Regularities of phase equilibria based on the Bjerrum-Guggenheim concept for the Fe-Al binary system

Abstract

A theoretically justified method of mathematical description of phase equilibrium lines based on the regularity of the behavior of components along the phase crystallization line has been developed. When analyzing the state diagrams of various systems, a regularity was found in the formation of crystallization fields of phases in the form of a correlation dependence between the osmotic coefficient of the crystallizing component and the ratio of its activity in the liquid and solid phases. The Bjerrum-Guggenheim osmotic coefficient can serve 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. Two types of generalized mathematical expression in the form of a modified Schroeder-Le Chatelier equation are proposed for the analytical description of the liquidus and solidus lines of state diagrams of a whole class of systems. These types make it possible to calculate the dependence between the composition and the temperature. Mathematical expressions describing the lines of monovariant phase equilibria are presented on a single analytical basis. Mathematical expressions represent the liquidus and solidus lines of the Fe-Al system for the corresponding elements and compounds using the Schroeder-Le Chatelier equation and the Bjerrum-Guggenheim coefficient (Фi). The linear nature of the change in the osmotic coefficient of crystallizing phases (Фi) on the ratio of the activity of the components in the ideal liquid and solid phases under the boundary conditions of the formation of crystallization fields of the phases was revealed. The type of change 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 structural units of the considered component with the second prevail, then a linear relationship is observed. When the formation of various groups from the initial components or the dissociation of a chemical compound takes place in the melt, the osmotic coefficient has a curved dependence. This research is funded by the Science Committee of the Ministry of Education and Science of the Republic of Kazakhstan (Grant No. AP08855453).