Abstract
A mathematical model of the diffusion interaction of a binary system with several phases on the equilibrium phase diagram is presented. The theoretical and calculated dependences of the layer thickness of each phase in the multiphase diffusion zone on the isothermal annealing time and the ratio of the diffusion parameters in the neighboring phases with an unlimited supply of both components were constructed. The phase formation and growth in the diffusion zone during “reactive” diffusion corresponds to the equilibrium state diagram for two components, and the order of their appearance in the diffusion zone depends only on the ratio of the diffusion parameters in the phases themselves and on the duration of the incubation periods. The dependence of phase appearance on the incubation periods, annealing time, and difference in the movement rates of the components across the interface boundaries was obtained. An example of the application of the model for processing the experimental data on phase growth in a two-component three-phase system was given.
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L. A. Molokhina, V. E. Rogalin, S. A. Filin, and I. A. Kaplunov, Russ. J. Phys. Chem. A 91, 1635 (2017).
L. N. Larikov, V. R. Ryabov, and V. M. Fal’chenko, Diffusion Processes in Solid-Phase Welding of Materials (Mashinostroenie, Moscow, 1975) [in Russian].
V. G. Shmorgun, Yu. P. Trykov, O. V. Slautin, et al., Izv. Vyssh. Uchebn. Zaved., Poroshk. Metall. Funkts. Pokryt., No. 4, 24 (2008).
V. Z. Bugakov, Diffusion in Metals and Alloys (Gostekhizdat, Leningrad, 1949) [in Russian].
A. R. Chelyadinskii, Vestn. Belorus. Univ., Ser. 1: Fiz. Mat. Inform., No. 2, 45 (2015).
A. G. Zakharov, S. A. Bogdanov, Yu. B. Kakurin, and N. A. Kakurina, Inzh. Vestn. Dona 35 (2–1), 6 (2015).
L. I. Roslyakova and I. N. Roslyakov, Uprochn. Tekhnol. Pokryt., No. 4 (112), 32 (2014).
K. P. Gurov, B. A. Kartashkin, and Yu. E. Ugaste, Interdiffusion in Multiphase Metallic Systems (Nauka, Moscow, 1981) [in Russian].
F. van Loo and G. Rieck, Acta Metallyrg. 21, 61 (1973).
V. I. Borisov and V. T. Borisov, Fiz. Met. Metalloved. 42, 496 (1976).
M. Ganseen and G. Rieck, Trans. Met. Soc. AJME 239, 1372 (1967).
G. D. Bastin and G. Rieck, Met. Trans. Soc. 5, 817 (1974).
N. F. Lashko and S. V. Lashko, Brazing of Metals (Mashinostroenie, Moscow, 1988) [in Russian].
P. M. Robinson and M. B. Biver, in Intermetallic Compounds, Ed. by J. H. Westbrook (Wiley, New York, 1967).
I. E. Petrunin, I. Yu. Markova, and A. S. Ekatova, Physical Metallurgy of Brazing (Metallurgiya, Moscow, 1976) [in Russian].
N. A. Krasnoshlyk and A. O. Bogatyrev, Khar’kov: Vost.-Evr. Zh. Pered. Tekhnol. 4 (5), 60 (2011).
E. N. Zubarev, Phys. Usp. 54, 473 (2011).
S. G. Ivanov, M. A. Gur’ev, and A. M. Gur’ev, Aktual. Probl. Mashinostroen., No. 2, 416 (2015).
A. I. Epishin, T. Link, A. O. Rodin, et al., Phys. Met. Metallogr. 116, 175 (2015).
V. Yu. Filimonov, Polzunov. Vestn., Nos. 1–4, 36 (2005).
A. S. Shirinyan, Phys. Solid State 52, 1267 (2010).
L. A. Molokhina, Fiz. Khim. Obrab. Mater., No. 1, 123 (1986).
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Original Russian Text © L.A. Molokhina, V.E. Rogalin, S.A. Filin, I.A. Kaplunov, 2017, published in Zhurnal Fizicheskoi Khimii, 2017, Vol. 91, No. 12, pp. 2014–2022.
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Molokhina, L.A., Rogalin, V.E., Filin, S.A. et al. Dependence of growth of the phases of multiphase binary systems on the diffusion parameters. Russ. J. Phys. Chem. 91, 2302–2309 (2017). https://doi.org/10.1134/S0036024417120214
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DOI: https://doi.org/10.1134/S0036024417120214