Materials science and electrochemical systems of practical interest

3 Materials science and electrochemical systems of practical interest 

Solid state materials that can conduct electricity, are electrochemically of interest with a view to (a) the conduction mechanism, (b) the properties of the electrical double layer inside a solid electrolyte or semiconductor, adjacent to an interface with a metallic conductor or a liquid electrolyte, (c) charge-transfer processes at such interfaces, (d) their possible application in systems of practical interest, e.g. batteries, fuel cells, electrolysis cells, and (e) improvement of their operation in these applications by modifications of the electrode surface, etc. 

In studies of these and other items, the impedance method is often invoked because of the diagnostic value of complex impedance or admittance plots, determined in an extremely wide frequency range (typically from 104 Hz down to 10 2 or 10 3 Hz). The data contained in these plots are analyzed by fitting them to equivalent circuits constructed of simple elements like resistances, capacitors, Warburg impedances or transmission line networks [101, 102]. Frequently, the complete equivalent circuit is a network made of sub-circuits, each with its own characteristic relaxation time or its own frequency spectrum. 

Although this approach is valuable in a qualitative sense, it is not always recognized that the method is not unambiguous. For example, the three networks represented in Fig. 28 will yield exactly the same frequency spectrum of Z and Z [102] if the relations quoted in the legend hold 

A more trivial point is the question of whether impedance measurements on such complex systems at extremely low frequencies do make sense. At 10 3 Hz, one period of a sine wave lasts more than 16 min, long enough for trivial or essential changes in system properties to occur. Such changes can be due to the perturbation, but can also be the result of, for example, recrystallization or progressive contamination of the interface. 

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