Branching-induced grain boundary evolution during directional solidification of columnar dendritic grains

We present an investigation of secondary and tertiary branching behavior in diverging grain boundaries (GBs) between two columnar dendritic grains with different crystallographic orientations, both by two-dimensional phase-field simulations and thin-sample experiments. The stochasticity of the GB trajectories and the statistically averaged GB orientations were analyzed in detail. The side-branching dynamics and subsequent branch competition behaviors found in the simulations agreed well with the experimental results. When the orientations of two grains are given, the experimental results indicated that the average GB orientation was independent of the pulling velocity in the dendritic growth regime. The simulation and experimental results, as well as the results reported in the literature exhibit a uniform relation between the percentage of the whole gap region occupied by the favorably oriented grain and the difference in the absolute values of the secondary arm growth directions of the two competitive grains. By describing such a uniform relation with a simple fitting equation, we proposed a simple analytical model for the GB orientation at diverging GBs, which gives a more accurate description of GB orientation selection than the existing models.