Diffusivity, Interfacial Free Energy, and Crystal Nucleation in a Supercooled Lennard-Jones Liquid

Tipeev, Azat O.; Zanotto, Edgar D.; Rino, José P.

doi:10.1021/acs.jpcc.8b10637

Cited by 44 publications

(51 citation statements)

References 106 publications

(289 reference statements)

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“…The effective surface energy of crystal-phase critical nuclei decreases linearly with increasing pressure in cases when pressure increase results in an increase of the degree of metastability. These results have been reconfirmed and further advanced in [87]. A linear increase of the surface tension with temperature was obtained by MD simulations of Ni and Al recently in [88].…”

Section: Brief Comparison With Experimental Data and Computer Simulatsupporting

confidence: 53%

“…This incorrect approach they had to compensate by curvature corrections to the surface tension, resulting in an increase of the surface tension with decreasing temperature or decreasing critical cluster size in order to arrive at an agreement between theory and simulation. This result is in contradiction with experimental data, molecular dynamics simulations, and theoretical predictions as summarized above and reconfirmed quite recently in [80,87]. (xii) Finally, being able to describe nucleation rate data by reaching an agreement between theory and experiment for only one selected temperature is commonly not considered as a convincing proof of the validity of the theoretical approach.…”

Section: Critical Analysis Of Some Alternative Approachesmentioning

confidence: 74%

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Entropy and the Tolman Parameter in Nucleation Theory

Schmelzer

Abyzov

Байдаков

2019

Entropy

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Thermodynamic aspects of the theory of nucleation are commonly considered employing Gibbs’ theory of interfacial phenomena and its generalizations. Utilizing Gibbs’ theory, the bulk parameters of the critical clusters governing nucleation can be uniquely determined for any metastable state of the ambient phase. As a rule, they turn out in such treatment to be widely similar to the properties of the newly-evolving macroscopic phases. Consequently, the major tool to resolve problems concerning the accuracy of theoretical predictions of nucleation rates and related characteristics of the nucleation process consists of an approach with the introduction of the size or curvature dependence of the surface tension. In the description of crystallization, this quantity has been expressed frequently via changes of entropy (or enthalpy) in crystallization, i.e., via the latent heat of melting or crystallization. Such a correlation between the capillarity phenomena and entropy changes was originally advanced by Stefan considering condensation and evaporation. It is known in the application to crystal nucleation as the Skapski–Turnbull relation. This relation, by mentioned reasons more correctly denoted as the Stefan–Skapski–Turnbull rule, was expanded by some of us quite recently to the description of the surface tension not only for phase equilibrium at planar interfaces, but to the description of the surface tension of critical clusters and its size or curvature dependence. This dependence is frequently expressed by a relation derived by Tolman. As shown by us, the Tolman equation can be employed for the description of the surface tension not only for condensation and boiling in one-component systems caused by variations of pressure (analyzed by Gibbs and Tolman), but generally also for phase formation caused by variations of temperature. Beyond this particular application, it can be utilized for multi-component systems provided the composition of the ambient phase is kept constant and variations of either pressure or temperature do not result in variations of the composition of the critical clusters. The latter requirement is one of the basic assumptions of classical nucleation theory. For this reason, it is only natural to use it also for the specification of the size dependence of the surface tension. Our method, relying on the Stefan–Skapski–Turnbull rule, allows one to determine the dependence of the surface tension on pressure and temperature or, alternatively, the Tolman parameter in his equation. In the present paper, we expand this approach and compare it with alternative methods of the description of the size-dependence of the surface tension and, as far as it is possible to use the Tolman equation, of the specification of the Tolman parameter. Applying these ideas to condensation and boiling, we derive a relation for the curvature dependence of the surface tension covering the whole range of metastable initial states from the binodal curve to the spinodal curve.

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Section: Brief Comparison With Experimental Data and Computer Simulatsupporting

confidence: 53%

Section: Critical Analysis Of Some Alternative Approachesmentioning

confidence: 74%

Entropy and the Tolman Parameter in Nucleation Theory

Schmelzer

Abyzov

Байдаков

2019

Entropy

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“…These techniques are rigorous but rather expensive from a computational point of view. For this reason, in the last ten years, a new technique has been proposed aimed to determine J denoted as Seeding [59][60][61][62][63][64][65] , where a solid cluster (equilibrated at a certain value of T and p) is inserted into an equilibrated liquid (at the same conditions T, p) to determine whether is critical or not. According to its time evolution in the N pT ensemble: it is critical if the probability to freeze and to melt are equal while there is no other possible result than these two options.…”

Section: Introductionmentioning

confidence: 99%

Interfacial Free Energy and Tolman Length of Curved Liquid–Solid Interfaces from Equilibrium Studies

et al. 2020

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In this work, we study by means of simulations of hard spheres the equilibrium between a spherical solid cluster and the fluid. In the NVT ensemble we observe stable/metastable clusters of the solid phase in equilibrium with the fluid, representing configurations that are global/local minima of the Helmholtz free energy. Then, we run NpT simulations of the equilibrated system at the average pressure of the NVT run and observe that the clusters are critical because they grow/shrink with a probability of 1/2. Therefore, a crystal cluster equilibrated in the NVT ensemble corresponds to a Gibbs free energy maximum where the nucleus is in unstable equilibrium with the surrounding fluid, in accordance with what has been recently shown for vapor bubbles in equilibrium with the liquid. Then, within the Seeding framework, we use Classical Nucleation Theory to obtain both the interfacial free energy γ and the nucleation rate. The latter is in very good agreement with independent estimates using techniques that do not rely on Classical Nucleation Theory when the mislabeling criterion is used to identify the molecules of the solid cluster. We therefore argue that the radius obtained from the mislabeling criterion provides a good approximation for the radius of tension, R s . We obtain an estimate of the Tolman length by extrapolating the difference between R e (the Gibbs dividing surface) and R s to infinite radius. We show that such definition of the Tolman length coincides with that obtained by fitting γ versus 1/R s to a straight line as recently applied to hard spheres.

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“…This analysis reinforces our approach of using a heterogeneous TTT‐curve to determine the critical cooling rates of oxide glasses because: (a) it is well‐known that most glass‐formers do not show measurable homogeneous nucleation; (b) even for fresnoite, the oxide glass‐former showing the highest homogeneous nucleation rates known, heterogeneous nucleation seem to dominate the R c . However, we emphasize that this scenario could change for materials having extremely high homogeneous nucleation rates, such as LJ (Lennard‐Jones) liquids, pure metals, water, ionic liquids, and some metallic alloys ( I ( T max ) ~ 10 30 m −3 s −1 ).…”

Section: Resultsmentioning

confidence: 99%

Viscosity and liquidus‐based predictor of glass‐forming ability of oxide glasses

et al. 2019

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Glass‐forming ability (GFA) is a measure of the easiness to vitrify a given substance. Theoretically, it is possible to make a glass from any liquid provided it is quenched from its liquidus temperature with a cooling rate above a critical value Rc to avoid crystallization. However, measuring GFA is a laborious and time‐consuming task. Moreover, predicting the GFA of substances that have never been vitrified is of greater interest. Here, we propose and evaluate a new parameter that can predict the glass forming ability of oxide mixtures. We derived a mother parameter, GFA = 1/Rc ∝ [U(Tmax) × TL]−1, where U(Tmax) is the maximum crystal growth rate, and TL is the liquidus temperature, which strongly correlates with the experimental critical cooling rates of oxide glass‐formers. A simplified version derived from the mother parameter—which does not need (scarce) crystal growth rate data and only relies on viscosity η and TL, GFA ∝ [η(TL)/TL2]—also correlates well with the Rc of several oxide compositions. This new GFA parameter, dubbed Jezica, works when heterogeneous nucleation prevails. It corroborates the widespread concept that substances having high viscosity at TL, and a low TL can be easily vitrified, and provides a powerful tool for the quest and design of novel glasses.

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Diffusivity, Interfacial Free Energy, and Crystal Nucleation in a Supercooled Lennard-Jones Liquid

Cited by 44 publications

References 106 publications

Entropy and the Tolman Parameter in Nucleation Theory

Entropy and the Tolman Parameter in Nucleation Theory

Interfacial Free Energy and Tolman Length of Curved Liquid–Solid Interfaces from Equilibrium Studies

Viscosity and liquidus‐based predictor of glass‐forming ability of oxide glasses

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