We report systematic results from ab initio calculations with density functional theory on three cubic structures, zincblende (zb), rocksalt (rs) and cesium chloride (cc), of the ten 3d transition metal nitrides. We computed lattice constants, elastic constants, their derived moduli and ratios that characterize mechanical properties. Experimental measurements exist in the literature of lattice constants for rs-ScN, rs-TiN and rs-VN and of elastic constants for rs-TiN and rs-VN, all of which are in good agreement with our computational results. Similarly, computed Vickers hardness (H V ) values for rs-TiN and rs-VN are consistent with earlier experimental results. Several trends were observed in our rich data set of 30 compounds. All nitrides, except for zb-CrN, rs-MnN, rs-FeN, cc-ScN, cc-CrN, cc-NiN and cc-ZnN, were found to be mechanically stable. A clear correlation in the atomic density with the bulk modulus (B) was observed with maximum values of B around FeN, MnN and CrN. The shear modulus, Young's modulus, H V and indicators of brittleness showed similar trends and all showed maxima for cc-VN. The calculated value of H V for cc-VN was about 30 GPa, while the next highest values were for rs-ScN and rs-TiN, about 24 GPa. A relation (H V ∝ θ 2 D ) between H V and Debye temperature (θ D ) was investigated and verified for each structure type. A tendency for anti-correlation of the elastic constant C 44 , which strongly influences stability and hardness, with the number of electronic states around the Fermi energy was observed.

We have studied the phase equilibria of three ceramic quasibinary systems Ti1−xZrxN, Ti1−xHfxN and Zr1−xHfxN (0 ≤ x ≤ 1) with density functional theory, cluster expansion and Monte Carlo simulations. We predict consolute temperatures (TC), at which miscibility gaps close, for Ti1−xZrxN to be 1400 K, for Ti1−xHfxN to be 700 K, and below 200 K for Zr1−xHfxN. The asymmetry of the formation energy ΔEf(x) is greater for Ti1−xHfxN than Ti1−xZrxN, with less solubility on the smaller cation TiN-side, and similar asymmetries were predicted for the corresponding phase diagrams. We also analyzed different energetic contributions: ΔEf of the random solid solutions were decomposed into a volume change term, ΔEvc, and a chemical exchange and relaxation term, ΔExc-rlx. These two energies partially cancel one another. We conclude that ΔEvc influences the magnitude of TC and ΔExc-rlx influences the asymmetry of ΔEf(x) and phase boundaries. We also conclude that the absence of experimentally observed phase separation in Ti1−xZrxN and Ti1−xHfxN is due to slow kinetics at low temperatures. In addition, elastic constants and mechanical properties of the random solid solutions were studied with the special quasirandom solution approach. Monotonic trends, in the composition dependence, of shear-related mechanical properties, such as Vickers hardness between 18 to 23 GPa, were predicted. Trends for Ti1−xZrxN and Ti1−xHfxN exhibit down-bowing (convexity). It shows that mixing nitrides of same group transition metals does not lead to hardness increase from an electronic origin, but through solution hardening mechanism. The mixed thin films show consistency and stability with little phase separation, making them desirable coating choices.