## 3 Results and Discussion  
### Preparation and Characterization of Sol-Gel Bi\({}_{2x}\)Hf\({}_{x}\)O\({}_{3+x/2}\) Powders  
Among wet-chemical techniques, the sol-gel process is widely used in the preparation of ceramic materials such as metal oxides, carbides, and nitrides due to the advantages over conventional processing technologies in low temperature of the reaction, flexible composition control, high purity, and the ability to develop processes for large-area applications [27]. We prepared Bi\({}_{2-x}\)Hf\({}_{x}\)O\({}_{3+x/2}\) powders by a sol-gel process. To explore the processing window for calcination, thermogravimetric analysis (TGA) was performed to reveal the physical and chemical phenomena of the harvested sol-gelled powders upon heating. Figure 1 showed the TGA curve of as-prepared SGBH100 powders as a function of temperature. Upon heating, there was a small weight loss (2.3%) from room temperature to 134 \({}^{\circ}\)C that can be attributed to the water evaporation and desorption within the precursors. Drastic weight loss (40.0%) arising from the decomposition of organic compounds occurred from 134 \({}^{\circ}\)C up to 357 \({}^{\circ}\)C. Thereafter, only trivial weight loss (0.4%) was exhibited to the end of the TGA test. Since the melting point of bismuth oxide is 824 \({}^{\circ}\)C, the calcination temperature for the sol-gelled powders is thus set within 400-800 \({}^{\circ}\)C at an interval of 100 \({}^{\circ}\)C.  
Figure 2 showed a typical series of SEM images of SGBH100 powders after calcining at 400-800 \({}^{\circ}\)C for 1h. All the calcined powders showed an irregular shape and severe agglomeration of small particles. The particle size of agglomerated powders ranged from 200 nm to 2 \(\upmu\)m. The agglomeration seems to increase with increasing calcination temperature. Similar behavior was observed for all the compositions of the sol-gelled powders investigated in the present work. The structure evolution of sol-gelled powders with various hafnium addition and calcining at different temperatures was investigated by the X-ray diffraction (XRD) technique. Figure 1: Thermal gravimetric (TGA) curve of sol-gelled SGBH100 powders. Figure 3 showed the XRD patterns for sol-gelled Bi2-xHfxO3+x/2 composite powders (x ranged from 0.00 to 0.30, SGB-SGBH150) after calcining at 400-800 \({}^{\circ}\)C for 1 h. The as-received sol-gelled powder was amorphous without diffraction peaks. After calcination at a temperature higher than 400 \({}^{\circ}\)C, crystalline peaks of various bismuth oxide phases can be observed. As shown in Figure 3a, the pristine sol-gelled powder (SGB series) exhibited a monoclinic \(\alpha\)-Bi2O3 phase (JCPDS card No.71-2274). The diffraction peaks' intensities increased with increasing calcination temperature. Bismuth oxides were reported with seven polymorphs, which are monoclinic \(\alpha\), tetragonal \(\beta\), body-centered cubic \(\gamma\), face-centered cubic \(\delta\), orthorhombic \(\epsilon\), triclinic \(\omega\), and high-pressure hexagonal phase [28]. The \(\alpha\)- Bi2O3 is a low-temperature stable phase and can undergo phase transformations to other phases under various thermal conditions and pressures. With a small amount of hafnium addition (x = 0.15, Bi/Hf = 92.5/7.5, SGBH075), the monoclinic \(\alpha\)-Bi2O3 phase was replaced by the formation of metastable B-Bi7.78H\({}_{0.22}\)O\({}_{12.11}\) tetragonal phase (JCPDS No. 43-0207) shown in Figure 3b. With an increasing amount of hafnium addition (x = 0.20 to 0.30), in addition to the major \(\beta\)-Bi7.78H\({}_{0.22}\)O\({}_{12.11}\) phase, minor \(\delta\)-Bi2O3 phase (cubic fluorite structure oxide, JCPDS No. 27-0052) can be observed after calcination at 400-600 \({}^{\circ}\)C for 1h.