Thermodynamic artifacts in liquid alloys
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Institute of Science and Technology, Physics
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.