Ultrasonic studies of the electronic structure of hexagonal metal crystals. I. Normal state in magnesium, zinc and cadmium

Abstract

Measurements have been made of the total electronic attenuation α , in the low temperature limit, of longitudinal ultrasound propagating along the <0001>, <10͞10>, and <11͞20> directions in pure magnesium, zinc and cadmium crystals. In magnesium this attenuation was obtained from data taken from 1.2 to 80 K and in zinc and cadmium from the application of the critical magnetic field in the superconducting state at 0.1 K. In the high-frequency limit α is proportional to the frequency of the sound v and values of N = lim ( α/v ) have been found by extrapolation from measurements between 30 and 450 MHz. For magnesium N = 0.20±0.01 dB cm -1 MHz -1 for all three propagation directions; in zinc N = 1.29, 0.143 and 0.067 dB cm -1 MHz -1 (±5%) for sound propagation along <0001>, <10͞10> and <11͞20> directions respectively. For cadmium the corresponding values are 0.99, 0.165 and 0.048 dB cm -1 MHz -1 (±5%). The anisotropy in N is partly due to elastic anisotropy and partly to the Fermi surface geometry. In zinc and cadmium, our measurements are in agreement with the Fermi surface due to Stark & Falicov (1967), in which the ‘butterflies’ and ‘cigars’ are absent. We have deduced average values of the deformation parameter K x for magnesium, zinc and cadmium, using the theory of Pippard. We show that the deformation parameter for strains along the c -axis in zinc and cadmium is much greater than for strains in the basal plane, whereas magnesium is isotropic. Electron mean free paths l u deduced from the ultrasonic data are compared with those obtained from resistivity measurements on our samples. Anisotropies in l u are attributed partly to Fermi surface geometry and partly to small angle scattering.