Thermodynamic Study on Solubility Products of Ti<sub>4</sub>C<sub>2</sub>S<sub>2</sub> in Fe Using First-Principles Calculations

This study elucidates the solubility product of Ti4C2S2 in steels by means of first-principles calculations and thermodynamic analysis. For this purpose, the Gibbs formation energy of Ti4C2S2 was calculated theoretically by considering the effect of lattice vibration and thermal expansion. In addition, the Gibbs energies of the bcc and fcc phases in the Fe–Ti–C ternary system were also obtained using the cluster expansion and cluster variation method. Although some experimental data were considered as required, those results were evaluated as the calculation of phase diagrams (CALPHAD)-type thermodynamic parameters through fitting to the sublattice model. By using those thermodynamic functions, an approximate expression of the solubility product for Ti4C2S2 was derived. The result agrees with an experimental result measured in a relatively large temperature range. Furthermore, the formation behavior of precipitates in typical interstitial-free steels was discussed, incorporating an earlier thermodynamic analysis on the Fe–Ti–S ternary system. The results show that NiAs-type TiS was the main precipitate at higher temperatures and that Ti4C2S2 was the main precipitate at lower temperatures.