Nuclear techniques such as perturbed angular correlation (PAC) sample the hyperfine interactions of a large number of probe atoms in specific crystallographic sites. Real crystals contain static defects producing a distribution of electric field gradients (EFGs) that add to the ideal EFG of the crystal at any given probe site. Also, dynamic defects like moving vacancies and interstitial atoms can be present in the crystal and contribute to the distribution of EFGs. The distribution of EFGs leads to line broadening and a change in the observed asymmetry parameter η since the total EFG no longer has the symmetry of the perfect crystal. When both defects are present in a material, obtaining quantitative information from the analysis of PAC spectra is usually very difficult since great care has to be taken to ensure that the source of line broadening is identified correctly. In order to relate the relationship between the static line broadening and changes in the asymmetry parameter η, a uniform random distribution of point charges was used to simulate the static defect EFG. PAC spectra collected on cubic niobium metal, cubic stabilized zirconia and Nb-doped tetragonal zirconia were fitted with this model. Although the quality of the fits is good, more work is needed to clarify the relationship between the new model parameters and the line broadening and asymmetry parameter derived from conventional model fits. The PAC spectra of Nb-doped tetragonal zirconia were fitted with a conventional static model to establish a reliable relationship between line broadening and the asymmetry parameter when only static defects are present in a sample. To account for effects of dynamic defects, a four state stochastic model for vacancy motion was adapted in order to include the line broadening and changes in the asymmetry produced by static defects. As a result, the activation energies corresponding to the rates at which a oxygen vacancy is trapped by, detraps from, and hops among equivalent sites about a PAC probe atom were calculated. The values that were found are physically reasonable, indicating that the dynamics of an oxygen vacancy around a PAC probe atom are satisfactorily described. / Graduation date: 2003