Phonon and Electron Drag Coefficients in Single-Crystal Aluminum

Measurements have been made of the attenuation of the fast and slow shear waves along the $〈110〉$ direction in an aluminum single crystal in the frequency range from 30 MHz to 170 MHz and in the temperature range 66^∘{}K to 300^∘{}K. The attenuation can be divided into a square-law frequency term and a term consistent with the theoretical form of the dislocation attenuation at high frequencies. On account of the fact that aluminum has three free electrons per atom and a low resistivity, the attenuation due to electron viscosity is large enough to measure at room temperature, and at low temperatures contributes the principal square-law component. The difference between the measured value and the electron component can be used to evaluate the phonon-viscosity square-law component. The asymptotic value of the dislocation attenuation can be used to evaluate the drag coefficient, and for the first time a definite electron drag coefficient is demonstrated. The measurements can be used to establish a ratio of 3·{}4 between the limiting nonlinearity radii for electrons and phonons. While the absolute value cannot be obtained with accuracy by this method---on account of a lack of knowledge of the number N̄ of dislocations per cc---theory indicates that the value should be between 0.9 and 1.6×{}10^-3 dyn sec/cm², which is a relatively large damping coefficient.