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Russia Yekaterinburg
Section Mechanics
Title Nucleation and growth of a new phase at the intermediate stage of phase transitions in metastable solutions and melts
Author(-s) Alexandrov D.V.a, Malygin A.P.a, Sukhachev I.S.a, Alexandrova I.V.a
Affiliations Ural Federal Universitya
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-Zel’dovich and Meirs are studied. A transient behavior of the number of particles and the mean crystal size is determined for supercooled melts.
Keywords nucleation, kinetics, solid phase growth, analytical solutions
UDC 532.78
MSC 80A20, 80A22
DOI 10.20537/vm160214
Received 23 May 2016
Language Russian
Citation Alexandrov D.V., Malygin A.P., Sukhachev I.S., Alexandrova I.V. Nucleation and growth of a new phase at the intermediate stage of phase transitions in metastable solutions and melts, Vestnik Udmurtskogo Universiteta. Matematika. Mekhanika. Komp'yuternye Nauki, 2016, vol. 26, issue 2, pp. 283-296.
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