The failure of the Classical Nucleation Theory at low temperatures resolved (original) (raw)
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Journal of Non-Crystalline Solids, 2016
The description of crystal nucleation rates in supercooled liquids in the framework of the classical nucleation theory (CNT) fails if one uses a fixed size of "structural units". To reconcile the experimental data and CNT, we assumed an increase of the size of the structural units that control nucleation with decreasing temperature for temperatures below the nucleation rate maximum, T b T max. This hypothesis was tested for several glassforming liquids, where crystal formation proceeds by bulk homogeneous nucleation. It can explain the temperature dependence of the nucleation rate in the range T b T max , where the description of nucleation rate by CNT drastically fails. The size of the structural units can be related either to the size of the cooperatively rearranging regions (CRR) or to an effective size parameter, accounting for corrections in the theoretical treatment of the kinetics of aggregation in multi-component systems via a quasi-one-dimensional description.
Critical assessment of the alleged failure of the Classical Nucleation Theory at low temperatures
Journal of Non-Crystalline Solids, 2020
The Classical Nucleation Theory allegedly fails to describe the temperature dependence of the homogeneous crystal nucleation rates below the temperature of maximum nucleation, Tmax. Possible explanations for this suspected breakdown have been advanced in the literature. However, the simplest hypothesis has never been tested, that it is a byproduct of nucleation datasets that have not reached the steady-state regime. In this work, we tested this possibility by analyzing published nucleation data for oxide supercooled liquids, using only nucleation and viscosity data measured in samples of the same glass batch that also have satisfied a steady-state regime test. Furthermore, all the uncertainty and regression confidence bands were computed and considered. Having this rigorous protocol, among the 6 datasets analyzed, we only found weak evidence supporting the existence of the nucleation break in 2 datasets. Our collective results thus indicate that the break at Tmax is not a common feature of all glass-formers.
Diffusion coefficients for crystal nucleation and growth in deeply undercooled glass-forming liquids
We calculate, employing the classical theory of nucleation and growth, the effective diffusion coefficients controlling crystal nucleation of nanosize clusters and the subsequent growth of micron-size crystals at very deep undercoolings, below and above Tg, using experimental nucleation and growth data obtained for stoichiometric Li2O·2SiO2 and Na2O·2CaO·3SiO2 glasses. The results show significant differences in the magnitude and temperature dependence of these kinetic coefficients. We explain this difference showing that the composition and/or structure of the nucleating critical clusters deviate from those of the stable crystalline phase. These results for diffusion coefficients corroborate our previous conclusion for the same glasses, based on different experiments, and support the view that, even for the so-called case of stoichiometric polymorphic crystallization, the nucleating phase may have a different composition and/or structure as compared to the parent glass and the evolving macroscopic crystalline phase. This finding gives a key to explain the discrepancies between calculated by classical nucleation theory and experimentally observed nucleation rates in these systems, in particular, and in deeply undercooled glass-forming liquids, in general
New insights on the thermodynamic barrier for nucleation in glasses: The case of lithium disilicate
Journal of Non-Crystalline Solids, 2005
An analysis is performed of the temperature dependence of the thermodynamic barrier to nucleation, W*(T), calculated from a fit of lithium disilicate glass data to the classical theory of nucleation. It is shown that, in order to obtain a satisfactory agreement between experimental and theoretical determinations of W*(T), lower values must be assigned to both the thermodynamic driving force and the surface energy as compared with the corresponding macroscopic values. This finding is consistent with theoretical considerations taking into account the effect that, in general, both the bulk and surface properties of the critical nuclei differ considerably from the respective properties of the newly evolving macroscopic phases. In addition, an anomalous increase of W*(T) with decreasing temperature is found near the glass transition interval. This increase is interpreted as a result of the effect of elastic strain on the thermodynamic driving force. The values of elastic strain energy estimated from the low temperature behavior of W*(T) are congruent with those calculated using the elastic constants of glass and crystal.
Journal of Non-Crystalline Solids, 2008
A new approach is proposed to explain the strong difference between the induction periods (nucleation time-lags) obtained from nucleation rate measurements and from crystal growth experiments for lithium silicate glasses; and their similar magnitude for a Na 2 O Á 2CaO Á 3SiO 2 glass. For these two glass families, the time-lags for nucleation estimated from crystal growth kinetics were compared with those directly obtained from nucleation experiments. A theoretical analysis was performed employing analytical solutions of the Frenkel-Zeldovich equation. In such analysis, the frequently assumed condition of size-independence of the thermodynamic properties of the crystallites was used. Provided this assumption is correct, time-lag data obtained in the two above mentioned ways should coincide. Consequently the significant difference between the values of nucleation time-lag for lithium silicate glasses from nucleation and growth data gives a strong indirect evidence for the deviation of the properties of critical nuclei from the respective parameters characterizing the state of the newly evolving macrophase. For Na 2 O Á 2CaO Á 3SiO 2 glass at intermediate stages of crystallization we show that the average composition of the growing crystals is close to that of the near-critical nuclei. The fact that the nucleation and growth rates of this soda-lime-silica glass refer to the same phase provides an explanation for the similarity of the induction periods estimated from nucleation and growth experiments.
Journal of Non-Crystalline Solids, 2000
The most basic assumption of the classical nucleation theory (CNT) is to treat nucleus/liquid surface energy, r, as a macroscopic property having a value equal to that of a planar interface, r I . Therefore, when the CNT is used to analyze experimental data, the size dependence of surface energy is often neglected. To date, there has been no reliable method to measure the surface energy of the nucleus/liquid interface except by ®tting nucleation rate data to the theory. In this case, one obtains the surface energy of critical size nuclei as a function of temperature. However, the ®tted r(T) dependence arises from two dierent factors: the temperature dependence of r for a planar interface and its size dependence. This paper focuses on the temperature dependence of the macroscopic value of surface energy, decoupling it from the size dependent part. TolmanÕs equation was used to eliminate the size dependence of surface energy from published nucleation data for two stoichiometric silicate glasses (Li 2 O á 2SiO 2 and Na 2 O á 2CaO á 3SiO 2 ). It is shown that the Tolman parameter may be chosen so that surface tension decreases with temperature; dr I adT`0. The value of dr I adT obtained in this way is close to theoretical predictions. Ó
The effect of heterogeneous structure of glass-forming liquids on crystal nucleation
Journal of Non-Crystalline Solids, 2017
A model for the description of crystal nucleation is proposed incorporating into classical nucleation theory concepts of spatial heterogeneity of glass-forming liquids. It is assumed that nucleation processes may proceed with detectable rates only in liquid-like (soft) regions and are suppressed in solid-like (rigid) parts. Determining appropriately the fraction of liquid-like solid-like regions in dependence on temperature this approach allows one to achieve a satisfactory agreement between classical nucleation theory and experiment not only at relatively high temperatures but also at temperatures lower than that of the nucleation rate maximum. The model was tested successfully on several silicate glasses revealing homogeneous volume nucleation. Some other phenomena in the interplay of crystallization and glass transition are also discussed giving an independent verification of the validity of our basic assumption.
Entropy
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 ...
Homogeneous crystal nucleation in silicate glasses: A 40 years perspective
Journal of Non-Crystalline Solids, 2006
We review a plethora of relevant experimental results on internal homogeneous crystal nucleation in silicate glasses obtained in the last four decades, and their analyses in the framework of the classical nucleation theory (CNT). The basic assumptions and equations of CNT are outlined. Particular attention is devoted to the analysis of the properties of the critical nuclei, which, to a large extent, govern nucleation kinetics. The main methods employed to measure nucleation rates are described and the possible errors in the determination of the crystal number density (and, correspondingly, in nucleation rates) are discussed. The basic regularities of both time and temperature dependencies of nucleation rates are illustrated by numerous experimental data. Experimental evidence for a correlation between maximum nucleation rates and reduced glass transition temperatures is presented and theoretically justified. Special attention is given to serious problems that arise in the quantitative description of nucleation rates when using the CNT, for instance: the dramatic discrepancy between calculated and measured nucleation rates; the high value of the crystal nuclei/melt surface energy, r cm , if compared to the expected value estimated via Stefan's rule; the increase of r cm with increasing temperature; and the discrepancies between the values of the surface energy and the time-lag for nucleation when independently estimated from nucleation and growth kinetics. The analysis of the above mentioned problems leads to the following conclusion: in contrast to Gibbs' description of heterogeneous systems underlying CNT, the bulk thermodynamic properties of the critical nuclei generally differ from those of the corresponding macro-phase resulting simultaneously in significant differences of the surface properties as compared with the respective parameters of the planar interfaces. In particular, direct experimental evidence is presented for compositional changes of the crystal nuclei during formation of the critical nuclei and their growth from critical to macro-sizes. In addition, detailed examinations of crystal nucleation and growth kinetics show a decrease of both the thermodynamic driving force for nucleation and of the critical nuclei/liquid interfacial energy, as compared with the respective properties of the macro-phase. However, despite significant progress in understanding crystal nucleation in glasses in the past four decades, many problems still exist and this is likely to remain a highly interesting subject for both fundamental and applied research for a long time.
Crystal nucleation in a glass during relaxation well below Tg
Journal of Chemical Physics, 2023
Until quite recently, in almost all papers on crystal nucleation in glass-forming substances it was assumed that nucleation proceeds in a completely relaxed supercooled liquid and hence at constant values of the critical parameters determining the nucleation rate for any given set of temperature, pressure, and composition. Here, we analyze the validity of this hypothesis for a model system by studying nucleation in a lithium silicate glass treated for very long times (up to 250 days) in deeply supercooled states, reaching 60 K below the laboratory glass transition temperature, Tg. At all temperatures in the considered range, T<Tg, we observed an enormous difference between the experimental number of nucleated crystals, N(t), and its theoretically expected value computed by assuming the metastable state of the relaxing glass has been reached. Analyzing the origin of this discrepancy, we confirmed that the key parameters determining the nucleation rates change with time as a result of the glass relaxation process. Finally, we demonstrate that, for temperatures below 683 K, this particular glass almost fully crystallizes prior to reaching the ultimate steadystate nucleation regime (e.g., at 663 K, it would take 176 years for the glass to reach 99% crystallization, while 2,600 years would be needed for complete relaxation). This comprehensive study proves that structural relaxation strongly affects crystal nucleation in deeply supercooled states at temperatures well below Tg, hence this phenomenon has to be accounted for in any crystal nucleation model.