A nonlinear instability analysis of crystallization processes with a two-phase zone / Alexandrov D.V. // Journal of Metastable and Nanocrystalline Materials. - 2004. - V. 20-21, l. . - P. 468-473.

ISSN:
14226375
Type:
Conference Paper
Abstract:
This study is based on the exact analytical solutions of the nonlinear model for solidification of binary melts with a mushy layer (these solutions are obtained in previous studies). The linear analysis of dynamic instability shown existence of oscillatory instability is also taken into account. A set of nonlinear evolutionary equations describing a behavior of perturbations is deduced. The weakly nonlinear approximation under consideration enables us to find two cumbersome equations for frequency and supercriticality of bifurcations. The distance between neighboring layers of impurity distribution in the solid phase is found. Theoretical predictions are in a good agreement with experimental data.
Author keywords:
Crystallization; Instabilities; Phase transitions; Two-phase zone
Index keywords:
Approximation theory; Bifurcation (mathematics); Interfaces (materials); Melting; Oscillations; Solidification; Instabilities; Nonlinear instability; Two-phase zones; Crystallization
DOI:
нет данных
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Affiliations Department of Mathematical Physics, Urals State University, Lenin ave. 51, Ekaterinburg, 620083, Russian Federation
Author Keywords Crystallization; Instabilities; Phase transitions; Two-phase zone
References Chalmers, B., (1964) Principles of Solidification, , John Wiley & Sons, New York; Flemings, M., (1974) Solidification Processing, , McGraw Hill, New York; Ravi, V.K., (1981) Imperfections and Impurities in Semiconductor Silicon, , JohnWiley & Sons, New York; Shashkov, Yu.M., (1960) Semiconductor Metallurgy, , Metallurgya Publishing House, Moscow; Mullins, W.W., Sekerka, R.F., (1964) J. Appl. Phys., 35, p. 444; Sekerka, R.F., (1965) J. Appl. Phys., 36 (1), p. 264; Sekerka, R.F., (1968) J. Crystal Growth, 3-4, p. 71; Wollkind, D.J., Segel, L.A., (1970) Phylos. Trans. Roy. Soc., Ser. A, 268, p. 351; Alexander, J.I.D., Wollkind, D.J., Sekerka, R.F., (1986) J. Crystal Growth, 79, p. 849; Yasuda, H., Notake, N., Tokieda, K., Ohnaka, I., (2000) J. Crystal Growth, 210, p. 637; Alexandrov, D.V., (2001) Acta Mater., 49, p. 759; Alexandrov, D.V., (2001) J. Crystal Growth, 222, p. 816; Fowler, A.C., (1985) IMA J. Appl. Math., 35, p. 159; Hills, R.N., Loper, D.E., Roberts, P.H., (1983) Q. J. Mech. Appl. Math., 36, p. 505; Alexandrov, D.V., (2000) Int. J. Fluid Mech. Res., 27 (2-4), p. 239; Hopf, E., (1948) Comm. Pure Appl. Math., 1 (3), p. 303; Landau, L.D., Lifshitz, E.M., (1959) Fluid Mechanics, , Pergamon Press, New York; Hagen, H., (1983) Synergetics. Instability Hierarchies of Self-Organizing Systems and Devices, , Springer Verlag, Berlin; Stuart, J.T., (1971) Ann. Rev. Fluid Mech., 3, p. 347; Stuart, J.T., (1960) J. Fluid Mech., 9 (2), p. 353; Conti, M., Marconi, U.M.B., (2000) Physica A, 280, p. 148; Guo, W., Kar, A., (1998) Acta Mater., 46 (10), p. 3485; Milvidskiy, M.G., Turovskiy, B.M., Layner, L.V., Berkova, L.A., (1964) Nauch. Tr. In.-i. Proyektn. In-ta Redkometallicheskoy Prom., 13, p. 142. , [in Russian]; Landau, A.I., (1958) Fiz. Metal. I Metallovedeniye, 6 (1), p. 148. , [in Russian]. [25] V.T; Khryapov, V.T., Tatarinov, V.A., Krupyshev, R.S., (1983) Engineering Experiments in Weightlessness, p. 59. , Ural Science Center of the USSR Academy of Sciences, Sverdlovsk [in Russian]
Correspondence Address Alexandrov, D.V.; Department of Mathematical Physics, Urals State University, Lenin ave. 51, Ekaterinburg, 620083, Russian Federation; email: Dmitri.Alexandrov@usu.ru
Editors Kiminami C.S.Bolfarini C.Botta F W.J.
Conference name Proceedings of the 10th International Symposium on Metastable Mechanically Alloyed and Nanocrystalline Materials (ISMANAM-2002)
Conference date 24 August 2003 through 28 August 2003
Conference location Foz do Ifuacu
Conference code 63901
Language of Original Document English
Abbreviated Source Title J. Metastab. Nanocryst. Mater.
Source Scopus