A stochastic Langevin dynamics study of correlated ionic motion in one dimensional solid electrolytes

The motion of mobile ions in one dimensional ionic conductors is described by stochastic Langevin dynamics. The interactions of the mobile ions with the framework lattice are approximated by a sum of periodic and random potentials, yielding a set of coupled Langevin equations, which are then solved numerically. The parameters in these phenomenological equations of motion include the potential in which the ion moves and the lattice temperature. Correlated motion is considered by including long range (Coulombic) and short range potentials among the mobile ions. Inclusion of these potentials incalculations describing systems with an integral ratio of total sites to mobile ions (commensuratestoichiometry) shifts the frequency dependent conductivity (increase of maximum frequency, decrease of dc conductivity) in a manner indicating that the mobile ions are driven towards their equilibrium positions. The conductivity then decreases with increasing effective charge. However, when the carrier/site ratio is not integral (incommensurate stoichiometry, e.g., potassium hollandite) the long range ion-ion interaction drives the mobile ions into arrays which are distorted near the vacancies. This lowers the effective potential barrier, and therefore is responsible for increasing the calculated diffusion coefficient and conductivity. As the strength of the ion-ion interactions is increased this cooperative behavior is enhanced. The results for potassium hollandite are in good agreement with x-ray scattering data.