## 3 Results and Discussion  
Figure 1a shows XRD analysis of the single phase BNKLBT ceramic. The XRD pattern of BNKLBT ceramic was analyzed using Bi\({}_{0.5}\)Na\({}_{0.5}\)TiO\({}_{3}\) (BNT, PDF#46-0001), Bi\({}_{0.5}\)K\({}_{0.5}\)TiO\({}_{3}\) (BKT, PDF#36-0339), LaTiO\({}_{3}\) (LTO, PDF#49-0426) and BaTiO\({}_{3}\) (BTO, PDF#31-0174) as reference comparisons. Similarly, Figure 1c shows XRD analysis of the BNKMBT ceramic with Bi\({}_{0.5}\)Na\({}_{0.5}\)TiO\({}_{3}\) (BNT, PDF#46-0001), Bi\({}_{0.5}\)K\({}_{0.5}\)TiO\({}_{3}\) (BKT, PDF#36-0339), MgTiO\({}_{3}\) (MTO, PDF#06-0494), and BaTiO\({}_{3}\) (BTO, PDF#31-0174) as reference comparisons. It is noticeable that the fabricated BNKLBT and BNKMBT ceramics possess crystalline single phase perovskite structures. Figure 1b shows the amplified 39-48\({}^{\circ}\) XRD analysis for BNKLBT and Figure 1d shows the amplified 38-48\({}^{\circ}\) XRD analysis for the BNKMBT ceramics, where peak splitting (002/200) is not visible, consistent with the coexistence of rhombohedral and tetragonal structures of the morphotropic phase boundary [17]. The sharp (200) peak at 45.8\({}^{\circ}\) confirms the cubic structure of both samples, and there are no rhomboheral or tetragonal phases [5]. From the amplified images of BNKLBT and BNKMBT it can be seen that both (111) and (200) diffraction peaks match the PDF card of the BTO material, whereas BTO consists of a cubic structure with the \(Pm\overline{3}m\) space group. Hence, both BNKLBT and BNKMBT ceramics appear to possess cubic structures with the space group \(Pm\overline{3}m\), but more confirmation is required. For further analysis of the structure of both high-entropy ceramics, the tolerance factor of the ceramics was measured as follows [16];  
\[t=\frac{(R_{A}+R_{O})}{\sqrt{2}(R_{B}+R_{O})} \tag{1}\]  
where \(R_{A}\) is the ionic radius of the A-site, \(R_{B}\) is the ionic radius of the B-site and \(R_{O}\) is the ionic radius of oxygen in the perovskite structure. The ionic radius of each constituent element is shown in Table 1.  
The cubic phase maintains a stable structure in the range of 0.9 \(\leq t\leq\) 1.0 [18]. Here the calculated tolerance factor for the BNKLBT ceramic is 0.99 and for BNKMBT ceramic is 0.958. [PERSON] et al., reported that high entropy perovskite materials show tolerance factors in the range 0.97 \(\leq t\leq\) 1.03 [19]. [PERSON] et al. reported a tolerance factor of 1.01 for a high-entropy ceramic with a cubic structure [16]. The tolerance factors of BNKLBT and BNKMBT ceramics are well within the range of the cubic phase. From XRD analysis of BNKLBT and BNKMBT ceramics at 45.8\({}^{\circ}\), a sharp (200) peak was found, which is the confirmation of the cubic phase of both ceramic samples. \begin{table}
\begin{tabular}{c c c c c c c c c} \hline
**Ions** & **Bi3+** & **Na+** & **K+** & **La3+** & **Mg2+** & **Ba2+** & **Ti4+** & **O2-** \\ \hline
**Ionic Radii (Å)** & 1.03 & 1.39 & 1.64 & 1.35 & 0.89 & 1.61 & 0.605 & 1.4 \\ \hline \end{tabular}
\end{table} 
Table 1: Ionic radii of R\({}_{A}\), R\({}_{B}\) and R\({}_{O}\). To further analyze the structural phases for BNKLBT and BNKMBT ceramics, Rietveld refinement of the XRD patterns of both samples were performed with FULLPROF software (Figure 2a,b). Here the cubic structure with the space group \(Pm\bar{3}m\) was treated as the reference structure. Figure 2a,b shows the refined XRD results, where the excellent \(R_{WP}\), \(R_{P}\) and \(\chi^{2}\) refined factors with \(R_{P}\) and \(R_{WP}\) are below 8%. The agreement between observed and calculated XRD patterns for BNKLBT and BNKMBT ceramics shows the existence of the cubic phase with the space group \(Pm\bar{3}m\). Figure 1: **(a,c)** XRD analysis comparison of high-entropy BNKLBT and BNKMBT ceramics with standard PDF card# data. **(b,d)** Amplified XRD analysis (20 = 38–48\({}^{\circ}\)) of BNKLBT and BNKMBT ceramics, respectively, clearly showing structural distortion of the fabricated ceramics.