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This study aims to clarify the growth process of the β-phase in Al-Mg-Si alloys from the point of view of morphological evolution. The orientation relationship, shape, growth process, misfit value, and interfacial condition between the β-phase and Al matrix were investigated using high-resolution transmission electron microscopy (HR-TEM), focused ion beam (FIB), and optical microscope (OM). In a previous study, the growth process and shape of the β-phase were determined using scanning electron microscopy (SEM). It was proposed that the truncated octahedron (8{111}, 6{100} facets) transforms into a hexahedron (6{100} facets). This study proposes that two new three-dimensional shapes of the β-phase exist between the truncated octahedron and hexahedron, and we identified the {111} β facets at the edges of the β-phase. We proposed the morphology evolution during the growth process of Mg 2 Si crystals and calculated the misfit to understand that the unstable {111} β facet has a higher misfit value compared to the {001} β and {011} β facets. Our observations provide insight into how they influence the behavior of Mg 2 Si crystals, which is crucial for predicting the microstructural evolution of Al-Mg-Si alloys and for designing materials with desired properties. • Investigated the morphology evolution of the β-phase in Al-Mg-Si alloys. • Explored β-phase orientation relationship, shape, and growth process using HR-TEM, FIB, and OM. • Discovered {111} β facets and proposed new three-dimensional shapes for the β-phase. • Calculated misfit values, revealing the instability of the (111) β facet compared to (001) β and (011) β facets. • Contributed to understanding microstructural evolution in Al-Mg-Si alloys and material design. [ABSTRACT FROM AUTHOR]