Electrical resistivity of voids

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Abstract
The electrical resistivity of spherical clusters of vacancies (voids) in the three simple metals sodium, magnesium and aluminium has been calculated by two different methods, one based on phase shift scattering and the other on pseudopotentials. In the phase shift method the clusters were represented by a spherical potential well, whose radius was adjusted to give a volume equal to that of the vacancies in the cluster and whose depth was determined so as to satisfy the Friedel sum rule for the phase shifts. In the other method, local screened pseudopotentials, situated at the vacant lattice sites, were used and the cross section of the cluster was determined from perturbation theory. The absolute values of the resistivity found by the two methods were in close agreement for magnesium and aluminium, though there was a substantial discrepancy in the case of sodium. Similar calculations for spherical interstitial clusters were also performed, although such clusters have not been observed experimentally. The results have the same general features as for the voids.