The phonon spectra of simple metals - higher order effects of the electron-ion interaction

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.

Name thesis:degree_name

Ph.D.

Level thesis:degree_level

Dissertation

Discipline thesis:degree_discipline

Physics

Year dc:date

2012

Author dc:creator

• Fehlner, William Robert

Contributors dc:contributor

• Pines, David

• phonon spectra
• simple metals
• electron-ion interation

Statement dc:rights

• ©1971 William Robert Fehlner

Language dc:language

en

Identifier

6032261

OAI identifier oai:identifier

oai:www.ideals.illinois.edu:2142/29854