Phase-field modeling of microstructural pattern formation during directional solidification of peritectic alloys without morphological instability

During the directional solidification of peritectic alloys, two stable solid phases (parent and peritectic) grow competitively into a metastable liquid phase of larger impurity content than both solid phases. When the parent or both solid phases are morphologically unstable, i.e. for a small temperature gradient/growth rate ratio ($G/v_p$), one solid phase usually outgrows and covers the other phase, leading to a cellular-dendritic array structure closely analogous to the one forming during monophase solidification of a dilute binary alloy. In contrast, when $G/v_p$ is large enough for both phases to be morphologically stable, the formation of the microstructure becomes controlled by a subtle interplay between the nucleation and the growth of the two solid phases. The structures that have been observed in this regime (in small samples where convection effects are suppressed) include alternate layers (bands) of the parent and peritectic phases perpendicular to the growth direction, which are formed by alternate nucleation and lateral spreading of one phase onto the other as proposed in a recent model {\rm [}R. Trivedi, Metall. and Mater. Trans. A {\bf 26}, 1 (1995){\rm ]}, as well as partially-filling bands (islands), where the peritectic phase does not fully cover the parent phase that grows continuously. We develop a phase-field model of peritectic solidification that incorporates nucleation processes in order to explore the formation of these structures. Simulations of this model shed light on the morphology transition from islands to bands, the dynamics of spreading of the peritectic phase on the parent phase following nucleation, which turns out to be characterized by a remarkably constant acceleration, and the type of growth morphologies that one might expect to observe in large samples under purely diffusive growth conditions.