Thermodynamic Properties of Melts in the Eu–Ge System

The isoperibolic calorimetry method was employed to determine, for the first time, the partial and integral mixing enthalpies for melts in the Eu–Ge system over the entire composition range at 1200 K and 1370–1440 K. The minimum mixing enthalpy for these melts was –49.1 ± 4.4 kJ/mol and was shown by the alloy with x_Ge = 0.45, while \(\Delta {\overline{H} }_{{\text{Eu}}}^{\infty }\) = –145.7 ± 22.3 kJ/mol and \(\Delta {\overline{H} }_{{\text{Ge}}}^{\infty }\) = –166.8 ± ± 19.8 kJ/mol at 1400 ± 3 K, correlating with the solid-state behavior of these melts. This allows categorizing these melts within the series of the Ge–Ln (lanthanide) systems and justifying the thermodynamic properties of melts in the Eu–Ge system, in particular, and in the Ge–Ln system, in general. Using the thermochemical properties for melts in the Eu–Ge system, the ideal associated solution model was employed to optimize and calculate the Gibbs energies, enthalpies, and entropies of formation for the melts, associates in melts, and intermetallics. A large number of associates, especially EuGe, formed in the studied melts because of the highest probability of collision between two dissimilar atoms in liquid alloys. The maximum mole fraction of the EuGe associate reached 0.48 and those of Eu₃Ge, Eu₂Ge, EuGe₂, and EuGe₃ were 0.2, 0.26, 0.24, and 0.26, respectively. The activities of components in melts of the Eu–Ge system showed substantial negative deviations from the ideal solution, correlating with our thermochemical properties. This all indicated strong interactions between dissimilar atoms in melts of the Eu–Ge system, likely involving the transfer of valence electrons of europium to the 4p orbital of germanium. The ΔG values over the entire composition range were greater than ΔH, with ΔG_min = –28.8 kJ/mol at x_Ge = 0.45. Moreover, the ΔG function was also almost symmetrical because of the entropy contribution (mixing entropy of the studied melts was negative, and ΔS_min = –15.0 J/mol K at x_Ge = 0.45). The calculations based on the ideal associated solution model also established that the \(\Delta {\overline{H} }_{{\text{Eu}}}^{\infty }\) values for melts in the Eu–Ge system increased insignificantly with temperature, while \(\Delta {\overline{H} }_{{\text{Ge}}}^{\infty }\) increased more substantially. This might be due to the break of covalent bonds between germanium atoms. Complete information on the thermodynamic properties of all phases was obtained, enabling a thermodynamic description of the Eu–Ge system for the first time.