FRINK Linked Data Fragments server

Matches in SemOpenAlex for { <https://semopenalex.org/work/W876482188> ?p ?o ?g. }

• W876482188 abstract " We give a semi-classical treatment of the problem of electrical conduction around a charged impurity ion in a metal. As the electrons flow past the ion they are scattered by its screened Coulomb potential and so introduce a velocity dependent distribution of charge. This charge distribution leads, through the Poisson equation, to a modification of the potential surrounding the ion through which the electrons are initially scattered; we look for a self-consistent or simultaneous solution to the Boltzmann and Poisson equations. This final velocity dependent charge distribution induces an electric field at the ion, so exerting a force on that ion. We identify two effects: (i) a screening force acting so as to reduce the effect of the external field on the ion, (ii) a drift force resulting from the direct collisions between electron, and ion. The process is described by a Boltzmann Transport equation which we solve at large distances from the ion. We derive the Green's Function for the equivalent integral equation, and then solve that equation by means of a Fourier Transform. In this technique we do not assume as in previous approaches that the ion is stationary or that its charge is small. The evaluation of the Green's Function does however involve the construction of an orbit model in which all scattered electrons pass through the ion itself and we do not expect this model to be of any use inside the screening radius. We turn to a method of expansion by spherical harmonics, suggested by Das in his thesis, in the hope that it may be of use at short range. In understanding a paradox of the method we lose a criterion for convergence and our confidence in the method. To do this we consider the electron mean free path to be infinite in this short range region. In this limit a quantum mechanical calculation of the self-consistent field gives a result identical to that from a classical weak charge calculation due to Peierls, in the same limit, with the significant addition of a cut-off in momentum space at twice the Fermi-momentum. It is this cut-off, for which Peierls had argued on physical grounds, that eliminates a divergence at the origin. We use it to calculate the force. We find that we may add Peierls' result where the Green's Function method is too insensitive. There are then three extra terms in the force, two due to drift and one to screening. However, the term we interpret as a screening correction may for large enough charge on the ion become greater than the direct field force. This may be due to an error in our interpretation as screening, or in the calculation itself. If it is the latter we propose a further calculation to check. In as far as the force on the ion derived in this thesis may be larger than the direct field force there is no disagreement with experimental data. Until we can understand the screening problem the result is not suitable for a detailed comparison with experiment." @default.
• W876482188 created "2016-06-24" @default.
• W876482188 creator A5065738324 @default.
• W876482188 date "1970-01-01" @default.
• W876482188 modified "2023-09-23" @default.
• W876482188 title "The motion of an ion in an electron gas" @default.
• W876482188 hasPublicationYear "1970" @default.
• W876482188 type Work @default.
• W876482188 sameAs 876482188 @default.
• W876482188 citedByCount "0" @default.
• W876482188 crossrefType "dissertation" @default.
• W876482188 hasAuthorship W876482188A5065738324 @default.
• W876482188 hasConcept C121332964 @default.
• W876482188 hasConcept C145148216 @default.
• W876482188 hasConcept C147120987 @default.
• W876482188 hasConcept C165995430 @default.
• W876482188 hasConcept C184779094 @default.
• W876482188 hasConcept C186603090 @default.
• W876482188 hasConcept C3768446 @default.
• W876482188 hasConcept C60799052 @default.
• W876482188 hasConcept C62520636 @default.
• W876482188 hasConcept C74650414 @default.
• W876482188 hasConcept C96716743 @default.
• W876482188 hasConceptScore W876482188C121332964 @default.
• W876482188 hasConceptScore W876482188C145148216 @default.
• W876482188 hasConceptScore W876482188C147120987 @default.
• W876482188 hasConceptScore W876482188C165995430 @default.
• W876482188 hasConceptScore W876482188C184779094 @default.
• W876482188 hasConceptScore W876482188C186603090 @default.
• W876482188 hasConceptScore W876482188C3768446 @default.
• W876482188 hasConceptScore W876482188C60799052 @default.
• W876482188 hasConceptScore W876482188C62520636 @default.
• W876482188 hasConceptScore W876482188C74650414 @default.
• W876482188 hasConceptScore W876482188C96716743 @default.
• W876482188 hasLocation W8764821881 @default.
• W876482188 hasOpenAccess W876482188 @default.
• W876482188 hasPrimaryLocation W8764821881 @default.
• W876482188 hasRelatedWork W1649305379 @default.
• W876482188 hasRelatedWork W1653835728 @default.
• W876482188 hasRelatedWork W1899130758 @default.
• W876482188 hasRelatedWork W1965185974 @default.
• W876482188 hasRelatedWork W1979574351 @default.
• W876482188 hasRelatedWork W1981416614 @default.
• W876482188 hasRelatedWork W1984399130 @default.
• W876482188 hasRelatedWork W1992089211 @default.
• W876482188 hasRelatedWork W2014130355 @default.
• W876482188 hasRelatedWork W2028170542 @default.
• W876482188 hasRelatedWork W2047628212 @default.
• W876482188 hasRelatedWork W2055495451 @default.
• W876482188 hasRelatedWork W2161125045 @default.
• W876482188 hasRelatedWork W2470517091 @default.
• W876482188 hasRelatedWork W2903775954 @default.
• W876482188 hasRelatedWork W2939100446 @default.
• W876482188 hasRelatedWork W2951315547 @default.
• W876482188 hasRelatedWork W3096663151 @default.
• W876482188 hasRelatedWork W3106261650 @default.
• W876482188 hasRelatedWork W342018286 @default.
• W876482188 isParatext "false" @default.
• W876482188 isRetracted "false" @default.
• W876482188 magId "876482188" @default.
• W876482188 workType "dissertation" @default.