A multi-phase-field model of eutectic and peritectic alloys: numerical simulation of growth structures

In this paper, we extend the multi-phase-field concept, recently developed to model pure systems involving grains, to multi-phase alloy systems. We derive a phase-field model in a general form which has the flexibility to model a variety of binary alloys. In particular, our new model provides a framework for describing and numerically simulating the solidification of both eutectic and peritectic systems. We report computations that exhibit a wide range of realistic phenomena, including eutectic lamellae spacing selection by the annihilation of lamellae through competitive over-growth by their neighbours as well as tip splitting of individual lamellae. Our results are consistent with the scaling predictions of the classical Jackson and Hunt theory of eutectic lamellae. With regards to peritectic growth, we report simulations that exhibit many characteristic features of the peritectic phase transition: below the peritectic temperature the peritectic phase grows preferentially along the properitectic phase by solute diffusion in the liquid until the parent phase is engulfed. The subsequent peritectic transformation continues by solid diffusion on a longer timescale.