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Zero-flux planes and flux reversals in Cu−Ni−Zn diffusion couples


Concentration profiles of isothermal diffusion couples in binary as well as multicomponent systems can be analyzed directly for interdiffusion fluxes without the need for a prior knowledge of interdiffusion coefficients. Such an analysis is presented and applied for the calculation of interdiffusion fluxes of each component at various sections of several diffusion couples in the Cu−Ni−Zn system investigated at 775°C. A major outcome of these calculations is the identification of “zero-flux planes” for the individual components within the diffusion zones of ternary couples. At a zero-flux plane the interdiffusion flux of a component goes to zero and on either side of the plane occurs a change or reversal in the direction of the interdiffusion flux of the component. The formation as well as the number of zero-flux planes of the components is dictated by the terminal alloys of the diffusion comple. The compositions of zero-flux planes for Ni and Cu identified in several Cu−Ni−Zn couples are found to correspond to composition points of intersection of diffusion paths and isoactivity lines drawn through the terminal alloys of the couples on a ternary isotherm.

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  1. 1.

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

    Article  CAS  Google Scholar 

  2. 2.

    J. S. Kirkaldy:Advances in Materials Research, vol. 4, p. 55, Interscience Publishers, New York, 1970.

    Google Scholar 

  3. 3.

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

    CAS  Google Scholar 

  4. 4.

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

    Article  CAS  Google Scholar 

  5. 5.

    A. G. Guy and V. Leroy:The Electron Microprobe, p. 543, John Wiley and Sons, 1966.

  6. 6.

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

    CAS  Google Scholar 

  7. 7.

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

    CAS  Google Scholar 

  8. 8.

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

    Google Scholar 

  9. 9.

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

    CAS  Google Scholar 

  10. 10.

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

    CAS  Google Scholar 

  11. 11.

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

    Article  CAS  Google Scholar 

  12. 12.

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

    Article  CAS  Google Scholar 

  13. 13.

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

    Google Scholar 

  14. 14.

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

    Article  CAS  Google Scholar 

  15. 15.

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

    Article  CAS  Google Scholar 

  16. 16.

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

    Article  CAS  Google Scholar 

  17. 17.

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

    CAS  Google Scholar 

  18. 18.

    T. O. Ziebold and A. R. Cooper:Acta Met., 1965, vol. 13, p. 465.

    Article  CAS  Google Scholar 

  19. 19.

    M. A. Dayananda:Trans. TMS-AIME, 1968, vol. 242, p. 1369.

    CAS  Google Scholar 

  20. 20.

    M. A. Dayananda:Met. Trans., 1971, vol. 2, p. 334.

    Article  Google Scholar 

  21. 21.

    P. T. Carlson, M. A. Dayananda, and R. E. Grace:Met. Trans. A. 1975, vol. 6A, p. 1245.

    CAS  Article  Google Scholar 

  22. 22.

    J. D. Whittenberger and M. A. Dayananda:Met. Trans., 1970, vol. 1, p. 3301.

    Article  CAS  Google Scholar 

  23. 23.

    ASM Metals Handbook, vol. 8, p. 427, ASM Publication, Metals Park, OH, 1970.

  24. 24.

    K. J. Anusavice and R. T. DeHoff:Met. Trans., 1972, vol. 3, p. 1279.

    Article  Google Scholar 

  25. 25.

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

    Article  CAS  Google Scholar 

  26. 26.

    G. A. Chadwick and B. B. Argent:Trans. Faraday Soc., 1961, vol. 57, p. 2138.

    Article  CAS  Google Scholar 

  27. 27.

    R. A. Rapp and F. Mack:Acta Met., 1962, vol. 10, p. 63.

    Article  CAS  Google Scholar 

  28. 28.

    B. A. Hargreaves:J. Inst. Metals, 1939, vol. 64, p. 115.

    Google Scholar 

  29. 29.

    B. B. Argent and D. W. Wakeman:Trans. Faraday Soc., 1958, vol. 59, p. 799.

    Article  Google Scholar 

  30. 30.

    V. A. Schneider and H. Schmid:Z Electrochem., 1942, vol. 48, p. 627.

    CAS  Google Scholar 

  31. 31.

    E. V. Cougherty and L. Kaufman:Acta Met., 1963, vol. 11, p. 1043.

    Article  Google Scholar 

  32. 32.

    T. G. Chart, T. K. Critchley, and R. Williams:J. Inst Metals., 1968, vol. 96, p. 224.

    CAS  Google Scholar 

  33. 33.

    W. W. Liang, J. W. Frank, and Y. A. Chang:Met. Trans., 1972, vol. 3, p. 2555.

    Article  CAS  Google Scholar 

  34. 34.

    C. Matano:Japn. J. Phys., 1933, vol. 8, p. 109.

    CAS  Google Scholar 

  35. 35.

    J. S. Kirkaldy:Can. J. Phys., 1957, vol. 35, p. 435.

    CAS  Google Scholar 

  36. 36.

    G. L. Kehl:Principles of Metallographic Laboratory Practice, p. 420, McGraw-Hill, NY, 1949.

    Google Scholar 

  37. 37.

    T. O. Ziebold and R. E. Ogilvie:Anal. Chem., 1964, vol. 36, p. 322.

    Article  CAS  Google Scholar 

  38. 38.

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

    Google Scholar 

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Correspondence to M. A. Dayananda.

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C. W. KIM, formerly a graduate student at Purdue University

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Dayananda, M.A., Kim, C.W. Zero-flux planes and flux reversals in Cu−Ni−Zn diffusion couples. Metall Mater Trans A 10, 1333–1339 (1979).

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  • Metallurgical Transaction
  • Diffusion Couple
  • Diffusion Path
  • Diffusion Zone
  • Interdiffusion Coefficient