Melt undercooling and nucleation kinetics

Perepezko, John H.; Wilde, Gerhard

doi:10.1016/j.cossms.2015.07.001

Cited by 51 publications

(29 citation statements)

References 86 publications

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“…Despite its long tradition, due to its complexity, the theoretical analysis of crystal nucleation and growth phenomena in glass-forming substances remains an actively developing field of research, with a variety of new topics and applications [1,2,3,4,5,6,7]. In the present paper, we address a particular but very important problem related to the description of the phase transformation kinetics that is specific for crystallization of glass-forming liquids, the effects of the glass transition and of the structural relaxation of the supercooled liquid on the crystallization kinetics in the vicinity and below the glass transition temperature.…”

Section: Introductionmentioning

confidence: 99%

Effects of Glass Transition and Structural Relaxation on Crystal Nucleation: Theoretical Description and Model Analysis

Schmelzer¹,

Тропин²,

Fokin³

et al. 2020

Preprint

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In the application of classical nucleation theory (CNT) and all other theoretical models of crystallization of liquids and glasses it is always assumed that nucleation proceeds only after the supercooled liquid or the glass have completed structural relaxation processes towards the metastable equilibrium state. Only employing such assumption, the thermodynamic driving force of crystallization and the surface tension can be determined in the way it is commonly performed. The present paper is devoted to the theoretical treatment of a different situation when nucleation proceeds concomitantly with structural relaxation. To treat the nucleation kinetics theoretically for such cases, we need adequate expressions for the thermodynamic driving force and the surface tension accounting for the contributions caused by the deviation of the supercooled liquid from metastable equilibrium. In the present paper, such relations are derived. They are expressed via deviations of structural order parameters from their equilibrium values. Relaxation processes result in changes of the structural order parameters with time. As a consequence, the thermodynamic driving force and surface tension, and basic characteristics of crystal nucleation, such as the work of critical cluster formation and the steady-state nucleation rate, also become time-dependent. We show that this scenario may be realized in the vicinity and below the glass transition temperature, and it may occur only if diffusion (controlling nucleation) and viscosity (controlling the alpha-relaxation process) in the liquid decouple. Analytical estimates are illustrated and confirmed by numerical computations for a model system. The theory is successfully applied to the interpretation of experimental data. Several further consequences of this newly developed theoretical treatment are discussed in detail. In line with our previous investigations, we reconfirm that only when the characteristic times of structural relaxation are of similar order of magnitude or longer than the characteristic times of crystal nucleation, elastic stresses evolving in nucleation may significantly affect this process. Completing the analysis of elastic stress effects, for the first time expressions are derived for the dependence of the surface tension of critical crystallites on elastic stresses. As the result, a comprehensive theoretical description of crystal nucleation accounting appropriately for the effects of deviations of the liquid from the metastable states and of relaxation on crystal nucleation of glass-forming liquids, including the effect of simultaneous stress evolution and stress relaxation on nucleation, is now available. As one if its applications, this theoretical treatment provides a new tool for the explanation of the low-temperature anomaly in nucleation in silicate and polymer glasses (the so-called \breakdown" of CNT at temperatures below the temperature of the maximum steady-state nucleation rate). We show that this anomaly results from much more complex features of crystal nucleation in glasses caused by deviations from metastable equilibrium (resulting in changes of the thermodynamic driving force, the surface tension, and the work of critical cluster formation, in the necessity to account of structural relaxation and stress effects) than assumed so far.

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Section: Introductionmentioning

confidence: 99%

Effects of Glass Transition and Structural Relaxation on Crystal Nucleation: Theoretical Description and Model Analysis

Schmelzer¹,

Тропин²,

Fokin³

et al. 2020

Preprint

View full text Add to dashboard Cite

show abstract

“…Despite its long tradition, due to its complexity, the theoretical analysis of crystal nucleation and growth phenomena in glass-forming substances remains an actively developing field of research, with a variety of new topics and applications [ 1 , 2 , 3 , 4 , 5 , 6 , 7 ]. In the present paper, we address a particular but very important problem related to the description of the phase transformation kinetics that is specific for crystallization of glass-forming liquids, the effects of the glass transition and of the structural relaxation of the supercooled liquid on the crystallization kinetics in the vicinity and below the glass transition temperature.…”

Section: Introductionmentioning

confidence: 99%

Effects of Glass Transition and Structural Relaxation on Crystal Nucleation: Theoretical Description and Model Analysis

Schmelzer

Тропин

Fokin

et al. 2020

Entropy

View full text Add to dashboard Cite

In the application of classical nucleation theory (CNT) and all other theoretical models of crystallization of liquids and glasses it is always assumed that nucleation proceeds only after the supercooled liquid or the glass have completed structural relaxation processes towards the metastable equilibrium state. Only employing such an assumption, the thermodynamic driving force of crystallization and the surface tension can be determined in the way it is commonly performed. The present paper is devoted to the theoretical treatment of a different situation, when nucleation proceeds concomitantly with structural relaxation. To treat the nucleation kinetics theoretically for such cases, we need adequate expressions for the thermodynamic driving force and the surface tension accounting for the contributions caused by the deviation of the supercooled liquid from metastable equilibrium. In the present paper, such relations are derived. They are expressed via deviations of structural order parameters from their equilibrium values. Relaxation processes result in changes of the structural order parameters with time. As a consequence, the thermodynamic driving force and surface tension, and basic characteristics of crystal nucleation, such as the work of critical cluster formation and the steady-state nucleation rate, also become time-dependent. We show that this scenario may be realized in the vicinity and below the glass transition temperature, and it may occur only if diffusion (controlling nucleation) and viscosity (controlling the alpha-relaxation process) in the liquid decouple. Analytical estimates are illustrated and confirmed by numerical computations for a model system. The theory is successfully applied to the interpretation of experimental data. Several further consequences of this newly developed theoretical treatment are discussed in detail. In line with our previous investigations, we reconfirm that only when the characteristic times of structural relaxation are of similar order of magnitude or longer than the characteristic times of crystal nucleation, elastic stresses evolving in nucleation may significantly affect this process. Advancing the methods of theoretical analysis of elastic stress effects on nucleation, for the first time expressions are derived for the dependence of the surface tension of critical crystallites on elastic stresses. As the result, a comprehensive theoretical description of crystal nucleation accounting appropriately for the effects of deviations of the liquid from the metastable states and of relaxation on crystal nucleation of glass-forming liquids, including the effect of simultaneous stress evolution and stress relaxation on nucleation, is now available. As one of its applications, this theoretical treatment provides a new tool for the explanation of the low-temperature anomaly in nucleation in silicate and polymer glasses (the so-called “breakdown” of CNT at temperatures below the temperature of the maximum steady-state nucleation rate). We show that this anomaly results from much more complex features of crystal nucleation in glasses caused by deviations from metastable equilibrium (resulting in changes of the thermodynamic driving force, the surface tension, and the work of critical cluster formation, in the necessity to account of structural relaxation and stress effects) than assumed so far. If these effects are properly accounted for, then CNT appropriately describes both the initial, the intermediate, and the final states of crystal nucleation.

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“…Relations of the form of Equation ( 3 ) are widely discussed in the literature [ 3 , 4 , 16 , 21 , 34 , 35 , 36 , 37 , 38 , 39 , 40 , 41 , 42 , 43 , 44 , 45 , 46 , 47 , 48 , 49 , 50 , 51 ], starting immediately with the work by Gibbs. They are denoted, following Kashchiev [ 36 ], as the first nucleation theorem.…”

Section: Introductionmentioning

confidence: 99%

Application of the Nucleation Theorem to Crystallization of Liquids: Some General Theoretical Results

Schmelzer

2019

Entropy

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Different aspects in applying the nucleation theorem to the description of crystallization of liquids are analyzed. It is shown that, by employing the classical Gibbs’ approach in the thermodynamic description of heterogeneous systems, a general form of the nucleation theorem can be formulated that is valid not only for one-component but generally for multi-component systems. In this analysis, one basic assumption of classical nucleation theory is utilized. In addition, commonly employed in application to crystallization, it is supposed that the bulk properties of the critical clusters are widely identical to the properties of the newly evolving crystal phase. It is shown that the formulation of the nucleation theorem as proposed by Kashchiev [J. Chem. Phys. 76, 5098-5102 (1982)], also relying widely on the standard classical approach in the description of crystal nucleation, holds for multi-component systems as well. The general form of the nucleation theorem derived by us is taken then as the starting point for the derivation of particular forms of this theorem for the cases that the deviation from equilibrium is caused by variations of either composition of the liquid phase, temperature, or pressure. In this procedure, expressions recently developed by us for the curvature dependence of the surface tension, respectively, its dependence on pressure and/or temperature are employed. The basic assumption of classical nucleation theory mentioned above is, however, in general, not true. The bulk and surface properties of the critical crystal clusters may differ considerably from the properties of the evolving macroscopic phases. Such effects can be incorporated into the theoretical description by the application of the generalized Gibbs approach for the specification of the dependence of the properties of critical crystal clusters on the degree of metastability of the liquid phase. Applying this method, it is demonstrated that a similar formulation of the nucleation theorem, as derived based on classical nucleation theory, holds true also in cases when a dependence of the state parameters of the critical clusters on the degree of deviation from equilibrium is appropriately accounted for.

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Melt undercooling and nucleation kinetics

Cited by 51 publications

References 86 publications

Effects of Glass Transition and Structural Relaxation on Crystal Nucleation: Theoretical Description and Model Analysis

Effects of Glass Transition and Structural Relaxation on Crystal Nucleation: Theoretical Description and Model Analysis

Effects of Glass Transition and Structural Relaxation on Crystal Nucleation: Theoretical Description and Model Analysis

Application of the Nucleation Theorem to Crystallization of Liquids: Some General Theoretical Results

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