Ordered orthorhombic phases of titanium monoxide

Symmetry analysis is carried out for the ordered phases of cubic monoxide TiO$_y$ with relative oxygen contents $y<1$ and $y>1$. It is established that a partially ordered orthorhombic phase (space group $Immm$)—a derivative of the orthorhombic M$_3$X$_2\square$ superstructure (at $y<1.0$) or the inverse superstructure M$_2\blacksquare$X$_3$ (at $y>1$)—may arise in TiO$_y$. The distribution of Ti and O atoms, oxygen vacancies $\square$, and titanium vacancies $\blacksquare$ in unit cells of the orthorhombic ordered phases is determined. The phases are formed through the order-disorder transition channel along two rays of a non-Lifshitz star $\{{\mathbf k}_4\}$, and the ordering proceeds as a first-order phase transition. The distribution functions of Ti atoms over the sites of metallic and O atoms over the sites of nonmetallic sublattices are calculated for the orthorhombic superstructures of cubic titanium monoxide TiO$_y$.