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The article presents the results of constructing a diagram of the phase composition of the Fe-S-Cu system and its mathematical model. Using the equations obtained in the work, a computer program was created and, using it, an analysis of phase formation in copper ores of various deposits was carried out. It was found that copper ore concentrates from the Berezovsk deposit in Kazakhstan contain Cu5FeS4 (20,22 %), CuS (14,21 %) and FeS2 (65,57 %), and copper ores from the Zyryanovsk deposit contain CuFeS2 (4,03 %), Cu5FeS4 (45,29 %) and FeS2 (50,68 %). Such data allows you to choose the optimal methods for further processing of concentrates, and the mathematical approach itself is more productive than the often used geometric one according to the rule of segments.

The article presents the results of a study of the slag mode of melting boron-containing silicochrome. It is shown that the addition of boron-containing fluxes to the silicochromium charge made it possible to reduce the thermal level of the melting process by reducing the melting temperature and viscosity of the final slags.

Mathematical diagrams of viscosity and crystallization temperatures of melts of the CaO – SiO2 – Al2 O3 – B2 O3 system were created. To obtain them, experimental studies were carried out using the simplex-lattice method of experiment planning. It was used to study 35 slags containing (wt.%) 9.8-52 CaO, 33.6-70.4 SiO2, 16.0-51.52 Al2 O3, 0-20 B2O3. The experiments were carried out on an electrovibrational viscometer in molybdenum equipment, in a stream of purified argon in the temperature range of 1 473–1 923 K.

Isothermal sections of the phase composition diagram of the Fe – Si – Cr – B system in the temperature range of 300 – 3 000 K with a step of 200 K are constructed. The diagram is shown at a temperature of 1 900 K, which is typical for silicochromium at the outlet from the furnace. A mathematical model of the diagram has been created in the form of a system of linear equations connecting the chemical composition of the metal with its phase. A computer program has been developed for the numerical calculation of the number of formed phases. Silicochromium with 0,3 – 0,5 % boron is located in the crystallization field CrSi2 – Si – SiB4 – FeSi.

A diagram of the phase composition of the three-component metal system Fe-Si-Cr is plotted. It has 12 phases: Fe, Si, Cr, Fe3Si, Fe2Si, Fe5Si3, FeSi, FeSi2, Cr3Si, Cr5Si3, CrSi and CrSi2. The dimensions of the fields formed and the prevalence of individual phases in them have been determined. The most common compounds in the system under study are FeSi, CrSi2 and Cr3Si. Isothermal sections of the diagram are plotted. A mathematical model of the diagram and a computer program have been created. After setting the chemical composition of the metal from the control panel and starting, the computer finds the field (triangle) where the metal is and displays its phase composition in mass percent on a monitor or print. An example of using the created model for calculating the phase composition of ferrosilicon grades is given. FeSi65, FeSi75 and ferrosilicochromium FeSiCr48. A satisfactory agreement was found between the calculated and experimental data.

The results are presented from laboratory tests on the use of fluxing agents for improving the sintering technology of refractory chromite ore in Kazakhstan. To solve the most efficient thermal process it is shown that reduction of the melting point of the charge through the use of fluxing agents with a low melting temperature and a low temperature promotes the formation of compounds in interaction with components of the ore phase. It is proposed to use the calcined colemanite and basaltic rocks as an effective flux. The optimal cost of fluxing agents is achieved ensuring reduction of the thermal level of the firing process by 100 degrees C., The results are presented from laboratory tests on the use of fluxing agents for improving the sintering technology of refractory chromite ore in Kazakhstan. To solve the most efficient thermal process it is shown that reduction of the melting point of the charge through the use of fluxing agents with a low melting temperature and a low temperature promotes the formation of compounds in interaction with components of the ore phase. It is proposed to use the calcined colemanite and basaltic rocks as an effective flux. The optimal cost of fluxing agents is achieved ensuring reduction of the thermal level of the firing process by 100 degrees C.

A complete thermodynamic modelling of chemical transformations during carbothermic reduction of barium and boron from oxides has been performed. It was shown that during the processing of charge with a high BaO: BaO:B2O3(3:1), barium carbide (BaC2), iron boride (FeB) and barium hexaboride (BaB6) are present as phase components in the smelting products, with the former predominantly noticeable. The data obtained allow us to conclude that it is possible to produce a new ferroalloy containing boron and barium. (Authors.), A complete thermodynamic modelling of chemical transformations during carbothermic reduction of barium and boron from oxides has been performed. It was shown that during the processing of charge with a high BaO: BaO:B2O3(3:1), barium carbide (BaC2), iron boride (FeB) and barium hexaboride (BaB6) are present as phase components in the smelting products, with the former predominantly noticeable. The data obtained allow us to conclude that it is possible to produce a new ferroalloy containing boron and barium. (Authors.)