**2. Experimental details**

Bulk Bi2Fe4O9 ceramic was synthesized through solid-state reaction route (SSR). The SSR is a commonly used synthesis method for obtaining polycrystalline bulk materials from solid reagents. This method provides a great deal of choices for starting materials like oxides, carbonates, etc. Since solids do not react with each other at room temperature, very high temperatures are usually employed to allow appropriate reaction to occur at a significant rate. Therefore, both thermodynamic and kinetic factors are important in SSR. In the SSR method, the solid reactants undergo a chemical reaction at high temperature in the absence of any solvent, thereby producing a stable product. High purity Bi2O3, Fe2O3 were carefully weighed and stoichiometrically mixed in an agate mortar for 5 hours. The powder was doubly thermally calcined consecutively at 650°C for 1 hour and 850°C for 6 hours with intermediate grinding in oxygen-containing medium. Finally, pellets were sintered at 850°C for 6 hours, resulting in good densification. Thermal heating (i.e. calcination and annealing) is a mean of controlling the structural changes, properties, and phase compositions [23]. In this case, introduction of oxygen leads to the formation of oxide compounds. For crystallinity and phase identification X-ray diffraction (XRD) pattern were taken using CuKα1 radiation (λ = 1.5406 Å) of a Bruker D8 Advance X-ray diffractometer. Crystal structure characterization of synthesized sample was performed by employing Rietveld whole profile fitting method using FullPROF software [22].

The sample quality, morphology, grain distribution, density/voids in the samples were studied with scanning electron microscope (JEOL, JSM-5600). Raman measurements on as synthesized sample was carried out on Jobin-Yovn Horiba LABRAM (System HR800) spectrometer with a 632.8 nm excitation source equipped with a Peltier cooled CCD detector. Dielectric measurements were made as a function of frequency in the range of 100 Hz–1 MHz on Novocontrol alpha-ANB impedance analyzer at room temperature. Ferroelectric measurement was carried out using a ferroelectric loop tracer based on Sawyer-Tower circuit. The *M-H* curve was performed using a Lakeshore VSM 7410 model.

### **3. Results and discussion**

#### **3.1 Crystal structure analysis**

The room temperature XRD pattern of bulk Bi2Fe4O9 sample is shown in **Figure 1(a)**. From the XRD pattern we can index the data in orthorhombic phase as shown in **Figure 1(a)**. The present XRD patterns matches with JCPDS

**Figure 1.**

*(a) Measured powder X-ray diffraction pattern for Bi2Fe4O9 ceramic at room temperature, (b) Rietveldrefined XRD pattern for Bi2Fe4O9, and (c) symmetric representation of the unit cell for Bi2Fe4O9 ceramic viewed in* abc *and* ab *planes.*

#01-74-1098 (Bi2Fe4O9) [24]. In order to further confirm structural data, Rietveld refinement of the XRD pattern for Bi2Fe4O9 sample was performed using FullPROF program and shown in **Figure 1(b)**. The composition of phase and its concentration in the structure have been determined using the Rietveld method, which is based on the estimation of the diffraction peak area and the analysis of their contributions to the entire X-ray diffraction. It should be noted here that XRD pattern having a small secondary phase peaks corresponding to the Fe2O3 and its phase concentration is less than 2%, which does not affect the measured properties of studied ceramic. The XRD pattern of parent Bi2Fe4O9 was refined with orthorhombic (*Pbam*) structure with lattice parameters *a* = 7.941(4) Å, *b* = 8.420(4) Å and *c* = 5.986(4) Å. The obtained lattice parameters are consistent with earlier reported data [25]. The Rietveld-refined calculated parameters of Bi2Fe4O9 are documented in **Table 1**. We have illustrated structural parameters for Bi2Fe4O9 ceramic, and also identify the residuals for weighted pattern *R*wp, the expected weighted profile factor *R*exp, and goodness of fit χ<sup>2</sup> . The selected bond lengths and bond angles are mentioned in **Table 1**. The average value of the Bi▬O bond is 2.482 Å. The generated orthorhombic structure of Bi2Fe4O9 ceramic is depicted in **Figure 1(c)**. In the crystal structure, chains of FeO6 octahedra parallel to the *c* axis are connected *via* FeO4 tetrahedra alternating with bismuth atoms along the *c* axis.

The symmetric pseudo-Voigt functions are used to calculate the degree of crystallinity based on the estimation of the diffraction width and shapes. We have measured the full width half maxima (FWHM) of the recorded diffraction lines, which allowed us to characterize the perfection of the crystal structure and evaluate the degree of crystallinity [21]. The value of % of crystallinity for Bi2Fe4O9 = 81.3% was calculated using the formula:

**7**

**Table 1.**

*Bi2Fe4O9 ceramic from XRD.*

*Structural, Electrical, and Magnetic Properties of Mullite-Type Ceramic: Bi2Fe4O9*

ρ

( ) 100 .

(2)

= 4.65%

Fe1▬O3▬Fe2 119.09 Fe2▬O4▬Fe2 172.00

*Area of Crystalline peaks Crystallinity Area of all peaks i e Crystalline Amorphous* <sup>=</sup> <sup>×</sup> <sup>+</sup> (1)

The *distortion of the crystal lattice* (*ρ*dil), which characterizes the number of defective or porous inclusions in the structure as a result of external influences, was

> 0 *dil* 1 100% ρ

Here, *ρ*0 is the density of the reference sample taken from the JCPDS #01-74-1098 database, *ρ* is the calculated density of the sample. Calculated value of distortion of

We used the Williamson-Hall plot to observed the effect of the phase composition on distortions and deformation of the crystal structure of Bi2Fe4O9 ceramic, based on estimating the angular dependence of the full width at half maximum (FWHM) of diffraction lines (**Figure 2**). We obtained the strain (ε) value for Bi2Fe4O9 ceramic is 0.00412 ± 0.0016. Thermal heating at high temperature helps to

*a* **= 7.941(4) Å** *b* **= 8.420(4) Å** *c* **= 5.986(4) Å V = 400.31(2) Å3 Atoms** *x y z R-***values** Bi 0.3230 0.1745 0.0000 *R*wp = 7.36% Fe1 0.0000 0.0000 0.2582 *R*exp = 3.41% Fe2 0.1465 0.3360 0.5000 *R*p = 4.61% O1 0.3485 0.4292 0.0000 χ<sup>2</sup>

O2 0.3671 0.4047 0.5000 *GoF* = 2.2

**Bond type Bond length (Å) Bond type Bond angle (°)** Bi▬O1 2.153 O1▬Bi▬O1 151.93 Bi▬O3 3.017 O3▬Bi▬O3 86.06 Fe1▬O1 2.047 Bi▬O1▬Bi 141.13 Fe1▬O2 1.962 O2▬Fe2▬O3 103.98 Fe1▬O3 2.022 O3▬Fe2▬O3 108.93 Fe2▬O1 3.485 O3▬Fe2▬O4 113.59 Fe2▬O2 1.846 Fe1▬O1▬Fe1 98.02 Fe2▬O3 1.901 Fe1▬O2▬Fe1 94.99 Fe2▬O4 1.805 Fe1▬O2▬Fe2 129.72

*Rietveld-refined room temperature structural parameters, important bond lengths, and bond angles for* 

O3 0.1312 0.2054 0.2413 O4 0.0000 0.5000 0.5000

ρ

=− ×

*DOI: http://dx.doi.org/10.5772/intechopen.93280*

found according to formula:

the crystal lattice is *ρ*dil = 3.1%.

reduce the distortion value [19].

*Structural, Electrical, and Magnetic Properties of Mullite-Type Ceramic: Bi2Fe4O9 DOI: http://dx.doi.org/10.5772/intechopen.93280*

$$\text{Crystallimity} = \frac{\text{Area of Crystal line peaks}}{\text{Area of all peaks} \left(\text{i.e Crystal line} + \text{Amorphous}\right)} \times \text{100}$$

The *distortion of the crystal lattice* (*ρ*dil), which characterizes the number of defective or porous inclusions in the structure as a result of external influences, was found according to formula:

$$\rho\_{dd} = \left(\mathbf{1} - \frac{\rho}{\rho\_{\diamond}}\right) \times \mathbf{1} \mathbf{o} \mathbf{o} \,\% \,\tag{2}$$

Here, *ρ*0 is the density of the reference sample taken from the JCPDS #01-74-1098 database, *ρ* is the calculated density of the sample. Calculated value of distortion of the crystal lattice is *ρ*dil = 3.1%.

We used the Williamson-Hall plot to observed the effect of the phase composition on distortions and deformation of the crystal structure of Bi2Fe4O9 ceramic, based on estimating the angular dependence of the full width at half maximum (FWHM) of diffraction lines (**Figure 2**). We obtained the strain (ε) value for Bi2Fe4O9 ceramic is 0.00412 ± 0.0016. Thermal heating at high temperature helps to reduce the distortion value [19].


#### **Table 1.**

*Rietveld-refined room temperature structural parameters, important bond lengths, and bond angles for Bi2Fe4O9 ceramic from XRD.*

**Figure 2.** *Williamson-Hall plot for Bi2Fe4O9 ceramic.*

#### **3.2 SEM analysis**

The surface morphological and microstructural properties of Bi2Fe4O9 compound was investigated using scanning electron microscopy (SEM). **Figure 3** (upper part) shows the SEM micrograph of Bi2Fe4O9 thermally sintered at 850°C for 10 hours. Typical SEM image shows that microstructures comprising of nonuniform distribution of grains with an estimated average grain size of 1.5 μm indicating polycrystalline nature. Even though the SEM image shows that there are some pores between loosely connected grains in the sample. The surface area of a catalyst is a key aspect to determine the adsorption capacity of reactants on the catalyst surface [26]. We have measured the active surface area using a Brunauer-Emmett-Teller (BET) measurement system at 77 K through nitrogen adsorptiondesorption isotherm method. The BET active surface area of Bi2Fe4O9 is 1.2 m<sup>2</sup> /g, which is in good agreement with the values reported in the literature [27]. In order to obtain photocatalytic efficiency, it is necessary to increase the specific surface area by doping or reducing grain sizes. In addition, we have measured the material's apparent density which is defined as the mass per unit volume of the material in absolute dense condition [28]. The obtained density of the present calcined Bi2Fe4O9 ceramic is 6.51 g/cm3 which match well with the density for the Bi2Fe4O9 (ρ = 6.48 g/cm3 ) from reference file: JCPDS card number 74-1098.

#### **3.3 Raman scattering analysis**

Raman scattering spectroscopy has been extensively utilized to study the crystal lattice vibrations. Raman scattering spectroscopy would also offer a distinctive potential as a sensitive probe for the spin dynamics and studying the effect of magnetic ordering. Raman spectrum of Bi2Fe4O9 at room temperature is depicted in lower part of **Figure 3**. The Raman active modes of the structure can be

**9**

**Figure 3.**

*type ceramic carried out at room temperature.*

*Structural, Electrical, and Magnetic Properties of Mullite-Type Ceramic: Bi2Fe4O9*

summarized using the irreducible representation 12*A*g + 12*B*1g + 9*B*2g + 9*B*3g, which is employed to describe Raman modes of orthorhombic (*Pbam* space group) [9]. In the measured Raman spectra all are the Ag modes (85, 93, 114, 210, 227, 280, 331, 366, 436, 465, 561, and 648 cm−1) accept modes in attendance at 164 (B2g) and 189 (B3g) 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 470 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 [9]. 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 [29] or cuprates [30, 31]. At higher frequency

*(Upper) Scanning electron microscope images of Bi2Fe4O9 and (lower) Raman spectra for Bi2Fe4O9 mullite-*

*DOI: http://dx.doi.org/10.5772/intechopen.93280*

*Structural, Electrical, and Magnetic Properties of Mullite-Type Ceramic: Bi2Fe4O9 DOI: http://dx.doi.org/10.5772/intechopen.93280*

**Figure 3.**

*(Upper) Scanning electron microscope images of Bi2Fe4O9 and (lower) Raman spectra for Bi2Fe4O9 mullitetype ceramic carried out at room temperature.*

summarized using the irreducible representation 12*A*g + 12*B*1g + 9*B*2g + 9*B*3g, which is employed to describe Raman modes of orthorhombic (*Pbam* space group) [9]. In the measured Raman spectra all are the Ag modes (85, 93, 114, 210, 227, 280, 331, 366, 436, 465, 561, and 648 cm−1) accept modes in attendance at 164 (B2g) and 189 (B3g) 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 470 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 [9]. 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 [29] or cuprates [30, 31]. At higher frequency

(>250 cm−1), it is unlikely the magnetic-order-induced bands correspond to onemagnon excitations but in rare-earth orthoferrites (*R*FeO3; *R* = Dy, Ho, Er, Sm, etc.) have frequencies below 25 cm−1 for comparison the zone-center magnons [32].

### **3.4 Dielectric and P-E loop studies**

The real part of permittivity (ε′) and loss tangent (tanδ) as a function of frequency of Bi2Fe4O9 ceramics near at surrounding temperature is shown in **Figure 4(a)** and **(b)**. The value of ε′ and tanδ for Bi2Fe4O9 are about 21.57 and 0.05, respectively at frequency 10 Hz. At higher frequency (~1 MHz) the value of ε′ and tanδ are 18.59 and 0.006, respectively. Dielectric behavior (i.e. ε′ and tanδ) decreases with increase in frequency and it is constant at higher frequency region. From **Figure 4(a)** and **(b)** we have found that the value of dielectric constant in the

**11**

**Figure 5.**

*room temperature.*

*Structural, Electrical, and Magnetic Properties of Mullite-Type Ceramic: Bi2Fe4O9*

whole frequency range (10 Hz–1 MHz) is nearly constant representing the low loss in the prepared ceramic. This result appears to be consistent with previous empirical analysis using the Maxwell-Wagner model with thermal activation across multiple band gaps in isolated impurities [15, 33]. **Figure 4(c)** shows the semilog plot of conductivity (*σ*) at room temperature with frequency. The study of the frequency dependence of the conductivity is a deep-rooted method for describing the hopping dynamics of the charge carrier. The conductivity plot exhibits both low and high frequency dispersion phenomena [34–37]. The low-frequency region corresponds

*(a) Polarization hysteresis P-E loop and (b) field-dependent magnetic hysteresis loop of Bi2Fe4O9 ceramic at* 

*DOI: http://dx.doi.org/10.5772/intechopen.93280*

*Structural, Electrical, and Magnetic Properties of Mullite-Type Ceramic: Bi2Fe4O9 DOI: http://dx.doi.org/10.5772/intechopen.93280*

whole frequency range (10 Hz–1 MHz) is nearly constant representing the low loss in the prepared ceramic. This result appears to be consistent with previous empirical analysis using the Maxwell-Wagner model with thermal activation across multiple band gaps in isolated impurities [15, 33]. **Figure 4(c)** shows the semilog plot of conductivity (*σ*) at room temperature with frequency. The study of the frequency dependence of the conductivity is a deep-rooted method for describing the hopping dynamics of the charge carrier. The conductivity plot exhibits both low and high frequency dispersion phenomena [34–37]. The low-frequency region corresponds

**Figure 5.** *(a) Polarization hysteresis P-E loop and (b) field-dependent magnetic hysteresis loop of Bi2Fe4O9 ceramic at room temperature.*

to the *dc* conductivity (*σ*dc), which is due to the band conduction, and it is frequency independent. The high-frequency region corresponds to the *ac* conductivity (*σ*ac), which is frequency dependent. To conclude, the electrical conductivity *σ* for Bi2Fe4O9 follows the Jonscher power law [37]: *σ*ac(ω) *= σ*dc + A(*T*)ω<sup>n</sup> . Here, *A* is the pre exponential factor and *n* is the power law exponent. The exponent *n* can have a value between 0 and 1. This parameter is frequency independent but temperature and material dependent.

Ferroelectric hysteresis *P(E*) loop of the Bi2Fe4O9 ceramic at room temperature represented in **Figure 5(a)**. The obtained loop indicates that there are ferroelectric properties with finite remanent polarization with the applied electric field in the prepared sample. Under an electric field of up to 10 kV/cm, the remanent polarization (2*P*r) of Bi2Fe4O9 was found to be 0.006 μC/cm<sup>2</sup> . The observed polarization values are closely consistent with literature results [38].

### **3.5 Magnetic analysis (***M-H* **curve)**

From the measured *M-H* loop of Bi2Fe4O9 ceramic (**Figure 5(b)**), the magnetic parameters we obtained are remanent magnetization (*M*r = 4.37 × 10−4 emu/g), coercivity (*H*c = 239.4 Oe) and saturation magnetization (*M*s *=* 0.024 emu/g). In our Bi2Fe4O9 ceramic, antiferromagnetic (AFM) and weak ferromagnetic (WFM) interactions exist simultaneously are consistent with the data reported earlier [15, 38–40]. The WFM order can be seen in the low magnetic field region. WFM order itself can be understood as a result of canted spin arrangements in two sublattices [41]. As the magnetic field increases, the ferromagnetic order saturates and the antiferromagnetic component dominates. There is even no sign of saturation. Obviously, in the prepared ceramic, *M*r and *M*s have achieved a non-zero value. We may note that the measured hysteresis curve confirm that the relationship between the applied magnetic field and the magnetization does not evidence of a linear behavior and shows the WFM. In the future, we can improve the magnetic and electric properties of Bi2Fe4O9 ceramics with the appropriate doping or preparation techniques.
