Inhomogeneous elastic response of silica glass

Long-range correlations in elastic moduli and local stresses at the unjamming transition

We explore the behaviour of spatially heterogeneous elastic moduli as well as the correlations between local moduli in model solids with short-range repulsive potentials. We show through numerical simulations that local elastic moduli exhibit long-range correlations, similar to correlations in the local stresses. Specifically, the correlations in local shear moduli exhibit anisotropic behavior at large lengthscales characterized by pinch-point singularities in Fourier space, displaying a structural pattern akin to shear stress correlations. Focussing on two-dimensional jammed solids approaching the unjamming transition, we show that stress correlations exhibit universal properties, characterized by a quadratic p2 dependence of the correlations as the pressure p approaches zero, independent of the details of the model. In contrast, the modulus correlations exhibit a power-law dependence with different exponents depending on the specific interaction potential. Furthermore, we illustrate that while affine responses lack long-range correlations, the total modulus, which encompasses non-affine behavior, exhibits long-range correlations.

Stringlet excitation model of the boson peak

The boson peak (BP), a low-energy excess in the vibrational density of states over the Debye contribution, is often identified as a characteristic of amorphous solid materials. Despite decades of efforts, its microscopic origin still remains a mystery. Recently, it has been proposed, and corroborated with simulations, that the BP might stem from intrinsic localized modes involving one-dimensional (1D) string-like excitations ("stringlets"). We build on a theory originally proposed by Lund that describes the localized modes as 1D vibrating strings, but we specify the stringlet size distribution to be exponential, as observed in simulations. We provide an analytical prediction for the BP frequency ωBP in the temperature regime well below the observed glass transition temperature Tg. The prediction involves no free parameters and accords quantitatively with prior simulation observations in 2D and 3D model glasses based on inverse power law potentials. The comparison of the string model to observations is more uncertain when compared to simulations of an Al-Sm metallic glass material at temperatures well above Tg. Nonetheless, our stringlet model of the BP naturally reproduces the softening of the BP frequency upon heating and offers an analytical explanation for the experimentally observed scaling with the shear modulus in the glass state and changes in this scaling in simulations of glass-forming liquids. Finally, the theoretical analysis highlights the existence of a strong damping for the stringlet modes above Tg, which leads to a large low-frequency contribution to the 3D vibrational density of states, observed in both experiments and simulations.

The nature of non-phononic excitations in disordered systems

The frequency scaling exponent of low-frequency excitations in microscopically small glasses, which do not allow for the existence of waves (phonons), has been in the focus of the recent literature. The density of states g(ω) of these modes obeys an ωs scaling, where the exponent s, ranging between 2 and 5, depends on the quenching protocol. The orgin of these findings remains controversal. Here we show, using heterogeneous-elasticity theory, that in a marginally-stable glass sample g(ω) follows a Debye-like scaling (s = 2), and the associated excitations (type-I) are of random-matrix type. Further, using a generalisation of the theory, we demonstrate that in more stable samples, other, (type-II) excitations prevail, which are non-irrotational oscillations, associated with local frozen-in stresses. The corresponding frequency scaling exponent s is governed by the statistics of small values of the stresses and, therefore, depends on the details of the interaction potential.

Theory of soliton self-frequency shift in silica optical microresonators with a modified Raman response by the Boson peak

We theoretically study the Raman-induced self-frequency shift of dissipative Kerr soliton in silica optical resonators by taking into consideration the Boson peak. We find that the Boson peak will greatly increase the soliton self-frequency shift and contribute even more than the shift induced by the Lorentzian response for certain pulse durations. We also show that the revised Raman shock time is associated with the pulse width even for a relatively long pulse. Moreover, we demonstrate that the background continuous wave decreases the self-frequency shift of the soliton via the interference with the soliton. Our theoretical and simulated results display excellent agreement with the previous experimental values in the silica-based Kerr-soliton microcomb.

The boson peak in silicate glasses: insight from molecular dynamics

In the low-frequency regime, ≈1 THz, glasses show an anomalous excess in their vibrational density of states called the boson peak (BP). The origin of BP has been a subject of debate since its first discovery a few decades ago. Although BP has been the focus of numerous studies, no conclusive answers have been found about its origins, which remained elusive to date. Here, we present results based on molecular dynamics of several binary and ternary silicate glasses with different network intermediates and modifier oxides. The vibrational density of states and the BP are reported for all the studied glasses. Their correlation with the elastic constant C44, structural, and dynamical properties are extensively discussed in terms of Voronoi atomic volume and the vibrational mean square displacement of Q4 species specifically. We also question the classical classification of alkali oxides as modifiers, and we suggest that Li2O plays the role of pseudo-intermediate oxide in lithium silicate glasses. This claim is supported by the effect of Li on various vibrational modes, and this effect differs from the other alkali metals. Furthermore, we demonstrate a correlation between the BP intensities and both the Voronoi volume of the Q4 and Q3 units and vibrational mean square displacements.

Strain-Controlled Critical Slowing Down in the Rheology of Disordered Networks

Networks and dense suspensions frequently reside near a boundary between soft (or fluidlike) and rigid (or solidlike) regimes. Transitions between these regimes can be driven by changes in structure, density, or applied stress or strain. In general, near the onset or loss of rigidity in these systems, dissipation-limiting heterogeneous nonaffine rearrangements dominate the macroscopic viscoelastic response, giving rise to diverging relaxation times and power-law rheology. Here, we describe a simple quantitative relationship between nonaffinity and the excess viscosity. We test this nonaffinity-viscosity relationship computationally and demonstrate its rheological consequences in simulations of strained filament networks and dense suspensions. We also predict critical signatures in the rheology of semiflexible and stiff biopolymer networks near the strain stiffening transition.

Effective elastic moduli of composites with a strongly disordered host material

The local elastic properties of strongly disordered material are investigated using the theory of correlated random matrices. A significant increase in stiffness is shown in the interfacial region, the thickness of which depends on the strength of disorder. It is shown that this effect plays a crucial role in nanocomposites, in which interfacial regions are formed around each nanoparticle. The studied interfacial effect can significantly increase the influence of nanoparticles on the macroscopic stiffness of nanocomposites. The obtained thickness of the interfacial region is determined by the heterogeneity lengthscale and is of the same order as the lengthscale of the boson peak.

Features of the propagation of phonons in graphene nanostructures. Fast high-frequency phonons in a quasi-flexural mode

The character of propagation in graphene nanostructures of quasi-flexural phonons, whose dispersion law differs from that of sound, is analyzed. Based on the calculation of the frequency dependences of the group velocities and the values of the path of quasiparticles for one period of oscillation, the frequency intervals are established at which: i) phonons propagate freely along all directions of reciprocal space—the propagon zone; ii) phonon propagation along some directions is impossible—diffuse zone; iii) phonons are localized at the nodes of the honeycomb lattice—the locon zone. A comparison is made with a similar classification of phonons in a three-dimensional crystal of cubic symmetry.

Anisotropic correlations of plasticity on the yielding of metallic glasses

We report computer simulations on the shear deformation of CuZr metallic glasses at zero and room temperatures. Shear bands emerge in athermal alloys at strain γ_{c}, with a finite-size effect found. The correlation of nonaffine displacement exhibits an exponential decay even after yielding in thermal alloys, but transits to a power law at γ>γ_{c} in athermal ones. The algebraic exponent is around -1 for the decay inside shear bands, consistent with the theoretical prediction in random elastic media. We quantify the anisotropic correlation with harmonic projection, finding the spectrum is weak in the exponential-decay regime, while it displays a strong polar and quadrupolar symmetry in the power-law regime. The nonvanishing quadrupolar symmetry at long distance signifies the nonlocality of plastic correlation in the athermal alloys. In contrast, the plastic correlation was found to be isotropic and localized at the yielding in the thermal alloys without shear bands.

Beyond the Average: Spatial and Temporal Fluctuations in Oxide Glass-Forming Systems

Atomic structure dictates the performance of all materials systems; the characteristic of disordered materials is the significance of spatial and temporal fluctuations on composition-structure-property-performance relationships. Glass has a disordered atomic arrangement, which induces localized distributions in physical properties that are conventionally defined by average values. Quantifying these statistical distributions (including variances, fluctuations, and heterogeneities) is necessary to describe the complexity of glass-forming systems. Only recently have rigorous theories been developed to predict heterogeneities to manipulate and optimize glass properties. This article provides a comprehensive review of experimental, computational, and theoretical approaches to characterize and demonstrate the effects of short-, medium-, and long-range statistical fluctuations on physical properties (e.g., thermodynamic, kinetic, mechanical, and optical) and processes (e.g., relaxation, crystallization, and phase separation), focusing primarily on commercially relevant oxide glasses. Rigorous investigations of fluctuations enable researchers to improve the fundamental understanding of the chemistry and physics governing glass-forming systems and optimize structure-property-performance relationships for next-generation technological applications of glass, including damage-resistant electronic displays, safer pharmaceutical vials to store and transport vaccines, and lower-attenuation fiber optics. We invite the reader to join us in exploring what can be discovered by going beyond the average.

Avalanches, Clusters, and Structural Change in Cyclically Sheared Silica Glass

We investigate avalanches and clusters associated with plastic rearrangements and the nature of structural change in the prototypical strong glass, silica, computationally. We perform a detailed analysis of avalanches, and of spatially disconnected clusters that constitute them, for a wide range of system sizes. Although qualitative aspects of yielding in silica are similar to other glasses, the statistics of clusters exhibits significant differences, which we associate with differences in local structure. Across the yielding transition, anomalous structural change and densification, associated with a suppression of tetrahedral order, is observed to accompany strain localization.

Local elastic properties of polystyrene nanocomposites increase significantly due to nonaffine deformations

We investigate the local elastic properties of polystyrene doped with SiO_{2} nanoparticles by analyzing the local density fluctuations. The density fluctuations were established from coarse-grained molecular dynamics simulations performed with the MARTINI force field. A significant increase in polystyrene stiffness was revealed within a characteristic range of 1.4 nm from the nanoparticle, while polystyrene density saturates to the bulk value at significantly shorter distances. The enhancement of the local elastic properties of the polymer was attributed to the effect of nonaffine deformations at the length scale below 1 nm, which was further confirmed through the random matrix model with variable strength of disorder.

Vibrational disorder and densification-induced homogenization of local elasticity in silicate glasses

We report the effect of structural compaction on the statistics of elastic disorder in a silicate glass, using heterogeneous elasticity theory with the coherent potential approximation (HET-CPA) and a log-normal distribution of the spatial fluctuations of the shear modulus. The object of our study, a soda lime magnesia silicate glass, is compacted by hot-compression up to 2 GPa (corresponding to a permanent densification of ~ 5%). Using THz vibrational spectroscopic data and bulk mechanical properties as inputs, HET-CPA evaluates the degree of disorder in terms of the length-scale of elastic fluctuations and the non-affine part of the shear modulus. Permanent densification decreases the extent of non-affine elasticity, resulting in a more homogeneous distribution of strain energy, while also decreasing the correlation length of elastic heterogeneity. Complementary 29Si magic angle spinning NMR spectroscopic data provide a short-range rationale for the effect of compression on glass structure in terms of a narrowing of the Si-O-Si bond-angle and the Si-Si distance.

The role of friction in statistics and scaling laws of avalanches

We investigate statistics and scaling laws of avalanches in two-dimensional frictional particles by numerical simulations. We find that the critical exponent for avalanche size distributions is governed by microscopic friction between the particles in contact, where the exponent is larger and closer to mean-field predictions if the friction coefficient is finite. We reveal that microscopic "slips" between frictional particles induce numerous small avalanches which increase the slope, as well as the power-law exponent, of avalanche size distributions. We also analyze statistics and scaling laws of the avalanche duration and maximum stress drop rates, and examine power spectra of stress drop rates. Our numerical results suggest that the microscopic friction is a key ingredient of mean-field descriptions and plays a crucial role in avalanches observed in real materials.

Sound damping in soft particle packings: the interplay between configurational disorder and inelasticity

We numerically investigate sound damping in disordered two-dimensional soft particle packings. We simulate evolution of standing waves of particle displacements and analyze time correlation functions of particle velocities and power spectra. We control the strength of inelastic interactions between the particles in contact to show how the inelasticity affects anomalous sound characteristics of disordered systems: Increasing the strength of inelastic interactions, we find that (i) sound softening vanishes and (ii) attenuation coefficients exhibit a transition from the Rayleigh law to quadratic growth. We also report (iii) how the Ioffe-Regel limit frequencies depend on the strength of inelasticity as useful information for experiments and applications of the sound in disordered media. Our findings suggest that sound damping in soft particle packings is determined by the interplay between elastic heterogeneities and inelasticity.

Open and Anisotropic Soft Regions in a Model Polymer Glass

The vibrational dynamics of a model polymer glass is studied by Molecular Dynamics simulations. The focus is on the “soft” monomers with high participation to the lower-frequency vibrational modes contributing to the thermodynamic anomalies of glasses. To better evidence their role, the threshold to qualify monomers as soft is made severe, allowing for the use of systems with limited size. A marked tendency of soft monomers to form quasi-local clusters involving up to 15 monomers is evidenced. Each chain contributes to a cluster up to about three monomers and a single cluster involves a monomer belonging to about 2–3 chains. Clusters with monomers belonging to a single chain are rare. The open and tenuous character of the clusters is revealed by their fractal dimension df<2. The inertia tensor of the soft clusters evidences their strong anisotropy in shape and remarkable linear correlation of the two largest eigenvalues. Owing to the limited size of the system, finite-size effects, as well as dependence of the results on the adopted polymer length, cannot be ruled out.

Continuum constitutive laws to describe acoustic attenuation in glasses

Nowadays metamaterials are at the focus of an intense research as promising for thermal and acoustic engineering. However, the computational cost associated to the large system size required for correctly simulating them imposes the use of finite-elements simulations, developing continuum models, able to grasp the physics at play without entering in the atomistic details. Still, a correct description should be able to reproduce not only the extrinsic scattering sources on waves propagation, as introduced by the metamaterial microstructure, but also the intrinsic wave attenuation of the material itself. This becomes dramatically important when the metamaterial is made out of a glass, which is intrinsically highly dissipative and with a wave attenuation strongly dependent on frequency. Here we propose a continuum mechanical model for a viscoelastic medium, able to bridge atomic and macroscopic scale in amorphous materials and describe phonon attenuation due to atomistic mechanisms, characterized by a defined frequency dependence. This represents a first decisive step for investigating the effect of a complex nano- or microstructure on acoustic attenuation, while including the atomistic contribution as well.

Stability dependence of local structural heterogeneities of stable amorphous solids

The universal anomalous vibrational and thermal properties of amorphous solids are believed to be related to the local variations of the elasticity. Recently it has been shown that the vibrational properties are sensitive to the glass's stability. Here we study the stability dependence of the local elastic constants of a simulated glass former over a broad range of stabilities, from a poorly annealed glass to a glass whose stability is comparable to laboratory exceptionally stable vapor deposited glasses. We show that with increasing stability the glass becomes more uniform as evidenced by a smaller variance of local elastic constants. We find that, according to the definition of local elastic moduli used in this work, the local elastic moduli are not spatially correlated.

Boson peak, elasticity, and glass transition temperature in polymer glasses: Effects of the rigidity of chain bending

The excess low-frequency vibrational spectrum, called boson peak, and non-affine elastic response are the most important particularities of glasses. Herein, the vibrational and mechanical properties of polymeric glasses are examined by using coarse-grained molecular dynamics simulations, with particular attention to the effects of the bending rigidity of the polymer chains. As the rigidity increases, the system undergoes a glass transition at a higher temperature (under a constant pressure), which decreases the density of the glass phase. The elastic moduli, which are controlled by the decrease of the density and the increase of the rigidity, show a non-monotonic dependence on the rigidity of the polymer chain that arises from the non-affine component. Moreover, a clear boson peak is observed in the vibrational density of states, which depends on the macroscopic shear modulus G. In particular, the boson peak frequency ω_BP is proportional to \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\sqrt{G}$$\end{document}G. These results provide a positive correlation between the boson peak, shear elasticity, and the glass transition temperature.

Tracking the Connection between Disorder and Energy Landscape in Glasses Using Geologically Hyperaged Amber

Fossil amber offers the unique opportunity to investigate an amorphous material that has been exploring its energy landscape for more than 110 million years of natural aging. By applying different X-ray scattering methods to amber before and after annealing the sample to erase its thermal history, we identify a link between the potential energy landscape and the structural and vibrational properties of glasses. We find that hyperaging induces a depletion of the vibrational density of states in the terahertz region, also ruling the sound dispersion and attenuation properties of the corresponding acoustic waves. Critically, this is accompanied by a densification with structural implications different in nature from that caused by hydrostatic compression. Our results, rationalized within the framework of fluctuating elasticity theory, reveal how upon approaching the bottom of the potential energy landscape (9% decrease in the fictive temperature) the elastic matrix becomes increasingly less disordered (6%) and longer-range correlated (22%).

Boson Peak Decouples from Elasticity in Glasses with Low Connectivity

We perform molecular-dynamics simulations of the vibrational and elastoplastic properties of polymeric glasses and crystals and the corresponding atomic systems. We evidence that the elastic scaling of the density of states in the low-frequency boson peak (BP) region is different in crystals and glasses. Also, we see that the BP of the polymeric glass is nearly coincident with the one of the atomic glasses, thus revealing that the former-unlike the elasticity-is controlled by nonbonding interactions only. Our results suggest that the interpretation of the BP in terms of the macroscopic elasticity, discussed in highly connected systems, does not hold for systems with low connectivity.

Local Deformation of Glasses is Mediated by Rigidity Fluctuation on Nanometer Scale

Microscopic deformation processes determine defect formation on glass surfaces and, thus, the material's resistance to mechanical failure. While the macroscopic strength of most glasses is not directly dependent on material composition, local deformation and flaw initiation are strongly affected by chemistry and atomic arrangement. Aside from empirical insight, however, the structural origin of the fundamental deformation modes remains largely unknown. Experimental methods that probe parameters on short or intermediate length-scale such as atom-atom or superstructural correlations are typically applied in the absence of alternatives. Drawing on recent experimental advances, spatially resolved Raman spectroscopy is now used in the THz-gap for mapping local changes in the low-frequency vibrational density of states. From direct observation of deformation-induced variations on the characteristic length-scale of molecular heterogeneity, it is revealed that rigidity fluctuation mediates the deformation process of inorganic glasses. Molecular field approximations, which are based solely on the observation of short-range (interatomic) interactions, fail in the prediction of mechanical behavior. Instead, glasses appear to respond to local mechanical contact in a way that is similar to that of granular media with high intergranular cohesion.

Propagative and diffusive regimes of acoustic damping in bulk amorphous material

In amorphous solids, a non-negligible part of thermal conductivity results from phonon scattering on the structural disorder. The conversion of acoustic energy into thermal energy is often measured by the dynamical dtructure factor (DSF) thanks to inelastic neutron or x-ray scattering. The DSF is used to quantify the dispersion relation of phonons, together with their damping. However, the connection of the dynamical structure factor with dynamical attenuation of wave packets in glasses is still a matter of debate. We focus here on the analysis of wave-packet propagation in numerical models of amorphous silicon. We show that the damped harmonic oscillator model fits of the dynamical structure factors give a good estimate of the wave packets mean free path, only below the Ioffe-Regel frequency. Above the Ioffe-Regel frequency and below the mobility edge, a pure diffusive regime without a definite mean free path is observed. The high-frequency mobility edge is characteristic of a transition to localized vibrations. Below the Ioffe-Regel frequency, a mixed regime is evidenced at intermediate frequencies, with a coexistence of propagative and diffusive wave fronts. The transition between these different regimes is analyzed in detail and reveals a complex dynamics for energy transport, thus raising the question of the correct modeling of thermal transport in amorphous materials.

Microscopic dynamics and failure precursors of a gel under mechanical load

Material failure is ubiquitous, with implications from geology to everyday life and material science. It often involves sudden, unpredictable events, with little or no macroscopically detectable precursors. A deeper understanding of the microscopic mechanisms eventually leading to failure is clearly required, but experiments remain scarce. Here, we show that the microscopic dynamics of a colloidal gel, a model network-forming system, exhibit dramatic changes that precede its macroscopic failure by thousands of seconds. Using an original setup coupling light scattering and rheology, we simultaneously measure the macroscopic deformation and the microscopic dynamics of the gel, while applying a constant shear stress. We show that the network failure is preceded by qualitative and quantitative changes of the dynamics, from reversible particle displacements to a burst of irreversible plastic rearrangements.

Edge mode amplification in disordered elastic networks

Understanding how mechanical systems can be designed to efficiently transport elastic information is important in a variety of fields, including in materials science and biology. Recently, it has been discovered that certain crystalline lattices present "topologically-protected" edge modes that can amplify elastic signals. Several observations suggest that edge modes are important in disordered systems as well, an effect not well understood presently. Here we build a theory of edge modes in disordered isostatic materials and compute the distribution g(κ) of Lyapunov exponents κ characterizing how modes penetrate in the bulk, and find good agreement with numerical results. We show that disordered isostatic materials generically act as levers with amplification of an order L^L where L is the system size, whereas more connected materials amplify signals only close to free surfaces. Our approach, which is based on recent results in "free" random matrix theory, makes an analogy with electronic transport in a disordered conductor.

Fluctuating Elasticity Mode in Transient Molecular Networks

Transient molecular networks, a class of adaptive soft materials with remarkable application potential, display complex, and intriguing dynamic behavior. By performing dynamic light scattering on a wide angular range, we study the relaxation dynamics of a reversible network formed by DNA tetravalent nanoparticles, finding a slow relaxation mode that is wave vector independent at large q and crosses over to a standard q^{-2} viscoelastic relaxation at low q. Exploiting the controlled properties of our DNA network, we attribute this mode to fluctuations in local elasticity induced by connectivity rearrangement. We propose a simple beads and springs model that captures the basic features of this q^{0} behavior.

Pressure Dependence of the Boson Peak of Glassy Glycerol

The pressure dependence of the boson peak (BP) of glycerol, including its behavior across the liquid-glass transition, has been studied using Raman scattering. A significant increase of the BP frequency was observed with pressure up to 11 GPa at room temperature. The pressure dependence of BP frequency ν_BP is proportional to (1+P/P₀)^1/3, where P and P₀ are the pressure and a constant, respectively, consistent with a soft potential model. The characteristic length of medium range order is close in size to a cyclic trimer of glycerol molecules, as predicted by the medium range order of a BP excitation using molecular dynamics simulations, and the pressure dependence of a characteristic medium range order is nearly constant. The pressure induced structural changes in glycerol can be understood in terms of the shrinkage of voids with cyclic trimers persisting to at least 11 GPa. Pressure dependence of the intermolecular O-H stretching mode indicates that the intermolecular hydrogen bond distances gradually decrease up to the glass transition pressure of ∼5 GPa and become nearly constant in the glassy state, indicating the disappearance of free volume in the dense glass.

Anomalous phonon scattering and elastic correlations in amorphous solids

A major issue in materials science is why glasses present low-temperature thermal and vibrational properties that sharply differ from those of crystals. In particular, long-wavelength phonons are considerably more damped in glasses, yet it remains unclear how structural disorder at atomic scales affects such a macroscopic phenomenon. A plausible explanation is that phonons are scattered by local elastic heterogeneities that are essentially uncorrelated in space, a scenario known as Rayleigh scattering, which predicts that the damping of acoustic phonons scales with wavenumber k as k^d+1 (in dimension d). Here we demonstrate that phonon damping scales instead as - k^d+1 ln k, with this logarithmic enhancement originating from long-range spatial correlations of elastic disorder caused by similar stress correlations. Our work suggests that the presence of long-range spatial correlations of local stress and elasticity may well be the crucial feature that distinguishes amorphous solids from crystals.

Yielding of glass under shear: A directed percolation transition precedes shear-band formation

Under external mechanical loading, glassy materials, ranging from soft matter systems to metallic alloys, often respond via formation of inhomogeneous flow patterns, during yielding. These inhomogeneities can be precursors to catastrophic failure, implying that a better understanding of their underlying mechanisms could lead to the design of smarter materials. Here, extensive molecular dynamics simulations are used to reveal the emergence of heterogeneous dynamics in a binary Lennard-Jones glass, subjected to a constant strain rate. At a critical strain, this system exhibits for all considered strain rates a transition towards the formation of a percolating cluster of mobile regions. We give evidence that this transition belongs to the universality class of directed percolation. Only at low shear rates, the percolating cluster subsequently evolves into a transient (but long-lived) shear band with a diffusive growth of its width. Finally, the steady state with a homogeneous flow pattern is reached. In the steady state, percolation transitions also do occur constantly, albeit over smaller strain intervals, to maintain the stationary plastic flow in the system.

Boson peak and Ioffe-Regel criterion in amorphous siliconlike materials: The effect of bond directionality

The vibrational properties of model amorphous materials are studied by combining complete analysis of the vibration modes, dynamical structure factor, and energy diffusivity with exact diagonalization of the dynamical matrix and the kernel polynomial method, which allows a study of very large system sizes. Different materials are studied that differ only by the bending rigidity of the interactions in a Stillinger-Weber modelization used to describe amorphous silicon. The local bending rigidity can thus be used as a control parameter, to tune the sound velocity together with local bonds directionality. It is shown that for all the systems studied, the upper limit of the Boson peak corresponds to the Ioffe-Regel criterion for transverse waves, as well as to a minimum of the diffusivity. The Boson peak is followed by a diffusivity's increase supported by longitudinal phonons. The Ioffe-Regel criterion for transverse waves corresponds to a common characteristic mean-free path of 5-7 Å (which is slightly bigger for longitudinal phonons), while the fine structure of the vibrational density of states is shown to be sensitive to the local bending rigidity.

Elasticity of frictionless particles near jamming

We study the linear elastic response of harmonic disk packings near jamming via three types of probes: (i) point forcing, (ii) constrained homogeneous deformation of subregions of large systems, and (iii) unconstrained deformation of the full system subject to periodic boundary conditions. For the point forcing, our results indicate that the transverse component of the response is governed by a lengthscale ξT, which scales with the confining pressure, p, as ξT∼p-0.25, while the longitudinal component is governed by ξL, which scales as ξL∼p-0.4. The former scaling is precisely the transverse lengthscale, which has been invoked to explain the structure of normal modes near the density of states anomaly in sphere packings, while the latter is much closer to the rigidity length, l*∼p-0.5, which has been invoked to describe the jamming scenario. For the case of constrained homogeneous deformation, we find that μ(R), the value of the shear modulus measured in boxes of size R, gives a value much higher than the continuum result for small boxes and recedes to its continuum limit only for boxes bigger than a characteristic length, which scales like p-0.5, precisely the same way as l*. Finally, for the case of unconstrained homogeneous deformation, we find displacement fields with power spectra, which are consistent with independent, uncorrelated Eshelby transformations. The transverse sector is amazingly invariant with respect to p and very similar to what is seen in Lennard-Jones glasses. The longitudinal piece, however, is sensitive to p. It develops a plateau at long wavelength, the start of which occurs at a length that grows in the p→0 limit. Strikingly, the same behavior is observed both for applied shear and dilation.

Dynamics in a tetrahedral network glassformer: vibrations, network rearrangements, and diffusion

We perform molecular dynamics simulation on a tetrahedral network glassformer using a model for viscous SiO2 by Coslovich and Pastore [J. Phys.: Condens. Matter 21, 285107 (2009)]. In this system, Si and O particles form a random network at low temperature T. We attach an ellipsoid to each particle to represent its time-averaged vibration tensor. We then examine the anisotropic vibrations of Si and O, where the ellipsoid orientations are correlated with the network. The ellipsoids exhibit marked vibrational heterogeneity. The configuration changes occur as breakage and reorganization of the network, where only one or two particles undergo large jumps at each rearrangement leading to diffusion. To the time-correlation functions, however, the particles surrounding these largely displaced ones yield significantly T-dependent contributions, resulting in a weak violation of the Stokes-Einstein relation. This crossover is mild in silica due to the small Si-O bond numbers per particle, while it is strong in fragile glassformers with large coordination numbers. On long timescales, jump events tend to occur in the same regions forming marked dynamic heterogeneity. We also calculate the diffusion constants and the viscosity. The diffusion obeys activation dynamics and may be studied by short-time analysis of irreversible jumps.

Atomic picture of elastic deformation in a metallic glass

The tensile behavior of a Ni60Nb40 metallic glass (MG) has been studied by using ab initio density functional theory (DFT) calculation with a large cell containing 1024 atoms (614 Ni and 410 Nb). We provide insight into how a super elastic limit can be achieved in a MG. Spatially inhomogeneous responses of single atoms and also major polyhedra are found to change greatly with increasing external stress when the strain is over 2%, causing the intrinsically viscoelastic behavior. We uncover the origin of the observed super elastic strain limit under tension (including linear and viscoelastic strains) in small-sized MG samples, mainly caused by inhomogeneous distribution of excess volumes in the form of newly formed subatomic cavities.

Elastic moduli of permanently densified silica glasses

Modelling the mechanical response of silica glass is still challenging, due to the lack of knowledge concerning the elastic properties of intermediate states of densification. An extensive Brillouin Light Scattering study on permanently densified silica glasses after cold compression in diamond anvil cell has been carried out, in order to deduce the elastic properties of such glasses and to provide new insights concerning the densification process. From sound velocity measurements, we derive phenomenological laws linking the elastic moduli of silica glass as a function of its densification ratio. The found elastic moduli are in excellent agreement with the sparse data extracted from literature, and we show that they do not depend on the thermodynamic path taken during densification (room temperature or heating). We also demonstrate that the longitudinal sound velocity exhibits an anomalous behavior, displaying a minimum for a densification ratio of 5%, and highlight the fact that this anomaly has to be distinguished from the compressibility anomaly of a-SiO₂ in the elastic domain.

Evolution of covalent networks under cooling: contrasting the rigidity window and jamming scenarios

We study the evolution of structural disorder under cooling in supercooled liquids, focusing on covalent networks. We introduce a model for the energy of networks that incorporates weak noncovalent interactions. We show that at low temperature these interactions considerably affect the network topology near the rigidity transition that occurs as the coordination increases. As a result, this transition becomes mean field and does not present a line of critical points previously argued for, the "rigidity window." Vibrational modes are then not fractons but instead are similar to the anomalous modes observed in packings of particles near jamming. These results suggest an alternative interpretation for the intermediate phase observed in chalcogenides.

Effects of coordination and pressure on sound attenuation, boson peak and elasticity in amorphous solids

Connectedness and applied stress strongly affect elasticity in solids. In various amorphous materials, mechanical stability can be lost either by reducing connectedness or by increasing pressure. We present an effective medium theory of elasticity that extends previous approaches by incorporating the effect of compression, of amplitude e, allowing one to describe quantitative features of sound propagation, transport, the boson peak, and elastic moduli near the elastic instability occurring at a compression ec. The theory disentangles several frequencies characterizing the vibrational spectrum: the onset frequency where strongly-scattered modes appear in the vibrational spectrum, the pressure-independent frequency ω* where the density of states displays a plateau, the boson peak frequency ωBP found to scale as , and the Ioffe-Regel frequency ωIR where scattering length and wavelength become equal. We predict that sound attenuation crosses over from ω(4) to ω(2) behaviour at ω0, consistent with observations in glasses. We predict that a frequency-dependent length scale ls(ω) and speed of sound ν(ω) characterize vibrational modes, and could be extracted from scattering data. One key result is the prediction of a flat diffusivity above ω0, in agreement with previously unexplained observations. We find that the shear modulus does not vanish at the elastic instability, but drops by a factor of 2. We check our predictions in packings of soft particles and study the case of covalent networks and silica, for which we predict ωIR ≈ ωBP. Overall, our approach unifies sound attenuation, transport and length scales entering elasticity in a single framework where disorder is not the main parameter controlling the boson peak, in agreement with observations. This framework leads to a phase diagram where various glasses can be placed, connecting microscopic structure to vibrational properties.

Role of disorder in the thermodynamics and atomic dynamics of glasses

We measured the density of vibrational states (DOS) and the specific heat of various glassy and crystalline polymorphs of SiO2. The typical (ambient) glass shows a well-known excess of specific heat relative to the typical crystal (α-quartz). This, however, holds when comparing a lower-density glass to a higher-density crystal. For glassy and crystalline polymorphs with matched densities, the DOS of the glass appears as the smoothed counterpart of the DOS of the corresponding crystal; it reveals the same number of the excess states relative to the Debye model, the same number of all states in the low-energy region, and it provides the same specific heat. This shows that glasses have higher specific heat than crystals not due to disorder, but because the typical glass has lower density than the typical crystal.

Compressibility and pressure correlations in isotropic solids and fluids

Presenting simple coarse-grained models of isotropic solids and fluids in d = 1 , 2 and 3 dimensions we investigate the correlations of the instantaneous pressure and its ideal and excess contributions at either imposed pressure (NPT-ensemble, λ = 0 or volume (NVT-ensemble, λ = 1 and for more general values of the dimensionless parameter λ characterizing the constant-volume constraint. The stress fluctuation representation F(Row)|λ=1 of the compression modulus K in the NVT-ensemble is derived directly (without a microscopic displacement field) using the well-known thermodynamic transformation rules between conjugated ensembles. The transform is made manifest by computing the Rowlinson functional F(Row)| also in the NPT-ensemble where F(Row)|λ=1 = K f 0(x) with x = P id/K being a scaling variable, P id the ideal pressure and f 0(x) = x(2-x) a universal function. By gradually increasing λ by means of an external spring potential, the crossover between both classical ensemble limits is monitored. This demonstrates, e.g., the lever rule F(Row)|λ= K[λ = (1 - λ)f 0(x)].

Heterogeneous shear elasticity of glasses: the origin of the boson peak

The local elasticity of glasses is known to be inhomogeneous on a microscopic scale compared to that of crystalline materials. Their vibrational spectrum strongly deviates from that expected from Debye's elasticity theory: The density of states deviates from Debye's law, the sound velocity shows a negative dispersion in the boson-peak frequency regime and there is a strong increase of the sound attenuation near the boson-peak frequency. By comparing a mean-field theory of shear-elastic heterogeneity with a large-scale simulation of a soft-sphere glass we demonstrate that the observed anomalies in glasses are caused by elastic heterogeneity. By observing that the macroscopic bulk modulus is frequency independent we show that the boson-peak-related vibrational anomalies are predominantly due to the spatially fluctuating microscopic shear stresses. It is demonstrated that the boson-peak arises from the steep increase of the sound attenuation at a frequency which marks the transition from wave-like excitations to disorder-dominated ones.

Acoustic excitations in glassy sorbitol and their relation with the fragility and the boson peak

We report a detailed analysis of the dynamic structure factor of glassy sorbitol by using inelastic X-ray scattering and previously measured light scattering data [B. Ruta, G. Monaco, F. Scarponi, and D. Fioretto, Philos. Mag. 88, 3939 (2008)]. The thus obtained knowledge on the density-density fluctuations at both the mesoscopic and macroscopic length scale has been used to address two debated topics concerning the vibrational properties of glasses. The relation between the acoustic modes and the universal boson peak (BP) appearing in the vibrational density of states of glasses has been investigated, also in relation with some recent theoretical models. Moreover, the connection between the elastic properties of glasses and the slowing down of the structural relaxation process in supercooled liquids has been scrutinized. For what concerns the first issue, it is here shown that the wave vector dependence of the acoustic excitations can be used, in sorbitol, to quantitatively reproduce the shape of the boson peak, supporting the relation between BP and acoustic modes. For what concerns the second issue, a proper study of elasticity over a wide spatial range is shown to be fundamental in order to investigate the relation between elastic properties and the slowing down of the dynamics in the corresponding supercooled liquid phase.