Electron-phonon interaction elastic effects

Redistribution of the phonon density of states due to local deformations caused by an introduction of an impurity Ln ion is of primary importance for electron-phonon interaction effects. In particular, for Pr CsCdBr3 the effective electron-phonon coupling is strongly suppressed due to a local increase of elastic forces in the activated crystal and the corresponding enhancement of correlation between displacement of the impurity Ln ion and its neighbors. When dealing with nanostructured materials, it is important to take into account... 

Equation (102) shows that MAQO can provide important information about the electronic parameters (extremal Fermi surface cross-sectional area, effective masses, electronic relaxation times) and about the electron-phonon interaction (strain derivatives of the cross-sectional area for different symmetry strains). With the help of this technique, combined with de Haas-van Alphen susceptibility measurements, one can put the deformation potential interaction and the temperature dependence of the elastic constants, discussed above in sect. 3.2, on a solid basis. In the following we discuss some compounds. 

In amorphous semiconductors, electron-electron interactions are important only when two electrons of opposite spin occupy the same localized state or for Mott hopping at the Fermi level at very low temperature. Electron-phonon interactions are always present and more important in disordered than ordered semiconductors. The electron-phonon (e-p) interaction has two kinds of effects, elastic or static and... 

A variety of experimental techniques are available for the investigation of the electron-lattice interaction. For static phenomena such as thermal expansion and magnetostriction one can use dilatometric and X-ray techniques. For dynamic effects such as elastic constant measurements, ultrasonic propagation and phonon dispersion the methods of sound velocity and attenuation measurements, and inelastic neutron or light scattering are available. In addition high-pressure work can give valuable information for some quantities. 

At low temperatures, when only the ground state of the lanthanide ion in the crystal field is populated, the total magnetic moment of the ion is the sum of the induced (Van Vleck) moment and the intrinsic moment (the latter differs from zero only in the degenerate state). The contributions to the magnetostriction and the elastic constants due to changes in the intrinsic magnetic moment of the lanthanide ion with lattice strain can be written explicitly when considering the effective spin Hamiltonian. The latter contains a smaller number of independent parameters (constants of spin-phonon interaction) than the Hamiltonian of the electron-deformation interaction (18) and is more suitable in the description of experimental data. 

The effect was investigated of the nature and energy of the interatomic interaction on the structure and physical properties of crystals. Factors were studied which determine the thermodynamic properties and their temperature dependences. The effect of various parameters on the form of the frequency spectmm of phonons was investigated, taking, as an example, crystals with a diamond-type structure. The problem was also studied of the determination of the elastic constants as derivatives of the crystal energy in terms of the distribution functions of the electron density, represented by various approximations. 

The electronic structure of rare-earth atoms with the configuration (Xe)4f"5d 6s gives rise to conduction bands with 5d and 6s character in the intermetallic compounds. The d bands can have a rather large density of states. Therefore the coupling of phonons to these itinerant electrons can be quite strong. In this chapter we review experimental effects caused by the interaction of conduction electrons with sound waves. These experiments mainly concern the anomalous temperature dependence of symmetry elastic constants and the presence of magnetoacoustic quantum oscillations observed in sound velocity and attenuation. 

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