Skip to main content
SpringerLink
Log in

Thermodynamic Assessment of Phosphorus Removal From Si-Fe Levitated Droplets

  • Original Research Article
  • Published:
Metallurgical and Materials Transactions B Aims and scope Submit manuscript

Abstract

In this paper, the thermodynamic behavior of phosphorus removal from Si-Fe alloys was investigated using a computational approach based on a molecular interaction model combined with the Miedema model and the Tanaka equation. In the Si-P system, the variation of the infinitely dilute activity coefficient of phosphorus with temperature is given as: \({\text{ln}}{\gamma }_{p in si}^{o}=-0.02573-2286.07/T\). In the Si-Fe-P system, the variation of the Fe-P interaction parameter as a function of temperature is represented by the expression: \({\varepsilon }_{P}^{Fe}=0.5095+548.69/T\). Based on the above theoretical analysis, the separation efficiency of phosphorus removal from the Si-Fe-P system was calculated, and the reliability of the model was evaluated using results from dephosphorization experiments conducted with electromagnetically levitated Si-Fe alloy droplets. It is found that a removal efficiency of 94.42 pct can be achieved with a refining time of 55 min at 2023 K in a 50 pct Ar-50 pct H2 gas atmosphere.

Graphical Abstract

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
Fig. 10
Fig. 11

Similar content being viewed by others

Abbreviations

\({G}_{m}^{E}\) :

Molar excess Gibbs free energy

\({\overline{G} }_{i}^{E}\) :

Partial molar excess Gibbs free energy of component i

\(R\) :

Gas constant

\(T\) :

System temperature

\({x}_{i}\) :

Molar fraction of component i

\({w}_{i}\) :

Mass fraction of component \(i\)

\({V}_{m}\) :

Molar volume

\({Z}_{i} ,{Z}_{j}\) :

Central molecular coordination number of component \(i\) and \(j\)

\({B}_{ij} , {B}_{ji}\) :

Pair-potential energy interaction parameters of the \(i-j\) binary system

\({k}_{B}\) :

Boltzma constant

\({k}_{B}\) :

Activity coefficient of component i

\(\text{N}{\gamma }_{i}^{0}\) :

Infinite dilute activity coefficient of component \(i\)

\(\text{N}{\varepsilon }_{ii}^{\prime} ,{\varepsilon }_{jj}^{\prime} ,{\varepsilon }_{ij}^{\prime} ,{\varepsilon }_{ji}^{\prime}\) :

Pair-potential energies

\(\text{N}{\rho }_{m}\) :

Molecular number density

\(\text{N}{r}_{o} ,{r}_{m}\) :

The beginning and first peak values of radial distance in a radial distribution function near the melting point

\(\text{N}\Delta {H}_{m}\) :

Enthalpy of fusion

\(\text{N}{T}_{m}\) :

Melting temperature

\(N{d}_{cov}\) :

Atomic covalent diameter

\(\text{N}{\Delta \overline{H} }_{m}^{0}\) :

Partial molar enthalpy at infinite dilution

\(\text{N}{\overline{S} }_{m}^{E}\) :

Partial molar excess entropy at infinite dilution

\(\text{N}{NZ}_{c}\) :

Close packed coordination number

\(\text{N}\phi\) :

Electronegativity

\(\text{N}{n}_{ws}\) :

Electron density

\(\text{N}u, p, r,\sigma\) :

Empirical constants

\(\text{N}{\varepsilon }_{i}^{i} , {\varepsilon }_{j}^{i}\) :

Interaction coefficient

\({t}_{0}, {t}_{t}\) :

Levitation refining time in the beginning and end

\({a}_{i}\) :

Activity of component \(i\)

\(\beta\) :

Separation coefficient

\({P}_{i}^{*}\) :

Saturated vapor pressure of component \(i\)

\({P}_{i}\) :

Partial pressure of solute \(i\) in gas phase

\(\eta\) :

Removal efficiency

\(M\) :

Molar mass

\({\rho }_{i}\) :

Mass density of component \(i\)

\({c}_{i}\) :

Concentration of component i at \({t}_{0}\) or \({t}_{t}\)

\({Ng}_{i}\) :

Weight of sample at \({t}_{0}\) or \({t}_{t}\)

\(A\) :

Surface area of levitated sample

\(V\) :

Volume of levitated sample

References

  1. K. Morita and T. Miki: Intermetallics, 2003, vol. 11, pp. 1111–17.

    CAS  Google Scholar 

  2. K. Le, Y.D. Yang, M. Barati, A. Mclean: Proceedings of the 3rd Pan American Materials Congress, Springer, Cham, 2017, pp. 125–33.

  3. M.D. Johnston and M. Barati: J. Non-Cryst. Solids, 2011, vol. 357, pp. 970–75.

    CAS  Google Scholar 

  4. N. Yuge, M. Abe, K. Hanazawa, H. Baba, N. Nakamura, Y. Kato, Y. Sakaguchi, S. Hiwasa, and F. Aratani: Prog. Photovoltaics, 2001, vol. 9, pp. 203–09.

    CAS  Google Scholar 

  5. Q. Wang, W. Dong, Y. Tan, D.C. Jiang, C. Zhang, and X. Peng: Rare Met., 2011, vol. 30, pp. 274–77.

    CAS  Google Scholar 

  6. B.G. Gribov and K.V. Zinov’ev: Inorg. Mater., 2003, vol. 39, pp. 653–62.

    CAS  Google Scholar 

  7. P.S. Ravishankar, L.P. Hunt, and R.W. Francis: J. Electrochem. Soc., 1984, vol. 131, p. 872.

    CAS  Google Scholar 

  8. D.C. Jiang, S.Q. Ren, S. Shi, W. Dong, J.S. Qiu, Y. Tan, and J.Y. Li: J. Electron. Mater., 2014, vol. 43, pp. 314–19.

    CAS  Google Scholar 

  9. P. Wu, Y.D. Yang, M. Barati, and A. McLean: High Temp. Mater. Process., 2014, vol. 33, pp. 477–83.

    CAS  Google Scholar 

  10. W. Yan, Y.D. Yang, W.Q. Chen, M. Barati, and A. McLean: Vacuum, 2017, vol. 135, pp. 101–08.

    CAS  Google Scholar 

  11. Z.M. You, H. Zhang, S.L. Cui, Z.H. Jiang, and I.H. Jung: Materials, 2023, vol. 16, p. 4099.

    CAS  Google Scholar 

  12. H.K. Hardy: Acta Metall., 1953, vol. 1, pp. 611–12.

    Google Scholar 

  13. G.M. Wilson: J. Am. Chem. Soc., 1964, vol. 86, pp. 127–30.

    CAS  Google Scholar 

  14. H. Renon and J.M. Prausnitz: AIChE J., 1968, vol. 14, pp. 135–44.

    CAS  Google Scholar 

  15. D.S. Abrams, F. Seneci, P.L. Chueh, and J.M. Chueh: Ind. Eng. Chem. Res., 1975, vol. 14, pp. 52–54.

    CAS  Google Scholar 

  16. A.R. Miedema, P.F. Chatel, and F.R. Boer: Physical B+C, 1980, vol. 100, pp. 1–28.

    CAS  Google Scholar 

  17. K.C. Chou and S.K. Wei: Metall. Mater. Trans. B, 1997, vol. 28B, pp. 439–45.

    CAS  Google Scholar 

  18. D.P. Tao: Thermochim. Acta., 2000, vol. 363, pp. 105–13.

    CAS  Google Scholar 

  19. D.P. Tao: Metall. Mater. Trans. B., 2002, vol. 33B, pp. 502–06.

    CAS  Google Scholar 

  20. T. Tanaka, N.A. Gokcen, and Z.I. Morita: Int. J. Mater. Res., 1990, vol. 81, pp. 349–53.

    CAS  Google Scholar 

  21. Q. Yu, J.J. Wu, W.H. Ma, and K. Liu: Silicon, 2017, vol. 9, pp. 355–62.

    CAS  Google Scholar 

  22. D.P. Tao: Metall. Mater. Trans. B., 2014, vol. 45B, pp. 2232–46.

    Google Scholar 

  23. D.P. Tao: J. Alloys Compd., 2008, vol. 457, pp. 124–30.

    CAS  Google Scholar 

  24. K. Liu, J.J. Wu, K.X. Wei, W.H. Ma, K.Q. Xie, S.Y. Li, et al.: Vacuum, 2015, vol. 114, pp. 6–12.

    CAS  Google Scholar 

  25. S.Y. Li, K. Liu, F. Wang, F.S. Xi, J.J. Wu, W.H. Ma, Y. Lei, Y.J. Wang, and X.N. Zhang: J. Min. Metall. Sect. B, 2020, vol. 56, pp. 69–76.

    Google Scholar 

  26. D.P. Tao: Metall. Mater. Trans. A., 2005, vol. 36A, pp. 3495–97.

    CAS  Google Scholar 

  27. T. Iida and R.I.L. Guthrie: The Physical Properties of Liquid Metals, Oxford University Press, Oxford, UK, 1988, pp. 19–46.

    Google Scholar 

  28. R.C. Evans: J. Am. Pharm. Assoc. (Scientific ed.), 1941, vol. 30, p. 121.

    Google Scholar 

  29. N.A. Gokcen: Statistical Thermodynamics of Alloys, Plenum Press, New York, 1986.

    Google Scholar 

  30. F.R. de Boer, R. Boom, W.C.M. Mattens, A.R. Miedema, and A.K. Niessen: Cohesion in Metals, North-Holland, Netherlands, 1988.

    Google Scholar 

  31. Y. Sun, D.P. Tao, J.J. Wu, X. Huang, and W.H. Ma: Vacuum, 2016, vol. 128, pp. 106–11.

    CAS  Google Scholar 

  32. G.W. Xu, B. Wang, H. Suzuki, S.Q. Gao, X.X. Ma, N. Nakagawa, et al.: J. Chem. Eng. Jpn., 1999, vol. 32, pp. 82–90.

    CAS  Google Scholar 

  33. Predel and Landolt-Börnstein: Group IV: Physical Chemistry, Springer, Berlin, 2006.

    Google Scholar 

  34. C. Wagner: Thermodynamics of Alloys, Addison-Wesley, Massachusetts, 1952, p. 51.

    Google Scholar 

  35. X.G. Huang: Ferrous Metallurgy Principle, 3nd ed., Metallurgical Industry Press, Beijing, CHN, 2008, pp. 104-105 (In Chinese).

  36. Q. Yu, J.J. Wu, W.H. Ma, Kai, Liu: Silicon, 2017, vol. 9, pp. 355–62.

  37. Y.B. Zheng, Z.Q. Chen, F. Chen, L. Qiao, and L.L. Mao: Metall. Eng., 2015, vol. 2(3), pp. 158–67.

    Google Scholar 

  38. J.X. Chen: Handbook of Common Diagrams, Tables and Data for Steelmaking, 2nd ed., Metallurgical Industry Press, Beijing, CHN, 2013, pp. 704-730 (In Chinese).

  39. H. Dalaker: Comput. Methods Mater. Sci., 2013, vol. 13, pp. 407–11.

    Google Scholar 

  40. J. Safarian and M. Tangstad: Metall. Mater. Trans. B., 2012, vol. 43B, pp. 1427–45.

    Google Scholar 

  41. I.H. Jung and Y.M. Zhang: JOM, 2012, vol. 64, pp. 973–81.

    CAS  Google Scholar 

  42. T. Miki, K. Morita, and N. Sano: Metall. Mater. Trans. B., 1996, vol. 27B, pp. 937–41.

    CAS  Google Scholar 

  43. Y.N. Dai, B. Yang: Vacuum Metallurgy for Nonferrous Metals and Materials, Metallurgical Industry Press, Beijing, CHN, 2000, pp. 38-47 (In Chinese).

  44. S. Shi, P.T. Li, J.X. Meng, D.C. Jiang, Y. Tan, and H.M. Asghar: Phys. Chem. Chem. Phys., 2017, vol. 19, pp. 28424–33.

    CAS  Google Scholar 

  45. L. Feng and W.Y. Shi: Int. J. Heat Mass Transfer, 2016, vol. 101, pp. 629–36.

    Google Scholar 

  46. H.L. Yan, C.W. Dong, H. Xiong, B. Yang, X.M. Chen, Y. Deng, et al.: Chin. J. Vac. Sci. Technol., 2015, vol. 35, pp. 1338–341. (In Chinese).

    CAS  Google Scholar 

  47. Y.H. Yun and C.Z. Zhang: J. Vac. Sci. Technol., 2015, vol. 35, pp. 386–90. (In Chinese).

    CAS  Google Scholar 

Download references

Acknowledgments

We greatly acknowledge the support of the Yunnan Provincial Department of Education Scientific Research Fund Project (Grant: 2023J0130), National Natural Science Foundation of China (Grant: 52074140) and Hunan Zhongke Electric Co. Ltd.

Competing interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Author information

Authors and Affiliations

  1. Faculty of Metallurgical and Energy Engineering, Kunming University of Science and Technology, Kunming, 650093, P.R. China

    Peng Yan, Guifang Zhang & Bing Yi

  2. Department of Materials Science and Engineering, University of Toronto, Toronto, ON, M5S 3E4, Canada

    Alexander McLean

  3. Hunan Zhongke Electric Co., Ltd, Yueyang, 414000, P.R. China

    Bing Yi

Authors
  1. Peng Yan
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Guifang Zhang
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Bing Yi
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Alexander McLean
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Guifang Zhang.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Supplementary Information

Below is the link to the electronic supplementary material.

Supplementary file1 (PDF 679 kb).

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Yan, P., Zhang, G., Yi, B. et al. Thermodynamic Assessment of Phosphorus Removal From Si-Fe Levitated Droplets. Metall Mater Trans B 54, 3377–3389 (2023). https://doi.org/10.1007/s11663-023-02915-0

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11663-023-02915-0

Search

Navigation