## 3 Results and Discussion
A certain extent of grain growth was observed in the BT#8 powder, which had a relatively high fraction of the rutile phase (Figure 9). The difference in the grain size of the sintered specimens according to the BaTiO\({}_{3}\) powder conditions can be explained using the step free energy related to the critical driving force for grain growth. When the shape of the grain is flat to show high anisotropy, the critical driving force for growth increases, and grain growth can be suppressed. However, when the grain surface is spherical, it forms an isotropic structure, and the step free energy decreases, resulting in a small critical driving force for grain growth. In particular, grain growth occurs more easily with a lower critical driving force. When the powders synthesized via the solid-state synthesis reaction using 100% anatase and 100% rutile TiO\({}_{2}\) are analyzed, flat-shaped grains with high anisotropy are observed (Figure 10). Moreover, in the case of the powders synthesized using the simple mixture of TiO\({}_{2}\), a similar flat and highly anisotropic morphology of the grains is observed. However, in the case of BaTiO\({}_{3}\) powders synthesized using the heated TiO\({}_{2}\) powder, the edges and vertices of the grains gradually change to form a spherical shape, creating an isotropic structure. Figure 2:0 Comparative analysis of the mean particle size of BaTiO\({}_{3}\) powders obtained via solid-state synthesis at 1000 and 1100 \({}^{\circ}\)C using composite TiO\({}_{2}\) and mixed TiO\({}_{2}\). Solid-state synthesis conditions: (a) 1000 \({}^{\circ}\)C \(\times\) 2 h and (b) 1100 \({}^{\circ}\)C \(\times\) 2 h.  
Therefore, BaTiO\({}_{3}\) powders using annealed TiO\({}_{2}\) are transformed to a state with a lower critical driving force for grain growth; therefore, grain growth can occur easily during sintering [42; 43; 44]. Figure 2:1 Fractured surface analysis of sintered specimens of BaTiO\({}_{3}\) powders obtained via solid-state synthesis under the conditions of 1000 \({}^{\circ}\)C \(\times\) 2 h. Sintering conditions: 1300 \({}^{\circ}\)C \(\times\) 2 h. (**a**) BT(A), (**b**) BT(R), (**c**) BT#1, (**d**) BT#2, (**e**) BT#3, (**f**) BT#5, (**h**) BT#6, (**i**) BT#7, and (**j**) BT#8. Figure 2:2 Microstructure analysis of solid-state-synthesized BaTiO\({}_{3}\) powders under the conditions of \(1100\)\({}^{\circ}\)C \(\times\) 2 h (magnification: 100 k\(\times\)). (**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. For powders synthesized via solid-state synthesis using composite TiO\({}_{2}\) under BT#1 to BT#4 conditions, a stable dielectric constant value of approximately 2400 was observed (Table 2). Moreover, when mixed TiO\({}_{2}\) was used for solid-state synthesis, the dielectric constant of the synthesized BaTiO\({}_{3}\) gradually decreased with an increasing rutile phase ratio (Figure 11). The dielectric constant is an essential piece of information when designing capacitors and in other circumstances where a material might be expected to introduce capacitance into a circuit. The dielectric constant is the ratio of the capacitance of the capacitor with test material as the dielectric to the capacitance of a capacitor with vacuum (or air) as the dielectric [45]. The changes in the dielectric constant were analyzed according to the temperature changes for the specimens sintered at 1300 \({}^{\circ}\)C with powders synthesized under the BT#1-BT#8 conditions, as shown in Figure 2:3 In the case of powders synthesized under the BT#1 to BT#4 conditions that used TiO\({}_{2}\) with a controlled anatase-rutile phase ratio through annealing, considerably high dielectric constant values were achieved near the Curie