<p>The lack of a thorough understanding of the solidification behaviors of the proeutectic Al₃Sc and the Al-Al₃Sc eutectic in a hypereutectic Al-Sc alloy stimulates the present dissertation. The major findings for the single-phase growth of the proeutectic Al₃Sc is summarized as follows: At a low cooling rate (~1 ºC·s^-1), the proeutectic Al₃Sc phase’s formation was governed by the lateral growth, exposing six flat {100} facets. At an intermediate cooling rate (~400 ºC·s^-1), the proeutectic Al₃Sc grew in a dendritic manner, with well-defined backbones extending in eight <111> directions and paraboloidal dendrite tips, although the dendrite tips and side-branches turned into faceted steps at a late growth stage,when the lateral growth prevailed. At a high cooling rate (~1000 ºC·s^-1), the proeutectic Al₃Sc primarily crystallized into an entirely seaweed-structured particle, which was composed of interior compact seaweeds and exterior fractal seaweeds. In order to verify the proposed dendritic and seaweed growth mechanisms for the proeutectic Al₃Sc, various morphological stability criteria were used, and fair agreement between the observed and the estimated characteristic length scales was reached.</p><p>On the Al-Al₃Sc eutectic side, it was found that a rod-typed Al₃Sc eutectic phase prevalently existed in an as-cast hypereutectic Al-Sc alloy that solidified via both slow cooling in air (~1 ºC·s⁻¹) and rapid cooling in a wedge-shaped copper mold (up to ~3000 ºC·s⁻¹). Al-Al₃Sc eutectic dendrites were identified within a narrow region near the edge of the wedge. The eutectic dendrites had an equiaxed dendritic contour and a rod eutectic structure inside. Quantitative assessments revealed that an interface undercooling of 48.2 ºC was required to form the eutectic dendrites, or in other words, to enter the coupled zone of the Al-Al₃Sc phase diagram. Furthermore, a phenomenon of scientific interest was discussed: When crystallizing under a near-equilibrium condition, the eutectic Al₃Sc phase formed a non-faceted morphology, in contradiction to its faceted nature. Based on the competitive growth criterion, it was deduced that the non-faceting of the eutectic Al₃Sc phase essentially reduced the interface undercooling for the resultant regular eutectic, in comparison to an otherwise irregular eutectic that would contain a faceted eutectic Al₃Sc phase.</p>