A brief history, starting from the caterpillar mechanism theory, was followed by a short summary of the theory of electric conduction and diffusion in both ionic and electronic mixed conductors. The cross-conductivity experiments in Ag2X (X = chalcogen) and the tracer technique for investigating the deviation from the Einstein relation were followed. In the middle part of the article, the more recently developed theoretical works on the electronic states of noble metal halides and alkali halides were given. These theoretical works have brought more microscopic evidence for the p–d hybridization in noble metal halides. Causality, stability and fractal were fundamental concepts in condensed matter physics. Next, investigations on a causality breaking found in ionic materials were followed. Design studies of new materials with functions such as high ionic conductivity or high diffusion coefficient were introduced.

From Caterpillar Model to Solid-State Ionics. M.Kobayashi: Solid State Ionics, 2004, 174[1-4], 57-66