Frequency Dependence of Dislocation Damping in Single-Crystal Copper

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Abstract
The frequency dependence of the amplitude-independent and amplitude-dependent dislocation damping was measured on the same high-purity copper single crystal in both the kilocycle and megacycle frequency ranges. The dislocation contribution to the elastic modulus was also measured in the kilocycle range. The results are discussed in terms of a theoretical calculation which treats the dislocation as a pinned elastic string which experiences a viscous drag proportional to its velocity. The kilocycle dislocation damping exhibited an approximately linear frequency dependence; however, a somewhat better fit to the data can be made with a relation of the form Δ=αω−1+βω. It is proposed that the term αω−1 is a contribution from the high-frequency side of a low-frequency dislocation damping maximum. The dislocation damping in the megacycle range was proportional to ω−1. The kilocycle and megacycle data are consistent with a curve of the form Δ=K[ωτ/(1+ω2τ2)] (except at the lower kilocycle frequencies measured), as predicted by the string model. The maximum is at 1.7 Mc/sec. Based on the agreement of the data with the theoretical model, the dislocation density is calculated to be 1.1×106 cm−2 and the average loop length to be 5.7×10−4 cm, assuming an exponential loop-length distribution. The modulus defect was found to be independent of frequency, except for a possible small rise with decreasing frequency below 30 kc/sec. The amplitude-dependent internal friction of the specimen in the kilocycle range was found to be frequency dependent in the annealed state and to be frequency independent in the irradiated state. The strain amplitude above which the specimen exhibited amplitude dependence was observed to increase with frequency in the kilocycle range.