Motion mechanisms in framework solid electrolytes: Correlated hopping and liquidlike diffusion

Motion mechanisms for ions in framework solid electrolytes are investigated. The results are obtained from numerical studies on a one-dimensional model system, utilizing the method of stochastic Langevin dynamics. We find that, for commensurate systems (for which one mobile ion occurs exactly every / lattice sites), the mechanism always involves correlated hops, and the ion-ion repulsion decreases (always) the total conductivity. For incommensurate systems, the conductivity changes from hopping to liquidlike as the interaction forces are increased to dominate the potential due to the framework lattice. Different assumed ion-ion potentials produce different correlations, both local and overall; the nearest-neighbor harmonic forces, such as are assumed in the Frenkel-Kontorova model, will generally produce substantially different correlation effects from the Coulomb repulsion. The frequency-dependent conductivity at low frequency is shown to be proportional to the square of the frequency; the proportionality coefficient is positive for correlated hopping mechanisms. A double-peaked structure in the frequency-dependent conductivity, due to local oscillation and to long-time, long-range diffusive behavior, is observed when particle-particle interactions are absent and damping is weak.