Measurement of the Magnitude of the Electronic Attenuation of Sound in Metals

Abstract

A discussion is presented of methods of measuring the total electronic component of the attenuation of sound waves in metals. Es werden Methoden zur Meseung der vollstilndigen elektronischen Komponente der Diimpfung von Sohallwellen in Metallen diskutiert.Considerable effort has been made to determine the magnitude of the electronphonon interaction in metals by means of the attenuation of sound waves. The aim of this note is to demonstrate that results can be obtained from relatively simple measurements.At these low phonon frequencies, several methods have been used for distinguishing the electronic component of the attenuation from other sources of dissipation. The most successful method has been on superconductors for which a t temperatures very much less than the transition temperature (T < T,) the electronic component decreases to zero so that the attenuation difference a (T = T,) -a (T = 0 ) gives the total electronic attenuation at T = T,. The frequency dependence of this effect has enabled Bliss and Rayne [l] to measure values of the anisotropy of the electronic attenuation in I n (longitudinal waves, q 1 > 1) (q is the sound wave vector and 1 the electron mean free path). In shear waves moreover Leibowitz and Fossheim [2] have been able to separate the electromagnetic and deformation potential parts of the electronic absorption in In (q l > 1) (see Appendix). This method is very powerful but is restricted to superconducting metals.The electronic component has also been distinguished from other absorption by measurements of the temperature dependence over a range where the electron mean free path is small, and there is little coupling to the sound wave down to the residual resistance region (e.g., Kolouch and McCarthy [3] polycrystalline Cu, q 1 < 1 ; Natale [a] polycrystalline K, q 1 < 1). This method is clean but relies on other sources of attenuation remaining constant with temperature.The limit q 1 > 1 should be investigated by this method as an extra Fermi surface parameter (I) is required for q 1 < 1 and values of I determined from the electrical conductivity seem always to give a value too small by a factor PW 1.6 compared with values taken from the attenuation either by comparison of the experimental magnitude with the free electron theory or from the Q of the magnetoacoustic effect.At high frequencies (and q I> 1) the electronic attenuation becomes dominant so that MacFarlane et al. [5] have been able to measure the frequency of

Theory of Electromagnetic Waves in Metals and Their Interaction with Ultrasonic Waves (III)

“…Below this field strength, the inductive attenuation is small but rises as -B2 (or even as -B4 for N , = N,, or open orbits not parallel to e ) 12831, whereas the field attenuation is N BF in general. Thus the nonelectronic attenuation may be measured also in high longitudinal magnetic fields B < B,[284].Theory of Electromagnetic Waves in Metals (111) 493 The change of the sound velocity (5.4) in a magnetic field is mainly due to the inductive terms of the force ( ( 5 . 5 ) , (5.6)) ( e x B ) .…”