## 3 Results and Discussion
### XRD Study TiO\({}_{2}\)/FTO and Au/TiO\({}_{2}\)/FTO Films  
TiO\({}_{2}\) has three polymorphic modifications: low-temperature phases anatase (tetragonal system, space group \(I4_{1}/amd\)) and brookite (orthorhombic system, space group \(Pbca\)), which irreversibly transform on heating into the high-temperature modification of rutile (tetragonal system, space group \(P4_{2}/mmm\)) [27; 28]. From the point of view of photocatalysis and photoelectrochemical application, the anatase phase is interesting. It is more active than rutile due to the rapid transfer of excitons from the bulk to the surface [29]. Figure 3 shows XRD pattern for TiO\({}_{2}\)/FTO (Figure 3a) and Au/TiO\({}_{2}\)/FTO.  
Figure 1: SEM image of the surface of a Au/TiO\({}_{2}\)/FTO composite film at various magnifications (**a–c**); EDS analysis of the photoelectrode before (**d**) and after (**e**) deposition of gold nanoparticles using the LCLLD method.  
From the analysis of XRD patterns, it was found that the porous TiO\({}_{2}\) film belongs to the tetragonal system with the unit cell parameters \(a\) = 3.7797(13) A, and \(c\) = 9.500(4) A and the volume \(V\) = 135.71(11) A\({}^{3}\) belonging to the space group of symmetry \(I\)4\({}_{1}\)/_amd_ (Figure 3a). The set of \(hkl\) indexes and d-space for TiO\({}_{2}\) are shown in Table S1. The LCLD process does not affect the structural properties of the porous TiO\({}_{2}\) film (Figure 3b). After the LCLD process, the unit cell parameters of the porous TiO\({}_{2}\) film are \(a\) = 3.7780(2) A, and \(c\) = 9.504(6) A and the unit cell volume is \(V\) = 135.80(17) A\({}^{3}\). The XRD pattern also has Au peaks, the weak intensity of the peaks is due to the small amount of gold, which is confirmed by the data of SEM (Figure 1) and TEM (Figure 2). According to XRD analysis, gold has a cubic crystal lattice, the unit cell parameter is \(a\) = 4.087(3) A, and the unit cell  
Figure 3: XRD pattern of (**a**) TiO\({}_{2}\)/FTO/glass and (**b**) Au/TiO\({}_{2}\)/FTO/glass photoelectrodes.  
Figure 2: TEM images of the Au/TiO\({}_{2}\) layer in cross-section mode at various magnifications (**a**–**c**); EDS map of the Au/TiO\({}_{2}\)/FTO layer (**d**).  
volume is \(V=68.29(15)\) A\({}^{3}\). The crystal lattice of gold belongs to the group of spatial symmetry \(Fm\)-\(3m\). The set of \(hkl\) indexes and d-space for Au are shown in Table S2.  
In addition to TiO\({}_{2}\) and Au, the XRD patterns show peaks associated with the transparent electrode FTO (SnO\({}_{2}\):F) (Figure 3a,b). The \(hkl\) indexes and d-space for SnO\({}_{2}\) is shown in Table S3.  
Since, according to SEM data (Figure 1), the particle sizes of TiO\({}_{2}\) and Au are less than 1000 nm, it is possible to make an approximate estimate of the average particle size, using the total profile fitting during the Rietveld refinement in Topas 4.2, taking into account instrumental FWHM peak broadening, which was measured from standard sample SiO\({}_{2}\). According to the calculation, the average diameter of TiO\({}_{2}\) particles before the LCLD process is 13.7(2) nm; after the LCLD process, the average diameter of TiO\({}_{2}\) particles is 12.9(2) nm. The average size of a gold nanoparticle is 19.2(11) nm.