Symmetry in crystals

1. Symmetry in crystals

2. Infinitely repeating lattices

4. An integral number of unit translations along any axis will arrive at an identical point.

5. A unit translation along any axis will arrive at an identical point

6. The composition of each unit should be identical.

7. A unit translation parallel to any axis will arrive at an identical point

10. Face centered lattice

12. Unit Cell

13. 3 axes, a, b, c and 3 angles , , and 

18. 4 3-fold axes along diagonals

20. 4-fold axis

22. 3 2-fold axes

24. 6-fold 1 6-fold axis

26. A cube with 1 diagonal shortened or lengthened.

27. 3-fold axis

29. 2-fold 1 2-fold axis

30. 2-fold axis

31. 2-fold axis 3-fold axis 4-fold axis 6-fold axis

36. Symmetry in Crystals

37. Rotational symmetry

38. Rotational symmetry Possible: 2, 3, 4, 6 - fold axes

39. Rotational inversion

40. Mirror plane

41. Screw axes: a combination of rotation and translation.

42. Screw axes: a combination of rotation and translation. 21 screw = 180o rotation + 1/2 cell translation

43. 31 screw = 120o rotation + 1/3 unit translation

45. Glide plane: a combination of mirror and translational symmetry.

46. Glide plane: a combination of mirror and translational symmetry. 1/2 unit translation

47. Given the 7 crystal systems and various symmetry operations, the number of ways a continuously repeating lattice can be formed is limited.

48. Theoretical studies of the geometries of crystals completed in 1890 demonstrated that there are 230 ways to put together an infinitely repeating lattice.

49. Unit Cell

50. Unit Cell Space group P1