Accelerated design of high-strength refractory multi-principal element alloys from first-principles calculations

To rapidly develop high-strength refractory multi-principal element alloys (RMPEAs), we systematically calculate elastic moduli and mechanical properties for a series of body-centered-cubic (bcc) RMPEAs using the first-principles method. By analyzing equiatomic V₃₃Nb₃₃Mo₃₄ and V₂₅Nb₂₅Mo₂₅ X ₂₅ ( X = Al, Ti, Zr, Hf, V, Nb, Ta, Cr, Mo, and W) bcc RMPEAs, we discover that the product of shear modulus ( G ) and electronegativity difference ( δ _χ ), i.e. , G × δ _χ , accurately predicts yield strength ( σ _y ). This criterion outperforms other empirical parameters such as valence electron concentration (VEC), G , or δ _χ alone. Specifically, higher G × δ _χ correlates with higher σ _y . The σ _y of V₂₅Nb₂₅Mo₂₅Cr₂₅ exceeds that of other equiatomic alloys, agreeing with existing experiments, thereby validating the reliability of our approach. Following the G × δ _χ criterion, we further design non-equiatomic V_{50- x} Nb_{50- x} Mo _x Cr _x bcc RMPEAs based on V₂₅Nb₂₅Mo₂₅Cr₂₅. We identify V₁₅Nb₁₅Mo₃₅Cr₃₅ as a target RMPEA, which exhibits the highest σ _y and good high-temperature softening resistance among all considered bcc RMPEAs. The universality of the G × δ _χ criterion is confirmed not only by current calculations but also by available experiments, as evidenced by the maximum Pearson correlation coefficient between σ _y and G × δ _χ . This work provides an effective paradigm for discovering high-strength bcc refractory alloys by strategically optimizing the G × δ _χ metric.