Internal energy and parameters of the order-disorder phase transition in titanium monoxide Ti[O.sub.y]

Quantum-mechanical ab initio calculations are used to simulate the free energy functions for titanium monoxide Ti[O.sub.y]. The effect of the long-range order of the [Ti.sub.5][O.sub.5] type superstructure on the internal energy of the compound is studied by the supercell method. The dependences of the configuration entropy and free energy on the long-range order parameter are determined. It is found that the order-disorder phase transition in titanium monoxide must occur in accordance with the mechanism of the first-order phase transition with a critical value of the long-range order parameter of 0.971. The calculated parameters of the phase transition are compared with the experimental data and the results obtained using the model of point charges and by calculating the Madelung energy. It is concluded that the short-range order and the phonon entropy must be taken into account in calculating the equilibrium phase diagrams for strongly nonstoichiometric compounds.