Original Article

Thermodynamic optimization of the SiO₂-MgO-NiO, SiO₂-Cu₂O-NiO, and SiO₂-FeO-NiO systems

¹ Instituto Politécnico Nacional, Escuela Superior de Ingeniería Química e Industrias Extractivas, Metallurgy and Materials, 07738, Mexico City, Mexico
² Tecnológico de Estudios Superiores de Ecatepec, Division of Mechanical, Mechatronics and Industrial Engineering, Ecatepec 55210, Estado de Mexico, Mexico
³ Instituto Politécnico Nacional, Unidad Profesional Interdisciplinaria de Ingeniería, Specific Vocational Training, San Agustín Tlaxiaca 42162, Hidalgo, Mexico

^* e-mail: This email address is being protected from spambots. You need JavaScript enabled to view it.

Received: 20 January 2026
Accepted: 7 May 2026

Abstract

In this study, a previously developed structural model for ternary silicate melts and glasses, which assumes that metallic oxides behave similarly in silicate melts, was used to calculate the thermodynamic properties and ternary phase diagrams of the SiO₂-NiO-FeO-Cu₂O-MgO system. The model allows calculation of ternary system properties using only data from binary subsystems, without requiring any ternary terms. The phase diagrams for the NiO-SiO₂ and Cu₂O-SiO₂ systems were optimized using a binary structural model. The ternary structural model was then applied to calculate the phase diagrams for SiO₂-FeO-NiO, SiO₂-Cu₂O-NiO, and SiO₂-MgO-NiO. The results showed that the mixing free energies for the NiO-SiO₂, Cu₂O-SiO₂, and FeO-SiO₂ binary systems are very similar, supporting the assumption of random mixing of metal cations in the silicate structure. The mixing free energy of liquid MgO-SiO₂ is much lower than that of binary NiO-SiO₂. Nevertheless, the calculated SiO₂-MgO-NiO phase diagram agreed with the experimental results.