Influence of Soret Effect on Redistribution of Alloying Elements Between the Coating and Substrate Under Conditions of External Heating

GENERAL PROBLEMS OF TRANSPORT THEORY
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An analytical solution has been obtained for a conjugate problem on redistribution of alloying elements between a coating and a substrate with account for the Soret effect caused by a temperature gradient under conditions of external heating and of the difference between the thermophysical and diffusional properties of conjugate layers. It is shown that the Soret effect can accelerate the diffusion of elements between the coating and substrate (when the thermal diffusion coefficient of a coating element is higher than that in the substrate) and retard it (in the opposite case), as well as lead to the leakage of the diffusant from the coating surface deep into the material.

Keywords

diffusion Soret effect surface heating interface between layers operational method asymptotic expansion 

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References

  1. 1.
    R. B. Bird, W. E. Stewart, and E. N. Lightfood, Transport Phenomena [Russian translation], Khimiya, Moscow (1974).Google Scholar
  2. 2.
    G. D. Rabinovich, Separation of Isotopes and of Other Mixtures by Thermal Diffusion [in Russian], Atomizdat, Moscow (1981). Google Scholar
  3. 3.
    G. Z. Gershuni, E. M. Zhukhovitskii, and A. A. Nepomnyashchii, Stability of Convective Flows [in Russian], Nauka, Moscow (1989).Google Scholar
  4. 4.
    M. A. Golub, S. K. Myasnikov, V. A. Malyusov, and V. V. Dil′man, Analysis of transition processes of admixture redistribution in the case of directed crystallization, Teor. Osn. Khim. Tekhnol., 25, No. 1, 3–10 (1991).Google Scholar
  5. 5.
    D. V. Alexandrov and D. L. Aseev, Directional solidification with a two-phase zone: thermodiffusion and temperaturedependent diffusivity, Comput. Mater. Sci., 37, 1–6 (2006).CrossRefGoogle Scholar
  6. 6.
    V. K. Andreev and N. L. Sobachkina, Motion of a Binary Mixture in Plane and Cylindrical Regions [in Russian], Sib. Fed. Univ., Krasnoyarsk (2012).MATHGoogle Scholar
  7. 7.
    M. V. Efimova, Instability of the separation surface of the equilibrium state of two binary mixtures with account for the Soret effect, Vychisl. Tekhnol., 12, No. 6, 34–43 (2007).MATHGoogle Scholar
  8. 8.
    I. Prigogine, Introduction to Thermodynamics of Irreversible Processes [Russian translation], Izd. Inostr. Lit., Moscow (1960).Google Scholar
  9. 9.
    H. Mehrer, Diffusion in Solid Bodies [Russian translation], Intellekt, Dolgoprudnyi (20110.Google Scholar
  10. 10.
    J. M. Pout et al. (Eds.), Surface Modification and Alloying by Laser, Ion, and Electron Beams [Russian translation], Mashinostroenie, Moscow (1987).Google Scholar
  11. 11.
    G. A. Bleikher, V. P. Krivobokov, and O. V. Pashchenko, Heat and Mass Transfer in a Solid Body under the Action of High-Power Beams of Charged Particles [in Russian], Nauka, Novosibirsk (1999).Google Scholar
  12. 12.
    F. F. Komarov, Ionic Implantation into Metals [in Russian], Metallurgiya, Moscow (1989).Google Scholar
  13. 13.
    A. G. Knyazeva and M. V. Chepak-Gizbrekht, Influence of thermal diffusion on the redistribution of an alloying element between the coating and substrate under conditions of surface heating, Izv. Vyssh. Ucheb. Zaved., Fiz., 56, No. 12 (2), 46–52 (2013).Google Scholar
  14. 14.
    O. N. Kryukova and M. V. Chepak-Gizbrekht, The influence of thermal diffusion on the redistribution of alloying element between the coating and base under surface heating, Adv. Mater. Res., 1040, 602–607 (2014).CrossRefGoogle Scholar
  15. 15.
    O. N. Kryukova and M. V. Chepak-Gizbrekht, Thermal activated elements redistribution between two-component coating and substrate, Key Eng. Mater., 685, 200–205 (2016).Google Scholar
  16. 16.
    K. P. Gurov, Phenomenological Thermodynamics of Irreversible Processes. Physical Principles [in Russian], Nauka, Moscow (1978).Google Scholar
  17. 17.
    A. G. Knyazeva, On modeling irreversible processes in materials with a large number of internal surfaces, Fiz. Mezomekh., 6, No. 5, 11–27 (2003).Google Scholar
  18. 18.
    A. G. Knyazeva, Cross effects in solid media with diffusion, Prikl. Mekh. Tekh. Fiz., 44, No. 3, 85–99 (2003).MATHGoogle Scholar
  19. 19.
    A. G. Knyazeva and V. N. Demidov, Coefficients of transfer for a three-component deformable alloy, Vestn. Permsk. Nats. Issled. Politekh. Univ., Mekh., No. 3, 84–99 (2011).Google Scholar
  20. 20.
    A. I. Vol′pert and V. S. Posvyanskii, On the positiveness of solution of equations of multicomponent diffusion and chemical kinetics, Khim. Fiz., 3, No. 8, 1200–1205 (1984).Google Scholar
  21. 21.
    N. V. Bukrina and A. G. Knyazeva, Algorithm of numerical solution of the problems of nonisothermal diffusion encountered in the processes of surface treatment, Fiz. Mezomekh., 9, No. 2, 55–62 (2006).Google Scholar
  22. 22.
    H. Mehrer, Numerical Data and Functional Relationships in Science and Technology. Diffusion in Solid Metals and Alloys, Springer, Berlin (1990).Google Scholar
  23. 23.
    N. N. Rykalin, A. A. Uglov, and N. I. Makarov, Heating of a two-layer plate in welding by a laser light flux, Dokl. Akad. Nauk SSSR, Tekh. Fiz., 169, No. 3, 565–568 (1966).Google Scholar
  24. 24.
    A. V. Luikov, Heat Conduction Theory, Textbook for Universities [in Russian], Vysshaya Shkola, Moscow (1967).Google Scholar
  25. 25.
    N. M. Belyaev and A. A. Ryadno, Methods of Heat Conduction Theory [in Russian], Part 2, Vysshaya Shkola, Moscow (1982).MATHGoogle Scholar
  26. 26.
    I. G. Dueck and A. G. Knyazeva, Approximate Calculation of the Characteristics of Ignition of a Condensed Substance under Conditions of Conjugate Heat Transfer [in Russian], VINITI, Moscow (1989).Google Scholar
  27. 27.
    A. G. Knyazeva, Approximate estimates of the characteristics of fuel ignition by a radiant flux through a barrier with different properties, Fiz. Goreniya Vzryva, 32, No. 1, 26–41 (1996).Google Scholar
  28. 28.
    H. Bateman and A. Erdélyi, Tables of Integral Transforms, Vol. 1. Fourier, Laplace, and Mellin Transformations [Russian translation], Nauka, Moscow (1969).Google Scholar
  29. 29.
    I. S. Grigor′ev and E. Z. Meilikhov, Physical Quantities, Handbook [in Russian], Énergoatomizdat, Moscow (1991).Google Scholar

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Authors and Affiliations

  1. 1.National Research Tomsk Polytechnic UniversityTomskRussia
  2. 2.Institute of Physics and Material ScienceSiberian Branch of the Russian Academy of SciencesTomskRussia

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