  Employing ab initio calculations, we discuss chemical, mechanical, and
dynamical stability of MoN-TaN solid solutions together with cubic-like MoN/TaN
superlattices, as another materials design concept. Hexagonal-type structures
based on low-energy modifications of MoN and TaN are the most stable ones over
the whole composition range. Despite being metastable, disordered cubic
polymorphs are energetically significantly preferred over their ordered
counterparts. An in-depth analysis of atomic environments in terms of bond
lengths and angles reveals that the chemical disorder results in (partially)
broken symmetry, i.e., the disordered cubic structure relaxes towards a
hexagonal NiAs-type phase, the ground state of MoN. Surprisingly, also the
superlattice architecture is clearly favored over the ordered cubic solid
solution. We show that the bi-axial coherency stresses in superlattices break
the cubic symmetry beyond simple tetragonal distortions and lead to a new
tetragonal $\zeta$-phase (space group P4/nmm), which exhibits a more negative
formation energy than the symmetry-stabilized cubic structures of MoN and TaN.
Unlike cubic TaN, the $\zeta\text{-TaN}$ is elastically and vibrationally
stable, while $\zeta$-MoN is stabilized only by the superlattice structure. To
map compositional trends in elasticity, we establish mechanical stability of
various Mo$_{1-x}$Ta$_x$N systems and find the closest high-symmetry
approximants of the corresponding elastic tensors. According to the estimated
polycrystalline moduli, the hexagonal polymorphs are predicted to be extremely
hard, however, less ductile than the cubic phases and superlattices. The trends
in stability based on energetics and elasticity are corroborated by density of
electronic states.
