Mathematical approach to investigation of synthesis processes at high temperatures

In our work, we present a method for estimation of the diffusion and reaction rates of synthesis at high temperatures using limited information from laboratory experiments, such as synthesis time and dimensions of reactants. Synthesis by sol-gel and solid-state reactions is considered. The inverse modeling problem is solved for one- and two-dimensional models. Explicit formulas for the diffusion coefficient and reaction rate as functions of temperature are obtained. The activation energies are calculated, and the lower bounds of diffusion and reaction rates are estimated, thus obtaining conditions for occurrence of synthesis.