Interactions phonon softening

However, as discussed extensively in review articles by Pouget [9] and by Barisic and Bjelis [10], the presence of both 2kF and 4kF anomalies, where kF is the Fermi wave vector of the quasi-one-dimensional electron gas, the fact that phonon softening at 2kF is relatively small, combined with theoretical considerations, have lead to the present-day viewpoint that electron-electron Coulomb interactions play an important role. 

A more precise measurement of local sample temperature is made possible by the anharmonicity of the crystal vibrational potential energy. Phonon-phonon interactions that reduce individual phonon lifetimes, phonon softening, and thermal expansion give rise to increasing peak width and a change in peak frequency... 

The actual volume collapse during the y—a transition indicates that the electron-phonon interaction is an important factor. Hence it is expected that some anomaly will be seen in the phonon spectra, which is associated with a possible softening in the transition arising from the electronic contribution, as is discussed for La by Pickett et al. (1980). To our knowledge, no phonon spectra of a-Ce are available to date due to the difficulties of sample preparation. Once available, the comparison of phonon spectra in the various phases of Ce metal will yield crucial insights into the nature of the phase transition. We note that phonon data for y-Ce shows evidence for a phonon softening which may be related to the y - a transformation (Stassis et al. 1979, 1982). 

A AH < kT has important consequences. As the temperature is lowered to where AHg, kT, strong electron-phonon interactions must manifest themselves. Direct evidence for mode softening and strong electron-phonon coupling in the internal Ty < T < 250 K has been provided by measurements of the Mdssbauer recoiless fraction and the X-ray Debye-Waller factor as well as of muon-spin rotation Therefore, it would be... 

It is obviously ideally suited to measuring the effect of the electron quantum fluctuations on the phonon frequency. What one immediately learns from Eq. (26) is that the propagator is quasistatic that is, the >m = 0 component dominates for T > co /2tt. This comes from the definition of the Matsubara frequencies for bosons [under Eq. (8)]. As far as the electrons are concerned, the atoms move very slowly (the adiabatic limit). If 2g2 gi> - g3 (see Fig. 5), the electrons are able to screen the slow lattice motion and thus soften the interactions. We are obviously interested in the 2kF phonons, which will be screened most effectively by the dominant 2kF charge response of the one-dimensional electron gas. 

Up to now, lattice dynamics calculations have addressed the translational phonons and the rotons separately. For the translational phonons one has used an isotropic (i.e. orientationally averaged) H2-H2 potential. The SCP method has been applied to the anharmonic vibrations [96], but it appeared to be necessary to introduce an approximate Jastrov function into this method (with one adjustable parameter) in order to obtain realistic results. The roton frequencies, and their softening at higher pressures (smaller volume) which precedes the disorder/order phase transition, have been calculated by the MF [97] and RPA [98] methods. Only quadrupole-quadrupole interactions were taken into account, and translation-rotation coupling was neglected. 

Softening of zone boundary LO phonons in the NaCl structure and also of the bulk modulus are the striking effects caused by the electron-phonon interaction due to volume modulations of the lanthanide ion by the phonons as calculated by Bennemann and Avignon (1979), Ghatak and Bennemann (1979) and Cantrell and Stevens (1984). One expects a strong scattering intensity from those deformations which also describe the phonon anomaly. 

The integrated absorbed intensity from the data of fig. 16.20 shows an anomalous reduction of about 40% as the temperature is lowered below the Curie temperature. This phenomena is believed associated with a softening of the phonons via the large magneto-elastic interaction. As a result the acoustic impedance should be strongly temperature dependent. 

The process of phonon scattering contributes less to the intrinsic vibratiorc Atomic undercoordination softens the optical phonons of nanostructures. Intergrain interaction results in emerging of the low-frequency phonons whose frequency undergoes blueshift with reduction in solid size. 

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