Short-range order and nonstoichiometry in titanium monoxide TiO$_y$ from DFT calculations

Structural models of short-range order in the arrangement of structural vacancies have been proposed for stoichiometric and nonstoichiometric compositions of titanium monoxide TiO$_y$. A combined effect of the short-range order and nonstoichiometry on the ground-state energy and the electronic structure of the compound has been investigated using the first-principles methods. The energetically favorable models of short-range order reproduce the local distribution of atoms and vacancies, which is characteristic of the Ti$_{5}$O$_{5(\operatorname{mon})}$ and Ti$_{5}$O$_{5(\operatorname{cub})}$ superstructures. In these models, the correlations between the vacancies of the metal sublattice and the vacancies of the nonmetal sublattice make a more significant contribution to the decrease in the energy of the compound as compared with the correlations between the vacancies in only one of the sublattices.