The general problem of analyzing acoustic measurements of dislocation anelasticity in the presence of unknown background contributions was considered for situations where the material treatment caused changes in the physical parameters which governed dislocation motion. The approach used focused upon 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 overdamped harmonic oscillator; with no restriction on the specific inertial, damping and restoring parameters. All of the dislocations were assumed to have the same values of these parameters, so that the contributions to damping and velocity had the form of Debye functions with a single relaxation time. All of the possible combinations of relaxation strength and relaxation time were considered, and curves were obtained for the derivatives of the damping and velocity, and the incremental exponents of the frequency dependence, as a function of the product of relaxation time and measurement frequency. Additional practical curves were presented of the ratio of the derivatives of the damping and velocity as a function of the measurable frequency exponents. For a given set of measurements, approximate values of the physical parameters deduced from these graphs could be used as starting values in a least-squares minimization scheme for determining the values of the relaxation time and the relative magnitudes of changes in relaxation strength and relaxation time.

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