Disordered multicomponent systems, occupying the mostly uncharted centres of phase diagrams, were proposed in 2004 as innovative materials with promising applications. The idea was to maximize the configurational entropy to stabilize (near) equimolar mixtures and achieve more robust systems, which became known as high-entropy materials. Initial research focused mainly on metal alloys and nitride films. In 2015, entropy stabilization was demonstrated in a mixture of oxides. Other high-entropy disordered ceramics rapidly followed, stimulating the addition of more components to obtain materials expressing a blend of properties, often highly enhanced. The systems were soon proven to be useful in wide-ranging technologies, including thermal barrier coatings, thermoelectrics, catalysts, batteries and wear-resistant and corrosion-resistant coatings. In this Review, we discuss the current state of the disordered ceramics field by examining the applications and the high-entropy features fuelling them, covering both theoretical predictions and experimental results. The influence of entropy is unavoidable and can no longer be ignored. In the space of ceramics, it leads to new materials that, both as bulk and thin films, will play important roles in technology in the decades to come. The valuable combination of disorder and non-metallic bonding gives rise to high-entropy ceramics. This Review explores the structures and chemistries of these versatile materials, and their applications in catalysis, water splitting, energy storage, thermoelectricity and thermal, environmental and wear protection.

High-entropy ceramics

Mechanical properties of high-entropy alloys with emphasis on face-centered cubic alloys

High-entropy materials have attracted considerable interest due to the combination of useful properties and promising applications. Predicting their formation remains the major hindrance to the discovery of new systems. Here we propose a descriptor-entropy forming ability-for addressing synthesizability from first principles. The formalism, based on the energy distribution spectrum of randomized calculations, captures the accessibility of equally-sampled states near the ground state and quantifies configurational disorder capable of stabilizing high-entropy homogeneous phases. The methodology is applied to disordered refractory 5-metal carbides-promising candidates for high-hardness applications. The descriptor correctly predicts the ease with which compositions can be experimentally synthesized as rock-salt high-entropy homogeneous phases, validating the ansatz, and in some cases, going beyond intuition. Several of these materials exhibit hardness up to 50% higher than rule of mixtures estimations. The entropy descriptor method has the potential to accelerate the search for high-entropy systems by rationally combining first principles with experimental synthesis and characterization.

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High-entropy high-hardness metal carbides discovered by entropy descriptors

A new class of high-entropy perovskite oxides

Bulk equiatomic (Hf-Ta-Zr-Ti)C and (Hf-Ta-Zr-Nb)C high entropy Ultra-High Temperature Ceramic (UHTC) carbide compositions were fabricated by ball milling and Spark Plasma Sintering (SPS). It was found that the lattice parameter mismatch of the component monocarbides is a key factor for predicting single phase solid solution formation. The processing route was further optimised for the (Hf-Ta-Zr-Nb)C composition to produce a high purity, single phase, homogeneous, bulk high entropy material (99% density); revealing a vast new compositional space for the exploration of new UHTCs. One sample was observed to chemically decompose; indicating the presence of a miscibility gap. While this suggests the system is not thermodynamically stable to room temperature, it does reveal further potential for the development of new in situ formed UHTC nanocomposites. The optimised material was subjected to nanoindentation testing and directly compared to the constituent mono/binary carbides, revealing a significantly enhanced hardness (36.1 ± 1.6 GPa,) compared to the hardest monocarbide (HfC, 31.5 ± 1.3 GPa) and the binary (Hf-Ta)C (32.9 ± 1.8 GPa).

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Processing and Properties of High-Entropy Ultra-High Temperature Carbides

Seven equimolar, five-component, metal diborides were fabricated via high-energy ball milling and spark plasma sintering. Six of them, including (Hf0.2Zr0.2Ta0.2Nb0.2Ti0.2)B2, (Hf0.2Zr0.2Ta0.2Mo0.2Ti0.2)B2, (Hf0.2Zr0.2Mo0.2Nb0.2Ti0.2)B2, (Hf0.2Mo0.2Ta0.2Nb0.2Ti0.2)B2, (Mo0.2Zr0.2Ta0.2Nb0.2Ti0.2)B2, and (Hf0.2Zr0.2Ta0.2Cr0.2Ti0.2)B2, possess virtually one solid-solution boride phase of the hexagonal AlB2 structure. Revised Hume-Rothery size-difference factors are used to rationalize the formation of high-entropy solid solutions in these metal diborides. Greater than 92% of the theoretical densities have been generally achieved with largely uniform compositions from nanoscale to microscale. Aberration-corrected scanning transmission electron microscopy (AC STEM), with high-angle annular dark-field and annular bright-field (HAADF and ABF) imaging and nanoscale compositional mapping, has been conducted to confirm the formation of 2-D high-entropy metal layers, separated by rigid 2-D boron nets, without any detectable layered segregation along the c-axis. These materials represent a new type of ultra-high temperature ceramics (UHTCs) as well as a new class of high-entropy materials, which not only exemplify the first high-entropy non-oxide ceramics (borides) fabricated but also possess a unique non-cubic (hexagonal) and layered (quasi-2D) high-entropy crystal structure that markedly differs from all those reported in prior studies. Initial property assessments show that both the hardness and the oxidation resistance of these high-entropy metal diborides are generally higher/better than the average performances of five individual metal diborides made by identical fabrication processing.

https://escholarship.org/content/qt99m7h5w8/qt99m7h5w8.pdf

High-Entropy Metal Diborides: A New Class of High-Entropy Materials and a New Type of Ultrahigh Temperature Ceramics.

Although high-entropy materials are attracting considerable interest due to a combination of useful properties and promising applications, predicting their formation remains a hindrance for rational discovery of new systems. Experimental approaches are based on physical intuition and/or expensive trial and error strategies. Most computational methods rely on the availability of sufficient experimental data and computational power. Machine learning (ML) applied to materials science can accelerate development and reduce costs. In this study, we propose an ML method, leveraging thermodynamic and compositional attributes of a given material for predicting the synthesizability (i.e., entropy-forming ability) of disordered metal carbides. The relative importance of the thermodynamic and compositional features for the predictions are then explored. The approach’s suitability is demonstrated by comparing values calculated with density functional theory to ML predictions. Finally, the model is employed to predict the entropy-forming ability of 70 new compositions; several predictions are validated by additional density functional theory calculations and experimental synthesis, corroborating the effectiveness in exploring vast compositional spaces in a high-throughput manner. Importantly, seven compositions are selected specifically, because they contain all three of the Group VI elements (Cr, Mo, and W), which do not form room temperature-stable rock-salt monocarbides. Incorporating the Group VI elements into the rock-salt structure provides further opportunity for tuning the electronic structure and potentially material performance.

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Discovery of high-entropy ceramics via machine learning

Enhancing plasticity in high-entropy refractory ceramics via tailoring valence electron concentration

In the last decade, single-phase high-entropy materials have attracted considerable research interest owing to their unexpected existence and unique combinations of properties. Recent development of 5-cation high-entropy carbides (HECs) has demonstrated alluring properties compared to the rule of mixtures and binary carbides. Proposed here is the development of ultrahigh-entropy carbides (UHECs) containing 6+ principal elements with greater combinatorial possibilities. The use of 6+ multi-cation compositions allows for the design of ceramics with further tunable properties, while likely possessing higher orders of entropic stabilization. There are 133 possible carbide compositions containing 6, 7, 8, or 9 refractory metal cations in equiatomic ratios. Candidate selection for fabrication and material testing was accelerated using a machine learning model that was originally trained to predict the synthesizability of five cation disordered metal carbides. Two compositions from each category of six through eight cations, one containing Cr and one without, plus the one possible nine cation carbide were fabricated and characterized. The potential for these 6+ cation UHECs as improved materials for oxidative environments is demonstrated by comparing the oxidation performance of a 5- and 7-cation system after 10 min at 1973 K in air. The oxidation behavior is correlated with Ellingham diagrams, and it is demonstrated that the 7-cation carbide has the ability to form a transitional stable 5+ cation HEC layer as elements preferentially form oxides, which results in significantly improved oxidation resistance.

William M. Mellor

Papers

High-Entropy Metal Diborides: A New Class of High-Entropy Materials and a New Type of Ultrahigh Temperature Ceramics.

Discovery of high-entropy ceramics via machine learning

Enhancing plasticity in high-entropy refractory ceramics via tailoring valence electron concentration

Development of ultrahigh-entropy ceramics with tailored oxidation behavior

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