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D Fioretto - One of the best experts on this subject based on the ideXlab platform.
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stress induced modification of the Boson Peak scaling behavior
Journal of Physical Chemistry B, 2013Co-Authors: S Corezzi, S Caponi, F Rossi, D FiorettoAbstract:The scaling behavior of the so-called Boson Peak in glass-formers and its relation to the elastic properties of the system remains a source of controversy. Here the Boson Peak in a binary reactive mixture is measured by Raman scattering (i) on cooling the unreacted mixture well below its glass-transition temperature and (ii) after quenching to very low temperature the mixture at different times during isothermal polymerization. We find that the scaling behavior of the Boson Peak with the properties of the elastic medium — as measured by the Debye frequency — holds for states in which the elastic moduli follow a generalized Cauchy-like relationship, and breaks down in coincidence with the departure from this relation. A possible explanation is given in terms of the development of long-range stresses in glasses. The present study provides new insight into the Boson Peak behavior and is able to reconcile the apparently conflicting results presented in literature.
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stress induced modification of the Boson Peak scaling behavior
arXiv: Soft Condensed Matter, 2013Co-Authors: S Corezzi, S Caponi, F Rossi, D FiorettoAbstract:The scaling behavior of the so-called Boson Peak in glass-formers and its relation to the elastic properties of the system remains a source of controversy. Here, the Boson Peak in a binary reactive mixture is measured by Raman scattering (i) on cooling the unreacted mixture well below its glass transition temperature and (ii) after quenching to very low temperature the mixture at different times during isothermal polymerization. These different paths to the glassy phase are able to generate glasses with different amounts of residual stresses, as evidenced by the departure of the elastic moduli from a Cauchy-like relationship. We find that the scaling behavior of the Boson Peak with the properties of the elastic medium --- as measured by the Debye frequency --- holds for states in which the system is able to release internal stress and breaks down in the presence of residual stresses. These findings provide new insight into the Boson Peak behavior and are able to reconcile the apparently conflicting results presented in literature.
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equivalence of the Boson Peak in glasses to the transverse acoustic van hove singularity in crystals
Physical Review Letters, 2011Co-Authors: A I Chumakov, R Ruffer, G Monaco, A Monaco, Wilson A Crichton, Alexey Bosak, A Meyer, F Kargl, L Comez, D FiorettoAbstract: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.
Alain Pasturel - One of the best experts on this subject based on the ideXlab platform.
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structural and dynamic origin of the Boson Peak in a cu zr metallic glass
Physical Review B, 2012Co-Authors: Noel Jakse, Abdallah Nassour, Alain PasturelAbstract:Using molecular dynamics simulations, we studied the short-time dynamics of the amorphous Cu50Zr50 alloy. We determined the occurrence of a well-defined Boson Peak in agreement with experimental observations. Our results indicate that the structural origin of the Boson Peak can be related to Cu and Zr atoms having large mean-square amplitudes in low-density defective local structures. Moreover, we show that these structural motifs display quasilocalized modes that resonantly couple with transverse phonons, leading to the accumulation of the low-energy modes around the Boson Peak. Finally, the correlation between the attenuation of sound and the Boson Peak is discussed.
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Structural and dynamic origin of the Boson Peak in a Cu-Zr metallic glass
Physical Review B, 2012Co-Authors: Noel Jakse, Abdallah Nassour, Alain PasturelAbstract:Using molecular dynamics simulations, we studied the short-time dynamics of the amorphous Cu 50Zr 50 alloy. We determined the occurrence of a well-defined Boson Peak in agreement with experimental observations. Our results indicate that the structural origin of the Boson Peak can be related to Cu and Zr atoms having large mean-square amplitudes in low-density defective local structures. Moreover, we show that these structural motifs display quasilocalized modes that resonantly couple with transverse phonons, leading to the accumulation of the low-energy modes around the Boson Peak. Finally, the correlation between the attenuation of sound and the Boson Peak is discussed. © 2012 American Physical Society.
D. A. Parshin - One of the best experts on this subject based on the ideXlab platform.
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Application of the random matrix theory to the Boson Peak in glasses.
arXiv: Disordered Systems and Neural Networks, 2019Co-Authors: D. A. Conyuh, Y. M. Beltukov, D. A. ParshinAbstract:The density of vibrational states $g(\omega)$ 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 $g(\omega)$ are obtained. The analysis of these equations shows that in the low-frequency region the vibrational density of states has the Debye behavior $g(\omega) \sim \omega^2$. 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.
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Boson Peak in various random-matrix models
JETP Letters, 2016Co-Authors: Y. M. Beltukov, D. A. ParshinAbstract:A so-called Boson Peak in the reduced density g (ω)ω^2 of vibrational states is one of the most universal properties of amorphous solids (glasses). It quantifies the excess density of states above the Debye value at low frequencies ω. Its nature is not fully understood and, at a first sight, is nonuniversal. It is shown in this work that, under rather general assumptions, the Boson Peak emerges in a natural way in very dissimilar models of stable random dynamic matrices possessing translational symmetry. This Peak can be shifted toward both higher and lower frequencies (down to zero frequency) by varying the parameters of the distribution and the degree of disorder in the system. The frequency ω_b of the Boson Peak appears to be proportional to the elastic modulus E of the system in all cases under investigation.
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vibrational instability two level systems and the Boson Peak in glasses
Physical Review B, 2007Co-Authors: D. A. Parshin, H R Schober, V L GurevichAbstract: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 $g(\ensuremath{\omega})∕{\ensuremath{\omega}}^{2}$. This mechanism is the vibrational instability of weakly interacting harmonic modes. Below some frequency ${\ensuremath{\omega}}_{c}⪡{\ensuremath{\omega}}_{0}$ (where ${\ensuremath{\omega}}_{0}$ 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 $I\ensuremath{\propto}{\ensuremath{\omega}}_{c}$ between the oscillators. Our theory predicts in a natural way a small value for the important dimensionless parameter $C=\overline{P}{\ensuremath{\gamma}}^{2}∕\ensuremath{\rho}{v}^{2}\ensuremath{\approx}{10}^{\ensuremath{-}4}$ for two-level systems in glasses. We show that $C\ensuremath{\approx}{(W∕\ensuremath{\hbar}{\ensuremath{\omega}}_{c})}^{3}\ensuremath{\propto}{I}^{\ensuremath{-}3}$ and decreases with increasing interaction strength $I$. The energy $W$ is an important characteristic energy in glasses and is of the order of a few Kelvin. This formula relates the two-level system's parameter $C$ with the width of the vibration instability region ${\ensuremath{\omega}}_{c}$, which is typically larger or of the order of the Boson Peak frequency ${\ensuremath{\omega}}_{b}$. Since $\ensuremath{\hbar}{\ensuremath{\omega}}_{c}\ensuremath{\gtrsim}\ensuremath{\hbar}{\ensuremath{\omega}}_{b}⪢W$, the typical value of $C$ and, therefore, the number of active two-level systems is very small, less than 1 per $1\ifmmode\times\else\texttimes\fi{}{10}^{7}$ of oscillators, in 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.
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pressure dependence of the Boson Peak in glasses
Physical Review B, 2005Co-Authors: V L Gurevich, D. A. Parshin, H R SchoberAbstract:The inelastic scattering intensities of glasses and amorphous materials has a maximum at a low frequency, the so called Boson Peak. Under applied hydrostatic pressure, $P$, the Boson Peak frequency, $\omega_{\rm b}$, is shifted upwards. We have shown previously that the Boson Peak is created as a result of a vibrational instability due to the interaction of harmonic quasi localized vibrations (QLV). Applying pressure one exerts forces on the QLV. These shift the low frequency part of the excess spectrum to higher frequencies. For low pressures we find a shift of the Boson Peak linear in $P$, whereas for high pressures the shift is $\propto P^{1/3}$. Our analytics is supported by simulation. The results are in agreement with the existing experiments.
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Quasilocal vibrations and the Boson Peak in glasses
Physica Status Solidi (c), 2004Co-Authors: D. A. ParshinAbstract:The problem of the low-frequency harmonic excitations and of the Boson Peak in glasses is reviewed in the scope of recent theoretical developments. It is shown that the Boson Peak inevitably appears in the reduced density of states g(ω)/ω2 of quasilocal vibrations in glasses which are additional to phonons harmonic excitations. We show that the same physical mechanism is fundamental for such seemingly different phenomenon as formation of the two-level systems in glasses. The fundamental reason for the Boson Peak and two-level system formation is an instability of the spectrum of quasilocal harmonic modes weakly interacting with the high frequency surrounding and with each other. The instability controlled by the anharmonicity creates a new stable universal spectrum of harmonic vibrations with a Boson Peak feature. We show that under pressure the Boson Peak in glasses is always shifted to higher frequencies. For high enough pressures P the Boson Peak frequency ωb ∝ P1/3. (© 2004 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)
H R Schober - One of the best experts on this subject based on the ideXlab platform.
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pressure dependence of the Boson Peak in glasses correlated and uncorrelated perturbations
Physical Review B, 2014Co-Authors: H R Schober, U. Buchenau, V L GurevichAbstract: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.
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vibrational instability two level systems and the Boson Peak in glasses
Physical Review B, 2007Co-Authors: D. A. Parshin, H R Schober, V L GurevichAbstract: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 $g(\ensuremath{\omega})∕{\ensuremath{\omega}}^{2}$. This mechanism is the vibrational instability of weakly interacting harmonic modes. Below some frequency ${\ensuremath{\omega}}_{c}⪡{\ensuremath{\omega}}_{0}$ (where ${\ensuremath{\omega}}_{0}$ 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 $I\ensuremath{\propto}{\ensuremath{\omega}}_{c}$ between the oscillators. Our theory predicts in a natural way a small value for the important dimensionless parameter $C=\overline{P}{\ensuremath{\gamma}}^{2}∕\ensuremath{\rho}{v}^{2}\ensuremath{\approx}{10}^{\ensuremath{-}4}$ for two-level systems in glasses. We show that $C\ensuremath{\approx}{(W∕\ensuremath{\hbar}{\ensuremath{\omega}}_{c})}^{3}\ensuremath{\propto}{I}^{\ensuremath{-}3}$ and decreases with increasing interaction strength $I$. The energy $W$ is an important characteristic energy in glasses and is of the order of a few Kelvin. This formula relates the two-level system's parameter $C$ with the width of the vibration instability region ${\ensuremath{\omega}}_{c}$, which is typically larger or of the order of the Boson Peak frequency ${\ensuremath{\omega}}_{b}$. Since $\ensuremath{\hbar}{\ensuremath{\omega}}_{c}\ensuremath{\gtrsim}\ensuremath{\hbar}{\ensuremath{\omega}}_{b}⪢W$, the typical value of $C$ and, therefore, the number of active two-level systems is very small, less than 1 per $1\ifmmode\times\else\texttimes\fi{}{10}^{7}$ of oscillators, in 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.
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pressure dependence of the Boson Peak in glasses
Physical Review B, 2005Co-Authors: V L Gurevich, D. A. Parshin, H R SchoberAbstract:The inelastic scattering intensities of glasses and amorphous materials has a maximum at a low frequency, the so called Boson Peak. Under applied hydrostatic pressure, $P$, the Boson Peak frequency, $\omega_{\rm b}$, is shifted upwards. We have shown previously that the Boson Peak is created as a result of a vibrational instability due to the interaction of harmonic quasi localized vibrations (QLV). Applying pressure one exerts forces on the QLV. These shift the low frequency part of the excess spectrum to higher frequencies. For low pressures we find a shift of the Boson Peak linear in $P$, whereas for high pressures the shift is $\propto P^{1/3}$. Our analytics is supported by simulation. The results are in agreement with the existing experiments.
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vibrations and relaxations in a soft sphere glass Boson Peak and structure factors
Journal of Physics: Condensed Matter, 2004Co-Authors: H R SchoberAbstract:The dynamics of a soft sphere model glass, studied by molecular dynamics, is investigated. The vibrational density of states divided by ω2 shows a pronounced Boson Peak. Its shape is in agreement with the universal form derived for soft oscillators interacting with sound waves. The excess vibrations forming the Boson Peak have mainly transverse character. From the dynamic structure factor in the Brillouin regime pseudo dispersion curves are calculated. Whereas the longitudinal phonons are well defined up to the pseudo zone boundary the transverse ones rapidly get over-damped and go through the Ioffe–Regel limit near the Boson Peak frequency. In the high q regime constant-ω scans of the dynamic structure factor for frequencies around the Boson Peak are clearly distinct from those for zone boundary frequencies. Above the Brillouin regime, the scans for the low frequency modes follow closely the static structure factor. This still holds after a deconvolution of the exact harmonic eigenmodes into local and extended modes. Also the structure factor for local relaxations at finite temperatures resembles the static one. This semblance between the structure factors mirrors the collective motion of chain-like structures in both low frequency vibrations and atomic hopping processes, observed in the earlier investigations.
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anharmonicity vibrational instability and the Boson Peak in glasses
Physical Review B, 2003Co-Authors: V L Gurevich, D. A. Parshin, H R SchoberAbstract:We show that a vibrational instability of the spectrum of weakly interacting quasilocal harmonic modes creates the maximum in the inelastic scattering intensity in glasses, the Boson Peak. The instability, limited by anharmonicity, causes a complete reconstruction of the vibrational density of states (DOS) below some frequency ${\ensuremath{\omega}}_{c},$ proportional to the strength of interaction. The DOS of the new harmonic modes is independent of the actual value of the anharmonicity. It is a universal function of frequency depending on a single parameter \char22{} the Boson Peak frequency ${\ensuremath{\omega}}_{b}$ which is a function of interaction strength. The excess of the DOS over the Debye value is $\ensuremath{\propto}{\ensuremath{\omega}}^{4}$ at low frequencies and linear in $\ensuremath{\omega}$ in the interval ${\ensuremath{\omega}}_{b}\ensuremath{\ll}\ensuremath{\omega}\ensuremath{\ll}{\ensuremath{\omega}}_{c}.$ Our results are in an excellent agreement with recent experimental studies.
W Schirmacher - One of the best experts on this subject based on the ideXlab platform.
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the Boson Peak
Physica Status Solidi B-basic Solid State Physics, 2013Co-Authors: W SchirmacherAbstract:The vibrational properties of glasses in the THz range differ very much from what is expected from Debye's elasticity theory: the density of states (DOS) deviates from Debye's ω2 law [the “Boson Peak” (BP)], the sound velocity shows a negative dispersion in the BP frequency regime and there is a strong increase in the sound attenuation near the BP frequency. These anomalies are related to an anomalous temperature dependence of the specific heat and thermal conductivity in the 10 K regime. An overview of the heterogeneous-elasticity theory is given, by means of which all these anomalies can be explained and shown to arise from the structural disorder, leading to spatial fluctuations of the shear modulus. Further, a very general model-independent explanation of the BP-related anomalies, based solely on symmetry arguments, is given.
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heterogeneous shear elasticity of glasses the origin of the Boson Peak
Scientific Reports, 2013Co-Authors: Alessia Marruzzo, W Schirmacher, Andrea Fratalocchi, G RuoccoAbstract:The local elasticity of glasses is known to be inhomogeneous on a microscopic scale compared to that of crystalline materials. Their vibrational spectrum strongly deviates from that expected from Debye's elasticity theory: The density of states deviates from Debye's law, the sound velocity shows a negative dispersion in the Boson-Peak frequency regime and there is a strong increase of the sound attenuation near the Boson-Peak frequency. By comparing a mean-field theory of shear-elastic heterogeneity with a large-scale simulation of a soft-sphere glass we demonstrate that the observed anomalies in glasses are caused by elastic heterogeneity. By observing that the macroscopic bulk modulus is frequency independent we show that the Boson-Peak-related vibrational anomalies are predominantly due to the spatially fluctuating microscopic shear stresses. It is demonstrated that the Boson-Peak arises from the steep increase of the sound attenuation at a frequency which marks the transition from wave-like excitations to disorder-dominated ones.
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thermal conductivity of glassy materials and the Boson Peak
EPL, 2006Co-Authors: W SchirmacherAbstract:A theory for the anomalous vibrational and thermal properties of disordered solids based on the model assumption of randomly fluctuating transverse elastic constants is presented. Mean-field expressions for the vibrational density of states and the energy diffusivity are derived with field-theoretical techniques. As in previous approaches of this type the Boson Peak (enhancement of the low-frequency density of states) is explained as a result of the frozen-in disorder and compares well with the experimental findings. The plateau in the temperature variation of the thermal conductivity and the behavior beyond the plateau is shown to arise from the enhanced scattering in the Boson Peak regime and to be essentially a harmonic phenomenon.
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collective nature of the Boson Peak and universal transBoson dynamics of glasses
Physical Review Letters, 2004Co-Authors: A I Chumakov, W Schirmacher, I Sergueev, U Van Burck, T Asthalter, R Ruffer, O Leupold, W PetryAbstract:: Using probe molecules with resonant nuclei and nuclear inelastic scattering, we are able to measure the density of states exclusively for collective motions with a correlation length of more than approximately 20 A. Such spectra exhibit an excess of low-energy modes (Boson Peak). This Peak behaves in the same way as that observed by conventional methods. This shows that a significant part of the modes constituting the Boson Peak is of collective character. At energies above the Boson Peak, the reduced density of states of the collective motions universally exhibits an exponential decrease.