Nucleation time-lag from nucleation and growth experiments in deeply undercooled glass-forming liquids

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 Na₂O · 2CaO · 3SiO₂ 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 Na₂O · 2CaO · 3SiO₂ 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.     

Heterogeneous slow dynamics and the interaction potential of glass-forming liquids

The role of the intermolecular interaction potential on the dynamic and thermodynamic properties of model glass-forming mixtures is investigated through molecular dynamics simulations. Variations of the repulsive exponent m in the well-studied Lennard-Jones Kob-Andersen mixture are shown to have a negligible effect on the fragility and dynamic correlation volumes when quenches are performed at constant pressure. The number of dynamically correlated particles, estimated from the temperature derivative of a two-point dynamic correlation function, is approximately invariant to m at any fixed relaxation time. Further, the density scaling property of a model tetrahedral network glass-former, based on inverse power law and Lennard-Jones potentials, is investigated. The optimal scaling exponent γ is close to zero and does not superpose the data well. The breakdown of density scaling is consistent with the absence of correlation between fluctuations of the virial and the potential energy. These results emphasize the crucial role of structural many-body correlations in glass-forming systems and show the need of investigations of more complex and realistic model liquids.     

A new criterion for the glass-forming ability of liquids

Based on theoretical calculations using the fragility concept and the nucleation theory for a model glass-forming system, we propose a dimensionless criterion, ?, expressed by T_rg(ΔT_x/T_g)^a, with T_rg, the reduced glass-transition temperature, ΔT_x, the width of the supercooled liquid region when heating a glass, T_g, the glass transition temperature, and a, the exponent. The application of this simple criterion to various glasses, including network, metallic, and molecular glasses (except pure water), indicates an excellent correlation between the critical cooling rate R_c and ? in a Log R_c-? single master plot with a = 0.143.     

Elastic models for the non-Arrhenius viscosity of glass-forming liquids

This paper first reviews the shoving model for the non-Arrhenius viscosity of viscous liquids. According to this model the main contribution to the activation energy of a flow event is the energy needed for molecules to shove aside the surrounding, an energy which is proportional to the instantaneous shear modulus of the liquid. Data are presented supporting the model. It is shown that the fractional Debye–Stokes–Einstein relation, which quantitatively expresses the frequently observed decoupling of, e.g., conductivity from viscous flow, may be understood within the model. The paper goes on to review several related explanations for the non-Arrhenius viscosity. Most of these are also ‘elastic models’, i.e., they express the viscosity activation energy in terms of short-time elastic properties of the liquid. Finally, two alternative arguments for elastic models are given, a general solid-state defect argument and an Occam’s razor type argument.     

Nucleation kinetics of sodium disilicate

The kinetics of crystal nucleation in Na₂O · 2SiO₂ have been determined over the range of undercoolings between 173 and 373°C. The plot of log(I_v?) versus $\text{1}\text{ΔT}{}^2{}_{\mathrm{r}}\text{T}{}^3{}_{\mathrm{r}}$ is a straight line of negative slope over some 13 orders of magnitude in I_v. The slope of this relation indicates a nucleation barrier of about 45 kT at ΔT_r = 0.2, and the intercept at $\text{1}\text{ΔT}{}^2{}_{\mathrm{r}}\text{T}{}^3{}_{\mathrm{r}}\text{= 0}$ is 10²⁶ cm^-3 sec^-1. poise. The results are in good agreement with predictions of the theory of homogeneous nucleation, even in the pre-exponential factor.     

Evaluation of glass-forming ability criterion from phase-transformation kinetics

Applying kinetic analysis upon crystallization of metallic glass, a quantitative relation between the critical cooling rate and the onset temperature of crystallization was obtained for glass-forming alloys. Effects of the onset temperature of crystallization, the liquidus temperature and the glass transition temperature on the critical cooling rate were analytically described. Three rules guiding the development of more reliable glass-forming ability criteria are suggested.     

Nucleation kinetics at strong supersaturation

Nucleation in an arbitrary d-dimensional system is considered. Two nucleation regimes are predicted within an original kinetic approach. The first regime (for a weak supersaturation) is characterized by the formation of a critical nucleus (critical nucleus regime). The second regime (for a strong supersaturation) corresponds to an uncontrollable growth of a cluster of any size (runaway nucleation regime). It is established that the nucleation regime is controlled by the metastability parameter M of the system under consideration. The analytical properties of the free energy of the nucleation system are investigated. It is demonstrated that a change in the parameter M leads to a considerable transformation of the nucleation barrier topography. The effect of the nucleation barrier height on the kinetics of nonstationary nucleation is described.     

Evaluation of the guided random parameterization method for critical cooling rate calculations

We focus on a recently suggested approach to the calculation of critical cooling rates for glass formation. It is a “random parameterization” method that is guided by a limited number of isothermal scanning calorimetry experiments. However, several assumptions have been made in its derivation that may not mirror the actual crystallization behavior of most supercooled liquids, which may jeopardize the estimation of glass forming ability. We evaluate those assumptions and the applicability of the method is tested for lithium disilicate glass (which displays moderate internal nucleation rates) and dibarium titanium silicate glass (which displays very high internal nucleation rates, similar to those of metallic glasses). Both glasses nucleate homogeneously and exhibit polymorphic crystallization. Our calculations show that some overlooked variables, such as the sample geometry, nucleation induction-times, surface crystallization and the breakdown of the Stokes–Einstein/Eyring equation, have significant roles on the calculated time–temperature–transformation curves during heating experiments. We demonstrate that the proposed random parameterization method can only be used when a glass forming liquid that undergoes internal crystallization is cooled from above its liquidus to various test temperatures. If the sample undergoes predominant surface crystallization or if it is heated to the test temperature several corrections must be made.     

A critical analysis of the glass-forming ability of alloys

Several empirical rules have been proposed during the past few years to synthesize bulk metallic glasses. But, the real reasons for the improved glass-forming ability of these alloys are still not clear and the ability to design alloy compositions to enable synthesis of larger diameter rods has not improved. The present work conducts a critical analysis of the existing data in terms of the different glass-forming criteria and concludes that the available parameters cannot satisfactorily predict the GFA and explain all the observed data. Reasons for this failure have been suggested.     

Relationship between viscous dynamics and the configurational thermal expansion coefficient of glass-forming liquids

We propose a model to describe the relationship between the viscosity of a glass-forming liquid and its configurational contribution to liquid state thermal expansion. The viscosity of the glass-forming liquids is expressed in terms of three standard parameters: the glass transition temperature (T_g), the liquid fragility index (m), and the extrapolated infinite temperature viscosity (η_∞), which are obtained by fitting of the Mauro–Yue–Ellison–Gupta–Allan (MYEGA) expression to measured viscosity data. The model is tested with experimental data for 41 different glass-forming systems. A good correlation is observed between our model viscosity parameter,h(T_g, m, η_∞), and the configurational coefficient of thermal expansion (i.e., the configurational CTE). Within a given class of glass compositions, the model offers the ability to predict trends in configurational CTE with changes in viscosity parameters. Since viscosity is governed by glass network topology, the model also suggests the role of topological constraints in governing changes in configurational CTE.     

Raman line shape analysis as a mean characterizing molecular glass-forming liquids

Raman scattering spectra in glass forming toluene were studied in the temperature range 50–323 K with the goal of extracting information about homogeneous, inhomogeneous and orientational broadening. It was found that the temperature dependence of inhomogeneous line width allows one to depict two peculiar temperatures: T_A and T_g, where T_g is the glass transition temperature and T_A is the temperature of transition from an Arrhenius-like to a non-Arrhenius behavior for the α-relaxation time dependence on temperature, τ_α(T). Temperature dependence of the orientational phase loss time τ_OPL was found to correspond well to τ_α at T > T_A and continues approximately Arrhenius behavior for lower temperature in contrast to τ_α(T). Also, a comparative analysis of homogeneous broadening of polarized and depolarized lines was done, which provided an estimation of the orientational broadening γ_NL(T). The found γ_NL(T) decreases linearly as the temperature decreases and goes to zero at T ~ T_c, where T_c is the critical temperature in framework of the mode-coupling theory (note that T_c is close to other peculiar temperatures T_B and T_β, but we did not intent to distinguish among them in the present work). Thus, it was shown that the Raman line shape analysis in molecular glass forming materials allows one to extract peculiar temperatures: T_A, T_g, and, probably, T_c.The test of the possibility to use a probe molecule for the Raman line shape analysis has revealed that the extracted data for probe molecule lines do not characterize the host matrices, at least in the low-viscous state (T > T_A).     

One master curve for self-diffusion of one atom in different glass-forming liquids

Self-diffusion of a single atom α in glass-forming liquids, A_xB_yC_z ?, is studied from a unified point of view based on the mean-field theory (MFT) proposed recently by the present author, where α ∈ {A, B, C,...} and x + y + z + cdots = 100. Several experimental data and simulation results available at present are then analyzed consistently with the aid of MFT. Thus, it is shown that there exists a master curve for the long-time self-diffusion coefficient D_S^L(α)of α atom, even though atom α belongs to any different multicomponent glass-forming liquids. This suggests that if a whole data set for D_S^L(α) in a simple glass-forming liquid is once found, only one data point for α atom in any other complex glass-forming liquids is enough to predict a whole control parameter dependence of D_S^L(α) for each α atom belonging to those liquids.     

Nucleation kinetics in deionized charged colloidal suspension

A systematic experimental study on the nucleation, crystallization and crystal-growth of one-component charged colloidal particles (122 nm diluted in pure water with densities between 0.5 μm⁻³ < n_p < 5 μm⁻³) is present by means of time resolved static light scattering spectroscopy revealing the heterogeneous and homogenous nature of the crystallization. The interactions between the charged colloidal particles are sufficiently strong to cause crystallization which described in terms of Debye-Hückel approximation. Crystallization starts always with the formation of compressed structurally heterogeneous precursor domains. The results show that the heterogeneous nucleation at the cell walls starts simultaneously with the homogeneous bulk nucleation and the rate density of the heterogeneous nucleation appears slightly higher. It has been also found that the overall crystallization consists of at least a two-step nucleation process involving formation of early stage nuclei or crystal precursor then followed by the main crystallization. The induction time, the number density of nuclei and the growth rate of crystals, is strongly dependent on particle concentration and on whether the nucleation are homogeneous in cell center or heterogeneous on cell walls.     

The crystallisation of alkaline-earth metal molybdates and tungstates from lithium chloride melts by continuous cooling. Nucleation mechanism and kinetics and induction periods

Calcium, strontium and barium molybdate (and tungstate) solutions in lithium chloride melts were crystallised in alumina and in platinum crucibles; saturated solutions were cooled from initial temperatures 700° to 800°C down to room temperature at cooling rates 40° to 200°C hr⁻¹. The nucleation and early crystal growth were investigated by chemical and differential thermal analysis and by optical microscopy studies. Crystallisation occurred through heterogeneous nucleation at low supersaturations. Heterogeneous nuclei formed slowly onto metal aluminate (and platinate) particles within the solution during induction periods from < 0.2 to 14 hr. The main growth surge then started and few new nuclei were formed. The nucleation probably terminated at times just after the times for maximum rate of formation of nuclei. Then, at any temperature, the induction periods (t ) varied inversely with cooling rate and with the rate (R_c) of development of excess solute concentration according to the relation, The parameters k₁ were related to the rate constants (k_n) for the heterogeneous nucleation. These constants in turn probably dependend on the free energy for formation of critical heterogeneous nuclei and thence on some nucleator vs solute surface energy ‘wetting’ function. The k₁ and k_n values at any temperature decreased in the order : they increased from 2 to 4 times for 100°C rise in temperature.     

High-temperature in situB NMR study of network dynamics in boron-containing glass-forming liquids

In situ high-temperature nuclear magnetic resonance (NMR) spectroscopy can be very useful for probing changes in structure and dynamics in glass-forming liquids, and is a unique method for observing chemical exchange among structural species (e.g. BO₃–BO₄, Qⁿ–Qⁿ⁺¹, and NBO–BO) at the seconds to microseconds time scales. High-temperature ¹¹B MAS NMR line shape measurements were made at about 100 K above the glass transitions on (Na₂O)_0.3(B₂O₃)_0.7 and (Na₂O)_0.2(B₂O₃)_0.21(Al₂O₃)_0.08(SiO₂)_0.51 glass-forming liquids. BO₃ and BO₄ groups are well resolved in ¹¹B MAS NMR spectra at 14.1 T with sample spinning at 5000 Hz. At higher temperatures, partial peak coalescence occurred due to exchange of BO₃ and BO₄. Temperature effects on borate speciation were also determined by varying the fictive temperature (T_f) of glasses, where T_f estimated from differential scanning calorimetry measurements. We combined these complementary data sets to model structural exchange in the liquid state. The time scale of BO₃–BO₄ exchange from NMR data, τ_NMR, appears to be “decoupled” from that of the macroscopic shear relaxation process τ_s derived from the viscosity, however, at higher temperatures, τ_s approaches τ_NMR. The “decoupling” at lower temperature may be related to intermediate-range compositional heterogeneities, and/or fast modifier cation diffusivities which trigger “unsuccessful” network exchange events.