title: First-principles phase diagram calculations for the rocksalt-structure quasibinary systems TiN-ZrN, TiN-HfN and ZrN-HfN.
abstract: 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: ΔEfof 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 TCand [Formula: see text] 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.
authors.affiliation: Department of Physics and Astronomy, University of Toledo, Toledo, OH 43606, USA.
authors.forename: Z T Y
authors.initials: ZT
authors.lastname: Liu
authors.forename: B P
authors.initials: BP
authors.lastname: Burton
authors.forename: S V
authors.initials: SV
authors.lastname: Khare
authors.forename: D
authors.initials: D
authors.lastname: Gall