Conductivity and ordering on the planar honeycomb lattice: A Monte Carlo study of transport and order parameters in β″ aluminas

The effects of ordering on the conductivity of carriers on a planar honeycomb lattice is studied using a modified Monte Carlo technique. The hopping model includes repulsion between carriers on nearest-neighbor sites. In agreement with previous work, we find an ordered region on the phase diagram for ion density ρ in the range 0.41≤ρ≤0.59 for sufficiently low temperatures. Within this composition range of the phase diagram, ordering effects on the conductivity and on its temperature dependence are very substantial; previous results which did not correctly include the ordering effects yield quite different conductivities. We also calculate correlation factors, diffusion coefficients, and several different kinds of order parameters. Experiments on systems such as Ba⁺⁺β″-alumina and AgCrSe₂ should be able to probe these ordered regions, and our results predict the influence of structure on the transport of the mobile ionic species in such compounds.