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The Theory of Diffusion Zone Formation during Surface Modification of Materials with Allowance for the Thermodiffusion Effects

  • STRUCTURE, PHASE TRANSFORMATIONS, AND DIFFUSION
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Abstract

Using asymptotic methods in the theory of differential equations, an analytical approximate solution to the problem of diffusion of interstitial atoms in a restricted medium under the condition of a constant temperature gradient is obtained. As follows from the analysis, this solution is applicable to plate samples undergoing thermal and ionic modification of one of the surfaces, whose thickness does not exceed the diffusion penetration depth of impurities, provided that a stationary temperature distribution over the thickness is established. For the certification of the proposed method, a comparison of the approximate solution with the numerical solution of the thermal diffusion problem is carried out. Conditions are obtained under which the contribution of thermal diffusion effects to the total diffusion mass transfer of the impurity is significant.

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REFERENCES

  1. T. Iton, T. Inada, and K. Kanekawa, “Doping of silicon by ion implantation,” Appl. Phys. Lett. 12, No. 8, 244–246 (1968).

    Article  Google Scholar 

  2. T. Iton and I. Ohdomari, “Analysis of radiation–enhanced diffusion of aluminum in silicon,” J. Appl. Phys. 41, No. 1, 434–436 (1970).

    Article  Google Scholar 

  3. M. Kurata, Y. Morikawa, K. Nagami, and H. Kuroda, “Remarks on the vacancy mechanisms in ion implantation,” Jpn. J. Appl. Phys. 12, No. 3, 472–473 (1973).

    Article  Google Scholar 

  4. I. S. Belashova and T. V. Tarasova, “Investigation of the kinetics of mass transfer during laser alloying of structural steels with carbon and silicon in the mode of surface fusion,” Uprochnyayushchie Tekhnologii i Pokrytiya, No. 4, 34–38 (2007) [in Russian].

    Google Scholar 

  5. A. Gurka and D. Kotsan’da, “Mass transfer in a high-gradient thermal field during friction welding and modification of the upper layer,” Phys. Mech. Mater., No. 2, 93–98 (2011).

  6. A. G. Knyazeva and M. V. Chepak-Gizbrekht, “Non-isothermic diffusion in binary system,” Izv. Vuzov. Fiz. 54, No. 11/3, 39–46 (2011) [in Russian].

  7. A. G. Knyazeva and M. V. Chepak-Gizbrekht, “Effect of thermal diffusion on the redistribution of the alloying element between the coating and the substrate under surface heating conditions,” Izv. Vuzov. Fiz. 56, No. 12/2, 46–51 (2013) [in Russian].

  8. M. V. Chepak-Gizbrekht, “Simulation of processes in the diffusion zone under conditions of surface heat treatment taking into account the Soret effect,” Abstract of Candidate’s Dissertation in Mathematics and Physics (Tomsk, 2017), p. 24 [in Russian].

  9. A. Nayfeh, Introduction to Perturbation Techniques (Wiley, New York, 1981).

    Google Scholar 

  10. A. G. Kesarev and V. V. Kondrat’ev, “To the theory of diffusion in inhomogeneous media: short times of the process,” Phys. Met. Metallogr. 106, No. 4, 327–331 (2008).

    Article  Google Scholar 

  11. A. G. Kesarev, V. V. Kondrat’ev, and I. L. Lomaev, “On diffusion theory in inhomogeneous media: thin-film source of diffusant,” Phys. Met. Metallogr. 118, No. 9, 872–878 (2017).

    Article  CAS  Google Scholar 

  12. A. G. Kesarev, V. V. Kondrat’ev, and I. L. Lomaev, “On the theory of atomic diffusion after ion implantation,” Phys. Met. Metallogr. 119, No. 11, 1101–1106 (2018).

    Article  CAS  Google Scholar 

  13. Processes of Interdiffusion in Alloys, Ed. by K.P. Gurova (Nauka, Moscow, 1974) [in Russian].

    Google Scholar 

  14. B. S. Bokshtein, S. Z. Bokshtein, and A. A. Zhukhovitskii, Thermodynamics and Kinetics of Diffusion in Solids (Metallurgiya, Moscow, 1974).

    Google Scholar 

  15. V. A. Ditkin and A. P. Prudnikov, A Handbook of Operational Calculus (Vysshaya Shkola, Moscow, 1965) [in Russian].

    Google Scholar 

  16. H. S. Carslaw and J. C. Jaeger, Conduction of Heat in Solids (Oxford Univ., New York, 1959).

    Google Scholar 

  17. C. J. Smithells, Metals Reference Book (Butterworths, London, 1967).

    Google Scholar 

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Funding

This work was carried out within the state assignment on topic “Pressure” no. АААА-А18-118020190104-3.

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Authors and Affiliations

  1. Mikheev Institute of Metal Physics, Ural Branch, Russian Academy of Sciences, 620108, Ekaterinburg, Russia

    A. G. Kesarev, V. V. Kondratyev & I. L. Lomaev

Authors
  1. A. G. Kesarev
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  2. V. V. Kondratyev
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  3. I. L. Lomaev
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Correspondence to I. L. Lomaev.

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Translated by E. Chernokozhin

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Kesarev, A.G., Kondratyev, V.V. & Lomaev, I.L. The Theory of Diffusion Zone Formation during Surface Modification of Materials with Allowance for the Thermodiffusion Effects. Phys. Metals Metallogr. 122, 134–140 (2021). https://doi.org/10.1134/S0031918X2102006X

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  • DOI: https://doi.org/10.1134/S0031918X2102006X

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