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:

17518113

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 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. © 2015 IOP Publishing Ltd.

Author keywords:

Lifshitz-Slyozov asymptotic solution; Ostwald ripening; universal distribution

Index keywords:

нет данных

DOI:

10.1088/1751-8113/48/3/035103

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https://www.scopus.com/inward/record.uri?eid=2-s2.0-84920089885&doi=10.1088%2f1751-8113%2f48%2f3%2f035103&partnerID=40&md5=2d5b38100aa810868797e69ede535429

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Поле	Значение
Art. No.	035103
Link	https://www.scopus.com/inward/record.uri?eid=2-s2.0-84920089885&doi=10.1088%2f1751-8113%2f48%2f3%2f035103&partnerID=40&md5=2d5b38100aa810868797e69ede535429
Affiliations	Department of Mathematical Physics, Ural Federal University, Lenin ave. 51, Ekaterinburg, Russian Federation
Author Keywords	Lifshitz-Slyozov asymptotic solution; Ostwald ripening; universal distribution
Funding Details	02.A03.21.0006, Russian Foundation for Basic Research; 13-01-96013-Ural, RFBR, Russian Foundation for Basic Research; 315, Russian Foundation for Basic Research
References	Ostwald, W., Blocking of Ostwald ripening allowing long-term stabilization (1901) Z. Phys. Chem., 37, pp. 385-390; Lifshitz, I.M., Slyozov, V.V., Kinetics of diffusive decomposition of supersaturated solid solutions (1959) Sov. Phys.-JETP, 8, pp. 331-339; Lifshitz, I.M., Slyozov, V.V., The kinetics of precipitation from supersaturated solid solutions (1961) J. Phys. Chem. Solids, 19, pp. 35-50; Wagner, C., Theorie der Alterung von Niederschlägen durch Umlösen (Ostwald-Reifung) (1961) Z. Elektrochem., 65, pp. 581-591; Slezov, V.V., Formation of the universal distribution function in the dimension space for new-phase particles in the diffusive decomposition of the supersaturated solid solution (1978) J. Phys. Chem. Solids, 39, pp. 367-374; Marder, M., Correlations and Ostwald ripening (1987) Phys. Rev., 36, pp. 858-874; Yao, J.H., Elder, K.R., Guo, H., Grant, M., Theory and simulation of Ostwald ripening (1993) Phys. Rev., 47, pp. 14110-14125; Penrose, O., The Becker-Döring equations at large times and their connection with the LSW theory of coarsening (1997) J. Stat. Phys., 89, pp. 305-320; Rubinstein, I., Zaltzman, B., Diffusional mechanism of strong selection in Ostwald ripening (2000) Phys. Rev., 61, pp. 709-717; Burlakov, V.M., Ostwald ripening in rarefied systems (2006) Phys. Rev. Lett., 97; Slezov, V.V., (2009) Kinetics of First-Order Phase Transitions; Shneidman, V.A., Early stages of Ostwald ripening (2013) Phys. Rev., 88; Ratke, L., Voorhees, P., (2002) Growth and Coarsening: Ostwald Ripening in Material Processing; Balluffi, R.W., Allen, S.M., Carter, W.C., (2005) Kinetics of Materials; Sagui, C., Ogorman, D.S., Grant, M., Nucleation, growth and coarsening in phase-separating systems (1998) Scanning Microsc., 12, pp. 3-8; Dubrovskii, V.G., Kazansky, M.A., Nazarenko, M.V., Adzhemyan, L.T., Numerical analysis of Ostwald ripening in two-dimensional systems (2011) J. Chem. Phys., 134; Lifshitz, E.M., Pitaevskii, L.P., (1981) Physical Kinetics; Sagui, C., Grant, M., Theory of nucleation and growth during phase separation (1999) Phys. Rev., 59, pp. 4175-4187; Ratke, L., Beckermann, C., Concurrent growth and coarsening of spheres (2001) Acta Mater., 49, pp. 4041-4054; Alexandrov, D.V., Malygin, A.P., Nucleation kinetics and crystal growth with fluctuating rates at the intermediate stage of phase transitions (2014) Modelling Simul. Mater. Sci. Eng., 22 (1); Alexandrov, D.V., Nizovtseva, I.G., Nucleation and particle growth with fluctuating rates at the intermediate stage of phase transitions in metastable systems (2014) Proc. R. Soc., 470; Alexandrov, D.V., Nucleation and crystal growth in binary systems (2014) J. Phys. A: Math. Theor., 47
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