Mathematical Modeling of Mechanochemical Synthesis of Precursor Particles

Abstract

A macroscopic mathematical model has been constructed for the mechanochemical synthesis of precursors in this work. The model comprises the equations of heat balance, which determines the temperature of the activated powder mixture in the volume of the mechanical activator; a chemical reaction, which describes a one-step reaction of the product formation from a mixture of two reagents; changes in the specific surface of mechanocomposite particles and the interface area, which take into account that the probability of its formation is proportional to the volume fractions of the reagents; dynamics of excess energy in the components of the powder mixture and the reaction product. The effect of physical and chemical parameters of the mixture components and the conditions of mechanical activation on the main synthesis characteristics such as the temperature, chemical conversion depth, the particle size of precursors, and their phase composition is studied in the work. The synthesis of precursors is shown to be the most effectively controlled by the following parameters, which vary in the experiment: the amount of inert diluent, mill power, the activation time, and the ambient temperature. The dynamics of synthesis is numerically investigated. In particular, it is shown that an increase in the amount of inert filler in the mixture and in the cooling rate of a high-energy mill as well as a decrease in the ambient temperature allow the mechanically activated system to switch to a controlled mode of mechanochemical synthesis, which contributes to the production of small-sized precursor powders.