## 3 Results and Discussion  
XRD was performed to determine the crystal structure of TiO\({}_{2}\)-based catalysts. The X-ray diffraction patterns of the reference TiO\({}_{2}\) compound as well as the Cu- and Zr-modified TiO\({}_{2}\) catalysts are presented in Figure 3. The results indicate that only characteristic peaks belonging to TiO\({}_{2}\) were found for all modified TiO\({}_{2}\) samples. Therefore, no separate Cu or Zr phases formed in these catalysts during preparation, but 87% anatase and 13% rutile were present in the phase of TiO\({}_{2}\). Figure 3: X-ray diffraction patterns of pure TiO\({}_{2}\) and Cu- and Zr-modified TiO\({}_{2}\) photocatalysts. Figure 2: Scheme of the TLS experimental setup. L1, L2, L3, L4, L5: lenses; M1, M2, M3, M4: turning mirrors; DM: dichroic mirror; NDF: neutral density filter. In order to test the loading of Cu and Zr in catalysts, EDX analysis was carried out on pressed powders. Figure 4 shows the EDX spectra of the unmodified and P25/Zr (1%)Cu (0.05) catalysts. The analysis shows that in addition to Ti and O elements, copper and zirconium peaks exist. The STEM-EDX mapping of Cu/Zr-modified TiO\({}_{2}\) by Ni TEM grid confirmed the homogeneous distribution of Cu and Zr on the surface of TiO\({}_{2}\) (Figure 5). The results of BET measurements indicate that the addition of Cu to TiO\({}_{2}\) decreased the surface area (46.5 m\({}^{2}\)/g) with respect to the specific surface area of the reference catalyst, which was 48.4 m\({}^{2}\)/g. On the contrary, zirconium increased the surface area (50.7 m\({}^{2}\)/g) and could contribute to enhancement of the photocatalytic properties of Zr-modified TiO\({}_{2}\). Interestingly, there was no observed Cu effect on the surface area in the presence of Zr (50.7 m\({}^{2}\)/g). To examine the band gap of TiO\({}_{2}\) materials, the absorption spectra were recorded and expressed as log \(\alpha\) = f(\(\lambda\)), where \(\alpha\) is the absorption coefficient and \(\lambda\) is the wavelength (Figure 6). The \(\alpha\) values were obtained from the measured (decadic) absorbances, \(A\), and thicknesses of samples, \(d\), according to the following relation. \[\alpha=2.303\frac{A}{d} \tag{1}\]  
Figure 4: Qualitative EDX spectra of (**a**) unmodified TiO\({}_{2}\) and (**b**) P25/Zr (1%)/Cu (0.05). Figure 5: STEM-EDX mapping of Cu- and Zr-modified TiO\({}_{2}\)/Cu (0.05%)/Zr (1%) photocatalyst. It is shown in Figure 6 that the absorption coefficient of TiO\({}_{2}\) for the 405-430 nm wavelength range increases relatively rapidly with the increase in the incident photon energy, which is an indication of a direct band gap. For \(\lambda<405\) nm, \(\alpha\) increases relatively slowly with the increase in the photon energy, which indicates the presence of an indirect band gap (the maximum valence band (VB) energy occurs at a different momentum value to the minimum in the conduction band (CB) energy) in the TiO\({}_{2}\) material. The electronic band structure of TiO\({}_{2}\), therefore, shows both band gaps. Thus, the photoabsorption is dominated by direct band gap transitions when the photon energy becomes equal to or greater than the direct band gap. At higher photon energies, the transitions are dominated by indirect band gap transition and the absorption coefficient begins to increase relatively slowly compared to its increase in the case of direct band gap [17; 18]. The indirect process proceeds at a much slower rate than direct transitions, as it requires three entities to intersect in order to proceed, namely an electron, a photon and a phonon, whereas in case of direct \(E_{g}\), an electron-hole pair is produced quite easily since the electron does not need to receive very much momentum. Determination of the band gap by UV-Vis spectrophotometry was based on the measurement of the diffuse reflectance of the examined samples (Figure 7) [17]. The sample thickness (\(\sim\)1 mm) ensured the condition of all light being absorbed or scattered before reaching the back surface of the sample [9; 11].