# Reasons for the High Electrical Conductivity of Bismuth Ferrite and Ways to Minimize It
## 3 Results
### About Ways to Minimize the Conductivity of BiFeO\({}_{3}\)  
One of the ways to stabilize BiFeO\({}_{3}\) and optimize its properties is its introduction [60; 61; 62; 63] into the REE composition. In this case, an increase in magnetoelectric coefficients is associated with the special magnetic properties of REE: despite the fact that their own ferromagnetic ordering occurs only at very low temperatures, the magnetic nature (_f_-ferromagnetism) of REE manifests itself in an increase in exchange interactions between other ferromagnetic ions, for instance, Fe\({}^{3+}\), which leads to an increase in the Neel temperature. This is facilitated by smaller (compared to Bi) radii of REE [44]. The introduction of sufficiently rigid highly ionized REE ions instead of easily deformable ions, for example, Bi, inevitably leads to a decrease in the Curie temperature and a convergence of the temperatures of the ferroelectric and antiferromagnetic transitions, which is highly desirable for practical applications. In addition, the substitution of part of Bi\({}^{3+}\) ions will lead to some increase in compositional disorder in the system, which will contribute to their manufacturability. The latter can be ensured by non-volatility and small-sized REE compared to Bi\({}^{3+}\). The thermal stability of BiFeO\({}_{3}\) modified with REE is increased, the range of optimal sintering temperatures widened, the phenomena associated with the melting of the synthesized product practically disappeared, the amount of impurities decreased. All these were prerequisites for the expected decrease in \(\sigma\) in BiFeO\({}_{3}\)/ REE. Figure 5 shows the dependences of the electrical conductivity (at room temperature) on the concentration of REE introduced into BiFeO\({}_{3}\), and Figure 6 the same dependence on the radii of the modifying elements. It can be seen that by doping BiFeO\({}_{3}\) with REE, in many cases it is possible to reduce \(\sigma\) and increase \(\varrho_{\rm v}\) by 2 \(\div\) 3 orders of magnitude. In this case, large-sized REE (tab.) with radii close to 0.99 A, introduced in amounts of up to 10 mol %, turned out to be the most effective. This is explained, in our opinion, by the creation of the most favorable dimensional conditions for the existence of BiFeO\({}_{3}\) and, as a consequence, a decrease in impurity phases (which an increase in \(\sigma\) is associated with) and stabilization of the rhombohedral structure typical of BiFeO\({}_{3}\). Figure 7 shows the dependences of the structural characteristics of SS with large REE on the content (\(x\)) of the latter. It is clearly seen that in all the cases the state diagrams contain five concentration regions corresponding to  
Figure 4: Diagram of directional parameters \(\upupsilon\) (characterizing the energy profitability of attaching atoms to each other along the directions of the highest concentration of electron density) and strength \(\mu\) and the region of existence of oxides with a perovskite-type structure (OSP). successive structural transformations \(R\)\(H\)\(+\)\(O_{1}\)\(+\)\(O_{2}\)\(\rightarrow\)\(O_{1}\)\(+\)\(O_{2}\)\(\rightarrow\)\(O_{2}\) with small variations in phase filling, and Figure 8 illustrates the dependences of the position of the boundaries of the existence of the pure \(Rh\)- phase, its mixture with the \(O_{1}\)- and \(O_{2}\)- phases, the values (\(\Delta R_{\rm A}\)/\(R_{\rm min}\))\(\cdot\)100% (where \(\Delta R_{\rm A}\) = \(R_{\rm B}\)\(-\)\(R_{\rm REE}\), \(R_{\rm min}\) = \(R_{\rm REE}\)), the differences of (\(\Delta V\)) between \(V_{\rm exp}\) and \(V_{\rm theor}\) on the radius, \(R\), REE. At lower \(R\) (<0.99 A), the shift of the \(Rh\)- boundary toward lower REE concentrations is obviously a consequence of a significant deviation of the conditions from those necessary for the formation of SS of substitution (\(\Delta R_{\rm A}\)/\(R_{\rm min}\) should be equal, according to various estimates, to less than 15% [64] or 28 \(\pm\) 2% [65]).