Skip to main content
Log in

A New Relationship Among Self- and Impurity Diffusion Coefficients in Binary Solution Phases

  • Communication
  • Published:
Metallurgical and Materials Transactions A Aims and scope Submit manuscript

Abstract

A new relationship among self- and impurity diffusion coefficients has been proposed for binary solution phases and verified via 30 solid solutions. In terms of this model, one impurity diffusion coefficient in a binary phase can be predicted once the other three diffusion coefficients are available. The application of the present model is exemplified in the Al-Mg system.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Fig. 1
Fig. 2
Fig. 3

References

  1. 1. Y. Du, L. Zhang, S. Cui, D. Zhao, D. Liu, W. Zhang, W. Sun and W. Jie: Science China Technological Sciences, 2012, vol. 55, pp. 306-328.

    Article  Google Scholar 

  2. 2. P. Hohenberg and W. Kohn: Phys. Rev., 1964, vol. 136, pp. B864.

    Article  Google Scholar 

  3. 3. W. Kohn and L. Sham: Phys. Rev. A, 1965, vol. 140, pp. 1133-1138.

    Article  Google Scholar 

  4. J.O. Andersson, L. Höglund, B. Jönsson and J. Ågren: Fundamentals and Applications of Ternary Diffusion. G.R. Purdy, ed., Pergamon, Oxford, 1990, pp. 153–63.

  5. 5. J. Xin, W. Zhang, J. Wang, D. Zhao, Y. Du, L. Zhang and B. Huang: Comput. Mater. Sci., 2014, vol. 90, pp. 32.

    Article  Google Scholar 

  6. 6. M. Mantina, Y. Wang, R. Arroyave, L.Q. Chen, Z.K. Liu and C. Wolverton: Phys. Rev. Lett., 2008, vol. 100, pp. 215901.

    Article  Google Scholar 

  7. 7. M. Mantina, S.L. Shang, Y. Wang, L.Q. Chen and Z.K. Liu: Phys. Rev. B, 2009, vol. 80, pp. 184111.

    Article  Google Scholar 

  8. 8. W. Zhang, L. Zhang, Y. Du, S. Liu and C. Tang: Int J Mater Res., 2014, vol. 105, pp. 13.

    Article  Google Scholar 

  9. 9. J. Askill: Empirical and Semi-Empirical Diffusion Relations, p. 2, Springer, US, 1970.

    Google Scholar 

  10. 10. O. Sherby and M.T. Simnad: Trans. ASM, 1961, vol. 54, pp. 227.

    Google Scholar 

  11. 11. A.D. Le Claire: Diffusion in Body-Centered Cubic Metals, p. 10, Metals Park, Ohio, 1965.

    Google Scholar 

  12. 12. S. Dushman and I. Langmuir: Phys. Rev., 1922, vol. 20, pp. 113.

    Google Scholar 

  13. 13. D. Lazarus: Phys. Rev., 1954, vol. 93, pp. 973-976.

    Article  Google Scholar 

  14. 14. A.D. Le Claire: Philos. Mag., 1962, vol. 7, pp. 141-167.

    Article  Google Scholar 

  15. 15. B.C. Zhou, S.L. Shang, Y. Wang and Z.K. Liu: Acta Mater., 2016, vol. 103, pp. 573-586.

    Article  Google Scholar 

  16. 16. C. Chen, L. Zhang, J. Xin, Y. Wang, Y. Du, F. Luo, Z. Zhang, T. Xu and J. Long: J. Alloys Compd., 2015, vol. 645, pp. 259-268.

    Article  Google Scholar 

  17. 17. S.L. Shang, H.Z. Fang, J. Wang, C.P. Guo, Y. Wang, P.D. Jablonski, Y. Du and Z.K. Liu: Corros. Sci., 2014, vol. 83, pp. 94-102.

    Article  Google Scholar 

  18. 18. D. Simonovic and M.H.F. Sluiter: Phys. Rev. B, 2009, vol. 79, pp. 054304.

    Article  Google Scholar 

  19. H.L. Lukas, S.G. Fries and B. Sundman: Computational thermodynamics: The Calphad Method., p. 129, Cambridge University Press, New York, 2007.

    Book  Google Scholar 

  20. C.Wagner and W. Schottky: Z. Whys. Chem., 1930, vol. 11, pp. 163-210.

    Google Scholar 

  21. 21. A. Engström and J. Ågren: Z. Metallkd., 1996, vol. 87, pp. 92.

    Google Scholar 

  22. 22. J.S. Bae, J.H. Yu, B-J. Lee and H.M. Lee: Z. Metallkd., 2000, vol. 91, pp. 672.

    Google Scholar 

  23. 23. G. Ghosh: Acta Mater., 2001, vol. 49, pp. 2609-2624.

    Article  Google Scholar 

  24. 24. C.E. Campbell, W.J. Boettinger and U.R. Kattner: Acta Mater., 2002, vol. 50, pp. 775-792.

    Article  Google Scholar 

  25. 25. W. Gong, L. Zhang, D. Yao and C. Zhou: Scripta Mater., 2009, vol. 61, pp. 100-103.

    Article  Google Scholar 

  26. 26. J. Wang, L.B. Liu, H.S. Liu and Z.P. Jin: Calphad., 2007, vol. 31, pp. 249-255.

    Article  Google Scholar 

  27. 27. Y.W. Cui, M. Jiang, I. Ohnuma, K. Oikawa, R. Kainuma and K. Ishida: Journal of Phase Equilibria and Diffusion, 2008, vol. 29, pp. 2-10.

    Article  Google Scholar 

  28. 28. J. Wang, H.S. Liu, L.B. Liu and Z.P. Jin: Calphad., 2008, vol. 32, pp. 94-100.

    Article  Google Scholar 

  29. 29. D. Liu, L. Zhang, Y. Du, H. Xu, S. Liu and L. Liu: Calphad., 2009, vol. 33, pp. 761-768.

    Article  Google Scholar 

  30. 30. L. Zhang, Y. Du, Q. Chen, I. Steinbach and B. Huang: Int J Mater Res., 2010, vol. 101, pp. 1461-1475.

    Article  Google Scholar 

  31. 31. B. Jönsson: Scand. J. Metall., 1994, vol. 23, pp. 201-208.

    Google Scholar 

  32. 32. B. Jönsson: Scand. J. Metall., 1995, vol. 24, pp. 21-27.

    Google Scholar 

  33. 33. N. Matan, H.M.A. Winand, P. Carter, M. Karunaratne, P.D. Bogdanoff and R.C. Reed: Acta Mater., 1998, vol. 46, pp. 4587-4600.

    Article  Google Scholar 

  34. 34. Y. Du and J.C. Schuster: Z. Metallkd., 2001, vol. 92, pp. 28-31.

    Google Scholar 

  35. 35. L. Höglund and J. Ågren: Acta Mater., 2001, vol. 49, pp. 1311-1317.

    Article  Google Scholar 

  36. 36. Y.W. Cui, K. Oikawa, R. Kainuma and K. Ishida: Journal of Phase Equilibria and Diffusion, 2006, vol. 27, pp. 333-342.

    Google Scholar 

  37. 37. J. Yao, Y.W. Cui, H. Liu, H. Kou, J. Li and L. Zhou: Calphad., 2008, vol. 32, pp. 602-607.

    Article  Google Scholar 

  38. 38. Y. Liu, L. Zhang, Y. Du, D. Yu and D. Liang: Calphad., 2009, vol. 33, pp. 614-623.

    Article  Google Scholar 

  39. 39. J. Wang, C. Leinenbach, H.S. Liu, L.B. Liu, M. Roth and Z.P. Jin: Calphad., 2009, vol. 33, pp. 704-710.

    Article  Google Scholar 

  40. 40. S.L. Shang, L.G. Hector, Y. Wang and Z.K. Liu: Phys. Rev. B, 2011, vol. 83, pp. 224104.

    Article  Google Scholar 

  41. 41. Y. Liu, D. Yu, L. Zhang and Y. Ge: Calphad., 2009, vol. 33, pp. 425-432.

    Article  Google Scholar 

  42. 42. Y. Liu, T. Pan, L. Zhang, D. Yu and Y. Ge: J. Alloy. Compd., 2009, vol. 476, pp. 429-435.

    Article  Google Scholar 

  43. 43. Y. Liu, Y. Ge, D. Yu, T. Pan and L. Zhang: J. Alloy. Compd., 2009, vol. 470, pp. 176-182.

    Article  Google Scholar 

  44. 44. Y. Liu, L. Zhang and D. Yu: Journal of Phase Equilibria and Diffusion, 2009, vol. 30, pp. 334-344.

    Article  Google Scholar 

  45. 45. Y. Liu, L. Zhang, T. Pan, D. Yu and Y. Ge: Calphad., 2008, vol. 32, pp. 455-461.

    Article  Google Scholar 

  46. 46. G. Lindwall and K. Frisk: Journal of Phase Equilibria and Diffusion, 2009, vol. 30, pp. 323-333.

    Article  Google Scholar 

  47. 47. S. Wang, P. Zhou, W. Zhang, S. Cui, L. Zhang, M. Yin, D. Liu, H. Xu, S. Liu and Y. Du: Calphad., 2012, vol. 36, pp. 127-134.

    Article  Google Scholar 

  48. 48. D. Liu, L. Zhang, Y. Du and Z. Jin: J. Alloy. Compd., 2015, vol. 634, pp. 148-155.

    Article  Google Scholar 

  49. 49. L. Zhang, Y. Du, Y. Ouyang, H. Xu, X.G. Lu, Y. Liu, Y. Kong and J. Wang: Acta Mater., 2008, vol. 56, pp. 3940-3950.

    Article  Google Scholar 

  50. 50. J. Combronde and G. Brebec: Acta Metallurgica, 1971, vol. 19, pp. 1393-1399.

    Article  Google Scholar 

  51. 51. N.L. Peterson and S.J. Rothman: Physical Review, 1967, vol. 163, pp. 645-649.

    Article  Google Scholar 

  52. S.K. Das, Y.M. Kim, T.K. Ha and I.H. Jung: Calphad, 2013, vol. 42, pp. 51-58.

    Article  Google Scholar 

  53. 53. S. Ganeshan, L.G. Hector Jr and Z.K. Liu: Comp. Mater. Sci., 2010, vol. 50, pp. 301-307.

    Article  Google Scholar 

  54. 54. S. Ganeshan, L.G. Hector Jr and Z.K. Liu: Acta Mater., 2011, vol. 59, pp. 3214-3228.

    Article  Google Scholar 

  55. Y.W. Cui, K. Oikawa, R. Kainuma and K. Ishida: Journal of Phase Equilibria and Diffusion, vol. 27, pp. 333-342., 2008

    Google Scholar 

Download references

The financial support from the “973” project (Grant No. Grant No. 2014CB644002), National Natural Science Foundation of China (Grant Nos. 51429101 and 51531009), and the project of innovation-driven plan in Central South University of China (Grant No. 2015CX004) is acknowledged. This work is also supported by the outstanding graduate project of Advanced Non-ferrous Metal Structural Materials and Manufacturing Collaborative Innovation Center.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Yong Du.

Additional information

Manuscript submitted January 11, 2016.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Xin, J., Du, Y., Shang, S. et al. A New Relationship Among Self- and Impurity Diffusion Coefficients in Binary Solution Phases. Metall Mater Trans A 47, 3295–3299 (2016). https://doi.org/10.1007/s11661-016-3537-0

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11661-016-3537-0

Keywords

Navigation