MIN12FAL_03_Internal Symmetry_Space Groups_Handout

i cell in isometric or tetragonal depending on

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Unformatted text preview: l (depending on vertical scale) Crystal Crystal structure Tetragonal Lattices Tetra c a2 = 0, 1, 2... a1 a 3D periodic arrangements of ionic groups. b a2 3D translation of 3D translation of lattice lattice points. a1 We can pick an alternative P lattice from the same pattern can pick an alternative lattice from the same pattern C and P are equivalent By convention, we choose the P alternative Tetragonal A? B? Against the tetragonal symmtery. A? symmtery. The others work the same way: Exclusions are either incompatible with the system or equivalent to one of the types listed Lattice hemimorphite Zn4Si2O7(OH)2•H2O Bloss (1971) Figure 7-1 Description of a crystal structure Lattice type + Properties of the basis 14 space lattices 32 point groups I 43m Additional symmetry Screw rotation Glide reflection 230 space groups The molecule symmetry conforms The molecule symmetry conforms to to the possible lattice symmetry _ I43m hexamethylenetetramine Primitive lattice Notice the orientations of the ethylene molecules a b c P21/n 21/n 2/m Ethylene (C2H6) 32 point groups for symmetrical arrangements of atoms, ions, or molecules without involving translations. Combination of Symmetry Operations Orthorhombic cell The orientations and symmtery of the molecules do not conform to possible lattice symmetry Pbca Benzene (C6H6) 32 32 Point Groups Point Point Groups Monoclinic Monoclinic system Plane lattice (010) projection viewed from the plain normal of (010), i.e., [010] ( [010]* or b*) in this case. m (001) projection viewed from the plain normal of (001), i.e., [001]* or c* in this case. in this case. Symmetry elements projected in a unit cell viewed from the plane normals of (010) and (001). Orthorhombic system Plane lattice Tetragonal Tetragonal system Hexagonal Hexagonal system Cubic Cubic system P 4m 3 2m a 111 110 Space Groups 32 32 point groups (object symmetry) + 14 space lattices 230 space 230 space groups (screw rotation and glide reflection rotation and glide reflection may be generated simultaneously). Obj Object symmetry conforms to one of the point groups for the crystal sy...
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This document was uploaded on 03/25/2014.

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