Vibrations and Phonons

The vibrations of the atoms in the crystalline lattice are important in understanding the thermal properties of both metallic and nonmetallic solids. The energy involved in these vibrations represents thermal energy hence lattice vibrations are primarily resporrsible for the heat capacity of solids. Also, these vibrations are able to transport heat and are the dominant source of thermal conductivity in nonmetals. Therefore, in order to understand thermal properties of solids, it is necessary to start with a general understanding of the nature of lattice d5mamics. 

---

In this section we study the interaction of a branch of electronic excitons with a mode of vibrations and phonons. The parameters in this model are the dispersion width 2B of the excitonic band, the average energy quantum hQ0 of the vibration, the coupling intensity, and the temperature. According to the ordering of these parameters, the system shows very different behavior, whose general treatment is beyond the scope of this section. We restrict ourselves to the usual cases that are relevant to the first singlet exciton of the anthracene crystal and to its absorption and emission mechanisms. 

S. Hirata S. Iwata (1998). J. Chem. Phys., 108, 7901-7908. Density functional crystal orbital study on the normal vibrations and phonon dispersion curves of all trans-polyethylene. 

Fig. 1. Simplistic view of a homogeneously broadened chromophore optical absorption spectrum at 0 K. The left-hand side shows the vibrational and phonon splitting of two electronic levels. The typical vibrational levels are split by 1000 cm", and the phonons form a quasi-continuous distribution of width approximately equal to 200 cm". The upper right-hand comer shows the absorption spectrum at 0 K with the sharp zero phonon lines of approximately 1 cm" width and the phonon wing with width approximately 200 cm". ... 

Ti, spin—lattice relaxation. Measures the rate of energy exchange between the spin system and the vibrational and phonon modes of the lattice. Has Bo dependence. 

Tip, spin—lattice in the rotating frame relaxation. While an on-resonance RF pulse is apphed, this parameter is a measure of the rate of energy exchange between the spin system and the vibrational and phonon modes of the lattice. 7 iP depends upon the magnitude of both Bo and Bi, where Bj is the amplitude of the RF pulse. 

Although the ab initio calculation of vibrational frequencies of molecular systems is a well-known practice, it is not so common in the case of crystalline systems. However, quantum-mechanical calculation of lattice vibrations and phonon spectra has become a subject of increasing interest and effective methods have been developed and implemented. In this respect, a recent review by Baroni et al. gives a detailed overview of the state of the art of ab initio calculation of vibrations and related properties for crystalline materials. Most of the current implementations are based on DFPT and use either plane waves or localized functions as a basis set. " As an example, calculated and experimental vibration frequencies at T are reported in Table 18 for... 

Fig. 12. Time-integrated emission and excitation spectra at T = 1.2 K and 10 K of (Ru(bpy-hj)3) in [Zn(bpy-h8)3](C104)2. The crystals were grown from water with a molar ratio in solution of Ru(ll) Zn(II) of 0.5%. The emission spectra a, b, c, and e were obtained by exciting at 514,5 nm (A 19436 cm the excitation spectrum d was detected at 17207 cm (A 477 cm satellite to origin I). The region of the electronic origins is reproduced at an enlarged scale. The energies of vibrational and phonon satellites are given relative to the respective electronic origins...

Fig. 21. Emission spectra and decay properties of neat [Ru(bpy)3)(PF()2. a Survey of the broadband spectrum at T = 1.3 K. Bands I and II correspond to the emission from state 11) and II), respectively. The bands are not resolved mainly due to overlapping vibrational and phonon satellites, b Spectral range of the electronic origins I and II at an enlarged scale. A and B represent different crystallographic sites, c Emission decay of the energetically higher lying site B. Tg is determined by a radiationless energy transfer from site B to site A. d Emission decay of state III) (site A) determined by spin-latice (sir) relaxation due to the direct process of sir to state 11), e Usual emission decay from state 11). f IWo-component decay due to superimposed emissions from state 11) and state 111 >...

---