Phonon-scattered incident electrons

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. 

Figure 3. Schematic Illustration of dispersion curves of an acoustic phonon, a band electron, and the SWAP. The Incident phonon -q Is scattered as q2. (Reproduced with permission from reference 5. Copyright 1985 Nljhoff.)...

More recent interest has focused upon the interpretation of the relative intensities of the electronic Raman transitions. The theory of electronic Raman spectroscopy has been well-summarized elsewhere [63, 202], and the electronic Raman scattering amplitude from an initial i/rf) to a final jfj) vibronic state (where the phonon states are the same, and usually zero-phonon (i.e. electronic) states) is given by (i/ r czpCF In this expression, the cartesian polarizations of the incident photon (hcv) and the scattered photon (hcvs) are a and p, respectively. The Cartesian electronic Raman scattering tensor is written as... 

Fig. 2 Schematic illustration of dispersion c irves of an acoustic phonon, a band electron and an acoustic polaron. The band electron is undergoing Cerenkov scattering by emission of a phonon q. The acoustic polaron is undergoing Doppler shifted phonon bouncing, the incident phonon -qi scattering as +q2 ...

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 ... 

Phonons interact with photons, electrons and neutrons, causing scattering. This causes a beam of radiation incident on a crystal to spread out, and a diffracted beam will be broadened by this extra contribution. The extent of the spreading is related to the phonon spectrum in the crystal, and its measurement gives information on the phonon distribution in the solid. 

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