## 3 Results and Discussion
### Characteristics of CeO\({}_{2}\) Nanomaterials
The surface oxygen reduction temperatures of the irregular nanoparticles and nanorods were significantly lower than that of the nanocubes. Such a result indicates that the irregular nanoparticles and nanorods possessed better activity at low temperatures as compared to the nanocubes. Furthermore, a very small amount of H\({}_{2}\) was consumed during the surface oxygen reduction for the nanocubes, which may be due to the extremely small surface areas exhibited by the nanocubes that resulted in the smaller amount of surface adsorbed oxygen. Interestingly, 12 MCeO\({}_{2}\)nr and 12 MCeO\({}_{2}\)nc possessed more active bulk oxygen due to their lower bulk oxygen reduction temperature than the same morphologies of 6 MCeO\({}_{2}\)nr and 6 MCeO\({}_{2}\)nc samples, respectively, which makes them more promising as DMMP thermocatalytic catalysts. This is confirmed later in the mechanism discussion section that DMMP is decomposed on CeO\({}_{2}\) mainly by the recycling between consuming surface oxygen and replenishment of bulk oxygen and the external oxygen. Therefore, the more active the bulk oxygen is, the more beneficial it is to the transfer of oxygen on CeO\({}_{2}\). Figure 2: TEM images of CeO\({}_{2}\) nanomaterials (**a**) 6 MCeO\({}_{2}\)nr, (**b**) 12 MCeO\({}_{2}\)nr, (**c**) 6 MCeO\({}_{2}\)nc, (**d**) 12 MCeO\({}_{2}\)nc, and (**e**) 2 MCeO\({}_{2}\)np. The scalebar is 100 nm and the insets show the length distribution histograms (28 nanoparticles were measured for each histogram by Nano Measurer software v1.2.5); (**f**) mean length distribution diagram of CeO\({}_{2}\)nr, CeO\({}_{2}\)nc, and CeO\({}_{2}\)np calculated from the length distribution histograms. Oxidation state of Ce and the nature of the surface oxygen species were characterized by X-ray photoelectron spectroscopy (Figure 4). The Ce 3d XPS spectra of the as-prepared CeO\({}_{2}\) nanomaterials consisted of two main peaks (V\({}_{0}\), V) and three satellite peaks (V\({}^{\prime}\), V\({}^{\prime\prime}\), V\({}^{\prime\prime}\)) that can be ascribed to Ce3d\({}_{5/2}\), and the remaining two main peaks (U\({}_{0}\), U) and three satellite peaks (U\({}^{\prime}\), U\({}^{\prime\prime}\), U\({}^{\prime\prime}\)) that can be ascribed to Ce3d\({}_{5/2}\). The binding energy peaks of V (882.14 eV), V\({}^{\prime\prime}\) (888.51 eV), V\({}^{\prime\prime}\) (898.05 eV), U (900.63 eV), U\({}^{\prime\prime}\) (907.32 eV), and U\({}^{\prime\prime}\) (916.45 eV) are attributed to Ce\({}^{4+}\), whereas Ce\({}^{3+}\) is linked to the photoelectron excitations of V\({}_{0}\) (880.2 eV), V\({}^{\prime}\) (884.7 eV), U\({}_{0}\) (898.65 eV), and U\({}^{\prime}\) (903.09 eV) [35]. The presence of Ce\({}^{3+}\) indicates the presence of non-stoichiometric CeO\({}_{2-X}\) on the surface of CeO\({}_{2}\) nanomaterials. Oxygen vacancies could be formed during the transformation of Ce\({}^{4+}\) into Ce\({}^{3+}\) by the following defect reaction: O\({}_{0}^{X}\)\(\leftrightarrow\)V\({}_{0}\)\({}^{\prime\prime}\) + 2e + \(\frac{1}{2}\)O(g), where O\({}_{0}^{X}\), V\({}_{0}\)\({}^{\prime\prime}\), and e are oxide ions in the lattice, doubly charged oxygen vacancies, and electrons in the conduction band made up of Ce 4f energy states, respectively [41]. It indicates the presence of oxygen vacancies on the surface of CeO\({}_{2}\) nanomaterials. Oxygen vacancies can play a critical role in the redox mechanism and oxygen migration toward the surface of CeO\({}_{2}\) nanomaterials. According to the previously reported methods [35; 42], Ce 3d spectra of the samples were fitted to calculate the content of Ce\({}^{3+}\) (Table 2). Based on the fitted result, the content of Ce\({}^{3+}\) in nanorods was higher than those in the irregular nanoparticles and nanocubes. Such a result may be due to the different oxygen vacancy formation energy at different exposed crystal planes for CeO\({}_{2}\) with different morphologies [43].