## 3 Results  
Figure 1 demonstrates dependences of structural parameters SS on concentration of the modifiers. Figure 1: Concentration dependences of the parameters \(a\), \(\alpha\), and volumes \(V_{\rm exp}\) and \(V_{\rm th}\) of the rhombohedral perovskite cell of Bi\({}_{1-x}\)Er\({}_{x}\)FeO\({}_{3}\) SS. The results showed that, along with SS, the compounds Bi\({}_{2}\)Fe\({}_{4}\)O\({}_{9}\), Bi\({}_{25}\)FeO\({}_{40}\), and Er\({}_{3}\)Fe\({}_{5}\)O\({}_{12}\) are formed in the samples under study, whose content increases with \(x\). The intensity of the strong lines of these compounds at \(x\) = 0.15 and 0.20 reaches 50%. The rhombohedral symmetry of the perovskite cell in SS is retained for all \(x\). In Figure 1, it can be seen that \(V_{\rm exp}\left(x\right)\) does not correspond to the dependence \(V_{\rm th}\left(x\right)\) calculated for the Er \(\rightarrow\) Bi substitution SS, a slight drop in \(V_{\rm exp}\left(x\right)\) is observed only in the range 0.00 \(<x\leq\) 0.05, with \(x\) > 0.05 \(V_{\rm exp}\) practically unchanged. From this it follows that in the structure of BiFeO\({}_{3}\) under selected conditions for the manufacture of ceramics can dissolve less than 5 mol % Er. Therefore, in Bi\({}_{1-x}\)Er\({}_{x}\)FeO\({}_{3}\) SS, an impurity compound with the garnet structure Er\({}_{3}\)Fe\({}_{5}\)O\({}_{12}\) is formed already at \(x\) = 0.05. The other two compounds are routine impurity phases, which cannot be eliminated during the synthesis of bismuth ferrite. Figure 2 demonstrates microstructure elements of BiFeO\({}_{3}\) ceramic samples before and after modifying with Er (\(x\) = 0.10; 0.20). Black regions with roundish or curvilinear boundaries are pores. They are localized over the surface non-uniformly. Ceramic grains (crystallites) were detected by etching their boundaries. It led to the formation of etching grooves, observed as dark lines along the boundaries of the crystallites. Both BiFeO\({}_{3}\) and Bi\({}_{1-x}\)Er\({}_{x}\)FeO\({}_{3}\) ceramics are polycrystalline structures with non-phase grained components. The brightest \"light\" crystallites represent the main phase. Gray grains are a fraction of minor phases. The average, as well as the maximum sizes of crystallites of the main \"light\" phase in the bismuth ferrite ceramics exceed the analogous parameters of the non-main \"gray\" phase. The interval of their values is also wider. When modifying, the maximum size of the crystallites of the \"light\" phase is somewhat reduced in the same way as their average size. Unlike the main phase, where the formation of large crystallites is suppressed, the introduction of a modifier leads to the growth of large grains of minor phases. In addition, with an increase in the Er content, a characteristic hexagonal shape of a part of such crystallites arises, which corresponds to the garnet structure (Figures 2 and 3). Thus, in the form of grains, we observe the appearance of an additional non-basic phase. The percentage of minor phases is also increasing. The interphase boundaries in the obtained multiphase objects are realized as boundary contacts in mixtures of crystallites of different phases, and at the level of substructures formed by the smallest grains of one phase inside the grains of another. Usually it leads to weakening of the dielectric properties by increasing the internal electromechanical loss, space charge accumulation at the interfaces, micro and mesoscopic areas having different electrical properties. The results of the dielectric dispersion study of objects are shown in Figure 3. As can be seen from the figures, in the temperature range of 300-500 K, the considered dependences experience anomalies in the form of strongly dispersion maxima of \(\varepsilon/\varepsilon_{0}\), which have a relaxation character. The observed phenomena are usually associated with the formation of the Maxwell-Wagner polarization [4], which occurs in heterogeneous media at the interface of volume elements with different electrical properties.