*3.4. Understanding of Growth Mechanism*

In the hydrothermal synthesis of BaTiO3 nanocrystals, TiO2 (P25) nanoparticles are used as the solid-state Ti source and seeds for crystal growth. The possible growth mechanism of the BaTiO3 nanocrystals by the hydrothermal process is shown in Figure 7. TiO2 nanoparticles first react with OH− ions in a strong alkaline solution to form a soluble titanium hydroxide complex, which can form a negatively charged Ti–O chain. These negatively charged Ti–O chains attract positively charged Ba2<sup>+</sup> or BaOH<sup>+</sup> ions to form BaTiO3 nuclei, on which the excess Ba2<sup>+</sup> species continue to grow in the strong alkaline solution under the hydrothermal conditions for a long time. The possible reactions for the growth of BaTiO3 nanocrystals can be described as follows:

$$\rm{TiO\_2(P25) + OH^- \to TiO(OH)\_2} \tag{1}$$

$$\text{TiO(OH)}\_{2} + \text{OH}^{-} + \text{H}\_{2}\text{O} \rightarrow \text{Ti(OH)}\_{6}^{2-} \tag{2}$$

$$\text{aTi(OH)}\_{6}^{2-} + \text{Ba}^{+} \rightarrow \text{BaTiO}\_{3} + \text{H}\_{2}\text{O} \tag{3}$$

**Figure 7.** Possible growth mechanism for the synthesis of BaTiO3 nanocrystals under the hydrothermal conditions using TiO2 nanoparticles (P25) as the seeds and Ti source.

Using TiO2 (P25) nanoparticles as the seeds and Ti source for the synthesis of BaTiO3 nanocrystals, the negatively charged Ti–O chains are first formed on the surface of TiO2 (P25) particles in the strong alkaline solution, and the whole TiO2 (P25) nanoparticles are then gradually transformed to the [Ti(OH)x] <sup>4</sup>−<sup>x</sup> species. The negatively charged Ti–O chains (i.e., [Ti(OH)6] <sup>2</sup>−) react with Ba2<sup>+</sup> ions to form BaTiO3 nanocrystals under hydrothermal conditions. The large spherical particles in situ formed on the TiO2 (P25) nuclei may overcome the agglomeration because of their weak attraction to each other. The small particles can be self-regulated by the interaction of van der Waals torque (Casimir Torque) under high-temperature Brownian motion via the orientation attachment mechanism [43]. During the long hydrothermal reaction, smaller crystals dissolve and re-deposit on larger particles for orientation attachment and crystal extension via the Ostwald ripening process. Therefore, the growth mechanism for the formation of BaTiO3 nanoparticles may involve the following steps: (1) TiO2 (P25) nanoparticles are transformed to [Ti(OH)x] <sup>4</sup>−<sup>x</sup> species in the strong alkaline solution; (2) Ba2<sup>+</sup> ions reacts with [Ti(OH)x] <sup>4</sup>−<sup>x</sup> species to form BaTiO3 nanocrystals; (3) small BaTiO3 nanocrystals grows to large ones via the Ostwald ripening process and the orientation attachment mechanism.
