A closer look at the computer modeling and sintering optimization in the preparation of YAG

Recently, 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 (Mackeviius et al. in Central Eur J Chem 10(2):380-385, 2012). There, we restricted ourselves to the one- and two-dimensional models. Having both adapted our computing program to the three-dimensional case and significantly speeded it up, now we are able present the results in the three-dimensional model. Solving an inverse modeling problem, we obtain explicit formulas for the diffusion coefficient and reaction rate as functions of temperature. We calculate the activation energies and other parameters, thus obtaining conditions for occurrence of synthesis. In addition, using the results of the three-dimensional model, we find the optimal temperature for energy consumption in the YAG synthesis.