## 3 Results and Discussion  
### Aging Dependency of the Resonance Frequencies of Reduced Ceria  
Since the aging degree of a TWC is correlated with its light-off temperature [22], and since the resonance frequency depends on catalyst temperature [6], the first series of experiments investigated the temperature dependence of the samples at different aging states in light-off experiments. At each aging state of the catalyst sample, three light-off experiments were conducted. Two runs were conducted under constant lean atmosphere of \(\lambda\) = 1.02 or under rich atmosphere at \(\lambda\) = 0.98. Starting at 80 \({}^{\circ}\)C, the temperature was increased with a constant rate heating of 20 K/min up to 600 \({}^{\circ}\)C. The third test was performed under periodical lean-rich switching between \(\lambda\) = 0.98 and 1.02 for 20 s each and a constant increase of the temperature with a rate of 10 K/min. The resonance frequencies obtained during heating for the fresh and the differently aged TWC samples are shown in Figure 2.  
At low temperatures, the resonance frequencies increase in all cases up to a maximum at about 190 \({}^{\circ}\)C followed by a decrease. Indicated by differences between the resonance frequency curves obtained from constant rich and lean feed gas as well as by the amplitudes of the air-fuel ratio oscillations, the catalysts' oxygen storage capacity is reduced with each aging step. This observation is mirrored by the calculated oxygen uptake of the sample when the step-like rich-lean changes in the feed gas are applied during heating. By integrating the excess oxygen, the amount of stored oxygen was calculated. It was based on the approach and equations reported in [23]. For that purpose, rich-lean switch were conducted. The integration started when the lambda probe signal upstream of the catalyst indicated a lean atmosphere and ended when the lambda probe downstream of the catalyst indicated lean exhausts. The results are shown in Figure 3 for samples in all three aging states. Figure 2: Resonance frequencies of a fresh and aged TWC samples at constant feed gas composition with \(\lambda\) = 1.02 (**dotted blue line**) and \(\lambda\) = 0.98 (**drawn red line**) and with alternating \(\lambda\) (**black line**) during light-off tests: (**a**) fresh sample; (**b**) aging state 1 (850 \({}^{\circ}\)C, 12 h); and (**c**) aging state 2 (1050 \({}^{\circ}\)C, additional 12 h). Besides the OSC decrease that occurs at higher temperature of some hundreds of degrees Celsius with aging, one finds an increasing OSC in the lower temperature range for both fresh and aged samples. Let us consider Figure 2 in detail. At \(\lambda=1.02\), the oxygen buffer is completely filled up, _i.e._, ceria exists in the form of Ce\({}^{4+}\). Therefore, the temperature dependency of the resonance frequency cannot be due to changes in the oxidation state of ceria. The line for \(\lambda=1.02\) can therefore be considered as a baseline, indicating the \"full\" oxygen buffer. Its temperature dependency may be explained by the volume expansion of the catalyst housing with temperature in conjunction with the increase of the electrical conductivity, as expected for an oxide semiconductor [24]. Both effects affect the resonance frequency. This has already been demonstrated in [25]. The resonance frequency differences between the curves at \(\lambda=0.98\) and \(1.02\), however, increase with increasing temperature. On the one hand, the electrical material properties, mainly the conductivity, of Ce\({}^{3+}\) are different to those of Ce\({}^{4+}\)[24]. On the other hand, the ratio of Ce\({}^{3+}\) to the total ceria amount increase with temperature at a constant feed gas \(\lambda\) of \(0.98\) resulting in a stronger decreasing curve compared to the one at \(\lambda=1.02\). In the fresh state, an additional effect can be observed in the resonance frequency plot in Figure 2a.