Crystallography of embedded particles in Al–Mg–Zn alloys. Symmetry analysis

Following a proper heat treatment, the alloy system Al–Mg–Zn shows a great wealth of precipitate particles forming coherent (η′ crystals) and incoherent (η crystals) boundaries with the Al matrix. Both the matrix crystal and the precipitate crystals are holohedral, as their point groups correspond to their metric symmetries ( and 6/mmm). On the basis of published orientational relationships for a principal variant of every known precipitate family, the full sets of orientational variants are deduced by the concepts of intersection groups, H^β, and variant generating sets, V^β. The intergrowth symmetry principle has been visualized by stereographic projections. Special attention has been given to patterns of superimposed lattice nodes in reciprocal space and the implications of overlap in terms of observable reflections. It has been uncovered, by artificially reducing the point group symmetry of the coherent η′ phase, where V^β is a proper subgroup of the matrix holohedral, that twin laws for merohedry are revealed when V^β is factorized into a weak direct product.