Roles of local reactivity on the solid‐state addition reaction kinetics

Abstract

A predominant factor of the diffusion‐controlled kinetics of a solid‐state addition reaction using powder is the particle size of the reactants, into which the other chemical species are migrating. However, diffusion‐controlled kinetic equations are seldom satisfactorily applicable even when the effects of particle size are thoroughly accounted. One of the representative nongeometrical items affecting the solid‐state reaction process is the reactivity of solids (ROS), which has not been accounted in any of the established kinetic equations. Change in ROS is the consequence of the imperfections of the crystalline solids. In this study, we try to discuss the effects of ROS on the solid‐state reaction kinetics. A typical solid‐state addition reaction, formation of BaTiO3 from the equimolar mixture of TiO2 and BaCO3, was chosen as a model. For this reaction, the rate‐determining step is established to be the diffusion of Ba2+ ions into TiO2. Since the defect concentration is known to be higher at the near‐surface region, the local distribution of ROS that is discussed here is based on a simple core‐shell model of the host TiO2 particles with higher reactivity at the shell part. The ratio of the rate of diffusion within the shell part relative to that of the core (factor n), and the ratio of shell thickness, Rs, relative to the particle radius, Rp, (factor g) were chosen as main parameters to be iterated. By systematically varying these two factors, n and g, we succeeded in minimizing the fluctuation of apparent diffusion rate constant by the particle size. Despite the oversimplified model and lacking experimental evidences of the hypothetical parameters, the present proposal may pave the way to introduce ROS and its local distribution into the reaction kinetics. We also discussed the effects of second phases by comparing the same reaction process observed from the decomposition of the reactant and formation of the products.