Crystal structure determination and space groups

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Presentation transcript:

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

32 point groups

14 Bravais Lattices

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

a axial glide

Cuprite

P 42

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

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

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

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.