Boson Peak Frequency Research Articles

Absorption dispersion below boson peak frequency in oxide glasses studied by THz-time domain spectroscopy

The dispersion properties of the absorption coefficients [α(ν)] of different multi-component silicate oxide glasses have been studied in the frequency region below the boson peak by using THz-time-domain spectroscopy. The value of α(ν)/ν2 has been shown to exhibit a minimum level (R) at low frequency and subsequently a linear increase in the form of r(ν/νBP + E) with increasing frequency, where νBP is the boson peak frequency and R, r, and E are material-specific constants. It has also been found that R ∝ r and E is a constant common to most glasses. This α(ν)/ν2 behavior is ascribed to the dispersion property of the light-vibration coupling coefficient under the reasonable vibrational density of state function. The minimum (constant) and linear terms of the α(ν)/ν2 spectrum are originated from the physical/chemical disorder-induced charge fluctuations in the long-range scale (constant term) and short-range scale (linear term), respectively. The fluctuating charge (σ1) caused by uncorrelated, long-range disorders has primary significance for determining the sub-THz absorption dispersion properties, and its value has been determined for each glass material.

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.

Universality of stringlet excitations as the origin of the boson peak of glasses with isotropic interactions

Nonphononic vibrations originating from disordered structures have garnered significant attention as a fundamental feature of glasses that distinguishes them from crystals. Recently, we discovered that one-dimensional (1D) stringlike vibrations without volume change are responsible for the boson peak in the reduced density of states of two-dimensional (2D) glasses [Y.-C. Hu and H. Tanaka, Nat. Phys. 18, 669 (2022)]. Here we investigate the vibrational properties of three-dimensional (3D) model glasses with isotropic repulsive and attractive interactions and find that the boson peak arises from stringlike quasilocalized transverse vibrations in these 3D systems. These results suggest that stringlike vibrations are the universal origin of the boson peak in both 2D and 3D model glasses, as long as the interaction is isotropic. Furthermore, we confirm that the characteristic frequency of the quasilocalized transverse vibrations, i.e., the boson peak frequency, coincides with the Ioffe-Regel limit of transverse phonons. These results imply the boson peak originates from the frequency-resonant scattering of transverse phonons by quasilocalized vibrations rather than phonon scattering due to elastic inhomogeneity. Our findings provide insights into the origin of low-temperature glass anomalies and inspire further research.

Novel anomalies of soft quasi-localized glassy mode in the vicinity of boson peak frequency

Novel anomalies of soft quasi-localized glassy mode in the vicinity of boson peak frequency

Pressure-Induced Structural Transformations and Electronic Transitions in TeO2 Glass by Raman Spectroscopy.

TeO2 glass has been studied by Raman spectroscopy up to the record pressure of 70 GPa. The boson peak frequency ωb exhibits a decrease of the ∂ωb/∂P slope at 5-6 GPa and saturates above 30 GPa with a practically constant value up to 70 GPa. Experiment and theory indicate that pressures up to 20 GPa induce the transformation of single Te-O-Te bridges to double Te-O2-Te bridges, leading to a more compact structure, while Raman activity developing at higher pressures around 580 cm-1 signals the increase of Te coordination from 4- to 6-fold. Natural bond orbital analysis shows that double Te-O2-Te bridges favor the s → d transition and promote the increase of Te coordination through d2sp3 hybridization. This transition leads to the formation of TeO6 octahedra, in strict difference with crystalline TeO2 at the same pressure range, and to the development of a 3D network that freezes the medium range order.

Low-frequency vibrational states in ideal glasses with random pinning.

Glasses exhibit spatially localized vibrations in the low-frequency regime. These localized modes emerge below the boson peak frequency ω_{BP}, and their vibrational densities of state follow g(ω)∝ω^{4} (ω is frequency). Here, we attempt to address how the localized vibrations behave through the ideal glass transition. To do this, we employ a random pinning method, which enables us to study the thermodynamic glass transition. We find that the localized vibrations survive even in equilibrium glass states. Remarkably, the localized vibrations still maintain the properties of appearance below ω_{BP} and g(ω)∝ω^{4}. Our results provide important insight into the material properties of ideal glasses.

Thermal conduction in a densified oxide glass: Insights from lattice dynamics

Thermal conductivity is an important property of oxide glasses, but its structural origins remain largely unknown. Here, we provide detailed modal information on thermal conductivity in a calcium aluminosilicate glass by relying on recent advances in lattice dynamics methods. We probe various structural features using molecular dynamics simulations by densifying the glass at pressures up to 100 GPa and studying the vibrational, mechanical, and thermal properties. We demonstrate good agreement between these simulations and complementary experiments, both of which indicate significant pressure-induced alteration of mechanical moduli, vibrational density of states, boson peak behavior, and thermal conductivity. We also find an intriguing correlation between the boson peak frequency and the total thermal conductivity in both the current glass series and a lithium borate glass series reported in literature. This correlation scales with the Debye frequency, suggesting that both parameters are associated with the transformation of the elastic medium under pressure.

Terahertz and Microwave Optical Properties of Single-Crystal Quartz and Vitreous Silica and the Behavior of the Boson Peak

Z-cut single-crystal quartz and vitreous silica (silica glass or fused silica) were evaluated for use as reference materials for terahertz and microwave measurements of complex permittivity, with Z-cut quartz confirmed as being suitable. Measurements of refractive indices and absorption coefficients for o-ray and e-ray in quartz and for vitreous silica are reported at frequencies between 0.2 and 6 THz and at 36 and 144 GHz, and compared with data reported in the literature. A previously unreported broad band was seen in the extraordinary absorption of quartz. The Boson peak in silica glass absorption was examined, and for the first time, two negative relationships have been observed: between the refractive index and the Boson peak frequency, and between the Boson peak height and its frequency.

Fast dynamics in a model metallic glass-forming material.

We investigate the fast β- and Johari-Goldstein (JG) β-relaxation processes, along with the elastic scattering response of glass-forming (GF) liquids and the boson peak, in a simulated Al-Sm GF material exhibiting a fragile-strong (FS) transition. These dynamical processes are universal in "ordinary" GF fluids and collectively describe their "fast dynamics," and we find these relaxation processes also arise in a GF liquid exhibiting a FS transition. String-like particle motion, having both an irreversible and a reversible nature (stringlets) component, occurs in the fast-dynamics regime, corresponding to a ps timescale. String-like collective motion associated with localized unstable modes facilitates irreversible and intermittent particle "jumping" events at long times associated with the JG β-relaxation process, while stringlets associated with localized stable modes and corresponding perfectly reversible atomic motion give rise to the boson peak. To further clarify the origin of the boson peak, we calculate the density of states for both the stringlet particles and the "normal" particles and find that the stringlet particles give rise to a boson peak, while the normal atoms do not. The growth of stringlets upon heating ultimately also leads to the "softening" of these excitations, and the boson peak frequency and shear modulus drop in concert with this softening. The growth of string-like collective motion upon heating in the fast-dynamics regime is further shown to be responsible for the growth in the intensity of the fast relaxation process. Relaxation in cooled liquids clearly involves a hierarchy of relaxation processes acting on rather different timescales and spatial scales.

Key role of retardation and non-locality in sound propagation in amorphous solids as evidenced by a projection formalism.

We investigate acoustic propagation in amorphous solids by constructing a projection formalism based on separating atomic vibrations into two, "phonon" (P) and "non-phonon" (NP), subspaces corresponding to large and small wavelengths. For a pairwise interaction model, we show the existence of a "natural" separation lengthscale, determined by structural disorder, for which the isolated P subspace presents the acoustic properties of a nearly homogenous (Debye-like) elastic continuum, while the NP one encapsulates all small scale non-affinity effects. The NP eigenstates then play the role of dynamical scatterers for the phonons. However, at variance with a conjecture of defect theories, their spectra present a finite low frequency gap, which turns out to lie around the Boson peak frequency, and only a small fraction of them are highly localized. We then show that small scale disorder effects can be rigorously reduced to the existence, in the Navier-like wave equation of the continuum, of a generalized elasticity tensor, which is not only retarded, since scatterers are dynamical, but also non-local. The full neglect of both retardation and non-locality suffices to account for most of the corrections to Born macroscopic moduli. However, these two features are responsible for sound speed dispersion and have quite a significant effect on the magnitude of sound attenuation. Although it remains open how they impact the asymptotic, large wavelength scaling of sound damping, our findings rule out the possibility of representing an amorphous solid by an inhomogeneous elastic continuum with the standard (i.e., local and static) elastic moduli.

Molecular vibration and Boson peak analysis of glucose polymers and ester via terahertz spectroscopy

Complex permittivity spectra were obtained herein by performing broadband terahertz (THz) spectroscopy on cellulose, paramylon, and paramylon ester. Absorption peaks observed for cellulose and paramylon at approximately 3 THz are attributed to hydrogen bonds. In addition, a broad absorption peak around 2 THz was observed for all the polymers, demonstrating a general feature of polymer glasses derived from weak interatomic van der Waals forces. The boson peak was observed for cellulose and paramylon ester. The boson peak frequency for cellulose nearly equaled that for glassy glucose—a unit structure of the cellulose polymer. Additionally, the insensitivity of cellulose to the polymerization degree was consistent with recent results obtained via molecular dynamics simulations. In contrast, the boson peak frequency of paramylon ester was markedly smaller than that of cellulose. These results demonstrate the importance of hydrogen bonds as determinants of the boson peak frequency.

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 ωBP is proportional to sqrt{G}. These results provide a positive correlation between the boson peak, shear elasticity, and the glass transition temperature.

Gas-phase water: Features of hydrogen bonding deduced from far-infrared VRT spectra proving the cluster formation in vacuum

Far-infrared vibration–rotation-tunneling (VRT) spectra of gas-phase water reported previously have been interpreted in terms of polaronic exciton coupled model. An increase of the energy gap (Δν) between the neighboring absorption lines, which is observed in the spectrum within a pattern responsible for water cluster absorption, correlates with spin–orbit coupling parameter (β). Namely, experimental ratio (Δνi+1/Δνi) = 1.188996 ± 0.051361 has been found in fair agreement with β= 1.19100654 that implies the accumulation of difference between the absorption and emission energies. This correlation means the electrons coupled with protons establishing hydrogen bonds accumulate the energy difference. Relation deduced earlier for Boson peak frequency admitted to estimate fast Debye relaxation time for water that is found to be 0.183704 ps.

Scaling for hard-sphere colloidal glasses near jamming

Hard-sphere colloids are model systems in which to study the glass transition and universal properties of amorphous solids. Using covariance matrix analysis to determine the vibrational modes, we experimentally measure here the scaling behavior of the density of states, shear modulus, and mean-squared displacement (MSD) in a hard-sphere colloidal glass. Scaling the frequency with the boson-peak frequency, we find that the density of states at different volume fractions all collapse on a single master curve, which obeys a power law in terms of the scaled frequency. Below the boson peak, the exponent is consistent with theoretical results obtained by real-space and phase-space approaches to understanding amorphous solids. We find that the shear modulus and the MSD are nearly inversely proportional, and show a singular power-law dependence on the distance from random close packing. Our results are in very good agreement with the theoretical predictions.

Polarized Raman spectroscopy ofv−SiO2under rare-gas compression

High-pressure polarized Raman spectra of vitreous silica are measured up to 8 GPa in a diamond-anvil cell at room temperature. The combined use of either a nonpenetrating pressurizing medium---argon---or a penetrating one---helium, allows one to separate density from stress effects on the Raman frequencies. In the framework of a simple central force model, the results emphasize the distinct role played by the shrinkage of the intertetrahedral angle Si-O-Si and the force-constant stiffening during the compression. The polarization analysis further reveals the existence of an additional isotropic component in the high-frequency wing of the boson peak. The pressure dependence of the genuine boson peak frequency is found to be much weaker than previously reported and even goes through a minimum around 2 GPa in remarkable coincidence with the anomalous compressibility maximum of silica.

Inelastic neutron spectroscopy as a tool to investigate nanoconfined polymer systems

Abstract The effect of a nanometer scale confinement (pore sizes 7.5 nm down to 2.5 nm) on the vibrational density of states (VDOS) and on the molecular dynamics of Poly(dimethyl siloxane) (PDMS) and Poly(methyl phenyl siloxane) (PMPS) is studied by inelastic neutron scattering. The high penetration depth of neutrons makes neutron scattering a suitable tool for the study of confined systems. Moreover, neutrons are sensitive to light nuclei therefore the confined polymers can be investigated directly, more or less independently of the confining host. Resulting findings are firstly, a reduction of the low frequency contributions to the VDOS below the Boson Peak frequency for both polymers. Including literature data, this reduction can be regarded as a more general feature for glass-forming systems confined by hard walls. Secondly, clear deviations in the temperature dependence of the mean squared displacement of the confined molecules compared to the bulk were found close to the thermal glass transition temperature, whereas localized methyl group rotations were only weakly influenced. Furthermore, the molecular dynamics is accessed. The combination of neutron Time-of-Flight with neutron backscattering, thus covering a broad dynamical range from sub ps to ns, reveal clear influence from confinement on the intermediate incoherent scattering function S(q,t). The latter was obtained by combining the inverse Fourier transform of the individual dynamical structure factors measured by the both methods. The time and q dependence of S(q,t) are discussed in detail for the local methyl group rotations and the segmental dynamics, considering both the interaction of the segments with the pore walls and possible geometrical confinement effects.

On the nontrivial wave-vector dependence of the elastic modulus of glasses

Recent theoretical models for the vibrations in glasses assume that the complex elastic modulus depends on frequency but not on the wave vector, $q$. This assumption translates in a simple $q$ dependence of the dynamic structure factor, which can be experimentally tested. Following the suggestion of a recent paper [U. Buchenau, Phys. Rev. E 90, 062319 (2014)], we present here a new analysis, performed in $q$ space, of inelastic x-ray scattering data of supercooled silica. The outcome of the analysis is compared to the more common approach in the frequency domain and indicates that the mentioned theoretical assumption is consistent with the data only below the boson peak frequency. At higher frequencies it gives rise to a breakdown of the classical second moment sum rule. This violation arises from the underlying assumption of the presence of a single excitation in the spectra. A comparison with the vibrational dynamics of $\ensuremath{\alpha}$-cristobalite suggests, on the contrary, that in the terahertz frequency domain the inelastic spectrum of the glass gains contributions from both acousticlike and opticlike modes. A microscopic theory of the vibrations in glasses cannot neglect the medium range order in their structure, which gives rise to dispersion curves within a pseudo-Brillouin zone.

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.

Boson peak as a probe of quantum effects in a glassy state of biomolecules: the case of L-cysteine.

Some physical properties of hydrated biomolecules, e.g., the occurrence of a boson peak, have been recognized to resemble those of glassy states. The present work shows that quantum fluctuations play a fundamental role in describing the glassy state of biomolecules, particularly at lower hydration levels. There is a linear relationship between the quantumness and the slope of the temperature dependence of the boson peak frequency, which is used to classify the extent of quantum contributions to the glassy state of glasses in general. Lastly, we demonstrate that the boson peak two-band spectral structure that is observed in some cases can be directly linked to the anisotropy of the elastic properties of the material. The amino acid L-cysteine is studied in detail. The findings are compared with previously reported data for other macromolecules.

Low Energy Excitations in Glasses and Melts

Glasses and amorphous materials show, coexisting with the sound waves, a variety of low energy excitations: tunneling, quasi-localized vibrations and relaxations. The latter two are observed well into the liquid state. Using molecular dynamics both were shown to be centered, at low temperatures, typically on more than ten atoms or molecular units, which form chainlike structures. With increasing frequency the interaction of the quasi-localized modes with the sound waves and with each other increases, they de-localize. However, even at the so-called boson peak frequency, where the sound waves become over-damped due to the interaction, the vibrations can be decomposed into local and extended modes. Closely correlated with t.he local vibrations are the local relaxations, which can be envisaged as collective jumps of groups of atoms. With rising temperature both the total jump length and the number of atoms participating increases. In the melt when single jumps are no longer resolved one still observes a collective motion of chains of atoms.