MIN12FAL_03_Internal Symmetry_Space Groups_Handout

# Obj object symmetry conforms to one of the point

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Unformatted text preview: stem of the lattice. 73 simple 73 simple space groups. Lattice Lattice + Objects with symmetry conformable to the lattice symmetry. Still may generate different space groups due to different orientation relationships between the objects different orientation relationships between the objects (lattice (lattice points) and the lattice symmetry elements. 73 Object symmetry comformable to the corresponding lattice symmetry Reduction Reduction of symmetry due to the object’s uncomformable symmetry. True space-group symmetry is lower than its lattice symmetry. space- Lattice symmetry: 2/m 2/m 2/m Object symmetry: m Monoclinic crystal with “orthorhombic lattice geometry” Orientation relationships could make the difference in space group symmetry Space Groups 32 32 point groups (object symmetry) + 14 space lattices 230 space 230 space groups (screw rotation and glide reflection (screw rotation and glide reflection may may be generated simultaneously). Obj Object symmetry conforms to one of the point groups for the crystal system of the lattice. 73 simple 73 simple space groups. Lattice Lattice + Objects with symmetry conformable to the lattice symmetry. Still may generate different space groups due to different orientation relationships between the objects different orientation relationships between the objects (lattice (lattice points) and the lattice symmetry elements. Orthorhombic abc Tetragonal c ‹a› ‹110› Hexagonal c ‹a› ‹210› Bloss (1971) Figure 7-2 Bloss Bloss (1971) Figure 7-2 7- Space Groups The 3-D point group symmetries can be combined with with translations to create the 230 3-D Space Groups 3New symmetry elements that combine translation with other operations Glides: Reflection + translation Screw Axes: Rotation + translation Screw Rotation Screw Rotation Screw Rotation Screw Rotation Screw Rotation Screw Rotation Screw Screw Rotation Screw Screw Rotation z, z + ¼ , z + ½ , z + ¾ in terms of height variations. Screw Rotation Positions of the of the motifs on the plan...
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