The kinetics of crystal growth and dissolution from the melt in Lennard-Jones systems

Báez, Luis A.; Clancy, Paulette

doi:10.1063/1.469225

Cited by 51 publications

(34 citation statements)

References 25 publications

(32 reference statements)

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“…Although a rigorous derivation of these notions is unavailable for crystallites, a quantity analogous to δ T has recently been evaluated from computer simulations [2]. It decreases with increasing size of the fluctuations.…”

Section: A Phase Field Theory Of Nucleationmentioning

confidence: 99%

“…The description of such fluctuations is problematic even in single component systems. One of the main difficulties is that the typical size of the critical fluctuations that form on the human time scale [1,2,3,4,5] is comparable to the thickness of the crystalliquid interface, which in turn extends to several molecular layers [6,7,8]. Therefore, the droplet model of the classical nucleation theory (CNT) that relies on a sharp interface and bulk crystal properties is expected to be inappropriate for describing such fluctuations.…”

Section: Introductionmentioning

confidence: 99%

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Phase field theory of crystal nucleation in hard sphere liquid

Gránásy

Pusztai

Tóth

et al. 2003

The Journal of Chemical Physics

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The phase field theory of crystal nucleation described in [L. Gránásy, T. Börzsönyi, T. Pusztai, Phys. Rev. Lett. 88, 206105 (2002)] is applied for nucleation in hard-sphere liquids. The exact thermodynamics from molecular dynamics is used. The interface thickness for phase field is evaluated from the cross-interfacial variation of the height of the singlet density peaks. The model parameters are fixed in equilibrium so that the free energy and thickness of the (111), (110), and (100) interfaces from molecular dynamics are recovered. The density profiles predicted without adjustable parameters are in a good agreement with the filtered densities from the simulations. Assuming spherical symmetry, we evaluate the height of the nucleation barrier and the Tolman length without adjustable parameters. The barrier heights calculated with the properties of the (111) and (110) interfaces envelope the Monte Carlo results, while those obtained with the average interface properties fall very close to the exact values. In contrast, the classical sharp interface model considerably underestimates the height of the nucleation barrier. We find that the Tolman length is positive for small clusters and decreases with increasing size, a trend consistent with computer simulations.

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Section: A Phase Field Theory Of Nucleationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Phase field theory of crystal nucleation in hard sphere liquid

Gránásy

Pusztai

Tóth

et al. 2003

The Journal of Chemical Physics

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“…ǫ = 137.07k and σ = 3.383Å are taken for Ar. Below 61.7 K, the simulations increasingly underestimate the true nucleation rate due to an unknown equilibration period caused by quenching the liquid to the nucleation temperature [15].…”

mentioning

confidence: 99%

“…Here F is obtained by numerically evaluating Eq. (1) after having the time-independent solutions inserted, while F 0 is the free energy of the initial [15]. Short-dashed lines show the limits of nucleation rate allowed by the error of the interfacial free energy.…”

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confidence: 99%

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Nucleation and Bulk Crystallization in Binary Phase Field Theory

2002

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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...

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Nucleation and Surface Melting of Ice

Oxtoby

1999

Ice Physics and the Natural Environment

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The kinetics of crystal growth and dissolution from the melt in Lennard-Jones systems

Abstract: Crystal growth and interface relaxation rates from fluctuations in an equilibrium simulation of the Lennard-Jones (100) crystal-melt system Simulations of crystal growth from Lennard-Jones melt: Detailed measurements of the interface structure

Cited by 51 publications

References 25 publications

Phase field theory of crystal nucleation in hard sphere liquid

Phase field theory of crystal nucleation in hard sphere liquid

Nucleation and Bulk Crystallization in Binary Phase Field Theory

Nucleation and Surface Melting of Ice

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