An improved magnetic model for thermodynamic modeling

The standard magnetic model in the current CALPHAD modeling is based on the Inden–Hillert–Jarl model and an empirical constraint due to Weiss and Tauer that can be used to connect ferromagnetism and antiferromagnetism. In this work, we demonstrate that many artifacts can be produced by using the current approach when modeling systems with elements of different forms of magnetism. We then propose several simple measures to improve the standard magnetic model so that a physically and numerically correct and more accurate description for the Gibbs energy of magnetic ordering can be obtained in normal situations. Especially, we have assumed that each magnetic phase always possesses both ferromagnetic and antiferromagnetic states, with one of them stable and the other non-stable. The concept of ‘effective magnetic moment’ has also been introduced as a measure of the maximum magnetic entropy. A case study on the Al–Cr–Fe system has been performed at 0 K showing the importance of reasonable description of the magnetic phase diagrams. It has been stressed that the extended magnetic model in this work can be further employed for bridging atomistic and phenomenological modeling for multi-scale simulation.