Computer modeling of synthesis of strontium stannates at high temperatures

Abstract

In our previous papers (Mackevičius et al. in Cent Eur J Chem 10(2):380–385, 2012; J Math Chem 50(8):2291–2302, 2012; J Math Chem 51(5):1249–1257, 2013), we presented a method for estimation of the diffusion and reaction rates of synthesis at high temperatures using limited information, such as synthesis time and dimensions of reactants, from real laboratory experiments. In this paper, we extend the method to the case where particles of two reactants react with the gas environment and apply it to the case of synthesis of strontium stannate $\mathrm{Sr}\mathrm{Sn}\mathrm{O}_{3}$. The synthesis is modeled by a reaction–diffusion system describing the dynamics of the concentrations of reactants and product in an appropriately constructed synthesis space. Solving in the latter an inverse modeling problem, we obtain explicit formulas for the diffusion coefficient and reaction rate as functions of temperature by calculating the activation energies and other parameters of synthesis. Our approach also allows us to explain why we have different reactions at different temperatures.