Statistical analysis of the low-temperature internal friction dislocation peak (Bordoni peak) in nanostructured copper

Abstract

The frequency-temperature relations for internal friction in nanostructured samples of Cu and of fiber composite Cu-32 vol.% Nb with structural fragment sizes of ∼200 nm are analyzed. Data from earlier experiments are used in which a Bordoni peak characteristic of highly deformed copper was found to be localized near a temperature of 90 K in the temperature dependence of the damping decrement for the oscillations (frequencies 73–350 kHz). This peak is caused by a resonance interaction of sound with a system of thermally activated relaxation oscillators, but its width is substantially greater than the width of the standard internal friction peak with a single relaxation time. The peak is analyzed statistically under the assumption that the broadening is caused by the random spread in the activation energy of the relaxation oscillators owing to strong distortions of the crystalline structure of the copper. Good agreement is obtained between the experimental data and the theory of Seeger in which the relaxation oscillators for the Bordoni peak are assumed to be thermally activated kink pairs in rectilinear segments of dislocation lines located in valleys of the Peierls potential relief. It is shown that the experimentally observed height of the peak corresponds to the presence, on the average, of one dislocation segment within a copper crystallite of size 200 nm. Empirical estimates of σP ≈ 2·107 Pa for the Peierls critical stress and ρd ≈ 1013 m−2 for the integrated density of intragrain dislocations are obtained. Nb fibers in the Cu-Nb composite facilitate the formation of nanostructured copper, but have no significant effect on the Bordoni peak.