Thermodynamic study on solubility products of Ti4C2S2in Fe using first- principles calculations

Michitoshi Saeki, Takako Yamashita, Hiroshi Ohtani

Research output: Contribution to journalArticlepeer-review


This study elucidates the solubility product of Ti4C2S2in steels by means of first-principles calculations and thermodynamic analysis. For this purpose, the Gibbs formation energy of Ti4C2S2was 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 Ti4C2S2was 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 Ti4C2S2was the main precipitate at lower temperatures.

Original languageEnglish
Pages (from-to)911-923
Number of pages13
JournalTetsu-To-Hagane/Journal of the Iron and Steel Institute of Japan
Issue number12
Publication statusPublished - 2020


  • Carbosulfide
  • First-principles calculation
  • IF steel
  • Solubility product
  • Sulfide

ASJC Scopus subject areas

  • Condensed Matter Physics
  • Physical and Theoretical Chemistry
  • Metals and Alloys
  • Materials Chemistry


Dive into the research topics of 'Thermodynamic study on solubility products of Ti4C2S2in Fe using first- principles calculations'. Together they form a unique fingerprint.

Cite this