Fractal-like structures in the self-similar crystallization with a two-phase zone / Alexandrov D.V., Bulitcheva S.V., Komarovski M.E., Malygin A.P. // Journal of Optoelectronics and Advanced Materials. - 2003. - V. 5, l. 3. - P. 635-640.

ISSN:

14544164

Type:

Conference Paper

Abstract:

In the case of the self-similar regime in time-dependent crystallization, the spatial coordinate, ζ, set along the solidification direction and time t are connected by means of the following relation: ζ ∼ √t. This scaling relation usually takes place for crystallization regimes far from the initial stage t = 0 of the process. We demonstrate that nonstationary crystallization processes in the presence of the mushy region are described by means of the fractal-like power laws at initial and self-similar stages.

Author keywords:

Crystal growth; Fractal; Self-similar crystallization

Index keywords:

Crystal growth; Fractals; Functions; Parameter estimation; Phase diagrams; Solidification; Thermodynamics; Spatial corodinates; Two-phase zones; Crystallization

DOI:

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https://www.scopus.com/inward/record.uri?eid=2-s2.0-0348224937&partnerID=40&md5=3f7baa0e8277336fc10fa92b2d1b50f0

Соавторы в МНС:

Другие поля

Поле	Значение
Link	https://www.scopus.com/inward/record.uri?eid=2-s2.0-0348224937&partnerID=40&md5=3f7baa0e8277336fc10fa92b2d1b50f0
Affiliations	Department of Mathematical Physics, Urals State University, Lenin ave. 51, Ekaterinburg 620083, Russian Federation
Author Keywords	Crystal growth; Fractal; Self-similar crystallization
References	Laudise, R.A., (1972) The Growth of Single Crystals, , Prentice Hall, New York; Brice, J.C., (1973) The Growth of Crystals from Liquid, , North Holland, Amsterdam; Rosenberg, F., (1979) Fundamentals of Crystal Growth, 1. , Springer, Berlin; Hobbs, P.V., (1974) Ice Physics, , Clarendon, Oxford; Chalmers, B., (1964) Principles of Solidification, , Wiley, New York; Morales-Sánchez, E., González-Hernández, J., Prokhorov, E., (2001) J. Optoelectron. Adv. Mater., 3 (2), p. 333; Langer, J.S., (1980) Rev. Mod. Phys., 52, p. 1; Hills, R.N., Loper, D.E., Roberts, P.H., (1983) Q. J. Appl. Math., 36, p. 505; Alexandrov, D.V., (2001) J. Crystal Growth, 222, p. 816; Alexandrov, D.V., (2001) Acta Mater., 49, p. 759; Alexandrov, D.V., Churbanov, A.G., Vabishchevich, P.N., (1999) Int. J. Fluid Mech. Res., 26, p. 248; Alexandrov, D.V., (2000) Int. J. Fluid Mech. Res., 27, p. 223; Huppert, H.E., Worster, M.G., (1985) Nature, 314, p. 703; Worster, M.G., (1986) J. Fluid Mech., 167, p. 481; Feder, J., (1988) Fractals, , Plenum Press, New York; Mandelbrot, B.B., (1982) Fractal Geometry of Nature, , Freeman, New York; Alexandrov, D.V., Ivanov, A.O., (2002) Doklady Physics, 47 (7), p. 499; Nagashima, K., Furukawa, Y., (2000) J. Crystal Growth, 209, p. 167
Correspondence Address	Alexandrov, D.V.; Department of Mathematical Physics, Urals State University, Lenin ave. 51, Ekaterinburg 620083, Russian Federation; email: Dmitri.Alexandrov@usu.ru
Language of Original Document	English
Abbreviated Source Title	J. Optoelectron. Adv. Mat.
Source	Scopus