## 3 Results and Discussion
However, under the mixing condition of BT#4, with the highest ratio of the rutile phase, atomized powders were observed to be agglomerated. In the case of powders synthesized under the mixing conditions of BT#5 to BT#8 at 1000 \({}^{\circ}\)C, grain growth was suppressed, compared to that of the powders synthesized using composite TiO\({}_{2}\). Next, a solid-state synthesis reaction was performed at 1100 \({}^{\circ}\)C under the mixing conditions of BT(A) and BT(R). Observation of the resulting microstructure shows that grain growth progressed to a higher extent compared to that of the powders synthesized at 1000 \({}^{\circ}\)C (Figure 6). In the case of BT(A), the synthesized powders comprised spherical-shaped particles. However, in the case of BT(R), morphology analysis of the synthesized powder revealed high anisotropy at the edges and in the uniaxial direction. In the case of BaTiO\({}_{3}\) powders synthesized at 1100 \({}^{\circ}\)C under the mixing conditions of BT#1 to BT#4, the growth of grains with sizes in the range of 268-446 nm was observed. However, numerous grains suppressed for growth were observed, as in the case of the powder synthesized using BT#4 at 1000 \({}^{\circ}\)C. In the case of BaTiO\({}_{3}\) powders synthesized at 1100 \({}^{\circ}\)C under the mixing conditions of BT#5 to BT#8, no grain growth was observed. Furthermore, the powder morphology of edges and anisotropic shapes were similar to those observed for the powders synthesized under different synthesis conditions at 1000 \({}^{\circ}\)C. The microstructure analysis of BaTiO\({}_{3}\) powders synthesized via the solid-state method at each calcination temperature under the respective TiO\({}_{2}\) conditions demonstrated that isotropic BaTiO\({}_{3}\) powders were formed when annealed TiO\({}_{2}\) powders were used. In addition, grain growth of the powders could be easily achieved using annealed TiO\({}_{2}\). Figure 4: Tetragonality of BaTiO\({}_{3}\) prepared using different TiO\({}_{2}\) samples through solid-state synthesis via Rietveld analysis: **(a)** 1000 \({}^{\circ}\)C \(\times\) 2 h and **(b)** 1100 \({}^{\circ}\)C \(\times\) 2 h.  
Figure 5: Microstructure of BaTiO\({}_{3}\) powders synthesized at 1000 \({}^{\circ}\)C under different TiO\({}_{2}\) conditions: (a) BT(A), (b) BT(R), (c) BT\(\#1\), (d) BT\(\#2\), (e) BT\(\#3\), (f) BT\(\#4\), (g) BT\(\#5\), (h) BT\(\#6\), (i) BT\(\#7\), and (j) BT\(\#8\). Figure 6: Microstructure of the BaTiO\({}_{3}\) powders synthesized at 1100 \({}^{\circ}\)C under different TiO\({}_{2}\) conditions: (**a**) BT(A), (**b**) BT(R), (**c**) BT\(\#\)1, (**d**) BT\(\#\)2, (**e**) BT\(\#\)3, (**f**) BT\(\#\)4, (**g**) BT\(\#\)5, (**h**) BT\(\#\)6, (**i**) BT\(\#\)7, and (**j**) BT\(\#\)8. The calcination of BaCO\({}_{3}\) and TiO\({}_{2}\) resulted in the formation of BaTiO\({}_{3}\) through a solid-state synthesis reaction involving interfacial contact and diffusion between the materials (Figure 7). The solid-state synthesis reaction can be represented using the following equations. \[\text{BaCO}_{3}+\text{TiO}_{2}\rightarrow\text{BaTiO}_{3}+\text{CO}_{2} \tag{1}\]  
\[\text{BaTiO}_{3}+\text{BaCO}_{3}\rightarrow\text{Ba}_{2}\text{TiO}_{4}+\text{ CO}_{2} \tag{2}\]  
\[\text{Ba}_{2}\text{TiO}_{4}+\text{TiO}_{2}\rightarrow\text{2 BaTiO}_{3} \tag{3}\]  
At the initial stage of the reaction, BaCO\({}_{3}\) contacts the surface of TiO\({}_{2}\), and BaTiO\({}_{3}\) is formed via diffusion and an interface reaction (Equation (1)). The continuous adsorption of BaCO\({}_{3}\) and diffusion of ions result in the development of an intermediate-phase Ba\({}_{2}\)TiO\({}_{4}\) (Equation (2)). Finally, Ba\({}^{2+}\) ions diffuse to the inside of TiO\({}_{2}\), forming BaTiO\({}_{3}\) (Equation (3)). In particular, the solid-state synthesis reaction using two materials, BaCO\({}_{3}\) and TiO\({}_{2}\), involves the synthesis of BaTiO\({}_{3}\) through the unilateral diffusion of Ba\({}^{2+}\) ions into TiO\({}_{2}\)[32].