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P. M. Grigoreva, E. N. Vilchevskaya

INFLUENCE OF DIFFUSION MODELS ON CHEMICAL REACTION FRONT KINETICS

A linear-elastic body is considered, in which a chemical reaction localized at the front is maintained, supported by the diffusion of the gaseous component through the layer of the newly- formed material. The comparative influence of mechanical stresses on the kinetics of the chemical reaction front is studied by taking into account the contribution of stresses to the surface reaction rate through the chemical affinity tensor and to the diffusion process through various stress dependences of the diffusion coefficient. As an example, the propagation of the centrally symmetric and axisymmetric reaction fronts in various boundary-value problems is considered with the use of different diffusion models.

The research was supported by the Russian Scientific Foundation, project No. 18-19-00160

Keywords: mechanochemistry, tensodiffusion, non-equilibrium thermodynamics

Bibliography:

1. Kao Dah-Bin, McVittie J.P., Nix W.D., Saraswat K.C. Two-dimensional silicon oxidation experiments and theory. In: 1985 International Electron Devices Meeting, IEEE, 1985, pp. 388–391. DOI: 10.1109/iedm.1985.190982.
2. Kao Dah-Bin, McVittie J.P., Nix W.D., Saraswat K.C. Two-dimensional thermal oxidation of silicon–I. Experiments. IEEE Transactions on Electron Devices, 1987, vol. 34, iss. 5, pp. 1008–1017. DOI: 10.1109/T-ED.1987.23037.
3. Sutardja P., Oldham W.G. Modeling of stress effects in silicon oxidation. IEEE Transactions on Electron Devices, 1989, vol. 36, no. 11, pp. 2415–2421. DOI: 10.1109/16.43661.
4. Paul Aloke, Laurila Tomi, Vuorinen Vesa, Divinski Sergiy V.I. Thermodynamics, diffusion and the Kirkendall effect in solids, Springer, 2014. DOI: 10.1007/978-3-319-07461-0.
5. Cui Z., Gao F., Qu J. Interface-reaction controlled diffusion in binary solids with applications to lithiation of silicon in lithium-ion batteries. Journal of the Mechanics and Physics of Solids, 2013, vol. 61, no. 2, pp. 293–310. DOI: 10.1016/j.jmps.2012.11.001.
6. Knyazeva A.G. Model of medium with diffusion and internal surfaces and some applied problems. Mater. Phys. Mech., 2004, vol. 7, no. 1, pp. 29–36.
7. Knyazeva A.G. Cross effects in solid media with diffusion. Journal of Applied Mechanics and Technical Physics, 2003, vol. 44, no. 3, pp. 373–384. DOI: 10.1023/A:1023485224031.
8. Toribio J., Kharin V., Lorenzo M., Vergara D. Role of drawing-induced residual stresses and strains in the hydrogen embrittlement susceptibility of prestressing steels. Corrosion Science, 2011, vol. 53, no. 10, pp. 3346–3355. DOI: 10.1016/j.corsci.2011.06.012.
9. Cui Z., Gao F., Qu J. A finite deformation stress-dependent chemical potential and its applications to lithium ion batteries. Journal of the Mechanics and Physics of Solids, 2012, vol. 60, no. 7, pp. 1280–1295. DOI: 10.1016/j.jmps.2012.03.008.
10. Freidin A.B. Chemical affinity tensor and stress-assist chemical reactions front propagation in solids. In: ASME 2013 International Mechanical Engineering Congress and Exposition, American Society of Mechanical Engineers, 2013, pp. V009T10A102-V009T10A102.
11. Freidin A.B. On the chemical affinity tensor for chemical reactions in deformable materials. Mechanics of Solids, 2015, vol. 50, no. 3, pp. 260–285. DOI: 10.3103/S0025654415030048.
12. Freidin Alexander B., Korolev Igor K., Aleshchenko Sergey P., Vilchevskaya Elena N. Chemical affinity tensor and chemical reaction front propagation: theory and FE-simulations. International Journal of Fracture, 2016, vol. 202, no. 2, pp. 245–259. DOI: 10.1007/s10704-016-0155-1.
13. Freidin A.B., Vilchevskaya E.N., Korolev I.K. Stress-assist chemical reactions front propagation in deformable solids. International Journal of Engineering Science, 2014, vol. 83, pp. 57–75. DOI: 10.1016/j.ijengsci.2014.03.008.
14. Freidin A., Morozov N., Petrenko S., Vilchevskaya E. Chemical reactions in spherically symmetric problems of mechanochemistry. Acta Mechanica, 2016, vol. 227, no. 1, pp. 43–56. DOI: 10.1007/s00707-015-1423-2.
15. Glansdorff P., Prigogine I. Thermodynamic theory of structure, stability and fluctuations. American Journal of Physics, 1973, vol. 41, no. 1, pp. 147–148.
16. Grinfelʹd M.J., ed. Thermodynamic Methods in the Theory of Heterogeneus Systems, Longman Scientific and Technical, 1991.
17. Kao Dah-Bin, McVittie J.P., Nix W.D., Saraswat K.C. Two-dimensional thermal oxidation of silicon. II. Modeling stress effects in wet oxides. IEEE Transactions on Electron Devices, 1988, vol. 35, no. 1, pp. 25–37. DOI: 10.1109/16.2412.
18. Loeffel K., Anand L. A chemo-thermo-mechanically coupled theory for elastic-viscoplastic deformation, diffusion, and volumetric swelling due to a chemical reaction. International Journal of Plasticity, 2011, vol. 27, no. 9, pp. 1409–1431. DOI: 10.1016/j.ijplas.2011.04.001.
19. Yen J.Y., Hwu J.G. Stress effect on the kinetics of silicon thermal oxidation. Journal of Applied Physics, 2001, vol. 89, no. 5, pp. 3027–3032. DOI: 10.1063/1.1342801.
20. Indeitsev D., Mochalova Y. Mechanics of multi-component media with exchange of mass and non-classical supplies. In: Dynamics of Mechanical Systems with Variable Mass, 2014, pp. 165–194.
21. Deal B.E., Grove A.S. General relationship for the thermal oxidation of silicon. Journal of Applied Physics, 1965, vol. 36, no. 12, pp. 3770–3778.
22. Delph T.J. Intrinsic strain in SiO 2 thin films. Journal of Applied Physics, 1998, vol. 83, no. 2, pp. 786–792. DOI: 10.1063/1.366759.
23. Lin M.T. Stress Effects and Oxidant Diffusion in the Planar Oxidation. Thesis and Dissertation, Lehigh University, 1999.
24. Vilchevskaya E.N., Freidin A.B., Morozov N.F. Kinetics of the chemical reaction front in centrally symmetric problems of mechanochemistry. Doklady Physics, 2015, vol. 60, iss. 4, pp. 175–179. DOI: 10.1134/S1028335815040072.
25. Vilchevskaya E.N., Freidin A.B. On kinetics of chemical reaction fronts in elastic solids. In: Surface Effects in Solid Mechanics, Springer, Berlin, Heidelberg, 2013, pp. 181–194.

                 

П. М. Григорьева, Е. Н. Вильчевская

ВЛИЯНИЕ ВЫБОРА МОДЕЛИ ДИФФУЗИИ НА КИНЕТИКУ ХИМИЧЕСКОЙ РЕАКЦИИ

Рассматривается линейно-упругое тело, в котором протекает локализированная на фронте химическая реакция, поддерживаемая диффузией газообразной компоненты через слой образующегося материала. Исследуется сравнительное влияние механических напряжений на кинетику фронта химической реакции посредством учета вклада напряжений в скорость поверхностной реакции через тензор химического сродства и в диффузионный процесс через различные зависимости коэффициента диффузии от напряжений. В качестве примера рассматривается распространение центрально-симметричного и осесимметричного фронтов реакции в различных краевых задачах при использовании разных моделей диффузии.

Благодарности: Исследование выполнено при поддержке гранта Российского научного фонда (проект № 18-19-00160)

Ключевые слова: механохимия, тензодиффузия, неравновесная термодинамика

Библиография:

1. Two-dimensional silicon oxidation experiments and theory / Dah-Bin Kao, J. P. McVittie, W. D. Nix, K. C. Saraswat // 1985 International Electron Devices Meeting. – IEEE, 1985. – P. 388–391.1. Two-dimensional silicon oxidation experiments and theory / Dah-Bin Kao, J. P. McVittie, W. D. Nix, K. C. Saraswat // 1985 International Electron Devices Meeting. – IEEE, 1985. – P. 388–391.
2. Kao D. B. et al. Two-dimensional silicon oxidation experiments and theory //Electron Devices Meeting, 1985 International. – IEEE, 1985. – С. 388-391.
3. Two-dimensional thermal oxidation of silicon–I. Experiments / Dah-Bin Kao, J. P. McVittie, W. D. Nix, K. C. Saraswat // IEEE Transactions on Electron Devices. – 1987. – Vol. 34, iss. 5. – P. 1008–1017. – DOI: 10.1109/T-ED.1987.23037.
4. Sutardja P., Oldham W. G. Modeling of stress effects in silicon oxidation // IEEE Transactions on Electron Devices. – 1989. – Vol. 36, no. 11. – P. 2415–2421. – DOI: 10.1109/16.43661.
5. Thermodynamics, diffusion and the Kirkendall effect in solids / Aloke Paul, Tomi Laurila, Vesa Vuorinen, Sergiy V. Divinski. – Springer, 2014.
6. Cui Z., Gao F., Qu J. Interface-reaction controlled diffusion in binary solids with applications to lithiation of silicon in lithium-ion batteries // Journal of the Mechanics and Physics of Solids. – 2013. – Vol. 61, no. 2. – P. 293–310. – DOI: 10.1016/j.jmps.2012.11.001.
7. Knyazeva A. G. Model of medium with diffusion and internal surfaces and some applied problems // Mater. Phys. Mech. – 2004. – Vol. 7, no. 1. – P. 29–36.
8. Knyazeva A. G. Cross effects in solid media with diffusion //Journal of applied mechanics and technical physics. – 2003. – Vol. 44, no. 3. – P. 373–384. – DOI: 10.1023/A:1023485224031.
9. Role of drawing-induced residual stresses and strains in the hydrogen embrittlement susceptibility of prestressing steels / J. Toribio, V. Kharin, M. Lorenzo, D. Vergara // Corrosion Science. – 2011. – Vol. 53, no. 10. – P. 3346–3355. – DOI: 10.1016/j.corsci.2011.06.012.
10. Cui Z., Gao F., Qu J. A finite deformation stress-dependent chemical potential and its applications to lithium ion batteries // Journal of the Mechanics and Physics of Solids. – 2012. – Vol. 60, no. 7. – P. 1280–1295. – DOI: 10.1016/j.jmps.2012.03.008.
11. Freidin A. B. Chemical affinity tensor and stress-assist chemical reactions front propagation in solids // ASME 2013 International Mechanical Engineering Congress and Exposition. – American Society of Mechanical Engineers, 2013. – P. V009T10A102-V009T10A102.
12. Freidin A. B. On the chemical affinity tensor for chemical reactions in deformable materials // Mechanics of Solids. – 2015. – Vol. 50, no. 3. – P. 260–285. – DOI: 10.3103/S0025654415030048.
13. Chemical affinity tensor and chemical reaction front propagation: theory and FE-simulations / Alexander B. Freidin, Igor K. Korolev, Sergey P. Aleshchenko, Elena N. Vilchevskaya // International Journal of Fracture. – 2016. – Vol. 202, no. 2. – P. 245–259. – DOI: 10.1007/s10704-016-0155-1.
14. Freidin A. B., Vilchevskaya E. N., Korolev I. K. Stress-assist chemical reactions front propagation in deformable solids // International Journal of Engineering Science. – 2014. – Vol. 83. – P. 57–75. – DOI: 10.1016/j.ijengsci.2014.03.008.
15. Chemical reactions in spherically symmetric problems of mechanochemistry / A. Freidin, N. Morozov, S. Petrenko, E. Vilchevskaya // Acta Mechanica. – 2016. – Vol. 227, no. 1, pp. 43–56. – DOI: 10.1007/s00707-015-1423-2.
16. Glansdorff P., Prigogine I. Thermodynamic theory of structure, stability and fluctuations // American Journal of Physics. – 1973. – Vol. 41, no. 1. – P. 147–148.
17. Thermodynamic Methods in the Theory of Heterogeneus Systems / ed. by M. J. Grinfelʹd. – Longman Scientific and Technical, 1991.
18. Two-dimensional thermal oxidation of silicon. II. Modeling stress effects in wet oxides / Dah-Bin Kao, J. P. McVittie, W. D. Nix, K. C. Saraswat // IEEE Transactions on Electron Devices. – 1988. – Vol. 35, no. 1. – P. 25–37. – DOI: 10.1109/16.2412.
19. Loeffel K., Anand L. A chemo-thermo-mechanically coupled theory for elastic–viscoplastic deformation, diffusion, and volumetric swelling due to a chemical reaction // International Journal of Plasticity. – 2011. – Vol. 27, no. 9. – P. 1409–1431. – DOI: 10.1016/j.ijplas.2011.04.001.
20. Yen J. Y., Hwu J. G. Stress effect on the kinetics of silicon thermal oxidation // Journal of Applied Physics. – 2001. – Vol. 89, no. 5. – P. 3027–3032. – DOI: 10.1063/1.1342801.
21. Indeitsev D., Mochalova Y. Mechanics of multi-component media with exchange of mass and non-classical supplies // Dynamics of Mechanical Systems with Variable Mass. – Springer, Vienna, 2014. – P. 165–194.
22. Deal B. E., Grove A. S. General relationship for the thermal oxidation of silicon // Journal of Applied Physics. – 1965. – Vol. 36, no. 12. – P. 3770–3778.
23. Delph T. J. Intrinsic strain in SiO 2 thin films // Journal of Applied Physics. – 1998. – Vol. 83, no. 2. – P. 786–792. – DOI: 10.1063/1.366759.
24. Lin M. T. Stress effects and oxidant diffusion in the planar oxidation : thesis and dissertation. – Lehigh University, 1999.
25. Vilchevskaya E. N., Freidin A. B., Morozov N. F. Kinetics of the chemical reaction front in centrally symmetric problems of mechanochemistry // Doklady Physics. – 2015. – Vol. 60, iss. 4. – P. 175–179. – DOI: 10.1134/S1028335815040072.
26. Vilchevskaya E. N., Freidin A. B. On kinetics of chemical reaction fronts in elastic solids // Surface effects in solid mechanics. – Springer, Berlin, Heidelberg, 2013. – P. 181–194.

                 
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