Scattering by Vibrations

Raman scattering arises from the radiating dipole moment induced by the electric field of incident electromagnetic radiation. The laws of momentum and energy conservation govern the interaction between a phonon and a photon. When we consider a solid containing numerous Bravais unit cells and each cell contains n atoms, there will be 3n modes of vibrations. Among the 3n modes, there will be three acoustic modes, LA, TAj and TA2 and 3(n — 1) optical modes. The acoustic mode represents the in-phase motion of the mass center of the unit cell or the entire solid. 

Therefore, the LFR should arise from the vibration of the entire nanosolid interacting with the host matrix. For a freestanding nanosolid, the LFTi corresponds to intercluster interaction. The optical mode is the relative motion of the individual atoms in a complex unit cell that contains more than one atom. For elemental solids with a simple such as the fee structure of Ag, there presents only acoustic modes. The structure for silicon or diamond is an interlock of two fee structures that contain in each cell two atoms in non-equivalent positions, so there will be three acoustic modes and three optical modes. The complex structure of compound ensures multiple optical modes. 

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Denisov, V. N., Mavrin, B. N. and Podobedov, V. B. (1987) Hyper-Raman scattering by vibrational excitations in crystals, glasses and liquids. Phys. Rep., 151, 1-92. 

The influence of molecular vibrations on the interference pattern was first studied by James in 1932 He discussed the intensity distribution (of X-ray scattering) by vibrating molecules, and determined the dependence of the intensity distribution on the vibrational amplitudes. 

Barker AS, Loudon R. Response functions in the theory of Raman scattering by vibrational and polariton modes in dielectric crystals. Rev Modern Phys 1972 44 18. 

Raman effect When light of frequency Vo is scattered by molecules of a substance, which have a vibrational frequency of j, the scattered light when analysed spectroscopically has lines of frequency v, where... 

The major role of TOF-SARS and SARIS is as surface structure analysis teclmiques which are capable of probing the positions of all elements with an accuracy of <0.1 A. They are sensitive to short-range order, i.e. individual interatomic spacings that are <10 A. They provide a direct measure of the interatomic distances in the first and subsurface layers and a measure of surface periodicity in real space. One of its most important applications is the direct determination of hydrogen adsorption sites by recoiling spectrometry [12, 4T ]. Most other surface structure teclmiques do not detect hydrogen, with the possible exception of He atom scattering and vibrational spectroscopy. 

The nature of the intemuclear distance, r, is the object of interest in this chapter. In Eq. (5.1) it has the meaning of an instantaneous distance i.e., at the instant when a single electron is scattered by a particular molecule, r is the value that is evoked by the measurement in accordance with the probability density of the molecular state. Thus, when electrons are scattered by an ensemble of molecules in a given vibrational state v, characterized by the wave function r /v(r), the molecular intensities, Iv(s), are obtained by averaging the electron diffraction operator over the vibrational probability density. 

When the electric field strength of the incident light is ED, the induced dipole will be m, = aE0 where a is the optical polarisability. The electric field strength of radiation scattered by the induced dipole Es, depends on second derivative of m1 with respect to time. The useful experimental quantities are intensities of scattered light (Is) and incident important light (is). These are respectively proportional to Es2 and E02, averaged over a vibrational period, i.e., from time t = 0 to 10/C, where 1 is wavelength of... 

Hayazawa, N., Ichimura, T., Hashimoto, M., Inouye, Y., and Kawata, S. 2004a. Amphhcation of coherent anh-Stokes Raman scattering by a metallic nanostructure for a high resolution vibration microscopy. J. Appl. Phys. 95 2676-81. 

When light is scattered by particles which are very small compared with any of the wavelengths, the ratio of the amplitudes of the vibrations of the scattered and incident light varies inversely as the square of the wavelength and the intensity of the lights themselves as the inverse fourth power. 

Consider the waves scattered by isotropic dipole oscillators in the thin slab of matter shown in Fig. 9.3 only part a is of concern at the moment. These waves add vectorially at point P to produce the resultant forward-scattered wave s the important point, which is by no means obvious yet, is that this resultant scattered wave is phase shifted 90° relative to the incident wave (in addition to the phase shift between the oscillators and the incident wave). The background necessary to show this has been presented in Chapter 3 Fig. 3.8 is similar to Fig. 9.3 except that in the former the scatterers were arbitrary particles. The transmitted field t at P is the vector sum of the incident field and the fields scattered by all the oscillators. If we assume that the direction of vibration of the incident wave is not rotated as it propagates through the slab, the transmitted field is given by (3.39) ... 

An expression for the electrical conductivity of a metal can be derived in terms of the free-electron theory. When an electric field E is applied, the free carriers in a solid are accelerated but the acceleration is interrupted because of scattering by lattice vibrations (phonons) and other imperfections. The net result is that the charge carriers acquire a drift velocity given by... 

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