the same lattice (28). However, the low surface area brought by the high-temperature operation drastically limits the utilization of HEMs for catalysis. Accessing nanostructures with increased surface area and more active sites has thereby motived the exploratory synthesis of HEMs, which can be broadly classified into three main categories. The first one is to rely on the nonequilibrium process, such as the carbothermal shock technique and the fast moving bed pyrolysis (FMBP) technique (29, 30). The thermodynamically favorable high-entropy phases are kinetically trapped during the ultrafast heating-cooling process. The short growth time in the scale of seconds or less also ensures formation of nanosized particles with enlarged surface areas. The second one is to exploit the techniques that create local extreme environments, such as ball milling and solvothermal synthesis (31, 32), to realize atomic mixing of different species. It is worth mentioning that the overall operation conditions of these methods still remain mild and thus benefit scale-up implementations. The third category is to turn to external factors in the liquid phase, such as solvent and ligand molecules in colloidal and polyol solutions (33, 34), to facilitate formation of nanoscale HEMs at relatively low temperatures (~200° to 300°C). The surface capping ligands can modify the energetic barrier for homogeneous nucleation and growth, yielding high-entropy nanocrystals instead of phase-segregated heterostructures.

Choosing catalytic reactions for HEMs is closely related with their microstructure and surface properties, which vary according to different synthetic approaches. For example, freestanding colloidal and polyol HEMs with good solution dispersibilities can be readily used for liquid-phase batch conversions such as selective hydrogenation and hydrodeoxygenation reactions (35, 36), while supported HEMs prepared with the carbothermal shock technique work better for gas-phase reactions such as methane combustion (37). It is also viable to combine two or more approaches or modify the existing protocol to tackle synthetic challenges for obtaining different types of HEMs. For instance, the hydrothermal method combined with ball milling produces high-entropy perovskite fluorides (HEPFs) (38), which cannot be successfully prepared using solely hydrothermal- or mechanochemistry-based methods. Carbothermal shock technique, which was originally developed to prepare HEA nanoparticles, has been successfully extended to the fabrication of HEO and sulfide nanoparticles (37, 39).

Despite variation of the synthetic routes to fabricating different subgroups of HEMs, which will be discussed in detail in the following sections, the associated characterization techniques are generalizable. Ideally, configurational entropy is maximized in a single phase where different constituent atoms are randomly distributed. However, the definition of HEM is flexible and inclusive. As shown in Fig. 1A, several possibilities with different degrees of order and disorder exist between the phase-segregated heterostructures and the ideal entropy-stabilized solid solutions. More and more studies have indicated that local clustering, surface reconstruction, and formation of interface and vacancy in the multiphase state also bring appealing attributes, further necessitating the elucidation of local structures. Topics including identification and quantification of active sites, mechanistic studies, and optimization of the catalytic performances all rely on precise characterization of HEMs, which is challenging because of the increased compositional and structural complexities. Nanostructuring, which has been widely applied to increase the number of active sites, further complicates the scenario because of the size and facet dependence of the structural parameters (11). Despite these challenges, advances have been accomplished to use diverse techniques to characterize nanostructured HEMs. We herein outline the diffraction, microscopic, and spectroscopic approaches that have been routinely used (Fig. 1B).

Fig. 1 Characterization of HEMs.

(A) Schematic showing structures with different degrees of order and disorder between interface formation and ideal random solid solutions containing five (or more than five) principal elements. (B) Schematic summarizing the diffraction, microscopy, and spectroscopy techniques for the characterization of HEMs. AES, Auger electron spectroscopy; LEIS, low-energy ion scattering spectroscopy; ETEM, environmental transmission electron microscopy. (C) Room temperature neutron PDF data of the Al1.3CoCrCuFeNi HEA and the simulated pattern based on the cubic structure. (D) Neutron PDF data of the Al1.3CoCrCuFeNi HEA at 1400°C and the simulated pattern based on the local structure model with short-range order. (C) and (D) are reproduced with permission from the Nature Publishing Group (43). (E) Atomic-resolution high-angle annular dark-field (HAADF) image of the CrMnFeCoNi HEA and corresponding EDS element maps for Cr, Mn, Fe, Co, and Ni. Reproduced with permission from the Nature Publishing Group (45). (F) Normalized EXAFS spectra of the MgNiCuCoZnOx HEO. Reproduced with permission from the Nature Publishing Group ( (113).

Diffraction is one of the most readily accessible and well-developed bulk techniques to examine the structures of crystalline materials. Powder x-ray diffraction (XRD) patterns enable quick evaluation of the phase purity in multicomponent system. Several structural parameters including lattice parameter, crystallinity, grain size, preferred orientation, and strain can be calculated through refinement of the diffraction data. However, limitations exist for the common in-laboratory diffraction instruments. Small grain sizes of nanoscale domains cause severe broadening of the diffraction peaks, which makes it difficult to identify the potential impurity peaks (40). Utilization of synchrotron- or neutron-based diffraction techniques with high-intensity light sources can mitigate this drawback, affording atomic-level information regarding structure distortion, atom displacement, site order and disorder, defect formation, and lattice strain (41). Meanwhile, total scattering measurements coupled with pair-distribution function (PDF) analysis permits analysis of the local atomic structures of nanoscale and even amorphous samples that do not exhibit well-defined Bragg diffraction peaks (42). As shown in Fig. 1 (C and D), Santodonato et al. (43) investigated the temperature-dependent evolution of local disorders in Al1.3CoCrCuFeNi using neutron PDF and demonstrated the great potential of complex systems beyond single-phase solid solutions.

Electron microscopy techniques, mostly including scanning electron microscopy (SEM), transmission electron microscopy (TEM), and scanning transmission electron microscopy (STEM), are dependent on the interactions between electrons and specimen and have been extensively applied to gain local information such as morphology and size of the materials. SEM covers a larger area of the sample, whereas TEM is typically more focused on a smaller area with higher resolutions. STEM, on the other hand, is more versatile with expanded functionalities. Annular dark-field STEM (ADF-STEM) permits atomically resolved visualization of the high-entropy structures, which unambiguously pinpoints the positions of the different atoms (Fig. 1E). Electron tomography allows three-dimensional reconstruction based on a series of single-tilted two-dimensional STEM images, yielding a complete picture of morphology and structure of nanoscale objects (44). Besides local structures, STEM coupled with energy-dispersive x-ray spectroscopy (EDS) or electron energy-loss spectroscopy (EELS) element maps could clarify local chemical compositions, which are important to appraise the structure homogeneity of HEMs. A recent study from Ding et al. (45) elucidated elemental distribution of the CrMnFeCoNi and CrFeCoNiPd alloys using atomic-resolution chemical mapping, providing direct experimental evidence for structure and composition tuning of HEAs. STEM-EDS element maps are more frequently applied to HEMs because of the higher sensitivities to metal elements with higher atomic numbers (46). In comparison, EELS is capable of identifying the oxidation states of the target element, yet more sensitive to detect light elements like C, N, and O. Recent progress in environmental transmission electron microscopy has fueled burgeoning interests in performing operando measurements, monitoring the change of structural and energetic features of catalysts under reaction conditions (47).

Complementary to EDS and EELS that focus on a small area of the sample, bulk spectroscopic techniques probe the bulk and surface structures together with the corresponding chemical states. X-ray absorption spectroscopy (XAS) is an element-specific tool to study the electronic and geometric parameters of the chemical species. X-ray absorption near-edge structure (XANES) allows identification of the oxidation state of the element. Local structure information is attainable by analyzing the extended x-ray absorption fine structure (EXAFS) spectra, which presents direct evidence for comparing the chemical environment of different atoms in HEMs (Fig. 1F). Identifying the catalytic active sites in HEMs can also be realized by monitoring the change of the oxidation states of different elements with operando XAS measurements (48). On the other hand, x-ray photoelectron spectroscopy (XPS) analyzes the chemical environment including elemental composition and oxidation states on the surface and subsurface regions. With etching or sputtering, XPS depth profiling probes the chemical compositions at different depths starting from the outmost surface. Overlap of the characteristic peaks from different elements may complicate interpretation of the core-level XPS spectra, while the associated satellite and plasmonic peaks can be used as informative fingerprints. Auger electron spectroscopy, which is based on a two-hole final state and thus is not affected by switching excitation lasers or applying various charging correction standards when plotted against kinetic energy, also brings valuable information on the chemical state of the target element (49).

In addition to experimental techniques, various computational approaches have been applied to predict and interpret the catalytic behaviors of HEMs. Density functional theory (DFT) calculations are able to evaluate geometric, electronic, and energetic parameters of the high-entropy catalysts for mechanistic studies (50). Machine learning emerges as a revolutionary tool to realize high-throughput screenings of possible structures and compositions in HEMs. The obtained results also afford synthetic guidelines for the targeted high-entropy phase, substantially accelerating the process of materials discovery and design. To assess the synthesizability and stability of the high-entropy catalysts, molecular dynamics and Monte Carlo methods have been used to predict formation and transformation of HEMs under different conditions (51). These computational tools can yield results that are complementary to the experimental data and even guide the experimental progress.

Given the multidimensional complexity in HEMs, it is pivotal to combine different techniques to draw a complete picture of the surface and bulk characteristics. For example, the average size of the HEA nanoparticles measured using TEM and STEM can be corroborated by the grain size estimated with Scherrer analysis of the powder XRD data (52). Oxidation states of the metal species can be determined by both STEM-EELS and XANES spectra, and the associated electronic and energetic characteristics can be further analyzed using DFT calculations. In addition, understanding the capability and limitation of each technique is crucial. To assess the structure homogeneity of HEMs, XRD only works for crystalline materials exhibiting well-defined diffraction peaks, while STEM-EDS elemental mapping can be applied for both crystalline and amorphous systems. Low-energy ion scattering spectroscopy has a higher surface sensitivity compared with that of XPS but cannot discriminate the different oxidation states (53). For computational investigations, DFT calculations generally yield relatively accurate results based on well-defined local structures. In contrast, molecular dynamics are more efficient and less expensive since a large number of atoms can be simultaneously computed, while the associated accuracy can be compromised.


As the prototype of HEMs, HEAs exhibit compelling mechanical properties for structural applications, such as outstanding fracture resistance, ultrahigh ductility and strength, and desirable thermal and physiochemical stabilities (5458). However, bulk HEAs can hardly be used for catalytic applications owing to the low surface area and limited elemental tunability (59, 60). In this section, we summarize recent advances in fabricating nanostructured HEAs for gas-phase thermocatalysis and liquid-phase electrocatalysis (Table 1). Both experimental and computational efforts have been directed to understanding the enhanced synergistic effects of the HEA catalysts, where simultaneous incorporation of multiple metal species optimizes surface adsorption properties for catalytic conversions.

Table 1 Summary of HEAs for thermocatalysis and electrocatalysis.

AO, alcohol oxidation; T, thermocatalysis; E, electrocatalysis.

View this table:

HEAs for thermocatalysis

Single-phase HEA nanoparticles having enriched catalytic active sites are appealing for catalysis but have remained synthetically challenging. Homogeneous mixing of different elements requires higher operating temperatures to overcome the thermodynamic barrier. However, it is difficult to maintain the nanoscale morphology at elevated temperatures because of migration and aggregation of nanoparticles. Hu and co-workers (29) circumvented this dilemma by developing the carbothermal shock method to synthesize a library of composition-tunable HEA nanoparticles. As illustrated in Fig. 2A, ultrafast joule heating via electrical current triggers instant decomposition of the metal precursors dispersed onto the carbon nanofiber support, which facilitates atomic mixing of different metals in a liquid-like state. The following rapid quenching process enables kinetic control over the thermodynamic mixing regimes. As a result, the metal atoms are kinetically trapped in the as-formed crystalline lattice. This ultrafast heating-cooling strategy surpasses the thermodynamic barrier, producing atomically mixed HEA nanoparticles rather than phase-separated heterostructures (Fig. 2B). Notably, HEA nanoparticles composed of up to eight arbitrary metallic elements (PtPdCoNiFeCuAuSn) were successfully prepared (Fig. 2C). As a proof-of-concept demonstration, the authors applied the quinary HEA nanoparticles (PtPdRhRuCe) for selective ammonia oxidation. The HEA nanocatalysts exhibited excellent activity (~100% conversion at 700°C), selectivity (>99% selectivity toward NO + NO2 rather than N2 + N2O), and stability (no degradation over ~30 hours at 700°C), which exceed the performance of the heterostructured PtPdRhRuCe catalysts prepared using the conventional wet impregnation method.

Fig. 2 HEAs for thermocatalysis.

(A) Schematic illustrating the carbothermal shock synthesis of the HEA nanoparticles (left) and temperature evolution during the rapid heating-cooling process (right). (B) Schematic comparing the phase-separated heterostructures synthesized by a conventional method with slow kinetics and the HEA nanoparticles prepared by the carbothermal shock approach. (C) Individual and low-magnification HAADF-STEM images with EDS element maps of octonary (PtPdCoNiFeCuAuSn) nanoparticles (left). Scale bar, 10 nm. Atomically resolved HAADF-STEM image with the fast Fourier transform (FFT) pattern showing the fcc structure (right). (A) to (C) are reproduced with permission from the American Association for the Advancement of Science (29). (D) Catalytic decomposition of ammonia using the RuRhCoNi (Ru-4) MEA nanoparticles, Ru and RhCoNi catalysts (left), and two RuRhCoNiIr samples prepared by the carbothermal shock method (Ru-5 MEA-NPs) and the traditional impregnation approach (Ru-5 IMP), respectively (right). (E) Performance comparison of the Ru-4 MEA and Ru-5 MEA nanoparticles with previously reported Ru-based catalysts for ammonia decomposition. (D) and (E) are reproduced with permission from the American Association for the Advancement of Science ( (64). (F) Schematic illustration highlighting the rate-limiting factors in Co-rich (HEA-Co45Mo25), optimal (HEA-Co25Mo45), and Mo-rich (HEA-Co15Mo55) catalysts for ammonia decomposition. Reproduced with permission from the Nature Publishing Group ( (67).

Carbothermal shock synthesis of HEA nanoparticles manifests the accessibility of single-phase HEA nanoparticles with intriguing catalytic properties. The following synthetic work extended to a portfolio of nanoscale HEA architectures ranging from aerosols to hollow nanoparticles (6163). However, fabrication of multielemental alloy (MEA) nanoparticles remains unpredictable because of the innumerable elemental combinations. The trial-and-error–type experiments, which have been long established, are time- and human resource–consuming. Hu and colleagues (64) further expedited this process by combining computational prescreening with experimental verification. The authors first applied DFT calculations to predict the thermodynamic formation barriers of the potential single MEA phase, based on which the dynamic movements of the metal atoms at synthetic (1500 K) and quenched (298 K) temperatures were further simulated using a hybrid Monte Carlo and molecular dynamic approach. Predicted as energetically stable and kinetically favorable using this combination strategy, single-phase Ru-4 MEA (Ru0.44Rh0.30Co0.12Ni0.14) and Ru-5 MEA (Ru0.25Rh0.25Co0.2Ni0.2Ir0.1) were prepared by the carbothermal shock technique. The MEA nanoparticles were applied to catalyze ammonia decomposition, which is a promising route for hydrogen storage because of the high hydrogen densities, convenience of liquifying with mild pressurization, and better safety (65). As shown in Fig. 2D, Ru-4 MEA exhibited a higher activity compared with that of the Ru and RhCoNi samples, and single-phase Ru-5 MEA nanoparticles outperformed the phase-separated sample with the same elemental composition. The catalytic performances of the MEA nanoparticles are also superior to that of the previously reported Ru-based catalysts (Fig. 2E), highlighting the competitiveness of the composition-tunable MEA nanoparticles.

The Co-Mo binary system with mixed Co-Mo sites is considered as one of the most promising earth-abundant and inexpensive catalysts for ammonia decomposition (66). However, the large miscibility gap between Co and Mo prevents continuous tuning of the surface properties that span a wide range. Wang and co-workers (67) overcame this miscibility issue by leveraging the entropy-induced stabilization in HEAs. With the carbothermal shock technique, the authors fabricated a series of single-phase CoxMoyFe10Ni10Cu10 (x + y = 70) nanoparticles with readily tunable Co/Mo ratios (denoted as HEA-CoxMoy). Compared with bimetallic CoxMoy that tend to generate phase-separated Co- or Mo-rich phases, incorporation of Fe, Ni, and Cu effectively enlarges the entropic contribution, producing a single solid-solution phase with the face-centered cubic (fcc) structure. The HEA-CoxMoy nanoparticles exhibited composition-dependent activities for ammonia decomposition. The most active HEA-Co25Mo45 catalyst reached a mass-specific rate of 0.74 gNH3 m−2 hour−1 at 500°C, representing improvement factors of ~24 versus bimetallic Co-Mo and ~19 versus Ru, respectively. This catalyst also exhibited outstanding thermal and chemical stabilities, showing negligible activity degradation over 50 hours under the continuous operation at 500°C.

Mechanistic studies were performed to unveil the composition-dependent activities of the HEA-CoxMoy catalysts. According to the temperature-programmed desorption (TPD) results of the preadsorbed atomic nitrogen (2*N→N2), the HEA-CoxMoy catalysts with higher Co/Mo ratios have lower values of the recombinative desorption energy of nitrogen (ΔEN). Plotting the ammonia decomposition rate and activation energy versus the determined ΔEN both yield a volcano-type curve, indicating an optimal adsorption of atomic nitrogen with intermediate surface binding strengths results in the best performance of ammonia decomposition. As illustrated in Fig. 2F, weak binding of atomic nitrogen on the Co-rich HEA-CoxMoy catalyst induces a higher kinetic barrier for dehydrogenation (NH3→*NH2→*NH→*N), while strong binding on the Mo-rich catalyst inhibits the recombination of atomic nitrogen to form nitrogen molecules. Therefore, continuous tuning of the Co/Mo ratio in the HEA-CoxMoy catalyst explores the vast compositional space that is previously inaccessible in conventional Co-Mo binary systems. Accordingly, the optimized surface with intermediate adsorption properties reaches a sweet spot between ammonia activation and recombination of atomic nitrogen, leading to maximized reactivity for ammonia decomposition.

HEAs for electrocatalysis

Electrocatalysis has played an ever-increasingly important role in sustainable and clean energy conversions. The compositional and structural diversity in HEAs permits continuous and enlarged tuning of the catalyst surface for efficient and selective electrochemical transformations. HEA electrocatalysts also afford a colorful palette to probe adsorption, activation, and conversion of molecular species bound to diverse surface sites. Systematic investigations, involving both experimental and theoretical efforts, have been conducted using HEAs to realize efficient and controlled electrochemical conversions of small molecules such as H2O, O2, CO2, alcohol, etc. The pronounced cooperative effects on the HEA surface could potentially break the scaling relationships for electrocatalysis, surpassing the long-established not-too-strong, not-too-weak guidance (68).

Oxygen reduction reaction. Oxygen reduction reaction (ORR) typically involves four proton-electron transfers to reduce oxygen to water (O2 + 4H+ + 4e → 2H2O) or two proton-electron transfers to produce hydrogen peroxide (O2 + 2H+ + 2e → H2O2) in acidic solutions. In alkaline media, the four-electron pathway yields hydroxide ions (O2 + 2H2O + 4e → 4OH), whereas the two-electron process produces peroxide ions (O2 + H2O + 2e → HO2 + OH) (69). The four-electron reaction is the cathode reaction in fuel cells and thus has attracted extensive interests for both fundamental and technological studies. The nonideal scaling relations among multiple intermediates including O*, OH*, and OOH* induce an overpotential of 0.3 to 0.4 V even for the most active ORR catalysts such as Pt and Pd, which constitutes a large portion of the overall overpotentials for fuel cells (70). Therefore, substantially lowered overpotential, faster electrochemical kinetics, and reduced cost are desired for ideal ORR catalysts.

Previous studies have suggested that surface binding of the oxygen-containing intermediates with optimal strength has become a well-accepted criterion for the discovery and design of efficient ORR catalysts (71, 72). While being used to rationalize the ORR activity of unary and traditional alloys, this theory can hardly be applied to HEAs owing to the inherent surface complexity. Moving a step forward, Rossmeisl and colleagues (73) developed a predictive model that predicts the surface adsorption energies of the ORR intermediates based on the local compositions. The authors calculated the *OH and *O adsorption energies on a random subset of possible surface binding sites on the (111) surface of the IrPdPtRhRu HEA. A linear regression model was accordingly constructed and then extended to the full span of the *OH and *O adsorption energies on all the possible surface sites (Fig. 3A). The corresponding near-continuum distribution of the adsorption energies indicates that the position and intensity of the adsorption energy peak can be modulated and potentially optimized through tailoring the surface composition of the HEA. Guided by the optimal *OH and *O adsorption energies, Ir0.102Pd0.320Pt0.093Rh0.196Ru0.289 was predicted to have a ~40-mV lower overpotential relative to that of Pt (111), which is the best pure metal surface for ORR. Interestingly, without constraining the number of the metal elements, the model predicted that Ir0.175Pt0.825 will be an even better ORR catalyst with a ~90-mV lower overpotential compared with that of Pt (111). The results that go beyond the multicomponent system demonstrate the universality of this computational model, which can function as an unbiased search engine to discover high-performance ORR catalysts with optimal elemental compositions.

Fig. 3 HEAs for electrocatalysis.

(A) Adsorption energies of *OH (left) and *O (right) based on DFT calculations, where each color represents an individual binding site. Reproduced with permission from Elsevier (73). (B) Comparison between the predicted OH* adsorption energies and the experimentally measured ORR activities. Reproduced with permission from Elsevier (74). (C) Schematic illustration of the combinatorial and high-throughput synthesis of MMNCs. Reproduced with permission from the National Academy of Sciences ( (75). (D) Comparison of the ORR activities (overpotentials at −0.5 V at normalized scale) of individual, binary, ternary, and quinary alloy nanoparticles prepared by the ionic liquid–assisted cosputtering method. Reproduced with permission from John Wiley and Sons (80). (E) The HER activities of the FeCoPdPtIr@GO synthesized by the FMBP method and loaded onto carbon paper (CP), Pt/C, and pure carbon paper. Reproduced with permission from the Nature Publishing Group ( (30). (F) Anodic and cathodic polarization curves of the CoFeLaNiPt HEMG catalyst and its individual components, all of which were prepared by the nanodroplet-mediated electrodeposition. Reproduced with permission from the Nature Publishing Group ( (100). (G) Comparison of the specific activity of electrochemical methanol oxidation using the HEA nanoparticles and the monometallic ones. The arrows show the scan directions of the cyclic voltammetry. Reproduced with permission from the American Chemical Society (34).

The surface adsorption properties of HEAs are determined by the ligand effect, which originated from the electronic perturbation from the metal species in the vicinity of the absorbate and the coordination effect arising from the distinct local coordination environments such as facets and atomic vacancies. The work from Rossmeisl and colleagues studied the impact of elemental composition that mostly tunes the ligand effect, while both effects need to be considered to achieve a more accurate prediction. Regarding this, Lu et al. (74) developed a neural network model based on DFT calculations to simultaneously explicate both the ligand and coordination effects. This combined model allows universal prediction of the *OH adsorption energies on the surface sites of IrPdPtRhRu with 12 different coordination structures. As shown in Fig. 3B, the general agreement between the experimentally measured activities and the computed adsorption energies validates the high accuracy of the prediction, which further permits decoupling of the ligand and coordination effects. In addition, a number of composition and structure factors including element identity, coordination number, neighbor atom distance, etc., can be systematically investigated to navigate the optimal *OH adsorption manner.

Compared with the rapid progress of computational approaches, the corresponding experimental development in exploring HEAs for ORR has lagged behind. This is mainly hindered by the lack of high-efficiency synthetic and measurement tools to evaluate different HEAs. Hu and colleagues (75) developed the high-throughput synthesis of multimetallic nanoclusters (MMNCs) through modifying the carbothermal shock technique. As illustrated in Fig. 3C, metal-salt precursors with desired recipes were dispersed onto carbon support, which were further patterned on the copper plate. Rapid radiative heating allowed one-batch synthesis of up to 88 MMNC samples with combinatorial elemental compositions, ranging from pure metals to quinary and octonary samples. For an expedited prescreening of the fabricated MMNC catalysts, the authors used a scanning droplet cell setup where the copper substrate functions as the current collector. The results showed that PtPdRhNi and PtPdFeCoNi exhibited much higher ORR activities relative to that of the Pt control, which was further validated using a prototypical rotating disk electrode. Another work by Ludwig and co-workers (76) demonstrated a closed-loop strategy that combines DFT calculation, machine learning, combinatorial synthesis, and high-throughput measurement to the discovery of advanced electrocatalysts. With a machine learning model trained by a DFT dataset of *OH and *O binding energies, the authors interrogated the composition-dependent ORR activity of the Ag─Ir─Pd─Pt─Ru HEA system. The identified HEAs with optimal adsorption properties were synthesized as thin films and measured using the scanning droplet cell. The obtained results were further analyzed to refine the theoretical model, bringing high prediction accuracies with iterative operations. These two examples combining high-throughput synthesis and theoretical predictions with rapid screening pipelines demonstrate the unprecedented capability to achieve accelerated and potentially automatic materials discovery for high-performance HEA catalysts.

To obtain monodisperse and freestanding HEA nanoparticles, Chen et al. (77) turned to colloidal synthesis. The authors prepared intermetallic PdCu nanoparticles, upon which Pt, Ni, and Co were simultaneously deposited on the surface via seed-mediated coreduction. Further annealing (600°C) of the PdCu@PtNiCo core@shell architectures triggered atomic diffusion across the core/shell interface, producing PdCuPtNiCo HEAs with well-retained nanoparticulate morphologies. The alkaline ORR performance of the HEA exceeded that of the heterostructured PdCu@PtNiCo without annealing and the commercial Pt/C catalyst. Rotating ring-disk electrode experiments indicated that oxygen is efficiently reduced on the surface of PdCuPtNiCo through the four-electron transfer pathway, which encompasses a lower ratio of peroxide relative to that of the Pt/C catalyst. Moreover, stability tests revealed that Pt diffuses out to form a Pt-rich skin that effectively prevents particle aggregation and structure degradation. The observed structure heterogeneity could be caused by the adsorbate-induced surface restructuring under electrochemical conditions, and more work is anticipated to elucidate the underlying mechanism.

Reducing the cost of the ORR catalyst is also important, especially considering their integration into practical devices such as fuel cells and metal-air batteries. Several attempts have been made to prepare nanoporous HEA alloys with low Pt contents (78, 79). Schuhmann and colleagues (80, 81) have systematically explored transition metal–based HEA electrocatalysts for ORR, with a particular focus on understanding the electrochemical behaviors on the multisite surface. Using an ionic liquid–assisted cosputtering method, the authors prepared the Cr─Mn─Fe─Co─Ni nanoparticles with the size less than 2 nm. The quinary HEA nanoparticles delivered an unexpectedly high ORR activity, which is even comparable to the performance of Pt under the same conditions (Fig. 3D). Furthermore, adjusting the Mn content in the Cr─Mn─Fe─Co─Ni system measurably modulated the ORR activity, which was further elaborated by using the inflection points of the voltammetric activity curves as the activity descriptor for ORR (82).

Despite the success in applying transition metal–based HEA catalysts for efficient ORR, little has been known considering how to interpret and predict the corresponding electrochemical activity curve. For unary or conventional alloyed electrocatalysts, one polarization curve is typically yielded in voltametric activity measurement. In contrast, the HEA catalysts exhibit a combination of several curves, corresponding to the diverse active sites with similar binding energies (83). With a simplified model, Schuhmann and colleagues managed to simulate the ORR activity curve in the Cr─Mn─Fe─Co─Ni system. Further experimental results showed that the HEA catalysts containing five or more elements outperformed the corresponding binary, ternary, and quaternary alloys in alkaline media. The broad adsorption energy distribution of the HEA catalysts partially covers more optimal binding energies for the intermediates, hence markedly boosting the ORR activity. This body of work from Schuhmann and colleagues affords a distinct route toward understanding the interrelationships among composition control, modification of surface adsorption of the ORR intermediates, and tuning of the electrochemical behaviors. The developed concept can be further extended to optimization of the catalyst stability, which is important for the design of robust noble metal–free ORR catalysts.

Oxygen evolution reaction. Similar to ORR, oxygen evolution reaction (OER) also involves four proton-coupled electron transfers with sluggish kinetics but based on the half-reactions where molecular oxygen is produced in acidic (2H2O → O2 + 4H+ + 4e) or alkaline media (4OH → O2 + 2H2O + 4e). To take advantage of the highly tunable surface properties, researchers have investigated bulk and nanostructured HEAs as OER catalysts (8486). Contrary to the reducing conditions in ORR, the high positive potentials required for OER tend to oxidize the surface of the metal catalysts and form metal oxides or (oxy)hydroxides (87). Recent studies have revealed that oxidation of HEAs is governed by the Kirkendall effects (88), where the metal atoms diffuse outward and form disordered oxidation layers. It is thereby important to note that in most cases, the active sites of the HEA catalysts for OER are the restructured oxide or (oxy)hydroxide surface layers instead of the original metallic phase. Ding et al. (89) observed the formation of a metal-core/oxide-shell structure in the nanoporous FeCoNiCrNb high-entropy intermetallic (HEI) Laves phase. Compared with that of the state-of-the-art RuO2 reference, this unique core-shell structure exhibited a higher OER activity, faster kinetics, and advantageous stability in alkaline solutions. In another study, Jin et al. (90) prepared a series of nanoporous AlNiCoIrM (M = Mo, Ni, V, Cu, and Cr) HEAs and applied electrochemical activation process to introduce an Ir-rich surface. The AlNiCoIrMo sample delivered a superior OER activity in acidic media, exceeding the performance of commercial IrO2. Computational investigations suggested that the increased covalency of the Ir─O bond in the surface mixed oxide sites is the main contribution to the enhanced OER activity. Analogously, Qiu et al. (91) prepared AlNiCoFeX (X = Mo, Nb, and Cr) nanostructures with oxide surface layers as alkaline OER catalysts, which were further integrated into the flexible direct ethanol fuel cells (92).

The appealing performances of HEAs functioning as both ORR and OER catalysts have spurred interests in the application of bifunctional oxygen electrocatalysts. This is particularly useful for metal-air batteries, which involve ORR during discharge and OER during charge. Using the carbothermal shock method, Hu and co-workers (93) synthesized a set of multimetallic nanoparticles for aprotic oxygen catalysis in Li-O2 batteries. They found that the stability of the electrocatalyst is closely related with the configurational entropy. With comparable activities, the octonary sample (RuIrCeNiWCuCrCo) outperformed the quaternary one (RuIrCeNi) in long-term operation, and the performance of the quaternary one exceeded that of the binary (RuIr) one. In comparison, the phase-segregated multimetallic catalysts synthesized using the wet impregnation approach suffered from severe oxidative degradation. Fang et al. (94) integrated the noble metal–free HEAs in aqueous Zn-air batteries and demonstrated the as-formed multicomponent surface oxides with favorable eg occupancy and optimal covalency of the metal-oxygen bond impart the enhanced electrochemical activity and stability.

Hydrogen evolution reaction. As the other half-reaction for electrocatalytic water splitting, hydrogen evolution reaction (HER) involves two proton-coupled electron transfers (2H+ + 2e → H2 in acidic media and 2H2O + 2e → H2 + 2OH in alkaline solutions) and only one intermediate species (H*) in the rate-determining step. The volcano plot describing the hydrogen adsorption free energy (ΔGH) on metal surfaces indicates that an active HER catalyst requires an optimal binding to the reaction intermediate that is neither too strong nor too weak. With an almost thermoneutral ΔGH, Pt proves to be the most active HER catalyst that requires minimal overpotential to achieve high hydrogen production rates in acidic solutions (70). HER has therefore been primarily applied as a model reaction to develop feasible synthetic techniques and probe structure-function relationships of nanostructured HEAs.

The abovementioned carbothermal shock method can be used to fabricate HEA nanoparticles supported on carbon nanofibers, while the applied joule heating can hardly be extended to catalyst supports with poor electrical conductivities. Gao et al. (30) developed a facile FMBP technique to overcome this issue. During synthesis, moving the supported precursors into the heating zone triggers rapid temperature increase (reaching 923 K within 5 s). The instant pyrolysis results in formation of the HEA nanoparticles containing up to 10 elements (MnCoNiCuRhPdSnIrPtAu). In contrast, the traditional fixed bed pyrolysis produces phase-separated heterostructures owing to a much slower heating rate (20 K/min). This approach can be readily extended to substrates with poor electrical conductivities, including graphene oxide (GO), γ-Al2O3, and zeolite. With electronic modulation via inclusion of Fe, Co, and Pd, the GO-supported quinary HEA nanoparticles (FeCoPdIrPt) exhibited enhanced HER activity and stability in alkaline solutions relative to that of the commercial Pt/C catalysts (Fig. 3E). In another research, Dai and colleagues (95) took advantage of the acoustic cavitation and achieved atomic mixing of different metal species under ambient conditions. These synthetic methods share the same merit with the carbothermal shock technique, where different metal atoms are mixed and kinetically trapped during the nonequilibrium process.

Mechanistic insights have also been revealed to uncover the electronic structures of nanostructured HEAs. The d-band theory, which has been widely used to rationalize the HER performance of unary and binary noble metal electrocatalysts (96), can hardly be applied to HEAs because of the strong synergy among different metals. To bridge this gap, Kitagawa and co-workers (97) examined the link between the electronic structure and the HER activity of the HEA catalyst. Hard X-ray photoelectron spectroscopy (HAXPES) was deployed to probe the valence band structure of the IrPdPtRhRu HEA nanoparticles, which exhibited measurably higher HER activities in both acidic and alkaline solutions compared with that of the monometallic catalyst and even the commercial Pt catalyst. The measured broad valence band spectrum of the HEA nanoparticles renders direct evidence for the hybridization of the metal orbitals. Interestingly, further analysis showed that the HEA catalyst does not follow the well-known correlation between the turnover frequency and the position of the experimental d-band center. This deviation may originate from the complex atomic arrangements and corresponding diverse local density of states on the HEA surface, indicating a potentially powerful route to surpassing the linear scaling relationship (68).

More broadly defined HEAs with varied structure orders, microstructures, and crystallinities have also been explored to catalyze HER. Jia et al. (98) combined the intrinsic site-isolation effect in intermetallics and strong chemical synergy in HEAs and fabricated a multinary HEI catalyst. The designed dual-phase FeCoNiAlTi HEI alloy displayed a dendritic L12 phase, where the Al and Ti atoms occupy the vertices and the Fe, Co, and Ni atoms settle on the face centers. DFT calculations suggest that the Ti atoms with strong adsorption energies facilitate H2O adsorption, whereas the isolated Al atoms coordinating with Fe, Co, or Ni provide a beneficial ΔGH for efficient adsorption and desorption of H*. In this way, the conversion of both reactant (H2O) and intermediate (H*) are promoted, collectively leading to enhanced HER performances that are superior to those of Pt. Yao et al. (99) fabricated a monolithic nanoporous CuAlNiMoFe electrode using a facile and scalable alloying/dealloying approach. The electroactive multielemental CuNiMoFe surface is in situ formed on the body-centered cubic (bcc) CuAlNiMoFe precipitates, which are seamlessly anchored on the Cu skeletons. The entropy-stabilized surface containing atomically mixed Cu, Ni, Mo, and Fe species facilitates H* adsorption and desorption, whereas the nanoporous Cu skeleton serves as an ideal current collector for electrical conduction as well as a robust morphological template that promotes the transport of ionic and molecular species for HER. High-entropy metallic glasses (HEMGs) with low crystallinities have also been fabricated by Glasscott et al. (100) using nanodroplet-mediated electrodeposition. By confining the metal salt precursors to water nanodroplets suspended in dichloroethane, the authors successfully governed the localized nucleation and domain growth. This electroshock synthesis strategy shares the same merit of kinetic control with the carbothermal shock approach. Nonetheless, the room temperature operation cannot provide enough energy to overcome the thermodynamic barrier to crystallization, thus yielding amorphous structures with homogeneous yet random atomic distributions. The quinary CoFeLaNiPt HEMG nanoparticles exhibited advantageous activity and stability functioning as both HER and OER catalysts, which is promising to drive overall water splitting (Fig. 3F).

Carbon dioxide reduction. Another key reaction for energy conversion is the electroreduction of carbon dioxide, where CO2 is electrochemically reduced to valuable chemicals and fuels. CO2 electrochemical reduction also involves multielectron transfers that are similar to ORR but yields a much broader scope of products including C1 products (carbon monoxide, formate, formaldehyde, methane, methanol, etc.), C2+ hydrocarbons and oxygenates, and heteroatom-containing chemicals (70, 101). Meanwhile, the simultaneous HER process in aqueous solutions also produces the unwanted H2 as the competing biproduct. Fabricating highly efficient and selective CO2 reduction catalysts toward value-added commodities is thereby greatly desired and has been actively pursued.

Rossmeisl and colleagues (102) investigated electrochemical CO2 and CO reduction on the HEA surface by combining DFT with supervised machine learning. The (111) facets of two quinary fcc HEAs, CoCuGaNiZn and AgAuCuPdPt, were chosen as the model systems. With the Gaussian process regression trained with the DFT-calculated adsorption energies of H and CO, the authors were able to assess the likelihood of yielding multicarbon products on all the possible surface microstructures. Further analysis illustrated the correlation between composition tuning and modulation of the CO and H adsorption energies, together with the trade-offs between activity and selectivity. On the basis of the criteria of weak H adsorption and strong CO adsorption, the authors identified binary GaNi as a locally optimal candidate, which was further experimentally verified.

Complementary to the computational predictions, Nellaiappan et al. (103) applied nanocrystalline AuAgPtPdCu HEAs for the electrocatalytic conversion of CO2. The Cu species with the Cu2+/Cu0 redox pair was determined as the main active site for CO2 reduction, whereas the other spectator components contribute to electronic and structural regulation of the single-atom Cu sites. At low overpotentials [−0.3 V versus reversible hydrogen electrode (RHE)], the HEA catalyst converts nearly all the CO2 to gaseous products (38.0% CH4, 29.5% C2H4, 4.0% CO, and 26.4% H2), which was attributed to the modification of the O* and CH3O* adsorption energies on the HEA surface according to DFT calculations. It is worth pointing out that much is still unknown about the exact behaviors of the CO2 reduction intermediates on the HEA surface. For instance, noticeable CO2 reduction activities were observed for the AuAgPtPdCu catalyst in the CO2-saturated K2SO4 solutions, but not in the CO2-saturated NaHCO3 electrolytes that have been commonly used. This unconventional feature can be useful for the design of pH-dependent electrocatalysts. Meanwhile, continuous tuning of the active sites on the HEA surface may favor cascade reactions where the intermediates produced on the neighboring sites react with each other through C─C coupling and promote the formation of higher-value chemicals.

Alcohol oxidation. As one of the most promising electrochemical setups to power electric vehicles, fuel cells enable continuous supply of electricity converted from the chemical energy of fuels. Direct alcohol fuel cells (DAFCs) are advantageous compared with the hydrogen-fed ones because of the higher volumetric density and convenience in storage and transport (104). Methanol and ethanol are two common fuels for DAFCs. The excellent corrosion resistance and strong synergistic effects make HEAs promising catalysts to catalyze efficient and complete oxidations of the alcohol fuels.

The platinum-group metals (PGMs), including Ru, Rh, Pd, Os, Ir, and Pt, have been extensively used as electrocatalysts for alcohol oxidations. While simple reactions can be triggered by mono- and bimetallic PGMs, it is difficult to drive complex reactions involving multiple proton-electron transfers and intermediate species. Kitagawa and co-workers (34) applied the PGM-HEA nanoparticles for electrocatalytic ethanol oxidation that involves as many as 12 proton-electron transfers. The PGM-HEA nanoparticles were prepared using a facile polyol method. As illustrated in Fig. 3G, the PGM-HEA nanoparticles efficiently catalyzed the ethanol oxidation reaction, exhibiting a much higher activity relative to that of the commercial Pd/C, Pd black, and Pt/C catalysts, respectively. In stark contrast, negligible activity was observed for the physical mixture of the six unary PGM nanoparticles. The PGM-HEA also delivered a mass activity more than 1.5 times higher than that of the most active catalyst to date (Au@PtIr/C). Moreover, compared with the ternary, quaternary, and quinary PGM alloys, the PGM-HEA exhibited the highest current density in the full potential range, reflecting its enhanced capability to efficiently catalyze oxidation of multiple intermediates. To better understand the contribution of each metal, the authors compared the cyclic voltammetry curves of each individual constituent in the presence and absence of ethanol. Pt and Pd are active for ethanol conversion but become poisoned by the adsorbed (CO)ad or CHx species. Os and Ru, although not directly active for ethanol conversion, facilitate oxidation of (CO)ad and thus mitigate the poisoning effect for Pt and Pd. Ir and Ru ensure that dehydrogenation or C─C cleavage occurs at a low potential, while further oxidation hinges on the Pt and Pd components. The atomically mixed metals in HEAs play distinct yet concerted functions that give rise to efficient and complete oxidation of ethanol.

Alloying PGMs with transition metal elements is another route to increasing the alcohol oxidation capability. Feng et al. (105) used a sparking mashup technique to fabricate up to 55 alloy nanoparticles ranging from binary alloys to HEAs. The as-synthesized Pt and Pd alloys displayed enhanced performances for the electrochemical oxidation of methanol, ethanol, and formic acid. Alloying Pt (or Pd) with other metal species modulates the electronic structure and weakens the binding of the CO-like intermediates and thus alleviates the related poisoning effect. In another study, Li et al. (106) prepared the Pt18Ni26Fe15Co14Cu27 HEA nanoparticles, which exhibited remarkable methanol oxidation activities and enhanced CO antipoisoning in alkaline solutions. Using DFT calculations, the authors analyzed the partial projected density of states of each element upon methanol adsorption and revealed an efficient site-to-site electron transfer process. This multisite HEA catalyst also showed superior activity and stability for HER in alkaline solutions (107) and pH-universal nitrogen reduction (108). In addition to HEAs with the fcc structure (109111), the one having the hexagonal close-packed (hcp) structure has also been synthesized by Yusenko et al. (112) for electrocatalytic oxidation of alcohol. Moreover, the authors realized phase tuning by modifying the elemental compositions. For instance, Ir0.19Os0.22Re0.21Rh0.20Ru0.19 has the hcp structure, whereas Ir0.26Os0.05Pt0.31Rh0.23Ru0.15 crystalizes in the fcc manner. This provides a starting point to understand polymorphism in HEAs, which has been somewhat limited due to the prevalence of the fcc-structured HEAs (Table 1).

Summary of HEAs for catalysis. To summarize, HEAs have shown enhanced performances catalyzing various thermal and electrochemical reactions. The advantageous catalytic properties of HEAs can be ascribed to the wider compositional tuning range, which even surpasses the miscibility limitation for conventional alloys. Confining five or more metal species at the atomic scale synergistically modifies the electronic and geometric characteristics on the HEA surface. The diverse surface sites accordingly introduce a wide scope of adsorption energies for the intermediates, bringing more opportunities for modulating the activity and selectivity. This is particularly useful for optimizing reactions that involve multiple charge transfers, such as electrochemical CO2 reduction and alcohol oxidation. The microstructure of the HEA catalysts also plays an important role, where higher surface area and robust metal/support interfaces are desired. In addition, the improved catalytic stability of HEAs, which has been taken for granted as a result of the entropy-induced stabilizations, can be a complicated topic and requires more investigations. Recent studies have revealed that HEAs are not impervious under electrochemical reactions (77), and the associated surface restructuring can be either beneficial or harmful. Understanding retention and reconstruction of the surface and subsurface structures, which vary according to different reaction environments (liquid and gas phases) and driving forces (thermal and electrochemical reactions), is thereby important to clarify the catalytic behaviors of the HEAs.


In 2015, Maria and colleagues (113) reported the entropy-induced stabilization of single-phase multicomponent oxides, in which Mg, Ni, Zn, Cu, and Co are randomly distributed in the rock salt oxide lattice (Fig. 4A). Since then, studies have unveiled more and more exotic properties for HEOs. Distinct from HEAs mostly having single-site occupancies in the fcc structure, HEOs have independent cation and anion sublattices that give rise to increased structural diversities (114). Therefore, in addition to the expanded tuning range in composition and structure, elucidating the impact of the increased entropic effects on the oxygen part, especially activation of lattice oxygen, has become the focus point for HEO-based catalysts. The ability to create and control oxygen defects in various HEO structures is particularly useful for increasing the catalytic activity of various oxidation reactions.

Fig. 4 HEOs for catalysis.

(A) XRD patterns showing the structure evolution of the equal molar mixture of MgO, NiO, ZnO, CuO, and CoO annealed in air at different temperatures. The diffraction peaks corresponding to the non–rock salt impurity phases are highlighted using arrows. Reproduced with permission from the Nature Publishing Group ( (113). (B) Schematics displaying the structures of the high-entropy rock salt, fluorite, and perovskite oxides. Oxygen atoms are in red, and the high-entropy metal sites are in blue/white. A and B sites in the perovskite oxide structures are highlighted in blue/white and green/white, respectively. (C) In situ Cu L2,3 edge XAS spectra of the Mg0.2Co0.2Ni0.2Cu0.2Zn0.2O catalyst in CO at 235°C (red to blue with a 60-min interval) and then switched to the O2 atmosphere at the same temperature (black). Reproduced with permission from the American Chemical Society (48). (D) Thermochemical water splitting performance of (FeMgCoNi)Ox, NiFe2O4, and CoFe2O4 and the calculated thermodynamic limit of CeO2. Reproduced with permission from the Royal Society of Chemistry (121). (E) Methane oxidation performance of 10-MEO-PdO, (Zr,Ce)0.6Mg0.3Pd0.1Ox (4-MEO-Pd), and PdOx supported on carbon paper at 648 K under dry conditions. Reproduced with permission from the Nature Publishing Group (37). (F) Schematic illustration for the mechanochemical synthesis of single Pd atoms supported on (CeZrHfTiLa)Ox and Pd clusters anchored on CeO2. Reproduced with permission from the Nature Publishing Group ( (31). (G) Temperature-dependent XRD patterns of the Au-HEO sample switched between 700° and 900°C (left) and the magnified in situ XRD intensity map in the first cycle heated from 700° to 900°C (right). Reproduced with permission from the Royal Society of Chemistry (126). a.u., arbitrary units.

The catalytic applications based on HEOs can be mainly divided into two categories. The first is to directly apply HEOs as catalysts, where the entropy-stabilized aliovalent cations lead to unique defect features and adjustable electronic properties in high-entropy rock salt, fluorite, and perovskite oxides (Fig. 4B). The oxide lattice affords a dynamic matrix to buffer the structural distortions among different cationic species. The second is to apply HEOs as robust supports to anchor the transition metal and noble metal active species. Probing the corresponding metal-support interactions affords more insights into the enthalpy-entropy correlations based on HEOs, which can be sometimes counterintuitive yet potentially powerful. In either case, understanding activation, stabilization, and migration of oxygen species on the surface and in bulk of HEOs is crucial, which will be discussed and compared in this section (Table 2).

Table 2 Summary of HEOs for thermocatalysis, electrocatalysis, and photocatalysis.

T, thermocatalysis; E, electrocatalysis; P, photocatalysis.

View this table:

HEOs as catalysts

HEOs with common rock salt and fluorite structures are appealing targets for thermocatalysis. Modified Jahn-Teller effects of the metal cations induce distorted structural and modified electronic features. Homogeneous and random distribution of the aliovalent cations in the oxide lattice fosters lattice oxygen activation in the form of defects. However, extreme synthetic conditions including elevated temperatures and high pressures frequently produce bulk samples with low surface areas. Oxygen partial pressure has also been demonstrated as an important factor that contributes to the formation of HEOs (37). Multiple synthetic strategies have thereby been tailored to access nanostructured HEOs for diverse catalytic reactions.

Selective oxidation of benzyl alcohol to benzaldehyde, benzoic acid, and benzyl benzoate has drawn wide interests to provide essential intermediates for the manufacture of medicines and agrochemicals. Feng et al. (8) found that a holey lamellar HEO catalyst has high activity for the solvent-free aerobic oxidation of benzyl alcohol. Using an anchoring and merging strategy, the authors prepared the rock salt Co0.2Ni0.2Cu0.2Mg0.2Zn0.2O HEO with a holey lamellar architecture. Structural reversibility between the multiphase state at 750°C and the single-phase at 900°C was monitored by the corresponding XRD patterns, which is important to demonstrate the entropy-induced transitions. The holey lamellar HEO was applied for aerobic oxidation of benzyl alcohol to benzoic acid and exhibited up to 98% conversion in 2 hours under the solvent-free atmospheric conditions. The bulk HEO counterpart as well as the arbitrary unary, binary, ternary, and quaternary counterparts exhibited a much lower activity. Further investigation revealed that the holey HEO promotes formation of oxygen vacancies due to the small domain size, random substitution of multiple metal cations, and oxygen consumption during the burning off of the GO support. The enriched oxygen vacancies on the holey HEO lead to enhanced oxygen delivery capacities and stronger adsorption to benzyl alcohol molecules relative to that of the bulk counterpart, giving rise to efficient molecular conversions. The rock salt MoNiCuZnCoOx has also been used for oxidative desulfurization oxides (115), which is a crucial process to eliminate sulfur contents in fossil fuels. The uniformly dispersed Mo6+ species and efficient activation of lattice oxygen in the HEOs facilitate an enhanced conversion of the thiophene derivatives compared with that of the Mo-based binary and ternary oxides.

Mesoporous metal oxides with tunable pore sizes, structures, and compositions are attractive for catalytic applications. Dai and co-workers (116) presented a facile mechanochemistry-assisted synthesis route of the mesoporous CuNiFeCoMgOx-Al2O3 hybrids. Metal precursors including aluminum isopropoxide and anhydrous metal chlorides, together with tunable soft templates, were introduced to the ball milling process. The as-obtained precursor was then calcinated, resulting in the formation of the rock salt HEO structure supported on the sponge-like alumina nanoarchitectures. CO oxidation was performed to evaluate the catalytic properties of the mesoporous unary metal oxide–Al2O3 and the HEO-Al2O3 hybrids. CuO-Al2O3 and HEO-Al2O3 exhibited the best activities with the T100 values of 220° and 260°C, respectively. Upon treatment in 1000 parts per million of SO2, the activity of CuO-Al2O3 markedly dropped, while the performance of HEO-Al2O3 remained almost unaltered. The rock salt HEO phase thus displayed a noteworthy enhancement in sulfur resistance in CO oxidations, which is of vital significance for industrial processes.

Although the metal cations randomly distributed in the HEO lattice can be viewed structurally equivalent, their roles in catalytic reactions vary. Some function as active sites that account for the adsorption and conversion of molecular species, while the others act as neighboring spectators that permit electronic or geometric regulation. To identify the active species in the rock salt HEO (Mg0.2Co0.2Ni0.2Cu0.2Zn0.2O) for CO oxidation, Fracchia et al. (48) used operando soft XAS to monitor the evolution of the L2,3 edge of Cu, Co, and Ni in different atmospheres. While XAS is typically considered as a bulk technique, the total electron yield mode endows the capability to probe the 3d states of the transition metal species on the surface and subsurface regions, which is particularly useful for catalytic studies. The authors found that Cu(II) in the HEO could be reduced to Cu(I) by CO at a temperature higher than 130°C (Fig. 4C), whereas Co and Ni remain unaltered under the same condition. This makes sense since Cu is the most anomalous one among the five elements taking the size- and structure-related and electronic effects into consideration (114). The Cu site was accordingly identified as the main active site for CO adsorption and oxidation. Moreover, the rock salt HEO exhibited a higher tolerance against reduction compared with that of CuO. This underscores the role of the increased configurational entropy in stabilizing Cu(II) in the cubic structure rather than transforming back to the original monoclinic structure.

Ceria-based fluorite oxides have also been revisited to initiate a series of entropy-centered discussions. According to the Gibbs free energy equation, the enhanced entropic contributions at higher temperatures may compensate more of the enthalpic effects, giving rise to higher stabilities under harsh operating conditions. Dai and colleagues (117) reported a mechanochemical strategy to fabricate heterostructured, ultrastable CuCeOx-HEO catalysts. CeO2 and HEO (MgZnCoCuNiOx) were individually prepared and then mixed for ball milling. Driven by the mechanochemistry-induced short-range high temperatures, Cu and Zn migrated from the HEO domain into the CeO2 lattice and formed CuZnCeOx solid solutions. Directly annealing the mixture of the cerium and metal precursors would only produce metal oxides deposited on the CeO2 surface. CuCeOx-HEO exhibited an outstanding high-temperature stability as almost no activity degradation was observed after calcination at 900°C. The HEO functions as a stabilized reservoir, which provides abundant Cu species that migrate across the oxide-oxide interface and form the stable CuCeOx structure. In contrast, CuO-CeO2 showed a marked activity deterioration after the treatment at 900°C, demonstrating the key role of the entropy-induced structure reconstruction at the oxide-oxide interface. Using a similar process, Shu et al. (9) overcame the intrinsic solubility limitation of the aliovalent metal cations in the fluorite structure. The authors simultaneously incorporated 10 mole percent (mol %) Cu2+, 10 mol % Co2+, 10 mol % Mg2+, 10 mol % Ni2+, and 10 mol % Zn2+ cations into the CeO2 lattice, which facilitate the formation of the vacancy-mediated reactive oxygen species as well as local lattice distortion. With diverse surface sites that alleviate competitive adsorption of different gaseous components, the entropy-stabilized multicomponent CeO2 catalysts permitted efficient treatment of CO-toluene-propylene and typical automotive exhaust and displayed enhanced thermal and hydrothermal stabilities.

Perovskite oxides are another class of appealing oxides because of the intrinsic dual-site cation occupancy and common oxygen nonstoichiometry (118). High-entropy perovskite oxides (HEPOs), where both A and B sites can be filled with different sets of metal cations, afford flexible electronic and physiochemical properties for catalytic applications. Using mechanical alloying followed by high-temperature oxidation, Edalati et al. (119) prepared a two-phase HEPO composed of 60 mol % of the monoclinic phase (AB2O7) and 40 mol % of the orthorhombic structure (A6B2O17), where A represents Ti, Zr, and Hf, and B represents Nb and Ta. With an overall composition of TiZrHfNbTaO11, this binary HEPO had a main bandgap of 2.9 eV and exhibited good light absorbance in both ultraviolet and visible-light regions, in stark contrast to the negligible light absorbance for the individual metal oxide component. The tunable electronic properties derived from the d0 configuration together with the enhanced light absorbance in the visible-light range give rise to efficient photocatalytic water splitting. In another study, Wang et al. (120) fabricated spinel (Co, Cu, Fe, Mn, Ni)3O4 nanoparticles anchored on carbon nanotubes as efficient alkaline OER electrocatalysts.

Zhai et al. (121) extended the cation-mixing strategy to a broader class of metal oxides, polycation oxides (PCOs), to catalyze two-step thermochemical water splitting (TWS) reactions. During this two-step process, metal oxides undergo a redox cycle, releasing oxygen at high temperatures (TH), and then get oxidized when triggering the thermochemical steam-to-H2 conversion at lower temperatures (TL). The partial molar entropy and enthalpy play crucial roles in maximizing the thermocatalytic conversion with low TH, as well as stabilizing the metal oxide phase. The authors combined sol-gel and solid-state methods to prepare the (FeMgCoNi)Ox PCO with coexisting rock salt and spinel phases. The performance of the (FeMgCoNi)Ox catalyst exceeded that of the previously reported materials, including spinel ferrites, substituted ceria, and Mn-based perovskite oxides (Fig. 4D). XANES data of the quenched (FeMgCoNi)Ox sample suggested that Fe is the only redox active element, while the role of the other spectator species remains elusive. Dynamic interactions across the interface between the rock salt and spinel domains and localized heating effects promote the thermochemical production of hydrogen, which can be integrated into large-scale chemical infrastructures. Strictly speaking, (FeMgCoNi)Ox does not fall in the category of HEMs since there are less than five principal components. However, the enthalpy-entropy correlations can still be exploited as a versatile guideline to improve the catalytic performances.

HEOs as supports

The excellent chemical and thermal stabilities and favorable formation of oxygen defects render HEOs as attractive candidates for catalyst supports. Noble metal species with various sizes, ranging from nanoparticles to atomic clusters and single atoms, have been anchored on HEOs. In a pioneering study, Dai and colleagues (122) deposited 0.3 weight % (wt %) of single Pt atoms on the rock salt NiMgCuZnCoOx through a codeposition approach. Thermal treatment at 900°C induced the formation of the surface-confined Pt─O─M bonds (M represents Ni, Mg, Cu, Zn, and Co). A subsequent reduction step with H2 converted the O─Pt─O─M (Pt4+) to the Pt─O─M (Pt2+) bonds, creating active sites for CO oxidation. No activity loss was observed for PtNiMgCuZnCoOx for 40 hours at 135°C, validating the appealing thermal and chemical stabilities of the HEO-supported catalysts. Following this work, Dai and co-workers have developed various synthetic routes toward HEO-supported noble metal catalysts under mild operating conditions. Leveraging the high local temperature induced by ball milling, the authors incorporated up to 5 wt % of noble metal species as a combination of single atoms and nanoclusters onto the NiMgCuZnCoOx support (123). 5 wt % of Ru and Pt, when loaded onto the HEO support, both exhibited enhanced activity, selectivity, and high-temperature stability for selective hydrogenation from CO2 to CO. In addition, Dai and co-workers (124) applied sonochemistry to fabricate high–surface area HEPOs to stabilize noble metal catalysts for CO oxidation. The acoustic cavitation causes formation, successive growth, and implosive collapse of microscopic bubbles, generating massive energy with local temperatures above 5000°C and pressures exceeding 2000 atm on a time scale of ≤10−9 s. The resulted local extreme conditions drove a homogeneous mixing of different metal atoms and consequent formation of the single-phase crystalline HEPO.

A recent breakthrough from Hu and colleagues (37) afforded well-defined guidelines to access multielement oxide (MEO) nanoparticles. On the basis of the carbothermal shock technique, the authors systematically studied the impact of temperature, oxidation, and entropy in the formation of single-phase MEO nanoparticles with rock salt, fluorite, spinel, and perovskite structures. Increasing the synthetic temperature and oxygen partial pressure and incorporating more metal cations were shown to favor the formation of the single-phase MEO nanoparticles ranging from unary to denary compositions. An efficient designing scheme was further demonstrated to optimize the nanostructured MEO catalysts for methane combustion. Alkali metals promoting the electron transfer, 3d-5d transition metals improving the redox properties through oxygen vacancy formation, and noble metal Pd that facilitates methane activation were optimized through a step-by-step screening process. The optimal denary (Zr,Ce)0.6(Mg,La,Y,Hf,Ti,Cr,Mn)0.3Pd0.1O2–x catalyst exhibited enhanced activity and stability when compared to the PdOx and quinary catalysts (Fig. 4E), which was attributed to the entropy-induced stabilization of Pd in a cationic state. The enriched library of MEO nanoparticles prepared using generalizable protocols promises great potential to build high-performance catalysts for expanded catalytic reactions.

Stabilizing noble metal atomic species on the oxide support is important to realize sustainable and efficient catalytic conversions. However, the relatively low Tammann temperature, the point at which noble metal species develop liquid-like behaviors and migrate on the oxide surface, leads to sintering of the catalysts and activity degradation (125). As an unconventional stabilization strategy, the enhanced entropic contributions would hypothetically favor the incorporation of foreign atoms into the underlying oxide structure. Dai and co-workers (31) demonstrated the entropy-driven stabilization of Pd single-atom catalysts (SACs) on the high-entropy fluorite oxides (HEFOs). As illustrated in Fig. 4F, the authors combined mechanical milling with high-temperature calcination to fabricate (PdyCeZrHfTiLa)Ox solid solutions, where Pd formed Pd─O─M bonds (M = Ce, Zr, Hf, Ti, and La) through cation substitution in the fluorite structure. In contrast, segregated Pd or PdO phases emerged when using unary, ternary, or quaternary fluorite oxides as substrate, validating the entropy-induced behavior. Employment of fumed silica as templates realized the construction of the porous Pd1@HEFO structure, exposing an appreciable amount of isolated Pd atoms on the oxide surface. Catalytic measurements reflected improved surface reducibility, and enriched oxygen vacancies promote adsorption and activation of molecular oxygen, encompassing enhanced CO oxidation activities. The Pd1@HEFO catalyst also exhibited outstanding thermal and hydrothermal stabilities for the simultaneous oxidation of CO, C3H6, and NO, indicating its potential for exhaust treatment of diesel engines.

To explicate the impact of the entropic effects in modifying the metal-support interactions, Dai and co-workers (126) investigated the dynamic behaviors of the HEO-supported noble metal species. Au, which is notorious for its strong tendency toward migration and aggregation at high temperatures, was selected. Au (1 wt %) was stoichiometrically added to the equimolar mixture of MgO, CoO, NiO, CuO, and ZnO and then annealed at 900°C. Interestingly, Au became well dispersed as cationic species along the formation of the rock salt single-HEO phase. Control experiments with lower annealing temperature (700°C) or fewer types of metal oxides (NiMgOx and NiMgZnOx) lead to the emergence of the separated Au phase, indicating that this unexpected dispersion of Au into the HEO lattice originated from the pronounced entropic contributions. Interestingly, a reversible behavior was observed for the Au-HEO sample. Au remains well dispersed within the HEO lattice at 900°C with enlarged configurational entropy, while it precipitates out on the oxide surface at 700°C when enthalpy effect takes control (Fig. 4G). The reversible dispersion and precipitation of the Au species into and out of the HEO support at different temperatures were correlated to distinct catalytic performances, as more exposed Au sites along the precipitation resulted in better CO oxidation activities. This study probes the dynamic interplay between the noble metal catalysts and the underlying HEO support. The self-regenerative phenomenon paves the way toward robust deposition of noble metal catalysts for high-temperature reactions. Entropy-favored construction of isolated atomic species instead of nanoscale particles also brings a fundamentally distinct pathway toward solving issues such as sintering, coking, and poisoning (127).

Summary of HEOs for catalysis. Introduction of the oxide lattice screens the entropic interactions among the metal cations, permitting independent cationic and anionic stabilizations. In addition to the expanded range in composition and structure, the involvement of oxygen species in multiple forms switches the research focus to oxidation reactions. Leveraging the entropic effects in HEOs to facilitate generation of active oxygen species under mild conditions has become the main momentum. The enhanced configurational entropy provides a distinct route to activating lattice oxygen through compensating the enthalpic gains. In parallel, the metal part functions as the adsorption site for small molecules (CO, CO2, CH4, and H2O), ions (H+ and OH), and organic hydrocarbons. Applying HEOs as catalyst supports shares the same merit of lattice oxygen activation, whereas the anchored noble metal species become the active sites. Anchoring single metal atoms on HEOs has blurred the boundary between catalyst and catalyst supports, affording a conceptually distinct alternative to robust SACs.

Another key difference between HEA and HEO catalysts is the different dependencies of surface and bulk characteristics. For HEAs, the reactants, intermediates, and products are confined on the metal surfaces. The energetic barrier for metal constituents to migrate is high, which is further restrained by the sluggish diffusion kinetics of HEAs. In contrast, the mobile oxygen species both on the surface and in bulk of metal oxides contribute to the catalytic performances, which have been proven for electrocatalytic OER and thermocatalytic methane oxidation (128, 129). Therefore, tailoring the creation, transformation, and migration of the activated oxygen species on the surface and in bulk of HEOs is of vital importance to optimize the associated catalytic capabilities.


Novel entropy-stabilized systems including high-entropy fluorides, nitrides, sulfides, phosphides, and inorganic-organic hybrids have also been designed and tailored for catalytic applications (Table 3). Compared with the oxygen atoms in HEOs, the greater orbital extension and energetic match of the p-orbitals in the nitrogen, phosphorous, and sulfur atoms with the d-orbitals of the metals introduce additional space for tuning the electronic structures (130). The identified structure-property relationships will also provide feedback and supplement to the established knowledge system of HEMs, which helps understand topics such as charge redistribution and vacancy mediation.

Table 3 Summary of novel HEMs for thermocatalysis and electrocatalysis.

T, thermocatalysis; E, electrocatalysis.

View this table:

Owing to the high electronegativity, fluorine has been considered as an important dopant to modify the adsorption energy of the OER intermediates. The ABF3-type perovskite fluorides have maximized metal-fluorine bonds with strong ionicity and intrinsic three-dimensional diffusion channels that favor oxygen transport. However, the low electrical conductivity hinders their application as efficient OER catalysts. Dai and colleagues (38) overcame this issue by introducing multiple cations to the B site to produce HEPFs. Single-phase potassium-based HEPFs, including K(MgMnFeCoNi)F3, K(MgMnCoNiZn)F3, K-(MnFeCoNiZn)F3, and K(MgCoNiCuZn)F3, were prepared by combining hydrothermal synthesis with ball milling. This combined synthetic strategy can be further extended to the preparation of the corresponding sodium-based as well as potassium- and sodium-mixed HEPFs. The optimized electrocatalyst, K0.8Na0.2(MgMnFeCoNi)F3, showed the highest alkaline OER activity, superior to that of the individual fluorite perovskite and the commercial IrO2 catalyst. The enhanced electrical conductivity and mass transfer, together with the dispersed and isolated B sites, collectively contribute to the excellent OER performance of K0.8Na0.2(MgMnFeCoNi)F3 (Fig. 5A). The as-formed metal oxide or oxyhydroxide layers on the surface of the HEPFs play a decisive role in accelerating the sluggish proton-coupled electron transfer process. HEO-fluoride solid solutions were also prepared via mechanical synthesis, where independent compositional tuning at both anionic and cationic sites enables outstanding OER performances (131).

Fig. 5 New high-entropy systems for catalysis.

(A) Comparison of the electrochemical resistance of the individual perovskite fluorides and the HEPFs. Reproduced with permission from the American Chemical Society (38). (B) Schematic showing the synthetic pathway toward high-entropy metal nitrides, combining the soft urea strategy with mechanochemistry. Reproduced with permission from John Wiley and Sons (132). (C) Comparison of the OER overpotentials and metal element numbers among unary, binary, ternary, and quaternary sulfides and quinary (CrMnFeCoNi)Sx high-entropy metal sulfides. Reproduced with permission from John Wiley and Sons (39). (D) Yield comparison of cyclic carbonates from CO2 cycloaddition with epoxides catalyzed by the HE-ZIF-BM, single-metal ZIFs (ZIF-8-BM, Cd-ZIF-8, and ZIF-67), and physical mixture of the three single-metal ZIFs (PM-ZIF), respectively. Reproduced with permission from John Wiley and Sons (134). (E) TEM image of the HE-MOF nanosheets and the Tyndall effect highlighted in the inset display good aqueous dispersibility. Reproduced with permission from the Royal Society of Chemistry (135).

More crystalline high-entropy compounds with advantageous electrochemical properties have been fabricated and interrogated. As illustrated in Fig. 5B, Dai and colleagues (132) prepared high-entropy metal nitrides using a soft urea strategy assisted by mechanochemical synthesis. Five equimolar metals including V, Cr, Nb, Mo, and Zr homogeneously distribute in the single-phase cubic nitride lattice. Hu and colleagues (39) prepared high-entropy metal sulfide nanoparticles by modifying the carbothermal shock technique. The ultrafast thermal pulse process facilitated the reaction between the metal atoms and sulfur, producing single-phase cubic-structured (CrMnFeCoNi)Sx nanoparticles. The OER performance of (CrMnFeCoNi)Sx exceeded that of the unary, binary, ternary, and quaternary sulfide counterparts (Fig. 5C), which was ascribed to the effective modulation of the electronic structure. The improved electrochemical performance was also demonstrated for high-entropy metal phosphides, which contain equimolar Co, Cr, Fe, Mn, and Ni in a hexagonal structure (133).

Because of the limited high-temperature stabilities of molecular linkers, the preparation of high-entropy inorganic-organic hybrids is considered synthetically challenging. Dai and co-workers (134) turned to mechanochemistry and successfully fabricated high-entropy zeolitic imidazolate frameworks (HE-ZIFs) under ambient conditions. During the ball milling process, the local short-range heating accelerates molecular diffusion, resulting in a random dispersion of Zn2+, Co2+, Cd2+, Ni2+, and Cu2+ in the ZIF lattice coordinated by the 2-methylimidazole linker. With the three-dimensional frameworks that are isomorphous with zeolites, the HE-ZIF maintained a high surface area (1147 m2 g−1) that is beneficial to the adsorption of molecular species. HE-ZIFs were applied for the cycloaddition of CO2 with epoxides to produce carbonates, which are routinely used in electrochemical and pharmaceutical industries. As shown in Fig. 5D, the five highly dispersed metal sites in the HE-ZIF function as efficient Lewis acidic sites in epoxide activation, giving rise to a higher yield for the conversion of CO2 compared with that of the single-cation ZIF and their physical mixtures. High-entropy metal-organic frameworks (HE-MOFs) with a two-dimensional flower-like morphology and good aqueous solubilities were also prepared as enhanced OER catalysts (Fig. 5E) (135).


Despite rapid developments in the synthesis, characterization, and catalytic applications of HEMs, only a small part of the wide compositional space has been explored. Most studies have been driven by the notion that HEMs could deliver better performances as an extension to conventional alloys. This has somewhat limited the catalytic applications of HEMs, since there is a much broader area involving more catalytic conversions awaiting to be investigated. HEMs have also exhibited great potential to fundamentally tackle issues that are considered challenging for unary and traditional multicomponent systems. This paradigm shift from “using materials that we have” to “engineering materials that we need” (76) could be a game-changing opportunity for both materials and catalysis communities to embrace. Here, we briefly outline the upcoming opportunities and challenges in this interdisciplinary field (Fig. 6A).

Fig. 6 Outlook for future studies of HEMs for catalysis.

(A) Schematic showing future opportunities and challenges in HEMs for catalysis. Advanced synthetic, characterization, and computational techniques will enable further exploration of the enthalpy-entropy correlation in HEMs. (B) Schematic showing the stepwise accumulation of the metal cations on the phenylazomethine dendrimer to prepare the atomically precise Ga1In1Au3Bi2Sn6. Reproduced with permission from the Nature Publishing Group ( (139). (C) Schematic showing the use of atom probe tomography to map the metal sequence in the multivariate MOF samples. Reproduced with permission from the American Association for the Advancement of Science (140). (D) High-resolution TEM image of the junction in an Au─Co─PdSn nanoparticle (scale bar, 3 nm), where the insets show the ADF-STEM image and corresponding EDS element map of the entire nanoparticle. The FFT patterns corresponding to the Au, Co, and PdSn domains are put at the bottom, and the three phase boundaries are highlighted with dashed lines. Reproduced with permission from the American Association for the Advancement of Science (141). (E) Ionic conductivities of the Li- and Na-doped MgCoNiCuZnOx HEOs at 20° and 80°C, which are notably improved compared with that of the nitrogen doped lithium phosphate glass (LIPON) solid electrolyte. Reproduced with permission from the Royal Society of Chemistry (146). (F) Structure evolution of the CoCrFeMnNi HEA as monitored by the XRD patterns, corresponding to the transition between the initial fcc lattice and the pressured-induced hcp structure. Reproduced with permission from the Nature Publishing Group ( (148). (G) Faradic efficiencies of the Cu1–xAgx bimetallics with different compositions for electrochemical CO reduction at −0.70 ± 0.01 V versus RHE. Reproduced with permission from the American Association for the Advancement of Science ( (149).

Synthesis and characterization

Controllable synthesis and precise characterization are the cornerstones for the discovery and design of HEM-based catalysts. The aims will be twofold from a materials perspective. The first is to increase the synthetic accessibility of HEMs, which is currently limited by the use of special instruments and exquisite tuning of the synthetic parameters. While entropy-stabilized systems are thermodynamically favorable at elevated temperatures, studies have indicated that it is possible to access various nanostructured HEMs at lower temperatures. Ball milling has been regarded as a revolutionary route to realizing atomic mixing of the ionic and molecular precursors under solvent-free or minimal-solvent conditions (136). Solvothermal synthesis, which induces an autocatalytic formation pathway of HEA nanoparticles, has also been demonstrated (32). Meanwhile, revisiting some of the entropy processes could bring additional inspirations for synthesis. For instance, cation exchange in colloidal nanocrystals is a process determined by enthalpic and entropic factors involving hard-soft acid-base interactions between metal cationic species and molecular ligands (137). Inspired by this, Schaak and co-workers (33) recently introduced multication exchange as a low-temperature pathway to colloidal high-entropy sulfide nanoparticles (Zn0.25Co0.22Cu0.28In0.16Ga0.11S). A continuous-flow reactor was also developed by Kusada et al. (138), which enables the nonequilibrium, scalable flow synthesis of the IrPdPtRhRu HEA nanoparticles with immiscible elemental combinations. The proven repeatability and unprecedented producibility could satisfy the requirement of large-scale chemical infrastructures. Further development of feasible, reliable, and scalable synthetic approaches could make HEMs more accessible for catalytic discussions that cover both fundamental and application-driven studies.

The second target is precise control of the size and structure of HEMs. Tailored synthetic protocols coupled with state-of-the-art characterization tools will bring atomic insights into the formation and configuration of HEMs. As illustrated in Fig. 6B, Tsukamoto et al. (139) reported the template synthesis of multimetallic subnanoclusters. The demonstrated atom hybridization provides an atomically resolved platform to probe interactions among different atoms and delicate tuning of the steric and electronic properties that are desirable for catalytic applications. Advanced characterization techniques, such as atom probe tomography demonstrated by Yaghi and colleagues (140) (Fig. 6C), will enable identification of the atomic configurations in both hard and soft HEMs. This is also useful to bridge the gap between surface atom sequence and corresponding adsorption behaviors of molecular species. Operando microscopic and spectroscopic techniques will monitor the dynamic change on the surface of HEMs under various reaction conditions. While studies have primarily focused on single-phase HEMs with maximized configurational entropy, a wider scope of multicomponent systems containing multiple phases should be evaluated. Engineering the interface between the segregated phase and the high-entropy domain or the one connecting different high-entropy domains in heterostructured nanoparticles (Fig. 6D) may improve the activity and selectivity of tandem catalysts, where balancing surface and interface energies becomes critical (141).

Theoretical investigation

Theoretical efforts that afford complementary insights into experimentation and accurate predictions will be of ever-increasing importance. Topics such as formation and stabilization of the high- and medium-entropy phases, interaction between the intermediate absorbates and the HEM surface, and high-throughput screening of potential chemical combinations all require inputs using computational tools. The well-established catalysis theory can hardly be extended to entropy-stabilized regimes owing to the unprecedented structural and compositional complexities. For example, in the case of the HEA electrocatalysts for ORR, the scaling relationship between the *OH and *OOH intermediates is conserved for the adsorption on the HEA surface, because they both bind at an on-top position. The scaling relation between *OH and *O, on the other hand, is no longer valid since they tend to bind in different manners (13). Therefore, additional parameters may be needed for theoretical discussions on HEMs for catalysis.

Machine learning has received a lot of attention because of its unparalleled capability to multiprocess data and automatically build analytical models to identify the optimal composition and structure of HEMs. However, it still requires designation of descriptors to enable assessment of the data points (142). Three common descriptors are geometric parameters that are determined by the atomic positions, electronic factors describing electronic structures, and energetic features involving adsorption energies of molecular species and formation energies of certain structures. Therefore, coordinating the use of these three descriptors and developing reliable machine learning models with decreased dependency on the DFT-calculated values are desired. In addition, different algorithms should be adopted for different purposes (143). For example, convolutional neural networks allow accurate and efficient prediction of electronic properties. In contrast, graph neural networks with more flexible inputs work better to probe the atomic structures involving atom and bonding information.

It is also important to analyze the deviation between experimental data and computational results, which will unveil additional parameters to include to achieve more accurate predictions. The stability debate on the HEA catalysts is a good example. Previous theoretical work indicated the structure of HEAs is thermodynamically stable, which can be ascribed to the sluggish diffusion kinetics (73, 74). However, surface structuring, restructuring, and phase segregation have been experimentally observed (77). This deviation could be resulted by the difference in the practical and simulated environment. Temperature difference could be a common cause, especially for DFT calculations. Monte Carlo methods have been used to help assess the stability of HEAs at high temperatures (37, 64). Besides, vacuum is typically adopted for calculations, whereas the gas- and solution-phase environments in practice are much more complex. Adsorbate-induced surface segregation, which has been widely studied for monometallic and alloy nanoparticles but not for HEAs (144, 145), can be an informative starting point to connect the experimental and computational results.

Probing the enthalpy-entropy correlation for catalysis

Another fundamental goal is to articulate the enthalpy-entropy correlation in HEMs and discover new properties or extrapolate defined features that have been applied for other applications to catalysis. For instance, the prototypical rock salt HEOs (Co0.2Ni0.2Cu0.2Mg0.2Zn0.2O) exhibited superior ionic (Li+ and Na+) mobilities (Fig. 6E), which was attributed to the promotion of oxygen vacancies in the highly disordered structures (146). In oxide-ion conductors, the defect pairs between the dopant cation and the oxygen vacancy need to be activated to facilitate movement of the oxygen ions (147). Ideally, the binding enthalpy (ΔHa) reaches a minimal value that corresponds to the maximum of the conductivity. For thermal catalysis, this nonclassical feature of HEOs can be used to improve the oxygen transport for high-temperature oxidation reactions. Entropy-induced reduction of the energetic barrier for lattice oxygen activation may endow HEOs as compelling catalyst supports. This is particularly useful for high-temperature reactions that rely on the intrafacial mechanism, where the inferior oxygen transport limits migration of the active oxygen species from the interior bulk lattice to the surface active sites (129).

Polymorphism, which has been demonstrated for the high-entropy Cantor alloy (CoCrFeMnNi) (148), will be another intriguing subject (Fig. 6F). The ability to realize atomic-level control of composition and configuration of HEMs has only been achieved with computational tools (73). Comparisons among different HEM catalysts with different structures but identical elemental composition and microstructure will help unveil the atomic arrangement that underpins the surface adsorption properties. Benchmarking the performance of HEMs with related systems is also important. This has been lacking due to the various forms of HEMs including bulk powders, thin films, nanoporous architectures, supported nanoparticles, and difficulty in identifying and quantifying the catalytic active sites for different reactions. Proper control with unified standards and reporting metrics will allow accurate attribution of the catalytic properties to the key features of HEMs.

Continuous composition tuning in a controlled manner is attractive for catalysis, as strong cooperative effects among different metals could bring synergistic properties that are inaccessible with the individual constituent. However, this has been greatly hampered by the large miscibility gap in the bulk phases. Recent advances in HEAs have indicated that tunable amounts of certain metals can be incorporated to the single entropy-stabilized phase. This affords a powerful route to overcoming the miscibility limitation and realizing the full potential of entropic stabilizations (67). Moreover, the gained knowledge between thermodynamic and kinetic factors can be extended to simple systems. For example, Hu and colleagues (149) overcame the inherent immiscibility in Cu-based bimetallic systems by using the carbothermal shock technique, which was first developed to prepare nanostructured HEAs. Cu0.9Ni0.1 and Cu0.9Ag0.1 exhibited enhanced capabilities for the electrochemical reduction of CO2 compared with that of pure Cu (Fig. 6G). Understanding and tailoring the nonequilibrium synthetic process will introduce access to the restricted area in traditional alloy systems.


HEMs have emerged as a versatile family of materials exhibiting intriguing catalytic properties. Here, we summarize recent advances in applying HEAs, HEOs, and beyond for catalytic applications. As the prototype of HEMs, HEAs provide diverse surface metal sites with highly tunable adsorption energies for reaction intermediates. Studies on HEOs as catalysts and catalyst supports demonstrate the feasibility of adjusting the oxygen part via controlling the configurational entropy. Besides hard materials, soft inorganic-organic hybrids have also been studied to fine-tune the Lewis acidic sites in a controlled manner. While these studies have unambiguously proven the significance of regulating the configurational entropy on the catalyst side, more work is anticipated to further interpret the correlation between structural and compositional engineering and optimization of the catalytic behaviors. Advanced synthetic, computational, and characterization approaches will give rise to an expanded and well-defined library of HEMs, with predictive tuning of the lattice, occupancy, surface, interface, defect, etc. Meanwhile, interactions between the reactants, intermediates, and products, and the catalytic platform with manageable entropic contributions will bring useful insights into efficient and selective catalytic reactions. These cohesive efforts will tie the catalysis and materials communities, introducing a new frontier for the discovery and design of efficient catalytic materials.

This is an open-access article distributed under the terms of the Creative Commons Attribution-NonCommercial license, which permits use, distribution, and reproduction in any medium, so long as the resultant use is not for commercial advantage and provided the original work is properly cited.


Acknowledgments: Funding: This work was supported by the U.S. Department of Energy, Office of Science, Office of Basic Energy Sciences, Chemical Sciences, Geosciences, and Biosciences Division, Catalysis Science Program. Author contributions: S.D. conceived the idea, and Y.S. and S.D. cowrote the paper. Competing interests: The authors declare that they have no competing interests. Data and materials availability: All data needed to evaluate the conclusions in the paper are present in the paper and/or the materials cited herein.

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