## 2 Materials and Methods  
The preparation of pure Bi\({}_{7}\)Fe\({}_{3}\)Ti\({}_{3}\)O\({}_{21}\) ceramic material and its gadolinium ion (Gd\({}^{3+}\))-doped counterpart was accomplished through the solid-state reaction method, utilizing simple oxides. The procedural details are explained in our previous paper [20; 21]. Figure 1 shows general scheme. To identify suitable synthesis parameters, the preliminary-mixed powders underwent thermal analysis (TG, DTG, DTA) within the temperature range T = (298-1298) K. The resulting data facilitated the determination of the synthesis temperature for all compounds, established at T\({}_{\text{s}}\) = 1123 K.  
The crystal structures of all examined samples were investigated using a BRUKER D8 Discover instrument equipped with a standard CuK\(\alpha\) radiator (\(\lambda\)Ka1 = 1.54056 A, \(\lambda\)Ka2 = 1.54439 A, Siemens KFL CU2 K, operating at 40 kV voltage and 40 mA current in the Bragg-Brentano diffraction geometry with a Gobel FGM2 mirror for parallel beam conditions). The diffraction angle 20 range was set from 15-80\({}^{\circ}\) with a step of 0.015\({}^{\circ}\) and an acquisition time of 2 s per step. All measurements were conducted at 298 K within the temperature-stabilized Anton Paar HTK 1200N chamber. Data processing involved the use of the Crystal Impact Match! application. The \(\lambda\)Ka2 signal component was deconvoluted and removed for each diffraction pattern, the background was subtracted, and the data were smoothed using the fast Fourier transform. The phase analysis was performed using the ICSD database. Crystallographic calculations were performed by means of the FullPROFver. 3.0 program, enabling Rietveld refinement and precise unit cell parameter calculations based on diffraction profile fitting [22]. The reference CIF file used for this analysis was  
\begin{table}
\begin{tabular}{l c c c} \hline \hline  & **Valence** & **Coordination Number** & **Ionic Radii Å [19]** \\ \hline Gd\({}^{3+}\) & III & 6 & 0.94 \\ \hline Bi\({}^{3+}\) & III & 6 & 1.03 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Comparison of the basic information about gadolinium and bismuth ions [19].  
Figure 1: General fabrication scheme for BGFT-x ceramic materials (for x = (0, 0.2, 0.4, 0.6)).  
obtained from the supplementary data in Ref. [23]. The calculated broadening of diffraction lines, specifically the full width at half maximum (FWHM), was employed to estimate the average crystallite sizes using the Debye-Scherrer formula [24]. The instrumental standard NIST SRM 660a (LaB\({}_{6}\)) was applied to eliminate the apparatus broadening component.  
The microstructure analysis was conducted using a scanning electron microscope (JEOL JSM-7100F TTL LV) equipped with an energy dispersion spectrometer (EDS). Qualitative and quantitative assessments of the chemical composition were performed employing the X-ray microanalysis method.  
Dielectric measurements were conducted using the Agilent E4980A impedance analyzer within a frequency range spanning from f = 1 kHz to f = 1000 kHz and at temperatures ranging from T = 300 K to T = 800 K. The measurements were carried out during the heating and cooling processes, with the rate of V = 2.5 K/min, and stabilised using a temperature controller. An Agilent E4980A LCR meter was used to measure the dielectric response.