Analytical approximation and numerical simulation of liquidus for non-equilibrium multi-component eutectic systems

Abstract

In the first part of the article, the methods of analytic approximation of melting curves for two-component systems and their visualization by means of computer graphics are considered. For two-component systems, a method is proposed for the approximate construction of a melting curve, based on their by approximation of polynomials of the first and second degree. The diagrams obtained by solving the Schroeder Le Chatelier system and the liquidus curves constructed on the basis of their approximation by polynomials are compared. The value of the maximum deviation of these approximations from each other is given. The errors of the diagrams of two systems are considered separately: Ba(ClO4)2 KClO4 and BaF2 BaSO4, obtained experimentally and constructed using a system of Schroeder Le Chatelier equations and their approximation by polynomials of the first and second degree. In the second part of the article, a method is proposed to construct crystallization surfaces for three-component systems based on the approximate formulas for calculation eutectic characteristics of the two-component and three-component systems, and the linear approximations of the three-component systems isotherms. Based on the proposed approximation procedure, a method for calculating the composition and temperature of eutectic for two-component systems, and the construction of three-component system isotherms in the Delphi visual programming environment with the user interface is created. The table of errors of the eutectic characteristics calculations for three-component systems is given. The results of visualization of numerical simulation of liquidus surfaces for three-component eutectic systems and their comparison with experimentally obtained samples of crystallization surfaces for two systems: Ba(ClO4)2 KClO4 and BaF2 BaSO2 are presented.