Ultrasonic attenuation in white tin crystals

Abstract

A detailed study of the temperature dependence of the longitudinal ultrasonic attenuation in single crystals of white tin is presented. Measurements have been made at temperatures from 0⋅8 to 4⋅2°K on pure and impure samples in the frequency range 40 to 290 Mc/s, corresponding to ql e values 0⋅45 to 90, where q is the ultrasonic wave vector and l e the free path of the conduction electrons. For high ql e an energy gap parameter A = 2∆(0)/ kT c is measured as an average over a narrow effective zone of the Fermi surface. For propagation along <001>, A = 3⋅15 ± 0⋅04; along <310>, A = 4⋅24 ± 0⋅04; along <100>, A = 3⋅55 ± 0⋅04; along <110>, A = 3⋅84 ± 0⋅07. The results are interpreted by assigning different energy gaps to different zones of the Fermi surface. Measurements with ql e ~ 0⋅5 yield A = 3⋅47 ± 0⋅06, independent of the propagation direction, showing that the effective zone extends to the whole Fermi surface for such low ql e . A simple two-gap model of a superconductor is used to show that the gaps measured here are weighted averages over an effective zone, and not minima. At lower temperatures the attenuation is shown to depend on the minimum gap, in agreement with the analysis of Privorotskii, but to be negligibly small for tin.