Statistical thermodynamic study of nonstoichiometric titanium monoxide: Determination of formation and interaction energies of vacancies

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Abstract
The energy and entropy of formation of titanium and oxygen vacancies as well as interaction energies between vacancies up to sixth-nearest neighbors have been determined in nonstoichiometric TiO. These values have been extracted from experimental partial molar enthalpy and entropy by means of a numerical method based on an enumeration of configurational states of defects in a small sample. As might be expected, a repulsion between like vacancies has been found. The calculations show that the repulsive interaction between titanium vacancies is very strong and limited to second neighbors (≃20 kcal/mol), while the repulsion between oxygen vacancies is weaker (≃5 kcal/mol between second neighbors) and is slowly decreasing as the separation between vacancies increases. More surprising are the interactions between unlike vacancies. A strong repulsion between first neighbors and a small attraction between second neighbors have been found. We show that all these interactions may be interpreted in terms of electronic structure and chemical bonding and that they allow one to understand in a qualitative way the low-temperature ordered structure of TiO.