Vacancy and labeled-particle hopping with interactions

Classical hopping of interacting particles on a regular lattice is considered in a model where strong repulsions at the saddle point make hopping to a vacant site unfavorable unless there is another vacant site nearby. This picture may be appropriate to metal hydrides at large hydrogen concentration. Physical arguments, analytic theory, and results of simulations are presented. They show that labeled-particle motion is mean-field-like (single hopping rate given by average over distribution) but that vacancy motion takes place on two time scales—rapid motion for pairs of vacancies and much slower diffusion of vacancies which are isolated initially. This picture is in agreement with the different hopping rates in ${\mathrm{PdH}}_{\mathrm{x}}$ inferred from ultrasonic attenuation and NMR, and can explain the large prefactor anomalies seen in proton NMR. Implications for other experiments such as the Gorsky effect, quasielastic neutron scattering, and NMR of the metal nucleus are discussed.