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Space groups

Space groups. Ex: 222. Space groups. Ex: 222. represents all elements in the lattice translation group. Space groups. Ex: 222. represents all elements in the lattice translation group. C 2 C 2 ' = C 2 " 1 t 2 t = 3 t. Space groups. Ex: 222. represents all elements in

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Space groups

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  1. Space groups Ex: 222

  2. Space groups Ex: 222 • represents all elements in the lattice translation group

  3. Space groups Ex: 222 • represents all elements in the lattice translation group C2 C2' = C2" 1t 2t = 3t

  4. Space groups Ex: 222 • represents all elements in the lattice translation group C2 C2' = C2" 1t 2t = 3t C2,t1 C2',t2 = C2", t3

  5. Space groups Ex: 222 C2 C2' = C2" 1t 2t = 3t C2,t1 C2',t2 = C2", t3

  6. Space groups Ex: 422 C2"' t4 C2" t3 C2' t2 C2 t1

  7. Space groups Ex: 422 C2"' t4 C2" t3 C2' t2 C2 t1

  8. Space groups Ex: 422 [110] C2"' t4 C2" t3 [010] C2' t2 [110] C2 t1 [100] tz = c/4, 2c/4, 3c/4, 0 41 42 43 t1 = a/2, b/2, c/2, 0 but t2 must be, e.g., a/2+b/2 tz t1 = t2

  9. Space groups Ex: 422 [110] P422 - tz = ti = 0 C2"' t4 C2" t3 [010] C2' t2 [110] C2 t1 [100] tz = c/4, 2c/4, 3c/4, 0 41 42 43 t1 = a/2, b/2, c/2, 0 but t2 must be, e.g., a/2+b/2 tz t1 = t2

  10. Space groups Ex: 422 [110] P422 - tz = ti = 0 C2"' t4 C2" t3 [010] C2' t2 [110] C2 t1 [100] tz = c/4, 2c/4, 3c/4, 0 41 42 43 t1 = a/2, b/2, c/2, 0 but t2 must be, e.g., a/2+b/2 tz t1 = t2

  11. Space groups Ex: 422 [110] P4212 - tz = 0, t1 = t2 = a/2 + b/2 C2"' t4 C2" t3 [010] C2' t2 [110] C2 t1 [100] tz = c/4, 2c/4, 3c/4, 0 41 42 43 t1 = a/2, b/2, c/2, 0 but t2 must be, e.g., a/2+b/2 tz t1 = t2

  12. Space groups Ex: 422 [110] P4212 - tz = 0, t1 = t2 = a/2 + b/2 C2"' t4 C2" t3 [010] C2' t2 [110] C2 t1 [100] tz = c/4, 2c/4, 3c/4, 0 41 42 43 t1 = a/2, b/2, c/2, 0 but t2 must be, e.g., a/2+b/2 tz t1 = t2

  13. Space groups Ex: 422 [110] P4122 - tz = c/4, t3 = 0, t4 = c/4 C2"' t4 C2" t3 [010] C2' t2 [110] C2 t1 [100] tz = c/4, 2c/4, 3c/4, 0 41 42 43 t1 = a/2, b/2, c/2, 0 but t2 must be, e.g., a/2+b/2 tz t3 = t4 = c/4 tz t4 = t1 = c/2 tz t1 = t2 = 3c/4

  14. Space groups Ex: 422 [110] P4122 - tz = c/4, t3 = 0, t4 = c/4 C2"' t4 1/4 1/4 1/4 3/8 1/8 3/8 3/8 1/8 1/8 C2" t3 [010] 1/8 3/8 1/8 3/8 C2' t2 [110] C2 t1 3/8 1/8 [100] 3/8 1/8 tz = c/4, 2c/4, 3c/4, 0 41 42 43 t1 = a/2, b/2, c/2, 0 but t2 must be, e.g., a/2+b/2 3/8 1/8 3/8 1/8 1/8 3/8 1/4 1/4 1/4 tz t3 = t4 = c/4 tz t4 = t1 = c/2 tz t1 = t2 = 3c/4

  15. Space groups Pmm2 & Cmm2 Xm ym = z2 1t 2t = 3t smt1smt2 = Aπ, t3

  16. Space groups t1can only be 0, b/2, c/2, b/2 + c/2 t1 = 0, b/2, c/2 t2 = 0, a/2, c/2 t3 = 0, c/2 1t w/ 3t = 0 1t = 2t = 3t = 0 Cmm2 1t 2t = 3t G consists of translations for C lattice (includes a/2 + b/2)

  17. Space groups t1can only be 0, b/2, c/2, b/2 + c/2 t1 = 0, b/2, c/2 t2 = 0, a/2, c/2 t3 = 0, c/2 1t w/ 3t = 0 1t = a/2 3t = 0 2t = a/2 Cmm2 1t 2t = 3t

  18. Space groups t1can only be 0, b/2, c/2, b/2 + c/2 t1 = 0, b/2, c/2 t2 = 0, a/2, c/2 t3 = 0, c/2 1t w/ 3t = 0 1t = a/2 + b/2 3t = 0 2t = a/2 + b/2 Cmm2 1t 2t = 3t

  19. Space groups t1can only be 0, b/2, c/2, b/2 + c/2 t1 = 0, b/2, c/2 t2 = 0, a/2, c/2 t3 = 0, c/2 1t w/ 3t = 0 1t = c/2 3t = 0 2t = c/2 Ccc2 1t 2t = 3t

  20. Space groups t1can only be 0, b/2, c/2, b/2 + c/2 t1 = 0, b/2, c/2 t2 = 0, a/2, c/2 t3 = 0, c/2 1t w/ 3t = 0 1t = a/2 + c/2 3t = 0 2t = a/2 + c/2 Ccc2 1t 2t = 3t

  21. Space groups t1can only be 0, b/2, c/2, b/2 + c/2 t1 = 0, b/2, c/2 t2 = 0, a/2, c/2 t3 = 0, c/2 1t w/ 3t = c/2 1t = 0 3t = c/2 2t = c/2 Cmc21 1t 2t = 3t

  22. Space groups t1can only be 0, b/2, c/2, b/2 + c/2 t1 = 0, b/2, c/2 t2 = 0, a/2, c/2 t3 = 0, c/2 1t w/ 3t = c/2 1t = 0 3t = c/2 2t = c/2 Cmc21 1t 2t = 3t All other translation combinations equiv-alent to Cmm2, Ccc2, or Cmc21

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