# Reasons for the High Electrical Conductivity of Bismuth Ferrite and Ways to Minimize It
## 4 Conclusions  
Solid solutions of the composition Bi\({}_{1-x}\)REE\({}_{x}\)FeO\({}_{3}\) (rare-earth elements, lanthanides, Ln: La, Pr, Nd, Sm, Eu, Gd, Tb, Dy, Ho, Er, Tu, Yb, Lu; x = 0.0-0.5; \(\Delta x\) = 0.025, 0.05, 0.10) were prepared by two-stage solid-phase synthesis followed by sintering by conventional ceramic technology with varying annealing temperatures. Comprehensive studies of the structure and specific electrical conductivity of the obtained experimental samples have been carried out. The study of the temperature dependences of \(\varepsilon^{\prime}/\varepsilon_{0}\), \(\varepsilon^{\prime\prime}/\varepsilon_{0}\) BiFeO\({}_{3}\) and BiFeO\({}_{3}\)/REE on different frequencies of the \(ac\) field showed the presence of a low-temperature relaxation maximum \(\varepsilon^{\prime}/\varepsilon_{0}\) (\(T\)) at (400 \(\div\) 500) K, which is not associated with any of the known phase transitions in BiFeO\({}_{3}\) and satisfies the Arrhenius law with \(E_{a}\) = 1.38 and 0.68 eV, \(\omega_{0}\) = 2.8\(\cdot\)10\({}^{16}\) and 2.97\(\cdot\)10\({}^{14}\) rad/s, for \(\varepsilon^{\prime}/\varepsilon_{0}\) (\(T\)) and tan\(\delta\) (T), respectively. The results obtained allowed us to make conclusions about the presence of Maskwell-Wagner relaxation, as well as to consider the physical mechanisms of macroevents developing in such heterogeneous media. The possibility of a significant (by 2-3 orders of magnitude) decrease in the electrical conductivity of BiFeO\({}_{3}\) by introducing into it large-size ions of rare-earth elements (La, Pr, Nd, Sm, Eu, Gd with 0.94 \(\leq R\leq\) 1.04 A) in amounts up to 10-mol % was presented. Preliminary estimates showed that the observed effect is due to a decrease in the chemical bond strength (\(\mu<\) 1.04) in BiFeO\({}_{3}\) upon its modification and stabilization of the structure due to the shift of BiFeO\({}_{3}\) into the region of existence of the perovskite structure. The presented results should be taken into account when developing devices using BiFeO\({}_{3}\)/REE materials. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multirow{2}{*}{**A-Element**} & \multirow{2}{*}{\(R\), \(\AA\)} & \(\mu\), **rel.** & \multirow{2}{*}{\(L_{\text{A-O}}\), \(\AA\)} & \multirow{2}{*}{\(a\), \(\AA\)} & \multirow{2}{*}{\(\Delta_{\text{A-O}}\), \(\AA\)} & \multirow{2}{*}{\(\Delta_{\text{A-O}}\)/\(L_{\text{A-O}}\), **rel. Units**} & \multicolumn{2}{c}{**Electronic Configurations**} \\  & & **Units** & & & & & **of Outer Layers** \\ \hline Bi & 1.20 & 1.04 & 2.73 & 3.95 & 0.070 & 0.030 & (S\({}^{2}\))p\({}^{3}\) \\ La & 1.04 & 0.36 & 2.69 & 3.93 & 0.110 & 0.040 & (f\({}^{6}\))ds\({}^{2}\) \\ Pr & 1.00 & 0.39 & 0.65 & 3.90 & 0.116 & 0.044 & (f\({}^{2}\))ds\({}^{2}\) \\ Nd & 0.99 & 0.40 & 0.63 & 3.88 & 0.120 & 0.045 & (f\({}^{3}\))ds\({}^{2}\) \\ Sm & 0.97 & 0.44 & 2.62 & 3.88 & 0.130 & 0.050 & (f\({}^{5}\))ds\({}^{2}\) \\ Eu & 0.97 & 0.47 & 2.60 & 3.86 & 0.140 & 0.054 & (f\({}^{6}\))ds\({}^{2}\) \\ Gd & 0.94 & 0.50 & 2.59 & 3.86 & 0.148 & 0.057 & (f\({}^{7}\))ds\({}^{2}\) \\ Ho & 0.86 & 0.52 & 2.55 & 3.83 & 0.150 & 0.059 & (f\({}^{10}\))ds\({}^{2}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Main crystal chemical characteristics of A-elements (A-Bi, La, Pr, Nd, Sm, Eu, Gd, Ho). **Author Contributions:** K.P.A.--original draft preparation, writing--review and editing, investigation; V.P.S.--review and validation; A.V.T., A.A.P.--discussion of results and data curation; L.A.S.--X-ray investigation; S.I.D., A.G.R., D.D.R.--data curation; L.A.V.--resources, L.A.R.--conceptualization, S.V.H., I.A.P., S.-H.C., H.-Y.W.--discussion of results. All authors have read and agreed to the published version of the manuscript. **Funding:** This work was financially supported by the Ministry of Science and Higher Education of the Russian Federation (State assignment in the field of scientific activity, Southern Federal University, 2020); Ministry of Science and Technology of the Republic of China (MOST108-2221-E-992-026-, MOST109-2221-E-992-091-).