Impact of 4<i>d</i> transition metals doping on the properties of TiVNbMo-based HEAs

Abstract This study employs ab initio density functional theory (DFT) combined with the exact muffin-tin orbitals (EMTO) method and coherent potential approximation (CPA) to systematically investigate the structural and mechanical properties of TiVNbMo-based refractory high-entropy alloys (RHEAs) doped with 4 d transition metals (Zr, Rh, Ag). Equiatomic TiVNbMoM (M = Zr, Rh, Ag) and non-equiatomic Ti (1− x ) VNbMoM x , TiV (1− x ) NbMoM x , TiVNb (1− x ) MoM x and TiVNbMo (1− x ) M x (with M = Zr, Rh, Ag; 0 ≤ x ≤ 1), were analyzed to evaluate phase stability, lattice parameters, elastic constants, and mechanical moduli. Results confirm the dominance of the body-centered cubic (bcc) phase in all equiatomic alloys, with valence electron concentration ( VEC = 4.8–6.2) and atomic size difference ( δ = 3.65%–6.18%) aligning with solid-solution formation criteria. However, Zr doping reduces bcc stability by lowering average d -electron occupancy, while Rh and Ag retain bcc dominance. Zirconium significantly expands the lattice parameter, whereas Rh reduces it. Mechanical analysis reveals that Rh enhances hardness in Rh-rich compositions, while Zr substitution at Ti sites improves ductility. All systems exhibit ductility ( B/G &gt; 1.75; ν &gt; 0.31). This study provides the first theoretical exploration of Rh and Ag doping effects on TiVNbMo RHEAs, demonstrating Rh’s unparalleled hardening capability and Zr’s dual role in lattice expansion and ductility enhancement. These findings, validated against experimental lattice constants and hardness, as well as theoretical elastic constants and moduli, require further experimental studies to confirm and extend the theoretical predictions.