A 3D computer model of the CaO-MgO-Al2O3 T-x-y diagram at temperatures above 1300 °C

Abstract

The research analyses the controversies surrounding the technique for the formation of a CaO-Al2O3 binary system and the nature of melting of compounds in it, i.e. whether the 12:7 compound is technically possible and whether the 1:1 and 1:2 compounds are congruently or incongruently melting compounds. It also discusses whether in the CaO-MgO-Al2O3 ternary system the following compounds can be formed: a 3:1:1 compound alone or, in addition to it, two more compounds of 1:2:8 and 2:2:14. A 3D model of the T-x-y diagram was created for the most common version, with six binary and three ternary compounds. Its high-temperature portion (above 1300°C) consisted of 234 surfaces and 85 phase regions. Ternary compounds were formed as a result of three peritectic reactions. Besides them, six quasi-peritectic and three eutecticinvariant reactions occurred in the system with the participation of the melt. The principle of construction for a threedimensional model involved a gradual transition from a phase reaction scheme (which is transformed into a scheme of uni- and invariant states) presented in a tabulated and then in a graphical form (a template of ruled surfaces and isothermal planes corresponding to invariant reactions) to a T-x-y diagram prototype (graphic images of all liquidus, solidus, and solvus surfaces). The design was concluded with the transformation of the prototype into a 3D model of the real system after the input of the base points coordinates (concentrations and temperatures) and the adjustment of curvatures of lines andsurfaces. The finished model provides a wide range of possibilities for the visualisation of the phase diagram, including the construction of any arbitrarily assigned isothermal sections and isopleths. The 3D model was designed with the help of the author’s software PD Designer (Phase Diagram Designer). To assess the quality of the 3D model, two  versions of an isothermal section at 1840 °C were compared: model section and a fragment of an experimental section near Al2O3.