Dislocation Contributions to the Modulus and Damping in Copper at Megacycle Frequencies

Abstract

The three elastic moduli of 99.999+% pure copper and their associated internal frictions have been measured at Mc frequencies between 4.2 and 250°K both before and after fast neutron bombardment. The changes produced by the irradiation were used to determine the dislocation contributions to the damping and moduli as a function of frequency and temperature. The dislocation damping showed the maximum predicted by Granato and Lücke to arise from the heavily damped bowing of dislocation loops. By calculating the resolved shear stress factors and measuring the dislocation density by etch pit counts, it was possible to determine the coefficient B which describes the viscous drag on a moving dislocation as well as the effective loop length l. The factor B was found to be 8×10−4 d sec/cm2 at 300°K and to decrease linearly with decreasing temperature, as predicted by Leibfried. The effective loop length appeared temperature independent and had a value of 3×10−4 cm in the sample examined most carefully. Cold-worked single crystals of the same copper were also studied. Two Bordoni type peaks in the damping vs temperature curves were located at 135 and 60°K at 10 Mc. Activation energies of 0.113 and 0.05 ev were determined by using low-frequency data taken from the literature.

Dislocation mobility in copper and zinc at 44°K

“…The current results in copper agree with those of indirect measurements which indicated that the drag _ coefficient is a decreasing function of temperature (8). The measurements in both copper and zinc at 44°K are supportive of a model for dislocation damping based on a dissipative force decreasing in magnitude as temperature is lowered.…”

Solitonic-exchange mechanism of surface diffusion

“…17 In our analysis, we treat m kink and ␣ as adjustable parameters. They are chosen by fitting with Eq.…”

A nonequilibrium irreversible thermodynamics model for material damping

“…11 in Alers and Thompson, 1961); while for well-anneal copper, relaxation time is about 0.067 ls at room temperature 300 K (Fig. 6 in Alers and Thompson, 1961). For polycrystalline aluminum, relaxation times of viscous slip of grain boundaries vary from about 2.5 ls at 600°C to 0.18 s at 285°C (estimated from Eq.…”

“…For example, for cold-worked copper, viscous relaxation times for dislocation motion vary from about 0.01 s at 65 K to 0.1 ls at 135 K ( Fig. 11 in Alers and Thompson, 1961); while for well-anneal copper, relaxation time is about 0.067 ls at room temperature 300 K (Fig. 6 in Alers and Thompson, 1961).…”