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

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

10.20944/preprints202008.0719.v1 ◽

2020 ◽

Author(s):

Juern W. P. Schmelzer ◽

Timur V. Tropin ◽

Vladimir M. Fokin ◽

Alexander S. Abyzov ◽

Edgar D. Zanotto

Keyword(s):

Surface Tension ◽

Structural Relaxation ◽

Driving Force ◽

Cluster Formation ◽

Supercooled Liquid ◽

Crystal Nucleation ◽

Metastable Equilibrium ◽

Theoretical Treatment ◽

Relaxation Processes ◽

Thermodynamic Driving Force

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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Organogold oligomers: exploiting iClick and aurophilic cluster formation to prepare solution stable Au4 repeating units

Dalton Transactions ◽

10.1039/c5dt00282f ◽

2015 ◽

Vol 44 (25) ◽

pp. 11437-11443 ◽

Cited By ~ 15

Author(s):

Xi Yang ◽

Shanshan Wang ◽

Ion Ghiviriga ◽

Khalil A. Abboud ◽

Adam S. Veige

Keyword(s):

Driving Force ◽

Cluster Formation ◽

Thermodynamic Driving Force ◽

Multiple Units

Cluster formation via multiple gold–gold bonds provides sufficient thermodynamic driving force to overcome entropic penalties to link multiple units and create solution stable organogold oligomers.

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Ice-Crystal Nucleation in Water: Thermodynamic Driving Force and Surface Tension. Part I: Theoretical Foundation

Entropy ◽

10.3390/e22010050 ◽

2019 ◽

Vol 22 (1) ◽

pp. 50 ◽

Cited By ~ 1

Author(s):

Olaf Hellmuth ◽

Jürn W. P. Schmelzer ◽

Rainer Feistel

Keyword(s):

Surface Tension ◽

Driving Force ◽

Mass Density ◽

Stable State ◽

Water System ◽

Ice Nucleation ◽

Crystal Nucleation ◽

Temperature And Pressure ◽

Homogeneous Freezing ◽

Ice Water

A recently developed thermodynamic theory for the determination of the driving force of crystallization and the crystal–melt surface tension is applied to the ice-water system employing the new Thermodynamic Equation of Seawater TEOS-10. The deviations of approximative formulations of the driving force and the surface tension from the exact reference properties are quantified, showing that the proposed simplifications are applicable for low to moderate undercooling and pressure differences to the respective equilibrium state of water. The TEOS-10-based predictions of the ice crystallization rate revealed pressure-induced deceleration of ice nucleation with an increasing pressure, and acceleration of ice nucleation by pressure decrease. This result is in, at least, qualitative agreement with laboratory experiments and computer simulations. Both the temperature and pressure dependencies of the ice-water surface tension were found to be in line with the le Chatelier–Braun principle, in that the surface tension decreases upon increasing degree of metastability of water (by decreasing temperature and pressure), which favors nucleation to move the system back to a stable state. The reason for this behavior is discussed. Finally, the Kauzmann temperature of the ice-water system was found to amount T K = 116 K , which is far below the temperature of homogeneous freezing. The Kauzmann pressure was found to amount to p K = − 212 MPa , suggesting favor of homogeneous freezing on exerting a negative pressure on the liquid. In terms of thermodynamic properties entering the theory, the reason for the negative Kauzmann pressure is the higher mass density of water in comparison to ice at the melting point.

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Ice-Crystal Nucleation in Water: Thermodynamic Driving Force and Surface Tension

10.20944/preprints201909.0164.v1 ◽

2019 ◽

Author(s):

Olaf Hellmuth ◽

Juern W. P. Schmelzer ◽

Rainer Feistel

Keyword(s):

Surface Tension ◽

Driving Force ◽

Mass Density ◽

Stable State ◽

Water System ◽

Crystallization Rate ◽

Ice Nucleation ◽

Crystal Nucleation ◽

Temperature And Pressure ◽

Homogeneous Freezing

A recently developed thermodynamic theory for the determination of the driving force of crystallization and the crystal–melt surface tension is applied to the ice–water system employing the new Thermodynamic Equation of Seawater TEOS-10. The deviations of approximative formulations of the driving force and the surface tension from the exact reference properties are quantified, showing that the proposed simplifications are applicable for low to moderate undercooling and pressure differences to the respective equilibrium state of water. The TEOS-10 based predictions of the ice crystallization rate revealed pressure-induced deceleration of ice nucleation with an increasing pressure, and acceleration of ice nucleation by pressure decrease. This result is in, at least, qualitative agreement with laboratory experiments and computer simulations. Both the temperature and pressure dependencies of the ice–water surface tension were found to be in line with the le Chatelier–Braun principle, in that the surface tension decreases upon increasing degree of metastability of water (by decreasing temperature and pressure), which favors nucleation to move the system back to a stable state. The reason for this behavior is discussed. Finally, the Kauzmann temperature of the ice–water system was found to amount TK=116K, which is far below the temperature of homogeneous freezing. The Kauzmann pressure was found to amount pK=-212MPa, suggesting favor of homogeneous freezing upon exerting a negative pressure on the liquid. In terms of thermodynamic properties entering the theory, the reason for the negative Kauzmann pressure is the higher mass density of water in comparison to ice at the melting point.

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The nucleation of cavities at grain boundaries

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100126299 ◽

1987 ◽

Vol 45 ◽

pp. 288-291

Author(s):

P. J. Goodhew

Keyword(s):

Surface Tension ◽

Surface Energy ◽

Grain Boundaries ◽

Radiation Damage ◽

Impurity Concentration ◽

Driving Force ◽

Nucleation And Growth ◽

Phase Boundaries ◽

Cavity Nucleation ◽

Spherical Bubble

Cavity nucleation and growth at grain and phase boundaries is of concern because it can lead to failure during creep and can lead to embrittlement as a result of radiation damage. Two major types of cavity are usually distinguished: The term bubble is applied to a cavity which contains gas at a pressure which is at least sufficient to support the surface tension (2g/r for a spherical bubble of radius r and surface energy g). The term void is generally applied to any cavity which contains less gas than this, but is not necessarily empty of gas. A void would therefore tend to shrink in the absence of any imposed driving force for growth, whereas a bubble would be stable or would tend to grow. It is widely considered that cavity nucleation always requires the presence of one or more gas atoms. However since it is extremely difficult to prepare experimental materials with a gas impurity concentration lower than their eventual cavity concentration there is little to be gained by debating this point.

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Effects of Annealing on Enthalpy Recovery and Nanomechanical Behaviors of a La-Based Bulk Metallic Glass

Metals ◽

10.3390/met11040579 ◽

2021 ◽

Vol 11 (4) ◽

pp. 579

Author(s):

Ting Shi ◽

Lanping Huang ◽

Song Li

Keyword(s):

Glass Transition ◽

Transition Temperature ◽

Glass Transition Temperature ◽

Metallic Glass ◽

Bulk Metallic Glass ◽

Structural Relaxation ◽

Supercooled Liquid ◽

Supercooled Liquid Region ◽

Liquid Region ◽

Nanoindentation Measurement

Structural relaxation and nanomechanical behaviors of La65Al14Ni5Co5Cu9.2Ag1.8 bulk metallic glass (BMG) with a low glass transition temperature during annealing have been investigated by calorimetry and nanoindentation measurement. The enthalpy release of this metallic glass is deduced by annealing near glass transition. When annealed below glass transition temperature for 5 min, the recovered enthalpy increases with annealing temperature and reaches the maximum value at 403 K. After annealed in supercooled liquid region, the recovered enthalpy obviously decreases. For a given annealing at 393 K, the relaxation behaviors of La-based BMG can be well described by the Kohlrausch-Williams-Watts (KWW) function. The hardness, Young’s modulus, and serrated flow are sensitive to structural relaxation of this metallic glass, which can be well explained by the theory of solid-like region and liquid-like region. The decrease of ductility and the enhancement of homogeneity can be ascribed to the transformation from liquid-like region into solid-like region and the reduction of the shear transition zone (STZ).

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