Skip to main content
SpringerLink
Log in

Thermodynamic Properties Prediction of Fe–Al–Ti Alloys Based on Atom and Molecule Coexistence Theory

  • STRUCTURE, PHASE TRANSFORMATIONS, AND DIFFUSION
  • Published:
Physics of Metals and Metallography Aims and scope Submit manuscript

Abstract

The thermodynamic properties for the full composition range of liquid Fe–Ti alloys were determined using the atom and molecule coexistence theory (AMCT). The thermodynamic model was also established to calculate the mass action concentration (activity) of the structural units in the above-mentioned binary alloy system. The temperature dependence of the activity coefficients \(\gamma _{i}^{\theta }\) of Ti dissolved in molten iron to form dilute solutions (\(0 \leqslant {{x}_{i}} \leqslant 0.01\)) relative to pure liquid, were also estimated. Simultaneously, the standard Gibbs free energy changes \({{\Delta }_{{{\text{sol}}}}}G_{{{\text{m,}}i}}^{{{\theta }}}\) of dissolving Ti in the iron of liquid Fe–Ti were also studied. The excess molar mixing enthalpy \({{\Delta }_{{{\text{mix}}}}}H_{{{\text{m, Fe}} - {\text{Ti}}}}^{{{\text{ex}}}}\), the excess molar mixing entropy \({{\Delta }_{{{\text{mix}}}}}S_{{{\text{m, Fe}} - {\text{Ti}}}}^{{{\text{ex}}}}\), and the excess molar mixing Gibbs free energy \({{\Delta }_{{{\text{mix}}}}}G_{{{\text{m, Fe}} - {\text{Ti}}}}^{{{\text{ex}}}}\) were also studied from 1873 to 2073 K. Meanwhile, the thermodynamic properties of activities and the excess Gibbs free energy of mixing were predicted in the Fe–Al–Ti ternary melts at 1873 K under conditions of various Fe/Al ratios.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1.
Fig. 2.
Fig. 3.
Fig. 4.
Fig. 5.
Fig. 6.
Fig. 7.
Fig. 8.
Fig. 9.

Similar content being viewed by others

REFERENCES

  1. P. Willemiin and M. Durand-Charre, “The nickel-rich corner of the Ni–Al–Ti system,” J. Mater. Sci. 25, 168–174 (1990).

    Article  Google Scholar 

  2. P. G. Nash, V. Vejins, and W. W. Liang, “The Al–Ni–Ti (aluminum-nickel-titanium) system,” Bull. Alloy Phase Diag. 3, 367–374 (1982).

    Article  Google Scholar 

  3. N. Njah and O. Dimitrov, “Microstructural evolution of nickel-rich Ni–Al–Ti alloys during aging treatments: the effect of composition,” Acta Metall. 37, 2559–2566 (1989).

    Article  CAS  Google Scholar 

  4. S. Duan, X. Shi, M. Zhang, B. Li, G. Dou, H. Guo, and J. Guo, “Determination of the thermodynamic properties of Ni–Ti, Ni–Al, and Ti–Al, and nickel-rich Ni–Al–Ti melts based on the atom and molecule coexistence theory,” J. Mol. Liq. 294, 111462 (2019).

    Article  CAS  Google Scholar 

  5. A. V. Zhelnina, M. S. Kalienko, and N. V. Shchetnikov, “Study of the Effect of Carbon on the Deformation Behavior and Microstructure of a Ti–10V–2Fe–3Al Alloy,” Phys. Met. Metallogr. 122, 154–160 (2021).

    Article  CAS  Google Scholar 

  6. A. V. Zhelnina, M. S. Kalienko, A. G. Illarionov, and N. V. Shchetnikov, “Transformation of the structure and parameters of phases during aging of a titanium Ti–10V–2Fe–3Al alloy and their relation to strengthening,” Phys. Met. Metallogr. 121, 1220–1226 (2020).

    Article  CAS  Google Scholar 

  7. E. V. Voronina, A. K. Al Saedi, A. G. Ivanova, A. K.  Arzhnikov, and E. N. Dulov, “Structural and phase transformations occurring during preparation of ordered ternary Fe–Al–M alloys (with M = Ga, B, V, and Mn) by mechanical alloying,” Phys. Met. Metallogr. 120, 1213–1220 (2019).

    Article  CAS  Google Scholar 

  8. V. I. Okulov, A. T. Lonchakov, and V. V. Marchenkov, “Semiconductor-like behavior of electric transport in Fe–V–Al-based metallic alloys and their uncommon magnetic properties,” Phys. Met. Metallogr. 119, 1325–1328 (2018).

    Article  CAS  Google Scholar 

  9. E. I. Shreder, A. D. Svyazhin, A. A. Makhnev, A. N. Ignatenkov, L. D. Sabirzyanova, and V. S. Gaviko, “Optical, electrical, and magnetic properties of Fe2Cr1 – xVxAl alloys,” Phys. Met. Metallogr. 99, 393–400 (2005).

    Google Scholar 

  10. A. Kostov and B. Friedrich, and D. Zivkovic, “Predicting thermodynamic properties in Ti–Al binary system by FactSageTM,” Comput. Mater. Sci. 37, 355–360 (2006).

    Article  CAS  Google Scholar 

  11. H. Renon and J. M. Prausnitz, “Local compositions in thermodynamic excess functions for liquid mixtures,” AICHE J. 14, 135–144 (1968).

    Article  CAS  Google Scholar 

  12. A. R. Miedema, P. F. De Chatel, and F. R. De Boer, “Cohesion in alloys-fundamentals of a semi-empirical model,” Phys. B+C 100, 1–28 (1980).

  13. D. P. Tao, “A new model of thermodynamics of liquid mixtures and its application to liquid alloys,” Thermochim. Acta 363, 105–113 (2000).

    Article  CAS  Google Scholar 

  14. I. Prigogine and R. Bingen, and A. Bellemans, “Effets isotopiques et proprietes thermodynamiques en phase condensee. III,” Physica 20, 633–654 (1954).

    Article  CAS  Google Scholar 

  15. F. Sommer, “Association model for the description of thermodynamic functions of liquid alloys,” Int. J. Mater. Res. 73, 77–86 (1982).

    Article  CAS  Google Scholar 

  16. J. Zhang and P. Wang, “The widespread applicability of the mass action law to metallurgical melts and organic solutions,” CALPHAD: Comput. Coupling Phase Diagrams Thermochem. 25, 343–354 (2001).

    Article  CAS  Google Scholar 

  17. J. Zhang, Computational Thermodynamics of Metallurgical Melts and Solutions (Metallurgical Industry Press, Beijing, 2007) [in Chinese].

    Google Scholar 

  18. R. C. Sharma and Y. A. Chang, “Thermodynamics and Phase relationships of transition metal-sulfur systems: Part III. Thermodynamic properties of the Fe–S liquid phase and the calculation of the Fe–S phase diagram,” Metall. Trans. B 10, 103–108 (1979).

    Article  Google Scholar 

  19. A. D. Pelton, S. A. Degterov, G. Eriksson, C. Robelin, and Y. Dessureault, “The modified quasichemical model I-binary solutions,” Metall. Mater. Trans. B 31, 651–659 (2000).

    Article  Google Scholar 

  20. Y. Chuang, K. Hsieh, and Y. A. Chang, “A thermodynamic analysis of the phase equilibria of the Fe–Ni system above 1200 K,” Metall. Trans. A 17, 1373–1380 (1986).

    Article  Google Scholar 

  21. T. X. Fan, G. J. Yang, J. Q. Chen, and D. Zhang, “Model prediction of thermodynamics activity in multicomponent liquid alloy,” Key Eng. Mater. 313, 19–24 (2006).

    Article  CAS  Google Scholar 

  22. S. Duan, S. Xiao, W. Yang, H. Guo, and G. Jing, “Determination of thermodynamic properties in full composition range of Ti–Al binary melts based on atom and molecule coexistence theory,” Trans. Nonferrous Met. Soc. China. 28, 1256–1264 (2018).

    Article  CAS  Google Scholar 

  23. A. Kostov, B. Friedrich, and D. Živković, “Thermodynamic calculations in alloys Ti–Al, Ti–Fe, Al–Fe and Ti–Al–Fe,” J. Min. Metall. Sect. B 44, 49–61 (2008).

    Article  CAS  Google Scholar 

  24. I. Ohnuma, Y. Fujita, H. Mitsui, K. Ishikawa, R. Kainuma, and K. Ishida, “Phase equilibria in the Ti–Al binary system,” Acta Mater. 48, 3113–3123 (2000).

    Article  CAS  Google Scholar 

  25. C. Guoguang and Z. Jian, “Calculating models of mass action concentrations for the metallic Fe–Al,” J. Univ. Sci. Technol. Beijing 13, 514–518 (1991).

    Google Scholar 

  26. J. Zhang and R. Zhu, “Thermodynamic properties of Mn–P and Fe–Mn–P melts,”, ” J. Univ. Sci. Technol. Beijing 7, 10–13 (2000).

    CAS  Google Scholar 

  27. X. Yang, J. Li, M. Wei, and J. Zhang, “Thermodynamic evaluation of reaction abilities of structural units in Fe‒O binary melts based on the atom-molecule coexistence theory,” Metall. Mater. Trans. B 47, 174–206 (2016).

    Article  Google Scholar 

  28. X. Yang, J. Li, D. Duan, F. Yan, and J. Zhang, “Thermodynamic evaluation of reaction abilities of structural units in Fe–C binary melts based on atom-molecule coexistence theory,” J. Iron Steel Res. Int. 25, 37–56 (2018).

    Article  Google Scholar 

  29. X. M. Yang, P. C. Li, J. Y. Li, M. Zhang, J. L. Zhang, and J. Zhang, “Representation reaction abilities of structural units and related thermodynamic properties in Fe–P binary melts based on the atom-molecule coexistence theory,” Steel Res. Int. 85, 426–460 (2014).

    Article  CAS  Google Scholar 

  30. X. Yang, M. Zhang, J. Zhang, P. Li, J. Li, and J. Zhang, “Representation of oxidation ability for metallurgical slags based on the ion and molecule coexistence theory,” Steel Res. Int. 85, 347–375 (2014).

    Article  CAS  Google Scholar 

  31. J. Zhang, “Calculating models of mass action concentrations for Fe–P and Cr–P melts and optimization of their thermodynamic parameters,” J. Univ. Sci. Technol. Beijing 6, 174–177 (1999).

    CAS  Google Scholar 

  32. J. Zhang, “Calculating model of mass action concentrations for Fe–Cr–P melts and optimization of thermodynamic parameters,” J. Univ. Sci. Technol. Beijing 1, 11–14 (1999).

    Google Scholar 

  33. X. M. Yang, M. Zhang, P. C. Li, J. Y. Li, and J. Zhang, “A thermodynamic model for representation reaction abilities of structural units in full composition range of Fe–Si binary melts based on the atom-molecule coexistence theory,” Iron Steel Res. Int. 84, 784–811 (2013).

    Article  CAS  Google Scholar 

  34. X. Yang, M. Zhang, P. Li, J. Li, J. Zhang, and J. Zhang, “A thermodynamic model for representation reaction abilities of structural units in Fe–S binary melts based on the atom-molecule coexistence theory,” Metall. Mater. Trans. B 43, 1358–1387 (2012).

    Article  CAS  Google Scholar 

  35. C. Wagner, Thermodynamics of Alloys (Addison-Wesley, 1952).

    Google Scholar 

  36. A. Y. Stomakhin and E. V. Lysenkova, “Activity coefficient of titanium in iron-based melts under nitride formation/dissolution conditions,” Russ. Metall. 2013, 834–839 (2013).

    Article  Google Scholar 

  37. W. Kim, J. Jo, C. Lee, and D. Kim, and J. Pak, “Thermodynamic relation between aluminum and titanium in liquid iron,” ISIJ Int. 48, 17–22 (2008).

    Article  CAS  Google Scholar 

  38. W. Cha, T. Nagasaka, T. Miki, Y. Sasaki, and M. Hino, “Equilibrium between titanium and oxygen in liquid Fe–Ti alloy coexisted with titanium oxides at 1873 K,” ISIJ Int. 46, 996–1005 (2006).

    Article  CAS  Google Scholar 

  39. Z. Morita, and K. Kunisada, “Solubility of nitrogen and equilibrium of Ti-nitride forming reaction in liquid Fe–Ti alloys,” Tetsu-to-Hagané 63, 1663–1671 (1977).

    Article  CAS  Google Scholar 

  40. Y. M. Bochkov, L. G. Apolovnikova, and A. S. Petrov, “Melting of steel Kh18N10T with lower contramination with nitride inclusions in vacuum induction furnaces,” Stal’ 1, 320–323 (1976).

    Google Scholar 

  41. T. Furukawa and E. Kato, “Thermodynamic properties of liquid Fe-Ti alloys by mass-spectrometry,” Tetsu-to-Hagané 61, 3060–3068 (1975).

    Article  CAS  Google Scholar 

  42. S. Wagner and G. R. S. Pierre, “Thermodynamics of the liquid binary iron–titanium by mass spectrometry,” Metall. Trans. 5, 887–889 (1974).

    Article  CAS  Google Scholar 

  43. R. J. Fruehan, “Activities in liquid Fe–Al–O and Fe‒Ti–O alloys,” Metall. Trans. 1, 3403–3410 (1970).

    Article  CAS  Google Scholar 

  44. J. Chipman, The deoxidation equilibrium of titanium in liquid steel,” Trans. Am. Inst. Min., Metall. Eng. 218, 767–768 (1960).

    CAS  Google Scholar 

  45. G. Han-Jie, Metallurgical Physical Chemistry (Metallurgical Industry, Beijing, 2004) [in Chinese].

    Google Scholar 

  46. X. Li, A. Scherf, M. Heilmaier, and F. Stein, “The Al-rich part of the Fe–Al phase diagram,” J. Phase Equilib. Diffus. 37, 162–173 (2016).

    Article  CAS  Google Scholar 

  47. M. Maeda, T. Kiwake, K. Shibuya, and T. Ikeda, “Activity of aluminum in molten Ti–Al alloys,” Mater. Sci. Eng., A 239, 276–280 (1997).

    Article  Google Scholar 

  48. S. Duan, H. Chen, H. Guo, and Y. Lian, “Representation of reaction abilities for Al–Ti binary melts based on the atom-molecule coexistence theory,” Chin. J. Eng. 38, 1377–1385 (2016).

    CAS  Google Scholar 

  49. O. Redlich and A. T. Kister, “Algebraic representation of thermodynamic properties and the classification of solutions,” Ind. Eng. Chem. 40, 345–348 (1948).

    Article  Google Scholar 

  50. G. Zhang, and K. Chou, “General formalism for new generation geometrical model: application to the thermodynamics of liquid mixtures,” J. Solution Chem. 39, 1200–1212 (2010).

    Article  CAS  Google Scholar 

  51. G. Zhang and K. Chou, “Estimating the excess molar volume using the new generation geometric model,” Fluid Phase Equilib. 286, 28–32 (2009).

    Article  CAS  Google Scholar 

  52. K. Chou and S. Wei, “Estimating the excess molar volume using the new generation geometric model,” Metall. Mater. Trans. B 28, 439–445 (1997).

    Article  Google Scholar 

  53. X. M. Zhong, Y. H. Liu, K. Chou, X. G. Lu, D. Zivkovic, and Z. Zivkovic, “Estimating ternary viscosity using the thermodynamic geometric model,” J. Phase Equilib. 24, 7–11 (2003).

    Article  CAS  Google Scholar 

  54. P. D. Desai, “Thermodynamic properties of selected binary aluminum alloy systems,” J. Phys. Chem. Ref. Data. 16, 109–124 (1987).

    Article  CAS  Google Scholar 

  55. P. G. Agraval, L. A. Dreval, and M. A. Turchanin, “Thermodynamic properties of iron melts with titanium, zirconium, and hafnium,” Powder Metall. Met. Ceram. 55, 707–716 (2017).

    Article  CAS  Google Scholar 

  56. K. Chou, W. Li, and F. Li, and M. He, “Formalism of new ternary model expressed in terms of binary regular-solution type parameters,” CALPHAD: Comput. Coupling Phase Diagrams Thermochem. 20, 395–406 (1996).

    Article  CAS  Google Scholar 

  57. K. Chou, “A general solution model for predicting ternary thermodynamic properties,” CALPHAD: Comput. Coupling Phase Diagrams Thermochem. 19, 315–325 (1995).

    Article  CAS  Google Scholar 

Download references

ACKNOWLEDGMENTS

The authors would like to thank the financial support from the Beijing Key Laboratory of Special Melting and Preparation of High-End Metal Materials at the School of Metallurgical and Ecological Engineering at the University of Science and Technology Beijing (USTB), China.

Author information

Authors and Affiliations

  1. School of Metallurgical and Ecological Engineering, University of Science and Technology, Beijing (USTB), 100083, Beijing, China

    Yao Su, Sheng-Chao Duan, Han-Jie Guo & Jing Guo

  2. Beijing Key Laboratory of Special Melting and Preparation of High-End Metal Materials, University of Science and Technology, Beijing (USTB), 100083, Beijing, China

    Yao Su, Sheng-Chao Duan, Han-Jie Guo & Jing Guo

Authors
  1. Yao Su
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Sheng-Chao Duan
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Han-Jie Guo
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Jing Guo
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Han-Jie Guo.

Ethics declarations

The authors declare that they have no conflicts of interest.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Yao Su, Duan, SC., Guo, HJ. et al. Thermodynamic Properties Prediction of Fe–Al–Ti Alloys Based on Atom and Molecule Coexistence Theory. Phys. Metals Metallogr. 123, 1287–1298 (2022). https://doi.org/10.1134/S0031918X21100604

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S0031918X21100604

Keywords:

Search

Navigation