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crystallography lll

Explore crystallography concepts including point groups, Bravais lattices, glide planes, and screw axes through space group diagrams and tables. Learn to describe crystal structures using lattice parameters, space group equipoints, and positional parameters.

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crystallography lll

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  1. crystallography lll

  2. Examples: Ccc2, P1, I 41/a 2/c 2/d, F 4/m 3 2/m, P 63/m 2/m 2/c lattice centering screw axis glide plane 230 space groups Combine 32 point groups (rotational symmetry) with a. 14 Bravais lattices (translational symmetry) glide planes (rotational + translational symmetry) - a, b, c, n, d screw axes (rotational + translational symmetry) - 21, 31, 32, 41, 42,43, 61, 62, 63, 64, 65

  3. Space group diagrams Example: P222 b a

  4. x,y,z x,y,z x,y,z x,y,z General equipoint: 4u (x,y,z) (x,y,z) (x,y,z) (x,y,z) Special equipoints: 1a (0,0,0); 1b (1/2,0,0); … 2i (x,0,0), (x,0,0); 2j (x,0,1/2), (x,0,1/2); … 2m (0,y,z) (0,y,0); … Space group diagrams Example: P222 b a

  5. Space group tables International Tables for Crystallography, Vol. A

  6. Example: LaB6 a = 4.1566 Å P 4/m 3 2/m La in 1a, B in 6f x = 0.207 Describing crystal structuresNeed: lattice parameters space group equipoints occupied positional parameters

  7. In P 4/m 3 2/m 1a - (0,0,0) 6f - (x,1/2,1/2) 6f - (1/2,x,1/2) 6f - (1/2,1/2,x) Describing crystal structures LaB6 a = 4.1566 Å P 4/m 3 2/m La in 1a, B in 6f x = 0.207 6f - (x,1/2,1/2) 1/2 0.207 1/2 1/2 6f - (1/2,x,1/2) 0.793 1/2 6f - (1/2,1/2,x)

  8. Exercises1. C a = 3.500Å F 41/d 3 2/m C in 8a F (0,0,0)+ (1/2,1/2,0)+ (1/2 ,0,1/2)+ (0,1/2,1/2)+ 8a: (0,0,0) (3/4,1/4,3/4) projection down [001]2. CaCu5 a = 5.082, c = 4.078Å P6/mmm Ca in 1a, Cu in 2c, 3g 2c: (1/3,2/3,0) (2/3,1/3,0) 3g: (1/2,0,1/2) (0,1/2,1/2) (1/2,1/2,1/2) projection down [001]

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