Point defects stabilise cubic Mo-N and Ta-N

Abstract

We employ ab initio calculations to investigate energetics of point defects in metastable rocksalt cubic Ta-N and Mo-N. Our results reveal a strong tendency to off-stoichiometry, i.e. defected structures are surprisingly predicted to be more stable than perfect ones with metal-to-nitrogen stoichiometry. Despite the similarity of Ta-N and Mo-N systems in exhibiting this unusual behaviour, we also point out their crucial differences. While Ta-N significantly favours metal vacancies, Mo-N exhibits similar energies of formation regardless of the vacancy type (VMo, VN) as long as their concentration is below . The overall lowest energies of formation were obtained for and , which are hence predicted to be the most stable compositions. To account for various experimental conditions during synthesis, we further evaluated the phase stability as a function of chemical potential of individual species. The proposed phase diagrams reveal four stable compositions, , , and , in the case of Mo-N and nine stable compositions in the case of Ta-N indicating the important role of metal under-stoichiometry, since and significantly dominate the diagram. This is particularly important for understanding and designing experiments using non-equilibrium deposition techniques. Finally, we discuss the role of defect ordering and estimate a cubic lattice parameter as a function of defect contents and put them in the context of existing literature theoretical and experimental data.