First-Principles Design of Refractory and Two-Dimensional High-Entropy Materials.

We present a first-principles investigation of refractory high-entropy alloys (RHEAs) of composition HfNbTaTiMoX, where X = V, Fe, Zr, or Re. Atomic disorder was modeled using a 108-atom special quasi-random structure based on a 3 × 3 × 3 supercell. Density functional theory calculations reveal a strong coupling among formation energy, bonding strength, and electronic structure. The total bond order density (TBOD) quantifies internal cohesion and correlates with mechanical response, with the Re-containing alloy showing the highest TBOD and stiffness, and the Zr-containing alloy the lowest TBOD and greatest ductility. Electronic density of states and partial charge analyses identify Re and Fe as dominant d-orbital contributors near the Fermi level, enhancing electronic stability in Re-HEA. Atomic size mismatch and d-band filling are found to control the strength–ductility balance, establishing Re as a promising alloying element for extreme-environment applications. Extending this framework, 75 two-dimensional high-entropy transition-metal dichalcogenide (HEA-TMDC) monolayers are designed and predicted to be mechanically and thermodynamically stable, offering tunable electronic, magnetic, and mechanical properties for next-generation quantum and energy devices.