Funct. Mater. 2021; 28 1: 158-169.

Based on the mathematical description of the kinetics of compaction and volumetric shrinkage of a porous body represented by a mixture of cermet powders, taking into account the mechanisms of diffuse coalescence and coagulation, a system of nonlinear differential equations of porosity and granularity was obtained for the solid-phase and liquid-phase stages of the sintering process under conditions of sequential temperature annealing, with certain speeds changes and durations. The obtained equations can be used to control the sintering process by adjusting the level, speed and duration of individual temperature conditions and technical parameters of the mixture, as well as choosing the composition, consistency and geometric characteristics of the components of the powder mixture for the manufacture of a material with desired physical and mechanical properties. The differential equations of the sintering process include the coefficients of volumetric, grain boundary, and surface diffusion, the calculation of which for multicomponent systems requires the calculation of both the self-diffusion coefficients of the components of the system and the coefficients of their mutual diffusion. The sintering process of powders of iron, cast iron and ceramic is considered as the mutual diffusion of two binary alloys: cast iron (iron + carbon) and fayalite (iron + ceramic). The calculation of the coefficient of mutual diffusion of the resulting alloy was carried out according to the Darken formula. For the numerical solution of the problem, the scheme of the Runge-Kutta method of the fourth order of accuracy with a variable integration step is used. A program complex for solving the problem has been developed, the calculation results are shown on the example of an alloy of a powder mixture of iron, cast iron and glass.