## 3 Results and Discussion
Figure 2e,f show the SAED patterns, the (200) distances between the crystal planes of FS-FT (0 g) and FS-FT (0.36 g) are 0.186 nm and 0.179 nm, respectively. The (200) interplanar spacing of FS-FT (0.36 g) is smaller than that of FS-FT (0 g), the reason for this being that the ionic radius of Fe\({}^{3+}\) within the lattice frame is smaller than that of Ti\({}^{4+}\)[22]. These findings align with the XRD data. The UV-VIS DRS of FS-FT is depicted in Figure 3a. The samples exhibit high absorption in visible and ultraviolet regions. The optical band gap (E\({}_{\text{g}}\)) of the samples was derived from the Tauc plot (F(R)hv)\({}^{2}\) versus hv, as outlined in Equation (2). \[\text{a}\hbar\text{v}=\text{C}\big{(}\hbar\text{v}-\text{E}_{\text{g}}\big{)}^{2} \tag{2}\]  
where \(\alpha\) represents the absorption coefficient, C is a constant, h denotes the photon energy, and E\({}_{\text{g}}\) refers to the band gap. In Figure 3b, the E\({}_{\text{g}}\) of FS-FT (0 g), FS-FT (0.18 g), FS-FT (0.27 g), FS-FT (0.36 g), and FS-FT (0.45 g) is 2.73, 2.53, 2.39, 2.24, and 2.18 eV, respectively. The data show that the doping of Fe\({}^{3+}\) can change the energy band gap to varying degrees, and the reason for this may be that the doping of Fe\({}^{3+}\) leads to hybridization between the d-orbitals of Ti\({}^{4+}\) and Fe\({}^{3+}\) in the nano-TiO\({}_{2}\), thereby reducing the energy band gap [23; 24; 25]. Figure 2: TEM images: (**a**) FS-FT (0 g), (**b**) FS-FT (0.36 g); HRTEM images: (**c**) FS-FT (0 g), (**d**) FS-FT (0.36 g); and SAED images: (**e**) FS-FT (0 g), (**f**) FS-FT (0.36 g). In photocatalytic experiments under the same conditions, the photocatalytic performance of the photocatalyst was analyzed by monitoring the degradation of the MO solution. First, 0.02 g of FS-FT with different levels of iron doping was placed in 10 mL of MO solution (C\({}_{0}\) = 10 mg/L) in a dark room until it reached the absorption\(-\)desorption equilibrium. The snap values of MO using FS-FT (0, 0.18, 0.27, 0.36, and 0.45 g) were 12.12%, 11.81%, 12.12%, 12.65%, and 11.83%, respectively. Figure 4a displays the UV-VIS spectra of MO prior to and after photodegradation in pure MO solution with FS-FT (0, 0.18, 0.27, 0.36, and 0.45 g). The photodegradation rates were 90.25%, 81.37%, 88.67%, 99%, and 79.36%, respectively. The results indicated that FS-FT (0.36 g) exhibited the highest photodegradation efficiency. Figure 4b illustrates the UV-VIS spectra of C\({}_{0}\) = 10 mg/L MO at different irradiation times during the photodegradation of MO using FS-FT (0.36 g). Figure 4c shows the degradation rates of MO solution using FS-FT (0-0.45 g). The data demonstrate that the degradation rate of MO solution using FS-FT (0.36 g) can reach 99% in 25 min. The results indicate that appropriate metal doping can boost the photocatalytic performance of TiO\({}_{2}\). When the concentration of doped Fe\({}^{3+}\) is too much, it will transform Fe\({}^{3+}\) from a capturing center into a recombination center, enhancing the re-association of charge carriers and suppressing the photodegradation of acid dyes, leading to a decreased degradation efficiency [17]. Figure 3: UV-VIS DRS of (**a**) FS-FT (0–0.45 g): Tauc plots for (**b**) FS-FT (0–0.45 g). Figure 4: (**a**) UV-VIS spectra of MO in pure MO solution prior to and after photodegradation using FS-FT (0–0.45 g); (**b**) time evolution of UV-VIS spectra for MO degradation using FS-FT (0.36 g); and (**c**) degradation speed of MO degraded using FS-FT (0–0.45 g) in pure MO solution. Under identical experimental conditions, the recovered FS-FT (0 g, 0.36 g) was utilized for cyclic degradation experiments of the MO solution. Figure 5a shows the photodegradation efficiency of MO using the recovered FS-FT (0 g) for five cycles. The abscissa of the five-cycle data corresponds to the horizontal coordinates of 0-25, 25-50, 50-75, 75-100, and 100-125 min, respectively.