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Symbolism

Symbolism. y. In Schönflies notation , what does the symbol S 2 mean?. ( x,y,z ). x. In International notation, what does the symbol mean?. y. ( x,y,z ). x. Symbolism: Crystal Systems. What rotational symmetries are consistent with a lattice (translational symmetry)?.

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Symbolism

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  1. Symbolism y In Schönflies notation, what does the symbol S2 mean? (x,y,z) x In International notation, what does the symbol mean? y (x,y,z) x

  2. Symbolism: Crystal Systems What rotational symmetries are consistent with a lattice (translational symmetry)? •  = angle between b and c •  = angle between a and c •  = angle between a and b c a b

  3. Symbolism: Bravais Lattices 7 Crystal Systems = 7 Primitive Lattices (Unit Cells): Including Centering: 14 Bravais Lattices (rhombohedral) “Centering?” •  = angle between b and c •  = angle between a and c •  = angle between a and b c a b

  4. Symbolism: Point Groups • Schönflies • Notation

  5. Symbolism: Crystallographic Point Groups 32 Point Groups Allowed Rotations = C1C2C3C4C6

  6. Symbolism: Crystallographic Point Groups (cont.)

  7. Symbolism: Symmetry Operations (4h = 4/mmm = 4/m 2/m 2/m) 4 / m mm + y x

  8. Symmorphic Space Groups Point Group= Space Group = SymmorphicSpace Groups (73): Nonsymmorphic Space Groups (157):

  9. Symmorphic Space Groups Space Group: I4/mmm Asymmetric Unit: Ba (2a): 0 0 0 Fe (4d): ½ 0 ¼ As (4e): 0 0 0.3544 BaFe2As2

  10. Symmorphic Space Groups What is the empirical formula of this compound? How many formula units are in the unit cell? Asymmetric Unit: Dy (4e) 0 0 0.203 Dy (4d) 0 0.5 0.25 Ni (8j) 0.273 0.5 0 B (16l) 0.274 0.111 0 B (16m) 0.269 0.269 0.152

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