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Metallurgical and Materials Transactions A

, Volume 45, Issue 1, pp 269–279 | Cite as

Host Atom Diffusion in Ternary Fe-Cr-Al Alloys

  • Diana Rohrberg
  • Karl-Heinz Spitzer
  • Lars DörrerEmail author
  • Anna J. Kulińska
  • Günter Borchardt
  • Anna Fraczkiewicz
  • Torsten Markus
  • Michael H. G. Jacobs
  • Rainer Schmid-Fetzer
Article

Abstract

In the Fe-rich corner of the Fe-Cr-Al ternary phase diagram, both interdiffusion experiments [1048 K to 1573 K (775 °C to 1300 °C)] and 58Fe tracer diffusion experiments [873 K to 1123 K (600 °C to 850 °C)] were performed along the Fe50Cr50-Fe50Al50 section. For the evaluation of the interdiffusion data, a theoretical model was used which directly yields the individual self-diffusion coefficients of the three constituents and the shift of the original interface of the diffusion couple through inverse modeling. The driving chemical potential gradients were derived using a phenomenological Gibbs energy function which was based on thoroughly assessed thermodynamic data. From the comparison of the individual self-diffusivities of Fe as obtained from interdiffusion profiles and independent 58Fe tracer diffusivities, the influence of the B2-A2 order–disorder transition becomes obvious, resulting in a slightly higher activation enthalpy for the bcc-B2 phase and a significantly lower activation entropy for this phase.

Keywords

Diffusion Couple Inverse Modeling Interdiffusion Coefficient Tracer Diffusion Welding Plane 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Nomenclature

Superscript denotes phase or domain unless otherwise noted

Aj, j = 1, m

m Constituents

cAj

Concentration of the constituent A j in mol A j /m3

Dj,l, j, l = 1, m

Diffusion coefficient in m2/s

Ei, i = 1, n

n Components

G

Integral Gibbs free energy in J/mol

\( G_{{A_{j} }} \)

Partial Gibbs free energy of the constituent A j in J/mol A j

\( G_{{E_{i} }} \)

Partial Gibbs free energy of the component E i in J/mol E j

\( G_{i}^{0\varphi } \)

Molar Gibbs energy of the element i in an arbitrary phase φ at 1 bar in J/mol

\( G_{\text{mag}}^{\varphi } \)

Magnetic contribution to the Gibbs energy in an arbitrary phase φ in J/mol

\( L_{ijk}^{\varphi } \)

k-th term of the Redlich–Kister expression of binary system ij of phase φ

\( M_{{A_{j} }} \)

Molar mass of the constituent A j in kg A j /molψ

\( m_{j,l} ,j, l = 1, m \)

Mobility of the constituent A j in m/s N

P

Pressure in N/m2

R

Ideal gas constant R = 8.314472 J/mol K

r(l)

Site fraction ratio

T

Temperature in K or °C

t

Time in s

V

Molar volume in m3/mol

\( x_{{A_{j} }} \)

Mole fraction of the constituent A j

\( x_{{E_{i} }} \)

Mole fraction of the component E i

\( \hat{x}_{{A_{j} }} \)

Moles of the constituent A j resulting from 1 mol of component mixture under local equilibrium conditions in mol

z

Depth perpendicular to the sample surface in m

δik

Kronecker delta

Notes

Acknowledgments

The authors are indebted to the Deutsche Forschungsgemeinschaft (DFG) for financial support and to Dr. Helmut Klein for interesting discussions on the A2-B2 transition. They are grateful to K. Herrmann for the electron beam microprobe measurements and to E. Ebeling and S. Fischer for technical assistance with the sample preparation and metallographic documentation.

References

  1. 1.
    H.C. Akuezue and J. Stringer: Metall. Trans. A, 1989, vol. 20A, pp. 2767–2781.CrossRefGoogle Scholar
  2. 2.
    P. Dawah-Tankeu, L. Dörrer, G. Borchardt, K. Gömann, W.M. Pragnell, H.E. Evans, and J. Le Coze: Proc. 6th Int. Conf. Microsc. Oxid. Sci. Rev., 2005, pp. 207–16.Google Scholar
  3. 3.
    L. Maréchal, B. Lesage, A.-M. Huntz, and R. Molins: Oxid. Met., 2003, vol. 60, pp. 1–28.CrossRefGoogle Scholar
  4. 4.
    B. Lesage, L. Maréchal, A.-M. Huntz, and R. Molins: Defect Diffus. Forum, 2001, vol. 194–199, pp. 1707–1712.CrossRefGoogle Scholar
  5. 5.
    A. Heesemann, E. Schmidtke, and F. Faupel: Scripta Mater., 1999, vol. 40, pp. 517–522.CrossRefGoogle Scholar
  6. 6.
    C. Cserhati, Ü. Ugaste, M.J.H. van Dal, N.J.H.G.M. Lousberg, A.A. Kodentsov, and F.J.J van Loo: Defect Diffus. Forum, 2001, Vol. 194-199, pp. 189–194.CrossRefGoogle Scholar
  7. 7.
    M. Danielewski, R. Bachorczyk, A. Milewska, and Y. Ugaste: Defect Diffus. Forum, 2001, vol. 194-199, pp. 223–228.CrossRefGoogle Scholar
  8. 8.
    I.V. Belova, G.E. Murch: Acta Mater., 2002, vol. 50, pp. 4617–4627.CrossRefGoogle Scholar
  9. 9.
    I.V. Belova, G.E. Murch: Philos. Mag. Lett., 2001, Vol. 81, pp. 661–666.CrossRefGoogle Scholar
  10. 10.
    R. Bouchet, R. Mevrel: Acta Mater., 2002, vol. 50, pp. 4887–4900.CrossRefGoogle Scholar
  11. 11.
    D. Rohrberg, K.-H. Spitzer, L. Dörrer, P. Dawah Tankeu, M. Podsiadlo, G. Borchardt, T. Markus and R. Schmid-Fetzer: Mater. High Temp., 2008, vol. 25, No. 4, pp. 247–255.CrossRefGoogle Scholar
  12. 12.
    M. Danielewski, B. Wierzba: Acta Mater., 2010, vol. 58, pp. G717–G727.Google Scholar
  13. 13.
    A. D. Gosman, W. M. Pun, A. K. Runchal, D. B. Spalding, M. Wolfstein: Heat and Mass Transfer in Recirculating Flows, Academic Press, London, 1969.Google Scholar
  14. 14.
    S.J. Rothman: in Diffusion in Crystalline Solids, G.E. Murch, A.S. Nowick, eds., Academic Press, Orlando, 1984, pp. 1–61.Google Scholar
  15. 15.
    J. Crank: The Mathematics of Diffusion, Clarendon Press, Oxford, 1997.Google Scholar
  16. 16.
    C.G. Schön: J. Phase Equilib., 2001, vol. 22, No. 3, pp. 287–290.CrossRefGoogle Scholar
  17. 17.
    K. Gschwend, H. Sato, and R. Kikuchi: J. Chem. Phys. 1978, vol. 69, No. 11, pp. 5006–5019.CrossRefGoogle Scholar
  18. 18.
    L.A. Girifalco: Statistical Physics of Materials, John Wiley & Sons, New York, 1973.Google Scholar
  19. 19.
    H. Mehrer: Diffusion in Solids, Springer, Heidelberg, 2007.Google Scholar
  20. 20.
    J. Philibert: Atom Movements, Diffusion and Mass Transport in Solids, Chap. V, Sect. VII.2, Les Éditions de Physique, Les Ulis, 1991.Google Scholar
  21. 21.
    S.J. Rothman, L.J. Nowicki, and G.E. Murch: J. Phys. F Met. Phys., 1980, vol. 10, pp. 383–398.CrossRefGoogle Scholar
  22. 22.
    M.H.G. Jacobs, R. Schmid-Fetzer, T. Markus, V. Motalov, G. Borchardt, and K.-H. Spitzer: Intermetallics, 2008, vol. 16, pp. 995–1005.CrossRefGoogle Scholar
  23. 23.
    M.H.G. Jacobs, R. Schmid-Fetzer: CALPHAD, 2009, vol. 33, pp. 170–178.CrossRefGoogle Scholar
  24. 24.
    R. Kainuma, M. Ise, K. Ishikawa, I. Ohnuma, and K. Ishida: J. Alloys Compd., 1998, vol. 269, pp. 173–180.CrossRefGoogle Scholar
  25. 25.
    K. Ishikawa, M. Ise, I. Ohnuma, R. Kainuma, and K. Ishida: Ber. Bunsenges. Phys. Chem., 1998, vol. 102, No. 9, pp. 1206–1210.CrossRefGoogle Scholar
  26. 26.
    H. L. Lukas, S. G. Fries, B. Sundman: Computational thermodynamics, the Calphad Method. Cambridge University Press, Cambridge, 2007.CrossRefGoogle Scholar
  27. 27.
    M. Hillert and M. Jarl: CALPHAD, 1978, vol. 2, pp. 227–238.CrossRefGoogle Scholar
  28. 28.
    M. Seiersten: in Thermochemical Database for Light Metal Alloys, vol. 2, I. Ansara, A.T. Dinsdale, and M.H. Rand, eds., European Communities, Luxembourg, 1998.Google Scholar
  29. 29.
    N. Dupin, I. Ansara, and B. Sundman: CALPHAD, 2001, vol. 25, No. 2, pp. 279–298.CrossRefGoogle Scholar
  30. 30.
    A. Taylor and R.M. Jones: J. Phys. Chem. Solids, 1958, vol. 6, pp. 16–37.CrossRefGoogle Scholar
  31. 31.
    F. Lihl and F. Ebel: Arch. Eisenhüttenwes. 1961, vol. 32, pp. 483–487.Google Scholar
  32. 32.
    A.T. Dinsdale: CALPHAD, 1991, vol. 15, No. 4, pp. 317–425.CrossRefGoogle Scholar
  33. 33.
    N.A. Dubrovinskaia, L.S. Dubrovinsky, and S.K. Saxena: CALPHAD, 1997, vol. 21, pp. 497–508.CrossRefGoogle Scholar

Copyright information

© The Minerals, Metals & Materials Society and ASM International 2013

Authors and Affiliations

  • Diana Rohrberg
    • 1
  • Karl-Heinz Spitzer
    • 1
  • Lars Dörrer
    • 1
    Email author
  • Anna J. Kulińska
    • 1
  • Günter Borchardt
    • 1
  • Anna Fraczkiewicz
    • 2
  • Torsten Markus
    • 3
  • Michael H. G. Jacobs
    • 1
  • Rainer Schmid-Fetzer
    • 1
  1. 1.Institut für MetallurgieClausthal-ZellerfeldGermany
  2. 2.École Nationale Supérieure des Mines de Saint-ÉtienneSaint-Étienne Cedex 2France
  3. 3.Forschungszentrum Jülich GmbH, Institut für Energie- und KlimaforschungJülichGermany

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