A comparative study of Kim-Kim-Suzuki (KKS), Partition Coefficient Relaxation (PCR), and Finite Interface Dissipation (FID) phase field models for rapid solidification

The properties and performance of additively manufactured metals are linked to, and sometimes directly controlled by, the microstructures formed under rapid solidification conditions in the melt pool. Predictive simulations of rapid solidification microstructures can provide understanding of the underlying materials phenomena and could replace and/or supplement expensive and time consuming physical experiments. Phase-field (PF) models are a natural and popular choice for this task, but multiple PF models for rapid solidification now exist and their relative merits have not been assessed in detail. Here we compare three PF models – Kim-Kim-Suzuki (KKS), partition coefficient relaxation (PCR), and finite interface dissipation (FID) – in terms of their results for (i) primary dendrite arm spacing, (ii) partition coefficient, and (iii) transition velocity between cellular and planar growth, all during rapid solidification. Ti-50 at.%Nb is used as a model alloy, with thermodynamic free energies imported from CALPHAD databases. The comparison is made at large growth rates where the system is under highly non-equilibrium conditions. We show that the PCR model converges roughly to the KKS model under these conditions, whereas the FID model produces somewhat different but still sensible results due to different underlying assumptions. The advantages of the PCR model are in numerical stability, close relation to the well-established KKS model, simplicity via use of a single kinetic interfacial parameter, and ease and efficiency of extension to alloys with more chemical elements. The advantages of the FID model are in physical interpretability, direct connection to the physical interfacial mobility, potentially greater flexibility via variation of two kinetic interfacial parameters, and proper convergence to no segregation at large velocities.