# Enhancing Methyl Orange Degradation with Laser-Generated ZnO and Ce-Doped ZnO Nanoparticles
## 3 Results and Discussion
### Characterizations  
#### 3.2.1 XRD Analysis  
In Figure 3a, XRD pattern (JCPDS No. 01-080-0075) for ZnO NPs reveals distinct peaks at 20 values of 31.76\({}^{\circ}\), 34.41\({}^{\circ}\), 36.25\({}^{\circ}\), 47.54\({}^{\circ}\), 56.58\({}^{\circ}\), 62.85\({}^{\circ}\), 66.36\({}^{\circ}\), 67.92\({}^{\circ}\), and 69.08\({}^{\circ}\) corresponding to the (100), (002), (101), (102), (110), (103), (200), (112), and (201) crystal planes, respectively. These peaks indicated the presence of the wurtzite hexagonal ZnO phase. The as-synthesized 1% Ce/ZnO samples exhibit peaks corresponding to the reflection planes of the cubic-structured CeO\({}_{2}\) (JCPDS No. 03-065-2975), as shown in Figure 3b. These distinctive peaks observed at 2\(\theta\) values of 28.86\({}^{\circ}\), 33.14\({}^{\circ}\), 47.24\({}^{\circ}\), 56.06\({}^{\circ}\), 59.22\({}^{\circ}\), and 69.84\({}^{\circ}\) in the 1% Ce-doped ZnO NPs have been indexed as the (111), (200), (220), (311), (222), and (400) crystal planes, respectively, representing the crystalline CeO\({}_{2}\) cubic phase. This finding provides evidence of Ce\({}^{3+}\) or Ce\({}^{4+}\) incorporation into the ZnO lattice [12]. Simultaneously, peaks at 32.44\({}^{\circ}\), 34.28\({}^{\circ}\), 35.84\({}^{\circ}\), 66.30\({}^{\circ}\), and 67.80\({}^{\circ}\) are attributed to the reflection planes (100), (002), (101), (200), and (112) of the wurtzite hexagonal ZnO phase, respectively [18; 19]. The Ce doping reaches saturation within the ZnO lattice at 1%, leading to the formation of a new phase (second phase) consisting of cubic CeO\({}_{2}\) in the 1% Ce/ZnO composite. As a result, it becomes evident that a considerable amount of Ce has been successfully accommodated within the ZnO lattice, leading to the formation of CeO\({}_{2}\). This indicates that once the doping concentration was reached, a significant portion of Ce was incorporated into the ZnO NP lattice. Consequently, the presence of the second phase (CeO\({}_{2}\)) becomes noticeable [19]. However, due to the contribution of CeO\({}_{2}\) to the diminished ZnO peak (Figure 3b), collecting ZnO diffraction data becomes challenging. Correspondingly, the crystallite size, \(D\), is obtained by employing the Debye-Scherrer formula [24]. \[D=\frac{0.9\lambda}{\beta cos\theta} \tag{6}\]  
where \(D\) is the average crystalline diameter in nanometers (nm); \(\beta\) denotes the full width at half maximum (in radian); \(\lambda\) refers to the X-ray wavelength, which is 0.15418 nm for Cu-target Ka radiation, and \(\theta\) represents the Bragg diffraction angle [25]. As presented in Tables S1 and S2, the crystal parameters according to the diffraction angle (2\(\theta^{\rm o}\)) and the Full Width at Half Maximum (FWHM), the crystallite size, as well as the d-spacing from several reflection planes for each peak are shown. The average crystal size of 1% Ce/ZnO (90 nm) was smaller compared to pure ZnO, which was 117 nm. This finding is in agreement with other findings reported elsewhere [24; 26; 27]. Ce-O-Zn bonds formed on the surface of Ce-doped ZnO samples limit or restrain the crystallites' growth, causing a decrease in crystallite size [28]. In addition, Ce doping reduces crystallite size because Ce\({}^{4+}\) has a larger ionic radius than Zn\({}^{2+}\) and may penetrate the ZnO matrix because of the low nitrate decomposition temperature. Therefore, Ce\({}^{4+}\) may diffuse into the ZnO matrix and replace the Zn\({}^{2+}\) position to produce CeO\({}_{2}\)[26; 29]. The ZnO lattice parameters \(a\) and \(c\) were calculated from the (100) and (002) peaks' positions, accordingly, as follows:  
\[a_{(100)}=\frac{\lambda}{\sqrt{3}\sin\theta} \tag{7}\]  
\[c_{(002)}=\frac{\lambda}{\sin\theta} \tag{8}\]  
Here, the crystallinity degree \(X_{c}\) is measured employing the following empirical relation:  
\[X_{c}=\left(\frac{0.24}{\beta_{(002)}}\right)^{3} \tag{9}\]  
in which \(\beta\) denotes the FWHM (in degrees) of (002) [PERSON]'s plane [30; 31].