3.1 Crystal structure analysis
Room temperature XRD pattern of Bi2Fe4O9 and Ba and Ce-doped Bi2Fe4O9 samples as prepared by Sol-gel route is shown in Fig. 1(a-d). As we mentioned before the Bi2Fe4O9 samples were calcined at different temperatures are further designated as (Bi2Fe4O9)650–850 for Bi2Fe4O9 calined at 650°C and 850°C and (Bi2Fe4O9)800–850 for Bi2Fe4O9 sample calcined at 800°C and 850°C. Finally these both samples have been sintered at 850 °C (8 h). For the samples (Bi2Fe4O9)650–850 and (Bi2Fe4O9)800–850 the diffraction peaks are well indexed with the orthorhombic structure of Bi2Fe4O9 (space group: Pbam), matche well with JCPDS card No. 74-1098 [13] with no trace of other impurity phases within the limit of instrument sensitivity. These result confirms that phase-pure Bi2Fe4O9 can be synthesized by sol-gel route. From Fig. 1(a, b), we can observe the broading of the peaks in (Bi2Fe4O9)650–850 sample due to low calcination temperature. Whereas, due to high calcination temperature, proper crystalline phase has been observerd in (Bi2Fe4O9)800–850 sample. Due to calcination temperature variation double peaks transforms into a single peak from sample (Bi2Fe4O9)650–850 to (Bi2Fe4O9)800–850. Furthermore, the refined lattice parameters of sample (Bi2Fe4O9)650–850 are a = 7.94 Å, b = 8.40 Å, and c = 5.92 Å; and a = 7.95 Å, b = 8.45 Å, c = 5.94 Å for (Bi2Fe4O9)800–850, revealing the slight expansion in both the ab plane and the c axis with doping contents increasing. In addition, with the increase of calcination temperature, there is a limited intensity increasing and narrowing of the diffraction peaks, indicative of better crystallization and the increase of crystalline sizes. Using the Debye Scherrer formula, the average crystalline size can be estimated to be about 52 nm, 80 nm for (Bi2Fe4O9)650–850 and (Bi2Fe4O9)800–850.
XRD for alkaline earth metal Ba+ 2 ion and rare earth Ce+ 3 ion doped Bi2Fe4O9 ceramics are shown in Fig. 1(c, d). For the doped samples the diffraction peaks are well indexed with the orthorhombic structure of Bi2Fe4O9 (space group: Pbam), matches well with (JCPDS: 25–0090). As witnessed from the Fig. 1(c,d) in the doped Bi2Fe4O9 samples, there is a shift in lower theta value due to ionic radius mismatch of dopent (ionic radius of Ba = 1.35, Ce = 1.01) with Bi+ 3 (0.96) ion. The ionic radius of Ba and Ce ions are greater then Bi ion that is why we are getting a shifting at lower theta value as comparison to parent Bi2Fe4O9 ceramic. The lattice parameters were obtained using indexing such as a = 7.101 Å, b = 8.50 Å, and c = 5.94 Å for Bi1.98Ba0.02Fe4O9, and a = 7.99 Å, b = 8.48 Å, and c = 5.93 Å for Bi1.98Ce0.02Fe4O9 sample. The crystalline size for Ce+ 3 and Ba+ 2 ions doped ceramics are found to be 62 and 65 nm, respectively
3.2 Microstructure analysis
The scanning electron microscope (SEM) was used to study the surface morphological and microstructural characteristics of pristine and doped Bi2Fe4O9 compound. Figure 2(a-d) shows typical SEM images of pristine and doped Bi2Fe4O9 samples. Compared with the pristine Bi2Fe4O9 sample, the grains of the doped Bi2Fe4O9 sample are randomly oriented and have the smaller grain size. The average grain size is estimated to be about 65 nm. As we can see in the SEM images, the particles of all these four samples are agglomerated and little porous in nature. Therefore, we can say that the particle size increses with increasing the calcination temperature as we can see in SEM image of (Bi2Fe4O9)800–850 sample. The typical SEM images reveals that microstructures are dense comprising of non-uniform grains with varying particles size indicating polycrystalline nature of as prepared samples. The SEM image also showed some poros among the loosely connected grains in the sample.
3.3 Raman scattring analysis
Raman spectrum of Bi2Fe4O9 at room temperature is depicted in Fig. 3(a-d). The Raman active modes of the structure can be summarized using the irreducible representation 12Ag + 12B1g + 9B2g + 9 B3g, which is employed to describe Raman modes of orthorhombic (Pbam space group) [13]. In the measured Raman spectra of (Bi2Fe4O9)650–850, the Ag modes are existed at 83, 95, 115, 122, 139, 222, 289 and 607 cm− 1. The agreement between experimental and predicted values is relatively good for the all frequency modes, dominated by Bi vibrations. The Raman peak centered at 472 cm− 1 is might be attributed to magnetic ordering effect on phonon line width consistent with earlier observation of bands at ~ 260 and 472 cm−1 due to magnon scattering. Similarly, for (Bi2Fe4O9)800–850 the obtained Raman Ag modes are at 91, 206, 282, 326, 365, 430, 554, and 640 cm− 1. We can analyze there are number of modes decreasing due to increasing in calcination temperature. The Ag modes for Bi1.98Ba0.02Fe4O9 are following (53, 93, 119, 183, 209, 313, 446 and 558 cm− 1). Similarly, for Bi1.98Ce0.02Fe4O9 the Ag modes are at 53, 68, 118, 183, 206, 308, 442, 560 cm− 1. It would be more practical to study the magnetic excitations in Bi2Fe4O9 under the assumption that they involve two-magnon processes, like in the well-known cases of ferrites [14] or cuprates [12, 15]. At higher frequency (> 250 cm− 1), it is unlikely the magnetic-order-induced bands correspond to one-magnon excitations but in rare-earth orthoferrites (RFeO3; R = Dy, Ho, Er, Sm etc.) have frequencies below 25 cm− 1 for comparison the zone-center magnons [16].
3.4 Dielectric response
The real part of permittivity (ε') as a function of frequency of Bi2Fe4O9 based ceramics at room temperature is shown in Fig. 4(a-d).The value of ε' for all Bi2Fe4O9 based samples are about 37, 75, 40 and 393 for (Bi2Fe4O9)650–850, (Bi2Fe4O9)800–850, (Bi1.98Ba0.02Fe4O9), and (Bi1.98Ce0.02Fe4O9) samples, respectively at frequency 10 Hz. At higher frequency (∼ 1 MHz), the values of ε' are 11.68, 12.90, 5.06 and 5.36 respectively for (Bi2Fe4O9)650–850, (Bi2Fe4O9)800–850, (Bi1.98Ba0.02Fe4O9), and (Bi1.98Ce0.02Fe4O9) samples, respectively. The above is comparable with the previous measurements pure Bi2Fe4O9. Dielectric constant (ε') decreases with increase in frequency and it is constant at higher frequencies region. From Fig. 4 we have found that the value of dielectric constant in the whole frequency range (100 Hz– 1 MHz) is nearly constant in the prepared ceramics. This result appears to be consistent with our previous empirical analysis using the Maxwell–Wagner model with thermal activation across multiple band gaps in isolated impurities [17]. The dielectric loss (tanδ) as a function of frequency of Bi2Fe4O9 based ceramics at room temperature is shown in Fig. 5. We have observed that the value of dielectric loss is low for (Bi2Fe4O9)650–850 among the entire prepared sample, dielectric relaxation are possible in all prepared sample.