A theory of the electrical resistivity of liquid metals

A new technique for the calculation of electron scatter~ng in metals is proposed and developed. The method is considered valid both for crystals, at temperatures well above the Debye temperature, and for liquids, at temperatures well below the critical point. It is based on the use of ~ero-order wave functions which closely resemble Bloch functions, with perturbations depending primarily upon the short~range disorder parameters .. Although the method is similar to the one proposed and developed by GUbanov, there is one important distinction: the present approach uses zero-order wave functions that are discontinuous at the primitive cell boundaries. This allows the inclusion of terms in the scattering matrix element that were neglected by Gubanov and, furthermore, gives a straightforward procedure for calculation of all terms in the matrix element.. The perturbation procedure using dis~ continuous wave functions is justified, not rigorously perhaps, hut very plausibly. The quasi-Bloch technique is limited only by the necessity for the existence of a local structure closely resembling that of crystals, and, should therefore be valid for any liquid metal at temperatures well below the critical point 0 This is in contrast to the pseudopotential method of Ziman and others$ which is valid only when the effective electron-ion interaction is smallo The pseudopotential method is probably val,i<;i also in the very high temperature region (near the critical pOint), so the two theories may be considered as cornplementary~ each having its own region of validity, with very little overlap bet,ween regionso The perturbation matrix element in the present theory contains two types of termso One is a contribution due to long=range disorder, which may be estimated in various wayso Since this term is dominant in sodium~ its value for other metals may be obtained from the experimentally determined resistivity of sodium, and from the assumption that the ratio o'f the nearest=neighbor distance to the mean free path due to long-range disorder is the same for all metals 'at their melting pointso This was Zimanis procedure for estimating his plasma resistance, and the sarne procedure was used hereo The second type of term involves a product of the short= range disorder parameters and various derivatives of the periodic part of the Bloch functions, integrated over the cell boundarieso To avoid the need for a computer in the calculations, the zero-order wave functions were written as solutions of a three=dimensional Kronig=Penn~y mode19 the strength of the potential being related to the band gaps in the solidso It eventually became necessary to approximate these wave functions, so the numerical calculations were of limited validityo They were intended9 however~ as illustrations of the use of the method and do not exhaust its potentialitieso Numerical values of the electron mean free paths were obtained for the liquid alkali and noble metals at the melting pointo The calculated values differed from experimental values by a maximum of ~O percento The agreement was better than that of any previous calculations and was considered satisfactory in view of the uncertainties both in the parameters and in the approximations used in the calculations.

Name thesis:degree_name

Ph.D.

Level thesis:degree_level

Dissertation

Discipline thesis:degree_discipline

Physics

Grantor

University of Illinois at Urbana-Champaign

Year dc:date

2011

Author dc:creator

• Tefft, Wayne Earl

Contributors dc:contributor

• Bardeen, John

• electrical resistivity
• liquid metals
• electron scattering in metals
• zero-order wave functions
• Bloch functions
• short-range disorder parameters

Statement dc:rights

• Copyright 1964 Wayne Earl Tefft

Language dc:language

en

Identifier

6137277

OAI identifier oai:identifier

oai:www.ideals.illinois.edu:2142/23961