Although ionic conductors have been thoroughly investigated, topological features of these materials' nanotextures have been surprisingly overlooked. Here, we report fabrication of a metal-oxide nanocomposite consisting of intertwined phases of platinum (Pt) metal and oxygen-ion conductive cerium oxide (CeO2), i.e., Pt#CeO2. Sectional TEM observations coupled with topological analysis demonstrated that Pt#CeO2 composites having different nanostructures can be classified with a topological measure that corresponds to the phase connectivity of CeO2, namely, the Betti number β 0, and another that corresponds to holes of the Pt phase, namely, the Betti number β 1. The samples' oxygen ionic conductivity Pt#CeO2 was measured at elevated temperatures in air by alternating current impedance spectroscopy. It was found that the nanostructure changed from a striped appearance to a maze-like appearance as the value of β 1 / β 0 decreased. Both the activation energy E and the pre-exponential factor σ 0 for the oxygen ionic conductivity were found to be independent of β 1 and exhibited linear, negative correlations with β 0. The topological connectivity of the ion-conductive CeO2 phase, which was quantified with the Betti number β 0, was suitable as a descriptor to correlate the image data of nanostructures with their ionic transport properties.
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