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

摘要

During the directional solidification of peritectic alloys, two stable solidphases (parent and peritectic) grow competitively into a metastable liquidphase of larger impurity content than either solid phase. When the parent orboth solid phases are morphologically unstable, i.e., for a small temperaturegradient/growth rate ratio ($G/v_p$), one solid phase usually outgrows andcovers the other phase, leading to a cellular-dendritic array structure closelyanalogous to the one formed during monophase solidification of a dilute binaryalloy. In contrast, when $G/v_p$ is large enough for both phases to bemorphologically stable, the formation of the microstructurebecomes controlledby a subtle interplay between the nucleation and growth of the two solidphases. The structures that have been observed in this regime (in small sampleswhere convection effect are suppressed) include alternate layers (bands) of theparent and peritectic phases perpendicular to the growth direction, which areformed by alternate nucleation and lateral spreading of one phase onto theother as proposed in a recent model [R. Trivedi, Metall. Mater. Trans. A 26, 1(1995)], as well as partially filled bands (islands), where the peritecticphase does not fully cover the parent phase which grows continuously. Wedevelop a phase-field model of peritectic solidification that incorporatesnucleation processes in order to explore the formation of these structures.Simulations of this model shed light on the morphology transition from islandsto bands, the dynamics of spreading of the peritectic phase on the parent phasefollowing nucleation, which turns out to be characterized by a remarkablyconstant acceleration, and the types of growth morphology that one might expectto observe in large samples under purely diffusive growth conditions.