The general problem of analyzing acoustic measurements of dislocation anelasticity in the presence of unknown background contributions was addressed for situations where material treatments induced 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 a single experimental variable, such as irradiation flux, annealing time, or applied stress. The equation of dislocation motion was taken to be that of an over-damped harmonic oscillator with no restrictions on the specific physical model for the inertial, damping, and restoring parameters. The problem was 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. Although the subsequent discussion remains focused on dislocations, the analytical approach was framed in such general terms that it could be applied to any relaxation or over-damped resonance having a Debye form. All possible combinations of changing relaxation strength and relaxation time were considered, and curves of the derivatives of the damping and velocity and the incremental exponents of the frequency dependence as a function of the product of the relaxation time and measurement frequency were presented. Since values for the abscissa in these plots could not be directly measured in an experiment, additional practical curves were presented of the ratio of derivatives of the damping and velocity versus the measurable frequency exponents. For a given set of measurements, approximate values of physical parameters determined from inspection of these graphs could be used as initial guesses in a least-squares minimization to determine values of the relaxation time and the relative magnitude of changes in relaxation strength and relaxation time. Two examples of data from the published literature were used to illustrate the method of analysis.

Analysis of Anelastic Dislocation Effects in the Presence of an Unknown Background. W.L.Johnson: Physical Review B, 2003, 68[6], 064108 (11pp)