Effect of Alloying Element X on Transformation Strains and Phase Stabilities between α′′ and β Ti-Nb-X (X = Al, Sn, Zr, Ta) Ternary Alloys from First-Principles Calculations

Abstract

The effect of alloying element X (X = Al, Sn, Zr, Ta) on the transformation strains and phase stabilities of Ti-12.5 at%Nb and Ti-25 at%Nb alloys was investigated. The principle strain, © 2 , was calculated as a function of the X concentration. The value of © 2 of Ti-12.5 at%Nb-6.25 at%Zr was larger than that of Ti-12.5 at%Nb-6.25 at%Ta. This is consistent with the experimental results. The difference of solution energy, ÁH ¡ 00 À¢ sol , was also calculated. The value of ÁH ¡ 00 À¢ sol increased with the addition of Al, Sn, Zr, and Ta to Ti-12.5 at% Nb-6.25 at%X alloys. We found a good linear correlation between the experimental values for the decrease of the martensitic transformation start temperature (Ms), dMs/ dc, and the calculated values of ÁH ¡ 00 À¢sol . The effect of the alloying element on the shape-memory properties of Ti-Nb-based alloys were evaluated from the first-principles calculations.

Phase stability and elastic properties ofβTi–Nb–X(X= Zr, Sn) alloys: anab initiodensity functional study

“…3.274 A°. Lattice constants of β Ti-Nb alloys are compared with those reported in previous theoretical studies and are found to be in excellent agreement [26,28,48]. However, it may be noted that the reported experimental values of lattice parameters [52][53][54] are higher than the calculated values.…”

“…As Nb increases, b/a and c/a values decreases and become equal at higher Nb content (43.5 and 50 at%) similar to the β (b/a=c/a=√2) phase. Lattice constants of α″ phase are compared with previously reported values in the literature and are found to be almost identical for the Ti-Nb alloys [28,42,47,48]. The change in lattice constants is quite small and is of the order of 10 −4 Å or less (∼0.003%) as the k-mesh and energy cut-off are further increased from the chosen optimized values.…”