Thermodynamic self-consistency issues related to the Cluster Variation Method: The case of the BCC Cr–Fe (Chromium–Iron) system

The Cluster Variation Method (CVM), introduced over 50 years ago by Prof. Dr. Ryoichi Kikuchi, is applied to the thermodynamic modeling of the BCC Cr–Fe system in the irregular tetrahedron approximation, using experimental thermochemical data as initial input for accessing the model parameters. The results are checked against independent data on the low-temperature miscibility gap, using increasingly accurate thermodynamic models, first by the inclusion of the magnetic degrees of freedom of iron and then also by the inclusion of the magnetic degrees of freedom of chromium. It is shown that a reasonably accurate description of the phase diagram at the iron-rich side (i.e. the miscibility gap borders and the Curie line) is obtained, but only at expense of the agreement with the above mentioned thermochemical data. Reasons for these inconsistencies are discussed, especially with regard to the need of introducing vibrational degrees of freedom in the CVM model.