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.     

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.     

Nucleation kinetics and critical cooling rate of glass-forming liquids

The critical cooling rate of a substance is the minimum linear rate at which its melt must be cooled to prevent crystallization entirely. In a number of systems this critical cooling rate has proved to be a useful quantitative experimental measure of the tendency to glass formation.The present paper describes a method of deriving theoretical values of the critical cooling rate from classical nucleation kinetics.In general, the calculated values show the correct tendency to glass formation.     

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.     

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.     

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.     

Effect of Ti addition on the crystallization behavior and glass-forming ability of Zr-Al-Cu alloys

The crystallization behavior of melt-spun (Zr₆₅Al_7.5Cu_27.5)_100−xTi_x (x = 0-15; in at.%) metallic glasses has been investigated by X-ray diffraction (XRD), transmission electron microscopy (TEM) and differential scanning calorimetry (DSC). The DSC traces showed an altered crystallization mode in the vicinity of 3 at.% Ti addition. A metastable icosahedral quasicrystal precipitated at the first crystallization stage of the Ti-bearing metallic glasses, which subsequently transformed to the stable Zr₂Cu-type phase in the followed exothermic reaction. The glass-forming abilities (GFAs) of these metallic glasses were assessed by the recognized GFA indicators T_rg, ΔT_x and γ. BMGs were easily made in the compositions containing 3-7 at.% Ti by means of copper mold casting. The validity of these parameters was clarified using the critical BMG forming diameter evidence.     

Dynamics in glass-forming mixtures: Comparison of behavior of polymeric and non-polymeric components

Recent experiments have shown that the segmental dynamics of dilute polymer chains in glass-forming matrices are substantially different than the dynamics of the host. In contrast, we show here that the dynamics of dilute low molecular weight species (tetracene and rubrene) are very similar to the dynamics of the host matrix. This is consistent with the view that self-concentration is a dominant factor in determining the dynamics of polymer chains in glass-forming mixtures; as a polymeric effect, self-concentration should be negligible for low molecular weight species. In addition, we show that self-concentration may play an important role in understanding segmental dynamics in concentrated polymer solutions.     

Molecular dynamics study of the dynamical behavior in ionic liquids through interionic interactions

We have focused on the interionic dynamics of an IL, 1-butyl-3-methylimidazolium cation with the anion, [PF₆]^?, [BMIm][PF₆], and have investigated the interionic interaction in the IL and the polarization effects on the system. Molecular dynamics simulations have been carried out to pursue the understanding of interionic properties in ILs at molecular level. The analyses of velocity cross-correlation functions have been performed to study the interionic interactions. We have computed the momentum correlation functions between ionic species. From simulation results, it is suggested that, at the short time region up to 1 ps, the velocity cross-correlation is predominantly governed by the longitudinal contribution. It is found out that, compared with the longitudinal correlation in the nonpolarizable model, the longitudinal motions are further influenced in the polarizable model. It is indicated that the behavior of mean-squared displacement of the cation at a long-time region is not influenced by polarization effects, while the anion shows important difference. Also, it is concluded that the cage effect in ILs could be reduced by many-body polarization effects.     

Determination of refractive indexes of dielectric films by the use of immersion liquids

Examples of using immersion liquids in ellilipsometry and multiple-beam interferometry are given. The refractive index of very thin (∼ 5.0 nm) silica films on silicon and on films of silicon nitride are determined by the ellipsometry method. The method of precise determination of refractive index of monolayer dielectric films is described when a precision equal to ± 3 · 10⁻⁴ was reached. A method of determination film thicknesses near the substrate surface in a twolayer system is suggested. The construction of different prisms is given by means of which the immersion liquids are inserted. The selection of the equations for the determination of refractive index in the multiple-beam interferometry is discussed. Two versions of the use of immersion liquids for the determination of refractive indexes of dielectric films by interferometry method are given.     

Calculation of thermodynamic parameters of melts from experimentally determined liquidus‐curves

Thermodynamic parameters of melts (ΔH_S, A₀, A₁) in the system Anorthite‐Diopside and Bi₂O₃‐Bi₄B₂O₉ have been calculated by a rigorous application of solution thermodynamics. The data are internally consistent and yield values of ΔH_S for Anorthite = 133 kJ/mole, Diopside = 81 kJ/mole, Bi₂O₃ = 19 kJ/mole and Bi₄B₂O₉ = 39 kJ/mole. The activity of Anorthite and Diopside in an anorhtitic melt deviates negative from ideality, whereas a diopsidic melt behaves almost ideal. In a “Bi₂O₃” melt the activity of the Bi₂O₃ component is strongly positive, that of Bi₄B₂O₉ is strongly negative. The opposite is observed for the “Bi₄B₂O₉” melt. All calculated liquidi except the Bi₄B₂O₉ liquidus closely match the experimental ones. In contrast to the experimental liquidus the calculated Bi₄B₂O₉ liquidus has an inflection point. The crest of the metastable spinode (solvus) for a “Bi₂O₃” melt is close to the liquidus indicating melt separation at undercooling. (© 2010 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Interrelation between shear modulus and the molecular parameters of viscous flow for glass forming liquids

The relationship between the free energy of viscous flow activation, the instantaneous modulus and the molar volume of kinetic units overcoming the barrier was derived by the author in the simplest form, ΔG^≠ = F_∞V¹, thirty-eight years ago. It was the result of the common solution for most general equations for the viscosity coefficient, the rate constant for shear relaxation in accordance with Maxwell’s relation. Here it is shown that this equation may be derived in the framework of the theory of elasticity and/or hydrodynamics. In this equation, V¹ = 8(r₀)³N_A, where V¹/N_A in the theory corresponds to the cube volume containing an inscribed molecule (atom) of radius r₀. The experimental proof of the equation shows that the atomic radii found from the viscous and elastic parameters match those obtained from direct structural investigations (X-ray and neutron scattering) with an average accuracy not worse than ∼5% (oxide, fluoride and chalcogenide glass melts). The theory needs development for molecular liquids with more complex structure. It is obvious that Maxwell’s relation is valid for modeling of viscous flow at the molecular level in supercooled liquids.     

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.     

Enhanced glass-forming ability of a Zr-based bulk metallic glass with yttrium doping

A significant enhancement in glass formation in a newly developed Zr₅₁Cu_20.7Ni₁₂Al_16.3 alloy has been achieved by yttrium doping. With just 0.5 at.% yttrium doping, the critical diameter of the as-cast alloys for glass formation has been increased from 3 mm to at least 10 mm. In the undoped, large-sized alloys, massive oxygen stabilized crystalline phases are observed but disappear in yttrium doped alloys. Very small amounts of stable α-Y₂O₃ phases found in the yttrium doped alloys, and their negligible effect on the metallic glasses’ properties, provide a superior solution to achieve metallic glasses with a high glass formability.     

The effect of Sn addition on the glass-forming ability of Cu-Ti-Zr-Ni-Si metallic glass alloys

The effect of Sn substitution for Ni on the glass-forming ability was studied in Cu₄₇Ti₃₃Zr₁₁Ni_8−xSn_xSi₁ (x=0,2,4,6,8) alloys by using thermal analysis and X-ray diffractometry. With increasing x from 0 to 8, the glass transition temperature, T_g, of melt-spun Cu₄₇Ti₃₃Zr₁₁Ni_8−xSn_xSi₁ alloys increased gradually from 720 to 737 K. On the other hand, the crystallization temperature, T_x, increased from 757 K at x=0 to 765 K at x=2, being nearly same with further increase of x. Partial substitution of Ni by Sn in Cu₄₇Ti₃₃Zr₁₁Ni₈Si₁ promotes the glass formation. Both amorphous Cu₄₇Ti₃₃Zr₁₁Ni_8−xSn_xSi₁ alloys prepared by melt spinning and injection casting showed similar crystallization process during continuous heating in DSC. Temperature range of undercooled liquid region exhibits good correlation with the critical diameter for the formation of an amorphous phase in injection casting.     

Effect of composition on the glass-forming tendency of barium aluminosilicate gels derived from metal alkoxides

The effect of composition on the glass-forming tendency of barium aluminosilicate gels derived from metal alkoxides with compositions near the theoretical composition of barium feldspar was studied. Results indicated that, in the experimental range, larger SiO₂ content and larger BaO/Al₂O₃ ratio were advantageous to glass formation. A criterion for glass formation in the studied system was established as (b+3−4y)/(2y+s(1+b)/(100−s))<J_c, where b is the BaO/Al₂O₃ ratio, s the mol percentage of SiO₂, y the fraction of four-coordinated aluminum over the total amount of aluminum, and J_c is a constant for a definite experimental condition. The criterion showed good fitness with the experimental results.