First-Principles Study on the Mechanical and Thermodynamic Properties of (NbZrHfTi)C High-Entropy Ceramics

(NbZrHfTi)C high-entropy ceramics, as an emerging class of ultra-high-temperature materials, have garnered significant interest due to their unique multi-principal-element crystal structure and exceptional high-temperature properties. This study systematically investigates the mechanical properties of (NbZrHfTi)C high-entropy ceramics by employing first-principles density functional theory, combined with the Debye-Grüneisen model, to explore the variations in their thermophysical properties with temperature (0–2000 K) and pressure (0–30 GPa). Thermodynamically, the calculated mixing enthalpy and Gibbs free energy confirm the feasibility of forming a stable single-phase solid solution in (NbZrHfTi)C. The calculated results of the elastic stiffness constant indicate that the material meets the mechanical stability criteria of the cubic crystal system, further confirming the structural stability. Through evaluation of key mechanical parameters—bulk modulus, shear modulus, Young’s modulus, and Poisson’s ratio—we provide comprehensive insight into the macro-mechanical behaviour of the material and its correlation with the underlying microstructure. Notably, compared to traditional binary carbides and their average properties, (NbZrHfTi)C exhibits higher Vickers hardness (Approximately 28.5 GPa) and fracture toughness (Approximately 3.4 MPa·m¹/²), which can be primarily attributed to the lattice distortion and solid-solution strengthening mechanism. The study also utilizes the quasi-harmonic approximation method to predict the material’s thermophysical properties, including Debye temperature (initial value around 563 K), thermal expansion coefficient (approximately 8.9 × 10⁻⁶ K⁻¹ at 2000 K), and other key parameters such as heat capacity at constant volume. The results show that within the studied pressure and temperature ranges, (NbZrHfTi)C consistently maintains a stable phase structure and good thermomechanical properties. The thermal expansion coefficient increasing with temperature, while heat capacity approaches the Dulong-Petit limit at elevated temperatures. These findings underscore the potential of (NbZrHfTi)C applications in ultra-high temperature thermal protection systems, cutting tool coatings, and nuclear structural materials.