Charge-dependent CALPHAD analysis of defect chemistry and carrier concentration for space charge layers

The development of conductive materials plays a crucial role in improving the efficiency of electrochemical processes. In polycrystalline materials, space charge layers (SCLs) adjacent to grain boundaries (GBs) often dictate charge transport behavior. This study explores relaxing the charge neutrality constraint in the CALculation of PHAse Diagrams (CALPHAD) approach as a new method to model the electrical conductivity effects of SCLs. A new charge-dependent defect chemistry analysis is applied to the wustite, magnetite, and hematite phases in the Fe–O binary system. Using pycalphad, charge-dependent results for the molar Gibbs energies, Brouwer diagrams, and charge carrier concentrations were determined for each phase at 1273K within the oxygen partial pressure stability ranges. With a negative charge of 0.16 × 10⁻¹⁹ C, the hematite and magnetite phases exhibit an increased charge carrier concentration. The opposite trend was observed for wustite. While further work is needed to quantify the electrical conductivity effects of the SCLs and GBs with this approach, it provides a robust thermodynamic foundation to rapidly develop and optimize conductive materials.