We report on the measurements of the ultrasonic attenuation and the d.c. resistance of a superconducting granular lead film as a function of both temperature and applied magnetic field. In the absence of an applied magnetic field, the d.c. resistance and ultrasonic attenuation can be accounted for, qualitatively, by using percolation theory. When a magnetic field is applied, we find that if we assume that both the ultra-sonic attenuation and the resistivity are proportional to the effective area through which the field penetrates the film, we can deduce magnetization curves for the film from the normalized attenuation and resistance data. The shapes of these magnetization curves are consistent with those of a type II superconductor
Measurements of the attenuation of longitudinal ultrasound in superconducting UPt3 show a peak, below H, 2, which depends strongly on the orientation of the field relative to the c axis. We propose an explanation of this peak in terms of a vortex phase transition in an unconventional superconducting state, which is consistent with recent neutron-scattering data.
%e present a model for the temperature dependence of the resistance and ultrasonic attenuation of a superconducting granular lead film. Treating the film as a network of random resistors and using percolation methods, we postulate that awhile the dc resistance is the resistance of an infinite network, the surface acoustic wave measures the average resistance of finite "subnetworks, " the sizes of which are on the order of the acoustic wavelength. The resistance of the infinite network will vanish when more than some critical fraction of the resistors in the network becomes equal to zero. However, when the resistance of the infinite network vanishes, some of the subnetworks will still have nonzero resistance, Consequently, the ultrasonic attenuation should be nonzero even when the dc resistance vanishes. This is in agreement with our experimental data.
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