## X-ray diffraction results

The effect of Bi substitution on the structural properties (DRX) of the BaTi0.80Fe0.20O3 (BTFO) product was studied for the percentages of (x = 0.00, 0.05, 0.10 and 0.15). The Fig. 1.a. shows the XRD patterns of these products. The coexistence of the characteristic peaks of the two hexagonal and tetragonal phases is clear for x = 0.00 (BTFO) and x = 0.05. Whereas for x = 0.10 and 0.15, the hexagonal phase disappears completely and the peaks of the tetragonal phase dominate. To better see the effect of Bi on the evolution of the BTFO structure, we zoomed on the two most intense peaks (101) of the tetragonal phase and (104) of the hexagonal phase (Fig. 1. b). We note that the intensity of the peak (104) decreases tofrom x = 0.0 to x = 0.05 and then disappears beyond this percentage. And the peak (101) of the tetragonal phase becomes stable beyond 0.05 of Bi and moves towards the lower angles for x = 0.05 and then towards the high angles at x = 0.10 and 0.15, which indicates the incorporation of Bi into the BTFO ceramic.

The fitting of these phases by using the rietveld refinement method is shown in Fig. 2 and indicate that all the diffraction peaks are indexed with the coexistence of tetragonal and hexagonal phase at x = 0.00 and 0.05 of prepared samples. While at x = 0.10 and 0.15 only the tetragonal phase is identified. The tetragonal phase becomes predominant with increasing of Bi contents and stabilizes at percentage higher than 0.10 of Bi substitution. This suggests that the concentration higher than 0.10 of Bi enhances the hexagonal phase formation. Thus, the structure of the present ceramics change from P63/mmc to P4mm with increasing x from 0.00 to 0.15 and there is no obvious secondary phase observed. These results of refinement confirm the XRD patterns observation.

The rietveld adjustment allowed us to determine the structural parameters of Ba1 − xBixTi0.8Fe0.2O3 ceramics for x = 0.00, 0.05, 0.10 and 0.15, ie the R-factors (Rp, Rwp and χ2), cell parameters and volume (see Table 1). According to these values we find that R < 15.0 and χ2 < 2.0, for the tetragonal phase, which indicates a better refinement of the powders15. The parameters of unit cell a, c and the tetragonality c / a are plotted on the Fig. 3, one notices that c/a decreases for x = 0.05 accompanied by a decrease of ‘a’ parameter due to the dominance Fe3+ ions with ionic radius (ri (Fe3+) = 0.645 Å) greater than the ionic radius, of the substituted Ti4+ ion (ri (Ti4+) = 0.605 Å). Whereas above this concentration of x = 0.05, when the hexagonal phase completely disappears, c/a increases almost linearly. This is probably due to the substitution of Bi3+ ion with (ri (Bi3+) = 1.2 Å) smaller than that of the substituted ion (ri (Ba2+) = 1.35 Å). It should be noted that this evolution, produced by the solid solution, is not only due to the substitution of a small ion to a larger one, but also to the creation of oxygen vacancies15.

The phase composition of crystallized powders was studied by Raman spectroscopy, a highly sensitive spectroscopic technique for probing the local structure of atoms. The Raman spectra of Ba1 − xBixTi0.80Fe0.20O3 for x = 0.00, 0.05, 0.10 and 0.15 are shown in Fig. 4. For x = 0.00, the spectra have seven bands at 120, 184, 248, 350, 500, 680, 880 cm− 1 related to the modes A1g, E1g, E1g, E2g, A1g, A1g and A1g respectively, characteristic of the hexagonal phase16 of BTFO. The band around 680 cm− 1 is related to Fe3+. Thus, it is possible to prove by Raman spectroscopy that the developed ceramic has a hexagonal phase. These results are consistent with those of the literature for iron-doped BaTiO3. By substituting BTFO by Bi, five peaks are observed at 178, 300, 504, 624 and 710 cm− 1, which correspond well to the tetragonal phase17,18. The band at 305 cm− 1, attributed to B1 + E (LO + TO), is characteristic of the tetragonal phase. The intensity of this band and the A1 band at 178 cm− 1 increases gradually, indicating an increase in tetragonality, which is in good agreement with the XRD. An offset of the position of the band between 710 and 720 cm− 1 was observed. We propose that doping with Bi3+ ions induces the valence change of Fe ions from high to low values to maintain the neutrality of the charge. Since the ionic radius of Fe2+ (0.76 Å) is greater than that of Fe3+ (0.645 Å) and Fe4+ (0.585 Å), the Fe - O bonds have a higher covalence so that the 710 cm− 1 band shifted to the higher frequency. In addition, the peak A1g at 680 cm− 1, characteristic of the hexagonal phase, shifts widely and decreases in intensity with Bi substitution for x = 0.05 and finally disappears at x = 0.10 and 0.15. This indicates the disappearance of the hexagonal phase at these levels of Bi.

The Fig. 5 shows the SEM micrographs of Ba1 − xBixTi0.80Fe0.20O3 ceramics for x = 0.00, 0.05, 0.10 and 0.15 sintered at 1200 °C for 6 hours. These images exhibit fine grains with different grains size. The size distribution of the formed grains is found to be non-uniform. The irregular morphology with various sizes of the grains is clearly noticeable in sample with x = 0.00, which shows the coexistence of smaller grains with larger ones.

The average grains size is found to be 1.478 µm, 1.896µ m, 1.990µ m and 3.188µ m, respectively, for x = 0.00, 0.05, 0.10 and 0.15. It is clear that the average grain size increases with increase of Bi content (Fig. 6). The grain form became more homogeneous with doping of Bi at x = 0.15 comparing with the others samples which grain forms are inhomogeneous especially at x = 0.00. Furthermore, the sample with x = 0.00 and 0.05 of Bi have different grains forms which may be reflect the coexistence of two phase in these materials. While at x = 0.10 and 0.15 the tetragonal grain form is clearly observed. These results were consistent with the DRX results

x | 0.00 | 0.05 | 0.10 0.10 | 0.15 |

Statistical parameters | Tetragonal Rp= 6.39 Rwp=8.54 χ2 = 1 | Hexagonal Rp= 8.31 Rwp=13.40 χ2 = 3.90 | Tetragonal Rp= 5.96 Rwp=7.53 χ2 = 1.34 | Hexagonal Rp= 7.55 Rwp=11.4 χ2 = 3.54 | Tetragonal Rp= 4.78 Rwp=6.11 χ2 = 0.960 | Tetragonal Rp= 6.71 Rwp= 8.66 χ2 = 1.56 |

Bragg R-factor | 55.13 | 36.02 | 36.5 | 40.6 | 21.8 | 14.6 |

Lattice constants (Å) | a = b = 4.00668 c = 4.03009 | a = b = 5.839 c = 13.7607 | a = b = 4.00524 c = 4.01916 | a = b = 5.654 c = 13.423 | a = b = 4.004677 c = 4.05988 | a = b = 4.005567 c = 4.081004 |

Volume (Å 3) | 64.697 | 406.309 | 64.475 | 420.19 | 63.54 | 62.86 |

Space group | P4mm | P 63/mmc | P4 m | P63/mmc | P4mm | P4mm |

## Dielectric properties

The Fig. 7 displays the evolution of the real part of the dielectric permittivity (ε’r) as a function of temperature (from R.T to 450 °C) at various frequencies (from 5 KHz to 2 MHz). There are tree dielectric anomalies. The first anomaly corresponds to the phase transition from the ferroelectric rhombohedral phase to the ferroelectric orthorhombic TR−O phase. It is present for all ceramics at different temperatures. The second anomaly corresponds to the phase transition from the ferroelectric orthorhombic phase to the ferroelectric TO−T tetragonal phase. While the third anomaly at high temperatures is the phase transition from the ferroelectric tetragonal phase to the paraelectric cubic phase Tm 19. These tree peaks are due to different phase transitions of BiFeO3 and BaTiO320.

The evolution of the maximum dielectric permittivity and temperature of the three phase transitions at a frequency of 5 KHz was also studied. It appears from the Fig. 8.a that the dielectric constant of BBTFO ceramics increases significantly with Bi doping for all phase transitions. This could be due to the role of conductive bismuth ions in the BaTiO3 network substituted the barium ions21. In addition, the Bi3+ ion substitutes Ba2+ for BaTiO3, so that the ionic volume of site A decreases due to vacancy of the barium, creating a larger active space for Ti4+. From the + 2 to + 3 increase in the ion of A site, a residual positive charge appears and the mutual effect between sites A and B (Ti4+) becomes stronger. Thus, the polarization of Ti4+ is improved, then the dielectric constant increases strongly22. This increase in ɛ’r 'with the increase in Bi is also found by S. Islam et al23, for the BaTiO3 ceramics substituted for Bi, but the values of ɛ’r that they obtained are greater than our values due to the Fe co-substitution.

The decrease of Tm (Fig. 8.b) with Bi doping indicates a partial substitution of Ba2+ ions by Bi3+ in the perovskite network. These results are in good agreement with those found by S. Islam et al23. Thus, the advantage of the co-substitution of BTF by the ions of Bi in site A is the maximization of the value of the dielectric permittivity and the minimization of the phase transition temperature.

All the present phase transitions present a clear diffuse behavior. To explain this type of behavior (ferroelectric with diffuse phase transition) the diffuseness character of the phase transition or the diffuseness coefficient (γ) was obtained by fitting the dielectric constant curves with the modified Uchino’s phase transition as given below24:

This equation may be written as the following:

## Ln [((ε’r,max / ε’r )-1)] = γ ln (T-Tm) - γ ln2δ

Where Tm is the temperature corresponding to the maximum of dielectric constant, ε’r,max is the permittivity at Tm, γ is the degree of dielectric relaxation. It value is 1 for normal ferroelectrics following CurieeWeiss law, 2 for ideal relaxor ferroelectrics. In general γ takes a value between these limits (1 < γ < 2) indicating an incomplete diffuse phase transition. The value of δ represents the degree of diffuseness for transition peaks. Linear relationships are observed in the plot of ln ((ε’r,max / ε’r )-1) versus ln (T-Tm) at 5 KHz frequency for all the samples as it is shown in Figs. 9, 10 and 11. By fitting the experimental data to the modified Uchino equation, We notice that certain values of the diffusivity parameter γ are close to 1 (table.2) but the transition always remains diffuse and relaxor behevior, this is can be explained by the large values of δ. The other values of γ between 1.49 and 2 indicate that the type of the transition is relatively diffuse and present a relaxor behavior. On the other hand, the values of "γ" greater than 2 or very less than 1, the distribution of the phase temperatures of these ceramics is no longer a Gaussian as it was described by Smolenski25 which limits the validity of the Uchino’s law of these compounds.

The diffusion factor δ (table.2) is maximum for x = 0.05 for the three phase transitions then decreases to x = 0.10 and thereafter increases to x = 0.15 of Bi. The maximum value of δ shows that the three phase transitions are very diffuse at x = 0.05, while they are less diffuse at x = 0.10.

The diffuse phase transition behavior observed in these ceramics can be induced by many reasons, such as the fluctuation of the microscopic composition, the melting of micropolar regions in macropolar regions or a coupling of the parameter order and local disorder generated by a local constraint. The disorder of the structure of the ceramics of Ba1 − xBixTi0.80Fe0.20O3 may result from a substitution of two ions Bi3+ and Fe3+ in the two crystallographic sites Ba2+ and Ti4+ respectively, thus leading to nanometric heterogeneity in the compounds and consequently to a distribution of various local Curie points26,27, then to a random distribution of the electric strain field in mixed oxide compounds which is the main reason leading to diffusion behavior as reported by Vugmeister28.

Table.2. Refined structural parameters of Ba1-xBixTi0.80Fe0.20O3 ceramics for x = 0.00, 0.05, 0.10 and 0.15.

Phase transition | x | 0.00 | 0.05 | 0.10 | 0.15 |

TR−O | δ | ---- | 86.17 | 29.22 | 56.7 |

γ | ---- | 1.49 | 2 | 2.00 |

TO−T | δ | ---- | ---- | 22.9 | 61 |

γ | ---- | ---- | 2.28 | 1.99 |

Tm | δ | ---- | 323 | 12.18 | 82.82 |

γ | ---- | 1.08 | 1.62 | 1.01 |

Dielectric constant as function of frequency: The Fig. 12 illustrates the real part of the dielectric constant (ε'r) as a function of frequency of Ba1 − xBixTi0.80Fe0.20O3 ceramics at x = 0.00, 0.05, 0.10 and 0.15 sintered at 1200 °C/6 h. All the compositions have higher values of the dielectric constant at low frequencies. The permittivity decreases gradually with increasing frequency and becomes constant at very high frequency. Such frequency-dependent dielectric behavior can be explained by Koops's theory which depends on the Maxwell Wagner model for non-homogeneous crystal structure29–31. This model suggests that a typical dielectric ceramic is composed of well conductive grains usually separated by resistive grain boundaries (low conductive). When an external electric field is applied to a dielectric ceramic, the charge carriers begin to migrate through the conductive grain and pile up at the boundaries of the resistive grain. As a result, a strong polarization (spatial charge polarization) occurs in the dielectric ceramic, resulting in high dielectric permittivity. In this case, the low-conductive grain boundaries contribute to the higher value of the permittivity at a lower frequency. Different types of polarization mechanisms are also responsible for the higher values of the permittivity in the low frequency region. Indeed, in the low frequency region, the four polarization mechanisms (ionic, electronic, dipolar polarization and space charge) contribute to the total polarization of the compound, which is responsible of a high dielectric permittivity. But with the increase of the frequency (i.e. in the high frequency region), the contribution of some of the polarization mechanisms to the total one is interrupted which results in lower permittivity values.

## Electric properties

To understand the high-temperature dielectric dispersion, the complex Cole–Cole equation was used to analyze the impedance data. The Fig. 10 shows the complex impedance spectrum plots of Ba1 − xBixTi0.80Fe0.20O3 ceramics for x = 0.05 at different measurement temperature from 100 °C to 400 °C. The feature of impedance spectra is almost similar at different temperatures. However all the curves showed a tendency to bend towards the abscissa to form semicircles with their centers on the real axis, having comparatively larger radius showing an ideal Debye type behavior32,33. The radius of curvature of the arcs decreases with increasing temperature, which reveals that the conductivity of the sample increases as temperature increases and indicate also a negative temperature coefficient of resistivity (NTCR) behavior of the test materials34,35

According to the impedance spectrum data obtained of Ba1 − xBixTi0.80Fe0.20O3 ceramics at x = 0.00, 0.05, 0.10 and 0.15 at 400 °C of measurement temperature (Fig. 11) the Complex impedance spectrum of all the samples shows the presence of an arc of a circle with the center below the real axis indicating the contribution of both ceramic’s boundaries and grain boundaries 36.

The electrical equivalent circuit corresponding to the sample impedance response is shown as inset of Fig. 11 and is represented by a number of elements, one R/C and other R/CPE connected in series. The values of resistance of both grain and grains boundaries are given by the fitting of the test materials by using the equivalent circuit plots. The Fig. 12 shows that the grains and grain boundaries resistivity increase with increasing of Bi contents from 0.00 to 0.05 indicating a positive temperature coefficient of resistivity (PTCR). While these resistivities decrease from x = 0.05 to 0.15 of Bi substitution showing a negative temperature coefficient of resistivity (NTCR).