Skip to main content
Log in

Modeling of kinetics of diffusive phase transformation in binary systems with multiple stoichiometric phases

  • Section I: Basic And Applied Research
  • Published:
Journal of Phase Equilibria and Diffusion Aims and scope Submit manuscript

Abstract

The thermodynamic extremal principle is used for the treatment of the evolution of a binary system under the assumption that all phases in the system are nearly stoichiometric with no sources and sinks for vacancies in the bulk. The interfaces between the individual phases are assumed to act as ideal sources and sinks for vacancies, and to have an infinite mobility. Furthermore, it is assumed that several phases are nucleated in the contact plane of the diffusion couple at the beginning of the computer experiment. Then, it is shown that the number of newly nucleated phases determines the maximum number of polyfurcations (i.e., branching of a single configuration into several distinct configurations) of the initial contact (Kirkendall) plane. The model is demonstrated on a hypothetical binary system with four stoichiometric phases. The inverse problem, namely, the determination of the tracer diffusion coefficients in newly nucleated phases from the thicknesses of new phases and the positions of polyfurcated Kirkendall planes, is treated too.

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.

Similar content being viewed by others

References

  1. H. Nakajima, The Discovery and Acceptance of the Kirkendall Effect: The Result of a Short Research Career,JOM, 1997,6, p 15–19

    Google Scholar 

  2. A. Paul, M.J.H. van Dal, A.A. Kodentsov, and F.J.J. van Loo, The Kirkendall Effect in Multiphase Diffusion,Acta Mater., 2004,52, p 623–630

    Article  Google Scholar 

  3. C. Wagner, The Evaluation of Data Obtained with Diffusion Couples of Binary Single-Phase and Multiphase Systems,Acta Metall., 1969,17, p 99–107

    Article  Google Scholar 

  4. S.R. Shatynski, J.P. Hirth, and R.A. Rapp, A Theory of Multiphase Binary Diffusion,Acta Metall., 1976,24, p 1071–1078

    Article  Google Scholar 

  5. D.S. Williams, R.A. Rapp, and J.P. Hirth, Multilayer Diffusional Growth in Silver-Zinc Alloys,Metall. Mater. Trans. A, 1981,12, p 639–652

    ADS  Google Scholar 

  6. G.X. Li and G.W. Powell, Theory of Reaction Diffusion in Binary Systems,Acta Metall., 1985,33, p 23–31

    Article  Google Scholar 

  7. E. Metin, O.T. Inal, and A.D. Romig Jr., Solutions to Multiphase Diffusion in Binary Metal Interstitial Systems,Metall. Mater. Trans. A, 2005,36, p 1407–1415

    Article  Google Scholar 

  8. M. Kajihara, Relationship Between Temperature Dependence of Interdiffusion and Kinetics of Reactive Diffusion in a Hypothetical Binary System,Mater. Sci. Eng., A, 2005,403, p 234–240

    Article  Google Scholar 

  9. F.D. Fischer and N.K. Simha, Influence of Material Flux on the Jump Relations at a Singular Interface in a Multicomponent Solid,Acta Mech., 2004,171, p 213–223

    Article  MATH  Google Scholar 

  10. M.J.H. van Dal, D.G.G.M. Huibers, A.A. Kodentsov, and F.J.J. van Loo, Formation of Co-Si Intermetallics in Bulk Diffusion Couples: Part I. Growth Kinetics and Mobilities of Species in the Silicide Phases,Intermetallics, 2001,9, p 409–421

    Article  Google Scholar 

  11. M.J.H. van Dal, A.A. Kodentsov, and F.J.J. van Loo, Formation of Co-Si Intermetallics in Bulk Diffusion Couples: Part II. Manifestations of the Kirkendall Effect Accompanying Reactive Diffusion,Intermetallics, 2001,9, p 451–456

    Article  Google Scholar 

  12. J. Svoboda, I. Turek, and F.D. Fischer, Application of the Thermodynamic Extremal Principle to Modeling of Thermodynamic Processes in Material Sciences,Philos. Mag., 2005,85, p 3699–3707

    Article  Google Scholar 

  13. L. Onsager, Theories and Problems of Liquid Diffusion,Ann. N. Y. Acad. Sci., 1945,46, p 241–265

    Article  Google Scholar 

  14. F.J.J. van Loo, Multiphase Diffusion in Binary and Ternary Solid-State Systems,Prog. Solid State Chem., 1990,20, p 47–99

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to J. Svoboda.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Svoboda, J., Gamsjäger, E., Fischer, F.D. et al. Modeling of kinetics of diffusive phase transformation in binary systems with multiple stoichiometric phases. JPED 27, 622–628 (2006). https://doi.org/10.1007/BF02736564

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02736564

Keywords

Navigation