Point defects stabilise cubic Mo-N and Ta-N

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 1 : 1 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 (V-Mo, V-N) as long as their concentration is below approximate to 15 at.%. The overall lowest energies of formation were obtained for Ta0.78N and Mo0.91N, 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, Mo0.84N, Mo0.91N, MoN0.69 and MoN0.44, 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 Ta0.75N and Ta0.78N 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.