Vacancy-strain coupling in ordered TiO

The structure of the partially ordered phase of TiO has been examined with a single crystal. While the space group is that first determined from powder X-ray diffraction and electron diffraction by Watanabe, Castle, Jostons & Malin [Acta Cryst. (1967). 23, 307-313], (B2/m), the average structure is somewhat different. There are waves of Ti and O ion vacancies every third (100) plane in the [010] direction of the monoclinic structure. The amplitude of the wave is twice as large for the Ti ion vacancies as for the O ion vacancies. There is no appreciable concentration of interstitial Ti ions in either the ordered phase or the disordered (cubic) phase. The ordering temperature T_c is 1026 (2)°C. The monoclinic angle is directly proportional to the square of the order parameter associated with vacancy ordering. A mean-field theory is developed that includes vacancy-vacancy and vacancy-electron interactions, and vacancy-strain coupling. This theory explains the main features of the order-disorder transition in this material.