# Reasons for the High Electrical Conductivity of Bismuth Ferrite and Ways to Minimize It
## 3 Results
### About the Causes of the High Conductivity of BiFeO\({}_{3}\)
BiFeO\({}_{3}\) begins to form in the temperature range of 770 \(\leq\) T\({}_{1}\)\(\leq\) 820 K; Bi\({}_{25}\)FeO\({}_{39}\) (silenite phase) appears earlier at lower temperatures of \(\sim\)720 K and is an intermediate compound; Bi\({}_{2}\)Fe\({}_{4}\)O\({}_{9}\) (multile phase) is present in BiFeO\({}_{3}\) at the stage of improving its structure (920 \(\div\) 1020 K) as a concomitant compound. Its formation is the result of structural A- non-stoichiometry of BiFeO\({}_{3}\)[39], a phenomenon typical of oxygen-octahedral compounds with the ReO\({}_{3}\) structure [40] and perovskite [41; 42; 43] containing ions of variable valence. A specific feature of such substances is the ability of a crystallographic shift to exclude an appearance of anionic vacancies (for various reasons), and in complex oxides (of the perovskite type), their equal number of cuboctahedral positions. Thus, a decrease in the A-O positions is nothing more than a self-organizing compensatory mechanism for eliminating point defects (vacancies) due to the organization of extended defects-crystallographic shift planes, while maintaining the highly ordered structure of anion-deficient oxides. In this case, the excess A-component, depending on its size factor and thermodynamic background, can be placed in regular B-positions; at irregular locations, forming an autoisomorphic substance [44] or an internal multiplicative [45] SS of implementation; in intergranular layers; or precipitate in the form of impurities [46]. In our case, probably as a result of the deficiency of A-positions (according to our calculations, it is at least 3%), excessive Bi\({}^{3+}\) ions appear, which displace Fe\({}^{3+}\) ions from oxygen octahedra (as follows from [47], the placement of Bi\({}^{3+}\) in A- and B-positions is possible), thereby creating the prerequisites for the formation of the Bi\({}_{2}\)Fe\({}_{4}\)O\({}_{9}\) compound (with a higher Fe content). In BiFeO\({}_{3}\), the appearance of the above described vacancies in the A- and O-sublattices may be due to the partial sublimation of volatile Bi\({}_{2}\)O\({}_{3}\) in the synthesis process of the compound [48] (according to the scheme Bi\({}^{3+}\)\({}_{1-\times\square}\)Fe\({}^{3+}\)O\({}^{2-}\)\({}_{3-1.5\times\square}\)\({}_{1.5\times\square}\) is a vacancy), partial reduction of Fe\({}^{3+}\)\(\rightarrow\) Fe\({}^{2+}\) (according to the scheme Bi\({}^{3+}\)Fe\({}^{3+}\)\({}_{1-\times}\) Fe\({}^{2+}\)\({}_{x}\)O\({}^{2-}\)\({}_{3-\times/2}\square\)\({}_{x/2}\)), the traditional loss of the part of oxygen in oxygen-octahedral media. Another mechanism for increasing \(\sigma\) of BiFeO\({}_{3}\) is based on structural instability due to its boundary position in a family of oxides with a perovskite type structure (OSP) (Figure 4, where \(\mu\) is the degree of stretching of A-O bonds and compression of B-O bonds due to the discrepancy between the sizes of ions and the sizes of voids of the closest packing [47; 49; 50]), as well as the proximity of sintering and incongruent (with decomposition) melting temperatures [38; 51]. This can lead to a slight violation of the stoichiometry of BiFeO\({}_{3}\) due to the formation of a noticeable amount of difficult to remove ballast phases [19; 20], including unreacted initial components [52]. This is facilitated by the narrow concentration-thermal interval of the existence of the BiFeO\({}_{3}\)[8; 9] phase, and quite wide crystallization regions of Bi\({}_{2}\)Fe\({}_{4}\)O\({}_{9}\) and Bi\({}_{25}\)FeO\({}_{39}\) compounds [7; 16; 51; 53], as well as the complexity of the reaction in the equimolar mixture of Bi\({}_{2}\)O\({}_{3}\) + Fe\({}_{2}\)O\({}_{3}\)[17; 18]. In [9] calculations of the thermodynamic potentials for the reactions of BiFeO\({}_{3}\) formation, from which it follows that it is not the most stable of the possible compounds in the Bi\({}_{2}\)O\({}_{3}\)-Fe\({}_{2}\)O\({}_{3}\) system, are provided.