A Check of Applicability of the Relaxation Model of Annealing to Calculation of Stresses in Low-Temperature Annealing of a Glass–Molybdenum Seal

The previously developed relaxation model for annealing of glass seals with other materials has been applied widely. It remains unclear whether there are a specific low temperature and very long-term isothermal treatments at which this simple model ceases to work correctly and requires complication or even revision. With the aim to determine the minimum fictive temperature at which the relaxation model of annealing of glass seal with an elastic material is still applicable, the stresses in the sandwich S52-2 glass–molybdenum seals are measured at different stabilization temperatures. The experimental temperature–time dependences of the stresses are compared with those calculated using the relaxation model of seal annealing. The use of this relatively simple model leads to a quite satisfactory agreement (even if not identical at all the temperatures) in the range from the glass transition temperature to 380°C for stabilization durations as long as 81 days. This treatment duration makes it possible to reach a structural temperature of 434°C, which is considerably lower than the structural temperature (525°C) obtained upon simple cooling of glass at a rate of 3 K/min.     

Finite Element Calculation of Refractive Index in Optical Glass Undergoing Viscous Relaxation and Analysis of the Effects of Cooling Rate and Material Properties

In this research, a methodology based on a numerical simulation model is presented to predict refractive index change introduced to two low T_g optical glasses, namely, P-SK57 and P-LASF47, by cooling. To model the structural relaxation behavior of glass around glass transition temperature, the Tool–Narayanaswamy–Moynihan (TNM) model is used. In addition, the fictive temperature of the glass samples during cooling is discussed. The effect of cooling rate on the fictive temperature of the glass samples is also presented. This study demonstrated that finite element method is capable of predicting refractive index of optical glass undergoing viscous relaxation. The simulated results in this study confirm that a higher cooling rate leads to a lower refractive index and a larger variation of refractive index in glass optics. The results also suggest that for glass, materials with high thermal conductivity and low heat capacity are preferred for compression molding process.     

Structural Relaxation Time of Bulk and Fiber Silica Glass as a Function of Fictive Temperature and Holding Temperature

The structural relaxation times of silica glass, both bulk glass and fiber glass at various fictive temperatures, were estimated at selected temperatures. The structural relaxation time of a glass is needed to estimate the rate of change of various glass properties in the glass transition temperature range. Traditionally, the Tool–Narayanaswamy model, in which activation energy of the relaxation time is divided into two parts, one representing the fictive temperature effect and the other representing the temperature effect, has been used. The model can explain the property changes of glass in the glass transition temperature range well when the change of the fictive temperature is small, but the model fails when the change of the fictive temperature is large, as was the case when a fiber sample was heat treated close to the glass transition temperature. The structural relaxation times estimated in the present work exhibited activation energies that varied with fictive temperature, unlike the assumption in the Tool–Narayanaswamy model. On the other hand, the relaxation time for both bulk glass and fiber glass exhibited the same temperature and fictive temperature dependence within experimental error. From these observations, one can see the source of discrepancy between the Tool–Narayanaswamy model and experimental data when the change in fictive temperature is large.     

Heat of Annealing in Simple Alkali Silicate Glasses

The enthalpy changes associated with annealing of glass were studied in simple and mixed alkali silicate glasses. The data indicate that during prolonged annealing the glass comes to a metastable equilibrium state and has a unique heat of solution which depends on its fictive temperature. The heats of solution of these glasses show a linear dependence on fictive temperature, and the magnitude of this dependence is related to the molar volume of the glass. The significance of these heat effects is discussed. The maximum heat effects which can occur on annealing sodium silicate glasses were measured and were approximately half as large as the enthalpy changes associated with the structural arrangements that occur during crystallization of these glasses.     

Diameter Dependence of the Refractive Index of Melt-Drawn Glass Fibers

The diameter dependence of the refractive index of as-formed glass fibers is examined. It is shown that the measured results on fibers of a soda–lime–silica glass can be satisfactorily explained by combining three factors: the diameter dependence of the cooling rate, the cooling rate dependence of the fictive temperature, and the dependence of glass properties on its fictive temperature.     

Method to Estimate Thermal Shrinkage Behavior of Glasses

We present a method to estimate the effect of heat treatment on the shrinkage behavior of glasses. As a pre-requisite, sensitivity of the glass density as a function of glass fictive temperature is measured using the sink–float method and the slope of the relationship is used to determine the linear thermal strain proportionality factor. Evolution of the fictive temperature for different temperature–time history is measured using the infrared spectroscopy method and the results are used to estimate the structural relaxation parameters in the temperature range of interest. The overall shrinkage behavior is predicted using the linear thermal strain factor and estimated change in fictive temperature due to the thermal treatment. The predicted shrinkage behavior is observed to be in good agreement with the independent dimensional change measurements performed on large glass sheets that have undergone similar thermal treatments.     

Relation Between Refractive Index and Elastic Moduli of a Borosilicate Glass After Heat-Treatment

Several specimens of a borosilicate glass were subjected to a series of different annealing schedules and the refractive indices and elastic moduli were measured and compared after each heat-treatment. The elastic moduli were determined by a dynamic resonance method at frequencies both within and slightly above the sonic range. The refractive indices were measured on the Grauer refractometer. A linear relation was found to exist between these two properties for specimens with different heat-treatments. A linear relation has already been established between refractive index and density by several investigators. This indicates that a single fictive temperature (τ) scale can be used to characterize the condition of a glass with respect to three properties: index of refraction, density, and elastic moduli.     

Is the structural relaxation of glasses controlled by equilibrium shear viscosity?

Knowledge of relaxation processes is fundamental in glass science and technology because relaxation is intrinsically related to vitrification, tempering as well as to annealing and several applications of glasses. However, there are conflicting reports—summarized here for different glasses—on whether the structural relaxation time of glass can be calculated using the Maxwell equation, which relates relaxation time with shear viscosity and shear modulus. Hence, this study aimed to verify whether these two relaxation times are comparable. The structural relaxation kinetics of a lead metasilicate glass were studied by measuring the refractive index variation over time at temperatures between 5 and 25 K below the fictive temperature, which was initially set 5 K below the glass-transition temperature. Equilibrium shear viscosity was measured above and below the glass-transition range, expanding the current knowledge by one order of magnitude. The Kohlrausch equation described very well the experimental structural relaxation kinetics throughout the investigated temperature range and the Kohlrausch exponent increased with temperature, in agreement with studies on other glasses. The experimental average structural relaxation times were much longer than the values computed from isostructural viscosity, as expected. Still, they were less than one order of magnitude higher than the average relaxation time computed through the Maxwell equation, which relies on equilibrium shear viscosity. Thus, these results demonstrate that the structural relaxation process is not controlled by isostructural viscosity and that equilibrium shear viscosity only provides a lower boundary for structural relaxation kinetics.     

Correlation between IR peak position and bond parameter of silica glass: Molecular dynamics study on fictive temperature (cooling rate) effect

The fictive temperature of glass is a consequence of its thermal history (cooling rate, primarily) and has a direct effect on physical and chemical properties of the glass. But, it is not easy to measure. The ability to nondestructively and spectroscopically measure it at room temperature would be of great benefit. Although empirical correlations have been established between fictive temperature and selected absorption peaks in the infrared spectra of silica glass, the fundamental understanding for this correlation has not been reported. Here, we use molecular dynamics simulations to show that the blue shift in the Si–O–Si asymmetric stretching peak of pure silica glass, which is known to correlate with a decrease in fictive temperature, can be attributed to a decrease in the average length of the Si–O bond in the silica network, not changes in the density or the Si–O–Si bond angle. The decrease in density at higher fictive temperatures of silica is associated with a decreased population of 5‐ and 6‐membered rings and broadening of the ring‐size distribution, and an increase in the average Si–O–Si bond angle.     

Structural relaxation dynamics of a silicate glass probed by refractive index and ionic conductivity

Relaxation occurs spontaneously in all glasses and is a fundamental step of important technological processes, such as annealing, crystal nucleation, and chemical strengthening by ion exchange. Despite extensive studies over the past decades, there are still conflicting results on whether the kinetics of structural relaxation depends on the analyzed property. Thus, in this study, we used a lithium disilicate glass as a model composition to determine the structural relaxation kinetics during physical aging experiments by measuring the time evolution of the refractive index and ionic conductivity down to 35 K below the initial fictive temperature. In all cases, variations in these properties were adequate to capture the structural changes throughout the aging experiments. At each temperature, the experimental relaxation data fit quite well with the classical stretched exponential relation. We also found that the relaxation process starts faster when probed by ionic conductivity than by refractive index; however, they show similar average relaxation times. These very small structural rearrangements are always the same, but ionic conductivity changes faster than refractive index at the beginning of the process. Our comprehensive results strongly indicate that relaxation dynamics is indeed dependent on the analyzed property.     

Effects of fictive temperature on the leaching of soda lime silica glass surfaces

The fictive temperature of glass characterizes the glass network structure and its thermal history, and thereby can influence ion and water transport in the glass surface. In this study, IR specular reflectance (SR), refractive index, and density measurements were used to characterize and confirm the effects of glass sample processing, especially the fictive temperature/thermal‐history variations. The subsequent acid leaching of these glasses created leached surface layers due to interdiffusion and reaction of hydrous species in the surface; the hydrogen depth profiles obtained with secondary ion mass spectrometry (SIMS) confirmed enhanced leaching with increasing fictive temperature. Attenuated total reflectance (ATR) in the mid‐ and near‐IR indicated increases in both SiOH and H₂O species with increasing fictive temperature. The relative intensities and shapes of the ATR peaks were found to vary between the samples suggesting that speciation of the hydrous reaction products (eg, strong and weakly hydrogen‐bonded OH) is also influenced by the original fictive temperature of the glass, but could not be quantitatively determined.     

DESIGN OF A FURNACE FOR ANNEALING OPTICAL GLASS1

Design of a natural-gas furnace for annealing optical glass.—Most of the furnaces built for annealing regular glassware are unsuitable for optical glass due to irregularity and inequality of temperatures. Working drawings are given for a successful optical glass annealing furnace operated by natural gas. The design is novel in the placing of the flues and burners in such a manner as to supply the heat and remove it in a symmetrical manner, thus obtaining uniformity of temperature.     

TRANSFORMATION REGION OF GLASS*

Evidence for the existence of a “transformation region” rather than a “transformation point” in the 10¹⁴ poise range of glasses has been produced by a variety of experiments, both static and dynamic. Refractive index was measured (1) on small specimens quenched in air and (2) directly in the furnace by the single-prism and three-prism methods. Quantitative agreement was obtained, and the method of quenched samples is recommended as the simplest of those tested. Thermal expansion coefficients were also determined on the quenched samples. Disannealing lowered the refractive index of glasses; for a borosilicate crown, by an order of 0.006. The change resulting from strains was comparatively small and in the opposite direction so that birefringence was found to be an untrustworthy indicator of the state of a glass. For a series of optical glasses, the difference between the refractive-index extremes is a function of the lowest temperature at which the minimum index can be realized. Thermal expansion coefficients may also vary with heat-treatment. Two limiting states of glass are postulated to explain the observations. In between these states lies the region of transformation, including an intermediate state for each temperature between the two limiting temperatures. For all of the glasses e-xamined, the extent of the transformation region was about 100°C. The rate of transformation into the low-temperature state may be studied from “equilibrium curves” by plotting stable refractive index as a function -of temperature. Whereas the conversion to the high-temperature state is instantaneous at the upper temperature of the transformation region, the conversion to the low-temperature condition demands a minimum time at each temperature, which explains why annealing is such a time-consuming process. The annealing time, however, may be drastically reduced by following the equilibrium curves in a stepwise fashion. With insufficient annealing, higher temperature states are frozen in and transformation continues even at room temperature as proved by measurements extending over sixteen months of study.     

Determination of Fictive Temperature of Soda-Lime Silicate Glass

Peak positions of silica structural bands, both in infrared absorption and reflection modes, were used earlier to measure the fictive temperature of silica glass. In the present study, the method was applied to determine the fictive temperatures of a soda-lime silicate glass. For the silicate glass, the IR absorption spectra produced a broad structural band which made the precise determination of peak position difficult, and only the IR reflection band was used. Equilibrium peak positions of ∼1056 cm⁻¹ IR band, due to Si-O stretching, were found to be directly correlated with the fictive temperature of the soda-lime silicate glass. The soda-lime glass exhibited an opposite dependence of the IR band position on the glass fictive temperature as compared to silica glass.     

Change in Refractive Index of a Borosilicate Glass Fiber Annealed Below the Glass Transformation Temperature

Glass fibers pulled from multihole bushings can have a slight difference in thermal history that causes a distribution in the refractive index that can be narrowed by annealing the fibers. The kinetics for the initial stage change in refractive index for fiber annealed between 300° and 500°C are best described by a second-order reaction with an activation energy of 120° 17 kj/mol. The improved uniformity in refractive index for annealed fibers is indicated by a decrease in the half-height width of the optical transmission versus temperature curve for glass fiber immersed in a liquid. The standard deviation in the refractive index of glass fibers with a bimodal distribution in diameter decreases from 8 × 10^-4≤0.0002 to 4 × 10^-4 0.0002 after the fibers are annealed at 400°C for 1 h.     

Ultrashort pulse laser processing of silica at high repetition rates—from network change to residual strain

We report on the analysis of silica-based glasses after processing with ultrashort laser pulses at high repetition rates. Heat accumulation leads to strong local heating of the glass. The subsequent quenching results in a fictive temperature rise that scales with the repetition rate. Consequently, the relative volume change leads to residual tensile strain within the modified volume of larger than 10⁻³, which is confirmed by wide-angle X-ray scattering (WAXS) measurements. Studying the surface topography after cleaving of laser-modified regions allows for quantification of the corresponding elastic strain as well as the glass density behavior on the fictive temperature.     

High-precision molding simulation prediction of glass lens profile for a new lanthanide optical glass

Precision glass lens molding (PGLM) is a recently developed method for fabricating glass optical components with high precision in large volumes. Lanthanum optical glasses are extensively used as optical materials owing to their superior optical properties, such as high refractive index, low dispersion, and high transparency. However, the transformation temperature of currently available high refractive index glass is generally above 650 °C and poses a challenge in manufacturing ultra-hard molds, durable coatings, and high-temperature molding equipment using PGLM. In this study, a preparation method for obtaining high refractive index, low -melting -point lanthanide optical glass (B-ZLaT198) used in PGLM was developed to reduce the transformation temperature. The developed method also characterizes the glass refractive indices and thermal-mechanical properties. To achieve the high-precision prediction of a molding shape in a simulation, a viscoelastic constitutive model of glass was established based on a micro-deformation uniaxial compression creep test. Moreover, by solving the Tool-Narayanasway-Moynihan model parameters based on the specific heat capacity fitting of optical glass at different heating and cooling rates, the input parameters of the structural relaxation model (SRM) for simulation prediction of aspheric glass lens profile deviation in the annealing stage were obtained. Finally, the profile deviation of the aspheric lens was predicted using a finite element model simulation. The results showed that the simulation’s predicted profile of an aspheric lens using the SRM model was in good agreement with that of experimental molding profile. In addition, using the SRM provided a higher prediction accuracy than that of the thermal expansion model in the annealing stage. Adopting the SRM was necessary for the annealing simulations of molding pressing and also verified the accuracy of the proposed viscoelastic characterization method for calculating the thermomechanical parameters of optical glasses.     

Stress and Volume Relaxation in Annealing Flat Glass

Laboratory simulation of the industrial process of annealing sheet glass has yielded data on the genesis of stresses in initially stress-free glass. The experimental results differed from expectations based on classical annealing theory in that stresses began to develop in the annealing range even when the glass was being cooled at a constant rate, i.e. even in the absence of any changes of temperature gradients within the glass. Typically, these stresses account for 40% of the total residual stress in glass annealed according to a linear schedule. The remaining 60% are the well-known thermoelastic stresses that arise later in the annealing process from the decay of temperature gradients in the glass. The stresses observed to arise in glass as it is being cooled at a constant rate are attributed to volume relaxation effects which, in parts of the annealing range, generate stresses rapidly enough that they are not dissipated by stress relaxation. A mathematical model of annealing is proposed that takes account of both stress and structural relaxation. The model fits the experimentally observed evolution of stresses during linear cooling. It also suggests that (with the activation energies of stress and structural relaxation about the same) the actual rate, at any given temperature, of structural relaxation is about 4 times lower than that of stress relaxation.