Size-Dependent Deviations from Matthiessen's Rule in Aluminum

Size-dependent deviations from Matthiessen's rule have been observed from 1.3 to above 40^∘{}K in thin foils and fine wires of aluminum. These deviations are consistent, in the regions of overlap, with data published by other investigators. The deviations are shown to be inconsistent with the two-parameter expression standardly used to describe impurity-produced deviations from Matthiessen's rule, unless the parameters are allowed to vary rapidly with temperature. Detailed comparisons of the data with the Blatt-Satz and the Azbel'-Gurzhi forms of Olsen's model for such deviations are given. An extension of the Blatt-Satz theory to thin foils predicts deviations of nearly the same magnitude in wires and foils if the foil thickness is equal to the wire diameter. The data are consistent with this prediction.