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ARTICLE

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

Yonggang Tong^1,*, Kai Yang¹, Pengfei Li¹, Yongle Hu¹, Xiubing Liang^2,*, Jian Liu³, Yejun Li⁴, Jingzhong Fang¹

1 College of Mechanical and Vehicle Engineering, Changsha University of Science and Technology, Changsha, 410114, China
2 National Institute of Defense Technology Innovation, Academy of Military Sciences PLA China, Beijing, 100091, China
3 National Engineering Research Center for Mechanical Products Remanufacturing, Army Academy of Armored Forces, Beijing, 100072, China
4 Hunan Key Laboratory of Super Microstructure and Ultrafast Process, School of Physics and Electronics, Central South University, Changsha, 410083, China

* Corresponding Authors: Yonggang Tong. Email: ; Xiubing Liang. Email:

(This article belongs to the Special Issue: Computational Analysis of Micro-Nano Material Mechanics and Manufacturing)

Computers, Materials & Continua 2026, 86(1), 1-15. https://doi.org/10.32604/cmc.2025.071890

Received 14 August 2025; Accepted 10 October 2025; Issue published 10 November 2025

Abstract

(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.

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