Kinetic Modeling of Aqueous and Hydrothermal Synthesis of Barium Titanate (BaTiO₃)

A rigorous kinetic model for the solution precipitation and hydrothermal synthesis of BaTiO 3 particles is proposed. Three elementary kinetic processes are considered: primary nucleation, secondary nucleation, and diffusion-controlled growth. Secondary nucleation accounts for the acceleration of the formation kinetics after an initial slow crystallization stage and the formation of BaTiO 3 particles with a polycrystalline substructure. The time evolution of yield, crystal size, and particle size is represented by means of discretized mass and population balance equations. The system is simulated by replacing the continuous particle distribution with a limited number of size classes. A modification of the discrete equation describing growth has allowed the simulation of diffusion-controlled growth. The properties of the system are obtained from the moments of the particle size distribution. A new algorithm capable of exactly calculating a generic number of moments has been developed. The model correctly describes the kinetic data for eight different experimental conditions, and the value of the adjustable parameters is consistent with the best physical estimates available. The present approach shows that knowledge-based synthesis of BaTiO 3 particles with tailored size and properties is possible, minimizing the need for trial and error experimentation.