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Analysis of Anelastic Dislocation Effects in the Presence of an Unknown Background



Ward L. Johnson


The general problem of analyzin- acoustic measurements of dislocation anelasticity in the presence of unknown background contributions is addressed for situations where material treatments induce changes in the physical parameters governing dislocation motion. The analytical approach focuses on the derivatives of the frequency-dependent acoustic damping and velocity with respect to single experimental variable, such as irradiation flux, annealing time, or applied stress. The equation of dislocation motion is taken to that of an overdamped harmonic oscillator with no restrictions on the specific physical model for the inertial, damping, and restoring parameters. The problem is simplified by considering all dislocations in a specimen to have the same values of these parameters, so that the contributions to the damping and velocity have the general form of Debye functions with a single relaxation time. All possiblecombinations of changing relaxation time and relaxation strength are considered, and curves of the derivatives and incremental exponents of the frequency dependence as a function of the product of the relaxation time and measurement frequency are presented. Since the relaxation time is not directly measurable, additional practical curves are presented of the ratio of derivatives of the dampingand velocity versus the measurable frequency exponents. For a given set of measurements, approximate values of physical parameters determined from inspection of these graphs can be used as initial guesses in a least-squares minimization. Two examples of data from the published literature are used to illustrate the method of analysis.
Physical Review B (Condensed Matter and Materials Physics)
No. 6


acoustics, anelasticity, dislocations, internal friction


Johnson, W. (2003), Analysis of Anelastic Dislocation Effects in the Presence of an Unknown Background, Physical Review B (Condensed Matter and Materials Physics), [online], (Accessed July 18, 2024)


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Created August 12, 2003, Updated June 2, 2021