Thermodynamic Analysis of Steels by Incorporating First-Principles Calculations into the CALPHAD Approach

Ohtani, Hiroshi; Hanaya, N.; Hasebe, Mitsuhiro

doi:10.4028/www.scientific.net/msf.539-543.2413

“…7. The symbols in these figures results by first-principles calculation [43][44][45] were compared with the present study in Table 1, which shows that the calculated values in this work show reasonable agreement with those by the previous studies. Calculations of the heat capacities for TiC and Ti 4 C 2 S 2 were performed by the finite displacement method, and the results are given in Figs.…”

Section: Ticsupporting

confidence: 87%

Thermodynamic Study on Solubility Products of Ti4C2S2 in Fe Using First-Principles Calculations

Saeki

¹

,

Yamashita²,

Ohtani

³

2020

ISIJ Int.

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This study elucidates the solubility product of Ti 4 C 2 S 2 in steels by means of first-principles calculations and thermodynamic analysis. For this purpose, the Gibbs formation energy of Ti 4 C 2 S 2 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-TiC 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 Ti 4 C 2 S 2 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 Ti 4 C 2 S 2 was the main precipitate at lower temperatures.

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“…and calculated [43][44][45] results, kJ/mol of atom Ref. The result was compared with the thermodynamic data 46) and thermodynamic analysis.…”

Section: 緒言mentioning

confidence: 99%

Thermodynamic Study on Solubility Products of Ti4C2S2 in Fe Using First-Principles Calculations

Saeki

¹

,

Yamashita²,

Ohtani

³

2020

Tetsu-to-Hagane

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0

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This study elucidates the solubility product of Ti 4 C 2 S 2 in steels by means of first-principles calculations and thermodynamic analysis. For this purpose, the Gibbs formation energy of Ti 4 C 2 S 2 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-TiC 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 Ti 4 C 2 S 2 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 Ti 4 C 2 S 2 was the main precipitate at lower temperatures.

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Fe-P-Ti (Iron-Phosphorus-Titanium)

Raghavan¹

2008

J Phs Eqil and Diff

3

0

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The previous review of the experimental data on this ternary system by [1988Rag], based on mainly on the work of [1959Vog] and[1965Kan], presented a liquidus projection, an isothermal section at 25°C and a reaction scheme for the Fe-FeP-Ti region. Recently, [2006Oht] made a CALPHAD-type thermodynamic analysis of the entire system, incorporating first-principles energy calculations. Binary SystemsThe Fe-P phase diagram [2006Oht, Massalski2] has the following compounds at ambient pressure: Fe 3 P (D0 e , Ni 3 Ptype tetragonal), Fe 2 P (C22, Fe 2 P-type hexagonal), FeP (B31, MnP-type orthorhombic), FeP 2 (C18, FeS 2 -marcasite type orthorhombic), and FeP 4 (monoclinic). There are two intermediate phases in Fe-Ti system: Fe 2 Ti (C14, MgZn 2 -type hexagonal) and FeTi (B2, CsCl-type cubic). The computed P-Ti phase diagram [2006Oht] shows the following intermediate phases: Ti 3 P (tetragonal, space group P4 2 /n), Ti 2 P (hexagonal, space group P6/mmm), Ti 1.7 P (orthorhombic, space group P2 1 2 1 2 1 ), Ti 5 P 3 (D8 8 , Mn 5 Si 3 -type hexagonal), Ti 4 P 3 (D7 3 , Th 3 P 4 -type cubic?), TiP (B i , AsTi-type hexagonal), and TiP 2 (orthorhombic, space group Pnma). The Computed Ternary Phase EquilibriaIn their thermodynamic modeling, [2006Oht] used a regular solution model for the liquid, face-centered cubic (fcc), body-centered cubic (bcc), and close-packed hexagonal (cph) phases. The C14 phase (Fe 2 Ti) was described by a three sub-lattice model to account for its wide homogeneity range. The slight solubility of Ti in Fe 3 P and Fe 2 P and the homogeneity ranges of Ti 5 P 3 and TiP were taken into account, by using a two sublattice model. The other binary compounds were modeled as stoichiometric phases. The small homogeneity range of the ternary compound FeTiP (anti PbCl 2 -type orthorhombic) was accounted for, by adopting a three sublattice model. The enthalpies of formation of the binary phosphides and the ternary phosphide FeTiP were evaluated from the electron band energy calculations, using the Full Potential Linearized Augmented Plane Wave (FLAPW) method. See [2006Oht] for details.The experimental phase diagram data of [1959Vog] and[1965Kan] were used in the optimization and the derived interaction parameters were listed. Four vertical sections along the Fe 3 P-FeTiP and Fe-FeTiP joins and at constant 7.5 mass % P and 7.5 mass % Ti respectively, computed by [2006Oht] are compared with the experimental data of [1959Vog] in Fig. 1-4. The agreement is fair. A liquidus Fig. 1 Fe-P-Ti computed vertical section along the Fe 3 P-FeTiP join [2006Oht] Fig. 2 Fe-P-Ti computed vertical section along the Fe-FeTiP join [2006Oht]

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Thermodynamic Analysis of Steels by Incorporating First-Principles Calculations into the CALPHAD Approach

Cited by 3 publications

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

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

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

Fe-P-Ti (Iron-Phosphorus-Titanium)

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