Diffraction of electrons in the Cubic Ti$_5$O$_5$ superstructure of titanium monoxide

Annealed titanium monoxide TiO$_{1.087}$ has been studied by the electron diffraction method. A cubic model of the Ti$_5$O$_5$ superstructure (Ti$_5$O$_5$ (Ti$_{90}\blacksquare_{18}$O$_{90}\square_{18}$)) of nonstoichiometric titanium monoxide Ti$_x$O$_z$ has been proposed on the basis of experimental data and representations about the disorder-order transition channel. It has been shown that reflections observed on the electron diffraction pattern are identified in the space group $Pm\bar{3}m$. The period of the unit cell of the cubic Ti$_5$O$_5$ superstructure is larger than that for the $B1$ basic disordered structure of Ti$_x$O$_z$ monoxide by a factor of 3. The disorder-order transition channel Ti$_x$O$_z$ (space group $Fm\bar{3}m$)–Ti$_{5}$O$_5$ (space group $Pm\bar{3}m$) includes 75 superstructure vectors of seven stars $\{\mathbf k_{10}\}$, $\{\mathbf k_7\}$, $\{\mathbf k_{6(1)}\}$, $\{\mathbf k_{6(2)}\}$, $\{\mathbf k_{4(1)}\}$, $\{\mathbf k_{4(2)}\}$, and $\{\mathbf k_1\}$. The distribution functions of Ti and O atoms over the sites of the cubic Ti$_5$O$_5$ (space group $Pm\bar{3}m$) superstructure have been calculated.