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 the carbon activity, oxygen partial pressure, and solution formation characteristics, in order to determine the optimum conditions for the formation of (Ti_0.75M_0.25)C via carbothermal reduction of oxide mixtures. The tendency to form (Ti_0.75M_0.25)C was predicted on the basis of the standard Gibbs free energies of formation (ΔGf∘) of (Ti_0.75M_0.25)C solid-solution carbides, calculated by first-principles simulations. It was concluded that at 1800 K, the (Ti_0.75Nb_0.25)C and (Ti_0.75Ta_0.25)C phases are more stable than the TiC–NbC and TiC–TaC mixtures, whereas the (Ti_0.75Zr_0.25)C and (Ti_0.75Hf_0.25)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 ΔGf∘ values and used to predict the tendencies to form solid-solution phases. The validity of the theoretical predictions was then verified using experimental results.