Abstract
Abstract Method for studying the phase equilibria of a titanium-based metal system from the standpoint of the Bjerrum–Guggenheim concept was proposed and a mathematical model was created that can be used to obtain low-percentage grades of ferrotitanium using silicon-aluminum reducing agents. In this work, binary systems Ti–Fe, Ti–Si and Ti–Al, simulating the main composition of ferrotitanium, are studied from a thermodynamic point of view. To establish the correlation dependences of the Bjerrum–Guggenheim coefficient in these binary systems, data were obtained on the nature of interparticle interaction in melts with the derivation of analytical expressions for the liquidus and solidus lines, and experimental data were also processed for the equilibrium compositions of the liquid and solid phases from the melting temperature of iron to stable eutectics. Two types of a generalized mathematical expression as the modified Le Chatelier–Shreder equation are proposed to analytically describe the liquidus and solidus lines of phase diagrams for a whole class of systems.