Download presentation

Presentation is loading. Please wait.

Published byCorey Horton Modified about 1 year ago

1
1 Colored symmetry Applications in: crystal surfaces & crystal growth strained materials twinning magnetic structures ferroelectrics other physical props textures (see Colored Symmetry by Shubnikov & Belov

2
2 Colored symmetry Applications in: crystal surfaces & crystal growth strained materials twinning magnetic structures ferroelectrics other physical props textures Spin moment structure in MnO determined by neutron diffrn - only Mn +2 ions shown (see Colored Symmetry by Shubnikov & Belov

3
3 Colored symmetry Applications in: crystal surfaces & crystal growth strained materials twinning magnetic structures ferroelectrics other physical props textures Will consider here only two colors - black & white (see Colored Symmetry by Shubnikov & Belov

4
4 Colored symmetry Anti-equality – Pair of gloves which are, say, black on outside & white on inside if both left-handed, can get: congruent equality - do nothing mirror anti-equality - turn one inside-out

5
5 Colored symmetry Anti-equality – Pair of gloves which are, say, black on outside & white on inside if both left-handed, can get: congruent equality - do nothing mirror anti-equality - turn one inside-out if right- & left-handed, can get: mirror equality - nothing congruent anti-equality - turn one inside-out

6
6 Colored symmetry New operations – anti-rotations (rotation + "sign change") 1' 2' 3' 4' 6' mirror anti-rotations (mirror rotation + "sign change") 1' 2' 3' 4' 6'

7
7 Colored symmetry New operations – anti-rotations (rotation + "sign change") 1' 2' 3' 4' 6' mirror anti-rotations (mirror rotation + "sign change") 1' 2' 3' 4' 6' c 11 c 12 c 13 0 c 21 c 22 c 23 0 c 31 c 32 c 33 0 0 0 0 ±1

8
8 Colored symmetry Polar & neutral figures – polar white outside, black inside black outside, white inside neutralblack inside & outside or white inside & outside

9
9 Colored symmetry Operations – mirror in xy plane - anti-symmetric 2' anti-reflection 1 0 0 0 0 1 0 0 0 0 -1 0 0 0 0 -1

10
10 Colored symmetry Operations – anti-rotation of 180° along x-axis 2' 1 0 0 0 0 -1 0 0 0 0 -1 0 0 0 0 -1

11
11 Colored symmetry Operations – anti-inversion 1' -1 0 0 0 0 -1 0 0 0 0 -1 0 0 0 0 -1

12
12 Colored symmetry Operations – 4'

13
13 Colored symmetry Operations – 4' 6' black underneath

14
14 Colored symmetry Operations – 2/m' black underneath

15
15 Colored symmetry Operations – 2/m' 2'/m white underneath black underneath

16
16 Colored symmetry Operations – 2'/m' white underneath black underneath

17
17 Colored symmetry Operations – 2'/m' 2'm'm white underneath black underneath

18
18 Colored symmetry Operations – 2m'm'

19
19 Colored symmetry Operations – 2m'm' 2'2'2

20
20 Colored symmetry Operations – 2/mm'm' white underneath black underneath

21
21 Colored symmetry Glides – g g' m=a' a=m'

22
22 The 36 lattice translations for colored groups

23
23 The 36 lattice translations for colored groups

24
24 The 46 dichromatic plane groups

25
25 The 46 dichromatic plane groups

26
26 The 46 dichromatic plane groups

27
27 The 46 dichromatic plane groups

28
28 Comments 1. Mirror translation ( ) – gives another mirror of same character if uncolored. If colored, new mirror is colored 2. Mirror translation (||) – colored translation gives colored glide

29
29 Comments 1. Mirror translation ( ) – gives another mirror of same character if uncolored. If colored, new mirror is colored 2. Mirror translation (||) – colored translation gives colored glide 3. Axis translation ( ) – new axis has same charater if uncolored. If colored, new axis is colored or uncolored, depending on the axis. Character is unchanged by colored translation 4. Axis translation (||) – colored translation makes axis colored screw or uncolored, depending on the axis

30
30 Comments 4.Axis translation (||) – colored translation makes axis colored screw or uncolored, depending on the axis 2 t || ' ––> 2 & 2 1 ' 2 1 t || ' ––> 2 1 & 2'

31
31 Comments 4.Axis translation (||) – colored translation makes axis colored screw or uncolored, depending on the axis 2 t || ' ––> 2 & 2 1 ' 2 1 t || ' ––> 2 1 & 2' 4 t || ' ––> 4 & 4 2 ' 4 1 t || ' ––> 4 1 & 4 3 '

32
32 Comments 5. n = odd axes cannot be black-white 6. Two intersecting 2-fold axes: 30° ––> new 645° ––> new 460° ––> new 3etc. new axis uncolored if 2-folds are same color…….otherwise, new axis is colored uncolored 4 colored 4

Similar presentations

© 2017 SlidePlayer.com Inc.

All rights reserved.

Ads by Google