Crystal Nucleation In Glasses Research Articles

Effect of structural relaxation on crystal nucleation in glasses

Applying the Classical Nucleation Theory (CNT) to crystallization of glasses encounters some difficulties. One of the most important aspects is that this theory overlooks structural relaxation by assuming that crystal nucleation proceeds in a relaxed, metastable, supercooled liquid (SCL). Considering this assumption, the thermodynamic driving force, diffusion coefficient, and surface tension should be constant at any given temperature. Here, we performed experiments for very extended times (up to about 2,200 hours at 703K), at temperatures below the laboratory glass transition, Tg=726K, of a lithium disilicate glass used as a model. Our results show that crystal nucleation starts concomitantly with the relaxation process of the glass towards the SCL, which strongly affects the nucleation kinetics, taking over 500 hours to reach the ultimate steady-state regime at this temperature. This very long relaxation process proceeds much slower than the well-known alpha-relaxation determining, e.g., the temporal evolution of the glass density, which takes only ~20 hours at this same temperature. Nevertheless, structural relaxation results in a decrease of the work of critical cluster formation leading to an upsurge of the nucleation rate. The increased nucleation rate mainly reflects this long structural relaxation mode of the glass and is not related to the classical transient nucleation, which has been exclusively employed so far in the interpretation of nucleation kinetics by most researchers, including ourselves, over the past 40 years. Our experimental results and analyses prove effect of glass relaxation on crystal nucleation and shed light on the alleged “breakdown” of the CNT at low temperatures.

Effect of Structural Relaxation on Crystal Nucleation in Glasses

Applying the Classical Nucleation Theory (CNT) to crystallization of glasses encounters some difficulties. One of the most important aspects is that this theory overlooks structural relaxation by assuming that crystal nucleation proceeds in a relaxed, metastable, supercooled liquid (SCL). Considering this assumption, the thermodynamic driving force, diffusion coefficient, and surface tension should be constant at any given temperature. Here, we performed experiments for very extended times (up to about 2,200 hours) at 703K, which well below the laboratory glass transition, [[EQUATION]] , of a lithium disilicate glass used as a model. Our results show that crystal nucleation starts concomitantly with the relaxation process of the glass towards the SCL, which strongly affects the nucleation kinetics, taking over 500 hours to reach the ultimate steady-state regime at this temperature. This very long relaxation is much slower than the well-known alpha relaxation process determining, e.g., the temporal evolution of the glass density, which takes only ~30 hours at this same temperature. Nevertheless, structural relaxation results in a decrease of the work of critical cluster formation leading to an upsurge of the nucleation rate. The increase of the nucleation rate mainly reflects this long structural relaxation mode of the glass and is not related to the classical transient nucleation, which has been exclusively employed in the interpretation of nucleation kinetics by most researchers, including ourselves, over the past 40 years. These experimental results and analyses prove that the theoretically predicted effect of glass relaxation on crystal nucleation, detailed in a forthcoming paper, is a well-founded possibility, and also sheds light on the alleged breakdown of the CNT at low temperatures.

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.

Nucleation of Crystals in Glass Based on Blast-Furnace Slag: Influence of Chemical Differentiation on the Process of Nucleation

Nucleation of Crystals in Glass Based on Blast-Furnace Slag: Influence of Chemical Differentiation on the Process of Nucleation

Homogeneous and Heterogeneous Crystal Nucleation in Glass of the Li2O–SiO2 System

The results of studying the kinetics of homogeneous (spontaneous) and heterogeneous (catalyzed) crystal nucleation in silicate glass is presented for glasses in the Li2O–SiO2 system. Nucleation is catalyzed via the photosensitive mechanism by adding poorly soluble impurities, shifting the glass composition towards the higher content of one of the components (autocatalysis), and by passing steam through the glass melt. The fundamental characteristics of crystal nucleation are obtained. The composition ranges with the maximum and minimum steady-state crystal nucleation rates are identified.

Hybrid Monte Carlo technique for modeling of crystal nucleation and application to lithium disilicate glass-ceramics

We propose a computational method for studying crystal nucleation in glasses and supercooled liquids, combining the techniques of cluster formation via Monte Carlo, Steinhardt order parameter biasing, and an implicit solvation model. Each of these techniques calculates an important contribution to the overall nucleating free energy. This hybrid Monte Carlo technique is applied to the canonical example of a lithium disilicate glass-ceramic, where it is found that the cluster formation and cluster-to-crystal transition energies are approximately equal. The known crystal precursor, lithium metasilicate, has a smaller thermodynamic barrier to nucleation compared to that of lithium disilicate. The solvation energy is small compared to the formation and crystallization energies; yet the metasilicate solvation energy is much lower, indicating easier precipitation compared to the disilicate cluster. Our hybrid Monte Carlo approach is generally applicable to study the nucleation and crystallization processes in any arbitrary glass or supercooled liquid.

Volume and Surface Nucleation of Crystals in Glass Based on Blast-Furnace Slag

Using differential thermal analysis, X-ray phase analysis, electron microscopy, and optical microscopy, the nucleation of crystals in glass obtained by blending metallurgical slag with silicon dioxide has been studied. The type of crystallization (homogeneous or heterogeneous, volume or surface) is revealed for each of nine compositions of synthesized glass. It is shown that the first crystalline phase in a volume crystallizing glass is perovskite (CaO·TiO2); in this phase a nucleation of the main phase occurs: melilite (solid solution of gehlenite 2CaO·Al2O3·SiO2 in akermanite 2CaO·MgO·2SiO2). The fundamental characteristics of homogeneous (for a catalizing phase, perovskite) and heterogeneous (for a catalyzed phase, melilite) of crystallization are determined: the steady state nucleation rate Ist, time of unsteady state nucleation τ, crystal growth rate U, and activation energy of frictional flow. The temperature dependences of Ist, τ, and U are obtained. The kinetics of the crystallization of glass is studied and the rates of the surface crystal growth are determined in the glass of nine compositions. The influence of grinding the particles of the original glass on the sequence of deposition of the crystalline phases was studied. Practical recommendations are presented for the use of blast-furnace slag as a raw material for the synthesis of glass and their further utilization.

Surface crystallization of glass based on blast furnace slags

Using differential thermal analysis, X-ray phase analysis, electron microscopy, and optical microscopy, surface nucleation of crystals in glass, obtained from metallurgical slags with the addition of SiO2, is studied. It is shown that the main phases, crystallized from the surface of the samples are melilite (solid solution of gehlenite 2СаО · Al2O3 · SiO2 in akermanite 2СаО · МgO · 2SiO2) and diopside (CaO · МgO · 2SiO2). The kinetics of the crystallization of glass is studied and the rates of the surface crystal growth are determined in the glass of nine compositions. The influence of the degree of dispersion of the particles of the original glass on the deposition order of the crystalline phases and the degree of crystallinity of the glass is studied.

Volumetric nucleation of crystals catalyzed by Cr2O3 in glass based on furnace slags

The features of the volumetric nucleation of crystals in glass obtained by melting furnace slags with the additive of SiO2, chromium sesquioxide Cr2O3, are studied by the methods of differential thermal and Xray phase analysis and optical microscopy. Upon the introduction of Cr2O3 as the catalytic additive, two phases are sequentially formed in the glass: magnesiochromite (MgO · Cr2O3) and diopside (CaO · MgO · 2SiO2). The characteristics of homogeneous and heterogeneous crystallization are determined: the stationary nucleation rate, nonstationary nucleation time, crystal growth rate, and their temperature dependences are obtained. Practical recommendations on the use of the obtained glass are given.

Homogeneous and heterogeneous nucleation of crystals of silver-containing glass and their optical properties

Noble metals nanoparticles are of interest for nonlinear optics devices. An important property of glass important property consists in the emergence of plasmon resonance (absorption band in the visible spectrum part). Bulk homogeneous and heterogeneous crystal nucleation in glass of stoichiometric composition, including lithium disilicate with additives of silver and cerium dioxide added individually and in combination, as well as the glass’s optical properties have been investigated. The emergence of plasmon resonance on Ag nanoparticles formed under the effect of X-ray radiation has been demonstrated.

Volume nucleation of crystals in glass based on blast-furnace slag

The nucleation of crystals in glass obtained by blending metallurgical slag with silicon dioxide has been studied. The type of crystallization (homogeneous or heterogeneous, volume or surface) is revealed for each of nine compositions of synthesized glass. It is shown that the first crystalline phase in a volume-crystallizing glass is perovskite (CaO · SiO2); in this phase a nucleation of the main phase occurs: melilite (solid solution of gehlinite 2CaO · Al2O3 · SiO2 in akermanite 2CaO · MgO · 2SiO2). The fundamental characteristics of homogeneous (for a catalizing phase, perovskite) and heterogeneous (for a catalyzed phase, melilite) of crystallization are determined: the steady-state nucleation rate I st, time of unsteady-state nucleation τ, crystal growth rate U, and activation energy of frictional flow. The temperature dependences of I st, τ, and U are obtained. Practical recommendations are presented for the use of blast-furnace slag as a raw material for the synthesis of glass and their further utilization.

Reduction of crystallization ability of sodium zinc phosphate glass under X-ray radiation

The effect of X-ray radiation on the crystallization ability of maximally homogenized sodium zinc phosphate glass with a minimal light scattering value of V v = 4 × 10−6 cm−1 has been investigated. The crystallization kinetics of the sodium zinc phosphate glass of the 33.9P2O5 · 56.6ZnO · 9.5Na2O (mol % from analysis) composition under the conditions of homogeneous nucleation and X-ray radiation have been studied. It has been demonstrated that the crystallization properties of phosphate glasses are more sensitive to the synthesis method than those of silicate glasses. It has been established that sodium zinc phosphate glass crystals represent the main crystalline phase precipitated in the glass of the above composition. The main parameters of nucleation have been determined in glass without preliminary radiation, including stationary nucleation rate I st, nonstationary nucleation time τ, and nucleation activation energy E τ. It have been found that the effect of the CuK α X-ray radiation leads to the slowing down or even cessation of the nucleation of crystals in glass (the result depends on the change in the radiation intensity along the sample depth) in the case when radiation takes place immediately during the nucleation thermal treatment of the sample in a high-temperature chamber of the X-ray device. The kinetics of sodium zinc phosphate crystallization in the samples upon their pretreatment by CuK α X-ray irradiation has been investigated. It has been shown that the rate of crystal nucleation in glasses exposed to X-ray radiation is lower than that in glasses without preliminary irradiation.

Crystal nucleation in glasses of phase change memory

We propose a theory of field induced crystal nucleation in disordered glass structure applicable to chalcogenide phase change memory. In the region of symmetry breaking strong electric fields, the nucleation is dominated by cylinder shaped particles with bias dependent nucleation barriers. Statistical fluctuations in microscopic structure of a glass translate into probabilistic distributions of induction times and threshold voltages having respectively log-normal and normal shape. These distributions are exponentially sensitive to the applied voltage, temperature, and material parameters.

A transmission electron microscopy study of phase separation and crystal nucleation in glasses containing Fe2O3 or P2O5 and Fe2O3

A transmission electron microscopy study of phase separation and crystal nucleation in glasses containing Fe2O3 or P2O5 and Fe2O3

Metastable phases in lithium disilicate glasses

This article deals with crystal nucleation in glass, with special emphasis on new findings about metastable phase formation in lithium disilicate glass (LS 2) and its effects on crystallization of the stable LS 2 crystal phase. The early crystallization stages of slightly sub-stoichiometric LS 2 glasses were probed with SAXS and selected area diffraction (SAD). The second task was accomplished by carefully measuring the crystal nucleation rate ( I), growth rate ( U), the time evolution of crystallinity and the apparent induction periods ( t′) for crystal nucleation and growth at 500°C ( T g ∼ 450°C). Finally, the independently determined kinetic parameters ( I and U) were used in a modified form of the JMAK equation, which account for transient nucleation conditions, to test the nucleation mechanism. Depending on the heat treatment, one or more metastable phases precipitate in the early crystallization stages of LS 2 glass, however, they do not play a significant role on the crystallization mechanism of the thermodynamically stable phase.

Diffuse interface approach to crystal nucleation in glasses

A diffuse interface theory of nucleation is applied to the crystallization of various glasses. This approach eliminates the problem of ‘anomalous’ nucleation prefactors and offers a method of distinguishing between homogeneous and bulk heterogeneous processes.

A theoretical and experimental assessment of systematic errors in nucleation experiments

Equations are derived for the fractional underestimate in the number of particles per unit volume, N v , and in nucleation rates, I 0, as obtained by stereological techniques from reflected light microscopy or SEM for typical cases of crystal nucleation in glasses. Three cases are considered: (i) instantaneous heterogeneous nucleation (mondispersed systems of particles); (ii) simultaneous homogeneous nucleation and growth in a single-stage heat treatment (uniform distribution of particles from the critical size to D M, where D M is the largest diameter); (iii) case (ii) with a double heat treatment (uniform size distribution from D M, the smallest diameter, to D M). Comparison with experimental nucleation data for BaO SiO 2 and Na 2O CaO SiO 2 glasses demonstrates that the equations derived predict well the observed underestimations Typical experiments with optical microscopy lead to underestimates from 3% to 14% for case (iii) and up to 50% for case (ii). To minimize these errors one should use a high magnification objective lens with reflection or transmitted light microscopy, or electron microscopy.

The quantitative determination of the effectiveness of nucleating agents

Consideration is given to the assessment of the effectiveness of nucleating agents in promoting heterogeneous crystal nucleation in glass. A quantitative measure of nucleation potency Q is the ratio of the free energies required to form a critical radius with and without nucleating agents present in the glass. Previously employed methods to determine Q are laborious and often require unverified assumptions concerning the nature of the nucleation process. A simple alternative scheme is proposed and illustrative calculations are presented for platinum induced nucleation of lithium disilicate glass. Further, it is shown that the combined use of this method and other techniques for determining Q could verify the hypothesis that temperature variation of glass-crystal surface tension is the cause of the discrepancies between the Classical Nucleation Theory and experimental data for homogeneous nucleation rates in simple silicate glasses.

Numerical modelling of crystal nucleation in glasses

Nucleation is important in influencing microstructures obtained by solidification. The fundamentals of crystal nucleation are most readily studied in glasses. Some recent results on metallic glasses are reviewed. Numerical modelling of transient nucleation kinetics can provide fits to measured data and can test theory. New extensions of the modelling to heterogeneous nucleation and to two-component systems with differing species mobilities are described.

Re-examination of the temperature dependence of the classical nucleation rate: Homogeneous crystal nucleation in glass

A comparison is made between the experimentally determined and predicted (Classical Nucleation Theory) temperature dependence of the homogeneous crystal nucleation rate in glass. Literature data for several glass-forming systems are analyzed. It is shown that the standard assumptions which are invoked to replace the free energy of activation for transport across the liquid-crystal interface, ΔG D, in favor of a more easily measured parameter (viscosity) are not required. It is demonstrated that ΔG D may be found experimentally by determining the temperature dependence of the nucleation transient time. Furthermore, it is shown that precise thermodynamic data are not necessarily required in order to make comparisons between the theoretically predicted and experimentally determined temperature variation of the nucleation rate. It is concluded that the temperature dependence of the classical homogeneous nucleation rate is still a matter of controversy.