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Glasses are materials that lack a crystalline microstructure and long-range atomic order. Instead, they feature heterogeneity and disorder on superstructural scales, which have profound consequences for their elastic response, material strength, fracture toughness, and the characteristics of dynamic fracture. These structure-property relations present a rich field of study in fundamental glass physics and are also becoming increasingly important in the design of modern materials with improved mechanical performance. A first step in this direction involves glass-like materials that retain optical transparency and the haptics of classical glass products, while overcoming the limitations of brittleness. Among these, novel types of oxide glasses, hybrid glasses, phase-separated glasses, and bioinspired glass-polymer composites hold significant promise. Such materials are designed from the bottom-up, building on structure-property relations, modeling of stresses and strains at relevant length scales, and machine learning predictions. Their fabrication requires a more scientifically driven approach to materials design and processing, building on the physics of structural disorder and its consequences for structural rearrangements, defect initiation, and dynamic fracture in response to mechanical load. In this article, a perspective is provided on this highly interdisciplinary field of research in terms of its most recent challenges and opportunities., (© 2022 The Authors. Advanced Materials published by Wiley-VCH GmbH.)

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

A hallmark of structural glasses and other disordered solids is the emergence of excess low-frequency vibrations on top of the Debye spectrum DDebye(ω) of phonons (ω denotes the vibrational frequency), which exist in any solid whose Hamiltonian is translationally invariant. These excess vibrations—a signature of which is a THz peak in the reduced density of states D(ω)/DDebye(ω), known as the boson peak—have resisted a complete theoretical understanding for decades. Here, we provide direct numerical evidence that vibrations near the boson peak consist of hybridizations of phonons with many quasilocalized excitations; the latter have recently been shown to generically populate the low-frequency tail of the vibrational spectra of structural glasses quenched from a melt and of disordered crystals. Our results suggest that quasilocalized excitations exist up to and in the vicinity of the boson-peak frequency and, hence, constitute the fundamental building blocks of the excess vibrational modes in glasses. [ABSTRACT FROM AUTHOR]

The disorder-induced attenuation of elastic waves is central to the universal low-temperature properties of glasses. Recent literature offers conflicting views on both the scaling of the wave attenuation rate Γ(ω) in the low-frequency limit (ω → 0) and its dependence on glass history and properties. A theoretical framework—termed Fluctuating Elasticity Theory (FET)—predicts low-frequency Rayleigh scattering scaling in − d spatial dimensions, Γ (ω) ∼ γ ω − d + 1 , where γ = γ(Vc) quantifies the coarse-grained spatial fluctuations of elastic moduli, involving a correlation volume Vc that remains debated. Here, using extensive computer simulations, we show that Γ(ω) ∼ γω3 is asymptotically satisfied in two dimensions (− d = 2) once γ is interpreted in terms of ensemble—rather than spatial—averages, where Vc is replaced by the system size. In doing so, we also establish that the finite-size ensemble-statistics of elastic moduli is anomalous and related to the universal ω4 density of states of soft quasilocalized modes. These results not only strongly support FET but also constitute a strict benchmark for the statistics produced by coarse-graining approaches to the spatial distribution of elastic moduli. [ABSTRACT FROM AUTHOR]

Soft quasilocalized modes (QLMs) are universally featured by structural glasses quenched from a melt, and are involved in several glassy anomalies such as the low-temperature scaling of their thermal conductivity and specific heat, and sound attenuation at intermediate frequencies. In computer glasses, QLMs may assume the form of harmonic vibrational modes under a narrow set of circumstances; however, direct access to their full distribution over frequency is hindered by hybridizations of QLMs with other low-frequency modes (e.g., phonons). Previous studies to overcome this issue have demonstrated that the response of a glass to local force dipoles serves as a good proxy for its QLMs; we, therefore, study here the statistical-mechanical properties of these responses in computer glasses, over a large range of glass stabilities and in various spatial dimensions, with the goal of revealing properties of the yet-inaccessible full distribution of QLMs' frequencies. We find that as opposed to the spatial-dimension-independent universal distribution of QLMs' frequencies ω (and, consequently, also of their stiffness κ = ω2), the distribution of stiffnesses associated with responses to local force dipoles features a (weak) dependence on spatial dimension. We rationalize this dependence by introducing a lattice model that incorporates both the real-space profiles of QLMs—associated with dimension-dependent long-range elastic fields—and the universal statistical properties of their frequencies. Based on our findings, we propose a conjecture about the form of the full distribution of QLMs' frequencies and its protocol-dependence. Finally, we discuss possible connections of our findings to basic aspects of glass formation and deformation. [ABSTRACT FROM AUTHOR]

The attenuation of long-wavelength phonons (waves) by glassy disorder plays a central role in various glass anomalies, yet it is neither fully characterized nor fully understood. Of particular importance is the scaling of the attenuation rate Γ(k) with small wavenumbers k → 0 in the thermodynamic limit of macroscopic glasses. Here, we use a combination of theory and extensive computer simulations to show that the macroscopic low-frequency behavior emerges at intermediate frequencies in finite-size glasses, above a recently identified crossover wavenumber k†, where phonons are no longer quantized into bands. For k < k†, finite-size effects dominate Γ(k), which is quantitatively described by a theory of disordered phonon bands. For k > k†, we find that Γ(k) is affected by the number of quasilocalized nonphononic excitations, a generic signature of glasses that feature a universal density of states. In particular, we show that in a frequency range in which this number is small, Γ(k) follows a Rayleigh scattering scaling ∼ k ¯ d + 1 (¯ d is the spatial dimension) and that in a frequency range in which this number is sufficiently large, the recently observed generalized-Rayleigh scaling of the form ∼ k ¯ d + 1 log(k0/k) emerges (k0 > k† is a characteristic wavenumber). Our results suggest that macroscopic glasses—and, in particular, glasses generated by conventional laboratory quenches that are known to strongly suppress quasilocalized nonphononic excitations—exhibit Rayleigh scaling at the lowest wavenumbers k and a crossover to generalized-Rayleigh scaling at higher k. Some supporting experimental evidence from recent literature is presented. [ABSTRACT FROM AUTHOR]

It is now well established that glasses feature quasilocalized nonphononic excitations-coined "soft spots"-, which follow a universal ω4 density of states in the limit of low frequencies ω. All glass-specific properties, such as the dependence on the preparation protocol or composition, are encapsulated in the nonuniversal prefactor of the universal ω4 law. The prefactor, however, is a composite quantity that incorporates information both about the number of quasilocalized nonphononic excitations and their characteristic stiffness, in an apparently inseparable manner. We show that by pinching a glass-i.e., by probing its response to force dipoles-one can disentangle and independently extract these two fundamental pieces of physical information. This analysis reveals that the number of quasilocalized nonphononic excitations follows a Boltzmann-like law in terms of the parent temperature from which the glass is quenched. The latter, sometimes termed the fictive (or effective) temperature, plays important roles in nonequilibrium thermodynamic approaches to the relaxation, flow, and deformation of glasses. The analysis also shows that the characteristic stiffness of quasilocalized nonphononic excitations can be related to their characteristic size, a long sought-for length scale. These results show that important physical information, which is relevant for various key questions in glass physics, can be obtained through pinching a glass. [ABSTRACT FROM AUTHOR]

The translational symmetry of solids, either orderedordisordered,gives rise to the existenceof lowfrequency phonons. In ordered systems, either crystalline solids or isotropic homogeneous continua, some phonons characterized by different wavevectors are degenerate, i.e.they share the exact same frequencyω; in finite-size systems, phonons forma discrete set of bandswith nq(ω)-fold degeneracy. Here we focus on understanding howthis degeneracy is lifted in the presence of disorder, and its physical implications.Using standard degenerate perturbation theory and simple statistical considerations,we predict the dependence of the disorder-induced frequency width of phonon bands to be Δω *** σ ω ω √Nq/√N, where σ is the strength of disorder andNis the totalnumber of particles. This theoretical prediction is supported by extensive numerical calculations for disordered lattices--characterized by topological,mass, stiffness and positional disorder--and for computer glasses, where disorder is self-generated, thus establishing its universal nature. The predicted scaling of phonon band widths leads to the identification of a crossover frequency ω† *** L-2/(d+2) in systems of linear size L in d > 2 dimensions,where the disorder-induced width of phonon bands becomes comparable to the frequency gap between neighboring bands. Consequently, phonons continuously cover the frequency rangeω > ω†,where the notion of discrete phonon bands becomes ill-defined.Twobasic applications of the theory are presented; first, we showthat the phonon scattering lifetime is proportional to (Δω)-1 forω < ω†. Second, thetheoryisapplied to the basic physics of glasses, allowing us to determine the range of frequencies in which the recently established universal density of states of non-phononic excitations can be directly probed for different system sizes. [ABSTRACT FROM AUTHOR]

Computational studies of supercooled liquids often focus on various analyses of their "underlying inherent states"--the glassy configurations at zero temperature obtained by an infinitely fast (instantaneous) quench from equilibrium supercooled states. Similar protocols are also regularly employed in investigations of the unjamming transition at which the rigidity of decompressed soft-sphere packings is lost. Here we investigate the statistics and localization properties of low-frequency vibrational modes of glassy configurations obtained by such instantaneous quenches. We show that the density of vibrational modes grows as ωβ with β depending on the parent temperature T0 from which the glassy configurations were instantaneously quenched. For quenches from high temperature liquid states we find β≈3, whereas β appears to approach the previously observed value β=4 as T0 approaches the glass transition temperature. We discuss the consistency of our findings with the theoretical framework of the soft potential model, and contrast them with similar measurements performed on configurations obtained by continuous quenches at finite cooling rates. Our results suggest that any physical quench at rates sufficiently slower than the inverse vibrational time scale--including all physically realistic quenching rates of molecular or atomistic glasses--would result in a glass whose density of vibrational modes is universally characterized by β=4. [ABSTRACT FROM AUTHOR]

It has been recently established that the low-frequency spectrum of simple computer glass models is populated by soft, quasilocalized nonphononic vibrational modes whose frequencies ω follow a gapless, universal distribution D(ω)∼ω4. While this universal nonphononic spectrum has been shown to be robust to varying the glass history and spatial dimension, it has so far only been observed in simple computer glasses featuring radially symmetric, pairwise interaction potentials. Consequently, the relevance of the universality of nonphononic spectra seen in simple computer glasses to realistic laboratory glasses remains unclear. Here, we demonstrate the emergence of the universal ω4 nonphononic spectrum in a broad variety of realistic computer glass models, ranging from tetrahedral network glasses with three-body interactions, through molecular glasses and glassy polymers, to bulk metallic glasses. Taken together with previous observations, our results indicate that the low-frequency nonphononic vibrational spectrum of any glassy solid quenched from a melt features the universal ω4 law, independently of the nature of its microscopic interactions. [ABSTRACT FROM AUTHOR]