Elastic knowledge base of bcc Ti alloys from first-principles calculations and CALPHAD-based modeling

Titanium alloys are being investigated as suitable materials for load-bearing implants because of their biocompatibility and mechanical properties. Stress shielding, a common issue with the current load-bearing implant materials, occurs due to a Young's modulus (E) mismatch between bone (∼10–40 GPa) and implants (such as Ti-6Al-4V ∼110 GPa), which leads to bone dying around the implant and ultimately implant failure. Reducing the Young's modulus of Ti alloys may overcome the issues of stress shielding and improve implant materials. In the present work, first-principles calculations have been used to predict the single crystal elastic stiffness coefficients (c_ij’s) for the Ti-containing ternary alloys Ti-X-Y (X ≠ Y = Mo, Nb, Sn, Ta, Zr) in the bcc lattice. It is found that the ternary Ti-X-Y (X ≠ Y = Mo, Nb, Ta) alloys behave similarly; so do the ternary Ti-X-Sn (X = Mo, Nb, Ta) alloys and the Ti-X-Zr (X = Mo, Nb, Ta) alloys. This is expected due to the similarity between the Mo, Nb and Ta elements. The results also show that the Ti-Zr-X alloys stabilized the bcc phase at lower alloying concentrations. The polycrystalline aggregate properties are also estimated from the c_ij’s, including bulk modulus, shear modulus and Young's modulus. The results show that Ti-alloys with compositions close to the bcc stability limit have the lowest E. In combination with previous predictions, a complete elastic database has been established using the CALPHAD (CALculation of PHAse Diagram) based modeling approach. The database results are compared with the E of higher order Ti alloys and shown to be able to predict the E accurately. This complete database forms a foundation to tailor Ti alloys for desired elastic properties.