Computational tuning of the elastic properties of low- and high-entropy ultra-high temperature ceramics

TL;DR

This work addresses tuning the elastic properties of ultra-high temperature ceramics (UHTCs) by exploring multi-component, entropy-stabilized rocksalt carbides with a high-dimensional composition space. It adopts a fine-tuned MACE-UHTC interatomic potential to predict ensemble-averaged elastic constants across equimolar and non-equimolar mixtures, revealing that lattice-mismatch–driven distortions cause significant deviations from the rule of mixtures in both low- and high-entropy regimes. A three-component equimolar candidate, HfCVCZrC, balances synthesizability with reduced Young’s modulus (approximately $E\approx 380$ GPa), and non-equimolar tuning can further lower $E$ to around $354$ GPa at the cost of higher effective stabilization temperature $T^{*}$ (up to about $3600$ K). Overall, the study demonstrates a scalable, first-principles–accurate pathway to tailor stiffness and toughness in UHTCs, enabling rapid discovery of composition-optimized coatings and components for extreme environments.

Abstract

Ultra-high temperature ceramics (UHTCs) represent a class of crystalline materials for extreme environments. They can withstand extremely high temperatures but are mechanically difficult to work with due to their inherent brittleness. Mixture compounds, in particular high-entropy mixtures, offer a pathway to tune the physical properties of UHTCs such as their elastic constants. Here we fine-tune the MACE-MPA-0 universal machine-learning potential on rocksalt carbide UHTCs containing group IV-V metals and demonstrate that not only do the elastic constants deviate from the rule of mixtures approximation in the high-entropy limit, but also in the low-entropy limit of binary and ternary mixtures. We find that this is caused by distortion imposed by the lattice mismatch, enabling the tuning of the physical properties of UHTC mixtures in both low- and high-entropy compounds. We identify a three-component mixture compound, HfCVCZrC, as the best balance between synthesizability and toughness, and apply our developed MACE-UHTC model to identify a range of non-equimolar candidate compositions of this compound which may enable the synthesis of a mixture UHTC with a Young's modulus up to 40 GPa below that of ZrC.

Figures (8)

• Figure 1: Overview of the chemical space covered by the finetuned MACE-UHTC model, shown through t-SNE projections of configuration-averaged MACE embeddings of the training data. Each point represents an atomic configuration and is colored by the number of metal species present, with example UHTC crystal structures displayed in the insets. Contour lines indicate regions of equal density.
• Figure 2: High-throughput screening of equimolar compounds for Young's modulus and synthesizability. (a) Pareto plot showing Young's modulus ($E$ in GPa) versus the effective stabilization temperature ($T^{*}$ in K). (b) Dependence of Young's modulus on lattice mismatch. (c) Dependence of effective stabilization temperature on lattice mismatch. Curves in (b) and (c) are guides to the eye.
• Figure 3: (a) Ternary diagram showing the dependence of the Young's modulus ($E$ in GPa) on the Hf-V-Zr composition in the HfCVCZrC compound. Dashed line indicates path in composition space plotted in Fig. \ref{['fig:discussions']}(b). (b) Ternary diagram showing the dependence of the effective stabilization temperature ($T^{*}$ in K) on the Hf-V-Zr composition in the HfCVCZrC compound. (c) Predictions for the Young's modulus and the effective stabilization temperature in the full non-equimolar composition space for the HfCVCZrC mixture UHTC compound.
• Figure 4: Demonstration of the importance of taking lattice distortions into account on (a) the Young's modulus of all equimolar compounds comparing the fully relaxed ensemble MACE-UHTC predictions to the (VCA-esque) approximation of a perfect rocksalt crystal in which only the volume is optimized (points colored according to the mismatch between the lattice constants of the component materials), and (b) the Young's modulus of HfCVCZrC along the path indicated in the inset according to the rule-of-mixtures and using MACE-UHTC with and without full relaxation.
• Figure S1: Comparison of the $T^{*}$ effective stabilization temperature with the DEED compensation temperatureDivilov2024 for equimolar mixture compounds where both quantities are known.