Semiempirical methods for calculating liquidus temperatures in oxide systems

Two semiempirical (geometrical and polynomial) methods are proposed for calculating liquidus temperatures in ternary and quaternary systems based on the data on equilibria in corresponding binary systems. The advantages, limitations, and peculiarities of application of the proposed semiempirical methods are considered. The reliability of the results of calculation of the liquidus temperatures in the Gd$_{2}$O$_3$–Y$_{2}$O$_3$–ZrO$_{2}$ system is illustrated by comparison with the available data on the phase equilibria. The possibility of estimating the position of the eutectic lines in multicomponent oxide systems in the temperature–composition coordinates is demonstrated. It is noted that the proposed semiempirical methods may find application in the future for estimating the values of liquidus temperatures in multicomponent systems to reduce the amount of experimental investigation of phase equilibria at high temperatures.