Structural Relaxation Of Glass Research Articles

Numerical and atomistic models for predicting structural relaxation in glasses

From optical fiber to high-tech displays, glass relaxation plays a critical role. Due to the non-equilibrium nature of glass, there is a constant evolution associated with relaxation that influences manufacturing and properties. Despite the importance of glass relaxation, it remains a challenge to understand and predict. Models to predict the behavior of glass relaxation have been proposed for more than 80 years and have become increasingly more accurate at the cost of simplicity. These models have also been influenced by the models that have come before them. In this article, we review the history of glass relaxation models and how they connect to modern computational approaches and discuss the remaining challenges of glass relaxation modeling.

Theory of structural relaxation in glass from the thermodynamics of irreversible processes

This work proposes a fundamental thermodynamic description of structural relaxation in glasses by establishing a link between the Prony series solution to volume relaxation derived from the principles of irreversible thermodynamics and asymmetric Lévy stable distribution of relaxation rates. Additionally, it is shown that the bulk viscosity of glass, and not the shear viscosity, is the transport coefficient governing structural relaxation. We also report the distribution of relaxation times and energy barrier heights underpinning stretched exponential relaxation. It is proposed that this framework may be used for qualitative and quantitative descriptions of the relaxation kinetics in glass.

Parameterization of photobleaching and photodarkening in-situ kinetics in thermally deposited GeSe2 thin films

Thermally evaporated chalcogenide glass thin films are known to be highly photosensitive revealing both metastable and transient photoinduced changes of optical transmission at the fundamental absorption edge region. In-situ kinetics of metastable photobleaching and transient photodarkening as well as following light-off relaxations for as-deposited GeSe2 thin films were studied and fitted with the stretched exponential function. Dependences of kinetic parameters β and τ on film thickness, temperature, sample prehistory and wavelength of light irradiation were analyzed. The obtained results were discussed within current approaches to mechanisms of photoinduced kinetic phenomena and structural relaxation in glasses.

Deciphering the intrinsic dynamics from the beam-induced atomic motions in oxide glasses.

Probing the microscopic slow structural relaxation in oxide glasses by X-ray photon correlation spectroscopy (XPCS) revealed faster than expected dynamics induced by the X-ray illumination. The fast beam-induced dynamics mask true slow structural relaxation in glasses and challenges application of XPCS to probe the atomic dynamics in oxide glasses. Here an approach that allows estimation of the true relaxation time of the sample in the presence of beam-induced dynamics is presented. The method requires two measurements either with different X-ray beam intensities or at different temperatures. Using numerical simulations it is shown that the slowest estimated true relaxation time is limited by the accuracy of the measured relaxation times of the sample. By analyzing the reported microscopic dynamics in SiO2, GeO2 and B2O3 glasses, itis concluded that the beam-induced dynamics show rich behavior depending on the sample.

Pressure dependence of density and structural relaxation of glass near the glass transition region

AbstractA simplified and effective pressure cell together with an experimental procedure has been developed and applied to compress samples of SCHOTT N‐BK7® glass under static high pressures in a piston‐cylinder apparatus. Results from the density and volume recovery measurements show that, the glass samples were effectively densified in piston‐cylinder apparatus with the density at room temperature increasing linearly with frozen‐in pressure. To explain the experimental data, we developed a mathematical model based on a suggestion by Gupta (1988) with two internal parameters, named fictive temperature (Tf) and fictive pressure (Pf), which fits the experimental data well.

Role of string-like collective atomic motion on diffusion and structural relaxation in glass forming Cu-Zr alloys.

We investigate Cu-Zr liquid alloys using molecular dynamics simulation and well-accepted embedded atom method potentials over a wide range of chemical composition and temperature as model metallic glass-forming (GF) liquids. As with other types of GF materials, the dynamics of these complex liquids are characterized by "dynamic heterogeneity" in the form of transient polymeric clusters of highly mobile atoms that are composed in turn of atomic clusters exhibiting string-like cooperative motion. In accordance with the string model of relaxation, an extension of the Adam-Gibbs (AG) model, changes in the activation free energy ΔGa with temperature of both the Cu and Zr diffusion coefficients D, and the alpha structural relaxation time τα can be described to a good approximation by changes in the average string length, L. In particular, we confirm that the strings are a concrete realization of the abstract "cooperatively rearranging regions" of AG. We also find coexisting clusters of relatively "immobile" atoms that exhibit predominantly icosahedral local packing rather than the low symmetry packing of "mobile" atoms. These two distinct types of dynamic heterogeneity are then associated with different fluid structural states. Glass-forming liquids are thus analogous to polycrystalline materials where the icosahedrally packed regions correspond to crystal grains, and the strings reside in the relatively disordered grain boundary-like regions exterior to these locally well-ordered regions. A dynamic equilibrium between localized ("immobile") and wandering ("mobile") particles exists in the liquid so that the dynamic heterogeneity can be considered to be type of self-assembly process. We also characterize changes in the local atomic free volume in the course of string-like atomic motion to better understand the initiation and propagation of these fluid excitations.

Direct measurement of the kinetics of volume and enthalpy relaxation of an Au-based bulk metallic glass

Structural relaxation of glasses below their glass transition is a well-studied phenomenon that still poses several open issues. With the advent of bulk metallic glasses with exceptionally low glass transition temperatures, new options are available that are based on the experimental assessment of the time dependence of several different thermodynamic quantities by direct measurements with high accuracy. In this contribution the first direct measurement of the isothermal relaxation of the volume and the enthalpy of an Au-based bulk metallic glassformer are reported and discussed with respect of the characteristics describing the underlying processes.

Simple nonlinear equation for structural relaxation in glasses

A wide range of glassy and disordered materials exhibit complex, nonexponential, structural relaxation (aging). We propose a simple nonlinear rate equation δ = a[1-exp(b δ)], where δ is the normalized deviation of a macroscopic variable from its equilibrium value, to describe glassy relaxation. Analysis of extensive experimental data shows that this equation quantitatively captures structural relaxation, where a and b are both temperature- and, more importantly, history-dependent parameters. This analysis explicitly demonstrates that structural relaxation cannot be accurately described by a single nonequilibrium variable. Relaxation rates extracted from the data imply the existence of cooperative rearrangements on a supermolecular scale.

Statistical mechanical approach to secondary processes and structural relaxation in glasses and glass formers

The interrelation of dynamic processes active on separated time-scales in glasses and viscous liquids is investigated using a model displaying two time-scale bifurcations both between fast and secondary relaxation and between secondary and structural relaxation. The study of the dynamics allows for predictions on the system relaxation above the temperature of dynamic arrest in the mean-field approximation, that are compared with the outcomes of the equations of motion directly derived within the Mode Coupling Theory (MCT) for under-cooled viscous liquids. By varying the external thermodynamic parameters, a wide range of phenomenology can be represented, from a very clear separation of structural and secondary peak in the susceptibility loss to excess wing structures.

Nonequilibrium thermodynamics: Structural relaxation, fictive temperature, and Tool-Narayanaswamy phenomenology in glasses

Starting from the second law of thermodynamics applied to an isolated system consisting of the system surrounded by an extremely large medium, we formulate a general nonequilibrium thermodynamic description of the system when it is out of thermal and mechanical equilibrium with the medium. Our approach allows us to identify the correct form of the Gibbs free energy and enthalpy. We also obtain an extension of the classical nonequilibrium thermodynamics due to de Donder in which one normally assumes thermal and mechanical equilibrium with the medium; see text. We find that the temperature and pressure differences between the system and the medium act as thermodynamic forces, which are normally neglected in the classical nonequilibrium thermodynamics. The Prigogine-Defay ratio is found to be greater than 1 merely due to the lack of equilibrium with the medium, even though we do not consider any internal order parameters. This shows that these forces should play an important role in relaxation processes. We then apply our approach to study the general trend during structural relaxation in glasses and establish the phenomenology behind the concept of the fictive temperature and of the empirical Tool-Narayanaswamy equation on firmer theoretical foundation.

Effect of Asymmetric Heat Transfer on Glass Deformations

During tempering or other heat treatment processes an uneven temperature field or even an asymmetric temperature field can be created in glass. In an asymmetric case glass can bend depending on the degree of temperature difference. With a known temperature field thermal strains, stress field, and deformations can be calculated. In the paper the theory governing the stress field and deformations is presented. A viscoelastic behavior with the structural relaxation of glass is taken into account.

Physical aging of confined glasses

The properties of glasses confined to the nanometre length-scale can deviate substantially from those found in bulk samples. Physical aging, the structural relaxation of glasses toward equilibrium, leads to time-dependent mechanical, electrical, optical properties, etc. This article highlights experimental work on the impact of confinement on the physical aging of molecular and polymeric glasses, a topic that is both scientifically interesting and technologically important. Experimental observations, as well as challenges and future work, are discussed.

A Nonequilibrium Statistical Mechanical Model of Structural Relaxation in Glass

We derive a new model of structural relaxation in glass based on nonequilibrium statistical mechanics and the Stillinger model of inherent structures. Our model follows the evolution of a system from its equilibrium liquid state through an arbitrary cooling path and allows for the computation of macroscopic properties as a function of time. Using this new model, we have numerically demonstrated for the first time the connection between the topography of a potential energy landscape in 1‐D and its corresponding fragility.

Slow Dynamics and the Glass Transition in Confining Systems

ABSTRACTThe slow dynamics associated with the structural relaxation of glass forming materials near the glass transition is very sensitive to the effects of small confining geometries. Based upon the experimental results of triplet state solvation dynamics, we explore the extent to which confinement effects can be rationalized solely in terms of interfacial dynamics which are modified relative to the bulk situation. The importance of the interfacial conditions is emphasized by observing the changes due to the surface chemistry, by comparing relaxation times at and further away from the surface, and by studying the effects of ‘soft’ versus ‘hard’ confining materials. While ‘hard’ confinement by porous solids is observed to result in slower dynamics and an increased glass transition temperature Tg for propylene glycol, our 4.6 nm nanodroplets suspended in a more fluid environment display faster structural relaxation, equivalent to a reduction of Tg as observed in free standing polymer films.

Structural relaxation in glasses: numerical exploration of variables of Narayanaswamy and Moynihan's model

The accurate description of the relaxation phenomenon near the glass transition temperature allows a better interpretation of differential scanning calorimetry (DSC) curves, since it can be separated from other thermal effects such as crystallization, melting, and recrystallization. The structural relaxation model of Narayanaswamy and Moynihan for thermorheological simple glasses was numerically explored for obtaining a grasp of the functional influence of the different parameters: i.e. relaxation enthalpy Δ h, non-linear parameter x, amplitude exponential distribution parameter b, and pre-exponential parameter A. It is known that when the relationship between the velocity of heat transfer in the cooling run ( q c) and the velocity of heating in the heating run ( q h) is equal to unity, the curves obtained in a DSC suffer only an horizontal translation for different absolute values of cooling and heating rates. It was found in this work that this criterion can be generalized, and curves also overlap by means of a horizontal translation when q c/ q h is a constant different from one, whichever the particular values of q c or q h will be. Finally, changes in the shape of the curves when using different values of q h and q c with a fixed q c/ q h relationship can be used as an indicator of the occurrence of other phenomena (i.e. recrystallization, melting, etc.) in addition to structural relaxation.

On the origin of the heat capacity feature of annealed ices and ice clathrates, and interpreting water’s diffusivity in terms of the entropy

In order to investigate the origins of (i) the spontaneous temperature rise on annealing pure hexagonal and cubic ices and ice clathrates and (ii) the sigmoid-shape increase in the heat capacity, C p , on heating the annealed samples, the enthalpy and entropy decrease on annealing of pure cubic ice and one ice clathrate have been determined from their C p data. This decrease is found to be much higher than that expected from orientational relaxation of H 2O molecules and that calculated from the spontaneous decrease in the Bjerrum or orientational defects concentrations. On this basis and the known observation that dopants not only decrease the relaxation time of the ices and ice clathrates but also modify the shape of the C p -increase feature, it is concluded that the spontaneous temperature rise on annealing occurs when some of the H 2O molecules achieve a preferential orientation, which is equivalent to their partial proton ordering. The sigmoid-shape C p -feature observed on heating the annealed samples is therefore due to the time- and temperature-dependent recovery of their random orientations or complete proton disorder. This is fundamentally different from structural relaxation in glasses whose entropy of disorder itself increases on heating. In a second aspect of the study, the known temperature dependence of the self-diffusion coefficient of water is used to calculate two fundamental quantities of the configurational entropy theory: (i) the size of the cooperatively rearranging regions, which is 4.7 molecules at 150 K, and (ii) the temperature-invariant energy, which is 7.4 kJ mol −1. These seem plausible and similar to those observed for other liquids. Finally, it is pointed out that a comparison of bulk water’s dielectric properties with those of the ions afflicted, two-molecule thick water layer between the platelets of sodium vermiculite clay [R. Bergman, J. Sweson, Nature 403 (2000) 283], is inappropriate on fundamental grounds.

Kinetics of structural relaxation in glasses: A hierarchical model of relaxation centers

A definition is proposed for the characteristic time of structural relaxation τstr. rel in metallic glasses—the universal parameter describing the kinetics of various processes associated with the structural relaxation. The behavior of τstr. rel in model situations of isothermal annealing of a glass and its heating at a constant rate is considered. In the former case, the time τstr. rel is equal to the age of the sample. In the latter case, after a time, τstr. rel reaches a steady-state value. This is in agreement with the τstr. rel values determined from the creep rate. The kinetics of structural relaxation is analyzed with due regard for the hierarchical structure of the phase space in glasses. The kinetic equation taking into account this feature is proposed, and the results of its numerical solution are given.

The reversible enthalpy relaxation in glassy metal alloys and polymers

Abstract Spontaneous changes in the enthalpy and entropy of six isothermally annealed Ni-based glassy metal alloys and one network structure organic polymer have been studied by differential scanning calorimetry. Both time and temperature effects of annealing have been investigated. The two classes of materials show a remarkably similar structural relaxation, thus creating a difficulty in reconciling the earlier conclusions that the so-called reversible relaxation observed for glassy metal alloys is unique, involves both chemical and topological short-range orders and needs to be modelled within the concepts of independent two-level systems. This is resolved by showing that the reversible relaxation is a reflection of the time- and temperature-dependent regain of the equilibrium state at temperatures when the enthalpy of the annealed state is less than that of the equilibrium state. Those local groups of atoms, whose diffusion is fast enough to allow loss of enthalpy and entropy on their approach to an equilibrium configuration state of low energy on annealing, absorb heat to reach their new equilibrium Configuration state of higher energy at a higher temperature on heating at a certain rate. Thus each mode of atomic diffusion in the structure has its own ‘mini glass transition temperature’, when the gain of its configurational entropy conies into evidence on heating at a certain rate. The origin of the reversible relaxation is in the broad distribution of activation energy for diffusion times arising from the temporal and spatial variations in the environments of atoms, similar or dissimilar, in the structure of a glassy metal alloy. The reversible relaxation can be modelled in terms of the non-exponential nonlinear character of structural relaxation in glasses, and its strength is expected to be less for glasses with a narrow distribution of diffusion times and lacking a significant contribution from other relaxations.

Numerical Simulation of Soda-Lime Silicate Glass Tempering

The paper deals with the computation of residual and transient stresses in a tempered glass plate. The modelling takes into account the viscoelastic behavior and the structural relaxation of glass. The evolution of stresses with time during the rapid cooling is computed. Simulation results are compared with experimental ones from the literature available. Levels of transient tensile stress in the surface are analysed.

Rate memory of structural relaxation in glasses and its detection by multidimensional NMR.

A new aspect of the nature of the relaxation rate distribution of $\ensuremath{\alpha}$ relaxation in glasses is analyzed for the example of a polymer: How long does a polymer segment remember its relaxation rate? For a two-state system we describe the rate memory in terms of a single dimensionless parameter. Applying the theory to multidimensional NMR exchange experiments, the rate memory of a polymer slightly above its glass transition temperature is determined. The rate memory is near its theoretical minimum, indicating strong coupling of the individual relaxation modes.