Effects of alloying elements on the elastic properties of bcc Ti-X alloys from first-principles calculations

Titanium alloys are great implant materials due to their mechanical properties and biocompatibility. However, a large difference in Young's modulus between bone (∼10–40 GPa) and common implant materials (ie. Ti-6Al-4V alloy ∼110 GPa) leads to stress shielding and possible implant failure. The present work predicts the single crystal elastic stiffness coefficients (c_ij’s) for five binary systems with the body centered cubic lattice of Ti-X (X = Mo, Nb, Ta, Zr, Sn) using first-principles calculations based on Density Functional Theory. In addition, the polycrystalline aggregate properties of bulk modulus, shear modulus, Young's modulus, and Poisson ratio are calculated. It is shown that the lower Young's modulus of these Ti-alloys stems from the unstable bcc Ti with a negative value of (c₁₁–c₁₂). The data gathered from these efforts are compared with available experimental and other first-principles results in the literature, which set a foundation to design biocompatible Ti alloys for desired elastic properties.