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Contrary to the well-known method of rigid potential, based on superposition of atomic potentials, we suggest the method of a compliant (deformation) potential accounting for the elastic properties of distributed ion and electron charges. The elasticity of electron and ion media leads to the discontinuities in the electron-phonon spectrum at the boundaries of the Brillouin zones. For polar dielectric it causes to the discontinuities at the boundaries of the first Brillouin zone and to the total or partial suppression of electron-phonon scattering in this zone. For all crystals because of thermal `broadening' of the crystal planes it causes to the discontinuities at the boundaries of all Brillouin zones and to the partial suppression of electron-phonon scattering in the higher zones.
O. A. Podsvirov
"Role of electron-phonon scattering in the production of absorption bands in electron microscopy", Proc. SPIE 3345, International Workshop on New Approaches to High-Tech Materials: Nondestructive Testing and Computer Simulations in Materials Science and Engineering, (1 January 1998); https://doi.org/10.1117/12.299580
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O. A. Podsvirov, "Role of electron-phonon scattering in the production of absorption bands in electron microscopy," Proc. SPIE 3345, International Workshop on New Approaches to High-Tech Materials: Nondestructive Testing and Computer Simulations in Materials Science and Engineering, (1 January 1998); https://doi.org/10.1117/12.299580