Point defects stabilise cubic Mo-N and Ta-N

We employ \textit{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 predicted to be more stable than perfect ones with 1:1 metal-to-nitrogen stoichiometry, in agreement with previous literature reports. While Ta-N significantly favours metal vacancies, Mo-N exhibits similar energies of formation regardless of the vacancy type ($V_\text{Mo}$, $V_\text{N}$) as long as their concentration is below $\approx15\,\text{at.\%}$. The overall lowest energy of formation were obtained for $\text{Ta}_{0.78}\text{N}$ and $\text{Mo}_{0.91}\text{N}$, which are hence predicted to be the most stable compositions. To account for various experimental condition 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, $\text{Mo}_{0.84}\text{N}$, $\text{Mo}_{0.91}\text{N}$, $\text{MoN}_{0.69}$ and $\text{MoN}_{0.44}$, in the case of Mo-N and nine stable compositions in the case of Ta-N indicating the crucial role of metal under-stoichiometry, since $\text{Ta}_{0.75}\text{N}$ and $\text{Ta}_{0.78}\text{N}$ significantly dominate the diagram. These results are important for understanding and designing experiments using non-equilibrium deposition techniques. Finally, we discuss a role of defects ordering and estimate a cubic lattice parameter as a function of a defect contents.