skip to main content
OSTI.GOV title logo U.S. Department of Energy
Office of Scientific and Technical Information

Title: Investigation of the stability of the flat crystallization front of a binary melt by a variational method

Abstract

The stability of the flat crystallization front of a dilute binary melt is investigated within the two-dimensional model of solidification taking into account the latent heat of fusion and the difference between thermal conductivities of the solid and liquid phases by the method of integral functionals with an unknown region of integration. The stationary problem of impurity diffusion in a crystallizing melt and heat propagation in a limited region {omega} is solved within the second-order approximation in the amplitude of deviation from a flat crystallization front. An expression for the functional is obtained whose value is proportional to the energy dissipated in the region {omega} owing to heat and mass transfer processes. The results obtained are compared with the literature data on the stability of the flat crystallization front of a binary melt.

Authors:
;  [1]
  1. National Academy of Sciences of Ukraine, Institute for Single Crystals (Ukraine), E-mail: sergey@isc.kharkov.com
Publication Date:
OSTI Identifier:
21091509
Resource Type:
Journal Article
Resource Relation:
Journal Name: Crystallography Reports; Journal Volume: 51; Journal Issue: 1; Other Information: DOI: 10.1134/S1063774506010202; Copyright (c) 2006 Nauka/Interperiodica; Article Copyright (c) 2006 Pleiades Publishing, Inc; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
36 MATERIALS SCIENCE; CRYSTALLIZATION; DIFFUSION; FUSION HEAT; HEAT; MASS TRANSFER; SOLIDIFICATION; STABILITY; THERMAL CONDUCTIVITY; VARIATIONAL METHODS

Citation Formats

Kanishchev, V. N., E-mail: vkanishev@mail.ru, and Barannik, S. V. Investigation of the stability of the flat crystallization front of a binary melt by a variational method. United States: N. p., 2006. Web. doi:10.1134/S1063774506010202.
Kanishchev, V. N., E-mail: vkanishev@mail.ru, & Barannik, S. V. Investigation of the stability of the flat crystallization front of a binary melt by a variational method. United States. doi:10.1134/S1063774506010202.
Kanishchev, V. N., E-mail: vkanishev@mail.ru, and Barannik, S. V. Sun . "Investigation of the stability of the flat crystallization front of a binary melt by a variational method". United States. doi:10.1134/S1063774506010202.
@article{osti_21091509,
title = {Investigation of the stability of the flat crystallization front of a binary melt by a variational method},
author = {Kanishchev, V. N., E-mail: vkanishev@mail.ru and Barannik, S. V.},
abstractNote = {The stability of the flat crystallization front of a dilute binary melt is investigated within the two-dimensional model of solidification taking into account the latent heat of fusion and the difference between thermal conductivities of the solid and liquid phases by the method of integral functionals with an unknown region of integration. The stationary problem of impurity diffusion in a crystallizing melt and heat propagation in a limited region {omega} is solved within the second-order approximation in the amplitude of deviation from a flat crystallization front. An expression for the functional is obtained whose value is proportional to the energy dissipated in the region {omega} owing to heat and mass transfer processes. The results obtained are compared with the literature data on the stability of the flat crystallization front of a binary melt.},
doi = {10.1134/S1063774506010202},
journal = {Crystallography Reports},
number = 1,
volume = 51,
place = {United States},
year = {Sun Jan 15 00:00:00 EST 2006},
month = {Sun Jan 15 00:00:00 EST 2006}
}