Glass Peak Research Articles

Glass-Like Phonon Dynamics and Thermal Transport in a GeTe Nano-Composite at Low Temperature.

In this work, the experimental evidence of glass-like phonon dynamics and thermal conductivity in a nanocomposite made of GeTe and amorphous carbon is reported, which is of interest for microelectronics, and specifically phase change memories. It is shown that, the total thermal conductivity is reduced by a factor of three at room temperature with respect to pure GeTe, due to the reduction of both electronic and phononic contributions. This latter, similarly to glasses, is small and weakly increasing with temperature between 100 and 300 K, indicating a mostly diffusive thermal transport and reaching a value of 0.86(7)Wm-1K-1 at room temperature. A thorough investigation of the nanocomposite's phonon dynamics reveals the appearance of an excess intensity in the low energy vibrational density of states, reminiscent of the Boson peak in glasses. These features can be understood in terms of an enhanced phonon scattering at the interfaces, due to the presence of elastic heterogeneities, at wavelengths in the 2-20 nm range. The findings confirm recent simulation results on crystalline/amorphous nanocomposites and open new perspectives in phonon and thermal engineering through the direct manipulation of elastic heterogeneities.

Boson peak in the vibrational spectra of glasses

A hallmark of glasses is an excess of low-frequency, nonphononic vibrations. It is manifested as a terahertz peak—the boson peak—in the ratio of the vibrational density of state (VDoS) and Debye's VDoS of phonons. Here, using experimental data, extensive computer simulations, and a mean-field model, we show that the nonphononic part of the VDoS itself features both a universal power-law tail and a peak at higher frequencies, entirely accounted for by quasilocalized nonphononic vibrations, whose existence and spectra power-law tail were recently established in computer glasses. We rationalize the variation of the peak's frequency and magnitude with glasses' thermal history, which is much weaker than the variation of the tail and may follow an opposite trend, and show that the peak's modes are composed of many spatially coupled quasilocalized nonphononic vibrations. Our results shed light on the origin, nature, and properties of the boson peak in glasses. Published by the American Physical Society 2024

Upper bound of fragility from spatial fluctuations of shear modulus and boson peak in glasses.

It is shown that the normalized rms fluctuation of the shear modulus on the medium-range order scale in glasses correlates with fragility: the higher fragility, the smaller the fluctuation amplitude. The latter is calculated within the heterogeneous elasticity theory using the data on the boson peak in glasses. On a smaller scale corresponding to cooperative structural relaxation, the normalized rms fluctuation of the infinite-frequency shear modulus was estimated using the data on the decoupling of viscosity and diffusion in supercooled liquids. These fluctuations are much smaller in amplitude, and, in contrast, they increase with increasing fragility. Extrapolation predicts intersection of both rms fluctuations and disappearing of the boson peak at the upper limit to fragility ≈180.

Amorphous solids as fuzzy crystals: A Debye-like theory of low-temperature specific heat

The formulation of a fundamental description of amorphous solids is a standing challenge in condensed matter physics. We construct a quantum mechanical model of isotropic amorphous solids as fuzzy crystals and establish an analytical theory of vibrations for glasses at low temperature. Our theoretical framework relies on the basic principle that the disorder in a glass is similar to the disorder in a classical fluid, while the latter is mathematically encoded by noncommutative coordinates in the Lagrange description of fluid mechanics. We find that the density of states in the acoustic branches flattens significantly, leading naturally to a boson peak in the specific heat as a manifestation of a van Hove singularity. The model is valid in the same range as Debye’s theory, namely up to circa 10% of the Debye temperature. Within this range, we find an excellent agreement between the theoretical predictions and the experimental data for two typical glasses, a-GeO2 and Ba8Ga16Sn30-clathrate.Our model supports the conceptual understanding of the nature of the boson peak in glasses as a manifestation of the liquid-like disorder. At the same time, it provides a novel, mathematically simple framework for a unitary treatment of thermodynamical and transport properties of amorphous materials and a solid background for inserting further elements of complexity specific to particular glasses.

Axially slanted laser illumination scheme for direct and accurate Raman spectroscopic determination of gemcitabine concentration in freeze-dried gemcitabine injection powder housed in a glass container

When Raman spectroscopy is employed for a direct in situ determination of ingredient concentration for a product stored in a glass container, minimization of the interfering glass background in the collected spectrum is demanding to secure a more accurate analysis. To meet this request, an axially slanted illumination (ASI) scheme slantingly irradiating laser on the headspace side of a glass container and positioning a detector beneath the container was demonstrated in this study. This ASI scheme was basically designed to increase the distance between the laser illumination spot and detector location to minimize the number of glass photons reaching the detector. The analytical utility of the scheme was evaluated for the determination of gemcitabine concentration (42.9–58.2 wt%) in the gemcitabine injection powder housed in a glass container. Using the ASI scheme, the spectral features of the gemcitabine powder became distinct with only a weak underlying glass background signal. For comparative purpose, when an axially perpendicular offset (APO) scheme perpendicularly irradiating laser on the side wall where the sample was filled was used, the magnitude of glass background was higher, and the most intense gemcitabine peak was largely buried in the glass peak. The accuracy for determination of gemcitabine concentration using the ASI scheme was superior with an error of 0.20 wt%, while 0.33 wt% with employing the APO scheme. Overall, this study demonstrates that the ASI scheme is a potentially versatile Raman spectroscopic tool for fast non-sampling analysis of other products stored in a glass container.

Application of the random matrix theory to the boson peak in glasses

The density of vibrational states g(ω) of an amorphous system is studied by using the random-matrix theory. Taking into account the most important correlations between elements of the random matrix of the system, equations for the density of vibrational states g(ω) are obtained. The analysis of these equations shows that in the low-frequency region the vibrational density of states has the Debye behavior g(ω) ∼ ω2. In the higher frequency region, there is the boson peak as an additional contribution to the density of states. The obtained equations are in a good agreement with the numerical results and allow us to find an exact shape of the boson peak.

Boson Peak Related to Ga Nanoclusters in AlGaN Layers Grown by Plasma-Assisted Molecular Beam Epitaxy at Ga-Rich Conditions

We report the results of systematic Raman spectroscopy studies of AlxGa1 –xN (x ~ 0.75) layers grown using plasma-assisted molecular beam epitaxy at various stoichiometric conditions and growth fluxes. The high-intensity asymmetric low-frequency peak obeying Bose statistics is discovered in Raman spectra of the layers grown by temperature-modulated epitaxy at strongly Ga-enriched conditions. Theoretical model is developed to explain the origin and the high intensity of the observed low-frequency peak, which is attributed to the presence of excessive metallic gallium in AlGaN layers and can be explained by vibrations of gallium clusters with a diameter of ~1 nm. The nature of the low-frequency peak is similar to that of the boson peak in glasses, which occupies the same frequency range in Raman spectra. We demonstrate the capabilities of Raman spectroscopy as an express and non-destructive technique for optimization of growth conditions of AlGaN layers to achieve simultaneously the atomically-smooth droplet-free surface morphology and the high structural quality.

Local inversion-symmetry breaking controls the boson peak in glasses and crystals

It is well known that amorphous solids display a phonon spectrum where the Debye $\sim \omega^2$ law at low frequency melds into an anomalous excess-mode peak (the boson peak) before entering a quasi-localized regime at higher frequencies dominated by scattering. The microscopic origin of the boson peak has remained elusive despite various attempts to put it in a clear connection with structural disorder at the atomic/molecular level. Using numerical calculations on model systems, we show that the microscopic origin of the boson peak is directly controlled by the local breaking of center-inversion symmetry. In particular, we find that both the boson peak and the nonaffine softening of the material display a strong positive correlation with a new order parameter describing the local inversion symmetry of the lattice. The standard bond-orientational order parameter, instead, is shown to be a poor correlator and cannot explain the boson peak in randomly-cut crystals with perfect bond-orientational order. Our results bring a unifying understanding of the boson peak anomaly for model glasses and defective crystals in terms of a universal local symmetry-breaking principle of the lattice.

Relation between the boson peak in glasses and van Hove singularity in crystals

We analysed the relation between the boson peak in glasses and the van Hove singularity in crystals. The comparison of the experimental results obtained for amorphous iron to the published data for two different iron crystals suggests that the appearance of the pseudo-Brillouin zone with corresponding flattening of the dispersion relations and the resulting boson peak in glasses are the fundamental effects caused by a finite and well-defined value of interatomic distance, i.e. simply by an atomistic character of nature. Accordingly, the Brillouin zone and the van Hove singularities in crystals can be considered as the crystalline counterparts, or ‘derivatives’, of these ‘glassy’ quantities. In addition, we analyse the options for observing the excess states in glasses caused by another effect, i.e. by phonon scattering. Possibly, this is indeed seen in the reduced DOS of ambient silica glass and amorphous iron in the 1–2 meV energy range.

Origin of the first sharp diffraction peak in glasses

Origin of the first sharp diffraction peak in glasses

Pressure dependence of the boson peak in glasses: Correlated and uncorrelated perturbations

The pressure dependence of the boson peak in glasses within the framework of the extended soft potential model is reconsidered, taking effects at small pressures into account. One of these is the pressure dependence of the elastic constants, changing the interaction between the soft localized modes and thus changing the quasilocalized vibrations (QLVs) of the boson peak. This and other effects require the introduction of additional parameters to describe all the different influences of the pressure in detail. As in the first treatment of the problem, the dominating high-pressure influence remains the creation of pressure forces, which have to be added to the random forces responsible for the boson peak formation. The pressure forces consist of a correlated and an uncorrelated part (correlated with respect to the already existing random forces). Both lead to the ${P}^{1/3}$ dependence observed in high-pressure experiments, but the uncorrelated part vanishes at small pressure $P$. The comparison to experiment is divided into a small pressure part, accessible through low-temperature heat capacity and thermal expansion measurements, and the high-pressure part, mostly Raman scattering measurements of the boson peak under pressure. The results suggest that the latter are dominated by the uncorrelated part of the forces, probably due to pressure-induced relaxations.

The transverse nature of the Boson peak: A rigidity theory approach

The transversal nature of the Boson peak in crystals and glasses is investigated by using a model inspired from rigidity theory of glasses. By tuning the rigidity of the network using second-neighbor interactions, we show that the transversal van Hove singularity – associated with the Boson peak – arises when the transverse dispersion branch touches for the first time the boundary of the first Brillouin zone, leading to an anomaly in the low frequency region. The frequency of the singularity is determined by the rigidity of the network. For the disordered version of the model, the singularity arises when the transversal dispersion branch touches the limit of a pseudo-Brillouin zone, suggesting that the Boson peak in glasses has a similar origin. Increasing rigidity shifts the position of the Boson peak towards high frequencies while its intensity decreases. This provides an important clue to understand pressure effects on the Boson peak in glasses and crystals.

Mean-square-displacement distribution in crystals and glasses: An analysis of the intrabasin dynamics

In the energy landscape picture, the dynamics of glasses and crystals is usually decomposed into two separate contributions: interbasin and intrabasin dynamics. The intrabasin dynamics depends partially on the quadratic displacement distribution on a given metabasin. Here we show that such a distribution can be approximated by a Gamma function, with a mean that depends linearly on the temperature and on the inverse second moment of the density of vibrational states. The width of the distribution also depends on this last quantity, and thus the contribution of the boson peak in glasses is evident on the tail of the distribution function. It causes the distribution of the mean-square displacement to decay slower in glasses than in crystals. When a statistical analysis is performed under many energy basins, we obtain a Gaussian in which the width is regulated by the mean inverse second moment of the density of states. Simulations performed in binary glasses are in agreement with such a result.

Equivalence of the Boson Peak in Glasses to the Transverse Acoustic van Hove Singularity in Crystals

We compare the atomic dynamics of the glass to that of the relevant crystal. In the spectra of inelastic scattering, the boson peak of the glass appears higher than the transverse acoustic (TA) singularity of the crystal. However, the density of states shows that they have the same number of states. Increasing pressure causes the transformation of the boson peak of the glass towards the TA singularity of the crystal. Once corrected for the difference in the elastic medium, the boson peak matches the TA singularity in energy and height. This suggests the identical nature of the two features.

Communication: High-frequency acoustic excitations and boson peak in glasses: A study of their temperature dependence

The results of a combined experimental study of the high-frequency acoustic dynamics and of the vibrational density of states (VDOS) as a function of temperature in a glass of sorbitol are reported here. The excess in the VDOS at approximately 4.5 meV over the Debye, elastic continuum prediction (boson peak) is found to be clearly related to anomalies observed in the acoustic dispersion curve in the mesoscopic wavenumber range of few nm(-1). The quasiharmonic temperature dependence of the acoustic dispersion curves offers a natural explanation for the observed scaling of the boson peak with the elastic medium properties.

Orientational disorder in some molecular solids in relation to the boson peak in glasses

Orientational disorder in some molecular solids is discussed in relation to the emphasis placed on transverse vibrational modes in glasses as the origin of the observed boson peak in two very recent contributions in Nature Materials. In particular, facts are here presented for (i) CH 4, (ii) C 60 and (iii) ethanol in their solid phases for (a) specific heat and (b) neutron scattering. The results for ethanol in particular do not fit in with the interpretation of the boson peak in terms of transverse acoustic phonons in disordered systems. Glasses will therefore have to be separated into at least two classes where the physical interpretation of the boson peak is concerned.

Vibrational instability, two-level systems, and the boson peak in glasses

We show that the same physical mechanism is fundamental for two seemingly different phenomena such as the formation of two-level systems in glasses and the Boson peak in the reduced density of low-frequency vibrational states g(w)/w^2. This mechanism is the vibrational instability of weakly interacting harmonic modes. Below some frequency w_c << w_0 (where w_0 is of the order of Debye frequency) the instability, controlled by the anharmonicity, creates a new stable universal spectrum of harmonic vibrations with a Boson peak feature as well as double-well potentials with a wide distribution of barrier heights. Both are determined by the strength of the interaction I ~ w_c between the oscillators. Our theory predicts in a natural way a small value for the important dimensionless parameter C ~ 10^{-4} for two-level systems in glasses. We show that C ~ I^{-3} and decreases with increasing of the interaction strength I. We show that the number of active two-level systems is very small, less than one per ten million of oscillators, in a good agreement with experiment. Within the unified approach developed in the present paper the density of the tunneling states and the density of vibrational states at the Boson peak frequency are interrelated.

On the role of atomic motion soft modes in acoustic phonon broadening below the boson peak in glasses

Abstract This Letter presents a mechanism of acoustic phonon broadening for frequencies lower than the boson peak frequency in glasses exhibiting a high-frequency sound above the boson peak. The mechanism is based on a resonant interaction of an acoustic phonon with harmonic vibrational excitations of soft modes in such glasses. The related width of the phonon is found to be independent of temperature and characterized by a power-law frequency dependence ν ϰ , with the exponent ϰ varying from ϰ ≈ 2 below the boson peak to ϰ ≈ 4 at lower frequencies. The dependencies do not appear to contradict some recent experimental data, for the glasses under discussion.

Origin of boson peak in glasses: Role of Ioffe–Regel crossover and atomic soft modes

A theoretical ‘ complete soft-mode-dynamics’ model of the origin and properties of the boson peak accompanied by a high-frequency sound, observed in glasses of a certain type, is described. The origin is determined by interaction of non-acoustic vibrations with acoustic phonons and a Ioffe–Regel crossover for their inelastic scattering. The non-acoustic excitations are associated with vibrations of atomic soft-mode ‘defects’. Two types of boson peak can be predicted in agreement with experiments.

Origin of boson peak in glasses: Role of atomic soft-mode excitations

In the present article, glasses are considered, for which THz frequency vibrational anomalies include both an experimentally observed boson peak and, above it, a ``high-frequency'' sound with well-defined acousticlike excitations. The phenomena are strongly related to an Ioffe-Regel crossover from a weak inelastic scattering of interacting acoustic and soft-mode (nonacoustic) vibrational excitations to a strong scattering and to an associated hybridization of both types of excitations. A theoretical soft-mode-dynamics model of the anomalies, actually containing a single material parameter, is presented, which is complete in the sense that it takes into account both the Ioffe-Regel crossover and a recently found ``vibrational instability'' effect due to elastic interactions between soft-mode vibrations. The basic vibrational density of states and the reduced density of states are calculated. The results appear to show that the qualitative features and scale estimations of the experimentally studied inelastic scattering intensities in the glasses under discussion can be described by the present complete soft-mode-dynamics model. The latter is compared with other recent theoretical models of the boson peak in glasses.