Substantiation of technology for the growth of monocrystalline leucosapphire from technically pure corundum

One of the stages of the preparation of porous granular corundum prior to its use in an installation for the industrial production of monocrystalline sapphire (type NIKA-M$60$) is high-temperature vacuum cleaning. The characteristics of the cleaning process are evaluated with mathematical models based on solidstate diffusion and Knudsen diffusion from porous particles and through a layer of porous particles. The solid-state diffusion of impurity atoms and the Knudsen flow of impurity vapors through the granule pores are described by analytical expressions with fitting coefficients identified with the use of numerical solutions. The model of the Knudsen flow through a layer of granular powder makes it possible to take into account blowing with a neutral gas (argon) in order to intensify the process. Cleaning times on the order of several hours were obtained in the presence of argon blowing at a flow rate of $10^{-5}$ kg/(m$^2$ s). Based on the NIKA-M$60$ unit, the flow rate is $7 \times 10^{-7}$ kg/s or $2.5$ g/h.