The basic concepts of crystallography, including unit cell, symmetry, crystal systems and origin specification are introduced. Bravais lattice, point groups, plane groups and space groups are presented for both 2D and 3D crystals. Equivalent positions, asymmetric unit, local (= non-crystallographic) and global symmetry are all described in detail with clear illustrations, both drawings and experimental EM images. Miller indices, d-spacings and symmetry elements in crystals and their effects in real and reciprocal space are shown. The effects of different symmetry elements in real and reciprocal space are given for inversion centres, rotation and screw axes and mirror and glide planes. All these features are presented in both mathematical form and illustrated with experimental EM images and ED patterns.
Keywords: crystallography, unit cell, symmetry, crystal systems, origin, Bravais lattice, plane group, space group, equivalent positions, asymmetric unit, reciprocal lattice, Miller indices, d-spacings, Laue groups, Laue equation, rotation axes, screw axes, mirror and glide planes
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