Crystal structure determination and space groups

Crystal structure determination

and space groups

H. K. D. H. Bhadeshia

32 point groups

14Bravais Lattices

7 crystal systems

14 Bravais lattices

add centre

s

32 point groups

macroscopic

symmetry

230 space groups

microsc

opic

symmetry

space groups locate atoms within a cell: help solve unknown structure

a axial glide

Cuprite

42

P

x

y

diagonal glide parallel to (100)

P n

Centre of symmetry at height 3/4

centre of symmetry

mirror triad

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

1/4

1/4

1/4

1/4

1/43/4

3/4

3/4

3/4

Lattice: face-centred cubic

Motif: C at 0,0,0 C at 1/4,1/4,1/4

1/4

1/4

1/43/4

3/4

Lattice: face-centred cubic

Motif: Zn at 0,0,0 S at 1/4,1/4,1/4

tetragonal

space group diagram

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

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.