Low-frequency vibrations in a model glass

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.

Boson-peak vibrational modes in glasses feature hybridized phononic and quasilocalized excitations

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.

A quasi-one-dimensional bulk thermoelectrics with high performance near room temperature

Pursuing efficient thermoelectricity from low-dimensional materials has been highly motivated since the seminal work of Hicks and Dresselhaus. In fact, many superior thermoelectric materials like Bi₂Te₃, Mg₃Sb₂/Mg₃Bi₂ and SnSe are quasi-two-dimensional (q2D), though the advantages of two-dimensionality appear to be diverse and sometimes controversial. Here, we report on a remarkably high thermoelectric performance in TlCu₃Te₂, which is quasi-one-dimensional (q1D) with a further reduced dimension. The thermoelectric figure of merit zT along its q1D axis amounts to 1.3 (1.5) at 300 (400) K, rivaling the best ever reported at these temperatures. The high thermoelectric performances benefit from, on one hand, large power factors derived from a center-hollowed, pancake-like Fermi pocket with q1D dispersion at the edge of a narrow band gap, and on the other hand, small lattice thermal conductivities caused by the large and anharmonic q1D lattice consisting of heavy, lone-pair-electron bearing (Tl⁺) and weakly-bonded (Cu⁺) ions. This compound represents the first bulk material with quasi-uniaxial thermoelectric transport of application level, offering a renewed opportunity to exploit reduced dimensionality for high-performance thermoelectricity.

Density of states below the first sound mode in 3D glasses

Glasses feature universally low-frequency excess vibrational modes beyond Debye prediction, which could help rationalize, e.g., the glasses’ unusual temperature dependence of thermal properties compared to crystalline solids. The way the density of states of these low-frequency excess modes D( ω) depends on the frequency ω has been debated for decades. Recent simulation studies of 3D glasses suggest that D( ω) scales universally with ω4 in a low-frequency regime below the first sound mode. However, no simulation study has ever probed as low frequencies as possible to test directly whether this quartic law could work all the way to extremely low frequencies. Here, we calculated D( ω) below the first sound mode in 3D glasses over a wide range of frequencies. We find D( ω) scales with ω β with β < 4 at very low frequencies examined, while the ω4 law works only in a limited intermediate-frequency regime in some glasses. Moreover, our further analysis suggests our observation does not depend on glass models or glass stabilities examined. The ω4 law of D( ω) below the first sound mode is dominant in current simulation studies of 3D glasses, and our direct observation of the breakdown of the quartic law at very low frequencies thus leaves an open but important question that may attract more future numerical and theoretical studies.

Low-Frequency Excess Vibrational Modes in Two-Dimensional Glasses

Glasses possess more low-frequency vibrational modes than predicted by Debye theory. These excess modes are crucial for the understanding of the low temperature thermal and mechanical properties of glasses, which differ from those of crystalline solids. Recent simulational studies suggest that the density of the excess modes scales with their frequency ω as ω^{4} in two and higher dimensions. Here, we present extensive numerical studies of two-dimensional model glass formers over a large range of glass stabilities. We find that the density of the excess modes follows D_{exc}(ω)∼ω^{2} up to around the boson peak, regardless of the glass stability. The stability dependence of the overall scale of D_{exc}(ω) correlates with the stability dependence of low-frequency sound attenuation. However, we also find that, in small systems, where the first sound mode is pushed to higher frequencies, at frequencies below the first sound mode, there are excess modes with a system size independent density of states that scales as ω^{3}.

Low-energy quasilocalized excitations in structural glasses

Glassy solids exhibit a wide variety of generic thermomechanical properties, ranging from universal anomalous specific heat at cryogenic temperatures to nonlinear plastic yielding and failure under external driving forces, which qualitatively differ from their crystalline counterparts. For a long time, it has been believed that many of these properties are intimately related to nonphononic, low-energy quasilocalized excitations (QLEs) in glasses. Indeed, recent computer simulations have conclusively revealed that the self-organization of glasses during vitrification upon cooling from a melt leads to the emergence of such QLEs. In this Perspective, we review developments over the past three decades toward understanding the emergence of QLEs in structural glasses and the degree of universality in their statistical and structural properties. We discuss the challenges and difficulties that hindered progress in achieving these goals and review the frameworks put forward to overcome them. We conclude with an outlook on future research directions and open questions.

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.

Mechanical disorder of sticky-sphere glasses. II. Thermomechanical inannealability

Many structural glasses feature static and dynamic mechanical properties that can depend strongly on glass formation history. The degree of universality of this history dependence and what it is possibly affected by are largely unexplored. Here we show that the variability of elastic properties of simple computer glasses under thermal annealing depends strongly on the strength of attractive interactions between the glasses' constituent particles-referred to here as glass "stickiness." We find that in stickier glasses the stiffening of the shear modulus with thermal annealing is strongly suppressed, while the thermal-annealing-induced softening of the bulk modulus is enhanced. Our key finding is that the characteristic frequency and density per frequency of soft quasilocalized modes becomes effectively invariant to annealing in very sticky glasses; the latter are therefore deemed "thermomechanically inannealable." The implications of our findings and future research directions are discussed.

Mechanical disorder of sticky-sphere glasses. I. Effect of attractive interactions

Recent literature indicates that attractive interactions between particles of a dense liquid play a secondary role in determining its bulk mechanical properties. Here we show that, in contrast with their apparent unimportance to the bulk mechanics of dense liquids, attractive interactions can have a major effect on macro- and microscopic elastic properties of glassy solids. We study several broadly applicable dimensionless measures of stability and mechanical disorder in simple computer glasses, in which the relative strength of attractive interactions-referred to as "glass stickiness"-can be readily tuned. We show that increasing glass stickiness can result in the decrease of various quantifiers of mechanical disorder, on both macro- and microscopic scales, with a pair of intriguing exceptions to this rule. Interestingly, in some cases strong attractions can lead to a reduction of the number density of soft, quasilocalized modes, by up to an order of magnitude, and to a substantial decrease in their core size, similar to the effects of thermal annealing on elasticity observed in recent works. Contrary to the behavior of canonical glass models, we provide compelling evidence indicating that the stabilization mechanism in our sticky-sphere glasses stems predominantly from the self-organized depletion of interactions featuring large, negative stiffnesses. Finally, we establish a fundamental link between macroscopic and microscopic quantifiers of mechanical disorder, which we motivate via scaling arguments. Future research directions are discussed.

The dependence of the boson peak on the thickness of Cu50Zr50 film metallic glasses

In this study, intensive calculations were performed to investigate the behavior of the low-temperature excess heat capacity of Cu50Zr50 ultrathin film metallic glasses. Our results show that there is a well-defined boson peak in the film metallic glasses and that the boson peak height exhibits an obvious size-dependent feature. Furthermore, there is a critical thickness dc in the curves between the boson peak height and the thickness, where the boson peak height changes abruptly. Through structural analysis, we found that the low-temperature excess heat capacity of the film metallic glasses is correlated with the density layering structure near the surface. The structural parameter S is defined by atomic density and it was found that the boson peak height is highly correlated with S. Our investigation of ultrathin film metallic glasses provides a deeper understanding about the structural origin of the boson peak in metallic glasses.

Acoustic resonance in periodically sheared glass: damping due to plastic events

Using molecular dynamics simulation, we study acoustic resonance in a low-temperature model glass by applying a small periodic shear at a boundary wall. Shear wave resonance occurs as the frequency ω approaches ωl = πc⊥l/L (l = 1, 2…). Here, c⊥ is the transverse sound speed and L is the cell width. At resonance, large-amplitude sound waves appear after many cycles even if the applied strain γ0 is very small. They then induce plastic events, which are heterogeneous on the mesoscopic scale and intermittent on timescales longer than the oscillation period tp = 2π/ω. We visualize them together with the extended elastic strains around them. These plastic events serve to damp sounds. We obtain the nonlinear damping Q-1 = tan δ due to the plastic events near the first resonance at ω ≅ ω1, which is linear in γ0 and independent of ω. After many resonant cycles, we observe an increase in the shear modulus (measured after switching-off the oscillation). We also observe catastrophic plastic events after a very long time (∼103tp), which induce system-size elastic strains and cause a transition from resonant to off-resonant states. At resonance, stroboscopic diffusion becomes detectable.

Extracting the properties of quasilocalized modes in computer glasses: Long-range continuum fields, contour integrals, and boundary effects

Low-frequency nonphononic modes and plastic rearrangements in glasses are spatially quasilocalized, i.e., they feature a disorder-induced short-range core and known long-range decaying elastic fields. Extracting the unknown short-range core properties, potentially accessible in computer glasses, is of prime importance. Here we consider a class of contour integrals, performed over the known long-range fields, which are especially designed for extracting the core properties. We first show that, in computer glasses of typical sizes used in current studies, the long-range fields of quasilocalized modes experience boundary effects related to the simulation box shape and the widely employed periodic boundary conditions. In particular, image interactions mediated by the box shape and the periodic boundary conditions induce the fields' rotation and orientation-dependent suppression of their long-range decay. We then develop a continuum theory that quantitatively predicts these finite-size boundary effects and support it by extensive computer simulations. The theory accounts for the finite-size boundary effects and at the same time allows the extraction of the short-range core properties, such as their typical strain ratios and orientation. The theory is extensively validated in both two and three dimensions. Overall, our results offer a useful tool for extracting the intrinsic core properties of nonphononic modes and plastic rearrangements in computer glasses.

Sound attenuation in finite-temperature stable glasses

The temperature dependence of the thermal conductivity of amorphous solids is markedly different from that of their crystalline counterparts, but exhibits universal behaviour. Sound attenuation is believed to be related to this universal behaviour. Recent computer simulations demonstrated that in the harmonic approximation sound attenuation Γ obeys quartic, Rayleigh scattering scaling for small wavevectors k and quadratic scaling for wavevectors above the Ioffe-Regel limit. However, simulations and experiments do not provide a clear picture of what to expect at finite temperatures where anharmonic effects become relevant. Here we study sound attenuation at finite temperatures for model glasses of various stability, from unstable glasses that exhibit rapid aging to glasses whose stability is equal to those created in laboratory experiments. We find several scaling laws depending on the temperature and stability of the glass. First, we find the large wavevector quadratic scaling to be unchanged at all temperatures. Second, we find that at small wavevectors Γ∼k^1.5 for an aging glass, but Γ∼k² when the glass does not age on the timescale of the calculation. For our most stable glass, we find that Γ∼k² at small wavevectors, then a crossover to Rayleigh scattering scaling Γ∼k⁴, followed by another crossover to the quadratic scaling at large wavevectors. Our computational observation of this quadratic behavior reconciles simulation, theory and experiment, and will advance the understanding of the temperature dependence of thermal conductivity of glasses.

Pinching a glass reveals key properties of its soft spots

It is now well established that glasses feature quasilocalized nonphononic excitations-coined "soft spots"-, which follow a universal [Formula: see text] 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 [Formula: see text] 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.

Nonlinear quasilocalized excitations in glasses: True representatives of soft spots

Structural glasses formed by quenching a melt possess a population of soft quasilocalized excitations-often called "soft spots"-that are believed to play a key role in various thermodynamic, transport, and mechanical phenomena. Under a narrow set of circumstances, quasilocalized excitations assume the form of vibrational (normal) modes, that are readily obtained by a harmonic analysis of the multidimensional potential energy. In general, however, direct access to the population of quasilocalized modes via harmonic analysis is hindered by hybridizations with other low-energy excitations, e.g., phonons. In this series of papers we reintroduce and investigate the statistical-mechanical properties of a class of low-energy quasilocalized modes-coined here nonlinear quasilocalized excitations (NQEs)-that are defined via an anharmonic (nonlinear) analysis of the potential-energy landscape of a glass, and do not hybridize with other low-energy excitations. In this paper, we review the theoretical framework that embeds a micromechanical definition of NQEs. We demonstrate how harmonic quasilocalized modes hybridize with other soft excitations, whereas NQEs properly represent soft spots without hybridization. We show that NQEs' energies converge to the energies of the softest, nonhybridized harmonic quasilocalized modes, cementing their status as true representatives of soft spots in structural glasses. Finally, we perform a statistical analysis of the mechanical properties of NQEs, which results in a prediction for the distribution of potential-energy barriers that surround typical inherent states of structural glasses, as well as a prediction for the distribution of local strain thresholds to plastic instability.

Finite-size effects in the nonphononic density of states in computer glasses

The universal form of the density of nonphononic, quasilocalized vibrational modes of frequency ω in structural glasses, D(ω), was predicted theoretically decades ago, but only recently revealed in numerical simulations. In particular, it has been recently established that, in generic computer glasses, D(ω) increases from zero frequency as ω^{4}, independent of spatial dimension and of microscopic details. However, it has been shown [Lerner and Bouchbinder, Phys. Rev. E 96, 020104(R) (2017)2470-004510.1103/PhysRevE.96.020104] that the preparation protocol employed to create glassy samples may affect the form of their resulting D(ω): glassy samples rapidly quenched from high-temperature liquid states were shown to feature D(ω)∼ω^{β} with β<4, presumably limiting the degree of universality of the ω^{4} law. Here we show that exponents β<4 are seen only in small glassy samples quenched from high-temperature liquid states-whose sizes are comparable to or smaller than the size of the disordered core of soft quasilocalized vibrations-while larger glassy samples made with the same protocol feature the universal ω^{4} law. Our results demonstrate that observations of β<4 in the nonphononic density of states stem from finite-size effects, and we thus conclude that the ω^{4} law should be featured by any sufficiently large glass quenched from a melt.

Aging effects on thermal conductivity of glass-forming liquids

Thermal conductivity of a model glass-forming system in the liquid and glass states is studied using extensive numerical simulations. We show that near the glass transition temperature, where the structural relaxation time becomes very long, the measured thermal conductivity decreases with increasing age. Second, the thermal conductivity of the disordered solid obtained at low temperatures is found to depend on the cooling rate with which it was prepared. For the cooling rates accessible in simulations, lower cooling rates lead to lower thermal conductivity. Our analysis links this decrease of the thermal conductivity with increased exploration of lower-energy inherent structures of the underlying potential energy landscape. Further, we show that the lowering of conductivity for lower-energy inherent structures is related to the high-frequency harmonic modes associated with the inherent structure being less extended. Possible effects of considering relatively small systems and fast cooling rates in the simulations are discussed.

Energy transport in glasses

The temperature dependence of the thermal conductivity is linked to the nature of the energy transport at a frequency ω, which is quantified by thermal diffusivity d(ω). Here we study d(ω) for a poorly annealed glass and a highly stable glass prepared using the swap Monte Carlo algorithm. To calculate d(ω), we excite wave packets and find that the energy moves diffusively for high frequencies up to a maximum frequency, beyond which the energy stays localized. At intermediate frequencies, we find a linear increase of the square of the width of the wave packet with time, which allows for a robust calculation of d(ω), but the wave packet is no longer well described by a Gaussian as for high frequencies. In this intermediate regime, there is a transition from a nearly frequency independent thermal diffusivity at high frequencies to d(ω) ∼ ω-4 at low frequencies. For low frequencies the sound waves are responsible for energy transport and the energy moves ballistically. The low frequency behavior can be predicted using sound attenuation coefficients.

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.

Theory for the density of interacting quasilocalized modes in amorphous solids

Quasilocalized modes appear in the vibrational spectrum of amorphous solids at low frequency. Though never formalized, these modes are believed to have a close relationship with other important local excitations, including shear transformations and two-level systems. We provide a theory for their frequency density, D_{L}(ω)∼ω^{α}, that establishes this link for systems at zero temperature under quasistatic loading. It predicts two regimes depending on the density of shear transformations P(x)∼x^{θ} (with x the additional stress needed to trigger a shear transformation). If θ>1/4, then α=4 and a finite fraction of quasilocalized modes form shear transformations, whose amplitudes vanish at low frequencies. If θ<1/4, then α=3+4θ and all quasilocalized modes form shear transformations with a finite amplitude at vanishing frequencies. We confirm our predictions numerically.

Low-frequency vibrational modes of stable glasses

Unusual features of the vibrational density of states D(ω) of glasses allow one to rationalize their peculiar low-temperature properties. Simulational studies of D(ω) have been restricted to studying poorly annealed glasses that may not be relevant to experiments. Here we report on D(ω) of zero-temperature glasses with kinetic stabilities ranging from poorly annealed to ultrastable glasses. For all preparations, the low-frequency part of D(ω) splits between extended and quasi-localized modes. Extended modes exhibit a boson peak crossing over to Debye behavior (Dex(ω) ~ ω2) at low-frequency, with a strong correlation between the two regimes. Quasi-localized modes obey Dloc(ω) ~ ω4, irrespective of the stability. The prefactor of this quartic law decreases with increasing stability, and the corresponding modes become more localized and sparser. Our work is the first numerical observation of quasi-localized modes in a regime relevant to experiments, and it establishes a direct connection between glasses' stability and their soft vibrational modes.

Excitation of vibrational soft modes in disordered systems using active oscillation

We propose a new method to characterize the spatial distribution of particles' vibrations in solids with much lower computational costs compared to the usual normal mode analysis. We excite the specific vibrational mode in a two dimensional athermal jammed system by giving a small amplitude of active oscillation to each particle's size with an identical driving frequency. The response is then obtained as the real time displacements of the particles. We show remarkable correlations between the real time displacements and the eigen vectors obtained from conventional normal mode analysis. More importantly, from these real time displacements, we can measure the participation ratio and spatial polarization of particles' vibrations. From these measurements, we find three distinct frequency regimes which characterize the spatial distribution and correlation of particles' vibrations in jammed amorphous solids. Furthermore, we can possibly apply this method to a much larger system to examine the low frequency behaviour of amorphous solids with a much higher resolution of the frequency space.

Statistics and Properties of Low-Frequency Vibrational Modes in Structural Glasses

Low-frequency vibrational modes play a central role in determining various basic properties of glasses, yet their statistical and mechanical properties are not fully understood. Using extensive numerical simulations of several model glasses in three dimensions, we show that in systems of linear size L sufficiently smaller than a crossover size L_{D}, the low-frequency tail of the density of states follows D(ω)∼ω^{4} up to the vicinity of the lowest Goldstone mode frequency. We find that the sample-to-sample statistics of the minimal vibrational frequency in systems of size L<L_{D} is Weibullian, with scaling exponents in excellent agreement with the ω^{4} law. We further show that the lowest-frequency modes are spatially quasilocalized and that their localization and associated quartic anharmonicity are largely frequency independent. The effect of preparation protocols on the low-frequency modes is elucidated, and a number of glassy length scales are briefly discussed.

Memory Effect Manifested by a Boson Peak in Metallic Glass

We explore the correlation between a boson peak and structural relaxation in a typical metallic glass. Consistent with enthalpy recovery, a boson peak shows a memory effect in an aging-and-scan procedure. Single-step isothermal aging produces a monotonic decrease of enthalpy and boson peak intensity; for double-step isothermal aging, both enthalpy and boson peak intensity experience, coincidently, an incipient increase to a maximum and a subsequent decrease toward the equilibrium state. Our results indicate a direct link between slow structural relaxation and fast boson peak dynamics, which presents a profound understanding of the two dynamic behaviors in glass.

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.

Structural relaxation in glassy polymers predicted by soft modes: a quantitative analysis

We present a quantitative analysis of the correlation between quasi-localized, low energy vibrational modes and structural relaxation events in computer simulations of a quiescent, thermal polymer glass. Our results extend previous studies on glass forming binary mixtures in 2D, and show that the soft modes identify regions that undergo irreversible rearrangements with up to 7 times the average probability. We study systems in the supercooled- and aging-regimes and discuss temperature- as well as age-dependence of the correlation. In addition to the location of rearrangements, we find that soft modes also predict their direction on the molecular level. The soft regions are long lived structural features, and the observed correlations vanish only after >50% of the system has undergone rearrangements.

Low temperature heat capacity of a severely deformed metallic glass

The low temperature heat capacity of amorphous materials reveals a low-frequency enhancement (boson peak) of the vibrational density of states, as compared with the Debye law. By measuring the low-temperature heat capacity of a Zr-based bulk metallic glass relative to a crystalline reference state, we show that the heat capacity of the glass is strongly enhanced after severe plastic deformation by high-pressure torsion, while subsequent thermal annealing at elevated temperatures leads to a significant reduction. The detailed analysis of corresponding molecular dynamics simulations of an amorphous Zr-Cu glass shows that the change in heat capacity is primarily due to enhanced low-frequency modes within the shear band region.

Impact of plastic deformation and shear band formation on the boson heat capacity peak of a bulk metallic glass

The effect of annealing on the low-temperature heat capacity of a bulk Pd38.5Ni40P21.5 metallic glass is investigated for as-quenched and deformed (rolled) states. Although the boson heat capacity peak increases with increasing strain, it relaxes faster and to a lower level compared to that of the as-quenched state after annealing treatments both below and above the glass transition temperature Tg. The glass is found to retain a certain "memory" on the room-temperature plastic deformation even after annealing above Tg. Indications for two counteracting processes that might be related to different types of shear bands are observed.

Vibrational modes identify soft spots in a sheared disordered packing

We analyze low-frequency vibrational modes in a two-dimensional, zero-temperature, quasistatically sheared model glass to identify a population of structural "soft spots" where particle rearrangements are initiated. The population of spots evolves slowly compared to the interval between particle rearrangements, and the soft spots are structurally different from the rest of the system. Our results suggest that disordered solids flow via localized rearrangements that tend to occur at soft spots, which are analogous to dislocations in crystalline solids.

Heat transport in model jammed solids

We calculate numerically the normal modes of vibrations in three-dimensional jammed packings of soft spheres as a function of the packing fraction and obtain the energy diffusivity, a spectral measure of transport that controls sound propagation and thermal conductivity. The crossover frequency between weak and strong phonon scattering is controlled by the coordination and shifts to zero as the system is decompressed toward the critical packing fraction at which rigidity is lost. We present a scaling analysis that relates the packing fraction dependence of the crossover frequency to the anomalous scaling of the shear modulus with compression. Below the crossover, the diffusivity displays a power-law divergence with inverse frequency consistent with Rayleigh law, which suggests that the vibrational modes are primarily transverse waves, weakly scattered by disorder. Above it, a large number of modes appear whose diffusivity plateaus at a nearly constant value before dropping to zero above the localization frequency. The thermal conductivity of a marginally jammed solid just above the rigidity threshold is calculated and related to the one measured experimentally at room temperature for most glasses.

Molecular dynamics simulation of structural and dynamic properties of selenium structures with different degrees of amorphization

We investigated Se structures of different degrees of disorder ranging from a 5% up to a 95% degree of amorphization. Starting from a trigonal crystalline structure we applied different strategies to introduce disorder into the Se configurations by irradiating atoms from their crystalline equilibrium positions. According to the symmetry of the trigonal phase, we introduced three types of disorder, i.e. the first type where only atoms forming layers of complete helical chains are shifted from their original positions (the thickness of these layers is chosen to represent the chosen degree of amorphicity), the second type where only atoms in planes-of respective thicknesses-lying perpendicular to the chains are displaced and the third type where only randomly chosen atoms are shifted from their crystalline equilibrium positions. After a thermal treatment of these disordered starting configurations, we calculated structural and dynamic properties (i.e. pair-correlation function and vibrational spectrum) and compared the results to both the original crystalline data and results obtained from corresponding glass structures.

Equilibrium density of states and thermodynamic properties of a model glass former

This paper presents an analysis of the thermodynamics of a model glass former. We have performed equilibrium sampling of a popular binary Lennard-Jones model, employing parallel tempering Monte Carlo to cover the crystalline, amorphous, and liquid regions of configuration space. Disconnectivity graphs are used to visualize the potential energy landscape in the vicinity of a crystalline geometry and in an amorphous region of configuration space. The crystalline global minimum is separated from the bulk of the minima by a large potential energy gap, leading to broken ergodicity in conventional simulations. Our sampling reveals crystalline global minima that are lower in potential energy than some of the previous candidates. We present equilibrium thermodynamic properties based on parallel tempering simulations, including heat capacities and free energy profiles, which depend explicitly on the crystal structure. We also report equilibrium melting temperatures.

Similarities in the Cp/T3 peaks in amorphous and crystalline metals

A low-temperature peak in C(p)/T(3) vs is ubiquitous to glasses. It arises from an abundance of low-frequency vibrations, the origin of which remains unclear. A comparable C(p)/T(3) vs peak is observed in crystals due to the dispersion of acoustic phonons and/or the excitation of optical phonons. We compared the C(p)/T(3) vs peaks in metallic and oxide glasses to elemental crystals by analyzing specific heat, phonon density of states, and elastic constant data. We observe no clear distinction in the peak temperature or amplitude between metallic glasses and crystals. Surprisingly, the peak is larger in single crystal Pd(40)Cu(40)P(20) than in glassy Pd(40)Cu(40)P(20).

Crystal phases of a glass-forming Lennard-Jones mixture

We compare the potential energy at zero temperature of a range of crystal structures for a glass-forming binary mixture of Lennard-Jones particles. The lowest-energy ordered state consists of coexisting phases of a single component face centered cubic structure and an equimolar cesium chloride structure. An infinite number of layered crystal structures are identified with energies close to this ground state. We demonstrate that the finite size increase of the energy of the coexisting crystal with incoherent interfaces is sufficient to destabilize this ordered phase in simulations of typical size. Two specific local coordination structures are identified as of possible structural significance in the amorphous state. We observe rapid crystal growth in the equimolar mixture.

Microscopic dynamics of molecular liquids and glasses: role of orientations and translation-rotation coupling

We investigate the dynamics of a fluid of dipolar hard spheres in its liquid and glassy phases, with emphasis on the microscopic time or frequency regime. This system shows rather different glass transition scenarios related to its rich equilibrium behavior, which ranges from a simple hard sphere fluid to long range ferroelectric orientational order. In the liquid phase close to the ideal glass transition line and in the glassy regime a medium range orientational order occurs leading to a softening of an orientational mode. To investigate the role of this mode we use the molecular mode-coupling equations to calculate the spectra straight phi"lm(q,omega) and chi"lm(q,omega). In the center of mass spectra straight phi"00(q,omega) and chi"00(q,omega) we found, besides a high frequency peak at omega(hf), a peak at omega(op), about one decade below omega(hf) x omega(op) has almost no q dependence and exhibits an "isotope" effect omega(op) proportional to I(-1/2), with I the moment of inertia. We give evidence that the existence of this peak is related to the occurrence of medium range orientational order. It is shown that some of these features also exist for schematic mode coupling models.