First-principles insights into the structural, electronic and mechanical behaviour of TiZrNbVMo series refractory high-entropy alloys

Refractory high-entropy alloys (RHEAs) comprising Ti, Zr, Nb, V, and Mo hold great promise for high-temperature and structural applications due to their tunable mechanical properties. In this study, first-principles calculations using the virtual crystal approximation (VCA) were employed to systematically investigate the structural and mechanical behavior of TiZrNbVMo alloys with varying elemental concentrations. The calculated lattice constants ranged from 3.15 to 3.29 Å, decreasing in Nb- and Mo-rich compositions and increasing with higher Ti and Zr content. Theoretical density varied from 6.55 to 8.37 g/cm³. All compositions met mechanical stability criteria. The highest elastic constant (C11 ≈ 450 GPa) and young's modulus (∼322 GPa) were observed in the Ti0.5 composition, indicating superior stiffness. Mo- and Nb-rich alloys exhibited lower C11 (∼165–222 GPa) and E (∼96–102 GPa), but maintained stability. Bulk and shear moduli followed similar patterns. Poisson's ratio exceeded 0.34 and B/G ratios were above 2.0, confirming good ductility. Hardness ranged from ∼5 to ∼29 GPa, with peak values in Ti-rich alloys. These results highlight the strong composition–property relationships in TiZrNbVMo RHEAs, enabling predictive design of high-strength, ductile alloys. This study offers rare insight into compositional tuning via VCA for the development of next-generation structural materials.