Dimensionality dependence of the conductivity dispersion in ionic materials

The dielectric response of many materials exhibits universal behavior in the form of a power law frequency dependence of the ac conductivity. This response is seen in all types of structures both crystalline and amorphous and for all types of polarizing species including dipoles and ions. Here I demonstrate that for ionic materials the power law exponent decreases with decreasing dimensionality of the ion conduction pathways. Although percolation concepts such as random walks on a self-similar fractal lattice provide a qualitative explanation, experimental findings instead indicate that the dispersion is the result of localized ion motion occurring on an atomic length scale.