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

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 pos-sible 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 regulari-ties 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 Chat-elier equation and the correlation dependence of the osmotic coefficient CYRILLIC CAPITAL LETTER EF', experimental and calculated data of the Bjerrum-Guggenheim osmotic coefficient (CYRILLIC CAPITAL LETTER EFi) 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 expres-sions 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.