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Numerical Simulations of Carbon and Nitrogen Composition-Depth Profiles in Nitrocarburized Austenitic Stainless Steels

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Abstract

Unusual composition-depth profiles have been observed after low-temperature nitrocarburization of austenitic stainless steels. When nitridation is performed after carburization, the carbon concentration in the nitrogen diffusion zone is reduced from ≈10 to ≈2 at. pct. Conversely, the carbon concentration in advance of the nitrogen diffusion zone is as high as 10 at. pct. This has been called a “push” effect of nitrogen on carbon, but this concept is non-physical. The profiles can be better understood from conventional thermodynamic principles, recognizing that (1) diffusion always occurs in response to gradients in chemical potentials and (2) the diffusivity of interstitial solutes in austenite is strongly concentration dependent, increasing dramatically with higher solute concentrations. Parameters from the CALPHAD literature quantitatively indicate that interstitial nitrogen and carbon in austenitic stainless steel mutually increase their chemical potentials. Based on these data, we have conducted numerical simulations of composition-depth profiles that correctly account for the chemical potential gradients and the concentration dependence of the diffusion coefficients for nitrogen and carbon. The simulations predict the “push” effect observed on nitridation after carburization, as well as the corresponding composition-depth profiles for other scenarios, e.g., carburization followed by nitridation or simultaneous nitridation and carburization (nitrocarburization).

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References

  1. Z.L. Zhang and T. Bell, Surf. Eng., Vol. 1, pp. 131-36, 1985.

    Article  Google Scholar 

  2. M. Gillham, R. Van der Jagt and B. Kolster (1996) Mater. World 4(8), pp. 460-62.

    Google Scholar 

  3. G.M. Michal, F. Ernst, H. Kahn, Y. Cao, F. Oba, N. Agarwal and A.H. Heuer, Acta Mater., Vol. 54, pp. 1597–606, 2006.

    Article  Google Scholar 

  4. G.M. Michal, F. Ernst and A.H. Heuer, Metall. Mater. Trans. A, Vol. 37A, pp. 1819–24, 2006.

    Article  Google Scholar 

  5. F. Ernst, Y. Cao, G.M. Michal and A.H. Heuer (2007) Acta Mater. 55, 1895–1906.

    Article  Google Scholar 

  6. H. Dong, Int. Mater. Rev., Vol. 55, No. 2, pp. 65-98, 2010.

    Article  Google Scholar 

  7. F. Ernst, A. Avishai, H. Kahn, X. Gu, G.M. Michal and A.H. Heuer, Metall. Mater. Trans. A, Vol. 40A, pp. 1768-80, 2009.

    Article  Google Scholar 

  8. J. Crank (1956) The Mathematics of Diffusion, Clarendon Press, Oxford, p. 172.

    Google Scholar 

  9. J.C. Fisher, J.H. Hollomon and D. Turnbull, Trans. AIME, Vol. 175, pp. 202-215, 1948.

    Google Scholar 

  10. L. Kaufman, S.V. Radcliffe and M. Cohen, Diffusional Decomposition of Austenite, New York, Interscience Publishers, pp. 313-51, 1962.

    Google Scholar 

  11. R.M. Asimow, Trans. AIME, Vol. 230, pp. 611-13, 1964.

    Google Scholar 

  12. R.H. Siller and R.B. McLellan, Trans. AIME, Vol. 245, pp. 697-700, 1969.

    Google Scholar 

  13. R.H. Siller and R.B. McLellan, Metall. Trans., Vol. 1, pp. 985-88. 1970.

    Google Scholar 

  14. G.G. Tibbetts, J. Appl. Phys., Vol. 51, No. 9, pp. 4813-16, 1980.

    Article  Google Scholar 

  15. F.C. Larché and J.W. Cahn, Acta Metall., Vol. 30, pp. 1835-45, 1982.

    Article  Google Scholar 

  16. J. Ågren, Scripta Metall., Vol. 20, pp. 1507-510, 1986.

    Article  Google Scholar 

  17. R.B. McLellan and C. Ko, Acta Metall., Vol. 36, No. 3, pp. 531-37, 1988.

    Article  Google Scholar 

  18. W.J. Liu, J.K. Brimacombe and E.B. Hawbolt, Acta Metall. Mater., Vol. 39, No. 10, pp. 2373-80, 1991.

    Article  Google Scholar 

  19. R.B. McLellan, Acta Mater., Vol. 45, No. 1, pp. 99-103, 1997.

    Article  Google Scholar 

  20. X. Gu, G.M. Michal, F. Ernst, H. Kahn, and A.H. Heuer: Metall. Mater. Trans. A, 2014, in press.

  21. X. Gu: Ph.D. Dissertation, Case Western Reserve University, 2011, https://etd.ohiolink.edu/ap:10:0::NO:10:P10_ETD_SUBID:52449.

  22. T.L. Christiansen and M.A.J. Somers, Int. J. Mater. Res., Vol. 99 (9), pp. 999-1005, 2008.

    Article  Google Scholar 

  23. T. Moskalioviene and A. Galdikas, Mater. Sci., Vol. 17, No. 1, pp. 11-15, 2011.

    Google Scholar 

  24. T. Moskalioviene, A. Galdikas, J.P. Rivière and L. Pichon, Surf. Coat. Technol., Vol. 205, Issue 10, pp. 3301-06, 2011.

    Article  Google Scholar 

  25. A. Galdikas and T. Moskalioviene, Comput. Mater. Sci., Vol. 50, Issue 2, pp. 796-99, 2010.

    Article  Google Scholar 

  26. A. Galdikas and T. Moskalioviene, Surf. Coat. Technol., Vol. 250, pp. 3742-46, 2011.

    Article  Google Scholar 

  27. C. Templier, J.C. Stinville, P. Villechaise, P.O. Renault, G. Abrasonis, J.P. Rivière, A. Martinavičius and M. Drouet, Surf. Coat. Technol., Vol. 204, Issues 16-17, pp. 2551-58, 2010.

    Article  Google Scholar 

  28. A. Martinavičius, G. Abrasonis, W. Möller, C. Templier, J.P. Rivière, A. Declémy and Y. Chumlyakov, J. Appl. Phys., Vol. 105, pp. 105-111, 2009.

    Google Scholar 

  29. S. Mändl and B. Rauschenbach, J. Appl. Phys., Vol. 91, pp. 9737-42, 2002.

    Article  Google Scholar 

  30. M. Tsujikawa, N. Yamauchi, N. Ueba, T.Sone and Y. Hirose, Surf. Coat. Technol., Vol. 193, pp. 309-13, 2005.

    Article  Google Scholar 

  31. N. Yamauchi, N. Ueda, K. Demizu, A. Okamoto, and T. Sone: Stainless Steel 2000: Proceeding of an International Current Status Seminar on Thermochemical Surface Engineering of Stainless Steel, Maney Publishing, London, 2001, pp. 247–61.

  32. M. Higashi, K. Shinkawa, and K. Kurosawa: Stainless Steel 2000: Proceeding of an International Current Status Seminar on Thermochemical Surface Engineering of Stainless Steel, Maney Publishing, London, 2001, pp. 407–13.

  33. D.L. Williamson, P.J. Wilbur, F.R. Fickett, and S. Parascandola: Stainless Steel 2000: Proceeding of an International Current Status Seminar on Thermochemical Surface Engineering of Stainless Steel, Maney Publishing, London, 2001, pp. 333–52.

  34. M.P. Fewell, P. Garlick, J.M. Priest, P.T. Burke, N. Dytlewski, K.E. Prince, K.T. Short, R.G. Elliman, H. Timmers, T.D.M. Weijers, and B. Gong: Stainless Steel 2000: Proceeding of an International Current Status Seminar on Thermochemical Surface Engineering of Stainless Steel, Maney Publishing, London, 2001, pp. 177–200.

  35. H. Du and M. Hillert, Z. Metal., Vol. 82, p. 310, 1991.

    Google Scholar 

  36. H. Du, J. Phase Equilib. Vol. 14, No. 6, pp. 682-93, 1993.

    Article  Google Scholar 

  37. R. Collin, S. Gunnarson, and D. Thulin: J. Iron Steel Inst., 210(10), pp. 785-89, 1972.

    Google Scholar 

  38. J. Ågren, Acta Metall., Vol. 30, pp. 841-51, 1982.

    Article  Google Scholar 

  39. O. Karabelchtchikova and R.D. Sisson, J. Phase Equilib. Diffus. Vol. 27, No. 6, pp. 598-604, 2006.

    Article  Google Scholar 

  40. T.L. Christiansen, K.V. Dahl and M.A.J. Somers, Mater. Sci. Technol., Vol. 24, No. 2, pp. 159-67, 2008.

    Article  Google Scholar 

  41. B. Lee, CALPHAD, Vol. 16, No. 2, pp. 121-49, 1992.

    Article  Google Scholar 

  42. J. Bratberg and K. Frisk, Metall. Mater. Trans. A, Vol. 35A, pp. 3649-63, 2004.

    Article  Google Scholar 

  43. J. Andersson, CALPHAD, Vol. 12, No. 1, pp. 9-23, 1988.

    Article  Google Scholar 

  44. K. Frisk, Metall. Trans. A, Vol. 21A, pp. 2477-88, 1990.

    Article  Google Scholar 

  45. K. Frisk, Z. Metal., Vol. 82, No. 1, pp. 59-66, 1991.

    Google Scholar 

  46. K. Frisk, CALPHAD, Vol. 15, No. 1, pp. 79-106, 1991.

    Article  Google Scholar 

  47. M. Hillert and C. Qiu, Metall. Trans. A, Vol. 22A, pp. 2187-98, 1991.

    Article  Google Scholar 

  48. K. Frisk, Z. Metal., Vol. 82, No. 2, pp. 108-17, 1991.

    Google Scholar 

  49. C. Qiu, CALPHAD, Vol. 16, No. 3, pp. 281-89, 1992.

    Article  Google Scholar 

  50. K. Frisk, CALPHAD, Vol. 14, No. 3, pp. 311-20, 1990.

    Article  Google Scholar 

  51. M. Necati Özisik: Finite Difference Methods in Heat Transfer, CRC Press, Boca Raton, Florida, 1994, pp. 118–20.

  52. R.P. Agarwala, M.C. Naik, M.S. Anand and A.R. Paul, J. Nucl. Mater., Vol. 36, pp. 41-47, 1970.

    Article  Google Scholar 

  53. J. Hirvonen and A. Anttila, Appl. Phys. Lett., Vol. 46, pp. 835-36, 1985.

    Article  Google Scholar 

  54. W. Anwand, S. Parascandola, E. Richter, G. Brauer, P.G. Coleman and W. Möller, Nucl. Instrum. Methods Phys. Res. B, Vol. 768, pp. 136-38, 1998.

    Google Scholar 

Download references

Acknowledgment

This research was supported by the Swagelok Company, the U.S. Department of Energy, the National Science Foundation, DARPA, the Naval Research Laboratory and the Office of Naval Research, and the Ohio Department of Development.

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Author notes

  1. Xiaoting Gu (Doctoral Student, Research Scientist)

    Present address: Atotech USA Inc., Cleveland, OH, USA

Authors and Affiliations

  1. Department of Materials Science and Engineering, Case Western Reserve University, Cleveland, OH, 44106, USA

    Xiaoting Gu (Doctoral Student, Research Scientist), Gary M. Michal (Professor), Frank Ernst (Professor), Harold Kahn (Research Associate Professor) & Arthur H. Heuer (Professor)

Authors
  1. Xiaoting Gu
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  2. Gary M. Michal
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  3. Frank Ernst
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  4. Harold Kahn
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Corresponding author

Correspondence to Xiaoting Gu.

Additional information

Manuscript submitted April 25, 2014.

Appendices

Appendix A

CALPHAD parameters used in this modeling:

$$ {}^{ \circ }G_{\text{Fe:C}}^{\text{hfcc}} \;^{[41]} = {}^{ \circ }G_{\text{Fe:Va}}^{\text{hfcc}} + {}^{ \circ }G_{\text{C}}^{\text{gra}} + 77207 - 15.877T\; {}^{ \circ }G_{\text{Cr:C}}^{\text{hfcc}} \;^{[42]} = {}^{ \circ }G_{\text{Cr:Va}}^{\text{hfcc}} + {}^{ \circ }G_{\text{C}}^{\text{gra}} - 13748.62 - 79.953T + 9.53T\ln T - 2701850/T+ 2.643 \times 10^{8} T^{ - 2} - 1.2 \times 10^{10} T^{ - 3} - 0.00142205T^{2} + 1.47721 \times 10^{ - 6} T^{3} \; {}^{ \circ }G_{\text{Ni:C}}^{\text{hfcc}} \;^{[41]} = {}^{ \circ }G_{\text{Ni:Va}}^{\text{hfcc}} + {}^{ \circ }G_{\text{C}}^{\text{gra}} + 62000 - 7.6T \; {}^{ \circ }G_{\text{Mo:C}}^{\text{hfcc}} \;^{[43]} = {}^{ \circ }G_{\text{Mo:Va}}^{\text{hfcc}} + {}^{ \circ }G_{\text{C}}^{\text{gra}} - 22700 - 8.93T - 750000T^{ - 1} \; {}^{ \circ }G_{\text{Fe:N}}^{\text{hfcc}} \;^{[44]} = {}^{ \circ }G_{\text{Fe:Va}}^{\text{hfcc}} + \frac{1}{2}{}^{ \circ }G_{{{\text{N}}_{2} }}^{\text{gas}} - 35997.6 + 367.138T - 36.45T\ln T - 6.4 \times 10^{ - 4} T^{2} \; {}^{ \circ }G_{\text{Cr:N}}^{\text{hfcc}} \;^{[44]} = {}^{ \circ }G_{\text{Cr:Va}}^{\text{hfcc}} + \frac{1}{2}{}^{ \circ }G_{{{\text{N}}_{2} }}^{\text{gas}} - 131744 + 141.997T - 8.5T\ln T \; {}^{ \circ }G_{\text{Ni:N}}^{\text{hfcc}} \;^{[45]} = {}^{ \circ }G_{\text{Ni:Va}}^{\text{hfcc}} + \frac{1}{2}{}^{ \circ }G_{{{\text{N}}_{2} }}^{\text{gas}} + 38680 + 143.09T - 10.9T\ln T + 0.00438T^{2} \; {}^{ \circ }G_{\text{Mo:N}}^{\text{hfcc}} \;^{[46]} = {}^{ \circ }G_{\text{Mo:Va}}^{\text{hfcc}} + \frac{1}{2}{}^{ \circ }G_{{{\text{N}}_{2} }}^{\text{gas}} - 80544 + 149.07T - 9.78T\ln T \; {}^{0}L_{\text{Fe:C,Va}}^{\text{fcc}} \;^{[41]} = - 34671 \; {}^{0}L_{\text{Cr:C,Va}}^{\text{fcc}} \;^{[41]} = - 11977 + 6.8194T \; {}^{0}L_{\text{Ni:C,Va}}^{\text{fcc}} \;^{[41]} = - 14902 + 7.5T \; {}^{0}L_{\text{Mo:C,Va}}^{\text{fcc}} \;^{[43]} = - 41300 \; {}^{0}L_{\text{Fe:N,Va}}^{\text{fcc}} \;^{[44]} = - 26150 \; {}^{0}L_{\text{Cr:N,Va}}^{\text{fcc}} \;^{[44]} = 20000 \; {}^{0}L_{\text{Mo:N,Va}}^{\text{fcc}} \;^{[46]} = - 52565 \; {}^{0}L_{\text{Fe:C,N}}^{\text{fcc}} \;^{[36]} = - 21893 \; {}^{0}L_{\text{Cr,Fe:C}}^{\text{fcc}} \;^{[41]} = - 74319 + 3.2353T \; {}^{0}L_{\text{Cr,Fe:N}}^{\text{fcc}} \;^{[44]} = - 128930 + 86.49T \; {}^{1}L_{\text{Cr,Fe:N}}^{\text{fcc}} \;^{[44]} = 24330 \; {}^{0}L_{\text{Cr,Fe:Va}}^{\text{fcc}} \;^{[41]} = 10833 - 7.477T \; {}^{1}L_{\text{Cr,Fe:Va}}^{\text{fcc}} \;^{[41]} = 1410 \; {}^{0}L_{\text{Cr,Fe:N,Va}}^{\text{fcc}} \;^{[44]} = - 162516 \; {}^{0}L_{\text{Fe,Ni:C}}^{\text{fcc}} \;^{[47]} = 49074 - 7.32T.$$
$$ {}^{1}L_{\text{Fe,Ni:C}}^{\text{fcc}} \;^{[47]} = - 25800 \; {}^{0}L_{\text{Fe,Ni:N}}^{\text{fcc}} \;^{[45]} = - 22710 + 5.19T \; {}^{1}L_{\text{Fe,Ni:N}}^{\text{fcc}} \;^{[45]} = 3334 \; {}^{0}L_{\text{Fe,Ni:Va}}^{\text{fcc}} \;^{[47]} = - 12054.355 + 3.27413T \; {}^{1}L_{\text{Fe,Ni:Va}}^{\text{fcc}} \;^{[47]} = 11082.1315 - 4.45077T \; {}^{2}L_{\text{Fe,Ni:Va}}^{\text{fcc}} \;^{[47]} = - 725.805174 \; {}^{0}L_{\text{Cr,Fe,Ni:C}}^{\text{fcc}} \;^{[47]} = - 8215 \; {}^{0}L_{\text{Cr,Fe,Ni:Va}}^{\text{fcc}} \;^{[47]} = 1618 \; {}^{0}L_{\text{Fe,Mo:C}}^{\text{fcc}} \;^{[43]} = 6000 \; {}^{0}L_{\text{Fe,Mo:Va}}^{\text{fcc}} \;^{[43]} = 28347 - 17.691T \; {}^{0}L_{\text{Cr,Ni:C}}^{\text{fcc}} \;^{[41]} = - 125935 + 95T \; {}^{0}L_{\text{Cr,Ni:Va}}^{\text{fcc}} \;^{[41]} = 8030 - 12.8801T \; {}^{1}L_{\text{Cr,Ni:Va}}^{\text{fcc}} \;^{[41]} = 33080 - 16.0362T \; {}^{0}L_{\text{Cr,Ni:N,Va}}^{\text{fcc}} \;^{[48]} = - 661270 + 305T \; {}^{0}L_{\text{Cr,Mo:N}}^{\text{fcc}} \;^{[46]} = - 40000 \; {}^{0}L_{\text{Cr,Mo:Va}}^{\text{fcc}} \;^{[49]} = 28890 - 7.962T \; {}^{1}L_{\text{Cr,Mo:Va}}^{\text{fcc}} \;^{[49]} = 5974 - 2.428T \; {}^{0}L_{\text{Mo,Ni:Va}}^{\text{fcc}} \;^{[50]} = 4803.7 - 5.96T \; {}^{1}L_{\text{Mo,Ni:Va}}^{\text{fcc}} \;^{[50]} = 10880. $$

Values are given in SI units and correspond to one mole of formula units.

Appendix B

The chemical potential of carbon in the FCC phase (Fe, Cr, Ni, Mo)1(C, N, Va)1:

$$ \mu_{\text{C}}^{\text{fcc}} = \frac{{\partial G_{\text{m}}^{\text{fcc}} }}{{\partial Y_{\text{C}} }} - \frac{{\partial G_{\text{m}}^{\text{fcc}} }}{{\partial Y_{\text{Va}} }} = Y_{\text{Fe}} \left( {{}^{ \circ }G_{\text{Fe:C}}^{\text{hfcc}} - {}^{ \circ }G_{\text{Fe:Va}}^{\text{hfcc}} } \right) + Y_{\text{Cr}} \left( {{}^{ \circ }G_{\text{Cr:C}}^{\text{hfcc}} - {}^{ \circ }G_{\text{Cr:Va}}^{\text{hfcc}} } \right) + Y_{\text{Ni}} \left( {{}^{ \circ }G_{\text{Ni:C}}^{\text{hfcc}} - {}^{ \circ }G_{\text{Ni:Va}}^{\text{hfcc}} } \right) + Y_{\text{Mo}} \left( {{}^{ \circ }G_{\text{Mo:C}}^{\text{hfcc}} - {}^{ \circ }G_{\text{Mo:Va}}^{\text{hfcc}} } \right) + {\text{R}}T\ln \left( {Y_{\text{C}} /\left( {1 - Y_{\text{C}} - Y_{\text{N}} } \right)} \right) + \left( {1 - 2Y_{\text{C}} - Y_{\text{N}} } \right)\left( {Y_{\text{Fe}} {}^{0}L_{\text{Fe:C,Va}}^{\text{fcc}} + Y_{\text{Cr}} {}^{0}L_{\text{Cr:C,Va}}^{\text{fcc}} + Y_{\text{Ni}} {}^{0}L_{\text{Ni:C,Va}}^{\text{fcc}} + Y_{\text{Mo}} {}^{0}L_{\text{Mo:C,Va}}^{\text{fcc}} } \right) - Y_{\text{N}} \left( {Y_{\text{Fe}} {}^{0}L_{\text{Fe:N,Va}}^{\text{fcc}} + Y_{\text{Cr}} {}^{0}L_{\text{Cr:N,Va}}^{\text{fcc}} + Y_{\text{Mo}} {}^{0}L_{\text{Mo:N,Va}}^{\text{fcc}} } \right) + Y_{\text{Fe}} Y_{\text{N}} {}^{0}L_{\text{Fe:C,N}}^{\text{fcc}} + Y_{\text{Cr}} Y_{\text{Fe}} \left( {{}^{0}L_{\text{Cr,Fe:C}}^{\text{fcc}} - {}^{0}L_{\text{Cr,Fe:Va}}^{\text{fcc}} - {}^{1}L_{\text{Cr,Fe:Va}}^{\text{fcc}} \left( {Y_{\text{Cr}} - Y_{\text{Fe}} } \right)} \right) - Y_{\text{Cr}} Y_{\text{Fe}} Y_{\text{N}} {}^{0}L_{\text{Cr,Fe:N,Va}}^{\text{fcc}} + Y_{\text{Fe}} Y_{\text{Ni}} \left( {{}^{0}L_{\text{Fe,Ni:C}}^{\text{fcc}} + {}^{1}L_{\text{Fe,Ni:C}}^{\text{fcc}} \left( {Y_{\text{Fe}} - Y_{\text{Ni}} } \right) - {}^{0}L_{\text{Fe,Ni:Va}}^{\text{fcc}} - {}^{1}L_{\text{Fe,Ni:Va}}^{\text{fcc}} \left( {Y_{\text{Fe}} - Y_{\text{Ni}} } \right) - {}^{2}L_{\text{Fe,Ni:Va}}^{\text{fcc}} \left( {Y_{\text{Fe}} - Y_{\text{Ni}} } \right)^{2} } \right) + Y_{\text{Cr}} Y_{\text{Fe}} Y_{\text{Ni}} \left( {{}^{0}L_{\text{Cr,Fe,Ni:C}}^{\text{fcc}} - {}^{0}L_{\text{Cr,Fe,Ni:Va}}^{\text{fcc}} } \right) + Y_{\text{Fe}} Y_{\text{Mo}} \left( {{}^{0}L_{\text{Fe,Mo:C}}^{\text{fcc}} - {}^{0}L_{\text{Fe,Mo:Va}}^{\text{fcc}} } \right) + Y_{\text{Cr}} Y_{\text{Ni}} \left( {{}^{0}L_{\text{Cr,Ni:C}}^{\text{fcc}} - {}^{0}L_{\text{Cr,Ni:Va}}^{\text{fcc}} - {}^{1}L_{\text{Cr,Ni:Va}}^{\text{fcc}} \left( {Y_{\text{Cr}} - Y_{\text{Ni}} } \right)} \right) - Y_{\text{Cr}} Y_{\text{Ni}} Y_{\text{N}} {}^{0}L_{\text{Cr,Ni:N,Va}}^{\text{fcc}} - Y_{\text{Cr}} Y_{\text{Mo}} \left( {{}^{0}L_{\text{Cr,Mo:Va}}^{\text{fcc}} + {}^{1}L_{\text{Cr,Mo:Va}}^{\text{fcc}} \left( {Y_{\text{Cr}} - Y_{\text{Mo}} } \right)} \right) - Y_{\text{Mo}} Y_{\text{Ni}} \left( {{}^{0}L_{\text{Mo,Ni:Va}}^{\text{fcc}} + {}^{1}L_{\text{Mo,Ni:Va}}^{\text{fcc}} \left( {Y_{\text{Mo}} - Y_{\text{Ni}} } \right)} \right). $$

The Chemical Potential of Nitrogen in the FCC Phase (Fe, Cr, Ni, Mo)1(C, N, Va)1:

$$ \mu_{\text{N}}^{\text{fcc}} = \frac{{\partial G_{\text{m}}^{\text{fcc}} }}{{\partial Y_{\text{N}} }} - \frac{{\partial G_{\text{m}}^{\text{fcc}} }}{{\partial Y_{\text{Va}} }} = Y_{\text{Fe}} \left( {{}^{ \circ }G_{\text{Fe:N}}^{\text{hfcc}} - {}^{ \circ }G_{\text{Fe:Va}}^{\text{hfcc}} } \right) + Y_{\text{Cr}} \left( {{}^{ \circ }G_{\text{Cr:N}}^{\text{hfcc}} - {}^{ \circ }G_{\text{Cr:Va}}^{\text{hfcc}} } \right) + Y_{\text{Ni}} \left( {{}^{ \circ }G_{\text{Ni:N}}^{\text{hfcc}} - {}^{ \circ }G_{\text{Ni:Va}}^{\text{hfcc}} } \right) + Y_{\text{Mo}} \left( {{}^{ \circ }G_{\text{Mo:N}}^{\text{hfcc}} - {}^{ \circ }G_{\text{Mo:Va}}^{\text{hfcc}} } \right) + {\text{R}}T\ln \left( {Y_{\text{N}} /\left( {1 - Y_{\text{C}} - Y_{\text{N}} } \right)} \right) - Y_{\text{C}} \left( {Y_{\text{Fe}} {}^{0}L_{\text{Fe:C,Va}}^{\text{fcc}} + Y_{\text{Cr}} {}^{0}L_{\text{Cr:C,Va}}^{\text{fcc}} + Y_{\text{Ni}} {}^{0}L_{\text{Ni:C,Va}}^{\text{fcc}} + Y_{\text{Mo}} {}^{0}L_{\text{Mo:C,Va}}^{\text{fcc}} } \right) + \left( {1 - 2Y_{\text{N}} - Y_{\text{C}} } \right)\left( {Y_{\text{Fe}} {}^{0}L_{\text{Fe:N,Va}}^{\text{fcc}} + Y_{\text{Cr}} {}^{0}L_{\text{Cr:N,Va}}^{\text{fcc}} + Y_{\text{Mo}} {}^{0}L_{\text{Mo:N,Va}}^{\text{fcc}} } \right) + Y_{\text{Fe}} Y_{\text{C}} {}^{0}L_{\text{Fe:C,N}}^{\text{fcc}} + Y_{\text{Cr}} Y_{\text{Fe}} \left( {{}^{0}L_{\text{Cr,Fe:N}}^{\text{fcc}} + {}^{1}L_{\text{Cr,Fe:N}}^{\text{fcc}} \left( {Y_{\text{Cr}} - Y_{\text{Fe}} } \right) - {}^{0}L_{\text{Cr,Fe:Va}}^{\text{fcc}} - {}^{1}L_{\text{Cr,Fe:Va}}^{\text{fcc}} \left( {Y_{\text{Cr}} - Y_{\text{Fe}} } \right)} \right) + \left( {1 - 2Y_{\text{N}} - Y_{\text{C}} } \right)Y_{\text{Cr}} Y_{\text{Fe}} {}^{0}L_{\text{Cr,Fe:N,Va}}^{\text{fcc}} + Y_{\text{Fe}} Y_{\text{Ni}} \left( {{}^{0}L_{\text{Fe,Ni:N}}^{\text{fcc}} + {}^{1}L_{\text{Fe,Ni:N}}^{\text{fcc}} \left( {Y_{\text{Fe}} - Y_{\text{Ni}} } \right) - {}^{0}L_{\text{Fe,Ni:Va}}^{\text{fcc}} - {}^{1}L_{\text{Fe,Ni:Va}}^{\text{fcc}} \left( {Y_{\text{Fe}} - Y_{\text{Ni}} } \right) - {}^{2}L_{\text{Fe,Ni:Va}}^{\text{fcc}} \left( {Y_{\text{Fe}} - Y_{\text{Ni}} } \right)^{2} } \right) - Y_{\text{Cr}} Y_{\text{Fe}} Y_{\text{Ni}} {}^{0}L_{\text{Cr,Fe,Ni:Va}}^{\text{fcc}} - Y_{\text{Fe}} Y_{\text{Mo}} {}^{0}L_{\text{Fe,Mo:Va}}^{\text{fcc}} - Y_{\text{Cr}} Y_{\text{Ni}} \left( {{}^{0}L_{\text{Cr,Ni:Va}}^{\text{fcc}} + {}^{1}L_{\text{Cr,Ni:Va}}^{\text{fcc}} \left( {Y_{\text{Cr}} - Y_{\text{Ni}} } \right)} \right) + \left( {1 - 2Y_{\text{N}} - Y_{\text{C}} } \right)Y_{\text{Cr}} Y_{\text{Ni}} {}^{0}L_{\text{Cr,Ni:N,Va}}^{\text{fcc}} + Y_{\text{Cr}} Y_{\text{Mo}} \left( {{}^{0}L_{\text{Cr,Mo:N}}^{\text{fcc}} - {}^{0}L_{\text{Cr,Mo:Va}}^{\text{fcc}} - {}^{1}L_{\text{Cr,Mo:Va}}^{\text{fcc}} \left( {Y_{\text{Cr}} - Y_{\text{Mo}} } \right)} \right) - Y_{\text{Mo}} Y_{\text{Ni}} \left( {{}^{0}L_{\text{Mo,Ni:Va}}^{\text{fcc}} + {}^{1}L_{\text{Mo,Ni:Va}}^{\text{fcc}} \left( {Y_{\text{Mo}} - Y_{\text{Ni}} } \right)} \right). $$

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Gu, X., Michal, G.M., Ernst, F. et al. Numerical Simulations of Carbon and Nitrogen Composition-Depth Profiles in Nitrocarburized Austenitic Stainless Steels. Metall Mater Trans A 45, 4268–4279 (2014). https://doi.org/10.1007/s11661-014-2377-z

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