Metallurgical and Materials Transactions B

, Volume 49, Issue 4, pp 2011–2021 | Cite as

Formation of Nitrogen Bubbles During Solidification of Duplex Stainless Steels

  • Kaiju Dai
  • Bo Wang
  • Fei Xue
  • Shanshan Liu
  • Junkai Huang
  • Jieyu Zhang


The nucleation and growth of nitrogen bubbles for duplex stainless steels are of great significance for the formation mechanism of bubbles during solidification. In the current study, numerical method and theoretical analysis of formula derivation were used to study the formation of nitrogen bubbles during solidification. The critical sizes of the bubble for homogeneous nucleation and heterogeneous nucleation at the solid–liquid interface during solidification were derived theoretically by the classical nucleation theory. The results show that the calculated values for the solubility of nitrogen in duplex stainless steel are in good agreement with the experimental values which are quoted by references: for example, when the temperature T = 1823 K and the nitrogen partial pressure \( P_{{N_{2} }} = 40P^{\varTheta } , \) the calculated value (0.8042 wt pct) for the solubility of Fe-12Cr alloy nitrogen in molten steel is close to the experimental value (0.780 wt pct). Moreover, the critical radii for homogeneous nucleation and heterogeneous nucleation are identical during solidification. On the one hand, with the increasing temperature or the melt depth, the critical nucleation radius of bubbles at the solid–liquid interface increases, but the bubble growth rate decreases. On the other hand, with the decreasing initial content of nitrogen or the cooling rate, the critical nucleation radius of bubbles at the solid–liquid interface increases, but the bubble growth rate decreases. Furthermore, when the melt depth is greater than the critical depth, which is determined by the technological conditions, the change in the Gibbs free energy for the nucleation is not conducive enough to form new bubbles.



The authors gratefully express their appreciation to the National Natural Science Foundation of China (No. 51474143) and the Shanghai Economic and Information Commission (No. Hu CXY-2013-1) for their financial support.

Supplementary material

11663_2018_1263_MOESM1_ESM.docx (121 kb)
Supplementary material 1 (DOC 121 kb)


  1. 1.
    J-O Nilsson, Materials science and technology 1992, vol. 8, pp. 685-700.CrossRefGoogle Scholar
  2. 2.
    G. Stein and I. Hucklenbroich, Materials and Manufacturing Processes 2004, vol. 19, pp. 7-17.CrossRefGoogle Scholar
  3. 3.
    Hans Berns, ISIJ international 1996, vol. 36, pp. 909-914.CrossRefGoogle Scholar
  4. 4.
    S. Xiong, H. Zeng, Y. Cao, and Q. Wang, J. Chongqing Univ.: Eng. Ed. 2014, vol. 13, pp. 11–16.Google Scholar
  5. 5.
    AG Svyazhin, LM Kaputkina, VE Bazhenov, Z Skuza, E Siwka and VE Kindop, The Physics of Metals and Metallography 2015, vol. 116, pp. 552-561.CrossRefGoogle Scholar
  6. 6.
    Y-H Park, J-W Kim, S-K Kim, Y-D Lee and Z-H Lee, Metallurgical and Materials Transactions B 2003, vol. 34, pp. 313-320.CrossRefGoogle Scholar
  7. 7.
    R. Arola, J. Wendt, and E. Kivineva, In Materials science forum (Trans Tech Publ: 1999), pp 297-302.Google Scholar
  8. 8.
    M.R. Ridolfi and O. Tassa, Intermetallics 2003, vol. 11, pp. 1335-1338.CrossRefGoogle Scholar
  9. 9.
    S.-H. Yang and Z.-H. Lee, Materials Science and Engineering: A 2006, vol. 417, pp. 307-314.CrossRefGoogle Scholar
  10. 10.
    K. Li, J. Liu, J. Zhang and S. Shen, Metallurgical and Materials Transactions B 2017, vol. 48, pp. 2136-2146.CrossRefGoogle Scholar
  11. 11.
    H. C. Zhu, Z. H. Jiang, H.B. Li, S.C. Zhang, G.H. Liu, J.H. Zhu, P.B. Wang, B.B. Zhang and G.W. Fan: Metall. Mater. Trans. B 2017, vol. 48B, pp. 2493–2503.Google Scholar
  12. 12.
    X.H. Huang: Principal of Iron and Steel Metallurgy, 3rd ed., Metallurgical Indusry Oress, Beijing, 2002, pp.91-95.Google Scholar
  13. 13.
    D. R. Anson, R. J. Pomfret and A. Hendry, Isij International 1996, vol. 36, pp. 750-758.CrossRefGoogle Scholar
  14. 14.
    G. Balachandran, M. L Bhatia, N. B. Ballal and P. Krishna Rao, Isij International 2001, vol. 41, pp. 1018-1027.CrossRefGoogle Scholar
  15. 15.
    H. Wada and R.D. Pehlke, Metallurgical Transactions B 1978, vol. 9, pp. 441-448.CrossRefGoogle Scholar
  16. 16.
    T. W. Clyne and W. Kurz, Metallurgical Transactions A 1981, vol. 12, pp. 965-971.CrossRefGoogle Scholar
  17. 17.
    Z. Ma and D. Janke, Isij International 2007, vol. 38, pp. 46-52.CrossRefGoogle Scholar
  18. 18.
    PanFe: Ferrum Alloy Thermodynamic Database, CompuTherm, Madison, WI, USA, 2015.Google Scholar
  19. 19.
    S. L. Chen, S. Daniel, F. Zhang, Y. A. Chang, X. Y. Yan, F. Y. Xie, R. Schmid-Fetzer and W. A. Oates, Calphad-computer Coupling of Phase Diagrams & Thermochemistry 2002, vol. 26, pp. 175-188.CrossRefGoogle Scholar
  20. 20.
    W. G. Whitman, International journal of heat and mass transfer 1962, vol. 5, pp. 429-433.CrossRefGoogle Scholar
  21. 21.
    S.N. Leung, C.B. Park, D. Xu, and H. Li and R. G. Fenton, Industrial & Engineering Chemistry Research 2006, vol. 45, pp. 7823-7831.CrossRefGoogle Scholar
  22. 22.
    Q. Ying: Principal of Steelmaking, 2nd ed., Metallurgical Indusry Oress, Beijing, 1980, pp.179-182.Google Scholar
  23. 23.
    A.H. Satir and H. K. Feichtinger, Zeitschrift Für Metallkunde 1991, vol. 52, pp. 689-697.Google Scholar

Copyright information

© The Minerals, Metals & Materials Society and ASM International 2018

Authors and Affiliations

  • Kaiju Dai
    • 1
    • 2
  • Bo Wang
    • 1
    • 2
  • Fei Xue
    • 1
    • 2
  • Shanshan Liu
    • 1
    • 2
  • Junkai Huang
    • 1
    • 2
  • Jieyu Zhang
    • 1
    • 2
  1. 1.State Key Laboratory of Advanced Special SteelShanghai UniversityShanghaiP. R. China
  2. 2.School of Materials Science and EngineeringShanghai UniversityShanghaiP. R. China

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