On the theory of Ostwald ripening: formation of the universal distribution / Alexandrov D. V. // JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL. - 2015. - V. 48, l. 3.

ISSN/EISSN:

1751-8113 / 1751-8121

Type:

Article

Abstract:

A theoretical description of the final stage of Ostwald ripening given by Lifshitz and Slyozov (LS) predicts that after long times the distribution of particles over sizes tends to a universal form. A qualitative behavior of their theory has been confirmed, but experimental particle size distributions are more broad and squat than the LS asymptotic solution. The origin of discrepancies between the theory and experimental data is caused by the relaxation of solutions from the early to late stages of Ostwald ripening. In other words, the initial conditions at the ripening stage lead to the formation of a transition region near the blocking point of the LS theory and completely determine the distribution function. A new theoretical approach of the present analysis based on the Slezov theory (Slezov 1978 Formation of the universal distribution function in the dimension space for new-phase particles in the diffusive decomposition of the supersaturated solid solution J. Phys. Chem. Solids 39 367-74; Slezov 2009 Kinetics of First-Order Phase Transitions (Weinheim: Wiley, VCH)) focuses on a relaxation dynamics of analytical solutions from the early stage of Ostwald ripening to its concluding state, which is described by the LS asymptotic regime. An algebraic equation for the boundaries of a transition layer independent of all material parameters is derived. A time-dependent function epsilon(tau) responsible for the evolution of solutions at the ripening stage is found. The distribution function obtained is more broad and flat than the LS asymptotic solution. The particle radius, supersaturation and number density as functions of time are determined. The analytical solutions obtained are in good agreement with experimental data.

Author keywords:

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

DOI:

10.1088/1751-8113/48/3/035103

Web of Science ID:

ISI:000346960900006

Соавторы в МНС:

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Другие поля

Поле	Значение
Month	JAN 23
Publisher	IOP PUBLISHING LTD
Address	TEMPLE CIRCUS, TEMPLE WAY, BRISTOL BS1 6BE, ENGLAND
Language	English
Article-Number	035103
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	Ministry of Education and Science of the Russian Federation {[}315, 02.A03.21.0006]; Russian Foundation for Basic Research {[}13-01-96013-Ural]
Funding-Text	Partial support from the Ministry of Education and Science of the Russian Federation (project nos. 315 and 02.A03.21.0006) and from the Russian Foundation for Basic Research (grant 13-01-96013-Ural) is acknowledged.
Number-of-Cited-References	22
Usage-Count-Last-180-days	1
Usage-Count-Since-2013	41
Journal-ISO	J. Phys. A-Math. Theor.
Doc-Delivery-Number	AX5IZ