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Title:  The phonon spectra of simple metals  higher order effects of the electronion interaction 
Author(s):  Fehlner, William Robert 
Doctoral Committee Chair(s):  Pines, David 
Department / Program:  Physics 
Discipline:  Physics 
Degree:  Ph.D. 
Genre:  Dissertation 
Subject(s):  phonon spectra
simple metals electronion interation 
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 electronion interaction and truncating the series in accord with the twoumk1app 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 longwavelength behavior of the phonon dynamical matrix in the twoumk1app approximation and this agrees with that calculated from the secondorder perturbation theory expression for the energy of the uniform metal. The contributions to the bulk modulus coming from the third and fourthorder 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 twoumk1app approximation, using a local pseudopotentia1 to represent the electronion interaction, and taking electronelectron interactions into account by means of a polarization potential. The third and fourthorder terms are comparable in size to the secondorder 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 twoumklapp 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 fourthorder 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. 
Issue Date:  197106 
Genre:  Dissertation / Thesis 
Type:  Text 
Language:  English 
URI:  http://hdl.handle.net/2142/29854 
Other Identifier(s):  6032261 
Rights Information:  ©1971 William Robert Fehlner 
Date Available in IDEALS:  20120213 
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Dissertations and Theses  Physics
Dissertations in Physics 
Graduate Dissertations and Theses at Illinois
Graduate Theses and Dissertations at Illinois