Multi-ternary extrapolation scheme for efficient coupling of thermodynamic data to a multi-phase-field model

[Display omitted] •A new multi-ternary extrapolation scheme for thermodynamic data is proposed.•The new scheme and two alternative methods are mathematically derived and reviewed.•All methods are quantitatively compared in terms of accuracy, stability and efficiency.•With all extrapolation methods a large speed-up of simulations is achieved.•The new multi-ternary scheme convinces with highest accuracy and stability. Phase-field simulation of technical multicomponent and multiphase alloys requires an efficient coupling to thermodynamic databases. Sophisticated interpolation or extrapolation methods allow reducing the frequency of time-intensive thermodynamic (quasi-)equilibrium calculations as has been shown for the multi-binary extrapolation scheme which already has proved to be successful. This paper presents a new multi-ternary extrapolation scheme which better approximates solute redistribution for non-dilute alloys as compared to the multi-binary scheme. Furthermore, numerical problems like multi-binary miscibility gaps can be effectively avoided. The new multi-ternary scheme is derived from the general multicomponent quasi-equilibrium approach and contrasted to the simpler multi-binary redistribution scheme. A quantitative comparison of the two methods is presented for solidification in the ternary system Al–Cr–Ni. The application to a commercial Ni-base superalloy finally demonstrates the potential for simulating multiphase equilibria in composition regions, in which the multi-binary approximation often fails.