First-principles investigations of ordering in binary α-Ti solid solutions

The ordering tendency in binary f-Ti solid solution containing 3sp or 4sp simple-metal (SM) or 3d transition-metal (TM) solute is investigated systematically by the linear muffin-tin orbital (LMTO) method within the atomic sphere approximation (ASA). We demonstrated that the effective pairwise interaction (EPI) energy in a solid solution is equal to half the solute-solute interaction energies and can be evaluated by a supercell total energy approach. The calculations of EPI energy both with and without volume relaxation of the supercells and local density of states (LDOS) show that the EPI energies of Ti-SM and Ti-TM solutions are dominated by different factors. For Ti-SM solutions, the EPI energies are of large absolute values with a negative sign, indicating strong ordering tendency in these solutions. The volume relaxation does not alter the EPI energy substantially. The calculated LDOS shows that the ordering tendency in Ti-SM solutions may be related to the hybridization between the electrons of the SM atoms when they are close to each other. For most Ti-TM solutions, if calculated without relaxation, the absolute EPI energies are very small; however, if calculated with relaxation, they are of relatively large positive values, indicating a clustering tendency in these solutions. By combining the calculated EPI energy and Flinn's model for short-range order (SRO) strengthening, the increase in critical shear stress sro due to SRO is estimated for Ti-SM alloys, and the results qualitatively agree with experiment.