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

Phase stability diagrams of Ti–M–O–C (M = Zr, Hf, Nb, and Ta) systems at 1800 K were constructed as a function of thecarbon activity, oxygen partial pressure, and solution formation characteristics, in order to determine the optimum conditionsfor the formation of (Ti0.75M0.25)C via carbothermal reduction of oxide mixtures. The tendency to form (Ti0.75M0.25)Cwas predicted on the basis of the standard Gibbs free energies of formation (ΔG◦f) 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 aremore stable than the TiC–NbC and TiC–TaC mixtures, whereas the (Ti0.75Zr0.25)C and (Ti0.75Hf0.25)C phases are less stablethan the corresponding TiC–ZrC and TiC–HfC mixtures. The phase stability diagrams of the Ti–M–O–C systems were thendrawn using the calculated ΔG◦f values and used to predict the tendencies to form solid-solution phases. The validity of thetheoretical predictions was then verified using experimental results.