Stochastic PAC models for vacancy motions with trapping and detrapping

In order to explain PAC data for tetragonal zirconia at temperatures betwee n 900 and 1300 degrees C, we have developed a four-state stochastic model. The model simulates vacancies which trap and detrap at a PAC probe nucleus. While trapped, the vacancies hop around the probe in equivalent sites. The four states in this Winkler-Gerdau stochastic theory are three trapped sta tes with equivalent electric field gradients (EFGs) of different orientatio ns and a detrapped state with a weaker EFG whose axis of symmetry is orient ed along the diagonal between the three trapped EFGs. There are three hoppi ng rates in this model: w, the rate a trapped vacancy hops around the probe , w(d), the detrapping rate, and w(t), the trapping rate. We report results of calculations for values of these hopping rates implied by our tetragona l zirconia data, and we report heuristic fitting functions which summarize the computer results and can be used to fit data efficiently for a wide ran ge of parameters.