1.1 Electrochemical impedance spectroscopy Impedance spectroscopy and frequency response analysis are powerful tools for investigating the electrical properties of electroceramic materials and devices. The first investigations into the frequency dependency of material properties as the dielectric polarization date back to the 19th century. The concept of determining the resistance of an electrolyte by AC-measurements, to eliminate the impact of electrode polarization, was first discussed in 1869. 1) The related challenges in the evaluation of resistances by AC-measurements have been summarized in. 2) Since that time we have also seen the development of the theoretical background of equivalent circuits, 3) as well as the analysis of polarizable and non-polarizable electrodes by AC-methods, including models to describe their electrical behavior. 4) AC-measurements became more and more popular for the analysis of materials and electrodes in the following decades. Milestones include: the work of Cole and Cole, who analyzed dispersion and absorption in dielectrics by alternating current measurements5) and suggested the Cole-Cole plot as a graphical tool for analyzing impedance data, the analysis of the impedance of galvanic cells by Sluyters6) as well as the investigations of the polarization in solid zirconia electrolytes by Bauerle, 7) who proved in his work that AC-measurements are useful for ceramic materials applied in batteries and fuel cells. While the impedance in all previously cited papers was measured with homemade setups, the introduction of frequency response analyzers in the 1970 s and software for impedance data analysis8), 9) dramatically increased the application of impedance spectroscopy (Fig. 1).

A review on the history of impedance spectroscopy is given in. 10) The theory and many practical hints are discussed in the books of Macdonald, 11), 12) Orazem13) and Lasia. 14) For a proper analysis of impedance spectra, including the distribution of relaxation times as discussed in the next chapters, any kind of error in the spectra should be carefully avoided. It is therefore recommended to follow the advice given in the chapters on impedance measurements, wiring of samples and errors in the above mentioned books, as well as in the manuals of the applied equipment. Furthermore, the testing of the validity of measured spectra is indispensable. Algorithms based on the Kramers-Kronig relation enable a detection of errors in the spectra. 15), 16) Appropriate software tools are available. 17)