Temperature-dependent elastic and thermodynamic properties of ZrC, HfC, and their solid solutions (Zr0.5Hf0.5)C

Zirconium carbide (ZrC) and hafnium carbide (HfC) have been identified as ultrahigh temperature ceramics with excellent thermal conductivity performance. The temperature profiles of ZrC and HfC have been studied; however, the temperature-dependent of solid solution of (Zr0.5Hf0.5)C is still lacking. Herein, we report the temperature-dependent elastic and thermodynamic properties of (Zr0.5Hf0.5)C using first-principles calculations. The covalent characters of ZrC, HfC, and (Zr0.5Hf0.5)C are weakened at high temperatures by analyzing their respective electronic structures. In addition, the equilibrium volumes at different temperatures can be determined from the energy-volume (E-V) curves under the quasi-harmonic approximation. Throughout the temperature ranges studied, the HfC material shows the highest bulk modulus and lowest thermal expansion. When T > 1000 K, (Zr0.5Hf0.5)C exhibits better shear and Young's modulus performance close to HfC and shows the highest anisotropy. The lattice thermal conductivity decreased as temperature increased for ZrC, HfC, and (Zr0.5Hf0.5)C, and (Zr0.5Hf0.5)C has the smallest lattice thermal conductivity. These results provide fundamental and useful information for the practical application of ZrC, HfC, and (Zr0.5Hf0.5)C.