The Stefan problem of solidification of ternary systems in the presence of moving phase transition regions / Alexandrov D. V.,Ivanov A. A. // JOURNAL OF EXPERIMENTAL AND THEORETICAL PHYSICS. - 2009. - V. 108, l. 5. - P. 821-829.

ISSN/EISSN:

1063-7761 / 1090-6509

Type:

Article

Abstract:

The process of solidification of ternary systems in the presence of moving phase transition regions has been investigated theoretically in terms of the nonlinear equation of the liquidus surface. A mathematical model is developed and an approximate analytical solution to the Stefan problem is constructed for a linear temperature profile in two-phase zones. The temperature and impurity concentration distributions are determined, the solid-phase fractions in the phase transition regions are obtained, and the laws of motion of their boundaries are established. It is demonstrated that all boundaries move in accordance with the laws of direct proportionality to the square root of time, which is a general property of self-similar processes. It is substantiated that the concentration of an impurity of the substance undergoing a phase transition only in the cotectic zone increases in this zone and decreases in the main two-phase zone in which the other component of the substance undergoes a phase transition. In the process, the concentration reaches a maximum at the interface between the main two-phase zone and the cotectic two-phase zone. The revealed laws of motion of the outer boundaries of the entire phase transition region do not depend on the amount of the components under consideration and hold true for crystallization of a multicomponent system.

Author keywords:

DIFFUSION-CONTROLLED SOLIDIFICATION; DILUTE BINARY ALLOY; NONLINEAR DYNAMICS; 2-PHASE ZONE; MUSHY ZONE; CRYSTALLIZATION; MELT; MODEL; TEMPERATURE; STABILITY

DOI:

10.1134/S1063776109050100

Web of Science ID:

ISI:000267222600010

Соавторы в МНС:

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Другие поля

Поле	Значение
Month	MAY
Publisher	MAIK NAUKA/INTERPERIODICA/SPRINGER
Address	233 SPRING ST, NEW YORK, NY 10013-1578 USA
Language	English
EISSN	1090-6509
Keywords-Plus	DIFFUSION-CONTROLLED SOLIDIFICATION; DILUTE BINARY ALLOY; NONLINEAR DYNAMICS; 2-PHASE ZONE; MUSHY ZONE; CRYSTALLIZATION; MELT; MODEL; TEMPERATURE; STABILITY
Research-Areas	Physics
Web-of-Science-Categories	Physics, Multidisciplinary
Author-Email	Dmitri.Alexandrov@usu.ru
ResearcherID-Numbers	Alexandrov, Dmitri/D-2516-2016
ORCID-Numbers	Alexandrov, Dmitri/0000-0002-6628-745X Ivanov, Alexandr/0000-0002-2490-160X
Funding-Acknowledgement	Russian Foundation for Basic Research {[}08-01-00298, 07-03-96069, 07-01-96091]; President of the Russian Federation {[}MD-4563.2008.2]
Funding-Text	This study was supported by the Russian Foundation for Basic Research (project nos. 08-01-00298, 07-03-96069 Ural, and 07-01-96091 Ural) and the Council on Grants from the President of the Russian Federation (grant no. MD-4563.2008.2).
Number-of-Cited-References	42
Usage-Count-Since-2013	4
Journal-ISO	J. Exp. Theor. Phys.
Doc-Delivery-Number	460WO