Stochastic PAC models for vacancy motions with trapping and detrapping

In order to explain PAC data for tetragonal zirconia at temperatures between 900 and 1300oC, 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 states with equivalent electric field gradients (EFGs) of different orientations and a detrapped state with a weaker EFG whose axis of symmetry is oriented along the diagonal between the three trapped EFGs. There are three hopping 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 tetragonal zirconia data, and we report heuristic fitting functions which summarize the computer results and can be used to fit data efficiently for a wide range of parameters. This revised version was published online in August 2006 with corrections to the Cover Date.