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 $\overline{N}$ of dislocations per cc—theory indicates that the value should be between 0.9 and 1.6×${10}^{-3\mathrm{}}$ dyn sec/${\mathrm{cm}}^2$, which is a relatively large damping coefficient.