Sequence of transformations during ordering of nonstoichiometric compounds with the formation of $M_3X_2$-type superstructures

A symmetry analysis of monoclinic, orthorhombic, and trigonal $M_3X_2$-type superstructures, which can be formed in highly nonstoichiometric $MX_y$ compounds with $B1$ structure, has been performed. Channels of disorder-order transitions $MX_y$ $\to$ $M_3X_2$ have been determined. It has been shown that two physically allowed sequences of transformations associated with the formation of $M_3X_2$ superstructures are possible in nonstoichiometric $MX_y$ compounds of Group IV transition metals with decreasing temperature, i.e., "cubic (space group $Fm\bar3m$) disordered $MX_y$ phase $\to$ orthorhombic (space group $Immm$) ordered $M_3X_2$ phase $\to$ orthorhombic (space group $C222_1$) ordered $M_3X_2$ phase" and "cubic (space group $Fm\bar3m$) disordered $MX_y$ phase $\to$ orthorhombic (space group $Immm$) ordered $M_3X_2$ phase $\to$ monoclinic (space group $C2$) ordered $M_3X_2$ phase.”