Impedance Spectroscopy in Solid State Ionics

Conventional two-electrode dc measurements on ceramics only yield conductivities that are averaged over contributions of bulk, grain boundaries and electrodes. Experimental techniques are therefore required to split the total sample resistance Rtot into its individual contributions. Four-point dc measurements using different electrodes for current supply and voltage measurement can, for example, be applied to avoid the influence of electrode resistances. In 1969 Bauerle [197] showed that impedance spectroscopy (i.e. frequency-dependent ac resistance measurements) facilitates a differentiation between bulk, grain boundary and electrode resistances in doped ZrC 2 samples. Since that time, this technique has become common in the field of solid state ionics and today it is probably the most important tool for investigating electrical transport in and electrochemical properties of ionic solids. Impedance spectroscopy is also widely used in liquid electrochemistry and reviews on this technique be found in Refs. [198 201], In this section, just some basic aspects of impedance spectroscopic studies in solid state ionics are discussed. 

Different kinds of plots based on impedance Z, admittance Z 1, modulus icoZ, or complex capacitance (z coZ) 1 can be used to display impedance data. In solid state ionics, particularly plots in the complex impedance plane (real versus imaginary part of Z) and impedance Bode-plots (log(Z) log(co)) are common. A RC element (resistor in parallel with a capacitor) has, for example, an impedance according to 

The frequency at which the currents via the resistor and the capacitor are equal and the imaginary part of the impedance reaches its maximum is the characteristic frequency cor (relaxation frequency) of a RC element. It is given by 

in simple cases each bulk layer, each grain boundary plane, and both electrodes of the brick layer model sample, can be represented by separate RC elements (Fig. 7b). The RC elements of the n bulk layers can be combined to a single RC element with the -fold resistance and the 1 / -fold capacitance of a single layer. The n — 1 grain boundary impedances can also be summed, as can the two electrode impedances, and hence the model sample corresponds to a series connection of three RC elements (Fig. 7c) with 

In experimental impedance spectroscopic studies, however, several factors may complicate the interpretation of the spectra and a few of these complications will briefly be touched upon i) If high conductivities are considered (a 10-3 S cm-1), then the corresponding relaxation frequencies are well above the measurement range of a conventional impedance set-up (frequencies up to ca. 10 MHz). Hence, processes with high conductivites cannot be separated by conventional impedance spectroscopy. ii) The assumption of a quasi-one-dimensional current flow, which is the basis of the above presented brick layer model, is often violated [203, 211-214]. Some complications due to multi-dimensional potential distributions will be discussed in Sec. 3.2.1. iii) Highly conductive regions perpendicular to the electrodes (e.g. highly 

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Boukamp BA (2004) Electrochemical impedance spectroscopy in solid state ionics recent advances. Solid State Ionics 169(1—4) 65—73... 

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