3.3 Twinning of crystals

This second chapter in Part 3 on twinning and domain structures deals with the twinning of crystals in all of its forms: growth twins, transformation twins and deformation twins. The treatment ranges from macroscopic considerations of the geometric orientation relations (twin laws) and the morphology of twins to the microscopic (atomistic) structures of the twin boundaries. Each of the following topics is accompanied by illustrative examples of actual twins and many figures: basic concepts and definitions: twinning, crystallographic orientation relations, composite (twin) symmetry, twin law; morphology of twins, description of twins by black–white symmetry; origin of twins and genetic classification; lattice classification of twinning: twinning by merohedry, pseudo-merohedry and ‘reticular' merohedry; twin boundaries: mechanical (strain) and electrical compatibility of interfaces; extension of the Sapriel approach to growth and deformation twins; twin boundaries: twin displacement and fault vectors; twin boundaries: atomistic structural models and HRTEM investigations of twin interfaces, twin textures, twinning dislocations, coherency of twin interfaces. Keywords: Σ3 bicrystal boundaries; Σ3 twin interface; eigensymmetry; Brazil twins; Dauphine twins; Dauphine–Brazil twins; Friedel's lattice theory; Japanese twins; La Gardette twins; Montmartre twins; Sapriel approach; aggregates; alternative twin operations; antiphase boundaries; bicrystals; black and white symmetry groups; boundary energy; complete twins; composite symmetry; composition plane; contact plane; contact relations; contact twins; cyclic twins; deformation twins; detwinning; diperiodic twins; dislocations; domain states; domains; dovetail twins; electrical constraints; fault vectors; ferroelastic–ferroelectric phases; ferroelastic phases; ferroelastic twins; ferroelasticity; growth-sector boundaries; growth twins; high-resolution transmission electron microscopy; intergrowths; inversion twins; isostructural crystals; lattice coincidence; lattice pseudosymmetry; low-energy boundaries; mechanical twins; merohedral twins; merohedry; monoperiodic twins; morphological classification; multiple twins; nanocrystalline materials; needle domains; non-ferroelastic twins; non-merohedral twins; non-pyroelectric acentric crystals; orientation relations; orientation states; penetration twins; pentagonal–decagonal twins; permissible boundaries; plagioclase twins; polycrystalline aggregates; polysynthetic twins; pseudo-coincidence; pseudo-merohedral twins; pseudo-merohedry; reflection twins; rotation twins; sector twins; shear strain; simple twins; spinel law; spinel twins; spontaneous shear; switching of domains; transformation twins; translation twins; triperiodic twins; tweed microstructure; twin axes; twin boundaries; twin displacement vector; twin domains; twin elements; twin formation; twin interfaces; twin lattice index; twin laws; twin obliquity; twin operations; twin rotations; twin textures; twinning; twinning dislocations; twinning relation; twins; twins of twins