Self-consistent total energy calculations were performed to investigate the effects of ternary additions of 3d, 4d and 5d transition metal elements (V, Cr, Mn, Fe, Co, Ni, Zr, Nb, Mo, Tc, Ru, Rh, Pd, Hf, Ta, W, Re, Os, Ir, Pt) to Ll0 ordered γ-TiAl. In general, we studied ordered solids of 4 atoms per unit cell. In the case of Mn additions larger supercells with up to 32 atoms were also treated. Minimizing the total energy with respect to volume and c/a ratio leads to the determination of lattice distortions due to alloying by the ternary elements. These distortions prove to be strongly dependent on whether the alloying element substitutes Al or Ti atoms. Furthermore, the site preference can be derived by comparing the formation energies of Ti
n-i, where X is the substituting element. As a result the change of the geometry of L10 TiAl due to alloying can be estimated and may thereby give insight into the conditions at semicoherent γ/γ′ and α2/γ interfaces, which are associated to be responsible for ductility improvements of γ-TiAl based alloys.