Glass-forming ability (GFA) is the easiness to vitrify a liquid on cooling, while glass stability (GS) is the glass resistance against devitrification on heating; but it is questionable if there is any direct relationship between these two parameters. Therefore, to test this possibility, we assess and compare GFA and several GS parameters through quantitative criteria. GFA and GS were calculated for six stoichiometric glass forming oxides that only present surface (heterogeneous) crystallization in laboratory time scales: GeO 2 , Na 2 O AE 2SiO 2 , PbO AE SiO 2 , CaO AE Al 2 O 3 AE 2SiO 2 , CaO AE MgO AE 2SiO 2 and 2MgO AE 2Al 2 O 3 AE 5SiO 2 ; plus Li 2 O AE 2SiO 2 and Li 2 O AE 2B 2 O 3 that, in addition to surface nucleation, also present homogeneous (internal) crystallization. We gauge GFA by the critical cooling rate, q cr , which was calculated from an estimated number of heterogeneous nucleation sites per unit surface, N s , and from experimental crystal growth rates, u(T), assuming a detectable surface crystallized fraction X c = 0.001. We define GS parameters by fourteen different combinations of the following characteristic differential thermal analysis (DTA) or differential scanning calorimetry (DSC) temperatures: the glass transition temperature (T g ), the onset crystallization temperature on heating ðT h x Þ, the peak crystallization temperature on heating ðT h c Þ, and the melting point (T m ). To obtain the experimental GS parameters for each glass we carried out DSC runs using coarse and fine powders, and completed the necessary data with literature values for T m . The results for fine and coarse particles were quite similar. Most of the GS parameters that consist of three characteristic DSC temperatures show excellent correlation with GFA, however, rather poor correlations were observed for parameters that use only two characteristic temperatures. We thus demonstrated that certain, but not all GS parameters can be used to infer GFA.

An analysis of the kinetic coefficient of crystal growth U(kin), recently proposed by Ediger et al. [J. Chem. Phys. 128, 034709 (2008)], indicates that the Stokes-Einstein/Eyring (SE/E) equation does not describe the diffusion process controlling crystal growth rates in fragile glass-forming liquids. U(kin) was defined using the normal growth model and tested for crystal data for inorganic and organic liquids covering a viscosity range of about 10(4)-10(12) Pa  s. Here, we revisit their interesting finding considering two other models: the screw dislocation (SD) and the two-dimensional surface nucleated (2D) growth models for nine undercooled oxide liquids, in a wider temperature range, from slightly below the melting point down to the glass transition region T(g), thus covering a wider viscosity range: 10(1)-10(13) Pa  s. We then propose and use normalized kinetic coefficients (M(kin)) for the SD and 2D growth models. These new kinetic coefficients restore the ability of viscosity to describe the transport part of crystal growth rates (M(kin)∼1/η and ξ∼1) from low to moderate viscosities (η<10(6) Pa  s), and thus the SE/E equation works well in this viscosity range for all systems tested. For strong glasses, the SE/E equation works well from low to high viscosities, from the melting point down to T(g)! However, for at least three fragile liquids, diopside (kink at 1.08T(g), η=1.6×10(8) Pa  s), lead metasilicate (kink at 1.14T(g), η=4.3×10(6) Pa  s), and lithium disilicate (kink at 1.11T(g), η=1.6×10(8) Pa  s), there are clear signs of a breakdown of the SE/E equation at these higher viscosities. Our results corroborate the findings of Ediger et al. and demonstrate that viscosity data cannot be used to describe the transport part of the crystal growth (via the SE/E equation) in fragile glasses in the neighborhood of T(g).

a b s t r a c tMicroscopy methods are usually employed to estimate the number density of super critical nuclei and the resulting crystal nucleation rates, I(T). These traditional techniques rely on a double-stage treatment, i.e. the development of the nuclei at a temperature higher than the previous nucleation temperature up to a size large enough to be visible with optical or electron microscopy. These methods can give reliable results for I(T), but are rather laborious and time-consuming. On the other hand, non-isothermal (DTA/ DSC) methods are, in principle, much faster. In this paper, we experimentally test two non-isothermal methods by comparison with a traditional optical microscopy method. We found that, if they are properly employed, non-isothermal methods can give useful kinetic information, which includes the crystal number density and nucleation rates, but to get accurate quantitative data they need some preliminary information about nucleation and growth rates in the studied glass and, in addition, are as laborious as the traditional microscopy methods! Ó

We collect and critically analyze extensive literature data, including our own, on three important kinetic processes--viscous flow, crystal nucleation, and growth--in lithium disilicate (Li(2)O·2SiO(2)) over a wide temperature range, from above T(m) to 0.98T(g) where T(g) ≈ 727 K is the calorimetric glass transition temperature and T(m) = 1307 K, which is the melting point. We found that crystal growth mediated by screw dislocations is the most likely growth mechanism in this system. We then calculated the diffusion coefficients controlling crystal growth, D(eff)(U), and completed the analyses by looking at the ionic diffusion coefficients of Li(+1), O(2-), and Si(4+) estimated from experiments and molecular dynamic simulations. These values were then employed to estimate the effective volume diffusion coefficients, D(eff)(V), resulting from their combination within a hypothetical Li(2)Si(2)O(5) "molecule". The similarity of the temperature dependencies of 1/η, where η is shear viscosity, and D(eff)(V) corroborates the validity of the Stokes-Einstein/Eyring equation (SEE) at high temperatures around T(m). Using the equality of D(eff)(V) and D(eff)(η), we estimated the jump distance λ ~ 2.70 Å from the SEE equation and showed that the values of D(eff)(U) have the same temperature dependence but exceed D(eff)(η) by about eightfold. The difference between D(eff)(η) and D(eff)(U) indicates that the former determines the process of mass transport in the bulk whereas the latter relates to the mobility of the structural units on the crystal/liquid interface. We then employed the values of η(T) reduced by eightfold to calculate the growth rates U(T). The resultant U(T) curve is consistent with experimental data until the temperature decreases to a decoupling temperature T(d)(U) ≈ 1.1-1.2T(g), when D(eff)(η) begins decrease with decreasing temperature faster than D(eff)(U). A similar decoupling occurs between D(eff)(η) and D(eff)(τ) (estimated from nucleation time-lags) but at a lower temperatureT(d)(τ) ≈ T(g). For T > T(g) the values of D(eff)(τ) exceed D(eff)(η) only by twofold. The different behaviors of D(eff)(τ)(T) and D(eff)(U)(T) are likely caused by differences in the mechanisms of critical nuclei formation. Therefore, we have shown that at low undercoolings, viscosity data can be employed for quantitative analyses of crystal growth rates, but in the deeply supercooled liquid state, mass transport for crystal nucleation and growth are not controlled by viscosity. The origin of decoupling is assigned to spatially dynamic heterogeneity in glass-forming melts.

Extensive data on the viscosity, covering 15 orders of magnitude, and crystal growth rate, covering seven orders of magnitude, of liquid diopside (CaO.MgO.2SiO(2)) were collected in a wide range of undercoolings from 1.10T(g) to 0.99T(m) (T(g) is the glass transition temperature and T(m) the melting point). The raw growth rate data were corrected for the increased interfacial temperature produced by the heat released during crystallization. A detailed analysis confirms that growth mediated by screw dislocations reasonably explain the experimental data in these wide ranges of temperatures and growth rates. Effective diffusion coefficients were calculated from crystal growth rates and from viscosity, and were then compared with measured self-diffusion coefficients of silicon and oxygen in diopside melt. The results show that oxygen and silicon control the diffusion dynamics involved in crystal growth and viscous flow. This study not only unveils the transport mechanism in this complex liquid, but also validates the use of viscosity (through the Stokes-Einstein or the Eyring equations) to account for the kinetic term of the crystal growth expression in a wide range of temperatures.

Recent publications demonstrate that the maximum homogeneous nucleation rates, I max , of silicate glasses strongly diminish with the reduced glass transition temperature, T gr (=T g /T m/L , where T g is the glass transition temperature and T m/L is the melting point or liquidus temperature). In addition, the critical cooling rates for metallic glass formation, R c , also drop with rising T gr . From these empirical observations as well as from theoretical considerations, it is expected that the maximum crystal growth rates, U max , also depend on T gr . In this paper we test and confirm this assumption by plotting experimental U max vs. T gr for 20 silicate glasses, and then use the most common crystal growth model -screw dislocation growth -to calculate and compare maximum experimental growth rates with theoretical predictions. Despite several assumptions made for the calculations, there is good agreement between theory and experiment, both in the magnitude of U max (T gr ) and in the temperature of the maximum crystal growth rate, T U max . These findings indicate that the screw dislocation growth model is a good approximation to describe crystal growth in silicate glasses.

The well-known Vogel-Fulcher-Tammann-Hesse equation (VFTH, log 10 Z ¼ A+B/(TÀT 0), Z in Pa s and T in K) has been extensively used in the description & characterization of cooperative molecular motion by means of the temperature dependence with viscosity, Z, e.g., using Angell's classification. Experimental evidence has been pointed out for the statistical correlation between its three adjustable parameters A, B and T 0 , which may bring questions on the reliability of fitted VFTH parameters. In this work VFTH equation was applied over a wide temperature range (between glass transition temperature, T g and the melting point, T m) for 38 oxide glasses, considering simple, binary and ternary compositions of silicates and borates systems. These systems include strong, moderate and fragile glass-forming liquids. For this task was used the Levenberg-Marquart non-linear fitting procedure to find viscosity parameters B and T 0 , maintaining A ¼ À5 fixed, intending to reduce the number of adjustable parameters. Despite this restriction, the VFTH equation has shown to adjust very well to experimental data in wide temperature range. Simple criteria were developed in the past to characterize glass-forming liquids, one of them (due to Angell) is the strong-fragile classification. In this work we apply correspondence analysis (CA) to verify the correlation between B and T 0 parameters as well as between T g and T m. CA is a descriptive and exploratory technique designed to analyze simple multi-way tables containing some measure of correspondence between rows and columns. From these results is possible to map either borate (and almost fragile) or silicate (usually strong up to near fragile) systems. As a statistical tool, CA corroborates correlation mainly between B and T 0 and justifies the use of B, T 0 and T g as the main parameters for the fragility indexes m ¼ BT g /(T g ÀT 0) 2 and D ¼ B/T 0 .

a b s t r a c tWe measured and collected literature data for the crystal growth rate, u(T), of l-cordierite (2MgO Á 2Al 2 O 3 Á 5SiO 2 ) and diopside (CaO Á MgO Á 2SiO 2 ) in their isochemical glass forming melts. The data cover exceptionally wide temperature ranges, i.e. 800-1350°C for cordierite and 750-1378°C for diopside. The maximum of u(T) occurs at about 1250°C for both systems. A smooth shoulder is observed around 970°C for l-cordierite. Based on measured and collected viscosity data, we fitted u(T) using standard crystal growth models. For diopside, the experimental u(T) fits well to the 2D surface nucleation model and also to the screw dislocation growth mechanism. However, the screw dislocation model yields parameters of more significant physical meaning. For cordierite, these two models also describe the experimental growth rates. However, the best fittings of u(T) including the observed shoulder, were attained for a combined mechanism, assuming that the melt/crystal interface growing from screw dislocations is additionally roughened by superimposed 2D surface nucleation at large undercoolings, starting at a temperature around the shoulder. The good fittings indicate that viscosity can be used to assess the transport mechanism that determines crystal growth in these two systems, from the melting point T m down to about T g , with no sign of a breakdown of the Stokes-Einstein/Eyring equation.