Size Effects in the Resistivity of Indium Wires at 4.2°K

Abstract

Measurements are reported of the dependence of the resistance (at 4.2°K) of high-purity polycrystalline indium wires on the wire diameter. Data, which were taken on recrystallized wires extruded through dies of various sizes, and also on a single extruded wire gradually reduced in diameter by etching, are compared with those of Olsen. It is pointed out that any variation of the bulk electron free path over the Fermi surface must be taken into account in the analysis of size effect data on wires unless they are extremely small in diameter. A calculation of the size effect at 0°K in monocrystalline wires and in "unidimensionally" polycrystalline wires having a diameter large compared to the mean free path is made for an arbitrary Fermi surface and free path anisotropy. The result of the calculation for the polycrystalline case, which is limited to metals having isotropic bulk conductivities, is similar to the Fuchs-Dingle result for the isotropic case except that the effective resistivity is much more strongly size dependent when a large mean free path anisotropy exists. It is concluded on the basis of this derivation that the size effect data on indium wires and anomalous skin effect data can be reconciled if a large anisotropy in the mean free path exists.