Low frequency component of the internal friction of single crystal copper and its relation to the Bordoni peak

Abstract

The internal friction of a face-centered metal such as copper, measured at low strain amplitudes, can by divided into a low frequency region and a high frequency region. Available data shows that in the low frequency region, the internal friction is nearly independent of the frequency and decreases to very small values at low temperatures. The internal friction and the modulus change, caused by neutron irradiation, can be analyzed to show that the low frequency region is caused by a series of relaxation processes having activition energies from 300 cal/mole to 10,000 cal/mole. Such a range of activition energies results if it is assumed that most dislocations lie originally along minimum energy positions and are displaced from these positions by thermal agitation. This proceeds by nucleation of Seeger type loops and results in impurity pinning for a large number of thermally displaced loops. It is shown that loops crossing n 1 + n 2 minimum energy positions will be more stable if part of the loop crosses the Peierl's energy barriers at a critical angle of 0.8° for screws and 0.22° for mixed dislocations in copper while the rest of the loop lies in minimum energy positions. This part of the loop can be displaced to any one of the n 1 + n 2 minimum energy positions without changing the total energy. Each time this type of segment moves from one well to another one it has to cross a Peierl's barrier. The activation energy of his segment motion depends on the length of the segment in the minimum energy position and the height of the Peierl's barrier. It is shown that this mechanism can account for the wide range of activation energies found experimentally. Assuming a reasonable dislocation number and loop length distribution, the background internal friction and modulus change can be accounted for quantitatively. When a polycrystal is permanently strained by a few per cent, an internal friction peak known as the Bordoni peak appears. According to the present theory this is due to the nucleating loop but the magnitude is larger than that for the Seeger theory on account of the multiple well model. The model agrees quantitatively with the measured results.