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Crystallography of embedded particles in Al–Mg–Zn alloys. Symmetry analysis
Author(s) -
Thorkildsen Gunnar,
Larsen Helge B.
Publication year - 2014
Publication title -
journal of applied crystallography
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.429
H-Index - 162
ISSN - 1600-5767
DOI - 10.1107/s1600576714019414
Subject(s) - point group , space group , crystallography , stereographic projection , intersection (aeronautics) , symmetry (geometry) , reciprocal lattice , homogeneous space , group (periodic table) , lattice (music) , one dimensional symmetry group , crystal (programming language) , symmetry group , matrix (chemical analysis) , physics , materials science , chemistry , mathematics , combinatorics , geometry , quantum mechanics , x ray crystallography , diffraction , computer science , acoustics , engineering , composite material , programming language , aerospace engineering
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.