Effect of Dislocations on Ultrasonic Wave Attenuation in Metals*

Abstract

The causes of energy dissipation and mechanical instabilities of the elastic constants in metals can usually be traced to the presence of an imperfection in the crystal lattice called a dislocation. Edge dislocations are regions in the lattice where an extra plane of atoms has been added or subtracted from an otherwise perfect crystal. Such dislocations can move through the crystal under the application of shearing stresses or because of thermal agitation. It is shown that the primary causes of energy dissipation in a metal are dislocation loops pinned at irregular intervals by impurity atoms. At very low temperatures these dislocations lie along minimum energy positions but at higher temperatures they can be displaced to the next minimum energy position. In going to the next position, the dislocation meets an energy barrier determined by the energy required to overcome the limiting shearing stress T130 and the energy to stretch the dislocation. This barrier causes a relaxation effect for which the dislocations lag behind the applied stress and abstract energy from the mechanical vibrations. By measuring the position and height of the relaxation peak as a function of frequency and temperature, evidence is obtained for the value of the limiting shearing stress, the number of dislocations per square cm., and the average loop length. The values obtained agree with other methods for measuring these quantities. At higher temperatures thermal agitation causes the loops to break away from their pinning impurity atoms. In the process, it is shown that a loss occurs which is independent of frequency and amplitude but which varies exponentially with the temperature. The activation energy found agrees with the calculated value for the binding energy of an impurity atom. Dislocations also occur at the boundaries between grains in the metal and produce a peak in the measured attenuation of a polycrystal which reaches a maximum at high temperatures and low frequencies- The activation energy for this process is determined by the energy required for a vacancy to diffuse