Ultra-high-entropy alloy nanoparticles: beyond five components†

Julien Mahin*^ab, Kohei Kusada*^bc and Hiroshi Kitagawa*^a
aDivision of Chemistry, Graduate School of Science, Kyoto University, Kitashirakawa-Oiwakecho, Sakyo-ku, Kyoto 606-8502, Japan. E-mail: kitagawa@kuchem.kyoto-u.ac.jp
^bInstitute for Advanced Study, Kyushu University, 6-1, Kasugakoen, Kasuga City, Fukuoka, 816-8580, Japan. E-mail: mahin.julien.luca.a.872@m.kyushu-u.ac.jp; kusada.kohei.236@m.kyushu-u.ac.jp
^cFaculty of Engineering Sciences, Kyushu University, 6-1, Kasugakoen, Kasuga City, Fukuoka 816-8580, Japan

First published on 24th June 2025

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Introduction

High-entropy alloys (HEAs), which are also referred to as multi-principal element alloys or multi-component alloys, include five or more components in near or equimolar ratios.^1,2 HEAs represent a major departure from traditional alloys, also referred to as principal-component alloys. As their name suggest, principal-component alloys are based on a single principal component to which low concentrations of other elements are added, and they are limited to the edges of the phase diagram to ensure miscibility and prevent phase separation. For high-entropy alloys however, including several components in relatively large proportions while avoiding phase separation is possible because of the high-entropy effect. This effect is due to an increase in the entropy term of the free energy equation, which can counterbalance the positive enthalpy of mixing of immiscible components (eqn (3)).³ Consequently, high-entropy alloys have made previously impossible compositions in the middle of the phase diagram accessible, opening the door to many novel applications and resulting in significant research interest in this field.^4–7 Although the HEA field started with material science research in the form of bulk HEAs, many studies were conducted for developing methods that can prepare HEAs in the nanoparticle form.^8–12 Nanoparticles are defined as possessing at least one dimension in the 1–100 nm range. Their extremely small sizes give rise to exceptional properties, such as luminescence, plasmon resonance, etc. In particular, they are central to the field of catalysis. Their high surface area and uncoordinated and diverse surface atoms leads to a high concentration of active sites on the surface as well as high atom efficiency which is crucial for precious metal catalysts. Most industrial heterogeneous catalysts rely on some form of nanoparticle as their main active ingredient. High-entropy alloy nanoparticles (HEANPs) are considered to be prime candidates for next-generation catalysts because of their very large compositional space.^13,14 Their unique properties enable access to normally immiscible elemental combinations and the finetuning of active site structures and adsorption energies of reaction intermediates, which lead to catalytic activity optimisation.^15,16 Although most research has focused on quinary alloys, novel synthetic methods have been established in recent years, and HEANPs with increasingly more components have been successfully prepared, expanding the accessible compositional space (Fig. 1).

The apparent lack of research on HEAs containing more than five elements is rooted in thermodynamics. Indeed, the initial high entropy effect hypothesis considered that the mixing entropy would always prevail over the mixing enthalpy. However, the high entropy effect has a logarithmic dependency on the component number, resulting in diminishing returns and there is a limit to how many elements can be added before the enthalpy increases or decreases too significantly and phase separation or the formation of an intermetallic phase occurs.¹⁷ Recent results suggest that for bulk HEAs there is a maximum theoretical amount of different elements that can have a stable single phase solid solution and has been estimated to be around 10–12 or even as low as seven.^18,19 There are two ways to circumvent this thermodynamic problem. One is to freeze a single-phase state stable at a high temperature through kinetics, achieving a metastable state. The other is by reduction of the particle size, which decreases the effect of the total lattice energy. The latter is one of the reasons most of the research work on high entropy alloys containing more than five elements has been carried out in the context of nanoparticles.

There are numerous reasons to investigate the elemental space beyond five elements. Firstly, in the interest of scientific curiosity and basic research. By mixing ever more diverse and numerous elements together, more opportunities to discover unprecedented properties are generated. Secondly, adding more elements also increases the so-called “core effects” such as the cocktail/ensemble effect.²⁰ Because the cocktail effect is directly related to the catalytic performance of the catalyst, it is reasonable to assume that adding more elements should improve the catalytic activity even further than regular HEAs. Another reason is that for catalysis, having more elements in a single particle results in improved active site diversity and thus possibly creates multifunctional catalysts, capable of catalysing complex multi-step reactions which might need several different active sites for each step.

In this review, we focus on such HEANPs containing six or more elements and consider the unique challenges that arise when synthesizing these complex materials, the novel strategies that have been successfully implemented to synthesise them, and the opportunities they provide in terms of applications. This is a burgeoning and fast-developing field, with most papers on the topic published during the last five years. Finally, we provide perspectives on challenges and future developments in this field.

Theoretical considerations

Yeh et al. were the first to define HEAs as alloys consisting at least five elements mixed in an equimolar or nearly equimolar ratio in amounts ranging from 5–35 at%.¹ Another important distinction is that true HEA should consist of a single-phase solid solution, though this definition becomes a bit cumbersome in terms of nomenclature when investigating HEA systems that are close to the phase separation threshold. Yeh and coworkers also introduced the concept of the four “core effects” of high entropy alloys: the high-entropy effect, lattice distortion, sluggish diffusion and the cocktail effect.^6,20,21 The high entropy hypothesis postulates that the increase in mixing entropy in alloys with five or more components should favour the formation of single-phase solid solutions as opposed to intermetallic or phase-separated structures. As will be explored in further detail later in this section, this hypothesis is a simplification and the mixing enthalpy needs to be considered for accurate phase formation prediction. The lattice distortion hypothesis implies that the different sizes and binding energies of the atomic components will cause increased lattice strain, with several important effects such as decreased electrical and thermal conductivity and increased hardness.²¹ In extreme cases, this distortion could cause the crystalline structure to collapse into an amorphous one. The sluggish diffusion hypothesis is based on the idea that because of the distorted lattice, instead of a regular potential, irregularities will occur and “deep traps”, states of low potential, could exits and slow down atomic diffusion significantly.²⁰ However, this hypothesis is still debated and has been validated only when normalizing data by the alloy melting temperature.²¹ Finally, the cocktail or ensemble effect is more of an abstract concept, which encompasses the idea of the presence of many elements resulting in synergistic effects, i.e. that the combination of different elements leading to an increase in functional properties superior to that predicted by just the rule of mixtures. The cocktail effect is thought to be one of the main reasons for the high catalytic activity of HEANPs and can explain why activities superior to that predicted by simple d-band theory are achieved.^16,22

In contrast to simple binary alloys, for which most combinations have been investigated and their miscibility characteristics are available through phase diagrams and computational methods such as CALPHAD software, the elemental space of HEAs is considerably more expansive and complex. For example, when considering 29 transition metal elements (excluding the radioactive element technetium), this results in only 406 equimolar binary alloy combinations (Fig. 2). Meanwhile, this number jumps to 10⁵ for five components and 4 × 10⁶ for eight components, which is far too large to investigate through trial-and-error and standard experimental methods. These possibilities are virtually endless if non-equimolar compositions are considered.

Rationalising the properties of HEA in terms of fundamental thermodynamic first principles is useful given the breadth of their combinatorial compositional space.

The entropy of mixing is a fundamental thermodynamic parameter that governs high-entropy alloys. Assuming a regular solution, the mixing enthalpy is calculated using the same formula as the ideal solution, where c_i is the molar fraction of component i (eqn (1)).^1,23

	(1)

For equimolar alloys, this expression can be simplified as (eqn (2)).

ΔSmix = Rlnn	(2)

Therefore, for an equimolar quinary alloy, ΔS_mix ≈ 1.5R = 13.38 J K⁻¹, which is often referred to as an alternative definition for HEAs.²¹ This review focuses on alloys containing six or more components.

As medium-entropy alloys are defined as having 1R ≤ ΔS_mix ≤ 1.5R (Fig. 2),⁴ we propose defining a new boundary for materials that contain 8 elements or more, and we refer to such materials as ‘ultra-high-entropy alloys (UHEAs)’, i.e. ΔS_mix ≥ 2R = 17.29 J K⁻¹. Curiously, although the high-entropy domain begins from five elements, most researchers use exactly five components, and reports on higher-order alloys are lacking. The lower amount of research on UHEA compositions can be attributed to an increase in the difficulty of synthesis; however, this seems to contradict the high-entropy hypothesis. From an entropy-only standpoint, the mixing entropy should increase as more elements are added and thus higher order alloys should be more stable. However, the mixing enthalpy becomes very positive for high-order alloys because it is difficult to find more than five elements with sufficiently similar properties to easily form a single-phase solid solution. Therefore, the synthesis of single-phase solid-solution UHEAs is more difficult than HEAs in practice. Further, the added complexity makes the characterisation and interpretation of the results more difficult, thereby requiring advanced techniques.

The prediction of the phase stability of an alloy of given composition is a way of estimating the difficulty in synthesising a well-defined single-phase solid solution alloy material based on its composition and merits careful consideration. Researchers initially adopted a qualitative approach that examines the most relevant properties of the elemental components (atomic size, crystal structure, reduction potential/electronegativity, melting point, etc.) to predict if certain alloy compositions will be relatively stable and thus easy to manufacture.

For example, the Hume-Rothery rules for solid-solution formation, which are a seminal work in this field, state that the individual components of an alloy must follow the following set of conditions:²⁴

• The atomic difference between any two components must be under 15%.

• Their crystal structures must be similar.

• They should have similar valencies (valence electron concentration, VEC).

• They should have similar electronegativity.

If all components have similar properties, one can assume that they will form a single-phase alloy. Conversely, a very different range of fundamental properties should result in phase separation. Although a qualitative approach is useful, a more quantitative evaluation of the stability of a given alloy composition based on first principles is desirable, and it has been previously investigated.^3,7,25–27 First, one can look at the mixing enthalpy of an alloy to determine the total mixing free energy and theoretically predict if a certain composition will be thermodynamically stable. Generally, only entropy is considered, and the entropy contribution to the mixing energy of five or more components is assumed to be sufficiently large for stabilising most alloy compositions. However, this is an oversimplification because a more complete picture of the energy of the system needs to be considered when more dissimilar elements are mixed. More recently, an upper limit to the entropic stabilisation effect around 10–12 components has been proposed.¹⁸ As the number of components increases, it becomes impossible for the elements to be chemically similar. A comparatively small increase in entropy in higher-order alloys, because the logarithmic relationship to the component number (eqn (2) and Fig. 2) cannot sufficiently compensate for the increase in mixing enthalpy from the repulsion between the various components. From a thermodynamic standpoint, the stability of a given alloy will be determined by its free energy of mixing (eqn (3)):

ΔGmix = ΔHmix − TΔSmix	(3)

Based on the regular solution assumption, the mixing enthalpy can be calculated using eqn (4):^25,28,29

	(4)

where Ω_ij represents the regular solution interaction parameter between components i and j, and c_i and c_j represent molar fractions of i and j, respectively. Therefore, Ω_ij can be calculated from the mixing enthalpy of a binary alloy of i and j based on the following relationship, which assumes that the energy of interaction is independent of the composition and temperature (eqn (5)):²⁹

	(5)

By substituting this into eqn (4), we obtain the following equation to calculate the total enthalpy of mixing of an alloy with n components (eqn (6)):

	(6)

Thus, the free energy of each alloy can be calculated assuming a regular solution and knowing only the binary mixing enthalpies of each constituent.^25,29 Consequently, the thermodynamic phase stability of a target HEA system can be predicted if one has access to a database of binary mixing enthalpies. Such databases are available in the literature. Takeuchi et al. used the Miedema model to estimate the mixing enthalpies of 79 different elements.³⁰ The Miedema model is a semi-empirical model that enables calculating binary enthalpies based on fundamental elemental properties such as the work function and electron density.^28,31 The resulting database considers most elements relevant to material science and is therefore extremely useful. However, it is not fully accurate because of its semi-empirical nature and assumptions.

More recently, Troparevsky et al. constructed a database of binary enthalpies for 30 elements based on density functional theory (DFT) calculations.¹⁹ Each data point involves several DFT calculations for different crystal systems and corresponds to the most stable structure for each binary combination. Consequently, although the elemental scope is more limited, their database is more accurate than that assembled by Takeuchi et al. Further, Troparevsky et al. attempted to establish selection rules for single-phase HEA formation. They argued that a single-phase solid solution could be formed only if the enthalpy of mixing of any two components of the alloy is between the following two threshold values: −22.8–13.4 kJ mol⁻¹ < ΔH^AB_mix < 3.57 kJ mol⁻¹. The two values for the lower boundary correspond to different annealing temperatures (1673 and 1000 K, respectively). If the mixing enthalpy between any two components is too high, it could lead to phase separation. Conversely, if it is too negative, intermediate phases such as intermetallic phases will likely form. According to this criterion, only a few senary, even fewer septenary, and no octonary HEA compositions were predicted to exhibit a thermodynamically stable solid-solution state. This selection rule can explain the apparent scarcity of HEANPs containing more than five elements reported in the literature. Further, other selection rules were proposed. For example, in terms of the total mixing enthalpy of the alloy, the generally accepted limits for single-phase formation are estimated to be −15 kJ mol⁻¹ ≤ ΔH_mix ≤ 5 kJ mol⁻¹ based on experimental data.^7,32,33

The thermodynamic calculations considered above assumed a regular solution, i.e. the components are randomly mixed, the packing is loose and that the atoms have similar sizes. Although random mixing is an acceptable assumption, close packing in solid-solution alloys and the possibility of very different atomic sizes being included in a HEA can cause significant deviations from this ideal behaviour. Zhang et al. considered the differences in size by calculating an atomic size-dependent parameter delta (δ) to classify different HEAs (eqn (7)):²⁵

	(7)

where n is the number of components, c_i is the atomic percentage of the i^th component, r_i is the atomic radius, and is the average atomic radius.²³ can be calculated as per eqn (8):

	(8)

Delta represents a measure of the differences in the atomic radii of the multi-component alloys. The larger the delta parameter, the greater the size mismatch in the alloy. In this review, the mixing enthalpy, entropy, and free energy, as well as the delta parameter for every material reviewed were calculated to compare these novel alloys systematically and quantitatively.

Another important consideration is the particle size. For nanoparticles, infinite solid assumptions are no longer valid because a significant percentage of atoms in a particle are at the particle surface. Nanoscale sizes reduce the effective influence of the enthalpy as the overall cohesion energy decreases, as shown by Qi et al. (eqn (9)).³⁴

	(9)

where N denotes the number of atoms per particle. Feng et al. used a similar approach and demonstrated that this effect could be equated to a negative contribution to the enthalpy term.²⁷ Based on this, they calculated that a particle size of 3 nm should result in a thermodynamic stabilisation effect equivalent to the entropic stabilisation of 25 elements (26.8 kJ mol⁻¹). These results confirm that preparing HEAs in the nanoparticle form is a viable strategy to achieve stable single-phase elemental compositions that are impossible in the bulk. In addition to the phase-formation rules, addressing crystal-structure selection rules is important. The close-packed structure adopted by HEAs is mostly determined by the average valency. The body-centred cubic (bcc) structure is favoured when the VEC is approximately 5, whereas the face centred cubic (fcc) structure is favoured at a higher VEC of ∼8.5.^7,35,36 HEAs generally form either fcc or bcc structures, and not hcp.^37–39 The exact reasons for the few observed hcp HEAs remain unclear; however, several hypotheses have been proposed; for example, most elements crystallise into either fcc or bcc structures, particularly at high temperatures, and the hcp structure has lower symmetry, lower configurational entropy, and less accommodation for atomic size mismatch.^37–39

Based on the theoretical concepts detailed above, we calculated the mixing entropy, mixing enthalpy, free energy of mixing, and delta parameter for all HEA materials considered in this review. This data, as well as the main characteristics of all the papers reviewed in this work is compiled in Table S1.† A lnLINK TOhe code developed that automates these calculations is also linked in the ESI†. The parameters were calculated based on experimentally determined alloy compositions, where available. Fig. 3 shows a map of HEANPs classified based on their mixing entropy and mixing enthalpy, calculated based on the binary enthalpy database reported by Takeuchi et al. using the Miedema model. An analogous figure using mixing enthalpies calculated using Troparevsky et al.'s database is included in the ESI (Fig. S2†). When the real composition is considered, some of these alloys fall below the high entropy limit of ΔS_mix = 1.5R because they contain a large amount of a single component, which is the case with majority component synthesis method (covered in the next section). Interestingly, even systems with large positive mixing enthalpies (>5 kJ mol⁻¹) form a single-phase solid solution, likely because of the nanoscale stabilisation effect. Furthermore, it is possible that these alloys are in a metastable kinetic state and will undergo phase separation under annealing conditions. Similarly, there is an apparent absence of intermetallic alloys. Indeed, based on the literature, thermodynamically if the enthalpy of mixing of an alloy is lower than −15 to −25 kJ mol⁻¹, it is likely that an intermetallic state should the most stable.^19,32 We also attribute this phenomenon of absence of intermetallics to kinetic trapping of metastable single-phase states. It is possible that the sluggish diffusion effect plays a role in preventing or slowing down the formation of intermetallic phases which require atomic diffusion for their arrangement. The sluggish diffusion effect might be greatly enhanced by the presence of many different elements in UHEA compositions. Indeed, in reports of high entropy intermetallics, an annealing step is generally required to obtain the intermetallic phase.⁴⁰ Further annealing studies are required to elucidate the most thermodynamically stable state, although annealing is often undesirable in the context of catalysis as it might cause sintering and loss of catalytic activity.

As shown in Fig. 4, the free energy of mixing at the synthesis temperature is plotted against the delta parameter for each alloy. An analogous figure using the free energy values calculated at room temperature is available in the ESI (Fig. S1†), as well as using the free energy values calculated based on Troparevsky et al.'s binary enthalpy database (Fig. S3 and S4†). In all cases, the free energy of mixing is negative or close to zero, indicating a spontaneous reaction. In the case of the same figure plotted using Troparevsky et al.'s mixing enthalpy database, all HEAs had a negative free energy of mixing at the reaction temperature (Fig. S4†). For bulk HEA systems, δ > 5% is considered the limit for single-phase solid-solution formation.⁷ Based on these results, nanoparticles can tolerate a considerably larger delta parameter than that of bulk alloys without phase separation, likely because of the nanoscale stabilisation effect. However, there does seem to be a slight trend of lower crystallinity for higher values of the delta parameter, and most of the lower crystallinity HEANPs have δ > 5%.

Some trends for the final crystal system and crystallinity obtained can be observed in Fig. 5, which plots the effect of the reaction temperature versus the mixing entropy. In general, a lower reaction temperature (room temperature) such as in the dealloying, lithium naphtalenide reduction or electroreduction methods results in amorphous or poorly crystalline HEANPs. In contrast, medium reaction temperatures (150–300 °C) such as those used in solution-phase chemical reduction methods result mostly in fcc crystalline nanoparticles. At higher temperatures, both crystalline and poorly crystalline HEANPs were obtained. The final structure of HEANPs synthesised at higher temperatures likely depends on the cooling rate. Indeed, the majority components synthesis methods, which use slow cooling rates, yield a single-phase crystalline structure in all cases. These observations suggest that low reaction temperatures and a fast cooling rate, conditions that prevent atomic diffusion, favour the isolation of an amorphous state, while high temperature and slow cooling can lead to more crystalline phases, as atomic diffusion is facilitated.

Finally, although the previous considerations are based on thermodynamics and relevant to the equilibrium state, an alternative way to achieve theoretically unstable alloy compositions is to kinetically isolate a non-equilibrium state. Indeed, freezing a non-equilibrium state by rapid quenching is one of the main approaches that has been deployed by researchers to explore the field of UHEA compositions.

Synthetic methods for the preparation of ultra-high-entropy alloy nanoparticles

The synthesis of nanoparticles containing six or seven elements (HEANPs) or eight or more elements (UHEANPs) present unique challenges. Although the synthesis of any nanoscale materials is not a trivial task, it becomes even more difficult when the composition must be carefully managed across many elements. The rigorous regulation of nucleation and growth processes, which are complicated by the simultaneous presence of many metal precursors, is necessary to precisely control and tune the particle size and shape. These various metal precursors have different reduction potentials, and therefore, different reduction kinetics which can lead to heterogeneous nucleation and phase separation or side reactions between the precursors. In addition, because of their large surface area, nanomaterials are susceptible to oxidation, particularly for low reduction potential metals, and this can drastically affect their properties. Finally, developed synthetic methods should be scalable to be relevant for real-world applications such as catalysis.

Despite these challenges, researchers demonstrated outstanding creativity and have developed many different methods for synthesising UHEANPs. Although most reports from different research groups used different synthetic methods, they can be grouped into a few overarching categories (Table 1). The first distinction is between bottom-up and top-down methods. To synthesize a nanomaterial, which is defined as possessing structures with at least one dimension in the 1–100 nm range, one can either break down bulk materials to smaller sizes (top-down methods) or build up starting from atomic or molecular building blocks (bottom-up methods). Subsequently, apart from a few exceptions, bottom-up methods for preparing (U)HEANPs can be subdivided into three different categories:

• Methods that rely on a very fast heating and cooling rate (>100 K s⁻¹) to achieve a stable high-entropy state and kinetically freeze it.

• Methods that rely on fast chemical reduction or electroreduction of precursors.

• Methods that rely on a majority element to minimize the overall mixing enthalpy.

Conversely, top-down manufacturing methods for UHEANPs synthesis fall into two categories:

• Methods based on ablation of bulk targets.

• Methods based on dealloying of a more reactive alloying majority element.

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Each of the methods developed to synthesise HEANPs containing six or more elements is categorised and explained, and their various advantages and drawbacks are considered.

Following the synthesis, thorough characterisation of the obtained HEA materials is necessary and essential. (U)HEANPs offer unique challenges in terms of characterisation because their inherent compositional diversity and criterion of at least five elemental components means the average elemental content for equimolar alloys will be at most 20% atomic and will be only lower for higher order alloys. The low elemental content complicates compositional characterisation and combined with the small sizes of the nanoparticles, represents a considerable challenge in terms of noise-to-signal ratio and requires absolute state-of-the-art characterisation techniques to accurately describe essential properties such as crystal structure, and alloy homogeneity. To determine the crystal structure and phase composition of the alloy nanoparticles, the technique of choice is powder X-ray diffraction (PXRD). However, because of the nanoparticle sizes, often high-quality data requires high intensity beamline of synchrotron facilities. Such high intensity light sources are particularly valuable because they can also enable in situ characterisation to study the dynamic evolution of HEANP under various conditions. Other characterisation techniques available at synchrotron facilities such as X-ray absorption spectroscopy (XAS) can give insight into the chemical environment of different elements, but implementation and interpretation for the complex HEA systems remains very challenging and requires further development. Given very small particle sizes are sometimes necessary to stabilize high order UHEANPs thermodynamically, atomic resolution imaging is often essential and most commonly achieved using aberration corrected transmission electronic microscopy techniques. In particular, high angle annular dark field scanning transmission electron microscopy (HAADF-STEM) is one of the main techniques of choice for HEANP characterization and enables structural imaging at the atomic level. Combined with elemental characterisation such as energy dispersive X-ray spectroscopy (EDX), compositional information on a single particle level can be obtained. Bulk information in terms of total composition can be determined by techniques such as X-ray fluorescence (XRF) or induced coupled plasma optical emission spectroscopy (ICP-OES) or induced coupled plasma mass spectrometry (ICP-MS). Lastly, the valence state of the various elements can be evaluated by the X-ray photoelectron spectroscopy (XPS) technique or XAS.

Bottom-up methods

Bottom-up methods for nanomaterial synthesis have advantages in terms of better control over the final particle size and shape. This added control comes at the cost of complexity and often less scalable synthesis processes.

Top-down methods

For traditional low-entropy nanomaterial manufacturing, top-down methods offer advantages such as simplicity of the process and equipment, scalability and low cost. However, this is under the assumption that the bulk starting materials are easy to manufacture. These advantages are not as obvious in the case of UHEANPs because of the additional challenge of ultra-high-entropy materials in terms of their high system enthalpy; the synthesis of a bulk UHEA may still be challenging at the macroscale. Therefore, the applicability of top-down methods requires careful consideration of the necessary starting bulk materials as bulk alloys often do not form a perfect solution.¹ However, it is also possible to prepare HEANPs from monometallic powder precursors as demonstrated by some of the methods detailed later.

Methods conclusions

We reviewed the different methods that have been developed to produce UHEA nanomaterials and discussed their characteristics, advantages and drawbacks, as summarised in Tables 1 and 2.

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Generally, the methods based on high heating and cooling rates provide the widest elemental range available because high temperatures entropically stabilise the single-phase state that is then isolated by fast quenching. Thus, these methods are most suited for fundamental studies, to explore the elemental space and they can be adapted to high-throughput compositional investigations. Furthermore, they have the advantage of producing catalyst materials with few necessary postprocessing procedures, which can further accelerate discovery. However, they are less suitable for scaling the UHEA production processes because they require specialised equipment, an inert atmosphere, high temperatures, and often involve support limitations. Solution-phase methods are more efficient and provide greater control over the particle size, shape and support. Therefore, they are better suited for finer optimisation and production scale up of previously discovered promising compositions. However, these methods often achieve size and shape control using surfactant molecules that must then be dealt with to maximise catalytic activity. Further, including low reduction potential elements remains another significant challenge. Majority elements methods are suitable for the scale up of defined materials owing to the simplicity of their process; however, they are limited by their compositional space by the majority element and offer less control over particle size and morphology compared to solution-phase methods. Dealloying methods are inefficient; however, they provide unique advantages, offering access to nanoporous morphologies that may yield higher catalytic activity or selectivity. However, they should be avoided in applications in which surface oxidation is undesirable. Finally, ablation methods offer few advantages in the field of UHEA as simplicity and scalability associated with the ablation of simpler materials is negated by the difficulties in the necessary bulk UHEA preparation. In some cases, this can be circumvented by starting from single metal powder precursors, but this strategy tends to result in a poor elemental distribution in the final nanoparticle product.

Applications of ultra-high-entropy alloy nanoparticles

In this section, we review the various applications for which UHEANPs have been investigated. Small particle sizes can increase the surface area and the diversity of surface active sites such as corners, edges or defects, all of which tend to be beneficial for catalytic purposes. Therefore, it is unsurprising that the most common application of UHEANPs is in catalysis. The increase in activity for HEANP catalysts is thought to originate from the cocktail or ensemble effect. The many constituent elements and random solid solution nature of HEAs enable large combinations of possible active sites to exist at the surface of the particles. Each of the elemental combinations will result in a different energy level, because of the neighbouring atoms of a central active site will act as different electronic modifiers, and a broadening of the surface states energies and valence band occurs.¹⁶ This effect greatly increases the likelihood of an active site with an ideal binding energy for a given reaction being present. It is reasonable to think therefore that by adding more elements, this effect should be further enhanced. Thus, the optimisation of the active site energy should be further increased, and the presence of different elements provides a more diverse selection of adsorption states for reactive species.⁶⁰ Following the same principle, more elements can improve the functionality of the catalysts and can be beneficial for complex reaction with several reaction steps which normally require different catalysts. With UHEANPs catalysts, catalysing different reaction steps on the same catalyst particle becomes possible.⁶⁵ Interestingly, since the activity enhancement depends on the electronic modification effect of neighbouring atoms, there is evidence that for HEANPs, larger particle sizes and lower surface curvature improve performance, contrary to common heterogeneous catalysis principles.⁶⁰ Among the various fields of catalysis, electrocatalysis is the most popular application for UHEANPs, likely because of the low temperature operating conditions of electrocatalysts, which reduces the likelihood of phase separation and degradation under operating conditions. Despite the main focus being on electrochemistry, some applications in thermocatalysis, photothermal conversion and liquid-phase catalytic hydrogenation have also been explored. Note that in many cases, researchers used a lower-order alloy for application demonstration, suggesting that adding more elements is not always beneficial for catalytic activity, particularly for simple reactions. For example, despite synthesising up to an octonary alloy via the carbothermal method, Yao et al. used a quinary PtPdRhRuCe HEA catalyst in the context of the ammonia oxidation reaction, possibly because higher order alloys did not improve the activity or decrease catalyst stability.⁴¹ Indeed, if one of the elements already offers excellent catalytic properties for a given reaction, adding more elements that are not active for that reaction to an alloy is more likely to “dilute” the key element and to result in activity decrease. In this review, only applications employing alloys with six or more elemental components are considered.

Electrocatalysis

The current climate emergency has created a critical requirement to decarbonise and electrify the chemical industry and to establish efficient energy conversion and storage technologies. Therefore, electrocatalysts have become an important research subject because several electrocatalytic processes are considered to play a key role in achieving the green energy transition. Hydrogen is one of the most important chemical feedstocks and used in various essential chemical processes such as the ammonia production. Further, hydrogen is actively considered for long-term energy storage to address the intermittency of renewable energy, and therefore, water splitting reaction (water electrolysis) has been extensively studied. This produces so-called ‘green’ hydrogen, i.e. hydrogen that can be produced only from renewable energy (assuming the electricity used in the process comes from fully renewable sources). Currently, it is more economical to produce hydrogen by steam-methane reforming based on fossil fuels, producing CO₂ and thus yielding ‘grey’ hydrogen. This can be attributed to the current high cost of electrolytic water splitting, linked to high costs of electricity as well as catalyst and electrolyser capital costs, low efficiency of the process (high overpotentials) and low cost of fossil fuels. Therefore, advances in catalyst technology could be decisive in lowering costs and increasing the competitiveness of green hydrogen over grey or blue hydrogen.

Batteries

Metal–air batteries have been extensively investigated in recent years because they can provide considerably higher theoretical energy densities than those of lithium-ion batteries. Their cathode requires a catalyst for the ORR, and therefore, UHEANPs have been investigated as promising cathode materials for metal–air batteries. Senary HEA-PtPdIrRuAuAg nanoribbons demonstrate good performance in Li–O₂ batteries with a low charge overpotential (0.49 V) and an excellent cycle life (100 cycles) under a limited capacity of 1000 mAh g⁻¹ at 0.50 A g⁻¹ (Fig. 28).⁸¹

Lacey et al. prepared a RuIrCeNiWCuCrCo UHEANP catalyst for Li–O₂ batteries using the carbothermal shock method⁴⁴ and found that increasing the number of components from binary to quaternary to octonary did not significantly influence the catalytic activity; instead, it greatly enhanced the durability of the catalyst. Higher-order elemental compositions prevented the oxidation of the active Ir and Ru elements. Chen et al. also investigated their convex cube-shaped Pt₃₄Fe₅Ni₂₀Cu₃₁Mo₉Ru HEANPs for Zn–O₂ batteries and achieved a peak power density of 150 mW, which was considerably higher than that of the mixed Pt/C + RuO₂ (118 mW). Yu et al. investigated their 12 component MnNiCuCoVFePtPdAuRuIrMo UHEANP as a catalyst for Zn–O₂ batteries (Fig. 29)⁸³ and achieved a higher open-circuit voltage (1.5 V) and maximum power density (122 mW cm⁻²) than that of the Pt/C–IrO₂-based Zn–air battery (1.43 V and 91 mW cm⁻²), respectively.

Thermocatalysis

Most of the chemical industry still relies on traditional thermally catalysed reactions. Any increase in efficiency by improving the catalytic activity is highly desirable as these processes are very energy demanding. Qiu et al. found that, despite the naturally formed thin oxide layer of γ-Al₂O₃, AlNiCuPtPdAu HEANPs exhibited greatly enhanced high-temperature stability (up to 600 °C) and CO oxidation activity.⁸² This oxide layer protected the nanoparticles from sintering at high reaction temperatures, maintaining their activity. The catalyst was active for CO oxidation despite the oxide layer indicates that it is not completely continuous. Despite many possible target reactions, almost no studies employed UHEANPs in thermocatalytic processes. This might be attributed to the instability of UHEA at higher temperatures, which is generally required for thermocatalytic reactions, as postulated by Troparevsky et al.¹⁹

Photothermal conversion

Photothermal conversion refers to the conversion of energy from light to thermal energy in the form of heat. Photothermal conversion can be implemented in various applications, including water purification, desalination and photothermal therapy for cancer treatment. Photothermal performance is determined by the light-harvesting ability and light-to-heat conversion efficiency. The FeCoNiTiVCrCu HEANPs produced by Li et al. through their arc-discharged plasma method managed to absorb more than 96% of the entire solar spectrum (250–2500 nm).⁷³ Furthermore, they achieved over 98% efficiency under one sun irradiation and a high evaporation rate of 2.26 kg m⁻² h⁻¹ (Fig. 30).

Further, Li et al. also produced even more complex FeCoNiCrYTiVCuAlNbMoTaWZnCdPbBiAgInMnSn UHEANPs using the same method, which demonstrated an absorption of >92% in the solar spectrum, solar steam efficiency of 99% (one solar irradiation), and water evaporation rate of 2.42 kg m⁻² h⁻¹ (Fig. 31).⁷⁴

Catalytic reduction of 4-nitrophenol

The reduction of 4-nitrophenol has been widely investigated as a model reduction reaction. Al Zoubi et al. found that CuAgNiFeCoRuMn@MgO showed higher conversion (100% at 1 min) than those of ternary CuAgCo@MgO and quinary CuAgCoNiFe@MgO catalysts (90% and 95%, respectively, at 1 min).⁵² AlCoCrFeNiV nanoparticles prepared by Kobayashi et al. achieved a 90% conversion of p-nitrophenol and 16 kJ mol⁻¹ activation energy, demonstrating that bcc nanoparticles were more active than their fcc counterparts.⁶⁴

Summary and outlook

Recently, significant research efforts and progress have been made in the development of HEANPs containing six or more components. The emergence of this new field of ultra-high-entropy materials has opened up exciting possibilities for the future such as alternative material design to precious metals for important catalytic transformations necessary for the energy transition and mitigation of the climate crisis. Along with its opportunities, this new field of research has its own set of challenges. We systematically assessed the thermodynamic concepts behind UHEANP phase stability, progress in the various synthetic methods that have been established to produce UHEANPs, and various applications for which these materials are investigated.

Theoretical considerations

From the theoretical perspective, researchers should consider the thermodynamic stability of their target materials quantitatively using a thermodynamic framework developed for predicting the phase stability of complex multi-elemental alloys. Composition-dependent parameters such as the free energy of mixing and the delta parameter can be used as effective tools for directly comparing various alloys and predicting their thermodynamic stability. Simple computational tools such as the code developed in this work can be useful in that regard. Because these tools rely on accurate binary mixing enthalpy databases, such databases should be improved, for instance, by building on the excellent work based on DFT made by Troparevsky et al.¹⁹ This thermodynamic framework is useful, particularly for comparison between different alloy compositions. However, metastable phases cannot be predicted through thermodynamics only. And recent research suggests that higher order HEA compositions might not be stable. The many experimental works compiled in this review shows that UHEANPs can be obtained because of kinetic freezing through rapid heating and cooling and through nanosize stabilization effects. Thus, experimental data and precise characterisation remains essential to accurately understand the field of UHEANPs. Further, this field will greatly benefit from a better understanding of the mechanisms underlying UHEANP formation, which remains difficult because of the many possible interactions between various precursors. Similarly, improved identification and understanding of the structure and nature of the catalytically active sites of UHEANPs using theoretical simulation tools can help guide compositional optimisation. Only an infinitesimal part of the available elemental space has been explored so far, and it would be impossible to fully investigate every combination; therefore, computational methods should be integrated with synthesis to guide HEANP design. Overcoming these challenges can help pave the way for significantly improving the design and control of UHEANP properties.

Design, synthesis and characterisation

The selection of elemental components of (U)HEANPs requires care, as each element will influence the final properties of the alloy, generally proportionally to its respective content. The objective of the research or desired application should drive the choice of composition. For catalysis applications, selecting elements that are known to be active for the reaction, as well as using d-band theory to predict how different elements will affect activity, is a good starting point. Based on ensemble effects, more elements should lead to better active site optimisation, though an overwhelming concentration of inactive elements is likely to decrease activity. Furthermore, compared to HEANPs, UHEANPs are faced with a greater possibility of phase separation. So, the selection of elements must be matched with the elemental range of the synthesis method of choice. Elements with very large size differences will result in high δ parameter, enhanced lattice distortion and possibly amorphous structures. Similarly, including elements of intermediate sizes will reduce the overall δ parameter, reduce lattice strain and favour crystalline single-phase solid solution structures. In the case of more fundamental studies, because of the complexity of the combinatorial elemental space, more systematic approaches to the elemental composition selection are useful. For example, changing or adding a single element of an otherwise fixed alloy composition to isolate its effect on the final material, or investigating elements by groups or series of elements.^16,60,87,88

Regarding the synthetic methods, bottom-up methods are the most promising approaches for the preparation of UHEANPs. Among these, rapid heating and cooling rate methods present considerable advantages for compositional exploration and high-throughput testing in the laboratory. However, they require very harsh and/or complicated experimental conditions and are difficult to scale. Synthetic methods that operate under simpler and milder conditions must be developed. (Electro)chemical reduction methods operate under considerably lower temperatures and offer more control over the final particle properties such as size, shape and composition, and are promising for large scale production. Majority element methods are also promising for scale up; however, they have limitations in compositional design. Top-down methods are less applicable compared to the case of monometallic nanomaterial synthesis because of their high energy consumption and the difficulty in preparing bulk HEA. However, among these, the dealloying method does have the merits of only requiring a principal component alloy and generating unique nanostructures. Currently, the control of particle size and shape remain elusive. Although some progress has been made, the field is far from achieving the exquisite control established for monometallic nanomaterials. Achieving similar control over the size of the particles, exposed facets, and crystal structures in UHEANP systems could greatly enhance catalytic activity. Finally, improved characterisation using microscopy and spectroscopy can greatly advance our understanding of UHEA nanomaterials, particularly in the case of individual atoms or specific active sites.

Applications

UHEANPs possess many advantages for catalytic applications, including active site diversity, multi-functionality, compositional versatility, reduced precious metal content and improved resistance to poisoning. Electrocatalytic applications of UHEANPs have been the most investigated possibly because they operate under mild conditions, which reduces the risk of phase separation. UHEANPs show great promise for important electrochemical reactions such as HER, OER, ORR and AOR. They are remarkably effective for complex reactions involving many intermediate steps, such as overall water-splitting catalysts and C2+ alcohol oxidation, given that the diversity of their surface composition can provide various active sites optimised for each reaction step. There is considerable potential to apply UHEANPs to other fields of catalysis such as in thermocatalysis and photocatalysis which remain largely unexplored. Strategies based on optimising the free energy, nano-size stabilisation and sintering inhibition can help ensure the structural stability of UHEANPs, extend their scope to harsher operating conditions and expand their field of applications.

Author contributions

Julien Mahin: conceptualization, data curation, formal analysis, funding acquisition, software, visualization, writing – original draft, writing – review & editing. Kohei Kusada: conceptualization, funding acquisition, supervision, writing – review & editing. Hiroshi Kitagawa: conceptualization, funding acquisition, supervision, writing – review & editing.

Conflicts of interest

There are no conflicts to declare.

Data availability

The data supporting this article have been included as part of the ESI.† The code used to calculate the free energy, mixing enthalpy databases, mixing entropy, and delta parameters of the multi-element alloys is available at https://github.com/julien-mahin/HEANPcalculator.git. The data repository includes binary enthalpy databases based on Takeuchi et al. and Troparevsky et al., dependencies, and instructions for reproducing the results.

Acknowledgements

The authors acknowledge the support from a Grant-in-Aid for Specially Promoted Research, No. 20H05623, and Grant-in-Aid for Scientific Research (B), No. 21H01762, Grant-in-Aid for Early Career Scientists No. 24K17587 and JST FOREST JPMJFR221P. This work was partially supported by the Demonstration Project of Innovative Catalyst Technology for Decarbonization through Regional Resource Recycling, the Ministry of the Environment, Government of Japan.

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Footnote

† Electronic supplementary information (ESI) available. See DOI: https://doi.org/10.1039/d5qi00884k

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