Stationary nucleation

Kashchiev, Dimo

doi:10.1016/b978-075064682-6/50014-7

Cited by 152 publications

(350 citation statements)

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“…To resolve these issues, we make use of a variation of the original nucleation theorem by Kashchiev [2,49], which links the variation of the pressure difference as a function of the ambient chemical potential to the density inside the solid droplet. This thermodynamic route bypasses the difficulties to employ the mechanical route from the pressure tensor, which is ill-defined for small droplets [65,66].…”

Section: Resultsmentioning

confidence: 99%

“…Here, ∆N c = N s + N l + N x − ρ l V is the number of additional particles present for critical droplets compared to a homogeneous liquid with density ρ l = N l /V l at volume V . This relation can be used to evaluate ∆F c for a large range of supersaturations by computing the function ∆N (µ l ) and evaluating, for one reference state point µ 0 , the nucleation work ∆F c (µ 0 ) (for example using FFS) [2],…”

Section: Nucleation Theoremmentioning

confidence: 99%

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Crystallization of hard spheres revisited. II. Thermodynamic modeling, nucleation work, and the surface of tension

Richard

Speck

2018

The Journal of Chemical Physics

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Combining three numerical methods (forward flux sampling, seeding of droplets, and finite-size droplets), we probe the crystallization of hard spheres over the full range from close to coexistence to the spinodal regime. We show that all three methods allow us to sample different regimes and agree perfectly in the ranges where they overlap. By combining the nucleation work calculated from forward flux sampling of small droplets and the nucleation theorem, we show how to compute the nucleation work spanning three orders of magnitude. Using a variation of the nucleation theorem, we show how to extract the pressure difference between the solid droplet and ambient liquid. Moreover, combining the nucleation work with the pressure difference allows us to calculate the interfacial tension of small droplets. Our results demonstrate that employing bulk quantities yields inaccurate results for the nucleation rate.

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Section: Resultsmentioning

confidence: 99%

Section: Nucleation Theoremmentioning

confidence: 99%

Crystallization of hard spheres revisited. II. Thermodynamic modeling, nucleation work, and the surface of tension

Richard

Speck

2018

The Journal of Chemical Physics

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“…These assumptions are generally based on considerations of statistical mechanics expressed in terms of the free energy of assemblies of proteins. See Kashchiev [20]. With a slight abuse of notation we will say that nucleation has occurred when a polymer of size nc has been created for the first time.…”

Section: Introductionmentioning

confidence: 99%

On the Asymptotic Distribution of Nucleation Times of Polymerization Processes

Pierpoint¹,

Sun²

2019

SIAM J. Appl. Math.

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In this paper, we investigate a stochastic model describing the time evolution of a polymerization process. A polymer is a macro-molecule resulting from the aggregation of several elementary sub-units called monomers. Polymers can grow by addition of monomers or can be split into several polymers. The initial state of the system consists mainly of monomers. We study the time evolution of the mass of polymers, in particular the asymptotic distribution of the first instant when the fraction of monomers used in polymers is above some positive threshold δ. A scaling approach is used by taking the mass N as a scaling parameter. The mathematical model used in this paper includes a nucleation property: If nc is defined as the size of the nucleus, polymers with a size less than nc are quickly fragmented into smaller polymers, at a rate proportional to Φ(N ) for some non-decreasing and unbounded function Φ. For polymers of size greater than nc, fragmentation still occurs but at bounded rates. If T N is the instant of creation of the first polymer whose size is nc, it is shown that, under appropriate conditions, the variable T N /[Φ(N ) nc−2 /N ] converges in distribution, and that the first instant L N δ when a fraction δ of monomers is polymerized has the same order of magnitude. An original feature proved for this model is the significant variability of the variable T N . This is a well known phenomenon observed in biological experiments but few mathematical models of the literature have this property. The results are proved via a series of technical estimates for occupation measures of some functionals of the corresponding Markov processes on fast time scales and by using coupling techniques.

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“…By combining Eqs. [21] and [22], one can derive the unique solution for C c and C m . In Figure 2(b), the diffusion fields for ferrite grains 1 and 2 intersect at point m. This means that the diffusion length for grain 1 cannot extend beyond point m (and similarly for grain 2).…”

Section: Soft Impingementmentioning

confidence: 99%

“…The number of ferrite nuclei formed is calculated using classical nucleation theory (CNT). [21][22][23] The moving austenite-ferrite interface is treated as progressing under mixed-mode [24] conditions. Analytical expressions for the carbon concentration at the interface and far away from the interface are derived for non-overlapping and overlapping of diffusion fields (soft impingement).…”

Section: Model Descriptionmentioning

confidence: 99%

Analysis of the Grain Size Evolution for Ferrite Formation in Fe-C-Mn Steels Using a 3D Model Under a Mixed-Mode Interface Condition

Fang

Mecozzi

Brück

et al. 2017

Metall Mater Trans A

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A 3D model has been developed to predict the average ferrite grain size and grain size distribution for an austenite-to-ferrite phase transformation during continuous cooling of an Fe-C-Mn steel. Using a Voronoi construction to represent the austenite grains, the ferrite is assumed to nucleate at the grain corners and to grow as spheres. Classical nucleation theory is used to estimate the density of ferrite nuclei. By assuming a negligible partition of manganese, the moving ferrite-austenite interface is treated with a mixed-mode model in which the soft impingement of the carbon diffusion fields is considered. The ferrite volume fraction, the average ferrite grain size, and the ferrite grain size distribution are derived as a function of temperature. The results of the present model are compared with those of a published phase-field model simulating the ferritic microstructure evolution during linear cooling of an Fe-0.10C-0.49Mn (wt pct) steel. It turns out that the present model can adequately reproduce the phase-field modeling results as well as the experimental dilatometry data. The model presented here provides a versatile tool to analyze the evolution of the ferrite grain size distribution at low computational costs.

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Stationary nucleation

Cited by 152 publications

References 0 publications

Crystallization of hard spheres revisited. II. Thermodynamic modeling, nucleation work, and the surface of tension

Crystallization of hard spheres revisited. II. Thermodynamic modeling, nucleation work, and the surface of tension

On the Asymptotic Distribution of Nucleation Times of Polymerization Processes

Analysis of the Grain Size Evolution for Ferrite Formation in Fe-C-Mn Steels Using a 3D Model Under a Mixed-Mode Interface Condition

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