Affiliation:
1. Perm State National Research University; Institute of Continuous Media Mechanics, Ural Branch, Russian Academy of Sciences
2. Perm State National Research University; Perm National Research Polytechnic University
Abstract
A new physical and mathematical model of silicon vapor transport under medium vacuum conditions has been developed, which makes it possible to explain the anomalously intense mass transfer of silicon during high-temperature silicification of a porous carbon material. A formula has been derived showing how the product must be supercooled in order for the condensation process to occur in its pores. The resulting modified diffusion equation makes it possible to determine quantitatively the flow of gaseous silicon into the sample, which is highly demanded in the implementation of the porous fiber carbidization technology and the subsequent complete saturation of the product pores with unreacted silicon. We introduce and quantify a new parameter, showing the contribution of convective transport to the overall mass transfer of silicon through an external gas medium, the role of which is played by argon. An exact analytical solution of the equation for silicon transfer in a one-dimensional formulation has been found for a layer of porous medium with a flat surface. The solution has the form of a logarithmic profile and allows us to calculate the flow of gaseous silicon at the entrance to the product. The proposed approach is demonstrated on the example of two-dimensional calculations performed by the finite difference method, however, the proposed model is easily generalized to the case of three-dimensional calculations with complex geometry, which always has to be dealt with in a real technological process. Calculations in a two-dimensional formulation have performed for two model systems: when the melt mirror and the product are parallel or perpendicular to each other. The dynamics of silicon vapor propagation in the retort has been studied. It is shown that in the conditions under consideration, gaseous silicon, after the onset of vaporization, fills the entire space of the retort in a characteristic time of less than 1 s.
Publisher
National University of Science and Technology MISiS
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