Math. Model. Nat. Phenom.
Volume 18, 2023
|Number of page(s)||16|
|Published online||06 January 2023|
Models of recrystallization activated by a diffusion flow of impurities from a thin-film coating with a convection term at the crystal surface: exact solutions
Belgorod State Technological University named after V. G. Shukhov,
Kostukova St., 46,
2 Financial University Under the Government of the Russian Federation 125167, Leningradsky Pr., 49, Moscow, Russia
* Corresponding author: firstname.lastname@example.org
Accepted: 21 October 2022
Two models of recrystallization are proposed taking into account the convective flux of impurity exchange between the polycrystalline and the thin-film coating. The special boundary modes of recrystallization described by the single-phase and two-phase Stefan problems with the boundary condition at coated surface containing the convective term. The exact solutions of the formulated problems corresponding to the grain-boundary concentration of impurities are obtained. The detail theoretical analysis focused on the third type problem shows that the concentration of impurities and the width of the recrystallized layer increase with an increase in the annealing time. An increase in intensity of impurity exchange between the polycrystalline and the coating promotes an increase in the width of the recrystallized layer. The recrystallization front position increases with an increase in the surface concentration of impurities and it decreases with an increase in the intensity of the impurity flux from the surface. The rate of recrystallization kinetics increases with an increase in the intensity of impurity exchange between the polycrystalline and the coating.
Mathematics Subject Classification: 82C70
Key words: Diffusion equation / diffusion coefficient / Stefan problem / moving boundary / diffusion flow / convective term
© The authors. Published by EDP Sciences, 2023
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