Impedance fitting

Figure C.3. Comparison of experimental impedance and impedance calculated using K-K relations for a UNS S31254 SS/diethylamine system at 0.840 V (SCE) and 25°C [11], (Reproduced from Polo JL, Cano E, Kong DY, Bastidas JM. Impedance fitting of 254SMO and AISI304 stainless steels under pitting conditions. Corrosion 2002 58(8) 670-4. With permission from the National Association of Corrosion Engineers.)...

The limiting equivalent circuit may be directly applied in analysis of power source performance because the direct-current response, which corresponds to the zero-frequency limit of the impedance spectrum, is of most importance. Conversion of Eqs (8) and (9) allow one to find the ohmic characteristics of a given power source at direct current. They also allow one to obtain a close initial guess for impedance fitting of the equivalent circuit by direct observation of the impedance plot. Ra will... 

Table 9-16. Impedance fit parameters of carbon steel in the presence of different inhibitor mixtures (two-time-constant transfer function).

It should be noted, though that defective semiconductors - for instance oxide layers on metals - typically do not show an ideal capacitive behavior which often leads to a strong frequency-dependence of the capacitance. There are many possible reasons for non-ideal behavior such as ionic participation , a frequency-dependent dielectric constant, contributions from the Helmoltz-layer or from surface states, non-ideal structure or nonideal donor distribution, as well as inhomogeneous depth distribution in the composition or structure of the oxide layer. Independent of the origin of the non-ideal behavior, the frequency dispersion can partially be corrected by replacing the capacitance in impedance fits by a so-called constant phase element (CPE), which takes into consideration the non-ideal nature of a capacitance. While the introduction of CPE may eliminate the... 

For large feeders and FIT system.s the ground fault current would be controlled naturally through the ground circuit impedance and a smaller ground conductor may suftlce. 

External events are accident initiators that do not fit well into the central PSA structure used for "internal events." Some "external events" such as fire due to ignition of electrical wires, or flood from a ruptured service water pipe occur inside the plant. Others, such as earthquakes and tornados, occur outside of the plant. Either may cause failures in a plant like internal events. External initiators may cause multiple failures of independent equipment thereby preventing action of presumably redundant protection systems. For example, severe offsite flooding may fli 1 the pump room and disable cooling systems. An earthquake may impede evacuation of the nearby populace. These multiple effects must be considered in the analysis of the effects of external events. 

Normally, the impedance plots are fitted to an often-complex equivalent circuit. Mathematically, this means searching for a global solution in R". However, problems arise if a complicated equivalent circuit is found which does not allow physical interpretation. Therefore, it is preferable to run a wide variety of experiments with different samples rather than trying to fit in detail the results of a single measurement in order to analyze the resulting impedance plots. 

Carbon monoxide seriously impedes transport of oxygen. The deadly effect of inhaled CO results from its reaction with hemoglobin. A CO molecule is almost the same size and shape as O2, so it fits into the binding pocket of the hemoglobin molecule. In addition, the carbon atom of CO forms a stronger bond to than does O2. Under... 

The capacitance of the cluster was calculated from a fit of the experimental data at 90 K to be 3.9 x 10 F. This value, which is very sensitive toward residual charges and nearby background charges, is close to the value of the microscopic capacitance, which was determined earlier by temperature-dependent impedance measurements [21]. Furthermore these results are found to be in good agreement with the capacitance data obtained on the above-mentioned gold nanoclusters on a XYL-modified Au(l 1 1) surface [13,22]. 

The impedance data were fitted to candidate electrical circuits using the non-linear weighted least-squares fitting program "EQIVCT" developed by Boukamp ( ). Graphical analysis was utilized to furnish reasonable first guesses of the circuit parameters for input to EQIVCT. 

We found an equivalent electrical circuit that fits best the LixC6 electrode behavior at high frequency. The circuit consists of a resistor R in parallel with a constant phase element (CPE). The latter is defined with a pseudo-capacitance Q and a parameter a with 0< a <1 [6], The impedance of... 

While it is convenient to use a standard cryostat, the cell has to be fitted in the sample space of the cryostat and the leads to the cell are usually fairly long - a specific draw-back for impedance measurements. Another disadvantage is the long cool-down times of these systems which may not allow one to rapidly freeze the electrolyte. However, for experiments not requiring sophisticated electrochemical experimentation this may be the most convenient experimental set-up. 

The technique of constructing an equivalent circuit for impedance analysis represents the exception to the general rule that a chosen model can be almost certain to be correct. It is all too easy to compile an equivalent circuit which fits the impedance data, but is altogether wrong. In fact, many practitioners would say that impedance studies are so susceptible to this fitting to a bogus model that another technique should always be applied as a form of validation . It is much more unlikely for two techniques to fit a particular model, and the latter still be wrong ... 

Figure 10.2 shows data, both experimental and simulated, for hexacyanofer-rate(ii) ion at a gold disc electrode. The Warburg line at 45° indicates a diffusion process (see Section 8.2.2). The continuous line represents impedance data simulated by the Eco Chimie GPES software (as described below). Here, the fit between theory and experiment is seen to be very good. 

As expected, the impedance responses obtained in practice do not fully match that of the model of Fig. 9.13. However, as shown by the typical case of Fig. 9.14 which illustrates the response obtained for a 5 mol% ClO -doped polypyrrole electrode in contact with a LiC104-propylene carbonate solution (Panero et al, 1989), the trend is still reasonably close enough to the idealised one to allow (possibly with the help of fitting programmes) the determination of the relevant kinetics parameters, such as the charge transfer resistance, the double-layer capacitance and the diffusion coefficient. 

Figure 26. Predictions of the Adler model shown in Figure 25 assuming interfacial electrochemical kinetics are fast, (a) Predicted steady-state profile of the oxygen vacancy concentration ( ) in the mixed conductor as a function of distance from the electrode/electrolyte interface, (b) Predicted impedance, (c) Measured impedance of Lao.6Cao.4Feo.8-Coo.203-(5 electrodes on SDC at 700 °C in air, fit to the model shown in b using nonlinear complex least squares. Data are from ref 171.

However, as we saw in section 3.3 for platinum on YSZ, the fact that i—rj data fits a Butler—Volmer expression does not necessarily indicate that the electrode is limited by interfacial electrochemical kinetics. Supporting this point is a series of papers published by Svensson et al., who modeled the current—overpotential i—rj) characteristics of porous mixed-conducting electrodes. As shown in Figure 28a, these models take a similar mechanistic approach as the Adler model but consider additional physics (surface adsorption and transport) and forego time dependence (required to predict impedance) in order to solve for the full nonlinear i—rj characteristics at steady state. 

---