Excess Density Of Vibrational States Research Articles

Excess Density of Vibrational States at Terahertz Frequencies in the IR Spectra of Glassy Polymers

The IR spectra of glassy polymers were studied in the terahertz range 0.27 − 6 THz (9–200 cm−1), where absorption appears due to both individual and collective torsional (libration) vibrations preceding the manifestation of relaxation dynamics. It is shown that collective torsional-vibrational modes, caused by the correlation of librational vibrations in a section of the chain commensurate with its thermodynamic segment, are responsible for the excess density of vibrational states at terahertz frequencies in the IR spectra of glassy polymers.

Universal features of the manifestation of the relationship between local and segmental dynamics of polymers at terahertz frequencies in IR spectra

Low-frequency IR- spectra of glassy polymers were obtained and analyzed at temperatures from 90 to 400 K. Temperature changes in the IR- spectra in the range from 10 to 140 cm-1 show three universal features: low-temperature, corresponding to the torsional-vibrational motion of monomer units, high-temperature, due to the influence of primary relaxation (glass transition) and intermediate, caused by the activation of conformational mobility in chains at a temperature of β-transition. This versatility extends both to polymers with universal chain-to-chain interactions and to those with hydrogen bonds. Keywords: IR spectra, excess density of vibrational states, bosonic peak, molecular dynamics, α- and β-relaxations.

Random Matrix Theory and the Boson Peak in Two-Dimensional Systems

The random matrix theory is used to describe the vibrational properties of two-dimensional disordered systems with a large number of degrees of freedom. It is shown that the correlated Wishart ensemble allows one to take into account the most significant mechanical properties of amorphous solids. In this ensemble, an excess density of vibrational states in comparison with the Debye law is observed, which is expressed in a peak in the reduced density of states g(ω)/ω. It is known as the boson peak, observed in many experiments and numerical calculations concerning two-dimensional and three-dimensional disordered systems. It is shown that the asymptotic behavior of the boson peak in two-dimensional systems has a number of features.

Применение теории случайных матриц для описания бозонного пика в двумерных системах

The random matrix theory is applied to describe the vibrational properties of two-dimensional disordered systems with a large number of degrees of freedom. It is shown that the most significant mechanical properties of amorphous solids can be taken into account using the correlated Wishart ensemble. In this ensemble, an excess vibrational density of states over the Debye law is observed as a peak in the reduced density of states g(ω)/ω. Such a peak is known as the boson peak, which was observed in many experiments and numerical simulations for two-dimensional and three-dimensional disordered systems. It is shown that two-dimensional systems have a number of differences in the asymptotic behavior of the boson peak.

Two-stage rejuvenation and the correlation between rejuvenation behavior and the boson heat capacity peak of a bulk metallic glass

The influence of severe plastic deformation on the rejuvenation behavior and the boson heat capacity peak of a Pd40Ni40P20 metallic glass is investigated for as-cast and pre-annealed states. Deformation by high-pressure torsion leads to a two-stage rejuvenation behavior, quantified by the structural enthalpy and fictive temperature, in coincidence with a strongly enhanced excess heat capacity at low temperatures, quantified by the boson peak height. Correlations between structural enthalpy, fictive temperature and the boson peak height were analyzed. The results show that the boson peak is not only related to the structural enthalpy but associated with the so-called “overshoot” of the glass transition. A universal link is established between the fictive temperature and the boson peak height, even under the joint influence of deformation and heat treatment. The significance of this link is that it sheds light on the structural connection between high-temperature relaxation and low-temperature excess vibrational density of states.

Intermittent Rejuvenation and the Correlation between Rejuvenation Behavior and the Boson Heat Capacity Peak of a Bulk Metallic Glass

The influence of severe plastic deformation on the rejuvenation behavior and the boson heat capacity peak of a Pd40Ni40P20 metallic glass is investigated for as-cast and pre-annealed states. Deformation by high-pressure torsion leads to an intermittent rejuvenation behavior, quantified by the structural enthalpy and fictive temperature, in coincidence with a strongly enhanced excess heat capacity at low temperatures, quantified by the boson peak height. Correlations between structural enthalpy, fictive temperature and the boson peak height were analyzed. The results show that the boson peak is not only related to the structural enthalpy but associated with the so-called overshoot of the glass transition. A universal link is established between the fictive temperature and the boson peak height, even under the joint influence of deformation and heat treatment. The significance of this link is that it sheds light on the structural connection between high-temperature relaxation and low-temperature excess vibrational density of states.

Low-temperature excess heat capacity and boson peak of mixed alkali effect in borate glass

When two dissimilar kinds of alkaline ions are used to co-doping oxide glass, a maximum in the electric resistivity or the expansion coefficient appears, that is called the mixed alkali effect. The heat capacity Cp of several rapidly-quenched mixed alkali borate glass was measured using a relaxation calorimeter to investigate the mixed alkali effect. A broad peak of Cp/T3 was observed with the maximum Tmax in the range 5–15 K, which is related to the excess vibrational density of states (VDoS) of a non-Debye nature. Such a peak is called the boson peak and it is also observed as the low-energy peak of inelastic neutron and light scattering experiments. The negative deviation from the linear relation of single alkali borate glasses between the alkali cation size and Tmax was clearly observed in a mixed lithium cesium borate glass. The mechanism of this deviation was discussed on the basis of the changes in the BO4 units and the nonbridging oxygens by co-doping. The universal nature of the master plot of Cp/T3 also shows the deviation from that of pure borate glass by the mixed alkali effect.

Low-temperature dynamics of (S)-4-(1-methylheptyloxy)-4ʹ-cyanobiphenyl (8*OCB) and (S)-4-(2-methylbutyl)-4ʹ-cyanobiphenyl (5*CB) in disordered crystalline and glassy phases

ABSTRACTThe inelastic neutron scattering (INS) spectra were measured for two materials of chiral molecules: (S)-4-(1-methylheptyloxy)-4ʹ-cyanobiphenyl (8*OCB) and (S)-4-(2-methylbutyl)-4ʹ-cyanobiphenyl (5*CB), revealing solid state polymorphism with two partially disordered crystalline phases I and II and glassy state of liquid and of crystalline phase in each substance. The experiments were performed in the energy range up to 30 µeV in the temperature range from 4 to 35 K. For 8*OCB the elastic scans were measured as well up to 300 K illustrating well the phase diagram. For all solid phases of both substances in the µeV range of INS spectra, the existence of the excess density of vibrational states over that typical for fully ordered crystalline phases was evidenced. Contribution of this so-called boson peak occurred to be much larger in glass of isotropic phase than in the phase II and glass of phase I of 8*OCB, while for 5*CB it was larger in the phase I and glass of phase II than in glass of cholesteric phase. The quasi-elastic broadening of elastic peak corresponding to stochastic reorientations in the ns time scale was detected for both substances. Comparison of the results obtained for glassy and crystalline phases of 8*OCB and 5*CB compounds have been given and confronted with those obtained previously in meV energy range.

Does the Boson Peaks Exist in Small Neutral Gold Clusters?

The Boson peaks are typically ascribed to an excess density of vibrational states for the small clusters. A well resolved boson peak is observed in the low-frequency portion of the spectrum. A starting point for our discussion is the behaviour of the boson peak, derived from the vibrational density of states and the temperature dependencies of the vibrational heat capacities of the re-optimized neutral gold clusters. This Boson peak is associated with the existence of intermediate range order (IRO) in the arrangements of atoms. The low frequency (Far Infrared FIR, IR-C 200-10 cm−1) containing this dominant spectral line (Boson peak) is interpreted in terms of its relationship to the amplitude and extent of the density fluctuations in atoms and is, thereby, considered a measure of the intermediate range order in these atoms. We found a systematic relation among the boson peak energy, the boson peak intensity per atom, and the zigzag-bond density; the peak energy decreases and the peak intensity increases as zigzag-bond density decreases.

Effect of Size, Temperature, and Structure on the Vibrational Heat Capacity of Small Neutral Gold Clusters

The vibrational heat capacity Cvib of a re-optimized neutral gold cluster was investigated at temperatures 0.5-300 K. The vibrational frequency of an optimized cluster was revealed by small atomic displacements using a numerical finite-differentiation method. This method was implemented using density-functional tight-binding (DFTB) approach. The desired set of system Eigen frequencies (3N -6) was obtained by diagonalization of the symmetric positive semi definite Hessian matrix. Our investigation revealed that the Cvib curve is strongly influenced by temperature, size, and structure and bond-order dependency. The effect of the range of interatomic forces is studied; especially the lower frequencies make a significant contribution to the heat capacity at low temperatures. In addition to that, we have exactly predicted the vibrational frequencies (ωi) which occur between 0.55 to 370.72 cm-1, depending on the nanoparticle morphology at T=0 for small neutral gold clusters AuN=3-20. This result has been proved and confirmed by the size effect values. It was found that beside the particle size, geometric shape, defect structure and an increase in asymmetry of nanoparticles effects on heat capacity. Surprisingly, the Boson peaks are typically ascribed to an excess density of vibrational states for the small clusters. Finally, temperature dependencies of the vibrational heat capacities of the re-optimized neutral gold clusters have been studied for the first time.

Phonon dispersion relation of metallic glasses

Experimental data on the phase sound speed of metallic glasses show anomalies in the terahertz range, reflecting an underlying complex behavior of their phonon dispersion spectrum not yet explained. We determine the phonon dispersion curve of metallic glasses by means of massive molecular dynamics simulations, allowing us to obtain the $\text{low-}q$ region behavior with unprecedented detail. Results confirm that the sound speed is constant below the THz range, down to the macroscopic limit. On the contrary, a hardening of the sound speed, more notable in the transverse case, is found in the THz range. This behavior is modeled in terms of a relaxation model. The model gives quantitative agreement and allows us to determine a new threshold frequency ${\ensuremath{\omega}}_{h}$, at the end of the boson-peak region. Above ${\ensuremath{\omega}}_{h}$ the shear modulus increases dramatically, reflecting the end of the amorphous-like acoustic propagation region characterized by the excess density of vibrational states.

Vibrational Heat Capacity of Gold Cluster AuN=14 at Low Temperatures

The vibrational heat capacity Cvib of a re-optimized neutral gold cluster AuN=14 was investigated at temperatures 0.5-300/950 K. The vibrational frequency of a optimized cluster was revealed by small atomic displacements using a numerical finite-differentiation method. This method was implemented using density-functional tight-binding (DFTB) approach. The desired set of system eigenfrequencies (3N-6) was obtained by diagonalization of the symmetric positive semidefinite Hessian matrix. Our investigation revealed that the Cvib curve is strongly influenced by temperature, size and structure dependency. The effect of the range of interatomic forces is studied, especially the lower frequencies make a significant contribution to the heat capacity at low temperatures. Surprisingly, the Boson peaks are typically ascribed to an excess density of vibrational states for the small clusters. Finally, temperature dependencies of the vibrational heat capacities of the re-optimized neutral gold cluster have been studied for the first time.

Excess vibrational density of states and the brittle to ductile transition in crystalline and amorphous solids.

The conditions which determine whether a material behaves in a brittle or ductile fashion on mechanical loading are still elusive and comprise a topic of active research among materials physicists and engineers. In this study, we present the results of in silico mechanical deformation experiments from two very different model solids in two and three dimensions. The first consists of particles interacting with isotropic potentials and the other has strongly direction dependent interactions. We show that in both cases, the excess vibrational density of states is one of the fundamental quantities which characterizes the ductility of the material. Our results can be checked using careful experiments on colloidal solids.

Low-temperature excess heat capacity in fresnoite glass and crystal.

The effect of thermal annealing on low-temperature excess heat capacity was investigated in fresnoite (Ba2TiSi2O8) glass. The amplitudes of the excess heat capacity decreased, and their positions shifted to a higher temperature by relaxation or crystallization. In particular, we revealed that the change in the excess heat capacity during transition from the glassy state to the crystalline state is relatively small compared with that of other oxides. Therefore, it is suggested that distribution of the excess vibrational density of states of the glass is similar to that of the corresponding crystal.

Elastic anomalies at terahertz frequencies and excess density of vibrational states in silica glass

We study the temperature dependence of acousticlike excitations measured by means of inelastic x-ray scattering at terahertz frequencies in silica glass. The apparent sound velocity shows, between 300 and 1600 K, the same temperature variation measured, at lower frequencies, by Brillouin light scattering. On the contrary the vibrations at the boson peak (BP) present a much stronger temperature dependence, as indicated by neutron scattering data. The measured dispersion and damping are used to compute the contribution to the vibrational density of states (VDOS) coming from the propagating acousticlike modes. This part of the VDOS accounts only for a fraction of the BP intensity, indicating that other kinds of excitation accumulate in this frequency range. It is consequently not surprising that the BP does not follow the temperature evolution of the Debye frequency, which describes the modification of the continuum medium. Finally we present a comparison between the experimentally accessible quantities and a recently proposed model for the vibrations in glasses, based on the assumption of random spatial variations of the shear modulus [Schirmacher, Europhys. Lett. 73, 892 (2006)].

Non-Debye excess heat capacity and boson peak of binary lithium borate glasses

The non-Debye excess heat capacities of binary lithium borate glasses with different Li 2O compositions of x = 8, 14 and 22 (mol%) are investigated to understand origin of the boson peak. The low-temperature heat capacities are measured between 2 and 50 K by a relaxation calorimeter. The experimental non-Debye heat capacities with x = 14 is successfully reproduced using the excess vibrational density of states measured by inelastic neutron scattering. This finding indicates that the non-Debye heat capacities of lithium borate glasses originate from the excess vibrational density of states measureable by inelastic neutron scattering. Moreover, it is demonstrated that all of the excess heat capacity spectra lie on a single master curve by the scaling using boson peak temperature and intensity.

Universal link between the boson peak and transverse phonons in glass

The physical properties of a topologically disordered amorphous material (glass), such as heat capacity and thermal conductivity, are markedly different from those of its ordered crystalline counterpart. The understanding of these phenomena is a notoriously complex problem. One of the universal features of disordered glasses is the 'boson peak', which is observed in neutron and Raman scattering experiments. The boson peak is typically ascribed to an excess density of vibrational states. Here, we study the nature of the boson peak, using numerical simulations of several glass-forming systems. We discovered evidence suggestive of the equality of the boson peak frequency to the Ioffe-Regel limit for 'transverse' phonons, above which transverse phonons no longer propagate. Our results indicate a possibility that the origin of the boson peak is transverse vibrational modes associated with defective soft structures in the disordered state. Furthermore, we suggest a possible link between slow structural relaxation and fast boson peak dynamics in glass-forming systems.

A low-frequency Raman study of glassy, supercooled and molten silica and the preservation of the Boson peak in the equilibrium liquid state

A temperature dependent Raman spectroscopic study of the Boson peak in silica is being presented. For the first time experimental data are obtained not only above the glass transition temperature but also above the melting point. The intriguing temperature dependencies exhibited by the Boson peak frequency and intensity are examined in detail. A comparison of the above features between the frequency-reduced and the true excess density of vibrational states revealed that the spectrum of the latter does not exhibit the anomalous trend of the Boson peak as regards the temperature dependence of its frequency, and further the number of the excess modes decreases with increasing temperature. The observability of the Boson peak in the normal liquid state as a well-resolved peak is also discussed in the context of recent theoretical and simulation works that relate the Boson peak with the details of the potential energy landscape of the supercooled liquid.

Vibrational dynamics of a glass forming liquid in nanoscopic confinement as probed by inelastic neutron scattering

In this article we present incoherent inelastic neutron scattering results, as a function of temperature, on the vibrational dynamics of a glass-forming liquid, namely propylene glycol, confined to the ∼26 Å pores of a controlled porous glass. The aim is to elucidate the effects induced by surface interactions ( chemical traps) and geometrical restrictions ( physical traps) on the fast microscopic dynamics of hydrogen-bonded liquids. The most prominent effect is the appearance of the ‘boson peak’ in the vibrational spectra. It is ascribed to an excess density of vibrational states due to quasilocalized collective atomic vibrations induced by confinement. A destructuring effect on the transient aggregates with the highest degree of connectivity, promoted by PG in the bulk phase, is hypothesized under confinement as a consequence of interactions, via hydrogen bond, between the hydroxyl groups (OH) of the PG molecule and the active silanol groups (Si–OH) on the surface of the porous glass. Interfacial and/or finite-size effects are also found to give rise to a destructuring effect, under confinement, of the disordered Longitudinal Acoustic Mode, together with a broadening of the highest frequency torsional vibration and a stabilization, vs. T, of the internal CCO bending vibration.

Low-temperature specific heats of porous silica xerogels of low densities

Low-temperature specific heat measurements have been performed in porous silica xerogels with densities varying from 670 to 1730 kg m −3 to study the low-energy vibrational dynamics. The specific heat, C p, shows a bump in the temperature range above 4 K, when reported in a plot of C p/ T 3 against the temperature, T. The bump is almost independent of the sample density and is close to the boson peak observed in melt-quenched amorphous silica (a-SiO 2). At temperatures <4 K, an additional contribution to that predicted by the Debye theory is observed. It follows an approximately linear temperature dependence ( C exc= aT 1+ v , v being equal to about 0.25). In the xerogel with the largest density, specific heat of about a factor 5 larger than that of a-SiO 2 is measured, which increases with decreasing sample density. By comparison with the corresponding properties of a-SiO 2, we conclude that the disorder introduced by the presence of pores does not measurably affect the excess density of vibrational states in a frequency range of the boson peak (BP), but increases the density of the two-level systems (TLS).