First-principles phase diagram calculations for the rocksalt-structure quasibinary systems TiN-ZrN, TiN-HfN and ZrN-HfN.

We have studied the phase equilibria of three ceramic quasibinary systems Ti1-x Zr x N, Ti1-x Hf x N and Zr1-x Hf x N (0  ⩽  x  ⩽  1) with density functional theory, cluster expansion and Monte Carlo simulations. We predict consolute temperatures (T C ), at which miscibility gaps close, for Ti1-x Zr x N to be 1400 K, for Ti1-x Hf x N to be 700 K, and below 200 K for Zr1-x Hf x N. The asymmetry of the formation energy ΔE f (x) is greater for Ti1-x Hf x N than Ti1-x Zr x N, 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: ΔE f of the random solid solutions were decomposed into a volume change term, [Formula: see text], and a chemical exchange and relaxation term, [Formula: see text]. These two energies partially cancel one another. We conclude that [Formula: see text] influences the magnitude of T C and [Formula: see text] influences the asymmetry of ΔE f (x) and phase boundaries. We also conclude that the absence of experimentally observed phase separation in Ti1-x Zr x N and Ti1-x Hf x N 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-x Zr x N and Ti1-x Hf x N 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.