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

Abstract: 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.

• The paper introduces the Entropy Forming Ability (EFA) descriptor to predict the synthesizability of high-entropy metal carbide systems.
• It employs high-throughput ab initio calculations on over 2700 configurations to identify promising 5-metal carbide compositions.
• Experimental validation shows stable single-phase formation and enhanced hardness, highlighting potential industrial applications.

High-Entropy High-Hardness Metal Carbides and Their Discovery Through Entropy Descriptors

The paper under review introduces a novel methodology aimed at identifying high-entropy metal carbide systems with potential applications in high-hardness environments. The authors present a description called the Entropy Forming Ability (EFA) to rationally predict the synthesizability of high-entropy materials. The study focuses primarily on refractory 5-metal carbides, demonstrating their utility through both theoretical predictions and experimental validations.

High-entropy materials, characterized by their highly disordered single-phase structures, have garnered increasing attention due to their intriguing properties and applications in various fields. One major challenge in the field is predicting the formation of such materials. The EFA descriptor posited by the authors evaluates a material's propensity to form a stable high-entropy phase by assessing the energy distribution spectrum of randomized calculations. A narrow energy distribution implies a greater likelihood of forming a disordered phase due to the low energetic cost of accessing multiple metastable configurations at finite temperatures.

The authors applied their EFA methodology to a matrix of 5-metal carbide systems, consisting of eight refractory metals, by calculating 49 distinct configurations per potential composition using the partial occupation (POCC) representation. Their high-throughput ab initio approach enabled them to calculate EFA values for 56 potential compositions, translating to over 2700 individual configurations. The EFA values informed their selection of nine compositions, which comprised the strongest candidates for synthesizing high-entropy carbides.

Experimental synthesis and characterization confirmed the predictions for the selected compositions. Six of the nine carbides formed stable single-phase structures with minimal lattice distortion measured by X-ray diffraction, validating their EFA threshold of about 50 (eV/atom)$^{-1}$. Some materials displayed Vickers hardness up to 50% higher than rule-of-mixtures estimates, attributing this enhancement to disorder-induced mechanical properties such as lattice strain and solid solution hardening.

Theoretical estimations of vibrational contributions to Gibbs free energy at 2000 K demonstrated that vibrational entropy did not account for the observed high-entropy stabilization, reinforcing the conclusion that configurational entropy plays a primary role.

The paper also underscores the challenge and opportunity presented by the complexity of the multi-component systems involved. Achieving homogeneous mixing is complicated by differences in precursor metallurgical conditions, which could include a variation in crystal structures and stoichiometries. Remarkably, the EFA successfully identified homogeneous compositions like MoNbTaVWC$_5$, notwithstanding considerable structural diversity in the individual metal carbide precursors.

In sum, the introduced EFA methodology provides an effective and efficient computational tool to predict the viability of high-entropy carbide systems. This approach bridges the gap between theoretical modeling and empirical validation, advancing the design and synthesis of new materials with potential industrial applications. The results invite further exploration into the variant substoichiometries, defect engineering, and potential technological impacts of these complex carbide systems. Through these methodologies, future high-entropy materials in other classes of ceramics and alloys may also be expedited, promoting innovation across advanced material domains.