Impedance brick layer model

Hence, 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... 

It is particularly interesting to test whether an analysis of a conventional macroscopic impedance measurement based on a brick layer model leads to the same results as obtained with microcontacts. The relaxation frequency of the grain boundary arc measured in the conventional impedance experiment (1.2 Hz) is similar to the mean value (3.0 Hz) deduced from the microelectrode experiments, although not identical. One possible reason for the moderate discrepancy is the inaccuracy with respect to the temperature measurement, which is somewhat difficult in the case of the microelectrode set-up. A temperature error of about 20 K could already explain the difference. 

It is worth comparing these locally obtained values with the effective conductivity creff of the same sample measured in a conventional setup. A measurement with macrosopic electrodes yields one semicircle in the complex impedance plane and an effective conductivity of 42 10 9 ft 1 cm-1. According to the brick layer model for... 

Choice of appropriate model IS is not a technique that can or should be apphed without prior knowledge of the system. Impedance spectra must be interpreted in the context of a model, be this a simple brick-layer model for a ceramic, or an advanced one based on electrode kinetics. When used in conjunction with electron microscopy, IS provides information about structure, and especially grain boundary structure. The microstructural information and the models derived from this are what make the conclusions of IS unequivocal. 

Impedance spectroscopy has been a useful tool for separating the grain-interior and grain-boundaiy contributions in many electroceramics. [48,49] In most analyses, the brick layer model, which assumes electrically and dimensionally homogeneous grain and grain boimdary, was used. [7,13,24-26] (Fig.3(b)) However, the distribution of the and Pgh values can become spatially uneven for the specimens under an electric field [50-53] or with a functionally graded composition. [54]... 

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