Tailoring concentrations of principal elements to promote Hall-Petch strengthening of NiCoCrFe high entropy alloys

Hall-Petch strengthening in high-entropy alloys (HEAs) involves complex interactions between grain boundary segregation and unstable stacking fault energy (USFE), yet their competitive roles remain unresolved. Here, we design three non-equiatomic NiCoCrFe HEAs (Ni₄₀Co₂₀Cr₂₀Fe₂₀, Ni₂₀Co₄₀Cr₂₀Fe₂₀ and Ni₂₀Co₂₀Cr₂₀Fe₄₀) to decouple these effects through controlled elemental variations. Systematic experiments reveal that: (i) Friction stress scales linearly with lattice distortion degree, confirming solid-solution strengthening dominated by atomic size misfit; (ii) Hall-Petch coefficients exhibit an anomalous sequence: Co40 (426 MPa μm^0.5) > Fe40 (360 MPa μm^0.5) > Ni40 (320 MPa μm^0.5), defying predictions from singular grain boundary segregation or USFE theories; (iii) A unified competition mechanism framework is established, classifying systems into four types: non-segregation, segregation-transition, weak segregation, and strong segregation. Crucially, in weak-segregation systems, higher USFE overrides Cr segregation to maximize Hall-Petch coefficient. This work provides fundamental insights into the antagonistic grain boundary segregation-USFE interplay governing Hall-Petch behavior, enabling targeted optimization of strength-ductility trade-offs in HEAs.