Fictive Temperature Research Articles

Influence of Ionizing Gas Flow on Structural Homogeneity of Type IV Silica Glass

Type IV silica glass is the key material in inertial navigation and optical field due to its high purity and unbroken structural network. Structural homogeneity of type IV silica glass, which is mainly affected by producing process, is one of the most important properties and determines its usability. The influence of ionizing gas flow of plasma was studied in this paper. Flow rate of working gas and protecting gas was changed and the depositing temperature field was measured. Structural homogeneity of deposited silica glass was discussed by optical homogeneity, fictive temperature and stress birefringence. Results show that more uniform temperature field can be obtained with higher working gas flow and lower protecting gas flow, and the structural homogeneity of type IV silica glass is better. But the proportion of working gas and protecting gas should not be larger than 2. When the working gas and protecting gas are 5 m3/h and 2.5 m3/h respectively, the structural homogeneity of type IV silica glass is the best.

The role of thermodynamic stability in the characteristics of the devitrification front of vapour-deposited glasses of toluene.

Physical vapour deposition (PVD) has settled in as an alternative method to prepare glasses with significantly enhanced properties, providing new insights into the understanding of glass transition. One of the striking properties of some PVD glasses is their transformation into liquid via a heterogeneous mechanism that initiates at surfaces/interfaces. Here, we use membrane-based fast-scanning nanocalorimetry (104 K s-1) to analyse the variables that govern the transformation mechanism of vapour-deposited toluene glasses with different stabilities. Thin films ranging from 20 to 250 nm were prepared at deposition temperatures between 0.70 and 1.15 times the glass transition temperature. We show how a propagating growth front is the initial transformation mechanism in all the vapour deposited samples, revealing a clear tendency to faster front velocities for less stable samples. Contrary to other glass-formers such as indomethacin, toluene shows a one-to-one relationship between limiting fictive temperature and front velocity. We associate this behaviour with the much simpler molecular geometry of toluene, which would prevent the presence of strong preferential molecular arrangements in the glass. However, the propagation distance of the growth front before the homogenous transformation mechanism dominates the transition is found to be dependent on the preparation conditions rather than on the thermal stability of the glass. Understanding the link between the growth variables and the properties of PVD glasses is crucial for finding and developing potential applications of this type of glass.

Revealing the connection between the slow β relaxation and sub-Tg enthalpy relaxation in metallic glasses

We report a new approach, i.e., the hyperquenching-calorimetric approach, by which the activation energy of slow β relaxation (Eβ) in metallic glasses can be determined. This method is based on the correlations among the kinetic liquid fragility index (m), the glass transition temperature (Tg), the characteristic fictive temperature (Tf,c), and the activation energy for sub-Tg enthalpy relaxation. Tf,c is the temperature at which Eβ is equal to the activation energy of the onset of the sub-Tg enthalpy relaxation of metallic glasses. The linear Tf,c/Tg ∼ m relation is attributed to the link between the contribution of the slow β relaxation to the entire relaxation process and the liquid fragility for metallic glasses. This relation is explained in terms of the potential energy landscape. The new approach reveals the inherent relation between the slow β relaxation and sub-Tg enthalpy relaxation in metallic glasses.

Processing effects on fracture toughness of metallic glasses

Measuring fracture toughness of metallic glasses (MGs) is challenging, and a large scatter has been observed which has been at least partially attributed to varying processing conditions. Here, we investigated the influence of main processing conditions, cooling rate and processing environment, on the fracture toughness of MGs. Through a thermoplastic forming based toughness evaluation approach, we found that processing effects can be dramatic and typically very specific to the alloy. Hence, general predictions of processing effects are challenging and MG specific characterization are required; however we offer some insight how the cooling rate effect can be explained with fictive temperatures.

Reconciling calorimetric and kinetic fragilities of glass-forming liquids

The liquid fragility index (mvis) describes the rate of viscosity change of a glass-forming liquid with temperature at the glass transition temperature (Tg), which is very important for understanding liquid dynamics and the glass transition itself. Fragility can be directly determined using viscosity measurements. However, due to various technical complications with determining viscosity, alternative methods to obtain fragility are needed. One simple method is based on measurement of the calorimetric fragility index (mDSC), i.e., the changing rate of fictive temperature (Tf) with heating (cooling) rate in a small Tf range around Tg. The crucial question is how mDSC is quantitatively related to mvis. Here, we establish this relation by performing both dynamic and calorimetric measurements on some selected glass compositions covering a wide range of liquid fragilities. The results show that mDSC deviates systematically from mvis. The deviation is attributed to the Arrhenian approximation of the log(1/qc)~Tg/Tf relationship in the glass transition range. We have developed an empirical model to quantify the deviation, by which mvis can be well predicted from mDSC across a large range of fragilities. Combined with the high-T viscosity limit (10–2.93Pa·s), we are able to obtain the entire viscosity curve of a glass-forming liquid by only performing DSC measurements.

Local structure of network modifier to network former ions in soda‐lime alumino‐borosilicate glasses

AbstractThe structure of soda‐lime alumino‐borosilicate glass was studied using molecular dynamics simulations of samples of varying compositions containing ~20 000 atoms each. Pair distribution functions (PDFs) of cations to oxygen were used for comparison to available experimental data to evaluate consistency between simulations and experiment. Additional PDFs and coordination of the network forming cations (Al/B/Si) to network modifiers (Ca/Na) were examined, which is difficult to measure experimentally. The results are consistent with available experimental data regarding cation‐oxygen bond lengths and network former to oxygen coordination numbers. Si and Al are predominantly 4‐coordinated, with a small concentration of overcoordinated species similar to experimental data. B varied as 3‐coordinated, BO3, and 4‐coordinated, BO4, as a function of the amount of Ca2+ and Na+ present, the ratio of Al2O3 to B2O3, and the fictive temperature of the sample, similar to experimental data. The simulations provide new information regarding the locations on the network modifiers to the +3 cations, Al and B. For instance, one Al ion can have multiple Na within 4 Å, but also the Na can be within 4 Å of several +3 cations. Such results would indicate a greater complexity of local structure that goes beyond the stoichiometric one +1 modifier ion near one +3 network former or one +2 modifier near two +3 formers in tetrahedral sites.

Relaxation dynamics of glasses along a wide stability and temperature range.

While lots of measurements describe the relaxation dynamics of the liquid state, experimental data of the glass dynamics at high temperatures are much scarcer. We use ultrafast scanning calorimetry to expand the timescales of the glass to much shorter values than previously achieved. Our data show that the relaxation time of glasses follows a super-Arrhenius behaviour in the high-temperature regime above the conventional devitrification temperature heating at 10 K/min. The liquid and glass states can be described by a common VFT-like expression that solely depends on temperature and limiting fictive temperature. We apply this common description to nearly-isotropic glasses of indomethacin, toluene and to recent data on metallic glasses. We also show that the dynamics of indomethacin glasses obey density scaling laws originally derived for the liquid. This work provides a strong connection between the dynamics of the equilibrium supercooled liquid and non-equilibrium glassy states.

Thermo-mechanical relaxation of stresses in a glass-metal junction

This work deals with the evaluation of the stress-strain state in an infinite layered cylindrical junction of glass with steel. Structural changes in the glass behavior are described by the Tool-Narayanaswamy-Mazurin-Moynihan model. The relaxation processes in the glass have been presented by the temperature regime depending of the fictive temperature Tf, the relaxation time τ' or the viscosity η and the thermal expansion coefficient α(1). The calculations of the stress components in the glass have been made by using the viscoelastic model. The presented model allows to find the optimal annealing conditions for the creation of the glass- metal composite material.

Radiation hardening of sol gel-derived silica fiber preforms through fictive temperature reduction.

The impact of fictive temperature (Tf) on the evolution of point defects and optical attenuation in non-doped and Er3+-doped sol-gel silica glasses was studied and compared to Suprasil F300 and Infrasil 301 glasses before and after γ-irradiation. To this aim, sol-gel optical fiber preforms have been fabricated by the densification of erbium salt-soaked nanoporous silica xerogels through the polymeric sol-gel technique. These γ-irradiated fiber preforms have been characterized by FTIR, UV-vis-NIR absorption spectroscopy, electron paramagnetic resonance, and photoluminescence measurements. We showed that a decrease in the glass fictive temperature leads to a decrease in the glass disorder and strained bonds. This mainly results in a lower defect generation rate and thus less radiation-induced attenuation in the UV-vis range. Furthermore, it was found that γ-radiation "hardness" is higher in Er3+-doped sol-gel silica compared to un-doped sol-gel silica and standard synthetic silica glasses. The present work demonstrates an effective strategy to improve the radiation resistance of optical fiber preforms and glasses through glass fictive temperature reduction.

Aging kinetics of levoglucosan orientational glass as a rate dispersion process and consequences for the heterogeneous dynamics view.

Aging kinetics of a glass is currently modeled in terms of slowing of its α-relaxation dynamics, whose features are interpreted in terms of dynamic heterogeneity, i.e., formation and decay of spatially and temporally distinct nm-size regions. To test the merits of this view, we studied the calorimetric effects of aging an orientational glass of levoglucosan crystal in which such regions would not form in the same way as they form in liquids, and persist in structural glasses, because there is no liquid-like molecular diffusion in the crystal. By measuring the heat capacity, Cp, we determined the change in the enthalpy, H, and the entropy, S, during two aging-protocols: (a) keeping the samples isothermally at temperature, Ta, and measuring the changes after different aging times, ta, and (b) keeping the samples at different Tas and measuring the changes after the same ta. A model-free analysis of the data shows that as ta is increased (procedure (a)), H and S decrease according to a dispersive rate kinetics, and as Ta is increased (procedure (b)), H and S first increase, reach a local maximum at a certain Ta, and then decrease. Even though there is no translational diffusion to produce (liquid-like) free volume, and no translational-rotational decoupling, the aging features are indistinguishable from those of structural glasses. We also find that the Kohlrausch parameter, originally fitted to the glass-aging data, decreases with decrease in Ta, which is incompatible with the current use of the aging data for estimating the α-relaxation time. We argue that the vibrational state of a glass is naturally incompatible with its configurational state, and both change on aging until they are compatible, in the equilibrium liquid. So, dipolar fluctuations seen as the α-relaxation would not be the same motions that cause aging. We suggest that aging kinetics is intrinsically dispersive with its own characteristic rate constant and it does not yield the α-relaxation rate. In this view, thermodynamic and other properties define the fictive temperature; the real or imaginary components of a dynamic property do not define it. While particles' overall motions may still play a crucial role in (structural) glass physics, we conclude that translational diffusion alone is not a requirement for structure stabilization on aging of a kinetically frozen state.

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

AbstractWe 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.

Molecular dynamics simulation of thermodynamic and structural properties of silicate glass: Effect of the alkali oxide modifiers

Molecular dynamics simulation was applied to elucidate the effect of adding alkali oxides (M2O)X(SiO2)(1−X)with M=(Na, Li or K) into silicate glass matrix. We are interested in the study of this effect particularly on structural and thermodynamic properties of the material. Some interesting results were obtained given a new insight on the bridging process and its reliability to the observed depolymerization phenomena affecting the existing SiO network and depending on both the kind of the alkali modifier and its molar fraction. We observed that the thermodynamic properties are influenced by these structural modifications. Indeed, the glass transition temperature Tg has been found to decrease as the molar fraction of modifier increases depending strongly on the alkali modifier kind. On the other hand, we extracted the fictive temperature from the calculated total energy of the system and determined the glass transition by studying the variation of the fictive temperature as a function of the conventional one using different cooling and heating rates.

Temperature Dependencies of Inter-Diffusion Coefficient and Mass-Transfer Coefficient of Chemical Strengthening

Chemical strengthening is a method of generating compressive stress on the glass surfaces by ion-exchange to improve their strengths since old ages. As its targets have been expanding to larger and thinner glasses recently, different strength profiles are required depending on the applications and selecting appropriate ion-exchange parameters becomes even more important. Therefore, we developed a simulation model of chemical strengthening which enables predicting the stress profiles by ion-exchange in order to help optimizing the ion-exchanging parameters. Parameter study using the simulation model with change of temperature results in precise stress prediction, the compressive stress on the surface with a margin of error of ± 3% and the depth of layer with that of ± 10%. Furthermore, the parameter study introduced following two technical findings; (1) both inter-diffusion coefficient and mass-transfer coefficient could obey the Arrhenius equation, (2) both actual temperature and fictive temperature could influence on the stress relaxation. These findings are of great importance in comprehending the phenomena associated with ion-exchange. It has possibilities for beneficial feedback to the composition development and optimum stress design in accordance with each application.

Effect of annealing on the laser induced damage of polished and CO2 laser-processed fused silica surfaces

We investigate the effect of different heat treatments on the laser-induced damage probabilities of fused silica samples. Isothermal annealing in a furnace is applied, with different temperatures in the range 700–1100 °C and 12 h annealing time, to super-polished fused silica samples. The surface flatness and laser damage probabilities at 3 ns, 351 nm are measured before and after the different annealing procedures. We have found a significant improvement of the initial laser damage probabilities of the silica surface after annealing at 1050 °C for 12 h. A similar study has been conducted on CO2 laser-processed sites on the surface of the samples. Before and after annealing, we have studied the morphology of the sites, the evolution of residual stress, and the laser-induced damage threshold measured at 351 nm, 3 ns. In this case, we observe that the laser damage resistance of the laser created craters can reach the damage level of the bare fused silica surface after the annealing process, with a complete stress relieve. The obtained results are then compared to the case of local annealing process by CO2 laser irradiation during 1 s, and we found similar improvements in both cases. The different results obtained in the study are compared to numerical simulations made with a thermo-mechanical model based on finite-element method that allows the simulation of the isothermal or the local annealing process, the evolution of stress and fictive temperature. The simulation results were found to be very consistent with experimental observations for the stresses evolution after annealing and estimation of the heat affected area during laser-processing based on the density dependence with fictive temperature. Following this work, the temperature for local annealing should reach 1330–1470 °C for an optimized reduction of damage probability and be below the threshold for material removal, whereas furnace annealing should be kept below the annealing point to avoid sample deformation.

Thermal history dependence of indentation induced densification in an aluminosilicate glass

The mechanical properties of glasses are not only determined by their chemical composition, but also by their thermal history, i.e., fictive temperature. In this paper, we consider an alkaline earth aluminosilicate glass composition which has been annealed to exhibit a wide range of fictive temperatures (~130K). Hardness and brittleness index have previously been shown to increase with decreasing fictive temperature, whereas the crack resistance decreases. Through quantification of the indentation depth before and after heat treatments, we show that these changes in micromechanical properties arise from an increased resistance to densification under the indenter when the glasses are annealed. We discuss these results in relation to the indentation size effect and the overall network compaction.

On the origin of Gaussian network theory in the thermo/chemo-responsive shape memory effect of amorphous polymers undergoing photo-elastic transition

Amorphous polymers are normally isotropic in their physical properties, however, upon stress their structural randomness is disturbed and they become anisotropic. There is a close connection between the optical anisotropy and the elastic (or mechanical) anisotropy, since both are related to the type of symmetry exhibited by the molecular structure. On the origin of Gaussian network theory, a phenomenological constitutive framework was proposed to study the photo-elastic transition and working mechanism of the thermo-/chemo-responsive shape-memory effect (SME) in amorphous shape memory polymers (SMPs). Optically refractive index was initially employed to couple the stress, strain and the anisotropy of the random link in macromolecule chain. Based on the Arrhenius law, a constitutive framework was then applied for the temperature dependence of optical (or elastic or mechanical) anisotropy according to the fictive temperature parameter. Finally, the phenomenological photo-elastic model was proposed to quantitatively identify the influential factors behind the thermo-/chemo-responsive SME in SMPs, of which the shape recovery behavior is predicted and verified by the available experimental data reported in the literature.

Structural recovery of a single polystyrene thin film using Flash DSC at low aging temperatures

The structural recovery of a single polystyrene thin film is studied using Flash differential scanning calorimetry (DSC) for aging temperatures ranging from 50.5 to 100.5 °C and for aging times of up to 18,000 s (300 min). A high fictive temperature glass with Tf′ = 117.0 ± 0.5 °C, obtained after cooling at 1000 K/s, is employed in this study. Structural recovery is investigated by monitoring the evolution of the fictive temperature, Tf, which initially remains unchanged and then decreases smoothly and approximately linearly with logarithmic aging time. Equilibrium is reached when Tf = Ta at the highest aging temperatures. The length of the initial plateau is longer for the lower aging temperatures and is related to the increase in the relaxation time with decreasing temperature along the glass line, increasing approximately one decade for every 21 K. This temperature dependence yields a normalized apparent activation energy (Ea/R) of approximately 13 kK for the mobility along the glass line. On the other hand, the apparent activation energy for the mobility along the liquid line is 102 kK.

Enthalpy recovery and its relation to shear response in an amine cured DGEBA epoxy

A description of enthalpy recovery for an amine-cured, digylcidyl ether of bisphenol A (DGEBA) epoxy (Epon 828/Jeffamine T403) was acquired through a series of experiments targeting the effects of the individual parameters: cooling rate, heating rate, aging temperature, and aging time. From these experiments, the peak temperature, Tp, and fictive temperature, Tf, were tracked as measures of the extent of structural relaxation. The KAHR formalism provides a standard for comparison to similar epoxies and was parametrized using the peak shift method. The resulting parameterization was then used to assess the relation between volumetric and shear relaxation. In particular, the KAHR model was used to predict volumetric relaxation time-temperature shift factors that are directly compared to measured time-temperature shift factors in shear. This unique methodology to assess equivalence between volumetric and shear relaxation shift factors further establishes the basis for this key assumption of continuum constitutive models based on rheological simplicity.

Effects of Thermal and Pressure Histories on the Chemical Strengthening of Sodium Aluminosilicate Glass

Glasses can be chemically strengthened through the ion exchange process, wherein smaller ions in the glass (e.g., Na+) are replaced by larger ions from a salt bath (e.g., K+). This develops a compressive stress (CS) on the glass surface, which, in turn, improves the damage resistance of the glass. The magnitude and depth of the generated CS depends on the thermal and pressure histories of the glass prior to ion exchange. In this study, we investigate the ion exchange-related properties (mutual diffusivity, CS, and hardness) of a sodium aluminosilicate glass, which has been densified through annealing below the initial fictive temperature of the glass or through pressure-quenching from the glass transition temperature at 1 GPa prior to ion exchange. We show that the rate of alkali interdiffusivity depends only on the density of the glass, rather than on the applied densification method. However, we also demonstrate that for a given density, the increase in CS and increase in hardness induced by ion exchange strongly depends on the densification method. Specifically, at constant density, the CS and hardness values achieved through thermal annealing are larger than those achieved through pressure-quenching. These results are discussed in relation to the structural changes in the environment of the network-modifier and the overall network densification.

Signatures of Structural Recovery in Polystyrene by Nanocalorimetry

The intrinsic isotherm, asymmetry of approach, and memory effect experiments are performed for a high fictive temperature polystyrene glass in enthalpy space using nanocalorimetry. Using aging at times as short as 0.01 s and relatively high aging temperatures allows the complete evolution of all three of the signatures of structural recovery to be obtained for the first time in enthalpy space. The results from down jump experiments are compared to those obtained at lower temperatures using conventional differential scanning calorimetry (DSC) with respect to the time required to reach equilibrium, the apparent activation energy, and the Tool–Narayanaswamy–Moynihan (TNM) model parameters, and these results are independent of the measurement method being used; on the other hand, the physical aging rate is higher for the high fictive temperature glass.