The frequency and temperature dependence of the dielectric constant and the electrical conductivity of the transparent glasses in the composition 0.5Cs2O-0.5Li2O-3B2O3 (CLBO) were investigated in the 100 Hz - 10 MHz frequency range. The dielectric constant for the as-quenched glass increased with increasing temperature, exhibiting anomalies in the vicinity of the glass transition and crystallization temperatures. The temperature coefficient of dielectric constant was estimated (35 \pm 2 ppm.K-1) using Havinga's formula. The dielectric loss at 313 K is 0.005 \pm 0.0005 at all the frequencies understudy. The activation energy associated with the electrical relaxation determined from the electric modulus spectra was found to be 1.73 \pm 0.05 eV, close to that of the activation energy obtained for DC conductivity (1.6 \pm 0.06 eV). The frequency dependent electrical conductivity was analyzed using Jonscher's power law. The combination of these dielectric characteristics suggests that these are good candidates for electrical energy storage device applications.
Boson peak and beta-relaxation are two intrinsic and markedly different dynamic modes of glasses, and their structural origins are long-standing issues. Through tuning atomic packing of a model metallic glass with microalloying of different types of elements, we find that low-temperature boson heat capacity peak evolves hand in hand with high-temperature beta-relaxation. A linear correlation between the boson peak temperature and the activation energy of beta-relaxation is disclosed. The coupling of the boson peak and the beta-relaxation indicates their common structural origin of the loosely …
Transparent glasses in the system 0.5Li2O-0.5M2O-2B2O3 (M=Li, Na and K) were fabricated via the conventional melt quenching technique. Amorphous and glassy nature of the samples were confirmed via the X-ray powder diffraction and the differential scanning calorimetry, respectively. The frequency and temperature dependent characteristics of the dielectric relaxation and the electrical conductivity were investigated in the 100 Hz - 10 MHz frequency range. The imaginary part of the electric modulus spectra was modeled using an approximate solution of Kohrausch-Williams-Watts relation. The stretch…
Inorganic glasses, produced by the melt-quenching of a concoction of minerals, compounds, and elements, can possess unique optical and elastic properties along with excellent chemical, and thermal durability. Despite the ubiquitous use of glasses for critical applications such as touchscreen panels, windshields, bioactive implants, optical fibers and sensors, kitchen and laboratory glassware, thermal insulators, nuclear waste immobilization, optical lenses, and solid electrolytes, their composition-structure-property relationships remain poorly understood. Here, exploiting largescale experimen…
The frequency and temperature dependence of the dielectric constant and the electrical conductivity of the transparent glasses in the composition Li2O-3B2O3 (LBO) were investigated in the 100 Hz- 10 MHz frequency range. The dielectric constant and the loss in the low frequency regime were electrode material dependent. Dielectric and electrical relaxations were respectively analyzed using the Cole-Cole and electric modulus formalisms. The dielectric relaxation mechanism was discussed in the framework of electrode and charge carrier (hopping of the ions) related polarization using generalized Co…
The frequency and temperature dependence of the dielectric constant, electric modulus and electrical conductivity of the transparent glasses in the composition 0.5Li2O-0.5Na2O-2B2O3 (LNBO) were investigated in the 100 Hz - 10 MHz frequency range. The dielectric data have been analyzed using Cole-Cole equation with an addition of the conductivity term. The electrical conductivity was found to be obeying Jonscher's universal law. The dielectric constant and the loss for the as-quenched glasses increased with increasing temperature, exhibiting anomalies in the vicinity of the glass transition and…
Studying the primary α- and secondary β-relaxation process has contributed significantly to the understanding of the structure and rheology of metallic glasses. In this letter, we report on a third relaxation mechanism indicated by a maximum in the loss modulus at low temperatures, which we term γ-relaxation. Contrary to the α- and β-relaxation mechanisms, this irreversible, low energy excitation causes a macroscopic rejuvenation, which we assign to non-affine atomic rearrangements in the matrix that are driven by thermal stresses during cooling. Observed in three different glassy alloys, the …
Break-down of the relationship between α-relaxation and equilibration in hydrostatically compressed metallic glasses
Institut Néel, Université Grenoble Alpes and Centre National de la Recherche Scientifique（格勒诺布尔阿尔卑斯大学内尔研究所与法国国家科学研究中心）；Institut Lumière Matière UMR CNRS 5306, Université Claude Bernard Lyon 1, CNRS（里昂第一大学克劳德·贝尔纳物质光研究所（CNRS联合研究单位5306））；European Synchrotron Radiation Facility（欧洲同步辐射装置）；Chair of Metallic Materials, Saarland University（萨尔兰大学金属材料系）；Department of physics, Institute of Energy Technologies, Universitat Politècnica de Catalunya- BarcelonaTech（加泰罗尼亚理工大学能源技术学院物理系）；Donostia International Physics Center（圣塞巴斯蒂安国际物理中心）；Centro de Física de Materiales (CSIC–UPV/EHU)（材料物理中心（西班牙高等科研理事会-巴斯克国立大学））；Chair of Metallic Materials, Berlin Institute of Technology (TU-Berlin)（柏林工业大学金属材料系）；Laboratoire Magmas et Volcans CNRS, IRD, OPGC, Université Clermont Auvergne（克莱蒙奥弗涅大学火山与岩浆实验室（CNRS、IRD、OPGC联合实验室））
Electrochemical Impedance Spectroscopy and Raman studies are performed on fast ion conducting, AgI-Ag2O-MoO3 glasses, over a wide range of composition to understand the features of structure, ion migration and their correlation. These features essentially involve diffusion and relaxation. The coefficients associated with diffusion process, especially, the diffusion coefficient, diffusion length and relaxation time has been determined by applying Nguyen-Breitkopf method. Besides, by tuning the concentration of the constituents, it is possible to obtain samples those exhibit two important struct…
Negative Strain-Rate Sensitivity in Metallic Glasses Driven by Rejuvenation-Relaxation Competition: Kinetic Monte Carlo Simulations and a Minimal Effective Model
Faculty of Mechanical Engineering, Kanazawa University（金泽大学机械工程学院）；Department of Mechanical Science and Bioengineering, The University of Osaka（大阪大学机械科学生物工程系）；Department of Earth and Space Science, The University of Osaka（大阪大学地球空间科学系）
This series discusses the origin of sound damping and dispersion in glasses. In particular, we address the relative importance of anharmonicity versus thermally activated relaxation. In this first article, Brillouin-scattering measurements of permanently densified silica glass are presented. It is found that in this case the results are compatible with a model in which damping and dispersion are only produced by the anharmonic coupling of the sound waves with thermally excited modes. The thermal relaxation time and the unrelaxed velocity are estimated.
Analytical representations in the time and frequency domains are derived for the most frequently used phenomenological fit functions for non-Debye relaxation processes. In the time domain the relaxation functions corresponding to the complex frequency dependent Cole-Cole, Cole-Davidson and Havriliak-Negami susceptibilities are also represented in terms of $H$-functions. In the frequency domain the complex frequency dependent susceptibility function corresponding to the time dependent stretched exponential relaxation function is given in terms of $H$-functions. The new representations are usefu…
While lot 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 fi…
The question of whether glass continues to relax at low temperature is of fundamental and practical interest. Here, we report a novel atomistic simulation method allowing us to directly access the long-term dynamics of glass relaxation at room temperature. We find that the potential energy relaxation follows a stretched exponential decay, with a stretching exponent $β= 3/5$, as predicted by Phillips' diffusion-trap model. Interestingly, volume relaxation is also found. However, it is not correlated to the energy relaxation, but is rather a manifestation of the mixed alkali effect.
A wide range of glassy and disordered materials exhibit complex, non-exponential, structural relaxation (aging). We propose a simple nonlinear rate equation dδ/dt = a [1-exp (bδ)], 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 descr…
The use of oxide glasses is pervasive throughout everyday amenities and commodities. Such glasses are typically electrical insulators, and endowing them with electrical conductivity without changing their salutary mechanical properties, weight, or thermoformability enables new applications in multifunctional utensils, smart windows, and automotive parts. Previous strategies to impart electrical conductivity include modifying the glass composition or forming a solid-in-solid composite of the glass and a conductive phase. Here we demonstrate using the latter strategy the highest reported room-te…
Slow relaxation occurs in many physical and biological systems. `Creep' is an example from everyday life: when stretching a rubber band, for example, the recovery to its equilibrium length is not, as one might think, exponential: the relaxation is slow, in many cases logarithmic, and can still be observed after many hours. The form of the relaxation also depends on the duration of the stretching, the `waiting-time'. This ubiquitous phenomenon iscalled aging, and is abundant both in natural and technological applications. Here, we suggest a general mechanism for slow relaxations and aging, whic…
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 sev-eral 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 metas…
Avalanche behaviors, characterized by power-law statistics and structural relaxation that induces shear localization in amorphous plasticity, play an essential role in deciding the mechanical properties of amorphous metallic solids (i.e., metallic glasses). However, their interdependence is still not fully understood. To investigate the influence of structural relaxation on elementary avalanche behavior, we perform molecular-dynamics simulations for the shear deformation test of metallic glasses using two typical metallic-glass models comprising a less-relaxed (as-quenched) glass and a well-re…
The temperature dependence of the frequency dispersion in the sound velocity and damping of vitreous silica is reanalyzed. Thermally activated relaxation accounts for the sound attenuation observed above 10 K at sonic and ultrasonic frequencies. Its extrapolation to the hypersonic regime reveals that the anharmonic coupling to the thermal bath becomes important in Brillouin-scattering measurements. At 35 GHz and room temperature, the damping due to this anharmonicity is found to be nearly twice that produced by thermally activated relaxation. The analysis also reveals a sizeable velocity incre…
Electrical conduction and relaxation phenomena in bismuth borate glasses in the composition 2Bi2O3-B2O3 (Bi4B2O9) were investigated. Dielectric studies carried out on these glasses revealed near constant loss (NCL) response in the 1 kHz to 1MHz frequency range at moderately high temperatures (300-450K) associated with relatively low loss (D=0.006) and high dielectric constant (εr'=37) at 1kHz,300K. The variation in AC conductivity with temperature at different frequencies showed a cross over from NCL response characterized by local ion vibration within the potential well to universal Joncher's…
We present field effect measurements on discontinuous 2D thin films which are composed of a sub monolayer of nano-grains of Au, Ni, Ag or Al. Like other electron glasses these systems exhibit slow conductance relaxation and memory effects. However, unlike other systems, the discontinuous films exhibit a dramatic slowing down of the dynamics below a characteristic temperature $T^*$. $T^*$ is typically between 10-50K and is sample dependent. For $T<T^*$ the sample exhibits a few other peculiar features such as repeatable conductance fluctuations in millimeter size samples. We suggest that the en…
Although it is indeed commonly believed that, as frozen supercooled liquids, glasses should continue to flow over the years (e.g., in the case of the stained-glass windows of medieval cathedrals), the dramatic increase of their viscosity below the glass transition temperature suggests, on the contrary, that their relaxation time is on the order of 10$^{32}$ years at room temperature. However, a recent study conducted by Mauro et al. reported the intriguing dynamics of the relaxation of a commercial Corning Gorilla Glass at room temperature, over 1.5 years. Here, we report a novel atomistic sim…
New metallic glasses containing La or Ce have been introduced that have dynamic properties bordering on extremes of conventional metallic glasses. This provides opportunity to test trends or correlations established before in molecular and polymeric glass-formers if exist the same exist in the broader family of metallic glasses. Due to the drastically different chemical and physical structure of metallic glass-formers than soft matter, there is no guarantee that any correlation found in the latter will hold in the former. If found, the result brings metallic glasses closer to the much wider cl…
Electrical modulus analysis of the frequency dependent conductivity data over the range from 100 Hz to 10 MHz and at temperature range of 140 oC to 300 oC were carried out on the mixed alkali vanadate glass samples having lithium and rubidium as alkali elements. The analysis of the data is done using Kohlrausch-Williams-Watts (KWW) equation which describes the relaxation behavior of the mobile species. We have used the Bergman equation (R. Bergman, J. Apl. Phys. 88 (2000) 1356.) for fitting the imaginary part of the electrical modulus. The stretching parameter beta derived from this fit shows …
The effect of cyclic loading on relaxation dynamics and mechanical properties of metallic glasses is studied using molecular dynamics simulations. We consider the Kob-Andersen three-dimensional binary mixture rapidly cooled across the glass transition and subjected to thousands of tension-compression cycles in the elastic range. It was found that during cyclic loading at constant pressure, the system is relocated to progressively lower levels of the potential energy, thus promoting greater densification and higher strength. Furthermore, with increasing stress amplitude, the average glass densi…
The time evolution of the pore size distributions and mechanical properties of amorphous solids at constant pressure is studied using molecular dynamics simulations. The porous glasses were initially prepared at constant volume conditions via a rapid thermal quench from the liquid state to the glassy region and allowing for simultaneous phase separation and material solidification. We found that at constant pressure and low temperature, the porous network becomes more compact and the glassy systems relocate to progressively lower levels of the potential energy. Although the elastic modulus and…
Mechanical relaxation behaviour of various natural volcanic glasses have been investigated in the temperature range RT-1200K using special low frequency flexure (f~0.63Hz) pendulum experiments. The rheological properties complex Young's modulus M* and internal friction 1/Q have been studied from a pure elastic solid at room temperature to pure viscous melt at log(eta[Pas])=8. Several relaxation processes are assumed to act: the primary alpha-relaxation (viscoelastic process, E_a=(344...554)kJ/mol) above the glass transition temperature T_g=(935...1105)K and secondary anelastic beta', beta and …
Fracture initiation in glassy polymers with no notch is studied together with the evolution at zero stress in the glassy state. Confocal microscopy observations and auto-correlation methods are used to characterize specimens of polymethyl methacrylate (PMMA) loaded at room temperature and subsequently unloaded. The evolution of the morphology and the location of the cracking submitted to elongation rate up to 8% are reported and analyzed during the zero-stress relaxation. The crackling (longitudinal crack, transverse crack and crazes) takes place mainly within a 10micron thickness layer from t…
The evolution of porous structure, potential energy and local density in binary glasses under oscillatory shear deformation is investigated using molecular dynamics simulations. The porous glasses were initially prepared via a rapid thermal quench from the liquid state across the glass transition and allowed to phase separate and solidify at constant volume, thus producing an extended porous network in an amorphous solid. We find that under periodic shear, the potential energy decreases over consecutive cycles due to gradual rearrangement of the glassy material, and the minimum of the potentia…
We study the effect of physical aging on the mechanical properties of a model polymer glass using molecular dynamics simulations. The creep compliance is determined simultaneously with the structural relaxation under a constant uniaxial load below yield at constant temperature. The model successfully captures universal features found experimentally in polymer glasses, including signatures of mechanical rejuvenation. We analyze microscopic relaxation timescales and show that they exhibit the same aging characteristics as the macroscopic creep compliance. In addition, our model indicates that th…
Linking the pressure dependence of the structure and thermal stability to α- and \b{eta}-relaxations in metallic glasses
European Synchrotron Radiation Facility（欧洲同步辐射装置）；Universitat Politècnica de Catalunya - BarcelonaTech（加泰罗尼亚理工大学）；Deutsches Zentrum für Luft- und Raumfahrt (DLR)（德国航空航天中心）；Deutsches Elektronen-Synchrotron DESY（德国电子同步加速器）；Donostia International Physics Center（圣塞巴斯蒂安国际物理中心）
In this communication we report the fluorine ion dynamics in mixed alkali oxyfluro vanadate glasses. We have measured the electrical conductivity using impedance spectroscopy technique Room temperature conductivity falls to 5 orders of magnitude from its single alkali values at 33 mol% of rubidium concentration. We have also estimated the distance between similar mobile ions using the density values. Assuming this distance as the hopping distance between the similar ions we have estimated the anionic (Fluorine ion in our case) conductivity. It is observed that the fluorine ion dynamics mimics …
We combine hydrodynamic and field theoretic methods to develop a general theory of phonons as Goldstone bosons in crystals, glasses and liquids based on non-affine displacements and the consequent Goldstones phase relaxation. We relate the conservation, or lack thereof, of specific higher-form currents with properties of the underlying deformation field -- non-affinity -- which dictates how molecules move under an applied stress or deformation. In particular, the single-valuedness of the deformation field is associated with conservation of higher-form charges that count the number of topologic…
We show that in monomeric supercooled liquids and glasses that are plastically flowing at a constant shear stress $σ$ while being deformed with strain rate $\dotε$, the microscopic structural relaxation time $τ_{\rm str}$ is given by the universal relation $σ/G_\infty\dotε$ with $G_\infty$ a modulus. This equality holds for all rheological regimes from temperatures above the glass transition all the way to the athermal limit, and arises from the competing effects of elastic loading and viscous dissipation. In macromolecular (polymeric) glasses, however, the stress decouples from this relaxatio…
Particles in structural glasses rattle around temporary equilibriumpositions, that seldom change through a process which is much faster than the relaxation time, known as particle jump. Since the relaxation of the system is due to the accumulation of many such jumps, it could be possible to connect the single particle short time motion to the macroscopic relaxation by understanding the features of the jump dynamics. Here we review recent results in this research direction, clarifying the features of particles jumps that have been understood and those that are still under investigation, and exa…
Understanding and controlling physical aging, i.e. the spontaneous temporal evolution of out-of-equilibrium systems, represents one of the greatest tasks in material science. Recent studies have revealed the existence of a complex atomic motion in metallic glasses, with different aging regimes in contrast with the typical continuous aging observed in macroscopic quantities. By combining dynamical and structural synchrotron techniques, for the first time we directly connect previously identified microscopic structural mechanisms with the peculiar atomic motion, providing a broader unique view o…
We have studied the liquid-like response of the surface of vapour-deposited glassy films of polystyrene to the introduction of gold nanoparticles on the surface. The build-up of polymer material was measured as a function of time and temperature for both as-deposited films, as well as films that have been rejuvenated to become normal glasses cooled from the equilibrium liquid. The temporal evolution of the surface profile is well described by the characteristic power law of capillary-driven surface flows. In all cases, the surface evolution of the as-deposited films and the rejuvenated films a…
We compute the dielectric response of glasses starting from a microscopic system-bath Hamiltonian of the Zwanzig-Caldeira-Leggett type and using an ansatz from kinetic theory for the memory function in the resulting Generalized Langevin Equation. The resulting framework requires the knowledge of the vibrational density of states (DOS) as input, that we take from numerical evaluation of a marginally-stable harmonic disordered lattice, featuring a strong boson peak (excess of soft modes over Debye $\simω_{p}^{2}$ law). The dielectric function calculated based on this ansatz is compared with expe…
Glassy polymers show strain hardening: at constant extensional load, their flow first accelerates, then arrests. Recent experiments under such loading have found this to be accompanied by a striking dip in the segmental relaxation time. This can be explained by a minimal nonfactorable model combining flow-induced melting of a glass with the buildup of stress carried by strained polymers. Within this model, liquefaction of segmental motion permits strong flow that creates polymer-borne stress, slowing the deformation enough for the segmental (or solvent) modes to then re-vitrify. Here we presen…
The dynamics of structural relaxation in a model polymer glass subject to spatially-homogeneous, time-periodic shear deformation is investigated using molecular dynamics simulations. We study a coarse-grained bead-spring model of short polymer chains below the glass transition temperature. It is found that at small strain amplitudes, the segmental dynamics is nearly reversible over about $10^4$ cycles, while at strain amplitudes above a few percent, polymer chains become fully relaxed after a hundred cycles. At the critical strain amplitude, the transition from slow to fast relaxation dynamics…
Polycrystalline LiMnBO3 is a promising cathode material for Li-ion batteries. In this work, we investigated the thermal, structural and electrical properties of glassy and nanocrystallized materials having the same chemical composition. The original glass was obtained via a standard meltquenching method. SEM and 7Li solid-state NMR indicate that it contains a mixture of two distinct glassy phases. The results suggest that the electrical conductivity of the glass is dominated by the ionic one. The dc conductivity of initial glass was estimated to be in the order of 10-18 S.cm-1 at room temperat…
The influence of cyclic loading and glass stability on structural relaxation and yielding transition in amorphous alloys was investigated using molecular dynamics simulations. We considered a binary mixture cooled deep into the glass phase and subjected to cyclic shear deformation where strain varies periodically but remains positive. We found that rapidly cooled glasses under asymmetric cyclic shear gradually evolve towards states with lower potential energy and finite stress at zero strain. At the strain amplitude just below a critical value, the rescaled distributions of nonaffine displacem…
We theoretically investigate the temperature dependence of the reversible structural relaxation time and diffusion constant of metallic glasses under pressure. 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 our numeri…
The influence of repeated thermal cycling on mechanical properties, structural relaxation, and evolution of the potential energy in binary glasses is investigated using molecular dynamics simulations. We consider a binary mixture with strongly non-additive cross interactions, which is annealed across the glass transition with different cooling rates and then exposed to one thousand thermal cycles at constant pressure. We found that during the first few hundred transient cycles, the potential energy minima after eachcycle gradually decrease and the structural relaxation proceeds via collective,…
We employ an atomic-scale theory within the framework of nonaffine lattice dynamics to uncover the origin of the Johari-Goldstein (JG) $β$-relaxation in metallic glasses (MGs). Combining simulation and experimental data with our theoretical approach, we reveal that the large mass asymmetry between the elements in a La$_{60}$Ni$_{15}$Al$_{25}$ MG leads to a clear separation in the respective relaxation time scales, giving strong evidence that JG relaxation is controlled by the lightest atomic species present. Moreover, we show that only qualitative features of the vibrational density of states …
We use the general statement of the second law applied to an isolated system, the glass in an extremely large medium, to prove that the entropy of the glass must decrease with time during its relaxation towards the supercooled liquid state. This result contradicts the claim of Mauro et al and their computational result of the entropy, according to which their entropy of the glass increases. Our approach using the isolated system completely bypasses the issue of ergodicity loss in glasses, as discussed in the comment.
X-ray photo-induced atomic motion in Phase Change Materials and conventional covalent chalcogenide glasses
Institut Néel, Université Grenoble Alpes and Centre National de la Recherche Scientifique（尼斯研究所，格勒诺布尔阿尔卑斯大学及法国国家科学研究中心）；Department of Physics, University of Trento（特伦托大学物理系）；Department of Chemistry, Aarhus University（奥胡斯大学化学系）；European Synchrotron Radiation Facility（欧洲同步辐射装置）；Deutsches Elektronen-Synchrotron DESY（德国电子同步加速器）；ICGM, Université de Montpellier, CNRS, ENSCM（材料化学与全球分子实验室，蒙彼利埃大学，法国国家科学研究中心及国立化学学院）
Unlike crystals, glasses age or devitrify over time, reflecting their non-equilibrium nature. This lack of stability is a serious issue in many industrial applications. Here, we show by numerical simulations that the devitrification of quasi-hard-sphere glasses is prevented by suppressing volume fraction inhomogeneities. A monodisperse glass known to devitrify with `avalanche'-like intermittent dynamics is subjected to small iterative adjustments to particle sizes to make the local volume fractions spatially uniform. We find that this entirely prevents structural relaxation and devitrification…
The relaxation dynamics and the vibrational spectra of amorphous solids, such as metal alloys, have been intensely investigated as well separated topics in the past. The aim of this review is to summarize recent results in both these areas in an attempt to establish, or unveil, deeper connections between the two phenomena of relaxation and vibration. Theoretical progress in the area of slow relaxation dynamics of liquid and glassy systems and in the area of vibrational spectra of glasses and liquids is reviewed. After laying down a generic modelling framework to connect vibration and relaxatio…
