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 · 2SiO 2 , PbO · SiO 2 , CaO · Al 2 O 3 · 2SiO 2 , CaO · MgO · 2SiO 2 and 2MgO · 2Al 2 O 3 · 5SiO 2 ; plus Li 2 O · 2SiO 2 and Li 2 O · 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 ( T x h ) , the peak crystallization temperature on heating ( T c h ) , 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. IDT C250 C290 C2865 G160 G183 PACS 64.70.Dv 81.10.Aj 1 Introduction There is now consensus that any material can vitrify if cooled from the molten state to the glass transition temperature, T g , at a rate fast enough to prevent crystallization. The slowest a material can be cooled down to T g without crystallization the easiest it is vitrified, and this property is denominated glass forming ability (GFA). A maximum allowed fraction of crystals, X c , usually taken between 0.1% and 0.0001%, is conventionally assumed to classify a material as glassy. One can thus define a critical cooling rate , q cr , to avoid a crystalline fraction higher than X c on cooling a liquid. Therefore, q cr gauges GFA. However, it is quite difficult to accurately measure q cr and the complexity increases for reluctant glass formers that require very high cooling rates. If one could devise indirect ways to estimate GFA would then avoid exhaustive laboratory investigations, and this is thus a key step for efficient development of new glasses and glass-ceramics. On the other hand, once a glass is made, for instance by fast quenching a melt, its stability against crystallization can be easily investigated. The resistance of a given glass against crystallization upon reheating defines glass stability (GS). GS is typically derived from characteristic temperatures that are determined from simple non-isothermal analyses, such as DTA or DSC. It is thus desirable to know how one can estimate GFA from GS measurements. However, the definitions of GS are somewhat arbitrary, only seldom have been rigorously tested and, as we will summarize below, it is controversial if there is any straightforward relationship between GFA and GS. In this work, we experimentally test the existence of possible correlations between precisely calculated critical cooling rates (GFA) and fourteen ways to characterize GS using DSC. We use eight stoichiometric glasses: GeO 2 (G), Na 2 O · 2SiO 2 (NS 2 ), CaO · MgO · 2SiO 2 (CMS 2 ), PbO · SiO 2 (PS), 2MgO · 2Al 2 O 3 · 5SiO 2 (M 2 A 2 S 5 ) and CaO · Al 2 O 3 · 2SiO 2 (CAS 2 ), which only show heterogeneous (surface) nucleation; plus Li 2 O · 2SiO 2 (LS 2 ) and Li 2 O · 2B 2 O 3 (LB 2 ) that also show homogeneous (internal) nucleation in addition to predominant surface nucleation. Therefore, the paper’s objective is to systematically verify possible relationships between GFA and GS parameters for glasses that crystallize via the most common nucleation mechanism, i.e. surface (heterogeneous) nucleation. 1.1 Literature review 1.1.1 Glass forming ability A variety of theories have been proposed to understand why some systems easily vitrify while others do not [1,2] . Ultimately, a high glass forming ability is associated with slow crystallization rates. Uhlmann [3] was one of the first to use the concept of crystallization kinetics controlling glass formation. His method refers to TTT (time–temperature–transformation) diagrams, which are temperature versus time graphs showing curves that correspond to specified fractions of transformed phase. A curve in a TTT diagram shows how one can set a thermal treatment to achieve a given fraction of transformed phase. To vitrify a liquid by cooling, the crystallized fraction of interest is normally the smallest detectable, usually assumed to be 10 −2 –10 −6 . A ‘nose’ arises in the TTT diagrams at a temperature T n and time t n where the rate of transformation is the fastest. According to the nose method , the critical cooling rate for glass formation, q cr n , is given by (1) q cr n = T m - T n t n . However, critical cooling rates calculated by the nose method are typically one order of magnitude greater than experimentally determined values [4] . Thus, this method can only be used to estimate relative critical cooling rates...

An analysis of the kinetic coefficient of crystal growth Ukin, 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. Ukin was defined using the normal growth model and tested for crystal data for inorganic and organic liquids covering a viscosity range of about 104–1012 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 Tg, thus covering a wider viscosity range: 101–1013 Pa s. We then propose and use normalized kinetic coefficients (Mkin) 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 (Mkin∼1/η and ξ∼1) from low to moderate viscosities (η<106 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 Tg! However, for at least three fragile liquids, diopside (kink at 1.08Tg, η=1.6×108 Pa s), lead metasilicate (kink at 1.14Tg, η=4.3×106 Pa s), and lithium disilicate (kink at 1.11Tg, η=1.6×108 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 Tg.

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 (Li₂O·2SiO₂) 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, O²⁻, and Si⁴⁺ 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 Li₂Si₂O₅ “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 $D_{eff}^{\eta }$ , 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 $D_{eff}^{\eta }$ by about eightfold. The difference between $D_{eff}^{\eta }$ 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 $T_d^U\approx 1.1-1.2T_g$ , when $D_{eff}^{\eta }$ begins decrease with decreasing temperature faster than $D_{eff}^U$ . A similar decoupling occurs between $D_{eff}^{\eta }$ and $D_{eff}^{\tau }$ (estimated from nucleation time-lags) but at a lower temperature$T_d^{\tau }\approx T_g$ . For T > T_g the values of $D_{eff}^{\tau }$ exceed $D_{eff}^{\eta }$ only by twofold. The different behaviors of $D_{eff}^{\tau }\left(T\right)$ and $D_{eff}^U\left(T\right)$ 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.