fig1

Figure 1. Thermodynamic results of Ti-Nb binary system. (A) Calculated equilibrium phase diagram (blue solid lines) and metastable phase diagram considering the β and ω phases (red solid line), where the spinodal decomposition occurs within the regions below the chemical spinodal. The T₀ curve for metastable β and ω equilibrium is also shown by the black shot dash line; the Ms line for β → α" is based on^[4]; (B) Gibbs energy curves of the metastable β and ω phases at different temperatures; (C) The second derivatives of the Gibbs energy of the β phase at 573 K and 673 K, respectively, which define the spinodal regions (24.0 at.% < c < 76.0 at.%) at 573 K and (31.0 at.% < $$ \bar{c} $$ < 69.0 at.%) at 673 K; (D) The critical concentration value, c₀(T), obtained from the intersection point of the β and ω Gibbs energy curves at different temperatures (c₀ = 26.7 at.% and 17.7 at.% at 573 K and 673 K, respectively); (E) The chemical free energy surface f_ch(c,η) of the Ti-Nb system in both the composition and structural order parameter space at 673 K, showing G and G at η = 0 and η = 1, respectively; (F) Enlarged chemical free energy surface at η =0, showing spinodal decomposition of the β matrix.