Constitutional and thermal defects in B8 2–SnTi 2

Abstract

Vacancy and antisite defect formation energies in B8 2–SnTi 2 are calculated by an ab initio approach. Three sublattices are introduced to account for the B8 2 structure. 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 B8 2–SnTi 2 alloys, the dominant thermal defects are composed of one antisite Ti atom and three Ti vacancies. In the Sn-rich B8 2–SnTi 2, the constitutional defects are Ti vacancies; the thermal defect below 1000 K is an interbranch where Ti vacancies are replaced by Sn antisites; at high temperatures, it is a four point-defect comprising one Ti antisite and three Ti vacancies. In the Ti-rich B8 2–SnTi 2, the constitutional defects are antisite Ti atoms and the thermal defect is a four point defect comprising one Ti antisite and three Ti vacancies. The effective defect formation enthalpies are derived at low temperature. The Gibbs energy as well as the Sn and Ti chemical potentials in B8 2–SnTi 2 phase are obtained as function of composition for various temperatures. The extension of the one-phase domain of B8 2–SnTi 2 in the Sn–Ti phase diagram is discussed.