Phase Stability Diagrams of Ti–M–O–C (M = Zr, Hf, Nb, and Ta) Systems at 1800 K

Abstract

Phase stability diagrams of Ti–M–O–C (M = Zr, Hf, Nb, and Ta) systems at 1800 K were constructed as a function of the carbon activity, oxygen partial pressure, and solution formation characteristics, in order to determine the optimum conditions for the formation of (Ti0.75M0.25)C via carbothermal reduction of oxide mixtures. The tendency to form (Ti0.75M0.25)C was predicted on the basis of the standard Gibbs free energies of formation $$ (\Delta {\text{G}}_{f}^{^\circ } ) $$ of (Ti0.75M0.25)C solid-solution carbides, calculated by first-principles simulations. It was concluded that at 1800 K, the (Ti0.75Nb0.25)C and (Ti0.75Ta0.25)C phases are more stable than the TiC–NbC and TiC–TaC mixtures, whereas the (Ti0.75Zr0.25)C and (Ti0.75Hf0.25)C phases are less stable than the corresponding TiC–ZrC and TiC–HfC mixtures. The phase stability diagrams of the Ti–M–O–C systems were then drawn using the calculated $$ \Delta {\text{G}}_{f}^{^\circ } $$ values and used to predict the tendencies to form solid-solution phases. The validity of the theoretical predictions was then verified using experimental results.