  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
Cr1-xTMxN1-0.5x 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 Cr1-xTMxN. The cubic Cr1-xMoxN1-0.5x and
Cr1-xWxN1-0.5x solid solutions exhibit large positive mixing enthalpies towards
isostructural phase decomposition into cubic B1-CrN and {\gamma}-Mo2N or
{\gamma}-W2N, 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,
Cr1-xMoxN1-0.5x and Cr1-xWxN1-0.5x, 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.
