The effect of elastic stresses on the thermodynamic barrier for crystal nucleation

Ferreira

et al. 2018

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To achieve a quantitative agreement of experimental data with theoretical predictions, in classical nucleation theory a curvature‐ or size‐dependence of the surface tension of critical clusters has to be accounted for. For its description, frequently the Tolman equation is chosen. Tolman derived his relation originally in application to droplets or bubbles in one‐component fluids assuming that nucleation is caused by variations of pressure. As shown here his approach and the resulting basic relations are applicable also to the description of crystal nucleation in multi‐component fluids if either pressure or temperature is changed. Estimates of the Tolman parameter in application to crystallization are advanced for both the mentioned cases. The Tolman parameter is shown to depend on the surface tension for a planar interface, the number of components in the liquid, the bulk properties of both the liquid and crystal phases, and the way the metastable state is generated. In addition, we develop a method of improving the precision in the specification of the curvature dependence of the surface tension in melt crystallization going beyond the Tolman equation in its original form. The results are applied successfully to the description of crystal nucleation in silicate glass‐forming melts.

Section: Introductionmentioning

confidence: 99%

Curvature dependence of the surface tension and crystal nucleation in liquids

Ferreira

et al. 2018

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“… and exhibiting such minimum, the range of active nucleation is found at temperatures far above the Kauzmann temperature. From an experimental point of view, this statement is confirmed by computations of the Kauzmann temperature from specific entropy data of liquid and crystal and its comparison with experimental measurements of homogeneous nucleation rates and their interpretation . From a theoretical point of view, the approach of the Kauzmann temperature is correlated with the approach to zero of the configurational entropy.…”

Section: Discussionmentioning

confidence: 99%

Thermodynamic Aspects of Pressure‐Induced Crystallization: Kauzmann Pressure

Fokin

2016

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General equations for the dependence of the thermodynamic driving force and the specific interfacial energy melt‐crystal of critical clusters on temperature and pressure are derived. Analytical estimates of these and related thermodynamic quantities are advanced directly applicable in the analysis of experimental data of crystal nucleation. Similar to the well‐known notation of a Kauzmann temperature, the concept of a Kauzmann pressure is introduced. It is shown that the thermodynamic driving force of crystal nucleation has maxima not only at the Kauzmann temperature but also at the Kauzmann pressure. Estimates of the magnitude of the thermodynamic driving force of crystallization at these states are given and some consequences are discussed.

“… (a) : N ( t )/( J ( T ) τ ) versus reduced time, t / τ , for glasses Li

_{2}

O · 2SiO

_{2}

(1)–(2) and 2Na

_{2}

O · CaO · 3SiO

_{2}

(3) – (4) for T = 430 (1) , 465 (2) , 465 (3) , and

470^{o}

C (4) . (b) : Reduced nucleation rate, J ( t , T )/ J ( T ), versus reduced time, t / τ …”

Section: Characteristic Time‐scales In Nucleation: Isothermal and Isomentioning

confidence: 99%

“…In Fig. , two different models are applied to the interpretation of experimental data . It is evident that the Wakeshima equation overestimates the number of clusters, in particular, at small nucleation times, while the Collins‐Kashchiev and Shneidman equations (with the chosen here parameter value for

t_{1}

) lead to widely equivalent results.…”

Section: Characteristic Time‐scales In Nucleation: Isothermal and Isomentioning

confidence: 99%

See 1 more Smart Citation

Time of Formation of the First Supercritical Nucleus, Time‐lag, and the Steady‐State Nucleation Rate

Байдаков

2016

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General equations are derived for the description of correlations between average time of formation of the first supercritical nucleus, time‐lag in nucleation, and steady‐state nucleation rate. In their implementation, a set of representative equations is employed modeling the time‐dependence of the nucleation rate as proposed first by Zeldovich and advanced by a variety of other authors. The analysis is performed for both isothermal–isobaric and time‐dependent process conditions. It is shown that, in general, the time of formation of the first supercritical nucleus depends both on time‐lag and the average time of formation of a supercritical nucleus at steady‐state conditions. The conditions are specified at which one of these characteristic times may dominate. In contrast to alternative statements it is also demonstrated that for isothermal–isobaric conditions, due to the Poisson character of nucleation, steady‐state nucleation rates can be determined without having at one's disposal a detailed knowledge of the time‐lag and the kinetic laws of approach of steady‐state nucleation conditions. Results of molecular‐dynamics simulations of crystal nucleation in Lennard‐Jones liquids are presented for an illustration of the general conclusions. Several applications of the results to the interpretation of experimental data are discussed.