## 3 Results and Discussion
It is relevant to note that when comparing the pristine BiOI with the BiOI/Fe\({}_{3}\)O\({}_{4}\) heterostructure, a decrease in the particle size is observed, increasing the specific surface area of the synthesized catalyst. This reduction in particle size can be attributed to the strong interactions between Fe\({}_{3}\)O\({}_{4}\) and BiOI. Figure 4 shows the TEM of the obtained materials. Figure 4a,b identify the magnetite; its morphology is constituted by nanospheres, which have a homogeneous distribution and a uniform diameter between 50-200 nm; the size and morphology are similar to magnetite obtained and reported using similar synthesis methodology [20; 49]. Adsorption/desorption isotherms of N\({}_{2}\) were performed to investigate the surface areas and pore size distributions of the obtained materials (Figure 5). The complete BET BiOI and BF-5 isotherm show an IVa-type isotherm with an H3 hysteresis loop, characteristic of mesoporous materials with high adsorption energy [50]. The Isotherm for Fe\({}_{3}\)O\({}_{4}\) is of an IVa type with an H1 hysteresis loop, suggesting cylindrical uniform pores with monolayer adsorption [51]. In addition, the pore size graph confirms that the materials are located in the mesoporous range (2-50 nm). Table 1 shows the values of the optical and surface properties of the synthesized samples. The BET surface analysis indicates that the BF-5 nanomaterial has a specific surface area intermediate between the pure BiOI sample and the synthesized magnetite. The BET surface area, the mean BJH pore diameter, and the BJH pore volume of BiOI/Fe\({}_{3}\)O\({}_{4}\) were 20.23 (m\({}^{2}\) g\({}^{-1}\)), 3.95 (nm), and 0.056 (cm\({}^{3}\) g\({}^{-1}\)), respectively. The improvement of the BET surface area can contribute to the generation of more active sites to improve the photocatalytic performance of BF-5 [52; 53]. It has been pointed \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Materials**} & **BET** & **Pore Diameter** & **Pore Volume** & **Eg** \\  & **(m\({}^{2}\) g\({}^{-1}\))** & **(nm)** & **(cm\({}^{3}\) g\({}^{-1}\))** & **(eV)** \\ \hline Pure BiOI & 61 & 13.34 & 0.250 & 1.95 \\ Fe\({}_{3}\)O\({}_{4}\) & 16 & 4.42 & 0.032 & 2.04 \\ BiOI/Fe\({}_{3}\)O\({}_{4}\) & 20 & 3.95 & 0.056 & 1.97 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Textural and optical properties of pure BiOI, Fe\({}_{3}\)O\({}_{4}\), and synthesized BiOI/Fe\({}_{3}\)O\({}_{4}\) (BF-5). Figure 5: N\({}_{2}\) adsorption–desorption isotherms (**a**) and pore size distribution (**b**) of BiOI pure, Fe\({}_{3}\)O\({}_{4}\), and BF-5. out in several studies that the surface area is an important factor in the generation of more active sites, improving the photocatalytic activity [54; 55]. The optical properties of the synthesized materials are detailed in Table 1, presenting each material's band gap energy values (Eg). These values were obtained using the Tauc Equation Equation (3), a method that provides a more accurate approximation than direct extrapolation of the UV-vis spectrum to determine the absorption start wavelength (start \(\lambda\)) [56; 57]. \[(\alpha hv)^{n}=A\ (hv-Eg) \tag{3}\]  
In this equation, \(\alpha\) represents the adsorption coefficient, \(A\) is the constant of proportionality, \(h\) is [PERSON]'s constant, \(v\) is the frequency, \(Eg\) is the energy band gap, and the exponent n value denotes the electronic transition's nature. The value of \(Eg\) can be obtained by extrapolating the slope of the curve to the x-axis intersection (see Figure 6). The graph (\(\alpha\)E) 1/p vs. E can be plotted to obtain the band gap of the straight section of the resulting curve. The point of intersection of the straight line's extension with the energy axis corresponds to the energy band gap [57]. For direct gap semiconductors, \(n\) is 2, and for indirect gap semiconductors, \(n\) is % [46; 58].