Relaxation In Glasses Research Articles

Thermodynamic approach for the understanding of the kinetics of heat effects induced by structural relaxation of metallic glasses

We present a novel approach to the understanding of heat effects induced by structural relaxation of metallic glasses. The key idea consists in the application of a general thermodynamic equation for the entropy change due to the evolution of a non-equilibrium part of a complex system. This non-equilibrium part is considered as a defect subsystem of glass and its evolution is governed by local thermoactivated rearrangements with a Gibbs free energy barrier proportional to the high-frequency shear modulus. The only assumption on the nature of the defects is that they should provide a reduction of the shear modulus—a diaelastic effect. This approach allows to determine glass entropy change upon relaxation. On this basis, the kinetics of the heat effects controlled by defect-induced structural relaxation is calculated. A very good agreement between the calculation and specially performed calorimetric and shear modulus measurements on three metallic glasses is found.

Impact of a temperature‐dependent stretching exponent on glass relaxation

AbstractThe nonexponential relaxation behavior of glass is governed by the dimensionless stretching exponent, β, which is typically assumed to be a constant but is more accurately described as a function of temperature. Herein, relaxation calculations of glassy materials are undertaken via an iterative differential equation‐based algorithm to determine when the use of a temperature‐dependent (or dynamic) stretching exponent is required to capture the industrially relevant evolution of fictive temperature components, which is necessary for process engineering. Results reveal a range of liquid fragility index (m) in which a static β description is roughly equivalent to the behavior observed with a dynamic β. However, fast primary (α) relaxation modes demonstrate unique behavior in systems exhibiting excessively strong or fragile liquid behavior when a temperature‐dependent stretching exponent is considered. In this special issue dedicated to the International Year of Glass, we also provide broader perspectives regarding the importance and impact of a temperature‐dependent β.

Structural Rearrangements During Sub-Tg Relaxation and Nucleation in Lithium Disilicate Glass Revealed by a Solid-State NMR and MD Strategy

Structural Rearrangements During Sub-Tg Relaxation and Nucleation in Lithium Disilicate Glass Revealed by a Solid-State NMR and MD Strategy

Isochronal superpositioning of the caged dynamics, the α, and the Johari-Goldstein β relaxations in metallic glasses.

The superposition of the frequency dispersions of the structural α relaxation determined at different combinations of temperature T and pressure P while maintaining its relaxation time τα(T, P) constant (i.e., isochronal superpositioning) has been well established in molecular and polymeric glass-formers. Not known is whether the frequency dispersion or time dependence of the faster processes including the caged molecule dynamics and the Johari-Goldstein (JG) β relaxation possesses the same property. Experimental investigation of this issue is hindered by the lack of an instrument that can cover all three processes. Herein, we report the results from the study of the problem utilizing molecular dynamics simulations of two different glass-forming metallic alloys. The mean square displacement 〈Δr2t〉, the non-Gaussian parameter α2t, and the self-intermediate scattering function Fsq,t at various combinations of T and P were obtained over broad time range covering the three processes. Isochronal superpositioning of 〈Δr2t〉, α2t, and Fsq,t was observed over the entire time range, verifying that the property holds not only for the α relaxation but also for the caged dynamics and the JG β relaxation. Moreover, we successfully performed density ρ scaling of the time τα2,maxT,P at the peak of α2t and the diffusion coefficient D(T, P) to show both are functions of ργ/T with the same γ. It follows that the JG β relaxation time τβ(T, P) is also a function of ργ/T since τα2,maxT,P corresponds to τβ(T, P).

Vortex structure of excitation fields in a supercooled glass-forming liquid and its relationship with relaxations

In the framework of the dynamic facilitation model, a glass former is structured with local cooperative excitations in space and time when approaching the glass transition, which is closely related to dynamic relaxations. We investigate the structure of excitation fields in supercooled ${\mathrm{Cu}}_{50}{\mathrm{Zr}}_{50}$ glass former, and reveal that the excitation fields feature the vortexlike structure beyond the well-known stringlike excitations. The vortex is developed from the stringlike excitations and frequently annihilates via the interactions between vortex and antivortex. The region favored by vortices exhibits percolationlike morphology. We find that the probability distributions of vortex core number are characterized by the discrete multiple mode, which is very analogous to the quantized mode of the slow-\ensuremath{\beta} type relaxation. Furthermore, the relaxation time derived from the formation rate of vortices as well as the corresponding activation energy coincide with the characteristic values of the slow-\ensuremath{\beta} relaxation in metallic glasses. Therefore, it is concluded that the vortex excitation is the origin of the slow-\ensuremath{\beta} relaxation in dynamic space. We further find that the activation energy and relaxation time associated with individual excitations agree well with the Johari-Goldstein \ensuremath{\beta} relaxation. It manifests a more intrinsic structural sign of the Johari-Goldstein \ensuremath{\beta} relaxation than the interpretation based on stringlike excitations.

Relaxation effect on crystal nucleation in a glass unveiled by experimental, numerical, and analytical approaches

In this work, we significantly extend our new approach for analyzing nucleation kinetics below the glass transition, Tg, which considers the structural relaxation effect. Using a 5BaO·8SiO2 (B5S8) glass, we showed a significant stepwise change in the nucleation relaxation time, τsr, with temperature in the Tg region, in contrast with the expected monotonous variation with temperature: τsr is four times shorter for the supercooled liquid than for the glass. Then, using a combination of new experimental data and theoretical (analytical and numerical) analyses, we advance an interpretation within the Classical Nucleation Theory (CNT) framework that brings together the nucleation rates in the T > Tg and T < Tg ranges. We show once more that the so-called “breakdown” of the CNT is merely the result of underestimated nucleation rates due to incomplete glass relaxation during limited experimental nucleation times, confirming our recent findings for Li2O·2SiO2 and 2Na2O·CaO·3SiO2. Finally, for the first time, we also show that due to the almost complete crystallization of the B5S8 glass, and likely of other glasses that exhibit sufficiently high nucleation and growth rates, the relaxation process cannot be finished in the low-temperature range and the ultimate steady-state nucleation regime cannot be reached. These combined results shed light on the complex nucleation behavior below Tg.

Sputter‐grown GeTe/Sb 2 Te 3 superlattice interfacial phase change memory for low power and multi‐level‐cell operation

The multi-level feature of GeTe/Sb2Te3 interfacial phase change memory was achieved by applying a designed voltage-based pulse. It stably demonstrated five multi-level states without interference for 90 cycles by varying the pulse width. GeTe/Sb2Te3 interfacial phase change memory demonstrated retention time of > 1.0 × 103 s, presenting the significantly low drift coefficient (ν) of < 0.009, indicating no resistivity drift due to the structure relaxation of glass. In addition, the reset energy consumption of GeTe/Sb2Te3 interfacial phase change memory was reduced by more than 85% compared to conventional Ge2Sb2Te5 phase change memory at each bottom electrode contact size. Multi-level-cell operation mechanism and gradual increase in conductance value of GeTe/Sb2Te3 interfacial phase change memory was explained by a partial resistance transition model where phase transition occurred partially in all layers. The result of the GeTe/Sb2Te3 interfacial phase change memory performance is expected to bring great advantages to the next-generation storage class memory industry that requires low energy and high density.

Microstructural effects on the dynamical relaxation of glasses and glass composites: A molecular dynamics study

One way to increase the ductility of metallic glasses is to induce heterogeneous microstructures, as for example in nanoglasses and crystal-glass composites. The heterogeneities have important consequences not only on the development of shear bands, but also on the structural relaxations in the glass phase. Experiments using dynamic mechanical spectroscopy (DMS) have been conducted, but an atomic-scale picture is still lacking. Here we apply DMS within molecular dynamics simulations to a classical CuZr metallic glass to study how structural relaxations and mechanical energy dissipation are affected by different microstructures, including nanoglasses, crystal-glass nanolaminates and glasses with spherical crystalline inclusions. We find that in a fully glassy system, not only the fraction but also the spatial homogeneity of “hard” icosahedral environments matter. When hard crystalline particles are introduced, the storage modulus simply results from volumetric averages consistent with the classical Voigt and Reuss bounds. On the other hand, loss moduli are much more complex and can be smaller or larger than in a pure glass depending on the microstructure and loading condition. Atomistic processes leading to these evolutions are discussed and remaining open questions are highlighted.

Local structure, glass transition, structural relaxation, and crystallization of functional oxide glasses investigated by Mössbauer spectroscopy and DTA

Local structure, glass transition, structural relaxation, and crystallization of functional oxide glasses investigated by Mössbauer spectroscopy and DTA

Modeling the relaxation and crystallization kinetics of glass without fictive temperature: Toy landscape approach

AbstractRelaxation and crystallization are key kinetic processes that must be understood to build a comprehensive understanding of the supercooled liquid and glassy states. Traditional approaches have been unable to capture the underlying physics accurately due to assumptions about phenomenological order parameters such as fictive temperature. In this work, we show that glass relaxation can be accurately modeled through a simplified “toy” enthalpy landscape approach, bypassing the use of fictive temperature. Moreover, the same simplified enthalpy landscape provides insights into the thermodynamics and kinetics of crystallization. The toy landscape approach recovers key predictions from the traditional fictive temperature description, but it is based on a more accurate physical framework, giving fundamental knowledge of the glass relaxation and crystallization processes.

Deep glassy state dynamic data challenge glass models: Elastic models

There is increasing experimental evidence that suggests that the dynamics of glass forming liquids do not diverge at finite temperature above zero Kelvin, at the same time there has been recent progress in the development of non-diverging glass transition models. In this work we examine two non-diverging models: the elastically collective nonlinear Langevin equation theory (ECNLE) and the shoving model, both of which relate an energy barrier in the glass formation process with elastic motion at small scales. The models are evaluated in comparison with the non-diverging dynamic data obtained in the deep glassy state (very stable) for a 20-million-year-old (20 Ma) ancient amber and for a vapor deposited amorphous Teflon obtained previously. We find that although both models are in qualitative agreement with the dynamic data for the two stable glasses, they still overestimate the actual relaxation times for the deep glassy state below the nominal glass transition temperature and for conditions corresponding to the equilibrium state or in a state in which the glass relaxation times are upper bounds to the equilibrium values. • Elastic glass models (Shoving and ECNLE) are evaluated in deep glassy state • Both models show sub-T g dynamics that do not diverge above 0 K • Both models still over-estimate the equilibrium relaxation time below T g • Other processes that shorten the dynamics at temperatures approaching T K are needed

Machine-learning integrated glassy defect from an intricate configurational-thermodynamic-dynamic space

Optimizing materials' properties and functions by controlling defects in the crystalline phase has been a cornerstone of materials science and condensed matter physics. However, this paradigm has yet to be established in the broadly defined amorphous materials, which implies the identification of very subtle structural features in an otherwise uniformly disordered medium. Here we propose and define a new integrated glassy defect (IGD), based on machine learning strategy informed by atomistic physics, and also by an extremely wide configurational, thermodynamic, and dynamic variables space of the disordered state. The IGD simultaneously includes positional topology and vibrational features, as well as the local morphology of the potential energy landscape. This unprecedented combination gives rise to a much more comprehensive and more effective definition of the ``glassy defect,'' much beyond the conventional, purely structural input. IGD can be used not only as an efficient predictor of athermal plasticity but is also transferable to detect both short-time vibrational anomalies (the boson peak), and long-time relaxation and diffusion dynamics in glasses. The integrated strategy is instrumental to build the long-sought structure-property relationship in complex media.

Dynamic mechanical relaxation and thermal creep of high-entropy La30Ce30Ni10Al20Co10 bulk metallic glass

Dynamic mechanical relaxation is a fundamental tool to understand the mechanical and physical properties of viscoelastic materials like glasses. Mechanical spectroscopy shows that the high-entropy bulk metallic glass (La30Ce30Ni10Al20Co10) exhibits a distinct β-relaxation feature. In the present research, dynamic mechanical analysis and thermal creep were performed using this bulk metallic glass material at a temperature domain around the β relaxation. The components of total strain, including ideal elastic strain, anelastic strain, and viscous-plastic strain, were analyzed based on the model of shear transformation zones (STZs). The stochastic activation of STZ contributes to the anelastic strain. When the temperature or external stress is high enough or the timescale is long enough, the interaction between STZs induces viscous-plastic strain. When all the spectrum of STZs is activated, the quasi-steady-state creep is achieved.

Characteristic of dynamic mechanical relaxation processes in Cu46Zr46Al8 and La43.4Ce18.6Ni24Al14 metallic glasses

Dynamic mechanical relaxation processes are very important to understand physical and mechanical properties of metallic glasses. In the current work, dynamic mechanical behaviors of La43.6Ce18.4Ni24Al and Cu46Zr46Al8 metallic glasses were investigated by mechanical spectroscopy. Unlike Cu46Zr46Al8 metallic glass, La43.6Ce18.4Ni24Al14 glassy system shows an evident slow β relaxation process. In addition, physical aging below the glass transition temperature Tg induces a reduction of intensity of the β relaxation. Evolution of the concentration of “defects” of metallic glasses was analyzed in the framework of Interstitialcy theory. Our research provides a new insight on understanding of the correlation between the structural heterogeneity and β relaxation of metallic glasses.

Nanoscale structural heterogeneity perspective on the improved magnetic properties during relaxation in a Fe-based metallic glass

Despite the mesoscopic isotropic nature of metallic glasses, there is a certain degree of structural heterogeneity down to the nanoscale. However, how structural heterogeneity affects the magnetic properties is still unclear. In this work, the relaxation-induced structural heterogeneity and magnetic properties evolution of Fe80Si9B11 metallic glass were investigated by atomic force microscopy (AFM) and Mössbauer spectroscopy. We revealed that the correlation-length of nanoscale heterogeneity relates closely with the ferromagnetic exchange interaction together with the magnetic anisotropy, providing experimental evidence of the intrinsic link between the nanoscale structural heterogeneity and magnetic properties for Fe-based metallic glasses. The degeneration of nanoscale structural heterogeneity induces the enhancement of the ferromagnetic exchange interaction and weakening of the magnetic anisotropy. Our results have a vital significance in understanding the structure-property relationship of metallic glass.

Intrinsic correlation between β relaxation and electronic heterogeneity in high entropy metallic glasses

In this work, we have successfully produced a series of equal atomic high- and medium-entropy metallic glasses (HE- and ME-MGs) with pronounced β relaxation. However, compared with the conventional MGs, it is difficult to understand the origin of the strong β relaxation behaviors in these HE-MGs based on the existing empirical knowledge. Here we studied the origin of β relaxation from the viewpoint of electronic heterogeneity by using X-ray photoelectron spectroscopy. It is found that the behaviors of β relaxation are closely associated with the valence states of the constituent elements, .i.e., the larger number of multivalent constituent elements, the more obvious of β relaxation. Moreover, it is found that the high percentage of high energy valence state in the same multivalent system can also promote β relaxation of the amorphous alloy. Our results provide new insight into understanding the origin of β relaxation and the correlation between dynamics and electronic structure in MGs.

Relaxation behavior of high-entropy bulk metallic glass: Influences of physical aging and cyclic loading

<p indent="0mm">In this study, the correlation among the relaxation behavior, deformation mechanism, and structural heterogeneity of metallic glasses is examined using La₃₀Ce₃₀Ni₁₀Al₂₀Co₁₀ high-entropy bulk metallic glass as the model glass. Dynamic mechanical analysis (DMA) was used to investigate the influences of physical aging and cyclic loading on the dynamic relaxation and deformation mechanism of the model glass. The correlation between the deformation units and the structural heterogeneity was analyzed on the basis of the activation energy spectrum (AES). The results demonstrated that La₃₀Ce₃₀Ni₁₀Al₂₀Co₁₀ high-entropy bulk metallic glass displays an apparent β relaxation. A more stable state can be achieved during physical aging below the glass transition temperature and in cyclic loading because the atomic rearrangements are suppressed during these processes. This structural relaxation during the physical aging process enables the transition from liquid-like regions to an elastic matrix. Further, more time is required to activate the deformation units that are frozen during the transition. The applied stress results in a decrease in the number of liquid-like regions, which suppresses the activation of the deformation units during the cyclic loading process. As a result, the intensity of the β relaxation in the metallic glass decreases. Therefore, the origin of the β relaxation in La₃₀Ce₃₀Ni₁₀Al₂₀Co₁₀ high-entropy bulk metallic glass is ascribed to the liquid-like regions.

Impact of High Pressure on Reversible Structural Relaxation of Metallic Glass

The temperature dependence of the reversible structural relaxation time and diffusion constant of metallic glasses under pressure is theoretically investigated. The compression not only changes the glassy dynamics, but also generates a metastable state along with a higher‐energy state where the system can rejuvenate. The relaxation times for forward and backward transitions in this two‐state system are nearly identical and much faster than the relaxation time without accounting for barrier recrossing. At ambient pressure, the expected irreversible relaxation process is recovered, and the numerical results agree well with prior experimental results. An increase in pressure has a minor effect on the relaxation time and diffusion constant that one computes without considering the influence of the metastable state, but it leads to a large reduction of the reversible relaxation time computed upon considering the metastable state. The presence of external compression is also shown to trigger a fragile‐to‐strong crossover in metallic glasses.

Spatial and temporal heterogeneity of Kohlrausch–Williams–Watts stress relaxations in metallic glasses

We perform a molecular dynamics (MD) stress relaxation simulation for Zr50Cu40Al10 metallic glass to confirm that the time dependency of stress relaxation conforms with the Kohlrausch–Williams–Watts (KWW) equation, and to derive the temperature dependency of the Kohlrausch exponent βKWW. We also calculate local plastic deformation based on atomic strain, then discuss the morphology of relaxation and calculate the probability density of stress relaxation with respect to the characteristic time of relaxation from the number of deformed atoms. Afterward, we derive the time dependency of stress relaxation as a mode-averaged decay function, which expresses spatial and temporal heterogeneity. Both the results of simulation and calculation reproduce the KWW relaxation form and are in good agreement, confirming the spatially and temporally heterogeneous nature of KWW relaxation. The heterogeneity of the stress relaxation of metallic glass is determined by local stress changes caused by microscopic local plastic deformation.

Fractional glassy relaxation and convolution modules of distributions

Solving fractional relaxation equations requires precisely characterized domains of definition for applications of fractional differential and integral operators. Determining these domains has been a longstanding problem. Applications in physics and engineering typically require extension from domains of functions to domains of distributions. In this work convolution modules are constructed for given sets of distributions that generate distributional convolution algebras. Convolutional inversion of fractional equations leads to a broad class of multinomial Mittag-Leffler type distributions. A comprehensive asymptotic analysis of these is carried out. Combined with the module construction the asymptotic analysis yields domains of distributions, that guarantee existence and uniqueness of solutions to fractional differential equations. The mathematical results are applied to anomalous dielectric relaxation in glasses. An analytic expression for the frequency dependent dielectric susceptibility is applied to broadband spectra of glycerol. This application reveals a temperature independent and universal dynamical scaling exponent.