Structural, thermodynamic, mechanical, and electronic properties of HfNbTaTiMoX ( X = V,Fe,Zr,Re ) high-entropy alloys

We present a comprehensive comparative study of four refractory high-entropy alloys (RHEAs), denoted as HfNbTaTiMo X ( X = V, Fe, Zr, Re), to elucidate the structural, thermodynamic, mechanical, and electronic factors governing their physical properties. Formation energies, elastic and thermodynamic properties, electronic structures, and charge-transfer characteristics were systematically analyzed, supported by the quantum-mechanical descriptor of total bond order density ( t BO ), which quantifies internal cohesion and local bonding characteristics. Our results reveal that the Re-containing HEA exhibits the highest t BO , stiffness, and thermal stability, originating from strong d -orbital hybridization and uniform charge distribution. In contrast, the Zr-containing HEA displays lower t BO , noticeable local lattice distortion, and enhanced ductility due to weaker bonding interactions. The Fe- and V-based HEAs demonstrate intermediate behavior, with Fe contributing substantially to the electronic states near the Fermi level and V-based HEAs exhibiting pseudogap-like stability. These findings indicate that atomic size mismatch and d -state occupancy play a key role in shaping the balance between strength and ductility. Importantly, they demonstrate that elemental substitution, particularly the inclusion of Re, provides a viable strategy for designing RHEAs that overcomes the conventional strength–ductility trade-off, thereby enabling their application in extreme environments such as aerospace, energy, and defense technologies. • First-principles analysis reveals structure–property correlations in HfNbTaTiMoX (V, Fe, Zr, Re) refractory high entropy alloys (RHEAs). • Elemental substitution tunes the strength–ductility–thermal-resilience balance in RHEAs. • Atomic size mismatch and charge transfer drive lattice distortion. • Re-containing alloy maximizes stiffness, bond order, and thermal stability (melting temperature, T m = 2321.9 K). • Zr-based HEA exhibits a larger lattice distortion and improves ductility. • Composition, size mismatch, lattice distortion, and bond order jointly correlate cohesion with mechanical performance in RHEAs.