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

Abstract

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 (Si₃N₄) and boron nitride (BN) are considered in a matrix of potassium bromide (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 μm. It is shown that the temperature is equalized by approximately 80% in 1 μs in the particles of Si₃N₄ and BN with a size of 5 μm in the KBr matrix. In the system of silicon nitride–copper, such alignment is performed for a particle with a diameter of 20 μm. 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 ~1 μs either match or are somewhat larger than the particles of diamond, cubic boron nitride, and γ-silicon nitride formed during the real shock-wave synthesis of these materials.