“…Incorporation of oxygen in Ti 1Àx Al x N leads to formation of metal vacancies, hence, making their treatment in theoretical models indispensable. [74][75][76] Arguments based on the energy of formation used to support experimental observations of often puzzling phase composition have been also applied to elucidate, for example, Si partitioning in TiAl intermetallics, [77] O-vacancy clustering in iron [78] or Fe atoms in Fe-Ti alloys, [79] to corroborate atom probe data of carbides in a Hf-Mo-C alloy, [80] to rationalize structure and mechanical properties of oxynitrides, [75,76,81] or to study borides, [82,83] a novel perspective class for hard coating applications.…”