Skip to main content
SpringerLink
Log in

An analysis of concentration profiles for fluxes, diffusion depths, and zero-flux planes in multicomponent diffusion

  • Published:
Metallurgical Transactions A Aims and scope Submit manuscript

Abstract

Concentration profiles developed during isothermal, multicomponent diffusion for a single-phase, solid-solid diffusion couple are expressed on the basis of a relative concentration variable for each component and analyzed for the determination of interdiffusion fluxes. The individual concentration profiles intersect at a common cross-over composition where the relative concentrations of all components are identical. New relations are developed for describing internal consistency among the concentration profiles of the various components. A link is made between the cross-over composition and the depths of the diffusion zone on either side of the Matano plane for a diffusion couple. The cross-over composition is interpreted as the average relative concentration of each component over the diffusion zone. The identification of a zero-flux plane from concentration profiles is also described. The analysis offers several advantages in presenting as well as checking the self-consistency of results as illustrated with a single phase Cu-Ni-Zn diffusion couple annealed at 775 °C.

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

Similar content being viewed by others

References

  1. L. Onsager:Ann. N. Y. Acad. Sci., 1945, vol. 46, p. 241.

    Article  CAS  Google Scholar 

  2. J.S. Kirkaldy:Advances in Materials Research, H. Herman, ed., Interscience Publishers, New York, NY, 1970, vol. 4, p. 55.

    Google Scholar 

  3. M. A. Dayananda and R. E. Grace:Trans. TMS-AIME, 1965, vol. 233, p. 1287.

    CAS  Google Scholar 

  4. J.S. Kirkaldy, R. J. Brigham, and D.H. Weichert:Acta Met., 1965, vol. 13, p. 907.

    Article  CAS  Google Scholar 

  5. A. G. Guy and V. Leroy:The Electron Microprobe, T. D. McKinley, K. F. J. Heinrich, and D. B. Wittry, eds., John Wiley and sons, 1966, p. 543.

  6. T. O. Ziebold and R. E. Ogilvie:Trans. TMS-AIME, 1967, vol. 239, p. 942.

    CAS  Google Scholar 

  7. J. P. Sabatier and A. Vignes:Mem. Sci. Rev. Metall., 1967, vol. 64, p. 225.

    CAS  Google Scholar 

  8. M. A. Dayananda, P. F. Kirsch, and R. E. Grace:Trans. TMS-AIME, 1968, vol. 242, p. 855.

    Google Scholar 

  9. A. Vignes and J.P. Sabatier:Trans. TMS-AIME, 1969, vol. 245, p. 1795.

    CAS  Google Scholar 

  10. T. Ericsson:J. Iron Steel Inst., 1970, vol. 208, p. 1109.

    CAS  Google Scholar 

  11. P.T. Carlson, M.A. Dayananda, and R.E. Grace:Metall. Trans., 1972, vol. 3, p. 819.

    CAS  Google Scholar 

  12. T.R. Heyward and J.I. Goldstein:Metall. Trans., 1973, vol. 4, p. 2335.

    CAS  Google Scholar 

  13. A. Brunch and S. Steeb:Z. Metall., 1974, vol. 65, p. 765.

    Google Scholar 

  14. R. T. DeHoff. K.J. Anusavice, and C.C. Wan:Metall. Trans., 1974, vol. 5, p. 1113.

    CAS  Google Scholar 

  15. T. D. Moyer and M.A. Dayananda:Metall. Trans. A, 1976, vol. 7A, p. 1035.

    CAS  Google Scholar 

  16. R. D. Sisson, Jr. and M. A. Dayananda:Metall. Trans. A, 1977, vol. 8A, p. 1849.

    CAS  Google Scholar 

  17. G. H. Cheng and M. A. Dayananda:Metall. Trans. A, 1979, vol. 10A, p. 1415.

    CAS  Google Scholar 

  18. G. W. Roper and D.P. Whittle:Metall. Sci., 1980, vol. 14, p. 21.

    Article  CAS  Google Scholar 

  19. A.G. Guy and J. Philibert:Z. Metall., 1965, vol. 56, p. 841.

    CAS  Google Scholar 

  20. H. Fujita and L. J. Gosting:J. Am. Chem. Soc, 1956, vol. 78, p. 1099.

    Article  CAS  Google Scholar 

  21. C. Bolze, D.E. Coates, and J.S. Kirkaldy:Trans. ASM, 1969, vol. 62, p. 794.

    CAS  Google Scholar 

  22. G. W. Roper and D.P. Whittle:Metall. Sci., 1980, vol. 14, p. 541.

    Article  CAS  Google Scholar 

  23. M. A. Dayananda, P. F. Kirsch, and R. E. Grace:Trans. TMS-AIME, 1968, vol. 242, p. 885.

    CAS  Google Scholar 

  24. J. I. Goldstein and A. E. Moren:Metall. Trans. A, 1978, vol. 9A, p. 1515.

    CAS  Google Scholar 

  25. C. Wan and R. T. DeHoff:Acta Met., 1977, vol. 25, p. 287.

    Article  CAS  Google Scholar 

  26. M. A. Dayananda and C. W. Kim:ScriptaMet., 1982, vol. 16, p. 815.

    Article  CAS  Google Scholar 

  27. M. A. Dayananda and C. W. Kim:Metall. Trans. A, 1979, vol. 10A, p. 1333.

    CAS  Google Scholar 

  28. F.J.A. den Broeder:Scripta Met., 1969, vol. 3, p. 321.

    Article  Google Scholar 

  29. G. W. Roper and D. P. Whittle:Scripta Met., 1974, vol. 8, p. 1357.

    Article  Google Scholar 

  30. G. A. Chadwick and B. B. Argent:J. Inst. Metals, 1959, vol. 88, p. 318.

    Google Scholar 

  31. C.W. Kim: Ph.D. Thesis, Purdue University, West Lafayette, IN, 1982.

    Google Scholar 

  32. D. D. Fitts:Nonequilibrium Thermodynamics, McGraw-Hill Book Co., Inc., New York, NY, 1962, p. 5.

    Google Scholar 

  33. C. W. Kim and M. A. Dayananda:Metall. Trans. A, 1983, vol. 14A, p. 857.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Purdue University, 47907, West Lafayette, IN

    M. A. Dayananda (Professor of Materials Engineering)

Authors
  1. M. A. Dayananda
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Dayananda, M.A. An analysis of concentration profiles for fluxes, diffusion depths, and zero-flux planes in multicomponent diffusion. Metall Trans A 14, 1851–1858 (1983). https://doi.org/10.1007/BF02645555

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02645555

Keywords

Search

Navigation