Simple atomic hopping among inequivalent octahedral sites in a body-centered tetragonal lattice

Using a formalism developed earlier, we obtain expressions for the frequency-dependent site occupation and distinguishable particle correlation functions for a system of atoms hopping among inequivalent sites in a three-dimensional lattice. Our model includes several different hopping rates and may qualitatively describe phenomena occurring in some transition-metal hydrides (or deuterides) in condensed phases or in some superionic conductors where more than one type of site is important. Specifically, our model describes the hopping of atoms among the octahedral sites of a body-centered tetragonal lattice with the sites along the $c$ axis taken to be preferentially occupied. (This configuration is one possibility suggested for a $\beta$ phase of vanadium hydride and deuteride.) The correlation functions obtained can be measured directly in inelasticneutron-scattering experiments. We have also made quantitatively crude estimates of $T_1$ appropriate to NMR experiments on the hopping atoms. Depending on the ratios of the various hopping rates, we find that our model is capable of describing a quadrupolar induced $T_1$ with a frequency-independent minimum as well as a dipolar induced $T_1$ with considerable structure including apparent (but not actual) changes in an activation energy.