Assessment of the effect of particle size on the rate of temperature alignment in systems used for shock-wave synthesis of diamond, cubic boron nitrade, and $\gamma$-phase of silicon nitride, based on a simple model

The change in the spatial distribution of relative temperatures in the system of a spherical particle located in the center of a spherical matrix is simulated. Silicon nitride $(\rm{Si}_3\rm N_4)$ and boron nitride $(\rm{BN})$ are considered in a matrix of potassium bromide $(\rm{KBr})$; graphite, diamond, and silicon nitride are studied in a copper matrix. Calculations are performed for the four sizes of particles: $1$, $5$, $20$, and $100\,\mu$m. It is shown that the temperature is equalized by approximately $80\%$ in $1\,\mu$s in the particles of $\rm{Si}_3\rm N_4$ and $\rm{BN}$ with a size of $5\,\mu$m in the $\rm{KBr}$ matrix. In the system of silicon nitride–copper, such equalization is performed for a particle with a diameter of $20\,\mu$m. For a diamond particle in the copper matrix, the particle size may be even greater. The particle sizes for which calculations showed a rather high rate of heat transfer in a time of $\sim 1\,\mu$s either match or are somewhat larger than the particles of diamond, cubic boron nitride, and $\gamma$-silicon nitride formed during the real shock-wave synthesis of these materials.