3.1. X-ray diffraction and morphological characterization
Room-temperature XRD data collected from the as-prepared samples with δ = 0.375 and δ = 0.50 are depicted in Fig. 1(a). The crystallographic study demonstrated that those samples adopt the brownmillerite-type structure with no traces of secondary phase. A structural transition from orthorhombic structure (Pnma) with the splitting of peaks can be observed on X-ray diffraction spectra. The structural transition appears for δ = 0.375 and δ = 0.5 corresponding to an Fe2+ concentration between 75 % and 100 %. As the amount of oxygen deficiency increases, the intensities of peaks decrease, as revealed with the most intense peak in Fig. 1(a).
The profile refinement was carried out using the Fullproof software [23] and the pseudo-Voigt functions were invested for peak profile fitting. The refined lattice parameters and the discrepancy factors are exhibited in Table. 1. The Rp and RWp factors displayed much higher values than expected, which is accounted for in terms of the peaks with small intensities [21]. The difference between the fitted and experimental intensities of the reflection peaks may be assigned to preferred orientation effects [23, 24].
Figure 1(b) and 1(c) characterizes the Rietveld refinement taking into account the sample with δ = 0.50. The reflection peaks were crystallized in the monoclinic system with P2/m space group. The average crystallite size was determined by well-known Scherer equation [25] and the results are outlined in Table. 1.
The elemental composition of the compound was measured by Energy dispersive X-ray analysis. EDX spectrum (Fig. 2) unveils the presence of characteristic peaks of La, Ba, Sr, Fe and O elements integrated during the preparation. The inset of the Fig. 2 illustrate the room temperature SEM micrographs of the La0.75Ba0.10Sr0.15FeO2.875−δ (δ = 0.375 and 0.50) sample. These images show unique chemical contrast corresponding to the ferrite phase. The polycrystalline nature of the samples was confirmed from the existence of a large number of grains and grain boundaries in the samples.
A large distribution of grains was detected in SEM micrograph. Polygonal shape grains of varying sizes were observed for all the composition.
3.2. FTIR characterization
The crystal structure of the perovskite was identified through Fourier transform infrared (FTIR) spectra highlighting its characteristic absorption bands [26]. Figure 3 presents the FT-IR spectrum measured at room temperature in the frequency range of 550–1000 cm− 1. The different vibration frequencies below 1000 cm− 1 are assigned to the metal-oxygen vibrations bands owing to the strong affinity of bonding in metal oxide linkages. The vibrational band present at 750 is attributed to the Fe-O-H bending vibrations [27]. The small peaks at around 850 cm− 1 are indicative of the presence of metal oxide-bonds, which are assigned to the vibrations of Fe-O and O-Fe-O Bonds [27].
The vibration recorded at 900 cm− 1 can be attributed to C-H bending vibrations [28].
For both samples, the spectra exhibit two bands characteristics of the metal cations’ stretching vibrations inside the tetrahedral and octahedral sites. The FTIR spectra of the above mentioned samples display two main absorption bands corresponding to the vibrations of tetrahedral and octahedral site complexes [29]. The stretching vibration of the tetrahedral site lies in the wave-number range 550–800 cm− 1 and the low frequency band below 550 cm− 1 is assigned to the stretching vibrations of octahedral complexes.
The absorption band corresponding to the tetrahedral complexes composed of several sub-bands, are marked in Fig. 3 with ν (1) being centered at ~ 750 cm− 1, ν (2) at ~ 680 cm− 1, ν (3) at ~ 630 cm− 1, ν (4) at ~ 610 cm− 1, ν (5) at ~ 580 cm− 1 and ν(6) at ~ 560 cm− 1. The existence of sub-bands is suggestive of the presence of Fe2+ ions in ferrite structure [30–32], which is basically assigned to the Jahn-Teller distortion produced by the Fe2+ ions. This observation goes in good agreement with the observation noted by Rathod on Li-Zn ferrites [33].
Referring to pervious state of art works, the origin of the splitting of the main absorption band is not well processed. However, this can be inferred through the complex vibrations of the tetrahedral complexes which are highly correlated to the octahedral site complexes.
3.3. Current-voltage analysis
Before discussing dielectric properties, the current-voltage characteristic (I-V) was undertaken in order to test the contact quality. Figure 4 portrays (I-V) and (J-V) (where J is the current density) variations for both structures recorded under different temperatures. The I-V curves exhibit two symmetric fragments of lines. This behavior confirms the presence of no depletion layer [34]. In other words, the electrons can drift between the two electrodes without being reduced by depletion layer. As a matter of fact, we infer that the contact is of ohmic type. This attitude was also confirmed by the linear variation of double log-log I-V variation. The log-log plots of I vs V is fitted with the relation I α Vn, where n is found to be equal to 1 (ohmic relation between current-voltage).
3.4. Electrical conductance analysis
Most of the brownmillerite compounds [2], where the total conductivity includes the contribution of electronic and ionic conductivity, stand for mixed conductors. Our compounds possess the contribution of both electron and oxide-ion conductivity in view of the presence of oxygen vacancies and mixed valence states of iron ions (Fe2+/Fe3+) [35].
The electrical conductance investigation over a wide temperature (300–620 K) and frequency (40–106 Hz) ranging for δ = 0.375 and 0.50 samples are illustrated in Fig. 5(a). This entity is indicated by the relation [36]
where σ is the conductivity, A is cross sectional area of material and l is its length.
The conduction is ensured by the hopping of electron from Fe3+ to Fe2+ ions and the presence of oxygen vacancy [35]. The increase in temperature enhances the hopping phenomenon resulting in an increase in the conduction process and therefore leading to the conductance increase [37].
The frequency dependence of conductance is examined by Jonscher’s law [38, 39]
G = G dc + Gac = Gdc + AωS Eq. 3
Referring to the expression stated above, Gdc and Gac represent the conductance in continuous and alternative current, respectively. A is a pre-exponential factor dependent on temperature, ω is the angular frequency and s is the frequency exponent (0 ≤ s ≤ 1).
We can infer from the conductance measurements that for each temperature, the spectrum can be divided into two parts. A Plateau appears at low frequencies (frequency independent conductance (40 Hz to 103 Hz)) attributed to dc-conductance bulk. The low-frequency plateau gets larger proportionally to the increase of temperature. The second part corresponds to the higher frequency dispersion region. This part corresponds to ac-conductance [40].
The experimental conductance data were fitted by Eq. 3 for the investigated samples. A typical example of this fitting at T = 500 K is illustrated in Fig. 5(b) (red solid line). A close agreement is traced between the experimental data and the fitted one. As noticed, the conductance decreases with the increase in δ rate. Departing from the electronic neutrality of δ = 0.375 (25% Fe3+, 75% Fe3+) and δ = 0.50 (100% Fe2+) compounds, we detect that the oxygen deficiency reduces the Fe2+/Fe3+ ratio. Thus, the number of hopping sites decreases. The presence of oxygen vacancy is responsible for the excess of Fe2+ ions over Fe3+ ions.
DC conductance findings resulting from conductance measurements at low frequencies are portrayed in Fig. 6(a) for both studied compounds. The activation energy values Ea corresponding to Gdc were estimated from the Arrhenius law as described by the following expression [41]
G dc = A0 exp(-Ea/KBT) Eq. 4,
where A0 is the pre-exponential factor, Ea is the activation energy and KB is the Boltzmann constant.
In view of the creation of oxygen defects (vacancies), a wide variation of conductivity is noticed. In addition to the three straight lines observed in the whole explored temperature range 300–620 K, we detect an interior region representing the plateau (as portrayed in Fig. 6(b)). Each one corresponds to a particular Ea which rises up proportionally to the corresponding temperature. The estimated values of Ea were highlighted in Table. 2. The determined values are very close to those previously obtained in oxygen vacancy ferroelectrics compounds [42].
The activation energy proves to be around 908 meV − 630 meV at high temperature (region VI). This finding can be assigned to the bigger charge than that of an electron. In other words, oxygen vacancies motion is the main responsible factor for conduction at high temperature [43, 44]. Relying upon other reports [45], the Ea of oxygen vacancy is around 1 eV. For region (II), the Ea attitude refers primarily to octahedral distortion obtained after oxygen vacancy creation [42]. The activation energy of low-temperature region (I) is attributed to the hopping process.
In region (III), we notice a metallic behavior confirming the existence of two charge carriers. Indeed, as temperature increases, the free electrons density increases as well. This enhances collision frequency between charge carriers and induces metallic behavior. At higher temperature, ion conduction appears and becomes predominant.
The creation of oxygen vacancies gives rise to additional properties of the compounds.
3.5. Permittivity analysis
The variation of dielectric (Fig. 7) constant with frequency demonstrates a normal behavior of polar dielectric materials [46] with giant constant (in the range of 104 at low frequency for δ = 0.375 sample) and shows that it is temperature dependent. This colossal dielectric constant is mainly assigned to interfacial polarization ameliorated after oxygen vacancy creation [11]. The value of ε’ decreases when frequency increases until it slowly reaches a constant value at higher frequencies. The observed behavior can be explained by Maxwell-Wagner polarization [47, 48]. It is noticeable that the magnitude of ε’ decreases heavily with the increase of the concentration of oxygen vacancy. The Giant value of dielectric constant is reported for La0.75Ba0.10Sr0.15FeO2.875−δ (δ = 0.375) samples around 5.104 Fm− 1 and about 300 Fm− 1 for La0.75Ba0.10Sr0.15FeO2.875−δ (δ = 0.50) samples. The probably explanation is the decrease of the number of dipoles sharing in the polarization process.
Moreover this decrease can be explained by an increase in FeO6 titling due to the insertion of oxygen vacancy [11].
The thermal variation of dielectric properties are examined at different frequencies (103, 104, 105 and 106 Hz) in Fig. 8. Two dielectric relaxations are observed. These dielectric peaks are seen around 500 K and 620 K for all frequencies. This critical temperature is known as transition temperature. The charge carriers hopping between Fe3+ and Fe2+ ions play the main role behind the dielectric relaxation at low temperature. Furthermore, the low temperature peak may refer to the transition from ferroelectric to anti-ferroelectric state.
However, at high temperature, the dielectric relaxation is associated with oxygen vacancy and the peak corresponds to the transition from anti-ferroelectric state to paraelectric state.
The sample displays a peaking behavior at a specific temperature, owing to the jumping frequency of an electron between Fe3+ and Fe2+, which becomes equal to the applied field frequency at this specific temperature. In fact, when both frequencies are the same, the polarization increases gradually until reaching its maximum. Then, the applied frequency keeps increasing while the other one can’t maintain this rise. This leads eventually to polarization decreasing. Thus, the dielectric constant decreases. Yet, this evolution can be assigned to intrinsic effects [11]. The oxygen vacancy creation increases the coulombic repulsive force between iron ions. When samples are exposed to an ac electric field, the iron ions can be displaced around without distorting the octahedral FeO6. From this perspective, this effect proves to be the cause of the increase in the dielectric constant proportional to the temperature.
The loss factor variation (Fig. 9) indicates a very similar trend as the dielectric constant exhibits two relaxer behaviors at low and high temperature. As reported in Fig. 9, the oxygen vacancy decreases the dielectric loss leading to a better use in future applications [8]. The decrease of dielectric loss with oxygen vacancy concentration is associated with the decrease of electrical conductance.