Using Blume's stochastic theory and the approach of Winkler and Gerdau,
time-dependent effects on perturbed angular correlation (PAC) spectra
due to defect motion in solids in the case of I = 5/2 electric
quadrupole interactions have been calculated. Detailed analysis for
several models, namely, N-state + Z (N = 3, 4, 6), XYZ + S(theta, phi),
and XYZ(eta_{f }) + Z(eta_{s}) models are reported
... [Show full abstract] here. The influence
on the perturbation function G_2(t) of the number of fluctuating
electric field gradient (EFG) states (N), the relative static EFG
strength ( gamma), the orientation of the symmetry axis of the static
EFG versus the fluctuating EFG ( theta, phi), and the asymmetry of the
EFGs (eta_{f}, eta _{s}) are studied. A large non -Hermitian complex
matrix (Blume matrix, B) has been solved for each of the above models.
Its eigenvalues have real parts and imaginary parts corresponding to the
damping factors and the frequencies in G_2(t), respectively. Damping and
static frequencies in G _2(t) have been observed in both slow and rapid
fluctuation regimes, i.e. suitable for the low and high temperature
regions, respectively. In the intermediate fluctuation regime, complex
behaviors of the damping factors and frequencies are observed due to the
mixing of the fluctuating EFG states. Approximate forms are given for G
_2(t) in the slow and rapid fluctuation regimes which cover a wide range
of temperatures and contain the most interesting physics. These
expressions allow one to fit PAC data for a wide range of temperatures
and dopant concentrations. An application of the 4-state symmetric model
is illustrated with data from a PAC study of ceria.