Lattice phonon modes

The dimerization of 28 has also been studied by Prasad, who used Raman spectroscopy to monitor both changes in intermolecular vibrations and lattice phonon modes [73]. The Raman spectrum shows the disappearance of alkene stretches at 997, 1180, 1593, and 1625 cm-1 as expected, and the appearance of cyclobutane modes at 878,979, and 1001 cm-1. Phonon modes broadened as the reaction progressed, and bands around 15-40 cm-1 showed a shift in frequency. Between about 50 and 66% conversion it was difficult to define distinct bands, but after that point product bands grew in distinctly. This amalgamation behavior is good evidence for a homogeneous reaction mechanism. 

In the crystal, the total number of vibrations is determined by the number of atoms per molecule, N, and the nmnber of molecules per primitive cell, Z, multiplied by the degrees of freedom of each atom 3ZN. In the case of a-Sg (Z =4, N =8) this gives a total of 96 vibrations ( ) which can be separated in (3N-6)—Z = 72 intramolecular or "internal" vibrations and 6Z = 24 intermo-lecular vibrations or lattice phonons ("external" vibrations). The total of the external vibrations consists of 3Z = 12 librational modes due to the molecular rotations, 3Z-3 = 9 translational modes, and 3 acoustic phonons, respectively. 

Ammonium alums undergo phase transitions at Tc 80 K. The phase transitions result in critical lattice fluctuations which are very slow close to Tc. The contribution to the relaxation frequency, shown by the dotted line in Fig. 6.7, was calculated using a model for direct spin-lattice relaxation processes due to interaction between the low-energy critical phonon modes and electronic spins. 

Summary. Coherent optical phonons are the lattice atoms vibrating in phase with each other over a macroscopic spatial region. With sub-10 fs laser pulses, one can impulsively excite the coherent phonons of a frequency up to 50THz, and detect them optically as a periodic modulation of electric susceptibility. The generation and relaxation processes depend critically on the coupling of the phonon mode to photoexcited electrons. Real-time observation of coherent phonons can thus offer crucial insight into the dynamic nature of the coupling, especially in extremely nonequilibrium conditions under intense photoexcitation. 

As the lattice interacts with light only through electrons, both DECP and ISRS should rely on the electron-phonon coupling in the material. Distinction between the two models lies solely in the nature of the electronic transition. In this context, Merlin and coworkers proposed DECP to be a resonant case of ISRS with the excited state having an infinitely long lifetime [26,28]. This original resonant ISRS model failed to explain different initial phases for different coherent phonon modes in the same crystal [21,25]. Recently, the model was modified to include finite electronic lifetime [29] to have more flexibility to reproduce the experimental observations. 

Semimetals bismuth (Bi) and antimony (Sb) have been model systems for coherent phonon studies. They both have an A7 crystalline structure and sustain two Raman active optical phonon modes of A g and Eg symmetries (Fig. 2.4). Their pump-induced reflectivity change, shown in Fig. 2.7, consists of oscillatory (ARosc) and non-oscillatory (ARnonosc) components. ARosc is dominated by the coherent nuclear motion of the A g and Eg symmetries, while Af nonosc is attributed to the modification in the electronic and the lattice temperatures. 

Fig. 38. ID model of metal surface reconstruction. The coupling between discrete phonon modes (dashed line) and the electron-hole pair continuum (hatched) produces lattice instability.

Vibrations in a real crystal are described by the lattice dynamical theory, discussed in section 2.1, rather than by the atomic oscillator model. Each harmonic phonon mode with branch index k and wavevector q then has, analogous to Eq. 

By scattering within molecular solids and at their surfaces, LEE can excite with considerable cross sections not only phonon modes of the lattice [35,36,83,84,87,90,98,99], but also individual vibrational levels of the molecular constituents [36,90,98-119] of the solid. These modes can be excited either by nonresonant or by resonant scattering prevailing at specific energies, but as will be seen, resonances can enhance this energy-loss process by orders of magnitude. We provide in the next two subsections specific examples of vibrational excitation induced by LEE in molecular solid films. The HREEL spectra of solid N2 illustrate well the enhancement of vibrational excitation due to a shape resonance. The other example with solid O2 and 02-doped Ar further shows the effect of the density of states on vibrational excitation. 

This competition between electrons and the heat carriers in the lattice (phonons) is the key factor in determining not only whether a material is a good heat conductor or not, but also the temperature dependence of thermal conductivity. In fact, Eq. (4.40) can be written for either thermal conduction via electrons, k, or thermal conduction via phonons, kp, where the mean free path corresponds to either electrons or phonons, respectively. For pure metals, kg/kp 30, so that electronic conduction dominates. This is because the mean free path for electrons is 10 to 100 times higher than that of phonons, which more than compensates for the fact that C <, is only 10% of the total heat capacity at normal temperatures. In disordered metallic mixtures, such as alloys, the disorder limits the mean free path of both the electrons and the phonons, such that the two modes of thermal conductivity are more similar, and kg/kp 3. Similarly, in semiconductors, the density of free electrons is so low that heat transport by phonon conduction dominates. 

Ions in the lattice of a solid can also partake in a collective oscillation which, when quantized, is called a phonon. Again, as with plasmons, the presence of a boundary can modify the characteristics of such lattice vibrations. Thus, the infrared surface modes that we discussed previously are sometimes called surface phonons. Such surface phonons in ionic crystals have been clearly discussed in a landmark paper by Ruppin and Englman (1970), who distinguish between polariton and pure phonon modes. In the classical language of Chapter 4 a polariton mode is merely a normal mode where no restriction is made on the size of the sphere pure phonon modes come about when the sphere is sufficiently small that retardation effects can be neglected. In the language of elementary excitations a polariton is a kind of hybrid excitation that exhibits mixed photon and phonon behavior. 

Figure 4.24 (a) Temperature dependence of the Eg phonon mode of TbV04 in Raman scattering. (After Elliott et al, 1972.f, (b) temperature variation of lattice parameters of TbVO. (After Will et al, 1972.)... 

For paramagnetic spin systems, there are two major processes of relaxation (55). One relaxation mode involves spin-flipping accompanied by lattice phonon creation and/or annihilation (spin-lattice relaxation), and the other mode is due to the mutual flipping of neighboring spins such that equilibrium between the spins is maintained (spin-spin relaxation). For the former mode of relaxation, th decreases with increasing temperature, and the latter relaxation mode, while in certain cases temperature dependent, becomes more important (th decreases) as the concentration of spins increases. 

In the hydrate lattice structure, the water molecules are largely restricted from translation or rotation, but they do vibrate anharmonically about a fixed position. This anharmonicity provides a mechanism for the scattering of phonons (which normally transmit energy) providing a lower thermal conductivity. Tse et al. (1983, 1984) and Tse and Klein (1987) used molecular dynamics to show that frequencies of the guest molecule translational and rotational energies are similar to those of the low-frequency lattice (acoustic) modes. Tse and White (1988) indicate that a resonant coupling explains the low thermal conductivity. 

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