The copper-magnesium system: calorimetric studies and phase diagram calculations

To enrich the existing knowledge of the thermodynamic properties of the Cu-Mg system, new complementary experimental and theoretical studies were carried out. The measurements of the change in the enthalpy of mixing of liquid Cu-Mg solutions were performed for Cu concentrations from 1 to 0.6 mole fractions and for several temperatures in the range from 1123 to 1402 K. It was found that the minimum change in the enthalpy of mixing of liquid solutions occurs for a copper concentration of approximately 0.4 mole fractions, and its value is slightly less than -7.5 kJ/mol. These measurements are the first in the range of Cu-rich solutions. The measurements of the change in the enthalpy of formation of intermetallic phases were carried out using liquid aluminum and liquid tin as a phase dissolution bath. It was found that the change in the enthalpy of formation of the Cu₂Mg phase is slightly lower than that of the CuMg₂ phase, and the measured values for the Al and Sn baths were: -11.6 (±0.6) kJ/mol·at. and -10.7 (±0.3) kJ/mol·at., and -11.1 (±0.4) kJ/mol·at. and -8.8 (±0.2) kJ/mol·at., respectively. The use of two distinct metallic baths enhances the accuracy and interpretability of the thermodynamic analysis. The theoretical studies included ab initio calculations of the heat of formation of solid phases Cu₂Mg and CuMg₂ and their heat capacities under constant pressure, in the temperature range from 300 to 800 K. Significant discrepancies were observed between the change in the enthalpies of phase formation obtained by different methods, as well as good agreement with the experimental data on heat capacities and those obtained from theoretical calculations. Based on experimental and theoretical data, the thermodynamic parameters of the phases were developed, and the phase diagram of the Cu-Mg system was calculated using the Calphad method.