Boson peak and its relation to acoustic attenuation in glasses

Experimental results on the density of states and on the acoustic modes of glasses in the THz region are compared to the predictions of two categories of models. A recent one, solely based on an elastic instability, does not account for most observations. Good agreement without adjustable parameters is obtained with models including the existence of nonacoustic vibrational modes at THz frequency, providing in many cases a comprehensive picture for a range of glass anomalies.     

Boson peak in Sm-Al-Co ternary metallic glasses and its possible structural origin

The low temperature specific heat of Sm-Al-Co ternary metallic glasses is investigated and a clear anomaly associated with the Boson peak is identified. While this anomaly depends slightly on the chemical composition, it has no dependence on external magnetic field. To figure out the mechanism of the Boson peak, we interpret the data within various model frameworks. Unlike earlier work, our study shows that this Boson peak is mainly ascribed to an additional T² term of the specific heat, which may originate from the quasi-two-dimensional and short-range ordered structure units possibly existing in the metallic glasses.     

Vibrational modes of sodium–tellurite glasses: Local structure and Boson peak changes

Raman spectra of xNa₂O−(1−x)TeO₂ glasses were measured and analyzed over a broad composition range. The network structure of the glass consists of a mixture of TeO₄ trigonal bipyramids and TeO₃ trigonal pyramidal units. Increase of alkali content results in conversion of the TeO₄ units into TeO₃ units with a varying number of non-bridging oxygen atoms. This local structure transformation becomes more evident at x=0.2, where rigidity percolation theory predicts a threshold for the rigid-to-floppy transition. However, other spectral features such as the composition dependence of the energy of the Boson peak do not support the occurrence of the stiffness transition. The controversial dependence of dynamical parameters such as the fragility index as a function of Na₂O concentration is also discussed.     

Boson peak in various random-matrix models

A so-called boson peak in the reduced density g(ω)ω² 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.     

二维胶体玻璃中玻色峰与结构无序度的关联

本文从实验上研究了胶体玻璃在相同面密度下随着体系结构无序程度的增加, 振动态密度和玻色峰的变化规律. 通过调制两种不同粒径的温敏性水凝胶的数量比来改变体系的无序程度. 通过分析无序体系的声子模式得到体系的振动特性. 研究发现, 随着无序度的增加, 态密度在低频区域增强、玻色峰增高、玻色峰的峰值向低频区域移动. 不同无序程度的样品引起玻色峰的低频声子模式都表现出准局域的特点, 且低频准局域声子模式与样品中无序结构存在关联.     

Boson peak measurements in neutron-irradiated quartz crystals

We have measured the low-frequency Raman scattering in neutron-irradiated quartz crystals with four different irradiation doses from 4.7×10¹⁹ n/cm² to 1×10²⁰ n/cm² and for 2 different crystallographic directions. For the used doses the range of density change of the investigated samples was 12% (the maximum change during amorphization is 14%) and the amorphous fraction varied from 35% to 100%. The same measurement was done in neutron-irradiated amorphous silica with a maximal dose 2×10²⁰ n/cm². In all cases we observed the boson peak in the Raman spectra. The position of the peak, at 67±3 cm^-1, was found to be the same for all the investigated samples independent of the dose. The shape of the peak for doses 6.8× 10¹⁹ n/cm² and higher was also found to be the same for 5 investigated samples (including irradiated vitreous silica). We found that the position of the boson peak in neutron-irradiated quartz crystals and vitreous silica corresponds to the Ioffe-Regel crossover frequency for phonons. The origin of the boson peak in neutron-irradiated quartz and vitreous silica can be attributed to local soft optic modes, which are analogous to the soft optic mode that drives the α–β transition in quartz.     

Boson expansions and Hartree-Bogoliubov theory

If the boson operators in boson expansions of the Hamiltonian are suitably replaced by c-numbers regarded as variational parameters, solutions of the Hartree-Bogoliubov or Hartree-Fock-Bogoliubov equations are obtained. The c-number replacement in the boson equations of motion yields solutions of the corresponding time-dependent self-consistent field equations.     

The Boson peak interpretation and evolution in confined amorphous water

We study the evolution of the Boson peak for water confined in cement paste obtained by means of Inelastic Neutron Scattering from room temperature to the deep supercooled regime. We analyze the data in terms of a universal-like model, developed for glass forming liquids in the frame of the energy landscape. In such a way it is possible to discriminate between the fragile and strong glass forming character of supercooled liquids and the dynamical crossover, fragile to strong, between them. Hence, we confirm the link between the Boson peak and the water polymorphism. In particular, the main result is represented by a crossover from a local energetic minima configuration to that characteristic of saddle points on going towards the deep supercooled regime up to the dynamical arrest.     

On the dynamic mean field theory of spin glasses

We derive in detail Sompolinsky's mean field theory of spin glasses using a diagram expansion of the effective local Langevin equation of Sompolinsky and Zippelius. We use a simpler generating functional than in the literature, on which the quenched average is very easily done. We pay special attention to the existence of an external field. We show that there are two different types of singularities for ω=0 in the equations. The first type, which leads to Parisi'sq(0), is connected with the local magnetisation. The second type, which leads toq′(x), is connected with the nonergodic behaviour. We show that the continuous limit of discrete Sompolinsky solutions has to be taken in order to be in accordance with the fluctuation dissipation theorem on infinite time scales. We discuss carefully the question of dynamical stability. We show that Sommers' solution is unstable only on an infinite time scale and thus remains an acceptable equilibrium theory with a broken symmetry. We argue that for ω=0 a formal violation of the fluctuation dissipation theorem is physically expected if the relaxation times are of the order of the switching time of the external field. From this point of view the spin-glass state is a steady state but not a real equilibrium state.     

Experimental evidence of the local character of vibrations constituting the Boson peak in amorphous solids

We report the first measurement of the density of states of low-energy vibrational excitations in a disordered solid via single-molecule (SM) spectroscopy. Optical spectra of many single tetra-tert-butylterrylene (TBT) molecules embedded to amorphous polyisobutylene (PIB) as spectral probes were recorded at low temperatures. The T dependences of SM spectral linewidths showed the broad distribution of local frequencies of vibrations under study. The obtained distribution was compared with the "Boson peak" in pure PIB measured in [R. Inoue, J. Chem. Phys. 95, 5332 (1991)] by neutron scattering. We found that embedding of a small amount of TBT into PIB does not influence markedly on the observed vibrational dynamics. These results prove the local character of low-energy vibrational excitations in glasses and the existence of relationship between these excitations and the Boson peak.     

On the theory of the central peak at structural phase transitions

A universal mechanism is proposed, which explains the appearance of the central peak by means of a transition from ergodic to nonergodic dynamical behaviour of the system at some temperatureT _g above the phase transition. A detailed investigation of the scalar lattice ⁴-model with defects is given. The relation between the nonergodic state and the appearance of precursor clusters and Raman scattering experiments is discussed.     

On the hydrodynamic theory of central peak in displacive structural phase transitions

A model involving nonlinear coupling between the overdamped phonon mode and temperature fluctuations is studied using the dynamic renormalization group method. It is shown that the behavior of the central peak in the dynamic form factor depends on the specific heat exponent α. For α < 0 and as T → T_c the central peak is found to merge with the over-damped phonon mode and the coupling goes to zero at T_c as (T ? T_c)^?α. An argument on the intensity of the central peak in the critical region in presented and it is concluded that the hydrodynamic coupling may not be the dominant mechanism of the central peak in SrTiO₃.     

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

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?${\nu }^{?}$, with the exponent ?   varying from ?≈2$?\approx 2$ below the boson peak to ?≈4$?\approx 4$ at lower frequencies. The dependencies do not appear to contradict some recent experimental data, for the glasses under discussion.     

Boson peak of AsxS1−x glasses and theoretical calculations of low frequencies clusters vibrations

The results of comparison of spectral position of the LF bands of g-As₂S₃ and g-As₂₂S₇₈ with theoretical calculations of vibrational spectra of different clusters (As₂S₄, As₂S₅, As₂S₆, AsS₃-As₃) in the LF region (10-85 cm⁻¹) are given. The torsion type vibrations of the small chain-like clusters are located in the same spectral region as Boson peak of As-S glasses system. They can make several contributions to the LF spectrum. The cluster lengths by weight distribution functions f(L)*L are from 5.5 to 10.1 Å and from 4.5 to 7.5 Å for g-As₂S₃ and g-As₂₂S₇₈, respectively. The lognormal fittings of the f(L)*L functions give the most probably values about the 7.6 Å (for g-As₂S₃) and 6.2 Å (for g-As₂₂S₇₈).     

The Boson peak in confined water: An experimental investigation of the liquid-liquid phase transition hypothesis

The Boson peak (BP) of deeply cooled confined water is studied by using inelastic neutron scattering (INS) in a large interval of the (P, T) phase plane. By taking into account the different behavior of such a collective vibrational mode in both strong and fragile glasses as well as in glass-forming materials, we were able to determine the Widom line that characterizes supercooled bulk water within the frame of the liquid-liquid phase transition (LLPT) hypothesis. The peak frequency and width of the BP correlated with the water polymorphism of the LLPT scenario, allowing us to distinguish the “low-density liquid” (LDL) and “high-density liquid” (HDL) phases in deeply cooled bulk water.Moreover, the BP properties afford a further confirmation of theWidom line temperature T_W as the (P, T) locus in which the local structure of water transforms from a predominately LDL form to a predominately HDL form.     

Acoustic attenuation in glasses and its relation with the boson peak

A theory for the vibrational dynamics in disordered solids [W. Schirmacher, Europhys. Lett. 73, 892 (2006), based on the random spatial variation of the shear modulus, has been applied to determine the wave vector (k) dependence of the Brillouin peak position (Omega(k)) and width (Gamma(k)), as well as the density of vibrational states [g(omega)], in disordered systems. As a result, we give a firm theoretical ground to the ubiquitous k2 dependence of Gamma(k) observed in glasses. Moreover, we derive a quantitative relation between the excess of the density of states (the boson peak) and Gamma(k), two quantities that were not considered related before. The successful comparison of this relation with the outcome of experiments and numerical simulations gives further support to the theory.     

Boson peak, flickering noise, backscattering processes and radiative transfer in random media

The method of matrix Green’s functions in the classical theory of electromagnetic waves is stated. This method allows to obtain a closed equation system in the presence of the random media for the calculation both coherent, and incoherent (fluctuating) components of radiation. The density and heterogeneity of scattering media can be arbitrary. The coherent channel is calculated independently. The fluctuating radiation distribution in the medium is developed initially by an interference pattern generated by the coherent channel. The limitations of the processes speed are absent. The theory embraces such phenomena as the boson peak, flickering noise, memory effect, backscattering processes and also conventional radiative transfer equation and Fresnel’s formulae.