The phonon spectra of simple metals - higher order effects of the electron-ion interaction
Fehlner, William Robert
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https://hdl.handle.net/2142/29854
Description
Title
The phonon spectra of simple metals - higher order effects of the electron-ion interaction
Author(s)
Fehlner, William Robert
Issue Date
1971-06
Doctoral Committee Chair(s)
Pines, David
Department of Study
Physics
Discipline
Physics
Degree Name
Ph.D.
Degree Level
Dissertation
Keyword(s)
phonon spectra
simple metals
electron-ion interation
Language
en
Abstract
Calculations of the phonon frequencies in simple metals are carried out takirtg into account the influence of the periodic ionic lattice on the electrons. These effects are calculated by expanding the phonon dynamical matrix in powers of the electron-ion interaction and truncating the series in accord with the two-umk1app approximation rather than the homogeneous response approximation. In the former, some terms of third and fourth order are retained, whereas in the latter, only terms of second order are retained, as has been customary in the past. An. expression for the bulk modulus is derived by studying the long-wavelength behavior of the phonon
dynamical matrix in the two-umk1app approximation and this agrees with that
calculated from the second-order perturbation theory expression for the
energy of the uniform metal. The contributions to the bulk modulus coming
from the third- and fourth-order terms in the dynamical matrix are shown to be significant quantitatively for. both potassium and aluminum.
Detailed calculations of the phonon spectrum of potassium are performed in the two-umk1app approximation, using a local pseudopotentia1 to represent the electron-ion interaction, and taking electron-electron interactions into account by means of a polarization potential. The third and
fourth-order terms are comparable in size to the second-order umk1app contribution, on the order of 10% of the observed frequency in the case of the longitudinal modes. On the other hand, these terms vanish identically for the transverse modes. By modification of the local pseudopotential, a fit to the experimental data is obtained in the two-umklapp approximation. The behavior of the various contributions to the dynamical matrix as the pseudopotential and polarization potential are varied is also investigated. In particular, the third- and fourth-order terms have only slight angular dependence when calculated with several reasonable pseudopotentials, thus explaining the previous success in obtaining fits in the homogeneous response
approximation.
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