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

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. (C) 2015 Elsevier B.V. All rights reserved.