Thermosolutal convection-induced freckle formation in steady and unsteady directional solidification: Analysis in Sn-Ni peritectic alloy

•Freckle formation is found in two regions before and after peritectic reaction.•Effects of both TGZM and G-T effects on dendritic evolution is confirmed.•Less/More freckle in deceleration/acceleration growth is explained.•Rayleigh number RaP which predicts two maximum in peritectic alloy is proposed. [Display omitted] Peritectic alloys have attracted more and more attention during past decades due to their growing applications. However, different from the current analysis on other alloys, freckle formation is witnessed in two regions in Sn–Ni peritectic alloy during directional solidification: the former (latter) one before (after) peritectic reaction. Besides, compared with the steady growth condition, fewer freckles can be observed in deceleration growth while more freckles are formed in acceleration growth. In addition, it has been demonstrated that the dendritic morphology is greatly influenced by the Gibbs-Thomson (G-T) and temperature gradient zone melting (TGZM) effects. A Rayleigh number RaP in consideration of both effects was proposed. The prediction of RaP in the mushy zone shows two maximums during peritectic solidification, confirming the freckle formation in two regions in this work. Furthermore, the influence of unsteady growth condition on the freckle formation can also be successfully predicted by RaP.