Thermodynamic assessment of Fe–Ti–S ternary phase diagram

A thermodynamic analysis of the Fe-Ti-S ternary system was performed by incorporating first-principles calculations into the calculation of phase diagrams (CALPHAD) method. To evaluate the Gibbs energy, the Debye-Grüneisen model was applied for some sulfides of the Ti-S binary system. In addition, the cluster expansion and cluster variation methods were used for the solid solution phases in the Ti-S binary and (Fe, Ti)S phases. The calculated Ti-S binary phase diagram showed good agreement with the experimental results. The very low solubility of the Ti solid solution in the Ti-S system, as reported by Murray, agreed well with our calculated results. A binodal phase decomposition of the liquid phase was expected in the S-rich region. The Gibbs energy curve of (Fe, Ti)S between FeS and TiS was found to be convex downward. This is characteristic of an isomorphic solid solution, attributed to the attractive interaction between Fe and Ti in (Fe, Ti)S. The vertical phase diagram between FeS and TiS, obtained using the thermodynamic database, was in good agreement with the experimental results of Mitsui et al. The solubility products of (Fe, Ti)S have been experimentally estimated previously. The calculated solubility product agreed with the experimental value of TiS.