Point defects stabilise cubic Mo-N and Ta-N

Abstract

We employ \\textit{ab initio} calculations to investigate energetics of point\ndefects in metastable rocksalt cubic Ta-N and Mo-N. Our results reveal a strong\ntendency to off-stoichiometry, i.e. defected structures are predicted to be\nmore stable than perfect ones with 1:1 metal-to-nitrogen stoichiometry, in\nagreement with previous literature reports. While Ta-N significantly favours\nmetal vacancies, Mo-N exhibits similar energies of formation regardless of the\nvacancy type ($V_\\text{Mo}$, $V_\\text{N}$) as long as their concentration is\nbelow $\\approx15\\,\\text{at.\\%}$. The overall lowest energy of formation were\nobtained for $\\text{Ta}_{0.78}\\text{N}$ and $\\text{Mo}_{0.91}\\text{N}$, which\nare hence predicted to be the most stable compositions. To account for various\nexperimental condition during synthesis, we further evaluated the phase\nstability as a function of chemical potential of individual species. The\nproposed phase diagrams reveal four stable compositions,\n$\\text{Mo}_{0.84}\\text{N}$, $\\text{Mo}_{0.91}\\text{N}$, $\\text{MoN}_{0.69}$ and\n$\\text{MoN}_{0.44}$, in the case of Mo-N and nine stable compositions in the\ncase of Ta-N indicating the crucial role of metal under-stoichiometry, since\n$\\text{Ta}_{0.75}\\text{N}$ and $\\text{Ta}_{0.78}\\text{N}$ significantly\ndominate the diagram. These results are important for understanding and\ndesigning experiments using non-equilibrium deposition techniques. Finally, we\ndiscuss a role of defects ordering and estimate a cubic lattice parameter as a\nfunction of a defect contents.\n