Diffraction spectra of order-order transition structural states in titanium monoxide

A new class of M$_{(n-i)}$X$_{(n-i)}$ superstructures ($n$ is an integer constant and $i$ is a rational variable) that are formed after incomplete equilibrium second-order order-order phase transitions in solid solutions and in compounds with atom-vacancy ordering is proposed. New superstructures are superpositions of partially disordered M$_{n^-}$X$_n$ superstructures of various symmetries in the matrix of the basic crystal structure. The model parameters affecting the positions and intensities of superstructure reflections on diffraction patterns have been studied by example of the high-temperature ordered phase $\beta$-TiO of titanium monoxide. It has been shown that the diffraction spectra of the low-symmetric M$_{(5-i)}$X$_{(5-i)}$ superstructure (space group $P1m1$) and the high-symmetric M$_5$X$_5$ superstructure (space group $Pm\bar{3}m$) at certain parameters are identical in the positions of superstructure reflections.