Niobium monoxide superstructures

The cubic and orthorhombic models of Nb$_3$O$_3$ and Nb$_6$O$_6$ superstructures of nonstoichiometric niobium monoxide Nb$_{0.75}$O$_{0.75}$ with double defects have been proposed for the first time on the basis of the symmetry analysis and concepts of the channel of a disorder–order transition and the distribution function. The channel of the disorder–order transition associated with the formation of considered model superstructures includes three superstructure vectors, which are the arms $\mathbf{k}_{10}^{(1)}$, $\mathbf{k}_{10}^{(2)}$ and $\mathbf{k}_{10}^{(3)}$ of the $\{\mathbf{k}_{10}\}$ Lifshitz star. The distribution functions of O and Nb atoms over the sites of the Nb$_3$O$_3$ and Nb$_6$O$_6$ superstructures have been calculated. It has been shown that a decrease in the temperature can be accompanied by the formation of the Nb$_3$O$_3$ cubic, Nb$_3$O$_3$ orthorhombic, and Nb$_6$O$_6$ orthorhombic phases through successive disorder–order and order–order transitions.