Phonon-scattered incident

On one level it is a quantum effect, and can be described in terms of photon—phonon scattering. The incident NIR beam is a source of photons, and the energy from the piezotransducer provides a source of lattice phonons that propagate through the crystal. As in all collision processes, the twin principles of conservation of momentum and conservation of energy apply. The momentum of a quantum particle is linked to its wavevector by hk. The energy is linked to its frequency by hjj. 

Thermal diffuse or phonon scattering. The incident electrons interact with atoms that are oscillating about their mean positions and lose or gain energy of the order of kT ( 0.025 eV at room temperature). This amount of energy is too small to be detected by any available electron spectrometer, and there is no evidence that these phonon-scattered electrons contain any microanalytical information. 

The polarization dependent relative as well as absolute intensities of the above transitions can be calculated by using Eq. (2) for the oscillator strength, Eq. (17) for the stress dependent valence band wave functions and the optical and phonon scattering selection rules., 5,11,17 yhe results of this calculation for the transverse modes in Si and GaP are presented in Table IV for the electric field vector of the incident light, E, polarized parallel (U) perpendicular (-1) to X. 

In order to provide a more quantitative picture of phonon scattering we consider the scattering of an electron in a plane wave state from a solid in the presence of phonons. We will denote the incident wave-vector of the electron hy k and the scattered wave-vector by k. The matrix element M k for the scattering process will be given by the expectation value of the scattering potential, that is, the potential of all the ions in the crystal, Vcriit), between initial and hnal states ... 

Nuclear absorption of incident X-rays (from the synchrotron beam) occurs elastically, provided their energy, y, coincides precisely with the energy of the nuclear transition, Eq, of the Mossbauer isotope (elastic or zero-phonon peak at = E m Fig. 9.34). Nuclear absorption may also proceed inelasticaUy, by creation or annihilation of a phonon. This process causes inelastic sidebands in the energy spectrum around the central elastic peak (Fig. 9.34) and is termed nuclear inelastic scattering (NIS). 

In crystalline solids, the Raman effect deals with phonons instead of molecular vibration, and it depends upon the crystal symmetry whether a phonon is Raman active or not. For each class of crystal symmetry it is possible to calculate which phonons are Raman active for a given direction of the incident and scattered light with respect to the crystallographic axes of the specimen. A table has been derived (Loudon, 1964, 1965) which presents the form of the scattering tensor for each of the 32 crystal classes, which is particularly useful in the interpretation of the Raman spectra of crystalline samples. 

Fig. 9. Incidence energy dependence of the vibrational state population distribution resulting when NO(u = 12) is scattered from LiF(OOl) at a surface temperature of (a) 480 K, and (b) 290 K. Relaxation of large amplitude vibrational motion to phonons is weak compared to what is possible on metals. Increased relaxation at the lowest incidence energies and surface temperatures are indicators of a trapping/desorption mechanism for vibrational energy transfer. Angular and rotational population distributions support this conclusion. Estimations of the residence times suggest that coupling to phonons is significant when residence times are only as long as ps. (See Ref. 58.)...

Raman scattering can be considered as inelastic scattering of a photon by the phonons of a crystal. For a one-phonon process, energy conservation leads to the relations to, = to, + to in the Stokes case and to, = to, - to in the anti-Stokes case. The incident and the scattered photons, denoted by i and s, respectively, also have momentum. The momentum / of a photon is calculated from / = m c and A to = mc2 as I - hco/c — hk. Because the momentum is a vector, one must write I = hk. Now there arises the question whether a phonon also has momentum. With a mechanical wave in a crystal there is no motion of the center of gravity, therefore a phonon has no momentum in the usual sense. In spite of this a quasi-momentum can be ascribed to it. This question has been treated by Sussmann °). One may write down a relation for the k vectors which corresponds to conservation of momentum if all wave vectors of thejAonons are within BZ 1, namely fc, =ks + k for the Stokes case and ki = ks-k for the anti-Stokes case. 

At 795 cm 1 LiI03 has a transverse A phonon. Fig. 5 shows the shift of the Raman line towards lower wave numbers for decreasing angles between the directions of the incident and scattered light. Because the wave vector triangle lies in the isotropic Ary-plane, k is always perpendicular to the optical axis and no directional dispersion is to be expected, therefore the shift of the line is due only to the variation of the magnitude of the wave vector. 

Consider first the simpler case of acousto-optic interaction in an isotropic medium (i.e. a standard acousto-optic modulator). If the wavevector of the incident light is ko, that of the scattered light k+ or k and that of the phonon K, we have for conservation of momentum... 

We must remark that the amplitude of these processes is generally weak compared to the direct exciton-photon amplitude, owing to the small libration amplitudes (of the order of 1 °) at low temperatures. It is still smaller when the incident light polarization is parallel to the molecular transition dipole. For instance, in anthracene-crystal excitation, we expect the exciton-photon-phonon contribution to be more important for the a than for the b polarization. On the contrary, these processes become much more important in nonresonant excitations, in Raman scattering for instance (cf. Section II.D). 

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