Zero phonon mode

The dispersion relationships of lattice waves may be simply described within the first Brillouin zone of the crystal. When all unit cells are in phase, the wavelength of the lattice vibration tends to infinity and k approaches zero. Such zero-phonon modes are present at the center of the Brillouin zone. The variation in phonon frequency as reciprocal k) space is traversed is what is meant by dispersion, and each set of vibrational modes related by dispersion is a branch. For each unit cell, three modes correspond to translation of all the atoms in the same direction. A lattice wave resulting from such displacements is similar to propagation of a sound wave hence these are acoustic branches (Fig. 2.28). The remaining 3N-3 branches involve relative displacements of atoms within each cell and are known as optical branches, since only vibrations of this type may interact with light. 

It is interesting to note that the lowest phonon mode with non-zero frequency at A = 0 is not a nodeless A g mode, but rather an E2g mode with four nodes in which the cross section of the CNT is vibrating with the symmetry described by the basis functions of and xy. The calculated frequency of the E g mode... 

The PL spectrum and onset of the absorption spectrum of poly(2,5-dioctyloxy-para-phenylene vinylene) (DOO-PPV) are shown in Figure 7-8b. The PL spectrum exhibits several phonon replica at 1.8, 1.98, and 2.15 eV. The PL spectrum is not corrected for the system spectral response or self-absorption. These corrections would affect the relative intensities of the peaks, but not their positions. The highest energy peak is taken as the zero-phonon (0-0) transition and the two lower peaks correspond to one- and two-phonon transitions (1-0 and 2-0, respectively). The 2-0 transition is significantly broader than the 0-0 transition. This could be explained by the existence of several unresolved phonon modes which couple to electronic transitions. In this section we concentrate on films and dilute solutions of DOO-PPV, though similar measurements have been carried out on MEH-PPV [23]. Fresh DOO-PPV thin films were cast from chloroform solutions of 5% molar concentration onto quartz substrates the films were kept under constant vacuum. 

EXAMPLE 5.5 Sketch the absorption and emission spectra at OK for bands with zero-phonon line at 600 nm, a coupling with an unique breathing mode of energy 200 cm and a Huang-Rhys parameter ofS = l. 

Fig. 4. The emission and excitation spectra of the luminescence of Cs2NaYCl6 Bi3+ at 5 K. The zero-phonon line (0-0) and the progression in the v, mode are indicated at the top. See also Table 1. After A.C. van der Steen, thesis, Utrecht (1980)...

Indium nitride has twelve phonon modes at the zone centre (symmetry group Cev), three acoustic and nine optical with the acoustic branches essentially zero at k = 0. The infrared active modes are Ei(LO), Ei(TO), Ai(LO) and Ai(TO). A transverse optical mode has been identified at 478 cm 1 (59.3 meV) by reflectance [6] and 460 cm 1 (57.1 meV) by transmission [24], In both reports the location of a longitudinal optical mode is inferred from the Brout sum rule, giving respective values of 694 cm 1 (86.1 meV) and 719 cm 1 (89.2 meV). Raman scattering of single crystalline wurtzite InN reveals Ai(LO) and E22 peaks at 596 cm 1 and at 495 cm 1 respectively [25],... 

Vibrational sideline structure retains the polarization of the purely electronic excitation. Within the crude Bom-Oppenheimer approximation, only totally symmetric vibrational modes are coupled to an electronic transition. Consequently, all vibrational sidelines have the same polarization as the purely electronic component (electronic origin or zero phonon line). There are two circumstances... 

By plotting the first-order Raman intensity as a function of temperature, one can determine accurately as the temperature where the intensity of the first-order Raman peaks becomes zero, as shown in Fig. 21.4a and b. For the Tc determination from the SLs spectra shown here, the TO2 and TO4 phonon lines (shown by arrows in Fig. 21.3) are the most suitable because they do not overlap with the second-order substrate features. (However, other optical phonon modes can be used in the same manner, provided that they are clearly observed in the spectra of the ferroelectric phase.) The results, with the phonon intensities normahzed by the Bose factor n -f 1 = (1 exp —h(o/kT)) ... 

As it follows from the (26) and Fig. 6, at the absence of the magnetic field (H = 0) the dynamic coupling does not exist and the unrenormalized acoustic phonon mode active in the CJTE linearly depends upon the wave vector. However when H is not zero the dynamic coupling drastically changes both the phonon and the electronic mode. 

It is important to note that the electronic mode (see (28) is not the soft one (it does not go to zero at T— > Tc). However the renormalized phonon mode does. That means that the phonon mode is responsible for the instability in the crystal what should be expected at the structural phase transition caused by the CJTE. 

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