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http://elar.urfu.ru/handle/10995/101802
Название: | On the theory of the unsteady-state growth of spherical crystals in metastable liquids |
Авторы: | Alexandrov, D. V. Alexandrova, I. V. |
Дата публикации: | 2019 |
Издатель: | Royal Society Publishing |
Библиографическое описание: | Alexandrov D. V. On the theory of the unsteady-state growth of spherical crystals in metastable liquids / D. V. Alexandrov, I. V. Alexandrova. — DOI 10.1098/rsta.2018.0209 // Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences. — 2019. — Vol. 377. — Iss. 2143. — 20180209. |
Аннотация: | Motivated by a large number of applications, we consider the process of non-stationary growth of spherical crystals in a supercooled binary melt. The moving-boundary problem describing the unsteadystate distributions of temperature and impurity concentration around the growing crystal as well as the dynamics of its radius and growth rate is solved by means of the methods of small-parameter expansion and Laplace-Carson integral transform. We show that the growth rate of crystals contains the main contribution (which is proportional to the supercooling degree) and the first correction (which is proportional to 2t, where t is time). The second correction is also found. The non-stationary temperature and concentration fields are determined as power functions of and t. We demonstrate that the first corrections to the dynamics of crystal radius R(t) and its growth rate V(t) play an important role. It is shown that R(t) andV(t) can change more than twice in comparison with the previously known steady-state solution with the course of time. Such a behaviour will significantly modify the dynamics of a polydisperse ensemble of crystals evolving in a metastable liquid. This article is part of the theme issue 'Heterogeneous materials: Metastable and non-ergodic internal structures'. ©2019 The Author(s) Published by the Royal Society. |
Ключевые слова: | CRYSTAL GROWTH METASTABLE LIQUID MOVING-BOUNDARY PROBLEM PHASE TRANSFORMATION CRYSTAL GROWTH CRYSTAL IMPURITIES DYNAMICS INTEGRAL EQUATIONS LIQUIDS PHASE TRANSITIONS SUPERCOOLING CONCENTRATION FIELDS HETEROGENEOUS MATERIALS IMPURITY CONCENTRATION METASTABLE LIQUID MOVING BOUNDARY PROBLEMS PARAMETER EXPANSION STEADY STATE SOLUTION SUPERCOOLING DEGREES GROWTH RATE |
URI: | http://elar.urfu.ru/handle/10995/101802 |
Условия доступа: | info:eu-repo/semantics/openAccess |
Идентификатор SCOPUS: | 85062423309 |
Идентификатор WOS: | 000465497000007 |
Идентификатор PURE: | d10b60a5-1202-4ae0-84c2-213219e35f61 9063287 |
ISSN: | 1364503X |
DOI: | 10.1098/rsta.2018.0209 |
Располагается в коллекциях: | Научные публикации ученых УрФУ, проиндексированные в SCOPUS и WoS CC |
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Файл | Описание | Размер | Формат | |
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2-s2.0-85062423309.pdf | 619,45 kB | Adobe PDF | Просмотреть/Открыть |
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