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This lecture discusses the stability of the solidification front in the context of alloy casting. It covers topics such as the rejection of solute by the solid, the enrichment of the liquid, and the formation of the first solid with the desired solute concentration. The conditions for instability related to temperature gradients and the mechanisms that affect solidification fronts are explored. The lecture also delves into mass flow of solute, concentration gradients, and the transformation of instability conditions. Various factors influencing solidification modes and microstructures are analyzed, including the impact of temperature profiles and mechanical aspects.