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



Z.T. Liu, Benjamin P. Burton, S. V. Khare, D. Gall


We have studied the phase equilibria of three ceramic quasibinary systems Ti(sub 1-x)Zr(sub x)N, Ti(sub 1-x)Hf(sub x)N and Zr(sub 1-x)Hf(Sub x)N (0 less x less 1) with density functional theory, cluster expansion and Monte Carlo simulations. We predict the consulate temperature (T(sub c), where the miscibility gap closes, for the first system Ti(sub 1-x)Zr(sub x)N to be 1400 K, for the second (Ti(sub 1-x)Hf(Sub x)N to be 700 K, and below 200 K for the third system Zr(sub 1-x)Hf(sub x)N. We further extracted impact of different energetic contributions on the thermodynamics of these alloys. (I) Excluding vibrational contribution to the free energy contribution, these T(sub c) values rise significantly to 2400 K for Ti(sub 1-x)Zr(sub x)N and 900 K for the Ti(Sub 1-x)Hf(sub x)N. (ii) The formation energy (deltaE(sub f) of the random solid solution configurations was decomposed by a two-step process, volume change and chemical-exchange-relaxation. The two processes result in partial cancellation and the asymmetry of the resultant ΔE(sub f) with respect to composition is more noticeable for the Ti(sub 1-x)Hf(sub x)N than Ti(sub 1-x)Zr(sub x)N, with less solubility on the smaller cation TiN side. Similar asymmetry was also predicted for the corresponding phase diagrams. In addition, the elastic constants and hardness of the random solid solutions were studied with the special quasirandom solution approach. Monotonic trends, with composition change, of shear related mechanical properties, such as Vickers hardness, between 18 to 23 GPa were predicted. Trends for Ti(Sub 1-x)Zr(sub x)N and Ti(sub 1-x)Hf(sub x)N exhibit down-bowing hehavior.
Chemical Geology


rocksalt-structure nitrides, first principles phase diagram calculations, vibration free energy


Liu, Z. , Burton, B. , Khare, S. and Gall, D. (2016), First-principles phase diagram calculations for the rocksalt-structure quasibinary systems TiN-ZrN, TiN-HfN and ZrN-HfN, Chemical Geology (Accessed June 14, 2024)


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Created December 1, 2016, Updated October 12, 2021