On the abilities and limitations of the linear, exponential and combined models to describe the temperature dependence of the excess Gibbs energy of solutions

Abstract

In this paper the performance of the linear, exponential and combined models to describe the temperature dependence of the excess Gibbs energy of solutions in the framework of the Redlich–Kister model is discussed. The models are not compared to existing Calphad optimized databases, rather they are tested against the 209 binary solid and liquid metallic alloys, for which reliable experimental data exist on the heat of mixing and Gibbs energy of mixing in the handbook of Predel. It was found that the linear model often leads to high-T artifact (artificial inverted miscibility gaps) and the excess Gibbs energy approaches infinity at high temperatures, which seems unreasonable. It was also found that although both the exponential and combined models can in principle lead to low-T artifact (liquid re-stabilization), in real systems it probably does not take place, at least for the “normal” systems (a system is “normal”, if the heat of mixing, excess entropy of mixing and excess Gibbs energy of mixing have the same sign at the temperature of measurement; 86% of all systems are found “normal”). The problem with the exponential model is that it is unable to describe the “exceptional” systems (14% of all systems). It is shown that the combined model is able to describe also these “exceptional” systems, as well. An algorithm is worked out to ensure that the combined model does not run into any high-T or low-T artifact, even when it is used to describe the “exceptional” systems. It is concluded that the T-dependence of the interaction energies for all solution phases described by the Redlich–Kister polynomials should be described by the combined model. In this way an improved databank on excess Gibbs energies of solution phases can be gradually built, not leading to any artifact.