CALPHAD modeling of κ- carbide dual ordering in Fe-Al-C ternary alloys

A novel four-sublattice model for the $\kappa$ phase, denoted as (Fe, Al)₃(Fe, Al)₁(C, Va)₁(C, Va)₃ was proposed to improve the thermodynamic prediction, such as equilibrium composition, phase stability of $\kappa$-carbide in Fe-Al-C system. The sublattice model explains the transformation from the disordered FCC solid solution to the ordered $\kappa$-carbide via concurrent ordering of substitutional and interstitial atoms. The dual ordering model can restrict the irregular contribution of configurational entropy arising at 20 at% C composition, which is an issue with the existing thermodynamic databases. For the CALPHAD assessment, $\kappa$-carbide was considered as a single, individual phase that is in equilibrium with the liquid, austenite ($\gamma$), ferrite ($\alpha$) or other intermetallic and carbide phases in the Fe-Al-C system. The formation energy calculated from density functional theory (DFT) showed that Fe₃Al–L1₂ phase is energetically more favorable than the Fe₃AlC–E2₁ phase, and C atoms in sublattice IV are not energetically favorable at all. The assessed parameters provided better accuracy than the existing database in the calculations of isothermal sections, liquidus projection, invariant reactions, and low-temperature phase compositions. The model is highly suitable for the low temperature (<800 °C) phase predictions. Thus, the improved Fe-Al-C model lays the foundation for the thermodynamic and kinetic studies of $\kappa$-carbide for designing new Fe-Mn-Al-C alloys and optimizing the heat treatment processes.