Point defects and chemical potentials in D8 8–Sn 3Ti 5

Abstract

The point defect formation energies in D8 8–Sn 3Ti 5 are obtained from first principles calculations. The D8 8 structure is hexagonal, hP16, P6 3/mcm, prototype Mn 5Si 3. Four sublattices are introduced to account for the D8 8 structure and for the possibility of inserting atoms in the 2b sites of the structure P6 3/mcm. The 2b sites are not occupied in the stoichiometric compound at T = 0 K. But the possibility exists that a few atoms occupy these sites at high temperature or for off-stoichiometric alloys. A statistical model based on a mean-field approximation is developed in the canonical ensemble. The defect concentrations are calculated as function of temperature and deviation from stoichiometry. For stoichiometric D8 8–Sn 3Ti 5 alloys, the dominant thermal defects are composed of Sn atoms in interstitial positions 2b of the D8 8 structure and Ti atoms in antisite position on the sites preferentially occupied by Sn atoms. In the Sn-rich D8 8–Sn 3Ti 5, the constitutional defects are Sn atoms in interstitial positions. In the Ti-rich D8 8–Sn 3Ti 5, the constitutional defects are Ti atoms in antisite position. The chemical potentials as well as the Gibbs energy are obtained as function of composition for various temperatures. The extension of the one-phase domain of D8 8–Sn 3Ti 5 in the Sn–Ti phase diagram is calculated.