Relaxation dynamics of the phase transformation process at its ripening stage / Alexandrov D.V. // Journal of Physics A: Mathematical and Theoretical. - 2015. - V. 48, l. 24.

ISSN:
17518113
Type:
Article
Abstract:
A complete analytical solution of the integro-differential model describing the transient phase transformation process at the Ostwald ripening stage is constructed. A new theoretical approach developed here is based on the recent theory (Alexandrov 2015 J. Phys. A: Math. Theor. 48 035103), where a new method was developed to account for the initial state (initial distribution function) at the ripening stage. The obtained relaxation solution contains two contributions proportional to e-τ (classical term) and e-4τ/3 (the term predicted by Slezov), where τ is the dimensionless time. The distribution function obtained is more broad than the Lifshitz-Slyozov solution, lies below it, and has a supplementary tail on the right of the blocking point u = 3/2, where u is the dimensionless spatial coordinate. The distribution function relaxes to earlier known solutions and is in good agreement with experimental data. The dynamics of number density and average radius of crystals is studied. The role of 'diffusion' term in the kinetic equation is discussed. © 2015 IOP Publishing Ltd.
Author keywords:
LifshitzSlyozov asymptotic solution; Ostwald ripening; relaxation dynamics; universal distribution
Index keywords:
нет данных
DOI:
10.1088/1751-8113/48/24/245101
Смотреть в Scopus:
https://www.scopus.com/inward/record.uri?eid=2-s2.0-84934876280&doi=10.1088%2f1751-8113%2f48%2f24%2f245101&partnerID=40&md5=1e825f2312ff131f63016121d2468c54
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Art. No. 245101
Link https://www.scopus.com/inward/record.uri?eid=2-s2.0-84934876280&doi=10.1088%2f1751-8113%2f48%2f24%2f245101&partnerID=40&md5=1e825f2312ff131f63016121d2468c54
Affiliations Department of Mathematical Physics, Ural Federal University, Lenin ave., 51, Ekaterinburg, Russian Federation
Author Keywords LifshitzSlyozov asymptotic solution; Ostwald ripening; relaxation dynamics; universal distribution
Funding Details 13-01-96013-Ural, RFBR, Ministry of Education and Science of the Russian Federation; 315, Ministry of Education and Science of the Russian Federation
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Correspondence Address Alexandrov, D.V.; Department of Mathematical Physics, Ural Federal University, Lenin ave., 51, Russian Federation
Publisher Institute of Physics Publishing
Language of Original Document English
Abbreviated Source Title J. Phys. Math. Theor.
Source Scopus