Thermodynamic artifacts in liquid alloys

Abstract

The experimental and literature values of the excess free energy of mixing of Al–Fe, Al–Mn, Al–Ti, and Li–Mg binary and Al–Li–Zn ternary liquid alloys were modeled in terms of self-consistent interaction energy parameters within the framework of RedlichKister (R-K) polynomials. Initially, these parameters were assumed to be linearly dependent on temperature (T-dependent). The linear T-dependent interaction parameters were used to study various thermodynamic properties, such as free energy of mixing, enthalpy of mixing, activity, and concentration fluctuation in long wavelength limit of the aforementioned liquid alloys at various temperatures. At temperatures close to the melting point, it was found that the thermodynamic properties of the liquid alloys agree well with the corresponding experimental values. However, at higher temperatures, thermodynamic properties of the liquid alloys showed unusual phase equilibrium conditions. These conditions were referred to be artifacts or artificial inverted miscibility gaps because they were only observed in theoretical calculations and not in experimental measurements. The linear T-dependent optimised parameters of R-K polynomials were, therefore, considered inadequate at higher temperatures to account for the presence of such artifacts in the thermodynamic properties of liquid alloys. Consequently, it became clear that the interaction energy parameters must be re-optimized in order to produce parameters appropriate throughout a broad range of T-dependence. The interaction parameters for the respective excess free energy of mixing of the aforementioned liquid alloys were then re-optimized within the R-K polynomial framework, considering the exponential T-dependence of the parameters. Again, the optimized exponential T-dependent interaction parameters were utilized to assess the thermodynamic properties of the liquid alloys. As in the prior case, the thermodynamic properties of the alloys were found to agree well with the corresponding experimental values at temperatures close to the melting point. In addition, the thermodynamic properties of the liquid alloys computed at higher temperatures with T-dependent exponential parameters were free of artifacts. This study, thus, shows clearly that the poor modelling of interaction energy parameters is responsible for the appearance of artifacts in the properties of liquid alloys. It was also found that the exponential T-dependent parameters can be used over a wide temperature range for the evaluation of the thermodynamic properties of liquid alloys without producing artifacts. In addition, the ternary Al–Li–Zn liquid alloy showed the critical mixing behaviour at a Li concentration of 0.3 and a temperature of 973 K at the x Al : x = 1 : 1 cross section from the Li corner. This interesting behaviour in the ternary Al–Li–Zn liquid alloy is recommended for further investigation.