Thermodynamics of structural vacancies in titanium monoxide from first-principles calculations

The structure, stability and electronic properties of the low oxygen oxides of titanium, TiOx with 1/3 <= x <= 3/2, have been studied by means of accurate first-principles calculations. In both stoichiometric and nonstoichiometric TiO there are large fractions of vacant lattice sites. These so-called structural vacancies are essential for understanding the properties and phase stability of titanium oxides. Structures with an ordered arrangement of vacancies were treated with a plane wave pseudo-potential method, while calculations for structures with disordered vacancies were performed within the framework of the Korringa-Kohn-Rostoker Green's function technique. The relaxed structural parameters in general compare well with experimental data, though some discrepancies exist for stoichiometric TiO in the ideal B1 structure, i.e., without any vacancies. The equation of state as well as the elastic properties are also derived. A monoclinic, vacancy-containing, structure of stoichiometric TiO is confirmed to be stable at low temperature and pressure. Experimentally a transition from a stoichiometric cubic structure with disordered vacancies to the ideal B1 structure without any vacancies has been observed at high pressure. It is discussed how this experimental observation relates to the present theoretical results for defect-containing and defect-free TiO.