Calculation of Residual Resistivity in Aluminum and Lead Alloys: The Effect of Multiple Plane-Wave Character on The Residual Resistivity in Polyvalent Metals

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Abstract
The residual resistivity in some aluminum and lead alloys has been calculated taking account of the mixing of plane waves near Brillouin-zone boundaries which intersect the Fermi surface in the extended-zone scheme. This effect was found to enhance the resistivity by a factor of 2 in Al and 3 in Pb over estimates by the free-electron theory, and to remove the systematic discrepancy existing heretofore between theory and experiment. Pseudopotentials of Ashcroft's form have been adopted, and impurity potentials are constructed by using the core radii determined in their pure metallic states and the dielectric function appropriate to the host metal. Various problems in the resistivity calculation, including the reliability of impurity potentials, have been examined in some detail.