  Solidification structures are determined by the interaction between the
interfacial processes and transport processes of heat and solute. In this
paper, we investigate planar instability in directional solidification.
Firstly, the interfacial evolution at the initial growth stage is simulated,
indicating the planar instability is represented by the transition from the
planar to the cellular. Secondly, to represent the history-dependence of
solidification, constant thermal gradient G and varying pulling speed VP are
used in the simulations. The results indicate the cooling rate R ( = G*VP)
dominates the overall propagation speed of the interface, to maintain the local
thermodynamic equilibrium. The solute segregation determines the stability of
the interface, by changing the excess free energy at the interface and
corresponding interface energy. Finally, the simulations of the grains with
different preferred crystallographic orientations are performed, indicating the
surface energy and its anisotropy do not affect the solute diffusion and planar
growth. The results also verify the conclusion that solute segregation
influences the interface energy and results in interface instability. On the
other hand, for the planar-cellular transition, the minimum surface stiffness
rule is more suitable than the maximum surface energy rule. The influence of
the solute concentration on the excess free energy and interface energy can be
applied to other solidification patterns induced by the interface instability,
which will be studied in the future.
