## 3 Results and Discussion  
### X-Ray Diffraction  
The phase composition and crystal structure of the PBZT doped with La\({}^{3+}\) samples were studied via the powder XRD technique, and the obtained diffractograms are shown in Figure 2.  
At first glance, they are very similar, but closer inspection shows substantial differences. In order to study the lattice parameters and contribution of phases in the samples, the Rietveld refinement method was used. Table 1 summarizes the results of the Rietveld procedure. In the case of PBZT, PBZT doped with La\({}^{3+}\) at concentrations \(x\) = 1 at.% and \(x\) = 2 at.%, the best numerical fit was obtained assuming a rhombohedral unit cell and R3c space group.  
For PBZT doped with La\({}^{3+}\) at concentrations \(x\) = 3 at.% and \(x\) = 4 at.%, two components (phases) were necessary to achieve satisfactory agreement between the model and the experiment (see the right panel of Figure 2). In this case, the dominating phase is cubic (Pm-3m space group). However, significant left-hand asymmetry of XRD peaks reveals the occurrence of a remnant rhombohedral component (red color in Figure 2). The value of lattice parameters of the rhombohedral component gradually increases with the growth of La concentration. One can note significantly broadened and overlapping peaks for the PBZT sample, possibly due to a relatively high level of internal strains. In contrast, for PBZT doped with La\({}^{3+}\) at concentrations \(x\) = 1 at.% and \(x\) = 2 at.%, well-separated twin peaks are visible. It seems that a small admixture of La (1-2 at.%) stabilizes the rhombohedral lattice of PBZT, while the higher concentration (3-4 at.% of La) causes a transformation to the cubic perovskite structure.  
Figure 1: The flowchart of the fabrication process of La-doped (Pb\({}_{0.75}\)Ba\({}_{0.25}\))(Zr\({}_{0.70}\)Ti\({}_{0.30}\))O\({}_{3}\) ceramics.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Sample** & **Crystal System** & **Space Group** & \begin{tabular}{c} **Lattice Param.** \\ **[A]** \\ \end{tabular} & \begin{tabular}{c} **Contrib.** \\ **[wt. \% ]** \\ \end{tabular} \\ \hline PBZT & \begin{tabular}{c} rhombohedral \\ (hex. axes) \\ \end{tabular} & R3c & \begin{tabular}{c} a = 5.8155 \\ c = 14.279 \\ \end{tabular} & 100 \\ \hline \(x=1\) at.\% La & \begin{tabular}{c} rhombohedral \\ (hex. axes) \\ \end{tabular} & R3c & \begin{tabular}{c} a = 5.8069 \\ c = 14.285 \\ \end{tabular} & 100 \\ \hline \(x=2\) at.\% La & \begin{tabular}{c} rhombohedral \\ (hex. axes) \\ \end{tabular} & R3c & \begin{tabular}{c} a = 5.8070 \\ c = 14.285 \\ \end{tabular} & 100 \\ \hline \(x=3\) at.\% La & \begin{tabular}{c} cubic \\ (hex. axes) \\ \end{tabular} & \begin{tabular}{c} Pm-3m \\ \end{tabular} & \begin{tabular}{c} a = 4.1056 \\ c = 5.8169 \\ c = 14.290 \\ \end{tabular} & 30.0 \\ \hline \(x=4\) at.\% La & \
\begin{tabular}{c} cubic \\ (hex. axes) \\ \end{tabular} & R3c &
\begin{tabular}{c} a = 4.1057 \\ c = 5.8170 \\ c = 14.290 \\ \end{tabular} & 28.9 \\ \hline \end{tabular}
\end{table}
Table 1: The results of structural investigations derived from Rietveld refinement of XRD data.  
Figure 2: The results of XRD studies for PBZT-25/70/30 ceramics doped with La\({}^{3+}\) at concentrations \(x=1\) at.%, \(x=2\) at.%, \(x=3\) at.%, and \(x=4\) at.%. The right panel shows a magnification of the peaks at \(20=64^{\circ}\). For reference, the top and bottom panels depict standard PDF2/COD XRD patterns for rhombohedral PZT and cubic PBZT.