The ac conductivity spectrum local motions and long range conduction

9 The ac conductivity spectrum local motions and long range conduction 

In materials that have high ionic conductivity, effects such as the above are undoubtedly very important. They show up particularly in materials that have a high concentration of mobile ions and in experimental values of the ac conductivity measured as a function of frequency. In materials with a high carrier concentration, mobile ions are inevitably quite close together, separated by at most a few angstroms. Consequently, ions cannot hop in isolation but are influenced by the distribution of mobile ions in their vicinity. This contrasts with the behaviour of dilute defect systems with low carrier concentrations. In these, the mobile ions are well separated from each other and their conduction can largely be treated in terms of isolated hops. 

Various theoretical attempts have been made to provide a quantitative interpretation of the dispersion region (Funke, 1986 Funke and Hoppe, 1990). While the situation is still not fully resolved, it is now clear that such a dispersion, which has been observed in a wide range of crystalline as well as glassy ionic conductors, is associated with ion-ion relaxation effects. The conductivity dispersion, ff(co), is usually linear in a plot of log a vs log CO, which means that it can be represented by a power law expression  

This behaviour is one example of a wide range of phenomena which are manifestations of Jonscher s Universal Law of Dielectric Response (Jonscher, 1977, 1983). 

We earlier defined the hopping rate parameter, cOp. It corresponds approximately to the frequency at which the conductivity dispersion commences, arrowed in Fig. 2.8. 

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