## 3 Results and Discussion  
### X-ray Diffraction  
To determine the crystal structure of the Bi\({}_{7-\mathrm{x}}\)Gd\({}_{\mathrm{x}}\)Fe\({}_{3}\)Ti\({}_{3}\)O\({}_{21}\) (BGFT-x) for x = (0, 0.2, 0.4, 0.6), X-ray analysis was conducted. The obtained XRD patterns (Figure 2) indicate that the examined ceramic materials are single-phase and exhibit the anticipated orthorhombic structure with the Fm2m (No. 42) space group. The exemplary profile fitting is shown in Figure 3.  
Figure 3: An exemplary pattern obtained from Rietveld refinement of Bi\({}_{6,4}\)Gd\({}_{0.6}\)Fe\({}_{3}\)Ti\({}_{3}\)O\({}_{21}\) powders (generated from WinPlotr). Figure 2: A set of experimental diffraction patterns of obtained BGFT-x (x = (0, 0.2, 0.4, 0.6)) powders with reference ICSD pattern of Aurivillius phase. The parameters of the unit cell of the discussed ceramic materials were determined from the structural analysis on the basis of XRD data. The results are presented in Table 2.  
The results of XRD studies and structure calculations revealed that the Aurivillius phase showed the ability to be doped with Gd\({}^{3+}\) ions. There are at least a few arguments as to this. In every single case of x, we observe phase-homogeneous XRD diffractograms. Apart from the target phase of Aurivillius, neither substrate residues nor intermediate phases from the equilibrium system consisted of bismuth, iron, titanium, gadolinium oxides, or other noted inclusions were noted. The content of such diffractograms is only a diffraction pattern of the BGFT-x (x = (0, 0.2, 0.4, 0.6)) system, differing only in subtle changes in the positions of Bragg lines profiles, which is the result of changes in the lattice constants. Analyzing the unit cell parameters, it is noticed that their volume changes tend to increase with respect to the dopant content. With an increase in the gadolinium level, for the adopted concentration range (from x = 0.2 to x = 0.6), the volume of the BGFT-x unit cell increases slightly for x = 0.4, and the elongation of the lattice constant (b) is accompanied by less commensurate shortening of the lattice constant (a), while neither directional nor significant changes in the constant (c) are found (Table 2). Moreover, the increasing concentration of gadolinium ions Gd\({}^{3+}\) causes a slight but gradual decrease in the theoretical density of the tested ceramic materials (calculated based on Formula (1)) (Table 2). The densities were calculated according to the formula given below:  
\[\rho=\frac{MZ}{VN_{A}} \tag{1}\]  
where \(M\)--molar mass of BGFT-x system, \(Z\)--the number of cell formula units (equal to 4 in each case), \(V\)--volume of unit cell, \(N_{A}\)--the Avogadro constant. It should be emphasized that the valence of gadolinium ions is identical to that of bismuth, so there is no risk of oxygen defects, and gadolinium would theoretically take the nodal position of bismuth in the unit cell. According to the assumptions, the doping was meant to substitute bismuth with gadolinium and maintain the total stoichiometry resulting from the valence of these elements. The nature of the bonds of bismuth and gadolinium with oxygen within this cell could be controversial here because the atomic radius of gadolinium is larger than that of bismuth (233 and 143 pm, respectively), while the relation of their ionic radii is exactly the opposite (here 94 and 103 pm) but also shows better compatibility in the latter case. Since the unit cell's expansion (albeit insignificant) takes place, this may suggest that in the BGFT-x systems; however, the proportion of atomic bonds is higher than ionic ones.