Tomsk scientists have developed a mathematical model that will help optimize the synthesis of complex metal compounds

Scientists of the Tomsk Scientific Center of the Siberian Branch of the Russian Academy of Sciences Oleg Lapshin and Oksana Ivanova proposed a mathematical model for studying two-step mechanochemical synthesis of inorganic substances in wave combustion mode. This model, published in the high-ranking journal Powder Technology , will help find optimal modes of production of expensive composites and significantly develop a new macrokinetic theory.

“Mathematical models are used in many science fields, complementing the results of experiments. Previously, other research teams have already created mathematical models that describe the combustion and synthesis of substances from mechanically pre-activated mixtures, but they used only a very limited number of parameters," says Oleg Lapshin, head of the laboratory for mathematical modeling of physical and chemical processes in heterogeneous systems, explaining the uniqueness of the work performed. “Our research team managed to build a complex model that comprehensively describes the effect of mechanical pre-treatment on mechanosynthesis of the final product by introducing the factors such as the formation of an interfacial area, process temperature, generation of various defects, initial mechanochemical transformations, abrasion of milling tools”.

The construction of such a model will help significantly develop a new macrokinetic theory. Although methods of powder pretreatment and synthesis in the combustion wave have been actively used for a long time, theoretical foundations in this field have encountered several difficulties. First, the nature of the phenomenon requires an interdisciplinary approach; second, there is a lack of accurate and reliable tools and techniques for the direct study of chemical reactions under intense dynamic stresses.

Using the new macrokinetic theory, the scientists of the TSC SB RAS have studied in detail the effect of preliminary mechanical activation on the synthesis of substance in the combustion wave and the quality of the final product. The choice of milling parameters of the starting mixture is of great importance. For example, a short mechanical activation may not ignite a mixture, while too long milling will produce by-products that negatively affect the synthesis of the substance.

Scientists have also proposed inverse problem methods that can find the kinetic constants that determine the initial mechanochemical transformation and abrasion during mechanical treatment. These constants are used to determine the parameters that are invariable for a certain system when other parameters are changed (powder mass, synthesis method, choice of combustion mode - wave or thermal explosion). This will simplify further experiments. Using a mathematical model and the inverse problem method, the scientists predicted how the two-step mechanochemical synthesis of niobium silicide would proceed.

A broad class of inorganic compounds produced by SHS (self-propagating high-temperature synthesis) is used in medicine, aviation, and space industry. Reaction mixtures are milled in a ball mill, and the synthesis of the desired composite takes place in a combustion wave. The advantages of this method are cost-effectiveness and environmental friendliness.