First-principles phase diagram calculations for the HfC–TiC, ZrC–TiC, and HfC–ZrC solid solutions

Abstract

We report first-principles phase diagram calculations for the binary systems HfC-TiC, TiC-ZrC, and HfCZrC. Formation energies for superstructures of various bulk compositions were computed with a plane-wave pseudopotential method. They in turn were used as a basis for fitting cluster expansion Hamiltonians, both with and without approximations for excess vibrational free energies. Significant miscibility gaps are predicted for the systems TiC-ZrC and HfC-TiC, with consolute temperatures in excess of 2000 K. The HfC-ZrC system is predicted to be completely miscibile down to 185 K. Reductions in consolute temperature due to excess vibrational free energy are estimated to be ϳ7%, ϳ20%, and ϳ0%, for HfC-TiC, TiC-ZrC, and HfC-ZrC, respectively. Predicted miscibility gaps are symmetric for HfC-ZrC, almost symmetric for HfC-TiC and asymmetric for TiC-ZrC.

Phase decomposition of TiC−ZrC solid solution prepared by spark plasma sintering

“…1 shows the phase diagram of the TiCÀ ZrC system [12][13][14][15][16][17]. This system is a complete solid solution and has an immiscibility dome below 2400 K. The 90TiCÀ 10ZrC solid solution sintered at 2373 K had a uniform microstructure, and decomposed into two phases at the heat treatment temperature of 1573 K. This behavior was in good agreement with the phase diagram.…”

“…The TiC À ZrC system is a complete solid solution system, and we have demonstrated that 10 mol% ZrC can significantly enhance the sinterability of TiC À ZrC composites by forming homogeneous solid solutions [10,11]. On the other hand, it is known that the TiC À ZrC system is immiscible at temperatures lower than 2400 K. By heat treating the TiC À ZrC solid solution at a temperature lower than the consolute temperature, the solution decomposes into two phases and forms self-assembled nanoscale composites yielding high mechanical properties [12][13][14][15].…”

First-principles calculation of phase equilibrium of V-Nb, V-Ta, and Nb-Ta alloys

“…29 A scheme based on bond-length-dependent transferable force constants has been used successfully in several studies. 28,31,63,64 We use this scheme to compute the contribution of lattice vibrations to the free energy of V-Nb, V-Ta, and Nb-Ta alloys. This method proceeds by parametrizing the bond-length dependence of the stiffness for each type of nearest-neighbor chemical bond.…”

First-principles calculation of sulfur–selenium segregation in ZnSe1−xSx: The role of lattice vibration

“…That is to say, the introduction of this scheme made computational efficiency higher. As this method has been used successfully in several studies [29][30][31][32], we used it to calculate the contribution of lattice vibrations to the free energies of ZnSe 1 À x S x alloys.…”