Mathematical modeling of the thermal explosion in mechanically activated SiO$_2$ + Al mixtures

A mathematical model of synthesis in a mechanically activated SiO$_2$ + Al mixture is constructed in the macroscopic approximation. It is demonstrated that preliminary mechanical activation makes it possible to obtain solid-phase ignition and to ensure synthesis of Al$_2$O$_3$ and Si products in the thermal explosion regime. Based on experimental data, thermophysical and thermokinetic constants of the process are determined.