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Metal Science and Metal Physics
ArticleName Mathematical description of the lines of monovariant phase equilibria on the MnO-SiO2 phase equilibrium diagram
DOI 10.17580/cisisr.2023.02.17
ArticleAuthor V. V. Tolokonnikova, S. O. Baisanov, Zh. K. Saulebek, A. S. Orlov

Chemical and Metallurgical Institute named after Zh. Abishev (Karaganda, Kazakhstan)

V. V. Tolokonnikova, Cand. Chem., Chief Researcher, "Metallurgical melts" laboratory, e-mail:
S. O. Baisanov, Dr. Eng., Prof., Director, Head of the "Metallurgical processes" laboratory, e-mail:
Zh. K. Saulebek, Master Student, 1st Category Engineer, e-mail:
A. S. Orlov, Dr. Eng., Senior Researcher of the Bor laboratory, e-mail:


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).

keywords Manganese, silicium, Bjerrum-Guggenheim coefficient, phases, crystallization, activity, phase equilibrium diagram, mathematical model

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Full content Mathematical description of the lines of monovariant phase equilibria on the MnO-SiO2 phase equilibrium diagram