## 3 Results and Discussion
### Preparation and Characterization of Sol-Gel Bi\({}_{2x}\)Hf\({}_{x}\)O\({}_{3+x/2}\) Powders
In Figure 3c, the XRD patterns for SGBH100 powders (x = 0.20, Bi/Hf = 90.0/10.0) exhibited a mixture of \(\beta\)-Bi7.78H\({}_{0.22}\)O\({}_{12.11}\) and \(\delta\)-Bi2O3 phases at a temperature ranged from 400-600 \({}^{\circ}\)C. After being treated at 700 \({}^{\circ}\)C and above, \(\beta\)-Bi7.78H\({}_{0.22}\)O\({}_{12.11}\) became dominant with almost no trace of \(\delta\)-Bi2O3 phase. Further increasing the hafnium addition to x = 0.25 (Bi/Hf = 87.5/12.5) showed the similar XRD patterns for SGBH125 powders (Figure 3d) where \(\delta\)-Bi2O3 phase was the major phase at low calcination temperature (400-600 \({}^{\circ}\)C) and \(-\)Bi7.78H\({}_{0.22}\)O\({}_{12.11}\) became dominant phase at 700-800 \({}^{\circ}\)C. The XRD results indicated that sol-gelled pristine bismuth oxide formed a stable monoclinic \(\alpha\)-Bi2O3 phase at room temperature. Hafnium additions enable the high temperature tetragonal and cubic phases (i.e., \(\beta\)-Bi7.78H\({}_{0.22}\)O\({}_{12.11}\) and \(\delta\)-Bi2O3). A high dosage of hafnium addition (x = 0.20 and above) and low calcination temperatures (600 \({}^{\circ}\)C  
Figure 2: The SEM for SGBH100 after calcining at (**a**) 400 \({}^{\circ}\)C (**b**) 500 \({}^{\circ}\)C (**c**) 600 \({}^{\circ}\)C (**d**) 700 \({}^{\circ}\)C (**e**) 800 \({}^{\circ}\)C for 1 h.  
and below) favors the formation of the \(\delta\)-Bi\({}_{2}\)O\({}_{3}\) phase. Whereas Bi\({}_{7.78}\)Hf\({}_{0.22}\)O\({}_{12.11}\) exhibited at hafnium addition of x = 0.15 and high calcination temperatures at 700-800 \({}^{\circ}\)C.  
[PERSON] et al. reported that the room-temperature monoclinic \(\alpha\)-Bi\({}_{2}\)O\({}_{3}\) transforms to the high-temperature cubic \(\delta\)-Bi\({}_{2}\)O\({}_{3}\) upon heating at 729 \({}^{\circ}\)C [29]. The mechanochemical process with heating at 820 \({}^{\circ}\)C for 24 h then quenching in air showed a stabilized \(\delta\)-Bi\({}_{2}\)O\({}_{3}\) structure through the formation of a solid solution with 10 mol % of HfO\({}_{2}\), while two \(\beta\)-Bi\({}_{2}\)O\({}_{3}\) phases were found with 2 mol % of HfO\({}_{2}\) dopant [30]. However, our results showed a sol-gel process with a high dosage of hafnium addition (x \(\geq\) 0.20) and low calcination temperatures (\(\leq\)600 \({}^{\circ}\)C) favors the formation of the \(\delta\)-Bi\({}_{2}\)O\({}_{3}\) phase. For HfO\({}_{2}\)-Bi\({}_{2}\)O\({}_{3}\) prepared by wet precipitation followed by calcination at 600 \({}^{\circ}\)C, heating the defect fluorite Hf\({}_{1\cdot x}\)Bi\({}_{x}\)O\({}_{2\cdot x/2}\) phases (x = 0.40 to 0.75) to temperatures from 700 to 950 \({}^{\circ}\)C leads to the formation of pseudocubic Bi\({}_{2}\)Hf\({}_{2}\)O\({}_{7}\), but it decomposes into HfO\({}_{2}\) and Bi\({}_{1.94}\)Hf\({}_{0.06}\)O\({}_{3.03}\) with the \(\beta\)-Bi\({}_{2}\)O\({}_{3}\) structure when heated to 1000 \({}^{\circ}\)C [31]. Figure 4 revealed the detailed microstructural examination for SGBH100 7 (x = 0.20, Bi/Hf = 90.0/10.0, calcination at 700 \({}^{\circ}\)C) powders by transmission electron microscopy (TEM). As shown in Figure 4a, the irregular shape of powders was noticed. Figure 4b revealed the powders with various sizes (probably due to the agglomeration of a few particles). High-resolution TEM images, Figure 4c, showed the d\({}_{(201)}\) spacing (3.18 A) associating with the theoretical value of the \(\beta\)-Bi\({}_{7.78}\)Hf\({}_{0.22}\)O\({}_{12.11}\) phase. Whereas Figure 4d presents the selected area electron diffraction patterns where (201), (002), (220), (222), and (213) diffraction planes corresponding to \(\beta\)-Bi\({}_{7.78}\)Hf\({}_{0.22}\)O\({}_{12.11}\) phase can be identified.