1. Crystal structure determination and space groups
H. K. D. H. Bhadeshia

2. 32 point groups

3. 14 Bravais Lattices

5. space groups locate atoms within a cell: help solve unknown structure
14 Bravais lattices
add centres
230 space groups
microscopic symmetry
7 crystal systems
32 point groups
macroscopic symmetry

10. a
axial glide

11. Cuprite

12. P 42

13. x y
diagonal glide parallel to (100)
P n

14. Centre of symmetry at height 3/4

15. centre of symmetry

16. mirror
triad

21. Caesium chloride
determine unit cell by diffraction to be cubic-P
how many atoms per unit cell?
space group of CsCl?
location of atoms?
36 space groups possible

23. Lattice: face-centred cubic Motif: C at 0,0,0 C at 1/4,1/4,1/4
3/4
1/4
3/4
1/4
3/4
1/4
1/4
3/4
1/4
Lattice: face-centred cubic
Motif: C at 0,0,0 C at 1/4,1/4,1/4

24. Lattice: face-centred cubic Motif: Zn at 0,0,0 S at 1/4,1/4,1/4
3/4
1/4
1/4
3/4
Lattice: face-centred cubic
Motif: Zn at 0,0,0 S at 1/4,1/4,1/4

25. tetragonal

26. space group diagram

27. Z. anorg. allg. Chem., 552: 69–80. doi: 10.1002/zaac.19875520907

29. Assignment
Draw an accurate stereographic projection of a cubic crystal, and mark on it the poles of the form 100, 110 and 111.
Without measuring angles, but using vector addition, mark accurately, poles of the form 112
Ensure that the method you use is clear.