**3.1 Structural characterization by XRD**

**Figure 1(a)** and **(b)** illustrate the XRD patterns of the pure BTFO and composite (BLB523) samples. The measured XRD data is examined through the Rietveld refinement procedure using the Fullprof software. The refinement result provides

**Figure 1.** *Rietveld refinement of the XRD patterns of (a) pure (BTFO) and (b) composite (BLB523) sample.*

*Structural, Magnetic, and Magnetodielectric Properties of Bi-Based Modified Ceramic Composites DOI: http://dx.doi.org/10.5772/intechopen.106569*


#### **Table 1.**

*Summary of the refined lattice parameters, crystallite size and strain of the BTFO and BLB523 composite.*

information related to the samples pure phase formation and structural parameters. For the pure BTFO sample, the single-phase refinement method is performed by considering the orthorhombic crystal structure (*A2*1*am* space group). In contrast, the tri-phase method is incorporated in order to refine the whole XRD pattern of the composite. The orthorhombic (*A2*1*am*) BTFO, rhombohedral (*R-3c*) LSMO, and orthorhombic (*Pbam*) BFO symmetry is provided as input sources during the composite refinement. Initially, the instrumental zero correction factor is refined in the refinement process, followed by the scale factor, cell parameters (*a*, *b*, and *c*), FWHM parameters (*u*, *v*, and *w*), background points, and atomic positions. The peak shape parameters and background points are fitted by providing the Pseudo-Voigt function and linear interpolation between the background points. After several refinement cycles, the theoretically simulated pattern is well matched with the experimental data points. Additionally, the lower value of χ<sup>2</sup> , *R*p, and *R*wp also confirm the good fitting of the theoretical model with the observed data points. The extracted structural parameters and phase fractions are presented in **Table 1**. It is observed that the lattice parameters of the composite phase show a slight deviation from that of the pure phase. It signifies the generation of lattice strain at the BTFO, LSMO, and BFO domain interfaces. The other composites also report a similar kind of variation [15]. The proposed phase fraction of the composite is well consistent with the refinement data. Hence, the existence of BTFO, LSMO, and BFO phases in the composite assure the formation of the BLB523 composite.

The mean lattice strain and crystallite size of the pure cum composite samples have been extracted from the Williamson-Hall (W-H) plot method. The mathematical expression of the W-H method is

$$
\beta \cos \theta = \frac{\mathbf{K} \lambda}{\mathbf{D}} + \mathbf{4} \varepsilon \sin \theta \tag{2}
$$

here θ denotes the Brrag's angle, ε is the lattice strain, λ is the incident wavelength of X-ray, *K* is the shape parameter (0.89 for spherical shape), *D* is the crystallite size in average, β denotes the full-width half maxima of the diffraction peak [16]. The estimated crystallite size and strain values are listed in **Table 1**. It is observed that the composite exhibits more strain than the pure sample.
