The exponential excess Gibbs energy model revisited

The exponential model for the temperature (T) dependence of the excess Gibbs energy of liquid solutions within the framework of the Redlich-Kister polynomials is proven to be an efficient tool to avoid high-T artefacts, such as an artificial inverted miscibility gap, caused by the linear model. However, it has been claimed that the exponential model can lead to a low-T artefact, i.e. to the artificial low-T re-stabilization of the liquid solution. As shown here, this claim is un-supported for all the 15 binary systems studied so far by the exponential model in the literature. Still, the artefact might appear for other systems, or for lower temperatures, as the 15 systems were modelled at and above 298 K. To make sure the low-T artefact does not appear, this paper introduces a new, low-T polynomial, which is matched with the exponential model at temperature T*, defined as the lowest liquidus temperature of the given system. The low-T model is described by a four parameter polynomial, obtained analytically from the two fitted parameters of the exponential model, ensuring that the four excess functions (the excess Gibbs energy, the heat of mixing, the excess entropy and the excess heat capacity) are continuous functions of T in the whole T-interval at any composition. When the complexity of the liquid alloy requires more than two semi-empirical parameters, the combined linear-exponential model should be used instead of the exponential model, with the same matching low-T polynomial. The inherently inconsistent nature of the recent LET function (see S.M. Liang, P. Wang, R. Schmid-Fetzer, Calphad 54 (216) 82-96) is discussed, as it was introduced to replace the exponential model. It is proven by the new simplified assessment of the Mg-Si system that the exponential model can be applied to this system without any artifact, contrary to the claim of Schmid-Fetzer et al., Calphad 31 (2007) 131-142.