## 3 Results and Discussion  
### Characteristics of CeO\({}_{2}\) Nanomaterials  
The crystallographic information of the as-prepared samples was determined using XRD, and the result is depicted in Figure 1. Based on the recorded XRD spectra for each sample, the detected peaks corresponded well with the characteristic peaks in the XRD spectrum of fluorite structure CeO\({}_{2}\) (JCPDS 34\(-\)0394, Space Group Fm3m), which indicates that CeO\({}_{2}\) with different morphologies were successfully prepared. By employing [PERSON]'s equation, the crystallite sizes of 2 MCeO\({}_{2}\)np, 6 MCeO\({}_{2}\)nr, 12 MCeO\({}_{2}\)nr, 6 MCeO\({}_{2}\)nc, and 12 MCeO\({}_{2}\)nc could be calculated to be 6.86 nm, 7.50 nm, 9.61 nm, 39.56 nm, and 49.46 nm, respectively (Table 1). The specific surface areas (\(S_{\text{BET}}\)) of the as-prepared CeO\({}_{2}\) nanomaterials were obtained with N\({}_{2}\) adsorption-desorption measurements. In Table 1, irregular CeO\({}_{2}\) nanoparticles and nanorods possessed significantly larger S\({}_{\text{BET}}\) as compared to the CeO\({}_{2}\) nanocubes. Furthermore, from the BET results, the S\({}_{\text{BET}}\) of CeO\({}_{2}\) nanomaterials with the same morphology increased with the reduction in size. Figure 2 shows the TEM images of the five as-prepared CeO\({}_{2}\) nanomaterials prepared via the hydrothermal method. Based on the results, it can be observed that the hydrothermal temperature and NaOH concentration used in the preparation process could result in significant differences in the morphologies of the samples. The formation mechanism of the CeO\({}_{2}\) nanomaterials with different morphologies can be attributed to the well-known dissolution/recrystallization process [39]. Figure 2e shows the TEM image of the irregular CeO\({}_{2}\) nanoparticles prepared with 2 M NaOH at 100 \({}^{\circ}\)C. It can be observed that as the concentration of NaOH increased beyond 2 M NaOH (Figure 2a,b), the as-obtained CeO\({}_{2}\) gradually exhibited a change in its morphology into nanorods due to the anisotropic growth of Ce(OH)\({}_{3}\) nuclei along the (110) direction. However, as the hydrothermal reaction temperature increased to 180 \({}^{\circ}\)C, Ce(OH)\({}_{3}\) would become unstable and it could oxidize to form CeO\({}_{2}\) nanocubes (Figure 2c,d). The CeO\({}_{2}\) nanocubes grew along each edge length direction with increasing NaOH concentrations. According to the TEM results, the average lengths of 6 MCeO\({}_{2}\)nr, 12 MCeO\({}_{2}\)nr, 6 MCeO\({}_{2}\)nc, 12 MCeO\({}_{2}\)nc, and 2 MCeO\({}_{2}\)np were 38.72 nm, 133.83 nm, 18.78 nm, 57.95 nm, and 5.02 nm, respectively, and this result is summarized in Figure 2f and Table 1. \begin{table}
\begin{tabular}{c c c c c c} \hline
**Catalyst** & **Temperature (\({}^{\circ}\)C)** & **C\({}_{\text{NaOH}}\) (mol/L)** & **Morphology** & **Mean Length (nm)** & **Crystallinity Size (nm)** & **S\({}_{\text{SET}}\) (m\({}^{2}\)/g)** \\ \hline
2 MCeO\({}_{2}\)np & 100 & 2 & Particles & 5.02 & 6.86 & 128.89 \\
6 MCeO\({}_{2}\)nr & 100 & 6 & Rods & 38.72 & 7.50 & 126.1 \\
12 MCeO\({}_{2}\)nr & 100 & 12 & Rods & 133.83 & 9.61 & 102.19 \\
6 MCeO\({}_{2}\)nc & 180 & 6 & Cubes & 18.78 & 39.56 & 31.13 \\
12 MCeO\({}_{2}\)nc & 180 & 12 & Cubes & 57.95 & 49.46 & 14.609 \\ \hline \end{tabular}
\end{table} 
Table 1: Synthesis conditions and physicochemical characteristics of the as-prepared CeO\({}_{2}\) nanomaterials with different morphologies. Figure 1: XRD patterns of the as-prepared CeO\({}_{2}\) nanomaterials. H\({}_{2}-\)TPR was used to examine the reducibility of the surface oxygen and bulk phase oxygen in the CeO\({}_{2}\) nanomaterial (Figure 3). The low temperature reduction peaks located between 300 \({}^{\circ}\)C and 650 \({}^{\circ}\)C correspond to the reduction of surface oxygen species, while the high temperature reduction peak located above 650 \({}^{\circ}\)C relates to the reduction of bulk phase oxygen species [40].