Superionic Conductors : The Independent Particle Model

Abstract

In parallel with the revived interest of experimental physics in fast ionic conductors [1](superionic conductors) there has been renewed interest in the theoretical aspects of this phenomenon. Basically one is dealing thereby with systems in which one species of atoms is in a liquid like state while the other forms a lattice which acts like a periodic potential on the ionic liquid. An example is AgI. Here a phase transition takes place at T=146°C above which the Ag-lattice is molten while the I-lattice still persists. From a theoretical point of view the dynamical behaviour of the ionic liquid in the potential of the remaining lattice is of particular interest. It shows diffusive as well as oscillatory features and it is of considerable interest to describe both in a unified way. The simplest model which one can apply for such a description is that of independent ions moving through the periodic potential. This constitutes certainly a severe approximation since one expects collective or interaction effects among the ions of the molten lattice to become important for small frequencies e.g. ω < 10 cm⁻¹. An indication for this is the appearance of considerable structure in the low frequency response of superionic conductors such as AgI in the microwave regime [2].