Use of first principles and Thermo-Calc to identify potential low elastic modulus titanium-based alloys for biomedical applications

Abstract

High alloyed β-phase stabilised titanium alloys are known to have low elastic moduli comparable to that of the human bone (≈30 GPa). The β-phase in titanium alloys exhibits an elastic modulus of about 60-80 GPa, which is nearly half that of α-phase (100-120 GPa). In this work, an attempt to develop a β-phase titanium-based alloy through first-principles calculations and Thermo-Calc calculations for biomedical applications was conducted. First-principles calculations were performed using the CASTEP code on a simple 2-atom bcc unit cell to predict the theoretical elastic modulus and mechanical stability of the Ti-Nb-Ta-Zr (TNTZ) system at 0 K. Thermo-Calc was used to determine the phase proportion diagrams of the proposed alloys at 500℃. The alloy comprised Ti-Nb_x-Ta₂₅-Zr₅ (x = 5, 10, 20, 30, 40) (at.%). The theoretical results suggested that increasing niobium content introduced both mechanical (cʹ > 0) stability of the alloys. Alloy Ti-Nb₅-Ta₂₅-Zr₅ gave the lowest elastic modulus of 55.23 ± 24.45 GPa which is half the elastic modulus of pure titanium (α phase). The phase proportion diagrams showed that up to 58.6 mol.% of β phase was retained at 20 at.% Nb, although the Voigt-Reuss-Hill Young’s modulus calculated from first principles increased with increasing niobium content while the α/β phase transformation temperature decreased down to 551.3℃ at 40 at.% Nb.