Distribution of vacancies in a hybrid M$_{(5-11/18)}$X$_{(5-11/18)}$ superstructure of a high-temperature ordered $\beta$-TiO phase

A new structural model of the high-temperature ordered $\beta$-TiO phase of titanium monoxide with vacancies in metallic and nonmetallic sublattices has been proposed. The model suggests that the vacancies are simultaneously distributed over sites of two partially disordered superstructures: monoclinic M$_{5}$X$_{5(\operatorname{mon})}$ (space group $C2/m$ $(A2/m)$) and cubic M$_{5}$X$_{5(\operatorname{cub})}$ (space group $Pm\bar{3}m$). The hybrid superstructure belongs to space group $P1m1$ of the monoclinic system. The proposed notation M$_{(5-11/18)}$X$_{(5-11/18)}$ of the hybrid superstructure takes into account an expansion of the vacancy sublattice due to the superposition of initial M$_{5}$X$_{5}$-type superstructures. It is shown that the arrangements of the superstructure reflections in the diffraction spectra of the M$_{(5-11/18)}$X$_{(5-11/18)}$ and M$_{5}$X$_{5(\operatorname{cub})}$ superstructures are identical.