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|Title:||A complete analytical solution of the Fokker–Planck and balance equations for nucleation and growth of crystals|
|Authors:||Makoveeva, E. V.|
Alexandrov, D. V.
|Publisher:||Royal Society Publishing|
|Citation:||Makoveeva, E. V. A complete analytical solution of the Fokker–Planck and balance equations for nucleation and growth of crystals / E. V. Makoveeva, D. V. Alexandrov. — DOI 10.1098/rsta.2017.0327 // Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences. — 2018. — Vol. 2113. — Iss. 376. — 20170327.|
|Abstract:||This article is concerned with a new analytical description of nucleation and growth of crystals in a metastable mushy layer (supercooled liquid or supersaturated solution) at the intermediate stage of phase transition. The model under consideration consisting of the non-stationary integro-differential system of governing equations for the distribution function and metastability level is analytically solved by means of the saddle-point technique for the Laplace-type integral in the case of arbitrary nucleation kinetics and time-dependent heat or mass sources in the balance equation. We demonstrate that the time-dependent distribution function approaches the stationary profile in course of time. This article is part of the theme issue ‘From atomistic interfaces to dendritic patterns’. © 2018 The Author(s) Published by the Royal Society. All rights reserved.|
NUCLEATION AND GROWTH
|metadata.dc.description.sponsorship:||Российский Фонд Фундаментальных Исследований (РФФИ), RFBR: 16-08-00932|
Data accessibility. This article has no additional data. Authors’ contributions. All authors contributed equally to this article. Competing interests. We declare we have no competing interests. Funding. This work was supported by the Russian Foundation for Basic Research (grant no. 16-08-00932).
|Appears in Collections:||Научные публикации, проиндексированные в SCOPUS и WoS CC|
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