## 3 Results and Discussion
In solid-state synthesis, the control of the surface characteristics, size, and morphology of TiO\({}_{2}\) is imperative for controlling the properties of BaTiO\({}_{3}\)[17]. The size effect has a significant impact on various properties of the powder [33; 34]. In the case of TiO\({}_{2}\), for powder sizes of approximately 50 nm, the surface energy of rutile TiO\({}_{2}\) is high at 1.78-2.08 J/m\({}^{2}\), whereas that of anatase TiO\({}_{2}\) is considerably lower at 1.28-1.40 J/m\({}^{2}\). In particular, for small-size powders, rutile TiO\({}_{2}\) has a high surface energy, thereby showing superior reactivity at the surface and interface compared to that of anatase TiO\({}_{2}\)[35; 36; 37]. The application of heat treatment to TiO\({}_{2}\) powders results in the formation of powders with a composite phase comprising anatase and rutile phases, and TiO\({}_{2}\) powders with sizes of approximately 50 nm undergo phase transformation to the rutile phase (XRD, TEM). Specifically, the as-formed composite TiO\({}_{2}\) powders consist of larger-sized grains (~150 nm) in the anatase phase and smaller-sized grains (~50 nm) in the rutile phase. Among these TiO\({}_{2}\) powders, rutile TiO\({}_{2}\) powders with a grain size of 50 nm have a high surface energy, and after their surface contact with BaCO\({}_{3}\), the reaction rate could be faster than that of other large-sized powders during the formation of BaTiO\({}_{3}\). The rutile TiO\({}_{2}\) powders with smaller sizes react with BaCO\({}_{3}\) at the initial stages of the solid-state synthesis process. In contrast, anatase TiO\({}_{2}\) powders undergo the reaction with BaCO\({}_{3}\) at later stages of the synthesis process owing to their lower surface energy. During the solid-state reaction, the driving force for grain growth is determined by the mean grains size and grain size distribution. TiO\({}_{2}\) powders with smaller-sized grains react with BaCO\({}_{3}\) at the initial stages of synthesis, and grain growth progresses. Therefore, the average grain size of the synthesized BaTiO\({}_{3}\) could increase [38; 39; 40; 41; 42]. Such increases in the grain size are confirmed via the mean grain size analysis of BaTiO\({}_{3}\) synthesized at calcination temperatures of 1000 and 1100 \({}^{\circ}\)C using annealed TiO\({}_{2}\). A comparative analysis of the mean grain size of calculated BaTiO\({}_{3}\) powders synthesized using composite TiO\({}_{2}\) and mixed TiO\({}_{2}\) was performed. The grain size of BaTiO\({}_{3}\) calcined at 1000 \({}^{\circ}\)C using composite  
Figure 7: Schematic of solid-state synthesis using BaCO\({}_{3}\) and TiO\({}_{2}\). TiO\({}_{2}\) was approximately 250-280 nm. In addition, the grain size increased further to 270-445 nm at a calcination temperature of 1100 \({}^{\circ}\)C. However, when mixed TiO\({}_{2}\) was used for the solid-state synthesis, the BaTiO\({}_{3}\) grain size was smaller than that obtained using composite TiO\({}_{2}\) (Figure 8). Powder compacts obtained under different conditions of BT(A) to BT#8 and calculated at 1100 \({}^{\circ}\)C were sintered at 1300 \({}^{\circ}\)C for 2 h. Based on the microstructure analysis of the fractured surface of the specimens, grains with a size of 3 \(\upmu\)m were observed in the sintered specimen prepared using the BT(A) powder. Furthermore, numerous pores were observed in the fractured surface analysis. In the case of the specimen prepared using the BT(R) powder, grains with a size of 2.3 \(\upmu\)m were observed. For the specimens obtained using powders prepared under the synthesis conditions of BT#1 to BT#4, grains with sizes of 27.7-31.9 \(\upmu\)m were observed. Although sintering densification did not occur under BT(A) and BT(R) conditions, under the conditions of BT#1 to BT#4 that used composite TiO\({}_{2}\), sufficient grain growth was observed. However, under the conditions of BT#5 to BT#8 that used a simple mixture of anatase and rutile TiO\({}_{2}\), sufficient grain growth, which was confirmed in the case of composite TiO\({}_{2}\), was not observed.