## 3 Results  
### Structural and Morphological Characteristics  
Figure 3 shows XRD patterns of intermediate phase In(OH)\({}_{3}\) and In\({}_{2}\)O\({}_{3}\) nanoparticles synthesized by the aforementioned thermal decomposition method, and were identified using JCPDS #160161 and JCPDS #060416, respectively. The diffraction patterns of both In(OH)\({}_{3}\) and In\({}_{2}\)O\({}_{3}\) nanoparticles were perfectly indexed to cubic structures. No impurity peak was observed; only sharp peaks existed, as shown in Figure 3. This means that the newly synthesized In\({}_{2}\)O\({}_{3}\) nanoparticles had good crystallinity, where In\({}_{2}\)O\({}_{3}\) nanoparticles were finally obtained by annealing the intermediate phase In(OH)\({}_{3}\) at 300 \({}^{\circ}\)C.  
The average crystallite size, \(D\), was estimated using the Scherrer equation [38] as follows:  
\[D=\frac{K\lambda}{\beta cos\theta}\]  
where \(\beta\) is the full width at half maximum (FWHM), \(K\) is the shape factor, and \(\lambda\) is the wavelength (Cu K\(\alpha\) = 1.54056 A). The average crystal size of the In\({}_{2}\)O\({}_{3}\) nanoparticles was \(\sim\)10 nm in diameter, slightly smaller than what was observed (\(\sim\)15 nm) in the SEM and TEM images. Figure 4 shows XRD patterns of catalyst-decorated In\({}_{2}\)O\({}_{3}\) nanoparticles such as Au/In\({}_{2}\)O\({}_{3}\), Pd/In\({}_{2}\)O\({}_{3}\), and Pt/In\({}_{2}\)O\({}_{3}\). The XRD patterns correspond to the cubic In\({}_{2}\)O\({}_{3}\) crystal structure (JCPDS # 060416), but the lack of diffraction peaks from metallic catalysts of Au, Pd, and Pt likely means that the nanoparticles must be very small or amorphous due to the small amount of catalyst added to the In\({}_{2}\)O\({}_{3}\) nanoparticles. A similar phenomenon was previously reported and was explained by the low content and small size of the catalysts [39]. Shifts of the XRD peaks did not seem to appear in the catalyst-decorated samples. Figure 3: X-ray diffraction patterns of intermediate phase In(OH)\({}_{3}\) and In\({}_{2}\)O\({}_{3}\) nanoparticles. Thus, it is considered that the added Au, Pd, and Pt were not incorporated into the In\({}_{2}\)O\({}_{3}\) lattice, but rather were immobilized on the surfaces of In\({}_{2}\)O\({}_{3}\) nanoparticles. Figure 5a-c shows TEM images of Au/In\({}_{2}\)O\({}_{3}\), Pd/In\({}_{2}\)O\({}_{3}\), and Pd/In\({}_{2}\)O\({}_{3}\) nanoparticles. Here, In\({}_{2}\)O\({}_{3}\) nanoparticles have a slightly darker color with a diameter of 10 to 20 nm, whereas metal nanoparticles appear as dark colors with a diameter of 5 to 15 nm. The shape of the metal particles is more clearly displayed in the order of Au, Pd, and Pt particles, and the Pt particles appear blurry in the TEM images. The particle sizes of In\({}_{2}\)O\({}_{3}\) and Au nanoparticles are estimated to be about 15 nm and 5 nm, respectively, as shown in Figure 5 (TEM image), where there is a lighter dark color for In\({}_{2}\)O\({}_{3}\) particles and darker color for Au particles. Au particles are also shown as white particles in Figure 6 (HAADF image). Figure 6a-c presents high-angle annular dark-field images (HAADF) of Au/In\({}_{2}\)O\({}_{3}\), Pd/In\({}_{2}\)O\({}_{3}\), and Pd/In\({}_{2}\)O\({}_{3}\) nanoparticles. The Au nanoparticles are clearly indicated by white dots with a diameter of \(\sim\)10 nm in Figure 6a, while Pd and Pt nanoparticles are also indicated by white dots, but with diameters of \(<\)5 nm and 5-10 nm, respectively. This is smaller than the Au nanoparticles shown in Figure 6b,c. HAADF is a STEM technique that produces an annular dark field image using very high angles, and incoherently scattered electrons. For elements with a higher atomic number, more electrons will scatter at higher angles due to the electrostatic interactions between the nuclear electron beams. Therefore, HAADF detectors detect larger signals from atoms with higher atomic numbers, making them appear brighter in the resulting image.