Theoretical and experimental analysis of Nb-based alloy membranes at non-dilute hydrogen concentration

Three alloys, Nb₃₅Mo₅Ti₃₀Co₂₅Fe₅, Nb₄₃Mo₅Ti₂₇Co₂₀Fe₅, and Nb₅₁Mo₅Ti₂₃Co₁₆Fe₅, were investigated theoretically and experimentally, and hydrogen absorption and hydrogen permeation were analyzed based on the chemical potential to extend Sieverts' law and Fick's first law from dilute hydrogen conditions to non-dilute hydrogen conditions. The equilibrium hydrogen pressure and equilibrium concentration relationship graph ln(P/r) ∼(1-r)², and the normalized hydrogen permeation flux and relative concentration relationship graph Jd ∼ C‾ln(P_u/P_d) show a clear linear relationship, from which the interaction parameter Ω of the hydrogen atoms with the alloy and the hydrogen diffusion mobility B were calculated; The interaction parameter and hydrogen diffusion mobility are temperature-dependent and are unaffected by variations in hydrogen concentration. Hydrogen permeable experiments and hydrogen embrittlement experiments demonstrate that Nb35Mo5Ti30Co25Fe5, Nb43Mo5Ti27Co20Fe5, and Nb51Mo5Ti23Co16Fe5 alloy membranes exhibit improved hydrogen permeability and resistance to hydrogen embrittlement compared to the original alloy. Among them, Nb₃₅Mo₅Ti₃₀Co₂₅Fe₅ has excellent hydrogen embrittlement resistance and hydrogen permeability. It does not fail after 120 h of long-term hydrogen permeation at 673 K. The normalized hydrogen permeation flux under the same condition is 1.22 and 1.18 times that of Pd and Pd–Ag, respectively, making it a promising material to replace Pd and its alloys.