Based on a combined computational and experimental study, we show that besides the thermodynamically stable β-MoN0.5 and δ2-MoN phases, also metastable γ-MoNx and its ordered relative γ′-MoNx can be synthesized by physical vapor deposition. The formation of the NaCl-based γ-MoNx phase is favored for nitrogen concentrations between 23 and 34 at.% (i.e., x = 0.30–0.53). Higher nitrogen contents (close to the 3:2 stoichiometry, hence, MoN0.67) favor the ordering of the vacancies at the nitrogen sublattice (hence, γ′-MoNx). The highest hardness of ∼33 GPa is obtained for single-phase cubic-structured γ-MoN0.53 coatings, whereas the ordered γ′-MoN0.67 coatings are slightly softer with a hardness of ∼28 GPa.

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The tendency for nitrogen deficiency in cubic Cr-Mo-N and Cr-W-N solid solutions is predicted by a comprehensive evaluation of the lattice spacing, mixing thermodynamics, and elastic properties using first-principles calculations and experimentally confirmed by means of X-ray diffraction. A major conclusion is that these systems exhibit significant amount of N vacancies whose amount scales linearly with the TM content, hence making the Cr 1-x TM x N 1-0.5x chemical formula more precise and informative to describe the chemical composition of cubic Cr-Mo-N and Cr-W-N solid solutions as compared with the conventionally used Cr 1-x TM x N. The cubic Cr 1-x Mo x N 1-0.5x and Cr 1-x W x N 1-0.5x solid solutions exhibit large positive mixing enthalpies towards isostructural phase decomposition into cubic B1-CrN and -Mo 2 N or -W 2 N, respectively. Their ductility increases with increasing Mo or W content and both systems exhibit significantly direction-dependent Young's moduli over the entire composition range, even when using the approach to study their polycrystalline behavior. The excellent agreement between experimentally obtained lattice parameters, Mo-and W-dependent nitrogen content, elastic properties and their calculated values for our model descriptions, Cr 1-x Mo x N 1-0.5x and Cr 1-x W x N 1-0.5x , allows to understand these complex material systems. Based on our results, we can conclude that their content of nitrogen vacancies scales with half of the alloying content Mo or W.2

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