MECHANICS

Modeling of gas exchange processes in the porous space between the surface of metal-ceramic boards and the refractory tooling under high-temperature sintering conditions

I. A. Zhukov^a, A. Yu. Krainov^a, K. M. Moiseeva^a, E. V. Ermolaev^bc, V. A. Egoshin^cab, Sh. N. Shugaepov^abc, R. Sh. Akhmetgaliev<sup>ca

a</sup> Tomsk State University, Tomsk, Tomsk, Russian Federation
^b Mari State University, Yoshkar-Ola, Russian Federation
^c JSC Semiconductor Devices Plant, Yoshkar-Ola, Russian Federation

Abstract: The convection and diffusion of impurities in the forming gas during the high-temperature sintering of ceramic products are simulated. The Leibenson model is used to describe the isothermal filtration gas flow in the porous space. The stationary fields of pressure, impurity vapor concentration, and velocity modulus of the gas mixture in the porous region between the rough plate and the microcircuit housing surface are determined. The characteristic time of convection and diffusion in the porous space between the metal plate and the ceramic-metal board surface is estimated. The conditions for the accumulation and release of impurities from the porous space of the metal plate under the bottom of the board are determined. The proposed mathematical models can be used to calculate the rate of impurity release from the porous space under the board bottom depending on the roughness of the metal plate surface.

Keywords: self-propagating high-temperature synthesis, sintering, titanium diboride, structure, mechanical properties, composite material, Ti-B-Fe system, hardness, strength characteristics.

UDC: 533.15; 666.3.017

Received: 27.02.2025
Accepted: September 6, 2025

DOI: 10.17223/19988621/97/6