Characterization of late-stage equiaxed solidification of alloys

We use a two-dimensional phase-field model coupled to a nucleation mechanism to study the evolution of interdendritic liquid pools during late-stage solidification of Mg–Al alloys under spatially uniform temperature and constant cooling rates. We obtain the channel size distribution (CSD) of liquid pools at solid fractions close to those where eutectic phase is expected to form and investigate the influence of cooling rate on the morphology of the CSD at different solidification stages. Our results show that the CSD is unimodal, exhibiting a peak at small channel widths followed by a shoulder and longer decay tail at large channel widths. This feature is correlated to the presence of two distinct liquid regions, small channels between secondary branches of the primary phase and larger channels between adjacent grains. We construct a cooling-rate/solid-fraction morphology diagram that shows the relative importance of the shoulder in the CSD. We characterize the mean and standard deviation of the CSD and show that, within the range of data examined, the mean channel size vs. cooling rate curves scale with solid fraction. The numerical tools developed for this work can also be used to analyze experimental results. We include the analysis of two experimental micrographs previously published by Paliwal et al.