The coupling of carbon non-stoichiometry and short-range order in governing mechanical properties of high-entropy ceramics

High-entropy carbide ceramics (HECCs) commonly exhibit non-stoichiometric compositions and short-range order (SRO) arising from diverse elemental mixing. In this study, taking (TiZrHfNb)C as a representative HECC, we explore the coupling effects of SRO and carbon non-stoichiometry based on density-functional theory (DFT) and machine learning (ML). DFT results indicate that carbon non-stoichiometry is favored in Ti and Nb environments due to enhanced local atomic relaxation and charge transfer, which contribute to improved d-d bonding interactions. DFT-based Monte Carlo (MC) simulations further reveal a clustering tendency of Ti and Nb elements that compete with carbon non-stoichiometry formation. These local features are effectively captured by ML models, enabling rapid assessment of the interplay among carbon deficiency, SRO, and their influences on the mechanical properties of HECCs. This work elucidates the microscopic local properties responsible for the macroscopic behavior, offering key insights for designing HECCs through careful element selection and local chemistry control.