The surface resistance of normal and superconducting tin at 36 kMc/s

Abstract A new calorimetric method has been developed to measure the surface resistance of plane single crystals of tin at 36 kMc/s. The normal resistance depends upon the orientations of the tetrad and dyad axes relative to the surface of the specimen and the direction of current flow in the surface, the form of the anisotropy being in good agreement with Pippard’s results for cylindrical single crystals of tin at 9·4 kMc/s. The frequency-dependence of the resistance differs somewhat from that expected for a metal under extreme anomalous conditions, and similar discrepancies are found when the results for specimens of copper and aluminium are compared with earlier work on these metals. Electron micrographs of the electropolished surfaces of the tin specimens show that the anisotropy of the resistance is not merely a surface effect, hence justifying its interpretation as a property of the bulk metal. A simple ellipsoidal model, which constitutes a convenient picture of a surface having certain geometrical characteristics in common with the actual Fermi surface of tin, is found to reproduce the principal features of the anisotropy. The temperature variation of the superconducting resistance may be described by the empirical functions used by Pippard to reduce his results, the shapes of the corresponding curves over certain ranges of temperature for different specimens at the two frequencies being similar, apart from orientation-dependent and frequency-dependent scaling factors. For specimens of different orientations the scaling factors are found to be proportional to each other and to the surface conductance in the normal state, and their ratio is independent of frequency. These results and the form of the frequency-dependence of the superconducting resistance confirm Pippard’s conclusion that the observed behaviour at high frequencies is difficult to reconcile with a 'two-parameter two-fluid’ model of a superconductor.