research papers
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, Hβ, and variant generating sets, Vβ. 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 Vβ is a proper subgroup of the matrix holohedral, that twin laws for merohedry are revealed when Vβ is factorized into a weak direct product.
Keywords: Al–Mg–Zn system; symmetry analysis; intersection groups; variant generating sets; superimposed lattices; twinning; group theory; weak direct products.
Supporting information
Portable Document Format (PDF) file https://doi.org/10.1107/S1600576714019414/ks5438sup1.pdf | |
Portable Document Format (PDF) file https://doi.org/10.1107/S1600576714019414/ks5438sup2.pdf | |
Portable Document Format (PDF) file https://doi.org/10.1107/S1600576714019414/ks5438sup3.pdf | |
Portable Document Format (PDF) file https://doi.org/10.1107/S1600576714019414/ks5438sup4.pdf |