Relationship between the critical temperature of thermal explosion and the thickness of a lead azide plane crystal

This paper describes the calculation of the relationship of the critical ambient temperature at which lead $\alpha$-azide is ignited and the relationship of the critical temperature of self-heating with the thickness of plane crystals with the use of the Semenov criteria and numerical solution of the differential equation of heat balance. The heat balance equation is analyzed for sustainability. Analytical expressions for the determination of critical ambient temperatures and self-heating temperatures. The calculations are carried out with the parameters of the heterogeneous reaction of thermal decomposition of lead azide in the mode of decreasing volume. The calculations results are in good agreement with the known experimental data. It is shown that the larger the activation energy of the exothermic reaction, the stronger the relationship of the critical temperature of ignition of lead $\alpha$-azide with the thickness of plane crystals.