Phonon frequency shift

Molecules vibrate at fundamental frequencies that are usually in the mid-infrared. Some overtone and combination transitions occur at shorter wavelengths. Because infrared photons have enough energy to excite rotational motions also, the ir spectmm of a gas consists of rovibrational bands in which each vibrational transition is accompanied by numerous simultaneous rotational transitions. In condensed phases the rotational stmcture is suppressed, but the vibrational frequencies remain highly specific, and information on the molecular environment can often be deduced from hnewidths, frequency shifts, and additional spectral stmcture owing to phonon (thermal acoustic mode) and lattice effects. 

The presence of isotopic impurities causes clear effects in the vibrational spectra. Almost all modes studied so far show frequency shifts on S/ S substitution [81, 107]. The average shift of the internal modes is ca. 0.6 cm , and of the external modes it is 0.1-0.3 cm (Tables 3, 4 and 5). Furthermore, the isotopomers which are statistically distributed in crystals of natural composition can act as additional scattering centers for the phonon propagation. Therefore, in such crystals the lifetime of the phonons is shortened in comparison with isotopically pure crystals and, as a conse-... 

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. 

A transition linearly coupled to the phonon field gradient will experience, from the perturbation theory perspective, a frequency shift and a drag force owing to phonon emission/absorption. Here we resort to the simplest way to model these effects by assuming that our degree of freedom behaves like a localized boson with frequency (s>i. The corresponding Hamiltonian reads... 

When metals have Raman active phonons, optical pump-probe techniques can be applied to study their coherent dynamics. Hase and coworkers observed a periodic oscillation in the reflectivity of Zn and Cd due to the coherent E2g phonons (Fig. 2.17) [56]. The amplitude of the coherent phonons of Zn decreased with raising temperature, in accordance with the photo-induced quasi-particle density n.p, which is proportional to the difference in the electronic temperature before and after the photoexcitation (Fig. 2.17). The result indicated the resonant nature of the ISRS generation of coherent phonons. Under intense (mJ/cm2) photoexcitation, the coherent Eg phonons of Zn exhibited a transient frequency shift similar to that of Bi (Fig. 2.9), which can be understood as the Fano interference [57], A transient frequency shift was aslo observed for the coherent transverse optical (TO) phonon in polycrystalline Zr film, in spite of much weaker photoexcitation [58],... 

Physically, the Brillouin spectrum arises from the inelastic interaction between a photon and the hydrodynamics modes of the fluid. The doublets can be regarded as the Stokes and anti-Stokes translational Raman spectrum of the liquid. These lines arise due to the inelastic collision between the photon and the fluid, in which the photon gains or loses energy to the phonons (the propagating sound modes in the fluid) and thus suffer a frequency shift. The width of the band gives the lifetime ( 2r)-1 of a classical phonon of wavenumber q. The Rayleigh band, on the other hand, represents the... 

Let us consider the result of the phonon frequencies shift at the transition. This shift is caused by the local change of the interaction between the lattice particles. Then, the shift of frequency of each mode may be written as [4] ... 

It is necessary to consider only the matrix elements (12a), (14) and the formula (15) at the integral calculations in the expression (17a). As a result, the integral expression for the transition probability in the unit of time is obtained, where the displacements of the phonon equilibrium positions and frequencies are taken into account simultaneously (see the detailed derivation but without the frequencies shift in Refs. [5, 8]) ... 

Bai et al. (2005) observed a phonon sideband with a frequency shift of 40-50 cm-1 located on the low-energy side of the 5Do <- 7Fo zero-phonon line (ZPL) in the 77 K excitation spectrum of Eu3+ Y203 NTs and NWs. However, vibronic sidebands generally appears at the high-energy side of the ZPL in the low-temperature excitation spectra since the vibronic transition involving the creation of a phonon with the annihilation of a photon is much more favored than the annihilation of a phonon at low temperature. The origin of this anomaly sideband remains unknown. 

The sensitivity of the phonon frequencies to temperature shows quite clearly the importance of their anharmonicity.42 The width of the Raman peaks, very small at low temperature ( 1cm-1), evolves in parallel with the frequency shift with temperature, which is still a consequence of the phonon-phonon interactions due to the anharmonicity. The fundamental reason for this strong anharmonicity, as well as the importance of the equilibrium-position shifts between 4 and 300 K,45 resides in the weakness of the van der Waals cohesive forces in the molecular crystal. 

Brillouin scattering provides information about the acoustic branches of the dispersion curves of the material under study. The measured frequency shift of the radiation is equal to that of the phonon under consideration (EQN (1)), and its wave vector is deduced from EQN (2), so the sound velocity may be calculated by ... 

The pressure dependence of N(EF) has been measured recently through the pressure dependence of the 13C-NMR Knight shift in K3Q0 [94]. In Fig. 25, a plot of In T P) versus K(P) is presented. As shown by this plot, linear behavior is effectively observed, which intersects the y axis at flph = 600 K and = N(EF)V = 0.3 at ambient pressure [94]. Thus the value of Tc appears to be governed by N(EF) and the pressure data suggest that high-frequency intraball phonons are likely to be involved in the superconductivity of fullerenes [20,94]. 

Sasaki K, Saito R, Dresselhaus G, Dresselhaus MS, Farhat H, Kong J (2008) Curvature-induced optical phonon frequency shift In metallic carbon nanotubes. Phys Rev B 77(24) 245441... 

Fj arises from a fourth-order interaction and is similar to F, except that an additional phonon is required making this channel less likely in most circumstances. F, and Fj are obviously population relaxation (T,) mechanisms but F3, which is also a fourth-order process, does not change the initial phonon population but modulates its frequency by exchange of two equal-frequency phonons on different phonon branches. Other, indirect, dephasing mechanisms have also been proposed, which rely on the modulation of the frequency shift terms via relaxation of the phonons involved in these terms. - ... 

The Raman technique is often applied for single crystals studies. The Raman effect occurs when a beam of monochromatic light with frequency o, passes through a crystal leading to inelastic scattering by the phonons of the crystal with frequency shifts coph of... 

The faster the impurity atom moves, the weaker its coupling to the phonon cloud is. Therefore the decrease of ujs corresponds to the vanishing of nonexponential decay effects as V increases. This behavior is displayed in Fig. 3 by the numerically calculated [from Eq. (8)] decay rate 7 and frequency shift... 

The NDR can be explained by the field effect, which splits the resonance scattering lines because of the frequency shifts at the turning points, and therefore the electron flow only partly contributes to the current. In accordance with the Pauli principle, the Fermi energy spectrum window given by the difference of Fermi functions results in a step-like increase of the current, when being overlapped with the transparency resonance at the bias voltage equals a multiple of the phonon quantum nil, as shown in Fig. 1. Since the transparency doublets are split faster than the Fermi windows are broadened out, after a... 

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