{"id":{"repo_id":"uiuc","oai_identifier":"oai:www.ideals.illinois.edu:2142/29854"},"canonical_url":"https://search.dev.ndltd.org/etd/uiuc/oai:www.ideals.illinois.edu:2142/29854","repository":{"repo_id":"uiuc","name":"University of Illinois - Urbana-Champaign","base_url":"https://www.ideals.illinois.edu/oai-pmh"},"display":{"title":"The phonon spectra of simple metals - higher order effects of the electron-ion interaction","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.","abstract_html":"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.","abstract_has_math":false,"creators":["Fehlner, William Robert"],"institution":null,"degree_name":"Ph.D.","degree_level":"Dissertation","degree_discipline":"Physics","degree_department":null,"school":null,"contributors":["Pines, David"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2012,"date_issued":"2012-02-13T19:32:38Z","date_published":"2012-02-13T19:32:38Z","updated_at":"2026-07-22T22:25:29Z","subjects":["phonon spectra","simple metals","electron-ion interation"],"languages":["en"],"rights":["©1971 William Robert Fehlner"],"rights_urls":[],"identifier_entries":[{"key":"dc:identifier","label":"Identifier","values":["6032261"],"render_values":[{"text":"6032261","href":null,"code":true}]}]},"links":{"outbound_url":"http://hdl.handle.net/2142/29854","outbound_label":"Handle","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Pines, David"]},{"key":"dc:creator","label":"Author","values":["Fehlner, William Robert"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2012-02-13T19:32:38Z","10000-01-01","1971-06"]},{"key":"dc:type","label":"Dc Type","values":["Dissertation / Thesis","text"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Physics"]},{"key":"thesis:degree_level","label":"Degree Level","values":["Dissertation"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Ph.D."]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["phonon spectra","simple metals","electron-ion interation"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language","label":"Dc Language","values":["en"]},{"key":"dc:rights","label":"Dc Rights","values":["©1971 William Robert Fehlner"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["http://hdl.handle.net/2142/29854","6032261"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["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.","Submitted by William Weathers (weathrs2@illinois.edu) on 2012-02-13T19:32:38Z No. of bitstreams: 1 1971_fehlner.pdf: 3816964 bytes, checksum: f2f566431494ce17693b67ca162946eb (MD5)","Made available in DSpace on 2012-02-13T19:32:38Z (GMT). No. of bitstreams: 1 1971_fehlner.pdf: 3816964 bytes, checksum: f2f566431494ce17693b67ca162946eb (MD5) Previous issue date: 1971-06","Restriction data tranferred 2014-07-01T11:09:51-05:00 Original Data Group with Access UIUC Users [automated] Release Date: none Reason: thesis","Item marked as restricted to the 'UIUC Users [automated]' Group (id=2) by William Weathers (weathrs2@illinois.edu) on 2012-02-13T19:32:38Z Item is restricted indefinitely.","thesis","U of I Only"]},{"key":"dc:title","label":"Title","values":["The phonon spectra of simple metals - higher order effects of the electron-ion interaction"]}]}],"canonical_facts":{"dc:contributor":["Pines, David"],"dc:creator":["Fehlner, William Robert"],"dc:date":["2012-02-13T19:32:38Z","10000-01-01","1971-06"],"dc:description":["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.","Submitted by William Weathers (weathrs2@illinois.edu) on 2012-02-13T19:32:38Z No. of bitstreams: 1 1971_fehlner.pdf: 3816964 bytes, checksum: f2f566431494ce17693b67ca162946eb (MD5)","Made available in DSpace on 2012-02-13T19:32:38Z (GMT). No. of bitstreams: 1 1971_fehlner.pdf: 3816964 bytes, checksum: f2f566431494ce17693b67ca162946eb (MD5) Previous issue date: 1971-06","Restriction data tranferred 2014-07-01T11:09:51-05:00 Original Data Group with Access UIUC Users [automated] Release Date: none Reason: thesis","Item marked as restricted to the 'UIUC Users [automated]' Group (id=2) by William Weathers (weathrs2@illinois.edu) on 2012-02-13T19:32:38Z Item is restricted indefinitely.","thesis","U of I Only"],"dc:identifier":["http://hdl.handle.net/2142/29854","6032261"],"dc:language":["en"],"dc:rights":["©1971 William Robert Fehlner"],"dc:subject":["phonon spectra","simple metals","electron-ion interation"],"dc:title":["The phonon spectra of simple metals - higher order effects of the electron-ion interaction"],"dc:type":["Dissertation / Thesis","text"],"thesis:degree_discipline":["Physics"],"thesis:degree_level":["Dissertation"],"thesis:degree_name":["Ph.D."]},"updated_at":"2026-07-22T22:25:29Z"}