Evolution of cluster size distribution in nucleation and growth processes

Bartels, J.; Lembke, U.; Pascova, R.; Schmelzer, Jürn W. P.; Gutzow, I.

doi:10.1016/0022-3093(91)90489-s

Cited by 58 publications

(28 citation statements)

References 23 publications

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“…The process of the evolution of the cluster size distribution in this particular system was analyzed for the first partly long ago [14,52] and extended to late stages of the evolution quite recently [53]. However, in these previous analysesfollowing the standard approach employed so far-it was assumed that the composition of the clusters is widely identical to the composition of the newly evolving phase.…”

Section: Time Evolution Of the Cluster Ensemblesmentioning

confidence: 99%

See 1 more Smart Citation

Dynamics of first-order phase transitions in multicomponent systems: a new theoretical approach

Schmelzer

Gokhman

Fokin

2004

Journal of Colloid and Interface Science

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Section: Time Evolution Of the Cluster Ensemblesmentioning

confidence: 99%

“…In the determination of the parameters, we will refer here to segregation processes in glass-forming melts (segregation of an AgCl-phase in a sodium borate glass) investigated intensively earlier [52,53]. As a first parameter, we fix the average volume per particle as ω α = ω β ∼ = 4.89 × 10 −29 m 3 .…”

Section: Time Evolution Of the Cluster Ensemblesmentioning

confidence: 99%

Dynamics of first-order phase transitions in multicomponent systems: a new theoretical approach

Schmelzer

Gokhman

Fokin

2004

Journal of Colloid and Interface Science

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“…Then, the present nuclei immediately start growing, whereas, at the same time, the homogeneous nucleation of additional magnetite crystallites is delayed by the so-called nucleation time lag. 13,14 Consequently, under these circumstances, two generations of particles of the same phase can develop which have well distinguishable mean dimensions. Another scenario that can lead to bimodal-type size distributions does not need the suggestion of heterogeneous or athermal nuclei, but is based on homogeneous nucleation and diffusion-limited growth only.…”

Section: Figmentioning

confidence: 99%

Formation of magnetic nanocrystals in a glass ceramic studied by small-angle scattering

Lembke

Hoell

Kranold

et al. 1999

Journal of Applied Physics

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The formation of nanosized crystallites of magnetite, Fe 3 O 4 , by heat treatment of a glass containing iron oxide was investigated. The magnetic properties of the glass ceramic manufactured strongly depend on the heat treatment conditions. The evolution of size distribution and volume fraction of the nanocrystallites formed was studied by small-angle x-ray scattering ͑SAXS͒. The size distribution of the nanocrystalline phase turned out to show bimodal shape. The possibility of magnetic contrast variation offered by small-angle neutron scattering ͑SANS͒ was utilized in order to distinguish the small-angle scattering of magnetite from the scattering contributions of nonmagnetic iron containing crystallites that can additionally be formed during the heat treatment. The results obtained reveal that both size grades of particles observed in the size distribution are superparamagnetic consisting of magnetite. The evolution of the volume fraction of magnetite in dependence on the heat treatment was found to be correlated with the magnitude of the specific saturation magnetization of the glass ceramic. The volume size distributions derived from magnetic SANS revealed peaks at smaller radii in relation to those from nuclear SANS and SAXS data. Therefore, the existence of a nonmagnetic surface layer is suggested that surrounds the magnetically active core of the magnetite nanocrystals.

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“…By this reason, a comparison of our approach with an earlier application 11 A similar to 11 but more comprehensive numerical analysis of the evolution of cluster size distributions in nucleation-growth processes was performed by us in 14,15 in order to interpret experimental results on segregation in solutions and in 16 in order to compare analytical computations on the characteristics of nucleation and growth processes 5,8 with results of numerical computations. These results of numerical computations are implemented also in Chapter 5 of the recent monograph 9 of one of the authors of the LSW-theory, V. V. Slezov.…”

Section: A Further Commentmentioning

confidence: 99%

“…2,11 The transition from nucleation to coarsening employing essentially the same equations is studied in detail in cited references. 9,[14][15][16] In their first fundamental theoretical analysis of Ostwald ripening, 12,17 Lifshitz and Slezov employed the term "coalescence" in a meaning identical to diffusion-limited or kinetic limited coarsening not accounting first initially for possible coagulation of large clusters. Such and a variety of additional effects have been incorporated later by Slezov and colleagues (c.f.…”

Section: A Further Commentmentioning

confidence: 99%

On the theoretical description of nucleation in confined space

Schmelzer

Abyzov

2011

AIP Advances

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In a recent paper, Kozisek [J. Chem. Phys. 134, 094508 (2011)] have demonstrated for four different cases of phase formation that the work of formation of critical clusters required to form in the system in some given time a first experimentally measurable cluster of the new phase depends in a logarithmic way on the volume of the system. This result was obtained based on the numerical solution of the kinetic equations describing nucleation and growth processes and the obtained in this way steady-state cluster size distributions. Here a straightforward alternative analytical interpretation of this result is proposed by computing directly the mean expectation times of formation of supercritical clusters. It is proven strictly that this result is generally independent of the kind of nucleation (homogeneous or heterogeneous) or specific realization (condensation, cavitation, crystallization, segregation, etc.) considered. It is shown that such behavior is simply a consequence of the linear dependence of the steady-state nucleation rate on the volume of the system, neither time-lag or primary depletion (due to the establishment of steady-state cluster size distributions for subcritical clusters) or secondary depletion (caused by the change of the state of the ambient phase due to the formation and growth of supercritical clusters and connected with finite size effects) are required for the interpretation of such result. In a second step, this analytical result is extended accounting for the growth of the supercritical cluster to directly measurable sizes. Finally, an analytical foundation of the method of determination of the critical supersaturation as employed by Kozisek is developed and the results obtained via the computation and analysis of steady-state cluster size distributions and calculation of mean expectation times for formation of the first supercritical clusters are compared. Some further general problems of nucleation and growth in finite closed systems are discussed, in addition

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Evolution of cluster size distribution in nucleation and growth processes

Cited by 58 publications

References 23 publications

Dynamics of first-order phase transitions in multicomponent systems: a new theoretical approach

Dynamics of first-order phase transitions in multicomponent systems: a new theoretical approach

Formation of magnetic nanocrystals in a glass ceramic studied by small-angle scattering

On the theoretical description of nucleation in confined space

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