Transition metals electron-phonon interaction

Peierls showed 74 [41,42] that an instability in a one-dimensional chain, with one electron per site, driven by electron-phonon interactions, can lead to a subtle structural distortion and to a first-order Peierls phase transition, at and below a finite temperature TP (the Peierls temperature) [42], For instance, at and below Tp either a dimerization into two sets of unequal interparticle distances d and d" (such that d + d" = 2d) or some other structural distortion must occur. The electronic energy of the metallic chain may also be lowered by the formation of a charge-density wave (CDW) of amplitude p(x) ... 

A. Electron-Phonon Interaction Parameterization Scheme. In observing the fluorescence decay rate from a given J-manifold, it is generally found that the decay rate is independent of both the crystal-field level used to excite the system and the level used to monitor the fluorescence decay. This observation indicates that the crystal-field levels within a manifold attain thermal equilibrium within a time short compared to the fluorescence decay time. To obtain this equilibrium, the electronic states must interact with the host lattice which induces transitions between the various crystal-field levels. The interaction responsible for such transitions is the electron-phonon interaction. This interaction produces phonon-induced electric-dipole transitions, phonon side-band structure, and temperature-dependent line widths and fluorescence decay rates. It is also responsible for non-resonant, or more specifically, phonon-assisted energy transfer between both similar and different ions. Studies of these and other dynamic processes have been the focus of most of the spectroscopic studies of the transition metal and lanthanide ions over the past decade. An introduction to the lanthanide work is given by Hiifner (39). 

The very recent measurement of the electron-phonon interaction in actinide systems will be followed by additional measurements along the lines developed for studies of the lanthanide and transition metal systems. Initial studies to contrast the various syterns will be important in establishing the relative magnitude of the electron-phonon coupling strength... 

The effects of electron-phonon interactions alone were described in Chapter 4. We showed that these interactions lead to a dimerized, semiconducting ground state and to solitonic structures in the excited states. On the other hand, the effects of electron-electron interactions in a polymer with a fixed geometry were described in Chapters 5 and 6. There it was shown that the electronic interactions cause a metal-insulator (or Mott-Hubbard) transition in undimerized chains. Electron-electron interactions also cause Mott-Wannier excitons in the weak-coupling limit of dimerized chains, and to both Mott-Hubbard excitons and spin density wave excitations in the strong coupling limit. 

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). 

Table 3.3 DOSs at the Fermi level N( p) and electron-phonon interaction parameters for transition metal nitrides.

X, Xff and 2, are the total electron-phonon interaction constant and the contributions of metal and nitrogen atoms y is the electron specific heat (mJ/mol K ) T is the superconductivity transition temperature (K). 

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