Results And Discussion

In the three-electrode configuration, a simplified equivalent circuit of the sample and the 1260 FRA is shown in Figure 1. The quantity of interest is Zwe> the true working electrode impedance. Analysis of the circuit shows, however, that the apparent impedance measured by the instrument is not simply Because of the voltage divider effect,

* Operated by Battelle Memorial Institute for the U.S. Department of Energy under contract DE-ACOÖ-76RLO 1830

where Z„r is the reference electrode impedance and Zinput is the input impedance of the instrument. When reference electrode impedance is substantial in relation to the input impedance of the instrument, the magnitude of the apparent impedance will be smaller than the true working electrode impedance. Because this distortion is complex in nature, phase shifts may be introduced in addition to changes in gain.

Since distortions occur when reference electrode impedance is non-negligible in relation to the input impedance of the machine, it is important to know both quantities. The input impedance of the analyzer can be obtained from the manufacturer. For the Solartron 1260 FRA, it is approximately 1 Mi2 resistance in parallel with a 35 pF capacitance. External attachments and cabling may increase this input capacitance. Since error gradually increases as reference electrode impedance approaches the instrument input impedance, one needs to define an acceptable tolerance. Conveniently, an acceptable error of 1% corresponds to tolerable reference electrode impedance of approximately 1% the input impedance. Alternatively stated, when reference electrode impedance reaches 1% of the input impedance, measured data will be in error from the true value by approximately 1%. For the 1260 FRA, this 1% tolerable threshold is plotted as the dotted line in Figure 2. At frequencies where reference electrode impedance exceeds this threshold, the measurement is in error by more than 1%. The impedances of the silver and the platinum reference electrodes used in this experiment are also plotted in Figure 2. They were obtained through the procedure outlined by Lagos et al, which allows the determination of individual electrode impedances (6).

Note the response of the reference electrodes can be approximated by an equivalent circuit consisting of a charge transfer resistance R« in parallel with a double layer capacitance Cdh both of which are in series with a contact spreading resistance Rj. Whereas R^ and CdI, which determine the lower frequency response of the electrode, are very dependent on electrode material, the contact resistance R,. determining the high frequency response is more influenced by electrolyte conductivity and contact size. The inverse relationship between R* and electrolyte conductivity has already been established by Newman (7). Through this spreading resistance, electrolyte conductivity enters into consideration when impedance responses at higher frequencies are of interest. In this experiment, the silver reference has lower spreading resistance because it deforms much more easily than platinum at 570°C and forms a larger contact. Because of the input capacitance in the instrument, the reference electrode impedance eventually exceeds the tolerable threshold at high frequencies, and distortions inevitably occur in the apparent spectra.

As shown in Figure 2, the platinum reference electrode impedance exceeds the threshold level at all frequencies. Thus, according to the voltage divider equation above, it is to be expected that apparent impedance measured with this platinum reference electrode will be in substantial error. It will be much smaller than the true working electrode impedance. Since the impedance of this platinum reference is almost half of the input impedance of the instrument at frequencies where the working electrode arc appears, the magnitude of the apparent impedance is expected to be only 2/3 of the true value. This is in fact what is observed experimentally, as shown in Figure 3. No phase shift was observed. Note that the high frequency intercepts have been shifted along Z' to facilitate comparison. In contrast, the impedance of the silver reference electrode is much lower at the same frequencies, below the tolerable level. Correspondingly, the apparent impedance accurately reflects the true working electrode impedance. Note that there are no tell-tale signs in the platinum reference data that a significant distortion is occurring. Without knowledge of the reference electrode impedance or comparison with the true impedance, data obtained with the platinum reference electrode would appear reasonably correct, however inaccurate, in all aspects.

Although not shown, the high frequency portion of both apparent spectra exhibits an extra capacitive arc above lOOKHz. This is also an artifact generated by the voltage divider effect. This distortion modifies the phase angle as well as gain. At this temperature, both the bulk feature and the grain boundary feature of zirconia exist at substantially higher frequencies than the capabilities of the instrument.

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