Phase stability, brittle-ductile transition, and electronic structures of the TiAl alloying with Fe, Ru, Ge, and Sn: a first-principle investigation

Phase stability, brittle-ductile transition, and electronic structures of M (M = Fe, Ru, Ge, and Sn) and content change of L10-TiAl (γ-TiAl) and B2-TiAl (β-TiAl) have been investigated using first-principle methods. It is found that M metal atoms preferentially occupy the Al (2e) sites in L10-TiAl and B2-TiAl. According to Pugh's ratio and Poisson's ratio, the brittle-ductile transition is predicted for L10-TiAl and B2-TiAl with Fe, Ru, Ge, and Sn. It is found that the brittle-ductile transition from brittle regions to ductile regions with the transition metal elements Fe and Ru in L10-TiAl and B2-TiAl at the low concentration is approximately from 0 to 6.25 at.%. However, the brittle-ductile transition of Ge and Sn at the high concentration approximates from 6.25 to 12.5 at.% in L10-TiAl, comparing with B2-TiAl which approximates from 12.5 to 18.75 at.%. Electronic structure analysis shows that the improvement of brittleness can be attributed to two factors, including different hybridizations of Al-2p (Ti-3d) orbits with Fe-3d (Ge-4p) and Ru-4d (Sn-5p) orbits and different bandwidths of pseudo-gap. Furthermore, the L10-TiAl and B2-TiAl at low concentration of Fe and Ru can increase the value of ELF, where Ge and Sn atoms become bigger at a high concentration in L10-TiAl and B2-TiAl. At last, elastic constant (C_ij), bulk modulus (B), shear modulus (G), and Young's modulus (E) of L10 and B2-TiAl with content change are systematically given.