Density functional theory of nucleation: A semiempirical approach

Nyquist, Rebecca M.; Talanquer, Vicente; Oxtoby, David W.

doi:10.1063/1.469827

Cited by 72 publications

(41 citation statements)

References 24 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The experiments indicate that classical nucleation theory ͑CNT͒ works fairly well for one-component systems of simple, nonpolar molecules. 4,8 In particular, CNT predicts the size of critical nuclei surprisingly well. However, for binary systems the agreement between the experimental observations and the predictions of CNT is worse.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Numerical study of gas–liquid nucleation in partially miscible binary mixtures

Wolde

Frenkel

1998

The Journal of Chemical Physics

View full text Add to dashboard Cite

We report a numerical study of homogeneous gas-liquid nucleation in a binary mixture. We study the size and the composition of the critical nucleus as a function of the composition and supersaturation of the vapor. As we make the ͑Lennard-Jones͒ mixture increasingly nonideal, we find that there is a regime where the critical nucleus is still miscible in all proportions, even though the bulk liquid phase is not. When these critical nuclei grow, their composition ''bifurcates'' to approach the value of one of the two bulk phases. For more strongly nonideal mixtures, the two species in the critical nucleus are no longer completely miscible: we observe droplets that are either rich in one species, or in the other. However, we do not find evidence for phase separation inside the critical nucleus-a scenario suggested by Talanquer and Oxtoby ͓J. Chem. Phys. 104, 1993 ͑1996͔͒. In fact, our simulations show that such demixed clusters have a higher free energy than critical nuclei that have an asymmetric composition.

show abstract

Section: Introductionmentioning

confidence: 99%

“…[1][2][3][4][5][6][7][8] From the measured nucleation rates, one can deduce the size and composition of the critical nuclei. 9 Such information makes it possible to test nucleation theories in much more detail than was hitherto possible.…”

Section: Introductionmentioning

confidence: 99%

Numerical study of gas–liquid nucleation in partially miscible binary mixtures

Wolde

Frenkel

1998

The Journal of Chemical Physics

View full text Add to dashboard Cite

show abstract

mentioning

confidence: 99%

“…Since the physical interface thickness is comparable to the typical size of critical fluctuations that are able to grow to macroscopic sizes, these fluctuations are nearly all interface. Accordingly, the diffuse interface models lead to a considerably more accurate description of nucleation than those based on a sharp interface [1,2].The phase field theory, a recent diffuse interface approach, emerged as a powerful tool for describing complex solidification patterns such as dendritic, eutectic, and peritectic growth morphologies [3]. It is of interest to extend this model to nucleation and post-nucleation growth including diffusion controlled "soft-impingement" of growing crystalline particles, expected to be responsible for the unusual transformation kinetics recently seen during the formation of nanocrystalline materials [4].…”

mentioning

confidence: 99%

Nucleation and Bulk Crystallization in Binary Phase Field Theory

2002

View full text Add to dashboard Cite

We present a phase field theory for binary crystal nucleation. In the one-component limit, quantitative agreement is achieved with computer simulations (Lennard-Jones system) and experiments (ice-water system) using model parameters evaluated from the free energy and thickness of the interface. The critical undercoolings predicted for Cu-Ni alloys accord with the measurements, and indicate homogeneous nucleation. The Kolmogorov exponents deduced for dendritic solidification and for "soft-impingement" of particles via diffusion fields are consistent with experiment.PACS numbers: 81.10. Aj, 82.60.Nh, 64.60.Qb Understanding alloy solidification is of vast practical and theoretical importance. While the directional geometry in which the solidification front propagates from a cool surface towards the interior of a hot melt is understood fairly well, less is known of equiaxial solidification that takes place in the interior of the melt. The latter plays a central role in processes such as alloy casting, hibernation of biological tissues, hail formation, and crystallization of proteins and glasses. The least understood stage of these processes is nucleation, during which seeds of the crystalline phase appear via thermal fluctuations. Since the physical interface thickness is comparable to the typical size of critical fluctuations that are able to grow to macroscopic sizes, these fluctuations are nearly all interface. Accordingly, the diffuse interface models lead to a considerably more accurate description of nucleation than those based on a sharp interface [1,2].The phase field theory, a recent diffuse interface approach, emerged as a powerful tool for describing complex solidification patterns such as dendritic, eutectic, and peritectic growth morphologies [3]. It is of interest to extend this model to nucleation and post-nucleation growth including diffusion controlled "soft-impingement" of growing crystalline particles, expected to be responsible for the unusual transformation kinetics recently seen during the formation of nanocrystalline materials [4].In this Letter, we develop a phase field theory for crystal nucleation and growth, and apply it to current problems of unary and binary equiaxial solidification.Our starting point is the free energy functionaldeveloped along the lines described in [5,6]. Here φ and c are the phase and concentration fields, f (φ, c) = W T g(φ) + [1 − P (φ)]f S + P (φ)f L is the local free energy density, W = (1 − c)W A + cW B the free energy scale, the quartic function g(φ) = φ 2 (1 − φ) 2 /4 that emerges from density functional theory [7] ensures the doublewell form of f , while the function P (φ) = φ 3 (10 − 15φ + 6φ 2 ) switches on and off the solid and liquid contributions f S,L , taken from the ideal solution model. (A and B refer to the constituents.) For binary alloys the model contains three parameters ǫ, W A and W B that reduce to two (ǫ and W ) in the one-component limit. They can be fixed if the respective interface free energy γ, melting point T f , and interface thickn...

show abstract

“…17,28 Numerous theoretical studies concerning n-nonane nucleation exist. Nyquist et al 29 computed the work of formation of critical n-nonane clusters using density functional theory with either the Yukawa potential and the LennardJones potential. They found that the two computations almost overlapped.…”

Section: Introductionmentioning

confidence: 99%

Gradient theory computation of the radius-dependent surface tension and nucleation rate for n-nonane clusters

Hrubý

Labetski

Dongen

2007

The Journal of Chemical Physics

View full text Add to dashboard Cite

The Van der Waals-Cahn-Hilliard gradient theory ͑GT͒ is applied to determine the structure and the work of formation of clusters in supersaturated n-nonane vapor. The results are analyzed as functions of the difference of pressures of the liquid phase and vapor phase in chemical equilibrium, which is a measure for the supersaturation. The surface tension as a function of pressure difference shows first a weak maximum and then decreases monotonically. The computed Tolman length is in agreement with earlier results ͓L. Gránásy, J. Chem. Phys. 109, 9660 ͑1998͔͒ obtained with a different equation of state. A method based on the Gibbs adsorption equation is developed to check the consistency of GT results ͑or other simulation techniques providing the work of formation and excess number of molecules͒, and to enable an efficient interpolation. A cluster model is devised based on the density profile of the planar phase interface. Using this model we analyze the dependency of the surface tension on the pressure difference. We find three major contributions: ͑i͒ the effect of asymmetry of the density profile resulting into a linear increase of the surface tension, ͑ii͒ the effect of finite thickness of the phase interface resulting into a negative quadratic term, and ͑iii͒ the effect of buildup of a low-density tail of the density profile, also contributing as a negative quadratic term. Contributions ͑i͒-͑iii͒ fully explain the dependency of the surface tension on the pressure difference, including the range relevant to nucleation experiments. Contributions ͑i͒ and ͑ii͒ can be predicted from the planar density profile. The work of formation of noncritical clusters is derived and the nucleation rate is computed. The computed nucleation rates are closer to the experimental nucleation rate results than the classical Becker-Döring theory, and also the dependence on supersaturation is better predicted.

show abstract

Density functional theory of nucleation: A semiempirical approach

Cited by 72 publications

References 24 publications

Numerical study of gas–liquid nucleation in partially miscible binary mixtures

Numerical study of gas–liquid nucleation in partially miscible binary mixtures

Nucleation and Bulk Crystallization in Binary Phase Field Theory

Gradient theory computation of the radius-dependent surface tension and nucleation rate for n-nonane clusters

Contact Info

Product

Resources

About