  Grain growth competition during directional solidification of a polycrystal
with hexagonal (hcp) symmetry (Mg-1wt%Gd alloy) is studied by phase-field
modeling, exploring the effect of the temperature gradient G on the resulting
grain boundary (GB) orientation selection. Results show that selection
mechanisms and scaling laws derived for cubic (fcc, bcc) crystals also apply to
hcp materials (within their basal plane), provided a re-estimation of fitting
parameters and re-scaling to account for the sixfold symmetry. While grain
growth competition remains stochastic with rare events of unexpected
elimination or side-branching along the developing GBs, we also confirm an
overall transition from a geometrical limit to a favorably oriented grain limit
behavior with an increase of thermal gradient within the dendritic regime, and
the progressive alignment of dendrites and GBs toward the temperature gradient
direction with an increase of G during the dendritic-to-cellular morphological
transition. Comparisons with original thin-sample directional solidification
experiments show a qualitative agreement with PF results, yet with notable
discrepancies, which nonetheless can be explained based on the stochastic
variability of selected GB orientations, and the statistically limited
experimental sample size. Overall, our results extend the understanding of GB
formation and grain growth competition during solidification of hcp materials,
and the effect of thermal conditions, nonetheless concluding on the challenges
of extending the current studies to three dimensions, and the need for much
broader (statistically significant) data sets of GB orientation selected under
well-identified solidification conditions.
