# 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\({}_{3}\)  
Figure 1 shows 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. The following facts are noteworthy: the enormous values of these quantities in the interval of (400 \(\div\) 800) K (1); the formation of a low-temperature relaxation maximum \(\varepsilon^{\prime}/\varepsilon_{0}\) at (400 \(\div\) 500) K, not associated with any of the known phase transitions (2); rapid growth of \(\varepsilon^{\prime}/\varepsilon_{0}\) at 600 K at all frequencies; the form in the range of (600 \(\div\) 700) K of a \"dome\" of this characteristic (3); the beginning of the formation of a \"dome\" \(\varepsilon^{\prime\prime}/\varepsilon_{0}\) at high frequencies at 800 K(4). To describe the process of low-temperature dielectric relaxation according to the data obtained from the dependences \(\varepsilon^{\prime}/\varepsilon_{0}\) (T) and tan\(\delta\) (T), the graphs ln\(\omega\) (1/T\({}_{\rm m}\)) (T\({}_{\rm m}\) are the temperatures of the extrema \(\varepsilon^{\prime}/\varepsilon_{0}\) and tan\(\delta\) measured at the frequency \(f=\omega/2\pi\)) presented in Figure 2.  
The presented dependences satisfy the Arrhenius law, which allows one to characterize the relaxation process using the activation energy, \(E_{a}\), and the average frequency of overcoming the potential barrier, \(\omega_{0}\). For the two plotted dependences, these parameters take significantly different values (\(E_{a}\) = 1.38 and 0.68 eV, \(\omega_{0}\) = 2.8 \(\times\) 10\({}^{16}\) and 2.97 \(\times\) 10\({}^{14}\) rad/s, respectively), indicating two independent relaxation processes occurring in the object. Based on the literature data, it can be argued that such values are typical for the Maskwell-Wagner relaxation [13; 14; 15], associated with the accumulation of free charges on the interface of components in spatially inhomogeneous media on the background of interlayer, interphase, and interphase structural rearrangements. The reason for the development of this situation, as well as the appearance of two relaxation processes, is the natural composite structure of BiFeO\({}_{3}\), which is formed on the basis of at least two (not counting BiFeO\({}_{3}\) itself) Bi-, Fe-containing compounds (Bi\({}_{25}\)FeO\({}_{39}\), Bi\({}_{2}\)Fe\({}_{4}\)O\({}_{9}\)) that almost always accompany the formation of BiFeO\({}_{3}\), remain in it (in different amounts) in the form of ballast phases [7; 16; 17; 18; 19; 20; 21; 22; 23; 24; 25] (we will talk about this in more detail below). A brief mention of the physical mechanisms of macroevents developing in such heterogeneous media should be made. It is known that in such materials an increase in the permittivity caused by the Maxwell-Wagner polarization is detected [23], and it is associated with the accumulation of charges at the boundaries of inhomogeneities in dielectrics [26]. Moreover, the increase in dielectric permittivity is always due to the electrical conductivity of the components (crystallites) of a heterogeneous dielectric [27; 28]. In experimental works [29; 30; 31], a gigantic increase in the permittivity is associated with relaxation polarization processes. In works [31; 32] an analysis of the growth of the low-frequency permittivity of a heterogeneous dielectric, which is a randomly inhomogeneous object, is made using finite elements and Monte Carlo methods. The author shows that the greatest increase in the dielectric permittivity occurs in the so-called \"reciprocal composite\", that is, in two-layer structures in which the dielectric permittivity of one component is significantly greater than that of the second one, whereas the specific conductivity of the  
Figure 2: Arrhenius plots describing relaxation processes on \(\varepsilon^{\prime}/\varepsilon_{0}\) (_T_) and tan\(\delta\) (_T_) dependences of BiFeO\({}_{3}\) ceramics.