Glass viscosity as a function of temperature and composition: A model based on Adam-Gibbs equation

This paper shows that a generalized Adam-Gibbs relationship reasonably approximates the real behavior of glasses with four temperature-independent parameters of which two are linear functions of the composition vector. The equation is subjected to two constraints, one requiring that the viscosity-temperature relationship approaches the Arrhenius function at high temperatures with a composition-independent pre-exponential factor and the other that the viscosity value is independent of composition at the glass-transition temperature. Several sets of constant coefficients were obtained by fitting the generalized Adam-Gibbs equation to data of two glass families: float glass and Hanford waste glass. Other equations (the Vogel-Fulcher-Tammann equation, original and modified, the Avramov equation, and the Douglass-Doremus equation) were fitted to a float-glass data series and compared with the Adam-Gibbs equation, showing that Adam-Gibbs glass appears an excellent approximation of real glasses even as compared with other candidate constitutive relations.     

Nanomechanical properties of commercial float glass

The float process produces flat glass with a tin-rich surface due to contact with the molten metal bath. The incorporation of tin into the glass network is expected to modify the mechanical properties of the surface and the relative durability of the two sides of the material. In this work nanoindentation was used to evaluate the elastic modulus and hardness of a 2 mm thick commercial float glass. The near-surface elastic modulus (depths < 400 nm) of both sides of the glass was elevated by up to 10%, and could not be attributed solely to the presence of tin. However, slight differences in hardness (<10%) between the air and tin sides of the float glass were observed. These results suggest that tin may alter the flow properties of the glass, but the elastic modulus changes are masked by other structural and chemical differences between the air and tin sides of the float glass.     

Design of a sheet forming apparatus for overflow fusion process by numerical simulation

The overflow fusion process is an important method for the manufacture of glass sheets and is currently used for the production of TFT/LCD display devices. The design of the forming apparatus is critical for obtaining very high surface quality glass to allow the successful application of semiconductor type materials. However, there is only little work presented in the literatures, because of difficulties and expansions in experiments. In this study, a numerical model for simulation of molten glass flow through an isopipe during the overflow fusion process was carried out. An explicit finite difference algorithm with the surface tracking method has been proposed. The effect of the geometry of the forming apparatus, flow rate and viscosity of molten glass on the flow patterns during overflow was investigated. It was found that the stability and flatness of the sheet glass was influenced by the design of the forming apparatus, and the flow rate and viscosity of molten glass flow. The tilt angle at the bottom the of a trough should be high enough (5–7°) to avoid the accumulation of molten glass. The smaller root angle (<50°) was better for recombination of two stream of glass. High flow velocity will induce an unsteady flow profile along the wall of the isopipe. A precise control of the working temperature was needed for maintaining an equal thickness along the isopipe.     

Surface crystallization of rare-earth aluminosilicate glasses

Surface crystallization in a rare-earth aluminosilicate glass (Nd₂O₃–Al₂O₃–SiO₂–TiO₂) was studied using an isothermal method and the crystal growth rate of the glasses was evaluated as a function of the composition. For measuring the surface crystal growth rate, two different methods: measurement of the crystal layer in the longitudinal and lateral growth direction. It was found that crystallization proceeded by surface crystallization only and TiO₂ did not act as a nucleating agent. The growth rate was strongly dependent on the viscosity of glass and agreed with prediction from the Preston model using the known viscosity and melting temperature. As the Si/Nd and Si/Al ratios decreased, the crystal growth rate increased. TiO₂ and Nd₂O₃ played the role of network modifier, which decreased the viscosity of the glass, facilitating crystallization of the rare-earth aluminosilicate glass.     

Application of the optical method for determining of the RMS roughness of porous glass surfaces

The application of an optical method for characterizing surface roughness is presented. This method was used for an examination of porous glass surfaces. The expressions relating the root mean square rms (σ) of a surface to its specular reflectance at normal incidence are used for σ ? λ, (λ - wavelength). For light of sufficiently long wavelength the decrease in the measured specular reflectance due to the surface roughness depends only on the root mean square (rms) height of the surface irregularities. On the basis of reflectance spectra, one can determine σ for the porous glass surfaces after technological processes. The measured reflectance spectra were compared with calculated ones for which the scattered component of light was taken into account. The parameters rms determined from the optical method are comparable to those obtained from atomic force microscopy examinations.     

Continuous cooling approximation for the formation of a glass

Non-isothermal equations describing the liquid-crystal transformation are derived using the isothermal Avrami equations. A theoretical expression for the critical cooling rate for the formation of a glass is found. Calculations based on this expression are in better agreement with experimental values than those derived from TTT (time-temperature-transformation) curves. A study performed on typical glass forming materials enables the glass forming ability (GFA) to be determined by experimentally measuring crystallization temperatures at different cooling rates which are easily accessible with commonly available technology. The behaviour of the rate constant for crystallization is also obtained from the same data in the experimental range considered. In both cases no previous knowledge of the parameters involved is needed.With some assumptions the values of the viscosity in the crystallization temperature range can be estimated.Although the study was performed for an Avrami index of 4 an extension to other values of n is made under some restricted conditions and a more general treatment is outlined.     

Oxygen and silver diffusion into float glass

In the float glass process, molten glass is floated on a molten metallic tin bath, such that tin penetrates the glass surface. Consequently, the glass has distinctly two different faces; the tin-penetrated face (bottom face) and the opposite face (top face). In this paper, the effects of tin on oxygen and silver diffusion into the top and bottom faces of a soda–lime–silica float glass are reported. It was revealed that oxygen diffusion from the atmosphere into the bottom face at temperatures above glass transition temperature was extremely suppressed near the surface region of the glass. This was not observed for the top face. This effect was ascribed to chemical reactions between the diffused oxygen and Sn²⁺ near the surface of the glass. Silver diffusion was also influenced by the tin due to chemical reactions of Ag⁺ ions with Sn²⁺, leading to the precipitation of nanometer-sized Ag crystals. As a result, the coloration due to the surface plasmon resonance of the Ag crystals was significantly different between the top and bottom faces because of differences in the nucleation and growth processes associated with the Ag crystals.     

Characterization of glass surface damaged by alumina abrasive grains

The quality of an optical glass component is influenced by the presence of surface and subsurface defects generated by machining processes, especially lapping. However, the damaged area is characterized by roughness and crack layers that contribute to reduce the component's mechanical and optical performances. Evaluation of these defects leads to the obtainment of the best finishing technique for optical glass components.In this work, the effect of the lapping technological parameters (lapping time and alumina abrasive grain size) on the glass surface roughness as well as the depth of the damaged layer were determined. Furthermore, a proportionality constant between the total height of the roughness profile (Rt) and the subsurface damage layer was calculated. The damaged depth was characterized using mechanical techniques and microscopic analysis. The obtained results show an important damage of the glass surface, since the first few seconds of contact time between the surface and the grains. The increase of the lapping time gives rise to the propagation of this damage to reach its maximum and then a material removal rate is observed. At the end of the operation, a defined final surface roughness and a subsurface damaged layer are obtained. The proportionality constant between the subsurface damage layer and the total height of the roughness profile (Rt) was found to be 6.7 ± 0.8.     

Fabrication of fluorine-doped silica glasses by the sol-gel method

Fluorine-doped silica glasses are produced by the sol-gel method for optical fiber preforms. In order to dope fluorine into silica glass, fluorinated silicon alkoxide, Si(OC₂H₅)₃F, is titrated into SiO₂ sol solutions. The fluorine content in silica glass depends on: the fluorine concentration in the gel, the specific surface area of SiO₂ particles and the heating rate in the sintering process. Fluorine-doped silica glass with a maximum relative refractive index difference of −0.93% is obtained. Using this technique, optical fibers with a triangular refractive index profile are fabricated with a minimum optical loss of 1.6 dB/km at 1.69 μm wavelength.     

Modeling of directional solidification in 2D and 3D cases

A method of numerical solution of the directional solidification problem for sharp interfaces is developed. The cellular-structure development is analyzed by calculating the concentration fields and consecutive profiles of the solid-liquid interface. The anisotropy of growth rate and surface tension is taken into account. The wavelength ranges in which distortions develop are determined and the dependences of the rate of increase in the distortion amplitude on the wavelength are found. The results obtained for the 2D and 3D cases are compared with the known experimental and calculated data.     

Gallium colloid formation during ion implantation of glass

Data are reported on the size and depth distribution of gallium colloids formed by gallium ion implantation at energies of 50 and 60 keV, and nominal doses up to 1.1 × 10¹⁷ ions/cm² into coverlip glass, float glass and white crown glass. Measurement techniques used to reveal colloid-induced changes include the wavelength dependence of optical reflectivity, transmission electron microscopy (TEM) and Rutherford backscattering (RBS). The reflectivity can be controlled by variations in ion dose, implant temperature and ion beam energy. The highest reflectivity is found after implants near 50°C and the level is extremely sensitive to the implant temperature. For controlled beam conditions, the reflectivity data are reproducible, despite there being variations in the colloid size and depth distributions as seen by TEM and RBS. The TEM data reveal that the depth distribution develops in two distinct regions, which at high concentration can precipitate into two layers of large colloids. Subsidiary experiments are reported to attempt to separate the effects of variations in the implant temperature and surface charging which influence the reflectivity, RBS and colloid formation.     

Dehydration of Er-doped phosphate glasses using reactive agent bubble flow method

This paper investigated on the dehydration of Er³⁺-doped phosphate glasses using O₂ + CCl₄ bubble flow method. The influence of parameters of dehydration effect was studied systemically. It was found that the dehydration rate was rather rapidly at the initial stage of bubbling. Increasing gas flow rate and temperature could drive the dehydration process toward lower OH concentration in the melts. The dehydration process was carried out in open system and analyzed by thermodynamic theory of open system, which clarified the process of eliminating of OH groups from the glass melts with bubbling time and gas flow rate. A time-dependent empirical equation about reaction rate constant was derived, and the relationships between rate constant and bubbling flow rate, and temperature were also discussed. This analytical method could be applicable to the dehydration of glass melt using other dehydration agents.     

Colloidal silver formation at the surface of float glass

The formation of colloidal silver during the heating in air of silver films on float glass has been observed. The presence of colloidal silver gives to a yellow color and an absorption band centered at 400–420 nm. The results of this study indicate that the formation of colloidal silver is strongly dependent upon the concentration of stannous tin in the glass. The optical density of the absorption band induced in the glass is much greater for samples silvered on the tin-rich face of the glass and varies with the thermal history of the sample. Removal of the outer few micrometers of the glass surface results in a radical change in the amount of colloidal silver formed. Silver colloids are formed only if the sample is heated in an atmosphere containing oxygen, suggesting that the silver must be ionized before it will diffuse into the glass. The colloid formation process has an activation energy of approximately 30 kcal/mol, which is very near that reported for silver-sodium interdiffusion in similar glasses.     

Behavior of a nematic liquid crystal in oscillatory flow at weak surface anchoring

The effect of the surface viscosity on the orientational dynamics of a nematic liquid crystal in an oscillatory flow has been studied. For the shear and the Poiseuille flows, the approximate analytical solutions of the nematodynamic equations are obtained at small flow amplitudes. The frequency range of the oscillatory flow is determined, in which the surface viscosity strongly affects the optical response of a nematic layer. The results obtained are compared with the data of direct numerical simulation of the nematodynamic equations and the method for the experimental determination of surface viscosity is proposed.     

Melting and solidification behavior of laser-crystallized silicon thin-films studied by transient conductance measurements

In this paper we report on transient conductance measurements during melting and solidification of thin silicon films on foreign substrates, which were irradiated with an excimer laser. The silicon films were deposited on borosilicate float glass or single crystal silicon wafers that were coated with different intermediate layers. Our results show that the laser fluence required to melt the entire Si layer is mainly determined by the silicon–substrate interfacial thermal resistance and not by the heat conductivity of the bulk substrate. The solidification velocity, on the other hand, is strongly influenced by the heat conductivity of the bulk substrate and reaches a maximum value of 0.95 m/s for c-Si compared to 2.19 m/s for borosilicate float glass.     

Second harmonic generation studies of intrinsic and extrinsic relaxation dynamics in poly(methy1 methacrylate)

Second harmonic generation (SHG) is used to monitor the reorientation a dopant chromophore in slightly entangled poly(methy1 methacrylate) (PMMA). The effect of charge and temperature on both the decay and the much less studied onset modes of SHG signal at temperatures above the glass transition has been examined. At variance with the theoretical predictions, it is shown that the onset and the decay times are not coincident. An isothermal experiment above the glass transition shows a lengthening of relaxation time of the decay mode due to successive poling process, which is ascribed to charge memory effects. In contrast, the latter do not affect the onset characteristic time. The effect of temperature above the glass transition on dopant rotation and polymer relaxations has been also examined. As temperature increases the relaxation times of both the onset and the decay modes decrease. If the surface charge and the charge memory effect are erased, the decay time compares quite well with the structural relaxation time. Differently, the onset time exhibits a partial decoupling.     

Dynamical scaling analysis using the Lillie Number for vitrification of deeply supercooled glycerol

Thermal response was measured for a deeply supercooled glycerol specimen by applying calorimetric temperature scanning rate spectroscopy, cooling the specimen from liquid at a slow constant cooling rate until glass transition was observed. The effective fraction of glass as a function of temperature was determined and a new definition of glass transition temperature, T_gC, as the temperature at which the effective glass fraction to be 0.5 was presented. The relation between this and the cooling rate showed the Arrhenius behavior. The effective glass fraction curves shifted linearly as a function of ln(cooling rate). When T was scaled to the Lillie Number, the glass fraction lay on a master curve, which was successfully fitted with a Kohlrausch–Williams–Watts function. The Kohlrausch exponent, the relaxation time as a function of temperature and the kinetic fragility index were determined. The results were compared with literature values.     

Precipitation of nanometer-sized SnO2 crystals and Sn depth profile in heat-treated float glass

The effect of oxygen diffusion from the atmosphere on tin depth profile in the bottom face of a soda-lime-silica float glass at temperatures above T_g was investigated. The heat treatment was performed in ¹⁸O₂/N₂ and argon (Ar) atmospheres. The significant diffusion of tin to the surface was observed for the glass heat-treated in ¹⁸O₂/N₂ atmosphere, resulting in the formation of a tin-enriched layer near the surface region. It was found that the tin was supplied from the region shallower than the ‘hump’ which is commonly observed in the tin profile of a commercial soda-lime-silica float glass. No significant change in the tin depth profile was observed for the glass heat-treated in Ar atmosphere. These results indicate that ¹⁸O diffusion into the glass, which causes the change in chemical state of tin from Sn²⁺ to Sn⁴⁺, induces the significant diffusion of tin. Furthermore, the precipitation of crystalline SnO₂ particles with a diameter of ∼1 nm was clearly recognized in the tin-enriched layer. This fact indicates that a phase separation was induced by the oxygen diffusion into the glass. Consequently, Sn²⁺ may be supplied to the surface in order to compensate for the marked decrease in Sn²⁺ concentration in the glass system. The significant diffusion of tin to the surface was suppressed by increasing the iron content in the glass. This suppression was ascribed to the increase in Sn⁴⁺ concentration as a result of the redox reaction between tin and iron because the diffusion coefficient of Sn⁴⁺ is much smaller than that of Sn²⁺.     

Sintering inhomogeneous glasses: Application to optical waveguides

Variations in viscosity or pore size within a glass body cause uneven contraction during sintering. Consequently, stresses develop which alter the local sintering rate and, in some cases, produce bulk flow. This paper illustrates how these stresses can be analyzed by analogy to thermal stress. As a particular example, sintering of optical waveguide preforms made by the OVPO process is examined in detail. The magnitude of the self-stresses, and the conditions required for bulk flow are determined.