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


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.


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.


Superscript denotes phase or domain unless otherwise noted

Aj, j = 1, m

m Constituents


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


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


Pressure in N/m2


Ideal gas constant R = 8.314472 J/mol K


Site fraction ratio


Temperature in K or °C


Time in s


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


Depth perpendicular to the sample surface in m


Kronecker delta



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.


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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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