Nucleation and growth of a new phase at the intermediate stage of phase transitions in metastable solutions and melts / Alexandrov D.V., Malygin A.P., Sukhachev I.S., Alexandrova I.V. // Vestnik Udmurtskogo Universiteta: Matematika, Mekhanika, Komp'yuternye Nauki. - 2016. - V. 26, l. 2. - P. 283-296.

ISSN:
19949197
Type:
Article
Abstract:
A complete analytical solution of an integro-differential model, which describes the intermediate stage of phase transitions in one-component melts and solutions without allowance for fluctuations in the crystal growth rates, is found. An exact analytical solution of the kinetic equation is determined within the framework of this model. The density of distribution function of crystals in sizes is found. An integro-differential equation for the system metastability level (for its supercooling/supersaturation) is derived for different kinetic mechanisms of particle nucleation. A complete analytical solution of this equation is constructed on the basis of saddle-point method for the Laplace-type integral (steepest descent method). Four approximations of the analytical solution are analyzed and its convergence is shown. The kinetic mechanisms of Weber-Volmer-Frenkel-ZePdovich and A loirs are studied. A transient behavior of the number of particles and the mean crystal size is determined for supercooled melts.
Author keywords:
Analytical solutions; Kinetics; Nucleation; Solid phase growth
Index keywords:
нет данных
DOI:
10.20537/vm160214
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https://www.scopus.com/inward/record.uri?eid=2-s2.0-85009742454&doi=10.20537%2fvm160214&partnerID=40&md5=c05d83cae80ab5442509d93bb04b5fa2
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Affiliations Department of Mathematical Physics, Laboratory of Multi-Scale Mathematical Modeling, Ural Federal University, pr. Lenina, 51, Yekaterinburg, Russian Federation; Institute of Mathematics and Computer Science, Ural Federal University, pr. Lenina, 51, Yekaterinburg, Russian Federation; Laboratory of Mathematical Modeling of Physical and Chemical Processes in Multiphase Media, Ural Federal University, pr. Lenina, 51, Yekaterinburg, Russian Federation
Author Keywords Analytical solutions; Kinetics; Nucleation; Solid phase growth
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Publisher Udmurt State University
Language of Original Document Russian
Abbreviated Source Title Vestn. Udmurt. Univ., Matematika, Mekhanika, Kompyuternye Nauki
Source Scopus