When analyzing a number of phase equilibrium diagrams of various types of systems, the regular relationship was found during the formation of phase crystallization fields in the form of a correlation dependence of the osmotic coefficient of a crystallizing component on the ratio of its activity in the liquid and solid phases. The Bjerrum-Guggenheim osmotic coefficient serves as a measure of the deviation of the energy properties of a real system from the ideal one described by the Schroeder-Le Chatelier equation. Mathematical expressions for the liquidus and solidus lines are obtained in the form of semi-empirical dependences on a single analytical basis, which make it possible to calculate the temperature dependence of the composition. Thus, a theoretically substantiated method for the mathematical description of the lines of monovariant phase equilibria has been developed, based on the regularities of the behavior of components in the melt. Mathematical expressions represent the crystallization fields of the phases of the MnO-SiO2 system for the corresponding components and compounds using the Schroeder-Le Chatelier equation and the correlation dependence of the osmotic coefficient Ф', experimental and calculated data of the Bjerrum-Guggenheim osmotic coefficient (Фi) are calculated. The type of variation in the Bjerrum-Guggenheim osmotic coefficient depends on the intermolecular interaction of the components in the melt. If only van der Waals forces of interaction between the components in the melt prevail, then a correlation dependence is observed. When groups from the initial compounds are formed in the melt, or processes of dissociation or, conversely, association occur, the osmotic coefficient is described by a curvilinear dependence. The paper presents mathematical expressions for the fields of crystallization of phases of the MnO-SiO2 system in the form of semi-empirical dependencies. The nature of the change in the Bjerrum-Guggenheim osmotic coefficient of the crystallizing component depending on the ratio of its activity in the liquid and solid phases is shown. This research is funded by the Science Committee of the Ministry of Education and Science of the Republic of Kazakhstan (Grant No. AP09259157).

Carrying out a series of fundamental studies in the field of physicochemical analysis, based on an approach that considers the phase state of alloys and accounts for the regular patterns of interaction of substances in multicomponent ores that are complex in both chemical and phase composition, makes it possible to formulate a number of scientifically substantiated practical recommendations. The aim of this work is to assess the degree of zinc sublimation from a magnesium alloy through the behavior of the Bjerrum–Guggenheim osmotic coefficient and the degree of dissociation of the congruent compound. The paper presents a method for processing phase equilibrium lines in a temperature–composition phase diagram, resulting in mathematical expressions for the liquidus and solidus lines on a unified analytical basis in the form of a semi-empirical dependence derived from the Schröder–Le Chatelier equation. Indirectly, through the Bjerrum–Guggenheim osmotic coefficient, the degree of dissociation of MgZn₂ in the Mg–Zn system was determined to range from 17% to 46%. This result is in good agreement with the conclusions of Nikolay Semyonovich Kurnakov regarding the degree of dissociation of congruent compounds inferred from the shape of the maximum on phase diagrams. For MgZn₂, this maximum is very smooth, i.e., the composition of the liquid phase changes continuously with deviation from stoichiometry, resulting in a symmetrical rounded peak. An experimental study was carried out using a SEM/EDS analytical complex to confirm the high volatility of zinc. The key zinc-concentrating phases were identified in the investigated processing products (slag, metal, and dust), which is consistent with the theoretical premises and explains the mechanism of zinc behavior during high-temperature processing of zinc-containing slags. The form of zinc occurrence in different phases was established. In the initial slag, the zinc content reaches 51.79%. In the metallic phase, zinc is detected as fine dispersed inclusions. In the collected dust (flue ducts), particles enriched in zinc up to 44.09 wt.% were identified.

Magnetization roasting followed by magnetic separation can upgrade ferruginous manganese raw materials, but its efficiency depends on the iron phase state after roasting. This study clarified the phase state and distribution of iron in magnetic and non-magnetic products obtained from ferruginous manganese ore and concentrate after magnetization roasting and dry magnetic separation. The materials were roasted at 600–650 °C using Shubarkol coal as a solid reducing agent and then separated at a magnetic field strength of 1.2 kOe. Chemical analysis, X-ray diffraction, and Mössbauer spectroscopy were used to relate separation results to iron phase states. The Mn/Fe ratio in the non-magnetic products increased from 3.92 to 10.87 for the ore and from 2.98 to 23.99 for the concentrate, while 76.25% and 88.26% of iron were transferred to the corresponding magnetic fractions. Mössbauer spectroscopy showed that magnetite-type spinel components, including Fe₃O₄ and substituted (Fe_1−xM_x)₃O₄, were mainly associated with the magnetic products. Hematite-like and paramagnetic Fe³⁺/Fe²⁺ components were also detected, indicating incomplete conversion of iron-bearing phases into magnetite-type spinels. The Mössbauer-area-weighted fraction of iron in magnetite-type spinel phases was 76.5% for the ore and 64.36% for the concentrate. These results explain the different separation behavior after roasting–magnetic treatment.