Quantitative analysis of damping and modulus effects in copper crystals using the ``vibrating-string'' dislocation model

Abstract

Internal friction and modulus measurements were made between 13 and 38 kHz as a function of temperature on several copper crystals into which a low density (∼ 10⁵–10⁶ cm⁻²) of dislocations had been introduced by deformation in compression. The dislocation contributions to damping and modulus defect were determined by comparison with duplicate measurements made after the dislocations had been immobilized by irradiation. Dislocation densities were evaluated by etch‐pit counting, and as a result enough information was obtained to determine absolute values for the loop length and drag coefficient in the vibrating‐string (Koehler/Granato‐Lücke) model of dislocation damping. The loop length was found to have appreciable temperature dependence and the drag coefficient was found to be higher by a factor of ∼ 15–∼65 than values obtained for copper by MHz damping and dislocation velocity measurements. Similar results were obtained in several samples and it is noted that the measured damping and modulus values are not greatly different from those obtained by other experiments. It thus appears that for the kHz frequency range in pure copper crystals basic elements of the string model require revision.