Boson peak

C. Distribution of Barriers and the Time Dependence of the Heat Capacity The Plateau in Thermal Conductivity and the Boson Peak... 

B. Mosaic Stiffening and Temperature Evolution of the Boson Peak The Negative Griineisen Parameter An Elastic Casimir Effect ... 

According to the quantum transition state theory [108], and ignoring damping, at a temperature T h(S) /Inks — a/ i )To/2n, the wall motion will typically be classically activated. This temperature lies within the plateau in thermal conductivity [19]. This estimate will be lowered if damping, which becomes considerable also at these temperatures, is included in the treatment. Indeed, as shown later in this section, interaction with phonons results in the usual phenomena of frequency shift and level broadening in an internal resonance. Also, activated motion necessarily implies that the system is multilevel. While a complete characterization of all the states does not seem realistic at present, we can extract at least the spectrum of their important subset, namely, those that correspond to the vibrational excitations of the mosaic, whose spectraFspatial density will turn out to be sufficiently high to account for the existence of the boson peak. 

As the starting point in the discusion, we consider a simplified version of the diagram of a tunneling center s energy states from Fig. 14 with e < 0, as shown on the left hand side of Fig. 21. We remind the reader that the e < 0 situation, explicitly depicted in Fig. 21, implies lower transition energies than when the semiclassical energy difference e > 0 and thus dominates the low-temperature onset of the boson peak and the plateau. 

Coupling the motion of the mosaic cell (TLS and boson peak) to phonons is necesssary to explain thermal conductivity therefore the interaction effects discussed later follow from our identification of the origin of amorphous state excitations. The emission of a phonon followed by its absorption by another cell will give an effective interaction, in the same way that photon exchange leads to... 

Boson Peak, a Signature of Delocalized Collective Motions in Glasses (Example FC as Sensor Molecule)... 

FC as sensor molecule has been used to investigate the low-energy mobility, i.e., the nature of the Boson peak and of the trawi-Boson dynamics, of toluene, ethylbenzene, DBF and glycerol glasses [102]. The spectator nucleus Fe is at the center of mass of the sensor molecule FC. In this way, rotations are disregarded and one selects pure translational motions. Thus, the low-energy part of the measured NIS spectra represents the DOS, g(E), of translational motions of the glass matrix (below about 15 meV in Fig. 9.39a). 

The so-called Boson peak is visible as a hump in the reduced DOS, g(E)IE (Fig. 9.39b), and is a measure of structural disorder, i.e., any deviation from the symmetry of the perfectly ordered crystal will lead to an excess vibrational contribution with respect to Debye behavior. The reduced DOS appears to be temperature-independent at low temperatures, becomes less pronounced with increasing temperature, and disappears at the glass-liquid transition. Thus, the significant part of modes constituting the Boson peak is clearly nonlocalized on FC. Instead, they represent the delocalized collective motions of the glasses with a correlation length of more than 20 A. 

Beyond the Boson peak, the reduced DOS reveals for all studied glasses a temperature-independent precisely exponential behavior, g(E)/E exp( / o) with the decay energies Eo correlating with the energies E of the Boson peak. This finding additionally supports the view that the low-energy dynamics of the glasses are indeed delocalized collective motions because local and quasilocal vibrations would be described in terms of a power law or a log-normal behavior [102]. 

Fig. 9.39 (a) Density of states (DOS), g E), obtained from NIS at 22 K on ferrocene as sensor molecule in toluene glass, (b) Reduced DOS, g(E)/E, for various glasses. Arrows indicate the energy of the Boson peak. (Taken from [102])... 

Kirillov, S. A., Spatial disorder and low-frequency Raman pattern of amorphous solid, with special reference to quasi-elastic scattering and its relation to Boson peak, J. Mol. Struct. 479, 279-284 (1999). 

At low temperature the material is in the glassy state and only small ampU-tude motions hke vibrations, short range rotations or secondary relaxations are possible. Below the glass transition temperature Tg the secondary /J-re-laxation as observed by dielectric spectroscopy and the methyl group rotations maybe observed. In addition, at high frequencies the vibrational dynamics, in particular the so called Boson peak, characterizes the dynamic behaviour of amorphous polyisoprene. The secondary relaxations cause the first small step in the dynamic modulus of such a polymer system. 

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