## 3 Results and Discussion  
XRD patterns of TiO\({}_{2}\), Fe\({}_{3}\)O\({}_{4}\) and Fe\({}_{3}\)O\({}_{4}\)@TiO\({}_{2}\) are shown in Figure 1. The prepared TiO\({}_{2}\) powder displayed a good crystallinity; the diffraction peaks of TiO\({}_{2}\) exhibited at 25\({}^{\circ}\), 38\({}^{\circ}\), 48\({}^{\circ}\), 54\({}^{\circ}\), 55.14\({}^{\circ}\) and 62.5\({}^{\circ}\) corresponded to the (101), (004), (200), (105), (211) and (204) lattice planes of TiO\({}_{2}\) (JCPDS No. 65-3369), respectively. The results show that no crystals are formed except the anatase crystals. The diffraction peaks of Fe\({}_{3}\)O\({}_{4}\) exhibited at 30.15\({}^{\circ}\), 35.59\({}^{\circ}\), 43.12\({}^{\circ}\), 53.45\({}^{\circ}\), 56.99\({}^{\circ}\) and 62.53\({}^{\circ}\) corresponded to the (220), (311), (400), (422), (511) and (440) lattice planes of the magnetite phase (JCPDS card 02-0387) [17], respectively. As shown in the XRD pattern of Fe\({}_{3}\)O\({}_{4}\)@TiO\({}_{2}\), there are (101), (004), (200), (105), (211) and (204) diffraction peaks of TiO\({}_{2}\) and (220), (422) and (400) diffraction peaks of Fe\({}_{3}\)O\({}_{4}\). The crystallite sizes of TiO\({}_{2}\) and Fe\({}_{3}\)O\({}_{4}\)@TiO\({}_{2}\) were calculated by applying the Scherrer formula to the diffraction peaks of the anatase crystallite plane. The calculation of crystallite sizes (D) was [18]:  
\[\mathrm{D}=\frac{\mathrm{K}\lambda}{\beta\cos\theta} \tag{2}\]  
where D is the grain size (nm), \(\lambda\) is the X-ray wavelength (nm), \(\beta\) is the full width at half maximum (rad), K is the Scherrer constant and \(\theta\) is the diffraction angle (\({}^{\circ}\)). According to the above formula, the grain sizes of TiO\({}_{2}\) and Fe\({}_{3}\)O\({}_{4}\)@TiO\({}_{2}\) are about 13.64 nm and 23.97 nm, respectively. The results of Raman spectroscopy are shown in Figure 2. The peaks of basic vibration modes of anatase TiO\({}_{2}\) were 144, 394, 514 and 636 cm\({}^{-1}\)[19]. The vibration at 144 cm\({}^{-1}\) of the Eg peak was due to the symmetric stretching vibration of the O-Ti-O bond in TiO\({}_{2}\), and its intensity decreases with the increase in exposed (001) facets. The A\({}_{1}\)g peak at 514 cm\({}^{-1}\) was generated by the antisymmetric bending vibration of O-Ti-O in TiO\({}_{2}\) and its intensity increased with the increase in exposed (001) facets. Therefore, the percentage of exposed (001) facets exposed for TiO\({}_{2}\) and Fe\({}_{3}\)O\({}_{4}\)@TiO\({}_{2}\) can be calculated by measuring the peak intensity ratio of the Eg and A\({}_{1}\)g modes [20]. The percentages of exposed (001) facets of TiO\({}_{2}\) and Fe\({}_{3}\)O\({}_{4}\)@TiO\({}_{2}\) were estimated to be 12.1% and 25.2%, respectively. The morphologies of Fe\({}_{3}\)O\({}_{4}\), TiO\({}_{2}\) and Fe\({}_{3}\)O\({}_{4}\)@TiO\({}_{2}\) are shown in Figure 3. The particle diameters of Fe\({}_{3}\)O\({}_{4}\), TiO\({}_{2}\) and Fe\({}_{3}\)O\({}_{4}\)@TiO\({}_{2}\) are about 390 nm, 100 nm and 120 nm, respectively. The size of Fe\({}_{3}\)O\({}_{4}\)@TiO\({}_{2}\) and TiO\({}_{2}\) particles is uniform, but there is particle agglomeration. The possible reason is that the spherical structure is corroded by acid during the compounding process. Combined with the results of FESEM and XRD, it is found that the particle size inferred from FESEM is larger than that obtained by XRD. It is suggested that the shape of larger particles is determined by the agglomeration of adjacent smaller crystallites [21]. EDS patterns and FESEM elemental mapping of Fe\({}_{3}\)O\({}_{4}\)@TiO\({}_{2}\) are shown in Figure 4. The results indicate that Ti and Fe elements are evenly distributed, which firmly confirms the incorporation of TiO\({}_{2}\) and Fe\({}_{3}\)O\({}_{4}\) in the composite. Figure 2: Raman spectra in the range of 100–800 cm\({}^{-1}\) for TiO\({}_{2}\) and Fe\({}_{3}\)O\({}_{4}\)@TiO\({}_{2}\). The UV-VIS diffuse reflectance spectra of Fe\({}_{3}\)O\({}_{4}\), TiO\({}_{2}\) and Fe\({}_{3}\)O\({}_{4}\)@TiO\({}_{2}\) particles are shown in Figure 5a,b.