  In alloy solidification, the transport processes of heat and solute result in
morphological instability of the interface, forming different patterns of
solidification structure and determining the mechanical properties of
components. As the first observable phenomenon of the morphological
instabilities, the planar instability influences the subsequent stages
significantly, deserving in-depth investigations. In this paper, the planar
instability in alloy solidification under varying conditions is studied.
Firstly, the dynamical evolution of the planar instability is performed by the
theoretical model and phase-field model, respectively. Secondly, to represent
the history-dependence of solidification, the varying parameters are adopted in
the simulations. Then the criterion of the planar instability under the varying
conditions is discussed. This paper considers the critical parameters of the
planar instability are the excess free energy at the interface and
corresponding interfacial energy. Finally, to validate the criterion, the
comparisons between the phase-field model and theoretical model are carried
out, showing good consistency. Moreover, solidification processes with
different preferred crystallographic orientations are performed, demonstrating
the effect mechanism of the excess free energy and interfacial energy on the
planar instability. The idea of the interfacial energy influencing the planar
instability could be applied to investigating other patterns induced by
interfacial instability.
