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, SI.

ISSN/EISSN:

1751-8113 / 1751-8121

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(-tau) (classical term) and e-4 tau/3 (the term predicted by Slezov), where tau 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.

Author keywords:

Ostwald ripening; Lifshitz-Slyozov asymptotic solution; universal distribution; relaxation dynamics SUPERSATURATED SOLID SOLUTIONS; DIFFUSIVE DECOMPOSITION; KINETICS; GROWTH

DOI:

10.1088/1751-8113/48/24/245101

Web of Science ID:

ISI:000355253100004

Соавторы в МНС:

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Другие поля

Поле	Значение
Month	JUN 19
Publisher	IOP PUBLISHING LTD
Address	TEMPLE CIRCUS, TEMPLE WAY, BRISTOL BS1 6BE, ENGLAND
Language	English
Article-Number	245101
EISSN	1751-8121
Keywords-Plus	SUPERSATURATED SOLID SOLUTIONS; DIFFUSIVE DECOMPOSITION; KINETICS; GROWTH
Research-Areas	Physics
Web-of-Science-Categories	Physics, Multidisciplinary; Physics, Mathematical
Author-Email	dmitri.alexandrov@urfu.ru
ResearcherID-Numbers	Alexandrov, Dmitri/D-2516-2016
ORCID-Numbers	Alexandrov, Dmitri/0000-0002-6628-745X
Funding-Acknowledgement	Russian Foundation for Basic Research and the Government of Sverdlovsk Region {[}13-01-96013-Ural]; Ministry of Education and Science of the Russian Federation {[}315]
Funding-Text	This work was supported by the Russian Foundation for Basic Research and the Government of Sverdlovsk Region {[}grant number 13-01-96013-Ural] and by the Ministry of Education and Science of the Russian Federation {[}grant number 315].
Number-of-Cited-References	20
Usage-Count-Since-2013	2
Journal-ISO	J. Phys. A-Math. Theor.
Doc-Delivery-Number	CJ1OK