Functional and multifunctional high-entropy materials

What are functional and multifunctional High-Entropy Materials?

Entropy-related phase stabilization can enable compositionally complex solid solutions of multiple principal elements. The massive mixing approach was originally introduced for metals and has recently been extended to ionic, semiconductor, polymer, and low-dimensional materials. Multi-element mixing can leverage novel types of random, weakly ordered, clustering and precipitation states in bulk materials as well as at interfaces and dislocations. The many possible atomic configurations offer opportunities to discover and exploit new functionalities, as well as create new local symmetry features, ordering phenomena, and interstitial configurations. This opens up a huge chemical and structural space in which unchartered phase states, defect chemistries, mechanisms, and properties, some previously thought to be mutually exclusive, can be reconciled in one material. Earlier research concentrated on mechanical properties such as strength, toughness, fatigue, and ductility. This Review shifts the focus towards multi-functional property profiles, including electronic, electrochemical, mechanical, magnetic, catalytic, hydrogen-related, Invar, and caloric characteristics. Disruptive design opportunities lie in combining several of these features, rendering high-entropy materials multi-functional without sacrificing their unique mechanical properties.

Max Planck Institut for Sustainable Materials: Functional High Entropy Alloys: https://www.nature.com/articles/s41578-024-00720-y Max Planck Institut for Sustainable Materials: Functional High Entropy Alloys: https://www.nature.com/articles/s41578-024-00720-y

Some basics about Multifunctional High-Entropy Materials

High-entropy materials (HEMs) are an emerging class of materials characterized by their multielemental composition, typically involving five or more elements in nearly equiatomic ratios. Unlike conventional alloys, which rely on one or two principal elements, HEMs exploit the high configurational entropy associated with multiple components to stabilize single-phase solid solutions. This entropy-driven stabilization prevents the formation of brittle intermetallic phases, even in systems with significant chemical complexity. The high-entropy alloy (HEA) concept, initially developed in metallic systems such as CrMnFeCoNi, has since expanded to a broader range of materials, including oxides, nitrides, carbides, and borides.

Max Planck Institut for Sustainable Materials: Functional High Entropy Alloys: https://www.nature.com/articles/s41578-024-00720-y Max Planck Institut for Sustainable Materials: Functional High Entropy Alloys: https://www.nature.com/articles/s41578-024-00720-y

The principle governing HEMs is the Gibbs free energy where a high entropy of mixing reduces the Gibbs free energy, thereby stabilizing single-phase structures. This effect is particularly pronounced at elevated temperatures, where the entropic contribution outweighs the enthalpic preferences for phase separation. For instance, in CrMnFeCoNi, the entropy of mixing is about 1.61 R (where R is the universal gas constant), sufficient to promote the formation of a face-centered cubic (FCC) structure over a wide temperature range.

For other (spec. non-metallic) HEMS, the enthalphy dominates: Recent research has extended the concept of HEMs to include high-entropy oxides (HEOs) such as (MgCoNiCuZn)\(_2\)O\(_4\), high-entropy nitrides like (TiZrHfNbTa)N, and high-entropy carbides such as (HfTaTiZrNb)C. These systems exhibit remarkable thermal, mechanical, and chemical properties. For example, (MgCoNiCuZn)\(_2\)O\(_4\) demonstrates enhanced electrochemical performance as a battery electrode material, owing to its structural stability and high electronic conductivity. Similarly, high-entropy nitrides exhibit excellent hardness and corrosion resistance, with (TiZrHfNbTa)N achieving hardness values exceeding 30 GPa, making them ideal candidates for wear-resistant coatings.

In addition to their mechanical properties, HEMs are increasingly recognized for their multifunctionality. High-entropy materials such as (HfTaTiZrNb)C combine high melting points (>4000 K) with exceptional thermal and electrical conductivity, making them suitable for applications in extreme environments. Moreover, high-entropy hydrides, like TiZrHfVNbH\(_x\), have shown promise for hydrogen storage due to their large hydrogen absorption capacity and tunable thermodynamic properties.

The multifunctionality of HEMs extends to their magnetic, catalytic, and caloric properties. For instance, high-entropy alloys such as FeCoNiAlCu exhibit tunable magnetic properties that can be adjusted through compositional changes. In catalysis, high-entropy oxides demonstrate excellent activity in oxygen evolution and reduction reactions, which are critical for fuel cell and electrolyzer technologies. Furthermore, the caloric effects in materials like (GdTbDyHoEr)Co have been exploited for magnetocaloric cooling applications, offering potential energy-efficient refrigeration solutions.

nature reviews materials: Multifunctional high-entropy materials, https://doi.org/10.1038/s41578-024-00720-y;   Free to read link: https://rdcu.be/dVSzn Figure 1: nature reviews materials: Multifunctional high-entropy materials, https://doi.org/10.1038/s41578-024-00720-y; Free to read link: https://rdcu.be/dVSzn
Multifunctional high-entropy materials
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Science behind Multifunctional High-Entropy Materials

Materials have always played a pivotal role in the development of human society. The range of accessible phase states, kinetics, transformation phenomena, and properties, however, has remained constrained by the fact that many materials used today are mostly based on one or two principal elements and typically use further elements only in low fractions.

Figure 1: nature reviews materials: Multifunctional high-entropy materials, https://doi.org/10.1038/s41578-024-00720-y;   Free to read link: https://rdcu.be/dVSzn Figure 1: nature reviews materials: Multifunctional high-entropy materials, https://doi.org/10.1038/s41578-024-00720-y; Free to read link: https://rdcu.be/dVSzn

Compositionally complex and high-entropy alloys (HEAs)1–4, consisting of multiple principal elements, open up this rather limited chemical composition space. The original idea consists of stabilizing equimolar solid solutions of 5 or more chemical elements through enhanced configurational entropy. Today, this approach is embraced more broadly and also encompasses materials that are not (only) entropy-stabilized, targeting compositionally complex materials that have large solid solution ranges in the centre regions of multicomponent phase diagrams5–8. This is due to the fact that first, only a few fully random and thermodynamically stable solid solution HEAs have been identified to date and that second, some compositionally complex materials are enthalpy-stabilized rather than entropy-stabilized, for example some ionic materials. Furthermore, most of these materials are metastable and are prone to decompose into several stable phases. Beneficial properties have, in part, emerged from random solid solution states (such as high distortions and atomic-scale symmetry breaking), ordering effects and precipitation. These features allow the introduction of kinetics, microstructure, and processing as additional degrees of freedom for material design. It is also understood today that HEAs do not need to be equimolar in their composition, provided that no single matrix element prevails, making the design approach much more versatile. It is further important to note that the design approach works likewise for the bulk as well as for internal interfaces and surfaces. Interfaces can be as important as the bulk for certain materials, such as catalysts, hard magnets, topological materials, or coatings. The two are connected under near-equilibrium conditions because the partitioning and mixing states of adjacent regions depend on each other, as stated by the Gibbs adsorption isotherm.
These examples of ‘relaxed-constraints’ multi-component material design opportunities thus give access to a wide range of continuously variable chemical compositions and properties and bring a large variety of additional microstructure phenomena into play9. In the latter context, kinetics, non-equilibrium phase transformations, and many chemical ordering and decoration phenomena produce a rich underlying lattice defect cosmos (point defects, dislocations, stacking faults, interfaces, surfaces, and so on), providing an additional versatile material design toolbox10–13. The resulting microstructures can differ profoundly from those in conventional alloys because the lattice defects can be chemically highly decorated, which can be used to alter their kinetic, thermodynamic, and functional features14,15.
The latter point requires explanation: the Gibbs adsorption isotherm16 and its kinetic analogues, such as the McLean isotherm17, state that the driving force for solute decoration to lattice imperfections comes from the reduced self-energy of the defect affected. This seems to suggest that the total magnitude of the decoration might be similar for defects in massive and dilute solid solutions or that the element with the highest segregation tendency (usually the element with low solubility and sufficiently high mobility) dominates the decoration. However, two theoretical considerations (and quantitative experimental findings about intense co-decoration based on atom probe tomography15,18) show that the magnitude of defect decoration can be higher in massive solid solutions. First, the magnitude of the chemical potential of the decorating elements, which determines the partitioning between matrix and defects, is much higher in high-entropy materials (HEMs) than in dilute solids. Second, classical adsorption isotherm formulations assume ideal solutions at the decorated defects, thus neglecting interactions among the segregating elements. However, the theories of compound isotherms and defect phase diagrams show that elemental interactions at co-decorated defects can lead to a higher total magnitude in (co-)segregation than in the dilute limit19. This, however, also implies that once highly co-segregated, these elements tend to form intermetallic or corresponding precursor phase states.
Each material design dimension offers multiple options for tuning, qualifying HEMs as the largest unchartered material design territory, fuelling expectations to discover new materials and phenomena. The advantage of the compositional complexity concept over conventional material design principles is the possibility for large and compositionally smooth chemical variations within the solid solution, even with elements immiscible in conventional alloys (and adjacent kinetic decomposition) states. This allows the shift of alloy compositions into ranges where promising material features can be seamlessly enhanced or damped without triggering (undesired) phase transformations, a typical feature of conventional materials. The wide and continuous compositional adjustment realm offered by HEMs allows the design of the magnitude and range of a wide spectrum of physical and chemical properties within defined phase spaces and the exploitation of the associated kinetic effects. Examples of the latter are high solute drag forces on interfaces (pinning, grain size stabilization) or pre-decoration and functionalization of grain boundaries by solutes (passivation and grain boundary protection)20,21. Another reason for studying compositional mixtures in materials for multi-functionality is that elements with high mutual solubility (such as Fe, Mn, Co, Ni, and Cr) have a strong influence on the Fermi surface and magnetic coupling so that interesting electronic, magnetic, and caloric properties can likely be triggered6,22–25.
This Review examines how these design options and their practically unbounded chemical adjustment opportunities can be used to create HEMs that exhibit novel property spectra and reconcile multiple functionalities, including feature combinations previously thought to be mutually exclusive in conventional alloys, while retaining their often excellent mechanical properties.
Reconciling conflicting properties is a general and long-standing challenge in material design. Examples can be found in magnetic and electrically conductive materials, where functional features are often in fundamental conflict with high mechanical strength and good ductility. In metals, high flow strength and strain hardening require multiple lattice defects such as dislocations and interfaces, whereas small hysteresis, soft magnetic response, and low electrical resistance require the opposite, namely, mobile magnetic domain walls and low scattering, both features which are adversely affected by lattice defects. This example indicates that the main reason for the conflict in realizing multi-functionality lies in the interplay among the electron, spin, and lattice degrees of freedom that enable functional properties and the lattice defects required for most mechanical properties, which lead to scattering and pinning effects.
Several multi-functional compositionally complex materials have been developed so far26,27. Specific examples are materials combining high strength, ductility, soft magnetism, resistance to corrosion28–31 at ambient32–38 and high temperatures39; or high selectivity, activity, and stability of electrocatalysts with high abundance of active sites40–43; or high cryogenic strength, toughness, and resistance to corrosion and hydrogen embrittlement44–46. Such synergies are rarely found in low-component materials (Figure 1).
Some of these multi-functional structure-property relations depend directly on the underlying solid-solution states, such as the concentration dependence of the yield strength, the maximum magnetic moment, and the electrical conductivity, whereas others also depend largely on microstructure, such as coercivity. It must be noted that the more solid solution elements are brought into a metal matrix, the more degrees of freedom arise for functional tuning and for stabilizing defects through chemical decoration. This means that access to novel functional properties becomes easier with higher solid solution content and variability of microstructure, and the spectrum of accessible non-equilibrium states becomes richer.

Max Planck Institut for Sustainable Materials Multi-Functional High Entropy Alloys for Magnet Design Max Planck Institut for Sustainable Materials Multi-Functional High Entropy Alloys for Magnet Design

In our work, we critically analyze and group the observed phenomena in multi-functional HEMs to identify governing principles, mechanisms, and correlations common to such compositionally complex solids, with a focus on identifying the underlying scientific principles and synergies of functional compositionally complex materials. We begin with materials with a lower number of functionalities to tune (such as electrical resistivity and conductivity and thermal expansion) and then proceed to more complex multi-functional cases such as thermoelectrics, hard magnets and catalysts. A few important methodological aspects are also discussed, such as high-throughput and artificial intelligence (AI)-assisted material design and sustainability. The former is critical for efficiently identifying new materials when exploring this high-dimensional phase space. The latter is essential because many elements used in HEMs are forbiddingly expensive and are associated with high greenhouse gas emissions.

A mechanically strong and ductile soft magnet with extremely low coercivity
Lowest possible coercivity and highest possible electrical resistivity are primary goals for SMMs, to reduce hysteresis-related and eddy-current-related energy losses, noise and the associated material damage1–3. Also, new SMMs with higher strength and ductility are needed, to operate under mechanically demanding loading conditions for safety-critical parts in transport and energy4. High strength and ductility also serve as measures for many other mechanical properties, such as high hardness5 and fracture toughness6. This multi-property profile creates a fundamental dilemma. The mechanical strength of metallic materials is produced by lattice defects and their elastic interactions with linear lattice faults that carry inelastic deformation, referred to as dislocations.
2022 Nature A mechanically strong and du[...]
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Max Planck Institut for Sustainable Materials Functional High Entropy Alloys for Magnets Lowest possible coercivity and highest possible electrical resistivity Max Planck Institut for Sustainable Materials Functional High Entropy Alloys for Magnets Lowest possible coercivity and highest possible electrical resistivity
A mechanically strong and ductile soft magnet with extremely low coercivity
Soft magnetic materials (SMMs) serve in electrical applications and sustainable energy supply, allowing magnetic flux variation in response to changes in applied magnetic field, at low energy loss1. The electrification of transport, households and manufacturing leads to an increase in energy consumption owing to hysteresis losses2. Therefore, minimizing coercivity, which scales these losses, is crucial3. Yet meeting this target alone is not enough: SMMs in electrical engines must withstand severe mechanical loads; that is, the alloys need high strength and ductility4. This is a fundamental design challenge, as most methods that enhance strength introduce stress fields that can pin magnetic domains, thus increasing coercivity and hysteresis losses5. Here we introduce an approach to overcome
Nature Com A mechanically strong and duc[...]
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