Density functional theory (DFT) calculations show that it is essential to consider the magnetic contribution to the
total energy for the end-members of the σ phase. A more straightforward method to use the DFT results in a
CALPHAD (Calculation of phase diagrams) description has been applied in the present work. It was found that
only the results from DFT calculations considering spin-polarization are necessary to obtain a reliable description
of the σ phase. The benefits of this method are: the DFT calculation work can be reduced and the CALPHAD
description of the magnetic contribution is more reliable. A revised thermodynamic description of the CoeCr
system is presented which gives improved agreement with experimental phase boundary data for the σ phase.